Extended Rayleigh Damping Model
Directory of Open Access Journals (Sweden)
Naohiro Nakamura
2016-07-01
Full Text Available In dynamic analysis, frequency domain analysis can be used if the entire structure is linear. However, time history analysis is generally used if nonlinear elements are present. Rayleigh damping has been widely used in time history response analysis. Many articles have reported the problems associated with this damping and suggested remedies. A basic problem is that the frequency area across which the damping ratio is almost constant is too narrow. If the area could be expanded while incurring only a small increase in computational cost, this would provide an appropriate remedy for this problem. In this study, a novel damping model capable of expanding the constant frequency area by more than five times was proposed based on the study of a causal damping model. This model was constructed by adding two terms to the Rayleigh damping model and can be applied to the linear elements in the time history analysis of a nonlinear structure. The accuracy and efficiency of the model were confirmed using example analyses.
RAYLEIGH SCATTERING MODELS WITH CORRELATION INTEGRAL
Directory of Open Access Journals (Sweden)
S. F. Kolomiets
2014-01-01
Full Text Available This article offers one of possible approaches to the use of the classical correlation concept in Rayleigh scattering models. Classical correlation in contrast to three types of correlations corresponding to stochastic point flows opens the door to the efficient explanation of the interaction between periodical structure of incident radiation and discreet stochastic structure of distributed scatters typical for Rayleigh problems.
Bayesian Predictive Models for Rayleigh Wind Speed
DEFF Research Database (Denmark)
Shahirinia, Amir; Hajizadeh, Amin; Yu, David C
2017-01-01
predictive model of the wind speed aggregates the non-homogeneous distributions into a single continuous distribution. Therefore, the result is able to capture the variation among the probability distributions of the wind speeds at the turbines’ locations in a wind farm. More specifically, instead of using...... a wind speed distribution whose parameters are known or estimated, the parameters are considered as random whose variations are according to probability distributions. The Bayesian predictive model for a Rayleigh which only has a single model scale parameter has been proposed. Also closed-form posterior...... and predictive inferences under different reasonable choices of prior distribution in sensitivity analysis have been presented....
van Breukelen, B.M.
2007-01-01
The Rayleigh equation relates the change in isotope ratio of an element in a substrate to the extent of substrate consumption via a single kinetic isotopic fractionation factor (α). Substrate consumption is, however, commonly distributed over several metabolic pathways each potentially having a
Modeling of Rayleigh wave dispersion in Iberia
Directory of Open Access Journals (Sweden)
José Badal
2011-01-01
Full Text Available Phase and group velocities of 15–70 s Rayleigh waves propagating across the Iberian Peninsula have been transformed into local dispersion curves by linear inversion of travel times. The procedure permits that the waveform dispersion to be obtained as a continuous period-dependent velocity function at grid points belonging to the area probed by the waves, thus providing phase- and group-velocity contour maps for several periods within the interval of interest. The regionalization process rests on a homogeneous initial data set in which the number of observations remains almost constant for all periods of reference. Damped least-squares inversion of the local dispersion curves for shear-wave velocity structure is performed to obtain depth-dependent S-wave velocity profiles at the grid points covering the model region. The reliability of the results should improve significantly owing to the use of phase and group velocities simultaneously. On this basis, we have built horizontal depth sections that give an updated view of the seismic velocity structure of the peninsula at lithospheric and upper mantle depths (20–200 km. After averaging all the pure-path S-wave velocities previously determined at each grid point, the velocity-depth models so obtained for major tectonic units allow the comparison between the Hercynian basement and other areas of Mesozoic folding and Tertiary basins.
International Nuclear Information System (INIS)
Zhang Ran-Ran; Xu Wei; Yang Gui-Dong; Han Qun
2015-01-01
In this paper, we consider the response analysis of a Duffing–Rayleigh system with fractional derivative under Gaussian white noise excitation. A stochastic averaging procedure for this system is developed by using the generalized harmonic functions. First, the system state is approximated by a diffusive Markov process. Then, the stationary probability densities are derived from the averaged Itô stochastic differential equation of the system. The accuracy of the analytical results is validated by the results from the Monte Carlo simulation of the original system. Moreover, the effects of different system parameters and noise intensity on the response of the system are also discussed. (paper)
Stochastic model of Rayleigh-Taylor turbulent mixing
International Nuclear Information System (INIS)
Abarzhi, S.I.; Cadjan, M.; Fedotov, S.
2007-01-01
We propose a stochastic model to describe the random character of the dissipation process in Rayleigh-Taylor turbulent mixing. The parameter alpha, used conventionally to characterize the mixing growth-rate, is not a universal constant and is very sensitive to the statistical properties of the dissipation. The ratio between the rates of momentum loss and momentum gain is the statistic invariant and a robust parameter to diagnose with or without turbulent diffusion accounted for
Study on Software Quality Improvement based on Rayleigh Model and PDCA Model
Ning Jingfeng; Hu Ming
2013-01-01
As the software industry gradually becomes mature, software quality is regarded as the life of a software enterprise. This article discusses how to improve the quality of software, applies Rayleigh model and PDCA model to the software quality management, combines with the defect removal effectiveness index, exerts PDCA model to solve the problem of quality management objectives when using the Rayleigh model in bidirectional quality improvement strategies of software quality management, a...
Energy Technology Data Exchange (ETDEWEB)
Rollin, Bertrand [Los Alamos National Laboratory; Andrews, Malcolm J [Los Alamos National Laboratory
2010-01-01
We present our progress toward setting initial conditions in variable density turbulence models. In particular, we concentrate our efforts on the BHR turbulence model for turbulent Rayleigh-Taylor instability. Our approach is to predict profiles of relevant parameters before the fully turbulent regime and use them as initial conditions for the turbulence model. We use an idealized model of the mixing between two interpenetrating fluids to define the initial profiles for the turbulence model parameters. Velocities and volume fractions used in the idealized mixing model are obtained respectively from a set of ordinary differential equations modeling the growth of the Rayleigh-Taylor instability and from an idealization of the density profile in the mixing layer. A comparison between predicted initial profiles for the turbulence model parameters and initial profiles of the parameters obtained from low Atwood number three dimensional simulations show reasonable agreement.
Energy Technology Data Exchange (ETDEWEB)
Rollin, Bertrand [Los Alamos National Laboratory; Andrews, Malcolm J [Los Alamos National Laboratory
2010-01-01
We present our progress toward setting initial conditions in variable density turbulence models. In particular, we concentrate our efforts on the BHR turbulence model for turbulent Rayleigh-Taylor instability. Our approach is to predict profiles of relevant variables before fully turbulent regime and use them as initial conditions for the turbulence model. We use an idealized model of mixing between two interpenetrating fluids to define the initial profiles for the turbulence model variables. Velocities and volume fractions used in the idealized mixing model are obtained respectively from a set of ordinary differential equations modeling the growth of the Rayleigh-Taylor instability and from an idealization of the density profile in the mixing layer. A comparison between predicted profiles for the turbulence model variables and profiles of the variables obtained from low Atwood number three dimensional simulations show reasonable agreement.
Modal model for the nonlinear multimode Rayleigh endash Taylor instability
International Nuclear Information System (INIS)
Ofer, D.; Alon, U.; Shvarts, D.; McCrory, R.L.; Verdon, C.P.
1996-01-01
A modal model for the Rayleigh endash Taylor (RT) instability, applicable at all stages of the flow, is introduced. The model includes a description of nonlinear low-order mode coupling, mode growth saturation, and post-saturation mode coupling. It is shown to significantly extend the range of applicability of a previous model proposed by Haan, to cases where nonlinear mode generation is important. Using the new modal model, we study the relative importance of mode coupling at late nonlinear stages and resolve the difference between cases in which mode generation assumes a dominant role, leading to the late time inverse cascade of modes and loss of memory of initial conditions, and cases where mode generation is not important and memory of initial conditions is retained. Effects of finite density ratios (Atwood number A<1) are also included in the model and the difference between various measures of the mixing zone penetration depth for A<1 is discussed. copyright 1996 American Institute of Physics
Potential Flow Model for Compressible Stratified Rayleigh-Taylor Instability
Rydquist, Grant; Reckinger, Scott; Owkes, Mark; Wieland, Scott
2017-11-01
The Rayleigh-Taylor Instability (RTI) is an instability that occurs when a heavy fluid lies on top of a lighter fluid in a gravitational field, or a gravity-like acceleration. It occurs in many fluid flows of a highly compressive nature. In this study potential flow analysis (PFA) is used to model the early stages of RTI growth for compressible fluids. In the localized region near the bubble tip, the effects of vorticity are negligible, so PFA is applicable, as opposed to later stages where the induced velocity due to vortices generated from the growth of the instability dominate the flow. The incompressible PFA is extended for compressibility effects by applying the growth rate and the associated perturbation spatial decay from compressible linear stability theory. The PFA model predicts theoretical values for a bubble terminal velocity for single-mode compressible RTI, dependent upon the Atwood (A) and Mach (M) numbers, which is a parameter that measures both the strength of the stratification and intrinsic compressibility. The theoretical bubble terminal velocities are compared against numerical simulations. The PFA model correctly predicts the M dependence at high A, but the model must be further extended to include additional physics to capture the behavior at low A. Undergraduate Scholars Program - Montana State University.
Zernike polynomial based Rayleigh-Ritz model of a piezoelectric unimorph deformable mirror
CSIR Research Space (South Africa)
Long, CS
2012-04-01
Full Text Available , are routinely and conveniently described using Zernike polynomials. A Rayleigh-Ritz structural model, which uses Zernike polynomials directly to describe the displacements, is proposed in this paper. The proposed formulation produces a numerically inexpensive...
A Numerical Model for Prediction of Residual Stress Using Rayleigh Waves
International Nuclear Information System (INIS)
Yuan, Mao Dan; Kang, To; Kim, Hak Joon; Song, Sung Jin
2011-01-01
In this work, a numerical model is proposed for the relation between the magnitudes and the depth residual stress with the velocity of Rayleigh wave. Three cases, stress-free, uniform stress and layered stress, are investigated for the change tendency of the Rayleigh wave speed. Using the simulated signal with variation of residual stress magnitude and depth, investigation of the parameters for fitting residual stress and velocity change are performed. The speed change of Rayleigh wave shows a linear relation with the magnitude and an exponential relation with the depth of residual stress. The combination of these two effects could be used for the depth profile evaluation of the residual stress
Modelling altered fractionation schedules
International Nuclear Information System (INIS)
Fowler, J.F.
1993-01-01
The author discusses the conflicting requirements of hyperfractionation and accelerated fractionation used in radiotherapy, and the development of computer modelling to predict how to obtain an optimum of tumour cell kill without exceeding normal-tissue tolerance. The present trend is to shorten hyperfractionated schedules from 6 or 7 weeks to give overall times of 4 or 5 weeks as in new schedules by Herskovic et al (1992) and Harari (1992). Very high doses are given, much higher than can be given when ultrashort schedules such as CHART (12 days) are used. Computer modelling has suggested that optimum overall times, to yield maximum cell kill in tumours ((α/β = 10 Gy) for a constant level of late complications (α/β = 3 Gy) would be X or X-1 weeks, where X is the doubling time of the tumour cells in days (Fowler 1990). For median doubling times of about 5 days, overall times of 4 or 5 weeks should be ideal. (U.K.)
Parameter identification in a generalized time-harmonic Rayleigh damping model for elastography.
Directory of Open Access Journals (Sweden)
Elijah E W Van Houten
Full Text Available The identifiability of the two damping components of a Generalized Rayleigh Damping model is investigated through analysis of the continuum equilibrium equations as well as a simple spring-mass system. Generalized Rayleigh Damping provides a more diversified attenuation model than pure Viscoelasticity, with two parameters to describe attenuation effects and account for the complex damping behavior found in biological tissue. For heterogeneous Rayleigh Damped materials, there is no equivalent Viscoelastic system to describe the observed motions. For homogeneous systems, the inverse problem to determine the two Rayleigh Damping components is seen to be uniquely posed, in the sense that the inverse matrix for parameter identification is full rank, with certain conditions: when either multi-frequency data is available or when both shear and dilatational wave propagation is taken into account. For the multi-frequency case, the frequency dependency of the elastic parameters adds a level of complexity to the reconstruction problem that must be addressed for reasonable solutions. For the dilatational wave case, the accuracy of compressional wave measurement in fluid saturated soft tissues becomes an issue for qualitative parameter identification. These issues can be addressed with reasonable assumptions on the negligible damping levels of dilatational waves in soft tissue. In general, the parameters of a Generalized Rayleigh Damping model are identifiable for the elastography inverse problem, although with more complex conditions than the simpler Viscoelastic damping model. The value of this approach is the additional structural information provided by the Generalized Rayleigh Damping model, which can be linked to tissue composition as well as rheological interpretations.
Pseudospectral modeling and dispersion analysis of Rayleigh waves in viscoelastic media
Zhang, K.; Luo, Y.; Xia, J.; Chen, C.
2011-01-01
Multichannel Analysis of Surface Waves (MASW) is one of the most widely used techniques in environmental and engineering geophysics to determine shear-wave velocities and dynamic properties, which is based on the elastic layered system theory. Wave propagation in the Earth, however, has been recognized as viscoelastic and the propagation of Rayleigh waves presents substantial differences in viscoelastic media as compared with elastic media. Therefore, it is necessary to carry out numerical simulation and dispersion analysis of Rayleigh waves in viscoelastic media to better understand Rayleigh-wave behaviors in the real world. We apply a pseudospectral method to the calculation of the spatial derivatives using a Chebyshev difference operator in the vertical direction and a Fourier difference operator in the horizontal direction based on the velocity-stress elastodynamic equations and relations of linear viscoelastic solids. This approach stretches the spatial discrete grid to have a minimum grid size near the free surface so that high accuracy and resolution are achieved at the free surface, which allows an effective incorporation of the free surface boundary conditions since the Chebyshev method is nonperiodic. We first use an elastic homogeneous half-space model to demonstrate the accuracy of the pseudospectral method comparing with the analytical solution, and verify the correctness of the numerical modeling results for a viscoelastic half-space comparing the phase velocities of Rayleigh wave between the theoretical values and the dispersive image generated by high-resolution linear Radon transform. We then simulate three types of two-layer models to analyze dispersive-energy characteristics for near-surface applications. Results demonstrate that the phase velocity of Rayleigh waves in viscoelastic media is relatively higher than in elastic media and the fundamental mode increases by 10-16% when the frequency is above 10. Hz due to the velocity dispersion of P
Modeling of Non-WSSUS Double-Rayleigh Fading Channels for Vehicular Communications
Directory of Open Access Journals (Sweden)
Carlos A. Gutiérrez
2017-01-01
Full Text Available This paper deals with the modeling of nonstationary time-frequency (TF dispersive multipath fading channels for vehicle-to-vehicle (V2V communication systems. As a main contribution, the paper presents a novel geometry-based statistical channel model that facilitates the analysis of the nonstationarities of V2V fading channels arising at a small-scale level due to the time-varying nature of the propagation delays. This new geometrical channel model has been formulated following the principles of plane wave propagation (PWP and assuming that the transmitted signal reaches the receiver antenna through double interactions with multiple interfering objects (IOs randomly located in the propagation area. As a consequence of such interactions, the first-order statistics of the channel model’s envelope are shown to follow a worse-than-Rayleigh distribution; specifically, they follow a double-Rayleigh distribution. General expressions are derived for the envelope and phase distributions, four-dimensional (4D TF correlation function (TF-CF, and TF-dependent delay and Doppler profiles of the proposed channel model. Such expressions are valid regardless of the underlying geometry of the propagation area. Furthermore, a closed-form solution of the 4D TF-CF is presented for the particular case of the geometrical two-ring scattering model. The obtained results provide new theoretical insights into the correlation and spectral properties of small-scale nonstationary V2V double-Rayleigh fading channels.
Multimode modelling of the Rayleigh-Taylor instability
International Nuclear Information System (INIS)
Town, R.P.J.; Findlay, J.D.; Bell, A.R.
1996-01-01
This paper presents a comparison of Haan's mode coupling model with two-dimensional hydrocode simulations. In the light of these results, a new saturation criterion is developed that is used in a new, extended mode coupling model. The new extended model accurately follows the mode development to amplitudes 2 to 3 times larger than Haan's model. (Author)
A model for near-wall dynamics in turbulent Rayleigh Bénard convection
Theerthan, S. Ananda; Arakeri, Jaywant H.
1998-10-01
Experiments indicate that turbulent free convection over a horizontal surface (e.g. Rayleigh Bénard convection) consists of essentially line plumes near the walls, at least for moderately high Rayleigh numbers. Based on this evidence, we propose here a two-dimensional model for near-wall dynamics in Rayleigh Bénard convection and in general for convection over heated horizontal surfaces. The model proposes a periodic array of steady laminar two-dimensional plumes. A plume is fed on either side by boundary layers on the wall. The results from the model are obtained in two ways. One of the methods uses the similarity solution of Rotem & Classen (1969) for the boundary layer and the similarity solution of Fuji (1963) for the plume. We have derived expressions for mean temperature and temperature and velocity fluctuations near the wall. In the second approach, we compute the two-dimensional flow field in a two-dimensional rectangular open cavity. The number of plumes in the cavity depends on the length of the cavity. The plume spacing is determined from the critical length at which the number of plumes increases by one. The results for average plume spacing and the distribution of r.m.s. temperature and velocity fluctuations are shown to be in acceptable agreement with experimental results.
Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface
Energy Technology Data Exchange (ETDEWEB)
Kim, No Hyu; Yang, Seung Yong [Korea University of Technology and Education, Cheonan (Korea, Republic of)
2007-12-15
Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness
Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface
International Nuclear Information System (INIS)
Kim, No Hyu; Yang, Seung Yong
2007-01-01
Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness
Self-consistent model of the Rayleigh--Taylor instability in ablatively accelerated laser plasma
International Nuclear Information System (INIS)
Bychkov, V.V.; Golberg, S.M.; Liberman, M.A.
1994-01-01
A self-consistent approach to the problem of the growth rate of the Rayleigh--Taylor instability in laser accelerated targets is developed. The analytical solution of the problem is obtained by solving the complete system of the hydrodynamical equations which include both thermal conductivity and energy release due to absorption of the laser light. The developed theory provides a rigorous justification for the supplementary boundary condition in the limiting case of the discontinuity model. An analysis of the suppression of the Rayleigh--Taylor instability by the ablation flow is done and it is found that there is a good agreement between the obtained solution and the approximate formula σ = 0.9√gk - 3u 1 k, where g is the acceleration, u 1 is the ablation velocity. This paper discusses different regimes of the ablative stabilization and compares them with previous analytical and numerical works
Directory of Open Access Journals (Sweden)
Dhaundiyal Alok
2017-09-01
Full Text Available This paper deals with the influence of some parameters relevant to biomass pyrolysis on the numerical solutions of the nonisothermal nth order distributed activation energy model using the Rayleigh distribution. Investigated parameters are the integral upper limit, the frequency factor, the heating rate, the reaction order and the scale parameters of the Rayleigh distribution. The influence of these parameters has been considered for the determination of the kinetic parameters of the non-isothermal nth order Rayleigh distribution from the experimentally derived thermoanalytical data of biomass pyrolysis.
Advection diffusion model for particles deposition in Rayleigh-Benard turbulent flows
International Nuclear Information System (INIS)
Oresta, P.; Lippolis, A.; Verzicco, R.; Soldati, A.
2005-01-01
In this paper, Direct Numerical Simulation (DNS) and Lagrangian Particle Tracking are used to precisely investigate the turbulent thermally driven flow and particles dispersion in a closed, slender cylindrical domain. The numerical simulations are carried out for Rayleigh (Ra) and Prandtl numbers (Pr) equal to Ra = 2X10 8 and Pr = 0.7, considering three sets of particles with Stokes numbers, based on Kolmogorov scale, equal to St k 1.3, St k 0.65 and St k = 0.13. This data are used to calculate a priori the drift velocity and the turbulent diffusion coefficient for the Advection Diffusion model. These quantities are function of the Stokes, Froude, Rayleigh and Prandtl numbers only. One dimensional, time dependent, Advection- Diffusion Equation (ADE) is presented to predict particles deposition in Rayleigh-Benard flow in the cylindrical domain. This archetype configuration models flow and aerosol dynamics, produced in case of accident in the passive containment cooling system (PCCS) of a nuclear reactor. ADE results show a good agreement with DNS data for all the sets of particles investigated. (author)
Energy Technology Data Exchange (ETDEWEB)
Henry de Frahan, M. T., E-mail: marchdf@umich.edu; Johnsen, E. [Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109 (United States); Belof, J. L.; Cavallo, R. M.; Ancheta, D. S.; El-dasher, B. S.; Florando, J. N.; Gallegos, G. F.; LeBlanc, M. M. [Lawrence Livermore National Laboratory Livermore, California 94551-0808 (United States); Raevsky, V. A.; Ignatova, O. N.; Lebedev, A. [Russian Federal Nuclear Center-VNIIEF, Sarov 607188 (Russian Federation)
2015-06-14
We present a set of high explosive driven Rayleigh-Taylor strength experiments for beryllium to produce data to distinguish predictions by various strength models. Design simulations using existing strength model parameterizations from Steinberg-Lund and Preston-Tonks-Wallace (PTW) suggested an optimal design that would delineate between not just different strength models, but different parameters sets of the PTW model. Application of the models to the post-shot results, however, suggests growth consistent with little material strength. We focus mostly on efforts to simulate the data using published strength models as well as the more recent RING relaxation model developed at VNIIEF. The results of the strength experiments indicate weak influence of strength in mitigating the growth with the RING model coming closest to predicting the material behavior. Finally, we present shock and ramp-loading recovery experiments.
Thermal Rayleigh-Marangoni convection in a three-layer liquid-metal-battery model
Köllner, Thomas; Boeck, Thomas; Schumacher, Jörg
2017-05-01
The combined effects of buoyancy-driven Rayleigh-Bénard convection (RC) and surface tension-driven Marangoni convection (MC) are studied in a triple-layer configuration which serves as a simplified model for a liquid metal battery (LMB). The three-layer model consists of a liquid metal alloy cathode, a molten salt separation layer, and a liquid metal anode at the top. Convection is triggered by the temperature gradient between the hot electrolyte and the colder electrodes, which is a consequence of the release of resistive heat during operation. We present a linear stability analysis of the state of pure thermal conduction in combination with three-dimensional direct numerical simulations of the nonlinear turbulent evolution on the basis of a pseudospectral method. Five different modes of convection are identified in the configuration, which are partly coupled to each other: RC in the upper electrode, RC with internal heating in the molten salt layer, and MC at both interfaces between molten salt and electrode as well as anticonvection in the middle layer and lower electrode. The linear stability analysis confirms that the additional Marangoni effect in the present setup increases the growth rates of the linearly unstable modes, i.e., Marangoni and Rayleigh-Bénard instability act together in the molten salt layer. The critical Grashof and Marangoni numbers decrease with increasing middle layer thickness. The calculated thresholds for the onset of convection are found for realistic current densities of laboratory-sized LMBs. The global turbulent heat transfer follows scaling predictions for internally heated RC. The global turbulent momentum transfer is comparable with turbulent convection in the classical Rayleigh-Bénard case. In summary, our studies show that incorporating Marangoni effects generates smaller flow structures, alters the velocity magnitudes, and enhances the turbulent heat transfer across the triple-layer configuration.
Energy Technology Data Exchange (ETDEWEB)
Henry de Frahan, M. T. [Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA; Belof, J. L. [Lawrence Livermore National Laboratory Livermore, California 94551-0808, USA; Cavallo, R. M. [Lawrence Livermore National Laboratory Livermore, California 94551-0808, USA; Raevsky, V. A. [Russian Federal Nuclear Center-VNIIEF, Sarov 607188, Russia; Ignatova, O. N. [Russian Federal Nuclear Center-VNIIEF, Sarov 607188, Russia; Lebedev, A. [Russian Federal Nuclear Center-VNIIEF, Sarov 607188, Russia; Ancheta, D. S. [Lawrence Livermore National Laboratory Livermore, California 94551-0808, USA; El-dasher, B. S. [Lawrence Livermore National Laboratory Livermore, California 94551-0808, USA; Florando, J. N. [Lawrence Livermore National Laboratory Livermore, California 94551-0808, USA; Gallegos, G. F. [Lawrence Livermore National Laboratory Livermore, California 94551-0808, USA; Johnsen, E. [Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA; LeBlanc, M. M. [Lawrence Livermore National Laboratory Livermore, California 94551-0808, USA
2015-06-14
A recent collaboration between LLNL and VNIIEF has produced a set of high explosive driven Rayleigh-Taylor strength data for beryllium. Design simulations using legacy strength models from Steinberg-Lund and Preston-Tonks-Wallace (PTW) suggested an optimal design that would delineate between not just different strength models, but different parameters sets of the PTW model. Application of the models to the post-shot results, however, shows close to classical growth. We characterize the material properties of the beryllium tested in the experiments. We also discuss recent efforts to simulate the data using the legacy strength models as well as the more recent RING relaxation model developed at VNIIEF. Finally, we present shock and ramp-loading recovery experiments conducted as part of the collaboration.
Reduced-Order Modeling of 3D Rayleigh-Benard Turbulent Convection
Hassanzadeh, Pedram; Grover, Piyush; Nabi, Saleh
2017-11-01
Accurate Reduced-Order Models (ROMs) of turbulent geophysical flows have broad applications in science and engineering; for example, to study the climate system or to perform real-time flow control/optimization in energy systems. Here we focus on 3D Rayleigh-Benard turbulent convection at the Rayleigh number of 106 as a prototype for turbulent geophysical flows, which are dominantly buoyancy driven. The purpose of the study is to evaluate and improve the performance of different model reduction techniques using this setting. One-dimensional ROMs for horizontally averaged temperature are calculated using several methods. Specifically, the Linear Response Function (LRF) of the system is calculated from a large DNS dataset using Dynamic Mode Decomposition (DMD) and Fluctuation-Dissipation Theorem (FDT). The LRF is also calculated using the Green's function method of Hassanzadeh and Kuang (2016, J. Atmos. Sci.), which is based on using numerous forced DNS runs. The performance of these LRFs in estimating the system's response to weak external forcings or controlling the time-mean flow are compared and contrasted. The spectral properties of the LRFs and the scaling of the accuracy with the length of the dataset (for the data-driven methods) are also discussed.
A Novel Approach for Blind Estimation of Reverberation Time using Rayleigh Distribution Model
Directory of Open Access Journals (Sweden)
AMAD HAMZA
2016-10-01
Full Text Available In this paper a blind estimation approach is proposed which directly utilizes the reverberant signal for estimating the RT (Reverberation Time.For estimation a very well-known method is used; MLE (Maximum Likelihood Estimation. Distribution of the decay rate is the core of the proposed method and can be achieved from the analysis of decay curve of the energy of the sound or from enclosure impulse response. In a pre-existing state of the art method Laplace distribution is used to model reverberation decay. The method proposed in this paper make use of the Rayleigh distribution and a spotting approach for modelling decay rate and identifying region of free decay in reverberant signal respectively. Motivation for the paper was deduced from the fact, when the reverberant speech RT falls in specific range then the signals decay rate impersonate Rayleigh distribution. On the basis of results of the experiments carried out for numerous reverberant signal it is clear that the performance and accuracy of the proposed method is better than other pre-existing methods
A Novel Approach for Blind Estimation of Reverberation Time using Rayleigh Distribution Model
International Nuclear Information System (INIS)
Hamza, A.; Jan, T.; Ali, A.
2016-01-01
In this paper a blind estimation approach is proposed which directly utilizes the reverberant signal for estimating the RT (Reverberation Time). For estimation a very well-known method is used; MLE (Maximum Likelihood Estimation). Distribution of the decay rate is the core of the proposed method and can be achieved from the analysis of decay curve of the energy of the sound or from enclosure impulse response. In a pre-existing state of the art method Laplace distribution is used to model reverberation decay. The method proposed in this paper make use of the Rayleigh distribution and a spotting approach for modelling decay rate and identifying region of free decay in reverberant signal respectively. Motivation for the paper was deduced from the fact, when the reverberant speech RT falls in specific range then the signals decay rate impersonate Rayleigh distribution. On the basis of results of the experiments carried out for numerous reverberant signal it is clear that the performance and accuracy of the proposed method is better than other pre-existing methods. (author)
A fractional model for dye removal
Directory of Open Access Journals (Sweden)
Ji-Huan He
2016-01-01
Full Text Available The adsorption process has a fractional property, and a fractional model is suggested to study a transport model of direct textile industry wastewater. An approximate solution of the concentration is obtained by the variational iteration method.
Model for the saturation of the hydromagnetic Rayleigh--Taylor instability
International Nuclear Information System (INIS)
Roderick, N.F.; Hussey, T.W.
1984-01-01
The saturation of the hydromagnetic Rayleigh--Taylor instability is caused by the reduction of driving current in the bubble region between the spikes formed as the instability develops. For short wavelengths linear magnetic field diffusion provides the necessary smoothing of the magnetic field to reduce the driving force. For wavelengths longer than the magnetic field diffusion length, the current is shorted through material which expands into the bubble region. This initially low density accumulates in the bubble and eventually provides a source of sufficiently high conductivity plasma which reduces the magnetic field penetration to the front of the bubble. Simple analytic models have been developed to verify and and quantify these predictions. These models have been compared with two-dimensional magnetohydrodynamic calculations for imploding plasma shells and give good agreement with these more detailed simulations
Modeling of the thermal boundary layer in turbulent Rayleigh-Bénard convection
Emran, Mohammad; Shishkina, Olga
2016-11-01
We report modeling of the thermal boundary layer in turbulent Rayleigh-Bénard convection (RBC), which incorporates the effect of turbulent fluctuations. The study is based on the thermal boundary layer equation from Shishkina et al., and new Direct Numerical Simulations (DNS) of RBC in a cylindrical cell of the aspect ratio 1, for the Prandtl number variation of several orders of magnitude. Our modeled temperature profiles are found to agree with the DNS much better than those obtained with the classical Prandtl-Blasius or Falkner-Skan approaches. The work is supported by the Deutsche Forschungsgemeinschaft (DFG) under the Grant Sh405/4 - Heisenberg fellowship and SFB963, Project A06.
Thin layer model for nonlinear evolution of the Rayleigh-Taylor instability
Zhao, K. G.; Wang, L. F.; Xue, C.; Ye, W. H.; Wu, J. F.; Ding, Y. K.; Zhang, W. Y.
2018-03-01
On the basis of the thin layer approximation [Ott, Phys. Rev. Lett. 29, 1429 (1972)], a revised thin layer model for incompressible Rayleigh-Taylor instability has been developed to describe the deformation and nonlinear evolution of the perturbed interface. The differential equations for motion are obtained by analyzing the forces (the gravity and pressure difference) of fluid elements (i.e., Newton's second law). The positions of the perturbed interface are obtained from the numerical solution of the motion equations. For the case of vacuum on both sides of the layer, the positions of the upper and lower interfaces obtained from the revised thin layer approximation agree with that from the weakly nonlinear (WN) model of a finite-thickness fluid layer [Wang et al., Phys. Plasmas 21, 122710 (2014)]. For the case considering the fluids on both sides of the layer, the bubble-spike amplitude from the revised thin layer model agrees with that from the WN model [Wang et al., Phys. Plasmas 17, 052305 (2010)] and the expanded Layzer's theory [Goncharov, Phys. Rev. Lett. 88, 134502 (2002)] in the early nonlinear growth regime. Note that the revised thin layer model can be applied to investigate the perturbation growth at arbitrary Atwood numbers. In addition, the large deformation (the large perturbed amplitude and the arbitrary perturbed distributions) in the initial stage can also be described by the present model.
Energy Technology Data Exchange (ETDEWEB)
Abd-Alla, A. M.; Abo-Dahab, S. M. [Taif University, Taif (Egypt); Khan, Aftab [COMSATS, Chakshahzad (Pakistan)
2015-10-15
In this paper, we investigated the propagation of surface waves in a rotating fibre-reinforced viscoelastic anisotropic media of a higher order and fraction orders of nth order including time rate of strain with voids. The general surface wave speed is derived to study the effect of rotation and voids on surface waves. Particular cases for Stoneley, Love and Rayleigh waves are also discussed. The results obtained in this investigation are more general in the sense that some earlier published results are obtained from our result as special cases. In order zero our results are well agreeing with classical results. Also by neglecting the reinforced elastic parameters and voids the results reduce to well known isotropic medium. Comparison was made with the results obtained in the presence and absence of rotation and parameters for fibre-reinforced of the material medium. It is observed that Love wave remains unaffected with respect to rotation and voids. It is also observed that, surface waves cannot propagate in a fast rotating medium. Numerical results are given and illustrated graphically.
International Nuclear Information System (INIS)
Abd-Alla, A. M.; Abo-Dahab, S. M.; Khan, Aftab
2015-01-01
In this paper, we investigated the propagation of surface waves in a rotating fibre-reinforced viscoelastic anisotropic media of a higher order and fraction orders of nth order including time rate of strain with voids. The general surface wave speed is derived to study the effect of rotation and voids on surface waves. Particular cases for Stoneley, Love and Rayleigh waves are also discussed. The results obtained in this investigation are more general in the sense that some earlier published results are obtained from our result as special cases. In order zero our results are well agreeing with classical results. Also by neglecting the reinforced elastic parameters and voids the results reduce to well known isotropic medium. Comparison was made with the results obtained in the presence and absence of rotation and parameters for fibre-reinforced of the material medium. It is observed that Love wave remains unaffected with respect to rotation and voids. It is also observed that, surface waves cannot propagate in a fast rotating medium. Numerical results are given and illustrated graphically.
A heuristic model for the nonlinear Rayleigh--Taylor instability in fast Z pinches
International Nuclear Information System (INIS)
Hussey, T.W.; Roderick, N.F.; Shumlak, U.; Spielman, R.B.; Deeney, C.
1995-01-01
A simple, heuristic model for the early nonlinear phase of the Rayleigh--Taylor instability (RTI) in thin-cylindrical-shell Z-pinch implosions has been developed. This model is based on the fact that, as the field--plasma interface is deformed, there is a component of the applied force that acts to move mass from the low mass per unit area bubble region into the higher mass per unit area spike region. The resulting reduced mass per unit area of the bubble causes it to be preferentially accelerated ahead of the spike. The pinch begins to radiate as the bubble mass first reaches the axis, and it continues to radiate while the mass that is entrained within the spikes and within unperturbed parts of the shell also arrives on axis. This model relates the time at which the bubble arrives on axis to an initial wavelength and amplitude of a single mode of the RTI. Then, by comparing this to the time at which the unperturbed mass reaches the axis, one estimates pinch thermalization time, a quantity that is determined experimentally. Experimental data, together with analytic models, have been used to choose appropriate initial wavelength and amplitude both for foils and for certain gas puff implosions. By noting that thermalization time is a weak function of these parameters, it is argued that one may use the same values for an extrapolative study of qualitatively similar implosions
Modeling and simulations of radiative blast wave driven Rayleigh-Taylor instability experiments
Shimony, Assaf; Huntington, Channing M.; Trantham, Matthew; Malamud, Guy; Elbaz, Yonatan; Kuranz, Carolyn C.; Drake, R. Paul; Shvarts, Dov
2017-10-01
Recent experiments at the National Ignition Facility measured the growth of Rayleigh-Taylor RT instabilities driven by radiative blast waves, relevant to astrophysics and other HEDP systems. We constructed a new Buoyancy-Drag (BD) model, which accounts for the ablation effect on both bubble and spike. This ablation effect is accounted for by using the potential flow model ]Oron et al PoP 1998], adding another term to the classical BD formalism: βDuA / u , where β the Takabe constant, D the drag term, uA the ablation velocity and uthe instability growth velocity. The model results are compared with the results of experiments and 2D simulations using the CRASH code, with nominal radiation or reduced foam opacity (by a factor of 1000). The ablation constant of the model, βb / s, for the bubble and for the spike fronts, are calibrated using the results of the radiative shock experiments. This work is funded by the Lawrence Livermore National Laboratory under subcontract B614207, and was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.
Fractional Order Models of Industrial Pneumatic Controllers
Directory of Open Access Journals (Sweden)
Abolhassan Razminia
2014-01-01
Full Text Available This paper addresses a new approach for modeling of versatile controllers in industrial automation and process control systems such as pneumatic controllers. Some fractional order dynamical models are developed for pressure and pneumatic systems with bellows-nozzle-flapper configuration. In the light of fractional calculus, a fractional order derivative-derivative (FrDD controller and integral-derivative (FrID are remodeled. Numerical simulations illustrate the application of the obtained theoretical results in simple examples.
Potential flow model for the hydromagnetic Rayleigh--Taylor instability in cylindrical plasmas
International Nuclear Information System (INIS)
Hwang, C.S.; Roderick, N.F.
1987-01-01
A potential flow model has been developed to study the linear behavior of the hydromagnetic equivalent of the Rayleigh--Taylor instability in imploding cylindrical plasmas. Ordinary differential equations are obtained for both (r,z) and (r,θ) disturbances. The model allows the study of the dynamic effects of the moving plasma on the development of the instability. The perturbation equations separate into a geometric part associated with the motion of the interface and a nongeometric part associated with the stability of the interface. In both planes the geometric part shows growth of perturbations for imploding plasmas. The surface is also unstable in both planes for plasmas being imploded by magnetic fields. Analytic solutions are obtained for constant acceleration. These show that the short wavelength perturbations that are most damaging in the (r,z) plane are not affected by the motion of the interface. In the (r,θ) plane the growth of longer wavelength disturbances is affected by the interface motion
Spanwise homogeneous buoyancy-drag model for Rayleigh-Taylor mixing and experimental evaluation
International Nuclear Information System (INIS)
Dimonte, Guy
2000-01-01
A buoyancy-drag model for Rayleigh-Taylor (RT) mixing is developed on the premise that the bubble and spike regions behave as distinct and spanwise homogeneous fluids. Then, mass conservation is applied accross the mixing zone to obtain their average mixture densities dynamically. These are used to explicitly calculate the inertia and buoyancy terms in the evolutionary equation. The only unknown parameter in the model is the Newtonian drag constant C∼2.5±0.6, which is determined from turbulent RT experiments over various Atwood numbers A and acceleration histories g(t). The bubble (i=2) and spike (i=1) amplitudes are found to obey the familiar h i =α i Agt 2 for a constant g and h i ∼t θ i for an impulsive g. For bubbles, both α 2 and θ 2 are insensitive to A. For the spikes, both α 1 and θ 1 increase as a power law with the density ratio. However, θ 1 is not universal because it depends on the initial value of h 1 /h 2 . (c) 2000 American Institute of Physics
Directory of Open Access Journals (Sweden)
Esteban Flores-Mendez
2012-01-01
Full Text Available This work is focused on studying interface waves for three canonical models, that is, interfaces formed by vacuum-solid, solid-solid, and liquid-solid. These interfaces excited by dynamic loads cause the emergence of Rayleigh's, Stoneley's, and Scholte's waves, respectively. To perform the study, the indirect boundary element method is used, which has proved to be a powerful tool for numerical modeling of problems in elastodynamics. In essence, the method expresses the diffracted wave field of stresses, pressures, and displacements by a boundary integral, also known as single-layer representation, whose shape can be regarded as a Fredholm's integral representation of second kind and zero order. This representation can be considered as an exemplification of Huygens' principle, which is equivalent to Somigliana's representation theorem. Results in frequency domain for the three types of interfaces are presented; then, using the fourier discrete transform, we derive the results in time domain, where the emergence of interface waves is highlighted.
A Fractionally Integrated Wishart Stochastic Volatility Model
M. Asai (Manabu); M.J. McAleer (Michael)
2013-01-01
textabstractThere has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of
Design Aspects of the Rayleigh Convection Code
Featherstone, N. A.
2017-12-01
Understanding the long-term generation of planetary or stellar magnetic field requires complementary knowledge of the large-scale fluid dynamics pervading large fractions of the object's interior. Such large-scale motions are sensitive to the system's geometry which, in planets and stars, is spherical to a good approximation. As a result, computational models designed to study such systems often solve the MHD equations in spherical geometry, frequently employing a spectral approach involving spherical harmonics. We present computational and user-interface design aspects of one such modeling tool, the Rayleigh convection code, which is suitable for deployment on desktop and petascale-hpc architectures alike. In this poster, we will present an overview of this code's parallel design and its built-in diagnostics-output package. Rayleigh has been developed with NSF support through the Computational Infrastructure for Geodynamics and is expected to be released as open-source software in winter 2017/2018.
A Computational Model of Fraction Arithmetic
Braithwaite, David W.; Pyke, Aryn A.; Siegler, Robert S.
2017-01-01
Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…
Numerical Modelling of Rayleigh Wave Propagation in Course of Rapid Impulse Compaction
Herbut, Aneta; Rybak, Jarosław
2017-10-01
As the soil improvement technologies are the area of a rapid development, they require designing and implementing novel methods of control and calibration in order to ensure the safety of geotechnical works. At Wroclaw University of Science and Technology (Poland), these new methods are continually developed with the aim to provide the appropriate tools for the preliminary design of work process, as well as for the further ongoing on-site control of geotechnical works (steel sheet piling, pile driving or soil improvement technologies). The studies include preliminary numerical simulations and field tests concerning measurements and continuous histogram recording of shocks and vibrations and its ground-born dynamic impact on engineering structures. The impact of vibrations on reinforced concrete and masonry structures in the close proximity of the construction site may be destroying in both architectural and structural meaning. Those limits are juxtaposed in codes of practice, but always need an individual judgment. The results and observations make it possible to delineate specific modifications to the parameters of technology applied (e.g. hammer drop height). On the basis of numerous case studies of practical applications, already summarized and published, we were able to formulate the guidelines for work on the aforementioned sites. This work presents specific aspects of the active design (calibration of building site numerical model) by means of technology calibration, using the investigation of the impact of vibrations that occur during the Impulse Compaction on adjacent structures. A case study entails the impact of construction works on Rayleigh wave propagation in the zone of 100 m (radius) around the Compactor.
Comparative study of void fraction models
International Nuclear Information System (INIS)
Borges, R.C.; Freitas, R.L.
1985-01-01
Some models for the calculation of void fraction in water in sub-cooled boiling and saturated vertical upward flow with forced convection have been selected and compared with experimental results in the pressure range of 1 to 150 bar. In order to know the void fraction axial distribution it is necessary to determine the net generation of vapour and the fluid temperature distribution in the slightly sub-cooled boiling region. It was verified that the net generation of vapour was well represented by the Saha-Zuber model. The selected models for the void fraction calculation present adequate results but with a tendency to super-estimate the experimental results, in particular the homogeneous models. The drift flux model is recommended, followed by the Armand and Smith models. (F.E.) [pt
Fractional diffusion models of nonlocal transport
International Nuclear Information System (INIS)
Castillo-Negrete, D. del
2006-01-01
A class of nonlocal models based on the use of fractional derivatives (FDs) is proposed to describe nondiffusive transport in magnetically confined plasmas. FDs are integro-differential operators that incorporate in a unified framework asymmetric non-Fickian transport, non-Markovian ('memory') effects, and nondiffusive scaling. To overcome the limitations of fractional models in unbounded domains, we use regularized FDs that allow the incorporation of finite-size domain effects, boundary conditions, and variable diffusivities. We present an α-weighted explicit/implicit numerical integration scheme based on the Grunwald-Letnikov representation of the regularized fractional diffusion operator in flux conserving form. In sharp contrast with the standard diffusive model, the strong nonlocality of fractional diffusion leads to a linear in time response for a decaying pulse at short times. In addition, an anomalous fractional pinch is observed, accompanied by the development of an uphill transport region where the 'effective' diffusivity becomes negative. The fractional flux is in general asymmetric and, for steady states, it has a negative (toward the core) component that enhances confinement and a positive component that increases toward the edge and leads to poor confinement. The model exhibits the characteristic anomalous scaling of the confinement time, τ, with the system's size, L, τ∼L α , of low-confinement mode plasma where 1<α<2 is the order of the FD operator. Numerical solutions of the model with an off-axis source show that the fractional inward transport gives rise to profile peaking reminiscent of what is observed in tokamak discharges with auxiliary off-axis heating. Also, cold-pulse perturbations to steady sates in the model exhibit fast, nondiffusive propagation phenomena that resemble perturbative experiments
Bonde, Jeffrey
2018-04-01
The dynamics of a magnetized, expanding plasma with a high ratio of kinetic energy density to ambient magnetic field energy density, or β, are examined by adapting a model of gaseous bubbles expanding in liquids as developed by Lord Rayleigh. New features include scale magnitudes and evolution of the electric fields in the system. The collisionless coupling between the expanding and ambient plasma due to these fields is described as well as the relevant scaling relations. Several different responses of the ambient plasma to the expansion are identified in this model, and for most laboratory experiments, ambient ions should be pulled inward, against the expansion due to the dominance of the electrostatic field.
Fractional virus epidemic model on financial networks
Directory of Open Access Journals (Sweden)
Balci Mehmet Ali
2016-01-01
Full Text Available In this study, we present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets. Since the long time series have a global memory effect, we represent our model by using the fractional calculus. This model operates on a network, where vertices are the stock markets and edges are constructed by the correlation distances. Thereafter, we find an analytical solution to commensurate system and use the well-known differential transform method to obtain the solution of incommensurate system of fractional differential equations. Our findings are confirmed and complemented by the data set of the relevant stock markets between 2006 and 2016. Rather than the hypothetical values, we use the Hurst Exponent of each time series to approximate the fraction size and graph theoretical concepts to obtain the variables.
A Fractional Micro-Macro Model for Crowds of Pedestrians Based on Fractional Mean Field Games
Institute of Scientific and Technical Information of China (English)
Kecai Cao; Yang Quan Chen; Daniel Stuart
2016-01-01
Modeling a crowd of pedestrians has been considered in this paper from different aspects. Based on fractional microscopic model that may be much more close to reality, a fractional macroscopic model has been proposed using conservation law of mass. Then in order to characterize the competitive and cooperative interactions among pedestrians, fractional mean field games are utilized in the modeling problem when the number of pedestrians goes to infinity and fractional dynamic model composed of fractional backward and fractional forward equations are constructed in macro scale. Fractional micromacro model for crowds of pedestrians are obtained in the end.Simulation results are also included to illustrate the proposed fractional microscopic model and fractional macroscopic model,respectively.
Fractional dynamical model for neurovascular coupling
Belkhatir, Zehor
2014-08-01
The neurovascular coupling is a key mechanism linking the neural activity to the hemodynamic behavior. Modeling of this coupling is very important to understand the brain function but it is at the same time very complex due to the complexity of the involved phenomena. Many studies have reported a time delay between the neural activity and the cerebral blood flow, which has been described by adding a delay parameter in some of the existing models. An alternative approach is proposed in this paper, where a fractional system is used to model the neurovascular coupling. Thanks to its nonlocal property, a fractional derivative is suitable for modeling the phenomena with delay. The proposed model is coupled with the first version of the well-known balloon model, which relates the cerebral blood flow to the Blood Oxygen Level Dependent (BOLD) signal measured using functional Magnetic Resonance Imaging (fMRI). Through some numerical simulations, the properties of the fractional model are explained and some preliminary comparisons to a real BOLD data set are provided. © 2014 IEEE.
Revised models of interstellar nitrogen isotopic fractionation
Wirström, E. S.; Charnley, S. B.
2018-03-01
Nitrogen-bearing molecules in cold molecular clouds exhibit a range of isotopic fractionation ratios and these molecules may be the precursors of 15N enrichments found in comets and meteorites. Chemical model calculations indicate that atom-molecular ion and ion-molecule reactions could account for most of the fractionation patterns observed. However, recent quantum-chemical computations demonstrate that several of the key processes are unlikely to occur in dense clouds. Related model calculations of dense cloud chemistry show that the revised 15N enrichments fail to match observed values. We have investigated the effects of these reaction rate modifications on the chemical model of Wirström et al. (2012) for which there are significant physical and chemical differences with respect to other models. We have included 15N fractionation of CN in neutral-neutral reactions and also updated rate coefficients for key reactions in the nitrogen chemistry. We find that the revised fractionation rates have the effect of suppressing 15N enrichment in ammonia at all times, while the depletion is even more pronounced, reaching 14N/15N ratios of >2000. Taking the updated nitrogen chemistry into account, no significant enrichment occurs in HCN or HNC, contrary to observational evidence in dark clouds and comets, although the 14N/15N ratio can still be below 100 in CN itself. However, such low CN abundances are predicted that the updated model falls short of explaining the bulk 15N enhancements observed in primitive materials. It is clear that alternative fractionating reactions are necessary to reproduce observations, so further laboratory and theoretical studies are urgently needed.
Dynamical models of happiness with fractional order
Song, Lei; Xu, Shiyun; Yang, Jianying
2010-03-01
This present study focuses on a dynamical model of happiness described through fractional-order differential equations. By categorizing people of different personality and different impact factor of memory (IFM) with different set of model parameters, it is demonstrated via numerical simulations that such fractional-order models could exhibit various behaviors with and without external circumstance. Moreover, control and synchronization problems of this model are discussed, which correspond to the control of emotion as well as emotion synchronization in real life. This study is an endeavor to combine the psychological knowledge with control problems and system theories, and some implications for psychotherapy as well as hints of a personal approach to life are both proposed.
Asymptotic dynamics for the Cucker-Smale-type model with the Rayleigh friction
International Nuclear Information System (INIS)
Ha, Seung-Yeal; Ha, Taeyoung; Kim, Jong-Ho
2010-01-01
We study the asymptotic flocking dynamics for the Cucker-Smale-type second-order continuous-time dynamical system with the Rayleigh friction. For mean-field communications with a positive lower bound, we show that an asymptotic flocking occurs for any compactly supported initial configuration in a large coupling regime. In contrast, in a small coupling regime, an asymptotic flocking is possible for a restricted class of initial configurations near complete flocking states. We also present several numerical simulations and compare them with our analytical results.
Asymptotic dynamics for the Cucker-Smale-type model with the Rayleigh friction
Energy Technology Data Exchange (ETDEWEB)
Ha, Seung-Yeal [Department of Mathematical Sciences, Seoul National University, Seoul 151-747 (Korea, Republic of); Ha, Taeyoung; Kim, Jong-Ho, E-mail: syha@snu.ac.k, E-mail: tha@nims.re.k, E-mail: jhkim@nims.re.k [National Institute for Mathematical Sciences, 385-16, 3F Tower Koreana, Doryong-dong, Yuseong-gu, Daejeon, 305-340 (Korea, Republic of)
2010-08-06
We study the asymptotic flocking dynamics for the Cucker-Smale-type second-order continuous-time dynamical system with the Rayleigh friction. For mean-field communications with a positive lower bound, we show that an asymptotic flocking occurs for any compactly supported initial configuration in a large coupling regime. In contrast, in a small coupling regime, an asymptotic flocking is possible for a restricted class of initial configurations near complete flocking states. We also present several numerical simulations and compare them with our analytical results.
Ardhuin, Fabrice; Lavanant, Thibaut; Obrebski, Mathias; Marié, Louis; Royer, Jean-Yves; d'Eu, Jean-François; Howe, Bruce M; Lukas, Roger; Aucan, Jerome
2013-10-01
The generation of ultra-low frequency acoustic noise (0.1 to 1 Hz) by the nonlinear interaction of ocean surface gravity waves is well established. More controversial are the quantitative theories that attempt to predict the recorded noise levels and their variability. Here a single theoretical framework is used to predict the noise level associated with propagating pseudo-Rayleigh modes and evanescent acoustic-gravity modes. The latter are dominant only within 200 m from the sea surface, in shallow or deep water. At depths larger than 500 m, the comparison of a numerical noise model with hydrophone records from two open-ocean sites near Hawaii and the Kerguelen islands reveal: (a) Deep ocean acoustic noise at frequencies 0.1 to 1 Hz is consistent with the Rayleigh wave theory, in which the presence of the ocean bottom amplifies the noise by 10 to 20 dB; (b) in agreement with previous results, the local maxima in the noise spectrum support the theoretical prediction for the vertical structure of acoustic modes; and (c) noise level and variability are well predicted for frequencies up to 0.4 Hz. Above 0.6 Hz, the model results are less accurate, probably due to the poor estimation of the directional properties of wind-waves with frequencies higher than 0.3 Hz.
Operator continued fraction and bound states
International Nuclear Information System (INIS)
Pindor, M.
1984-01-01
The effective Hamiltonian of the model space perturbation theory (multilevel Rayleigh-Schroedinger theory) is expressed as an operator continued fraction. In the case of a nondegenerate model space the expression becomes an operator branched continued fraction. The method is applied to the harmonic oscillator with the kinetic energy treated as the perturbation and to the anharmonic oscillator
Modeling electron fractionalization with unconventional Fock spaces.
Cobanera, Emilio
2017-08-02
It is shown that certain fractionally-charged quasiparticles can be modeled on D-dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges, then this approach fractionalizes the Abelian charges only. In particular, the mth-root of a spinful fermion carries charge e/m and spin 1/2. Just like taking a root of a complex number, taking a root of a fermion yields a mildly non-unique result. As a consequence, there are several possible choices of quantum exchange statistics for fermion-root quasiparticles. These choices are tied to the dimensionality [Formula: see text] of the lattice by basic physical considerations. One particular family of fermion-root quasiparticles is directly connected to the parafermion zero-energy modes expected to emerge in certain mesoscopic devices involving fractional quantum Hall states. Hence, as an application of potential mesoscopic interest, I investigate numerically the hybridization of Majorana and parafermion zero-energy edge modes caused by fractionalizing but charge-conserving tunneling.
Parameter estimation in fractional diffusion models
Kubilius, Kęstutis; Ralchenko, Kostiantyn
2017-01-01
This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides s...
Fractional-moment Capital Asset Pricing model
International Nuclear Information System (INIS)
Li Hui; Wu Min; Wang Xiaotian
2009-01-01
In this paper, we introduce the definition of the 'α-covariance' and present the fractional-moment versions of Capital Asset Pricing Model,which can be used to price assets when asset return distributions are likely to be stable Levy (or Student-t) distribution during panics and stampedes in worldwide security markets in 2008. Furthermore, if asset returns are truly governed by the infinite-variance stable Levy distributions, life is fundamentally riskier than in a purely Gaussian world. Sudden price movements like the worldwide security market crash in 2008 turn into real-world possibilities.
Modeling of heat conduction via fractional derivatives
Fabrizio, Mauro; Giorgi, Claudio; Morro, Angelo
2017-09-01
The modeling of heat conduction is considered by letting the time derivative, in the Cattaneo-Maxwell equation, be replaced by a derivative of fractional order. The purpose of this new approach is to overcome some drawbacks of the Cattaneo-Maxwell equation, for instance possible fluctuations which violate the non-negativity of the absolute temperature. Consistency with thermodynamics is shown to hold for a suitable free energy potential, that is in fact a functional of the summed history of the heat flux, subject to a suitable restriction on the set of admissible histories. Compatibility with wave propagation at a finite speed is investigated in connection with temperature-rate waves. It follows that though, as expected, this is the case for the Cattaneo-Maxwell equation, the model involving the fractional derivative does not allow the propagation at a finite speed. Nevertheless, this new model provides a good description of wave-like profiles in thermal propagation phenomena, whereas Fourier's law does not.
State-Space Modelling of Loudspeakers using Fractional Derivatives
DEFF Research Database (Denmark)
King, Alexander Weider; Agerkvist, Finn T.
2015-01-01
This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response of a fractio......This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response...... of a fractional harmonic oscillator, representing the mechanical part of a loudspeaker, showing the effect of the fractional derivative and its relationship to viscoelasticity. Finally, a loudspeaker model with a fractional order viscoelastic suspension and fractional order voice coil is fit to measurement data...
New method dynamically models hydrocarbon fractionation
Energy Technology Data Exchange (ETDEWEB)
Kesler, M.G.; Weissbrod, J.M.; Sheth, B.V. [Kesler Engineering, East Brunswick, NJ (United States)
1995-10-01
A new method for calculating distillation column dynamics can be used to model time-dependent effects of independent disturbances for a range of hydrocarbon fractionation. It can model crude atmospheric and vacuum columns, with relatively few equilibrium stages and a large number of components, to C{sub 3} splitters, with few components and up to 300 equilibrium stages. Simulation results are useful for operations analysis, process-control applications and closed-loop control in petroleum, petrochemical and gas processing plants. The method is based on an implicit approach, where the time-dependent variations of inventory, temperatures, liquid and vapor flows and compositions are superimposed at each time step on the steady-state solution. Newton-Raphson (N-R) techniques are then used to simultaneously solve the resulting finite-difference equations of material, equilibrium and enthalpy balances that characterize distillation dynamics. The important innovation is component-aggregation and tray-aggregation to contract the equations without compromising accuracy. This contraction increases the N-R calculations` stability. It also significantly increases calculational speed, which is particularly important in dynamic simulations. This method provides a sound basis for closed-loop, supervisory control of distillation--directly or via multivariable controllers--based on a rigorous, phenomenological column model.
Analysis of Drude model using fractional derivatives without singular kernels
Directory of Open Access Journals (Sweden)
Jiménez Leonardo Martínez
2017-11-01
Full Text Available We report study exploring the fractional Drude model in the time domain, using fractional derivatives without singular kernels, Caputo-Fabrizio (CF, and fractional derivatives with a stretched Mittag-Leffler function. It is shown that the velocity and current density of electrons moving through a metal depend on both the time and the fractional order 0 < γ ≤ 1. Due to non-singular fractional kernels, it is possible to consider complete memory effects in the model, which appear neither in the ordinary model, nor in the fractional Drude model with Caputo fractional derivative. A comparison is also made between these two representations of the fractional derivatives, resulting a considered difference when γ < 0.8.
Picasso, G. O.; Basili, V. R.
1982-01-01
It is noted that previous investigations into the applicability of Rayleigh curve model to medium scale software development efforts have met with mixed results. The results of these investigations are confirmed by analyses of runs and smoothing. The reasons for the models' failure are found in the subcycle effort data. There are four contributing factors: uniqueness of the environment studied, the influence of holidays, varying management techniques and differences in the data studied.
Miao, W.; Li, G.; Niu, F.
2016-12-01
Knowledge on the 3D sediment structure beneath the Gulf of Mexico passive margin is not only important to explore the oil and gas resources in the area, but also essential to decipher the deep crust and mantle structure beneath the margin with teleseismic data. In this study, we conduct a joint inversion of Rayleigh wave ellipticity and phase velocity at 6-40 s to construct a 3-D S wave velocity model in a rectangular area of 100°-87° west and 28°-37° north. We use ambient noise data from a total of 215 stations of the Transportable Array deployed under the Earthscope project. Rayleigh wave ellipticity, or Rayleigh wave Z/H (vertical to horizontal) amplitude ratio is mostly sensitive to shallow sediment structure, while the dispersion data are expected to have reasonably good resolution to uppermost mantle depths. The Z/H ratios measured from stations inside the Gulf Coastal Plain are distinctly lower in comparison with those measured from the inland stations. We also measured the phase velocity dispersion from the same ambient noise dataset. Our preliminary 3-D model is featured by strong low-velocity anomalies at shallow depth, which are spatially well correlated with Gulf Cost, East Texas, and the Lower Mississippi basins. We will discuss other features of the 3-D models once the model is finalized.
Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation
Petráš, Ivo
2011-01-01
"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...
Table-sized matrix model in fractional learning
Soebagyo, J.; Wahyudin; Mulyaning, E. C.
2018-05-01
This article provides an explanation of the fractional learning model i.e. a Table-Sized Matrix model in which fractional representation and its operations are symbolized by the matrix. The Table-Sized Matrix are employed to develop problem solving capabilities as well as the area model. The Table-Sized Matrix model referred to in this article is used to develop an understanding of the fractional concept to elementary school students which can then be generalized into procedural fluency (algorithm) in solving the fractional problem and its operation.
Palomeras, Imma; Villasenor, Antonio; Thurner, Sally; Levander, Alan; Gallart, Josep; Harnafi, Mimoun
2016-04-01
The Iberian Peninsula and Morocco, separated by the Alboran Sea and the Algerian Basin, constitute the westernmost Mediterranean. From north to south this region consists of the Pyrenees, the result of interaction between the Iberian and Eurasian plates; the Iberian Massif, a region that has been undeformed since the end of the Paleozoic; the Central System and Iberian Chain, regions with intracontinental Oligocene-Miocene deformation; the Gibraltar Arc (Betics, Rif and Alboran terranes) and the Atlas Mountains, resulting from post-Oligocene subduction roll-back and Eurasian-Nubian plate convergence. In this study we analyze data from recent broad-band array deployments and permanent stations on the Iberian Peninsula and in Morocco (Spanish IberArray and Siberia arrays, the US PICASSO array, the University of Munster array, and the Spanish, Portuguese, and Moroccan National Networks) to characterize its lithospheric structure. The combined array of 350 stations has an average interstation spacing of ~60 km, comparable to USArray. We have calculated the Rayleigh waves phase velocities from ambient noise for short periods (4 s to 40 s) and teleseismic events for longer periods (20 s to 167 s). We inverted the phase velocities to obtain a shear velocity model for the lithosphere to ~200 km depth. The model shows differences in the crust for the different areas, where the highest shear velocities are mapped in the Iberian Massif crust. The crustal thickness is highly variable ranging from ~25 km beneath the eastern Betics to ~55km beneath the Gibraltar Strait, Internal Betics and Internal Rif. Beneath this region a unique arc shaped anomaly with high upper mantle velocities (>4.6 km/s) at shallow depths (volcanic fields in Iberia and Morocco, indicative of high temperatures at relatively shallow depths, and suggesting that the lithosphere has been removed beneath these areas
International Nuclear Information System (INIS)
Otero, F A; Frontini, G L; Elicabe, G E
2011-01-01
An analytic model for the scattering of a spherical particle with spherical inclusions has been proposed under the RG approximation. The model can be used without limitations to describe an X-ray scattering experiment. However, for light scattering several conditions must be fulfilled. Based on this model an inverse methodology is proposed to estimate the radii of host particle and inclusions, the number of inclusions and the Distance Distribution Functions (DDF's) of the distances between inclusions and the distances between inclusions and the origin of coordinates. The methodology is numerically tested in a light scattering example in which the host particle is eliminated by matching the refractive indices of host particle and medium. The results obtained for this cluster particle are very satisfactory.
Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases
Directory of Open Access Journals (Sweden)
Fazal Haq
2017-01-01
Full Text Available The fractional order Susceptible-Infected-Recovered (SIR epidemic model of childhood disease is considered. Laplace–Adomian Decomposition Method is used to compute an approximate solution of the system of nonlinear fractional differential equations. We obtain the solutions of fractional differential equations in the form of infinite series. The series solution of the proposed model converges rapidly to its exact value. The obtained results are compared with the classical case.
Palomeras, I.; Villasenor, A.; Thurner, S.; Levander, A.; Gallart, J.; Harnafi, M.
2014-12-01
The westernmost Mediterranean comprises the Iberian Peninsula and Morocco, separated by the Alboran Sea and the Algerian Basin. From north to south this region consists of the Pyrenees, resulting from Iberia-Eurasia collision; the Iberian Massif, which has been undeformed since the end of the Paleozoic; the Central System and Iberian Chain, regions with intracontinental Oligocene-Miocene deformation; the Gibraltar Arc (Betics, Rif and Alboran terranes), resulting from post-Oligocene subduction roll-back; and the Atlas Mountains. We analyzed data from recent broad-band array deployments and permanent stations in the area (IberArray and Siberia arrays, the PICASSO array, the University of Munster array, and the Spanish, Portuguese and Moroccan National Networks) to characterize its lithospheric structure. The combined array of 350 stations has an average interstation spacing of ~60 km. We calculated the Rayleigh waves phase velocities from ambient noise (periods 4 to 40 s) and teleseismic events (periods 20 to 167 s). We inverted the phase velocities to obtain a shear velocity model for the lithosphere to ~200 km depth. Our results correlate well with the surface expression of the main structural units with higher crustal velocity for the Iberian Massif than for the Alpine Iberia and Atlas Mountains. The Gibraltar Arc has lower crustal shear velocities than the regional average at all crustal depths. It also shows an arc shaped anomaly with high upper mantle velocities (>4.6 km/s) at shallow depths (volcanic fields in Iberia and Morocco, indicative of high temperatures at relatively shallow depths, and suggesting that the lithosphere has been removed beneath these areas.
Spiking and bursting patterns of fractional-order Izhikevich model
Teka, Wondimu W.; Upadhyay, Ranjit Kumar; Mondal, Argha
2018-03-01
Bursting and spiking oscillations play major roles in processing and transmitting information in the brain through cortical neurons that respond differently to the same signal. These oscillations display complex dynamics that might be produced by using neuronal models and varying many model parameters. Recent studies have shown that models with fractional order can produce several types of history-dependent neuronal activities without the adjustment of several parameters. We studied the fractional-order Izhikevich model and analyzed different kinds of oscillations that emerge from the fractional dynamics. The model produces a wide range of neuronal spike responses, including regular spiking, fast spiking, intrinsic bursting, mixed mode oscillations, regular bursting and chattering, by adjusting only the fractional order. Both the active and silent phase of the burst increase when the fractional-order model further deviates from the classical model. For smaller fractional order, the model produces memory dependent spiking activity after the pulse signal turned off. This special spiking activity and other properties of the fractional-order model are caused by the memory trace that emerges from the fractional-order dynamics and integrates all the past activities of the neuron. On the network level, the response of the neuronal network shifts from random to scale-free spiking. Our results suggest that the complex dynamics of spiking and bursting can be the result of the long-term dependence and interaction of intracellular and extracellular ionic currents.
A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics
Lei, Dong; Liang, Yingjie; Xiao, Rui
2018-01-01
We develop a fractional model to describe the thermomechanical behavior of amorphous thermoplastics. The fractional model is composed of two parallel fractional Maxwell elements. The first fractional Maxwell model is used to describe the glass transition, while the second component is aimed at describing the viscous flow. We further derive the analytical solutions for the stress relaxation modulus and complex modulus through Laplace transform. We then demonstrate the model is able to describe the master curves of the stress relaxation modulus, storage modulus and loss modulus, which all show two distinct transition regions. The obtained parameters show that the modulus of the two fractional Maxwell elements differs in 2-3 orders of magnitude, while the relaxation time differs in 7-9 orders of magnitude. Finally, we apply the model to describe the stress response of constant strain rate tests. The model, together with the parameters obtained from fitting the master curve of stress relaxation modulus, can accurately predict the temperature and strain rate dependent stress response.
The fractional volatility model: An agent-based interpretation
Vilela Mendes, R.
2008-06-01
Based on the criteria of mathematical simplicity and consistency with empirical market data, a model with volatility driven by fractional noise has been constructed which provides a fairly accurate mathematical parametrization of the data. Here, some features of the model are reviewed and extended to account for leverage effects. Using agent-based models, one tries to find which agent strategies and (or) properties of the financial institutions might be responsible for the features of the fractional volatility model.
Energy Technology Data Exchange (ETDEWEB)
Egly, H
2007-10-15
This thesis deals with the dynamics of accelerated ablative front spreading in Inertial Confinement Fusion experiments. ICF is designed for the implosion of a deuterium-tritium spherical target. The outer shell, the ablator, is irradiated providing a high level pressure inside the target. During this first stage, the ablation front propagating inwards is perturbed by hydrodynamics instabilities, which can prevent the fusion reaction in the decelerated stage. We propose here a study on Rayleigh-Taylor instabilities during ablation process, in the two dimensional case. In order to obtain a numerical solution, we perform an asymptotic analysis in the limit of a high temperature ratio, between the remaining cold ablator and the hot ablated plasma. This study is divided in two steps. First, the thermo-diffusive part of the set of equations is approximated by a Hele-Shaw model, which is then perturbed by the hydrodynamics part. Using a vortex method, we have to solve the advection of a vortical sheet moving with the ablation front. We compute the numerical solution on an Eulerian mesh coupled with a marker method. The thermal part is computed by implementing the Fat Boundary Method, recently developed. The hydrodynamic part is obtained from a Finite Volume scheme. (author)
International Nuclear Information System (INIS)
Nuzhnyj, A.S.; Rozanov, V.B.; Stepanov, R.V.; Shumskij, S.A.
2005-01-01
Stability of target compression in the laser thermonuclear synthesis is discussed. The process is determined by developing the Rayleigh-Taylor instability (RNI). A program unit for description of the RNI evolution by its initial distributions is developed. The results of statistical analysis of the RT mixing calculations are given. The analysis is carried out by means of learning base system and is substantiated on the generalization of great number of data, fulfilled by means of the neural network methods [ru
International Nuclear Information System (INIS)
Hillier, Andrew; Isobe, Hiroaki; Shibata, Kazunari; Berger, Thomas
2012-01-01
The launch of the Hinode satellite led to the discovery of rising plumes, dark in chromospheric lines, that propagate from large (∼10 Mm) bubbles that form at the base of quiescent prominences. The plumes move through a height of approximately 10 Mm while developing highly turbulent profiles. The magnetic Rayleigh-Taylor instability was hypothesized to be the mechanism that drives these flows. In this study, using three-dimensional (3D) MHD simulations, we investigate the nonlinear stability of the Kippenhahn-Schlüter prominence model for the interchange mode of the magnetic Rayleigh-Taylor instability. The model simulates the rise of a buoyant tube inside the quiescent prominence model, where the interchange of magnetic field lines becomes possible at the boundary between the buoyant tube and the prominence. Hillier et al. presented the initial results of this study, where upflows of constant velocity (maximum found 6 km s –1 ) and a maximum plume width ≈1.5 Mm which propagate through a height of approximately 6 Mm were found. Nonlinear interaction between plumes was found to be important for determining the plume dynamics. In this paper, using the results of ideal MHD simulations, we determine how the initial parameters for the model and buoyant tube affect the evolution of instability. We find that the 3D mode of the magnetic Rayleigh-Taylor instability grows, creating upflows aligned with the magnetic field of constant velocity (maximum found 7.3 km s –1 ). The width of the upflows is dependent on the initial conditions, with a range of 0.5-4 Mm which propagate through heights of 3-6 Mm. These results are in general agreement with the observations of the rising plumes.
Large deflection of viscoelastic beams using fractional derivative model
International Nuclear Information System (INIS)
Bahranini, Seyed Masoud Sotoodeh; Eghtesad, Mohammad; Ghavanloo, Esmaeal; Farid, Mehrdad
2013-01-01
This paper deals with large deflection of viscoelastic beams using a fractional derivative model. For this purpose, a nonlinear finite element formulation of viscoelastic beams in conjunction with the fractional derivative constitutive equations has been developed. The four-parameter fractional derivative model has been used to describe the constitutive equations. The deflected configuration for a uniform beam with different boundary conditions and loads is presented. The effect of the order of fractional derivative on the large deflection of the cantilever viscoelastic beam, is investigated after 10, 100, and 1000 hours. The main contribution of this paper is finite element implementation for nonlinear analysis of viscoelastic fractional model using the storage of both strain and stress histories. The validity of the present analysis is confirmed by comparing the results with those found in the literature.
A void fraction model for annular two-phase flow
Energy Technology Data Exchange (ETDEWEB)
Tandon, T.N.; Gupta, C.P.; Varma, H.K.
1985-01-01
An analytical model has been developed for predicting void fraction in two-phase annular flow. In the analysis, the Lockhart-Martinelli method has been used to calculate two-phase frictional pressure drop and von Karman's universal velocity profile is used to represent the velocity distribution in the annular liquid film. Void fractions predicted by the proposed model are generally in good agreement with a available experimental data. This model appears to be as good as Smith's correlation and better than the Wallis and Zivi correlations for computing void fraction.
Fractional-order in a macroeconomic dynamic model
David, S. A.; Quintino, D. D.; Soliani, J.
2013-10-01
In this paper, we applied the Riemann-Liouville approach in order to realize the numerical simulations to a set of equations that represent a fractional-order macroeconomic dynamic model. It is a generalization of a dynamic model recently reported in the literature. The aforementioned equations have been simulated for several cases involving integer and non-integer order analysis, with some different values to fractional order. The time histories and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the macroeconomic dynamic model proposed here involves the public sector deficit equation, which renders the model more realistic and complete when compared with the ones encountered in the literature. The results reveal that the fractional-order macroeconomic model can exhibit a real reasonable behavior to macroeconomics systems and might offer greater insights towards the understanding of these complex dynamic systems.
Knapmeyer-Endrun, Brigitte; Golombek, Matthew P.; Ohrnberger, Matthias
2017-10-01
The SEIS (Seismic Experiment for Interior Structure) instrument onboard the InSight mission will be the first seismometer directly deployed on the surface of Mars. From studies on the Earth and the Moon, it is well known that site amplification in low-velocity sediments on top of more competent rocks has a strong influence on seismic signals, but can also be used to constrain the subsurface structure. Here we simulate ambient vibration wavefields in a model of the shallow sub-surface at the InSight landing site in Elysium Planitia and demonstrate how the high-frequency Rayleigh wave ellipticity can be extracted from these data and inverted for shallow structure. We find that, depending on model parameters, higher mode ellipticity information can be extracted from single-station data, which significantly reduces uncertainties in inversion. Though the data are most sensitive to properties of the upper-most layer and show a strong trade-off between layer depth and velocity, it is possible to estimate the velocity and thickness of the sub-regolith layer by using reasonable constraints on regolith properties. Model parameters are best constrained if either higher mode data can be used or additional constraints on regolith properties from seismic analysis of the hammer strokes of InSight's heat flow probe HP3 are available. In addition, the Rayleigh wave ellipticity can distinguish between models with a constant regolith velocity and models with a velocity increase in the regolith, information which is difficult to obtain otherwise.
International Nuclear Information System (INIS)
Gao Yitian; Tian Bo
2003-01-01
A variable-coefficient unstable nonlinear Schroedinger model is hereby investigated, which arises in such applications as the electron-beam plasma waves and Rayleigh-Taylor instability in nonuniform plasmas. With computerized symbolic computation, families of exact analytic dark- and bright-soliton-like solutions are found, of which some previously published solutions turn out to be the special cases. Similarity solutions also come out, which are expressible in terms of the elliptic functions and the second Painleve transcendent. Some observable effects caused by the variable coefficient are predicted, which may be detected in the future with the relevant space or laboratory plasma experiments with nonuniform background existing
Directory of Open Access Journals (Sweden)
Deimel Christian
2014-03-01
Full Text Available The most common method for simulating cavitating flows is using the governing flow equations in a form with a variable density and treats both phases as incompressible in combination with a transport equation for the vapour volume fraction. This approach is commonly referred to as volume of fluid method (VoF. To determine the transition of the liquid phase to vapour and vice versa, a relation for the mass transfer is needed. Several models exist, based on slightly differing physical assumptions, for example derivation from the dynamics of single bubbles or large bubble clusters. In our simulation, we use the model of Sauer and Schnerr which is based on the Rayleigh equation. One common problem of all mass transfer models is the use of model constants which often need to be tuned with regard to the examined problem. Furthermore, these models often overpredict the turbulent dynamic viscosity in the two-phase region which counteracts the development of transient shedding behaviour and is compensated by the modification proposed by Reboud. In the presented study, we vary the parameters of the Sauer-Schnerr model with Reboud modification that we implemented into an OpenFOAM solver to match numerical to experimental data.
A generic interference model for uplink OFDMA networks with fractional frequency reuse
Tabassum, Hina
2014-03-01
Fractional frequency reuse (FFR) has emerged as a viable solution to coordinate and mitigate cochannel interference (CCI) in orthogonal frequency-division multiple-access (OFDMA)-based wireless cellular networks. The incurred CCI in cellular networks with FFR is highly uncertain and varies as a function of various design parameters that include the user scheduling schemes, the transmit power distribution among multiple allocated subcarriers, the partitioning of the cellular region into cell-edge and cell-center zones, the allocation of spectrum within each zone, and the channel reuse factors. To this end, this paper derives a generic analytical model for uplink CCI in multicarrier OFDMA networks with FFR. The derived expressions capture several network design parameters and are applicable to any composite fading-channel models. The accuracy of the derivations is verified via Monte Carlo simulations. Moreover, their usefulness is demonstrated by obtaining closed-form expressions for the Rayleigh fading-channel model and by evaluating important network performance metrics such as ergodic capacity. Numerical results provide useful system design guidelines and highlight the trade-offs associated with the deployment of FFR schemes in OFDMA-based networks. © 2013 IEEE.
A generic interference model for uplink OFDMA networks with fractional frequency reuse
Tabassum, Hina; Dawy, Zaher; Alouini, Mohamed-Slim; Yilmaz, Ferkan
2014-01-01
Fractional frequency reuse (FFR) has emerged as a viable solution to coordinate and mitigate cochannel interference (CCI) in orthogonal frequency-division multiple-access (OFDMA)-based wireless cellular networks. The incurred CCI in cellular networks with FFR is highly uncertain and varies as a function of various design parameters that include the user scheduling schemes, the transmit power distribution among multiple allocated subcarriers, the partitioning of the cellular region into cell-edge and cell-center zones, the allocation of spectrum within each zone, and the channel reuse factors. To this end, this paper derives a generic analytical model for uplink CCI in multicarrier OFDMA networks with FFR. The derived expressions capture several network design parameters and are applicable to any composite fading-channel models. The accuracy of the derivations is verified via Monte Carlo simulations. Moreover, their usefulness is demonstrated by obtaining closed-form expressions for the Rayleigh fading-channel model and by evaluating important network performance metrics such as ergodic capacity. Numerical results provide useful system design guidelines and highlight the trade-offs associated with the deployment of FFR schemes in OFDMA-based networks. © 2013 IEEE.
Tempered fractional time series model for turbulence in geophysical flows
Meerschaert, Mark M.; Sabzikar, Farzad; Phanikumar, Mantha S.; Zeleke, Aklilu
2014-09-01
We propose a new time series model for velocity data in turbulent flows. The new model employs tempered fractional calculus to extend the classical 5/3 spectral model of Kolmogorov. Application to wind speed and water velocity in a large lake are presented, to demonstrate the practical utility of the model.
Tempered fractional time series model for turbulence in geophysical flows
International Nuclear Information System (INIS)
Meerschaert, Mark M; Sabzikar, Farzad; Phanikumar, Mantha S; Zeleke, Aklilu
2014-01-01
We propose a new time series model for velocity data in turbulent flows. The new model employs tempered fractional calculus to extend the classical 5/3 spectral model of Kolmogorov. Application to wind speed and water velocity in a large lake are presented, to demonstrate the practical utility of the model. (paper)
Application of Integer and Fractional Models in Electrochemical Systems
Directory of Open Access Journals (Sweden)
Isabel S. Jesus
2012-01-01
Full Text Available This paper describes the use of integer and fractional electrical elements, for modelling two electrochemical systems. A first type of system consists of botanical elements and a second type is implemented by electrolyte processes with fractal electrodes. Experimental results are analyzed in the frequency domain, and the pros and cons of adopting fractional-order electrical components for modelling these systems are compared.
Tian, Zhen; Huo, Linsheng; Gao, Weihang; Li, Hongnan; Song, Gangbing
2017-10-01
Wave-based concrete structural health monitoring has attracted much attention. A stress wave experiences significant attenuation in concrete, however there is a lack of a unified method for predicting the attenuation coefficient of the stress wave. In this paper, a simple and effective absorption attenuation model of stress waves in concrete is developed based on the Rayleigh damping model, which indicates that the absorption attenuation coefficient of stress waves in concrete is directly proportional to the square of the stress wave frequency when the damping ratio is small. In order to verify the theoretical model, related experiments were carried out. During the experiments, a concrete beam was designed in which the d33-model piezoelectric smart aggregates were embedded to detect the propagation of stress waves. It is difficult to distinguish direct stress waves due to the complex propagation paths and the reflection and scattering of stress waves in concrete. Hence, as another innovation of this paper, a new method for computing the absorption attenuation coefficient based on the time-reversal method is developed. Due to the self-adaptive focusing properties of the time-reversal method, the time-reversed stress wave focuses and generates a peak value. The time-reversal method eliminates the adverse effects of multipaths, reflection, and scattering. The absorption attenuation coefficient is computed by analyzing the peak value changes of the time-reversal focused signal. Finally, the experimental results are found to be in good agreement with the theoretical model.
Fractional dynamical model for neurovascular coupling
Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem
2014-01-01
The neurovascular coupling is a key mechanism linking the neural activity to the hemodynamic behavior. Modeling of this coupling is very important to understand the brain function but it is at the same time very complex due to the complexity
Fractional and multivariable calculus model building and optimization problems
Mathai, A M
2017-01-01
This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable ...
On an Estimation Method for an Alternative Fractionally Cointegrated Model
DEFF Research Database (Denmark)
Carlini, Federico; Łasak, Katarzyna
In this paper we consider the Fractional Vector Error Correction model proposed in Avarucci (2007), which is characterized by a richer lag structure than models proposed in Granger (1986) and Johansen (2008, 2009). We discuss the identification issues of the model of Avarucci (2007), following th...
Rayleigh reciprocity relations: Applications
International Nuclear Information System (INIS)
Lin Ju; Li Xiao-Lei; Wang Ning
2016-01-01
Classical reciprocity relations have wide applications in acoustics, from field representation to generalized optical theorem. In this paper we introduce our recent results on the applications and generalization of classical Rayleigh reciprocity relation: higher derivative reciprocity relations as a generalization of the classical one and a theoretical proof on the Green’s function retrieval from volume noises. (special topic)
Likelihood inference for a nonstationary fractional autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Ørregård Nielsen, Morten
2010-01-01
This paper discusses model-based inference in an autoregressive model for fractional processes which allows the process to be fractional of order d or d-b. Fractional differencing involves infinitely many past values and because we are interested in nonstationary processes we model the data X1......,...,X_{T} given the initial values X_{-n}, n=0,1,..., as is usually done. The initial values are not modeled but assumed to be bounded. This represents a considerable generalization relative to all previous work where it is assumed that initial values are zero. For the statistical analysis we assume...... the conditional Gaussian likelihood and for the probability analysis we also condition on initial values but assume that the errors in the autoregressive model are i.i.d. with suitable moment conditions. We analyze the conditional likelihood and its derivatives as stochastic processes in the parameters, including...
Chromo-Rayleigh interactions of dark matter
International Nuclear Information System (INIS)
Bai, Yang; Osborne, James
2015-01-01
For a wide range of models, dark matter can interact with QCD gluons via chromo-Rayleigh interactions. We point out that the Large Hadron Collider (LHC), as a gluon machine, provides a superb probe of such interactions. In this paper, we introduce simplified models to UV-complete two effective dark matter chromo-Rayleigh interactions and identify the corresponding collider signatures, including four jets or a pair of di-jet resonances plus missing transverse energy. After performing collider studies for both the 8 TeV and 14 TeV LHC, we find that the LHC can be more sensitive to dark matter chromo-Rayleigh interactions than direct detection experiments and thus provides the best opportunity for future discovery of this class of models.
Rayleigh scattering from ions near threshold
International Nuclear Information System (INIS)
Roy, S.C.; Gupta, S.K.S.; Kissel, L.; Pratt, R.H.
1988-01-01
Theoretical studies of Rayleigh scattering of photons from neon atoms with different degrees of ionization, for energies both below and above the K-edges of the ions, are presented. Some unexpected structures both in Rayleigh scattering and in photoionization from neutral and weakly ionized atoms, very close to threshold, have been reported. It has recently been realized that some of the predicted structures may have a nonphysical origin and are due to the limitation of the independent-particle model and also to the use of a Coulombic Latter tail. Use of a K-shell vacancy potential - in which an electron is assumed to be removed from the K-shell - in calculating K-shell Rayleigh scattering amplitudes removes some of the structure effects near threshold. We present in this work a discussion of scattering angular distributions and total cross sections, obtained utilizing vacancy potentials, and compare these predictions with those previously obtained in other potential model. (author) [pt
An approximate fractional Gaussian noise model with computational cost
Sø rbye, Sigrunn H.; Myrvoll-Nilsen, Eirik; Rue, Haavard
2017-01-01
Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood
Directory of Open Access Journals (Sweden)
Bashir Ahmad
2013-02-01
Full Text Available In this article, we discuss the existence of solutions for a boundary-value problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented.
Fractional Heat Conduction Models and Thermal Diffusivity Determination
Directory of Open Access Journals (Sweden)
Monika Žecová
2015-01-01
Full Text Available The contribution deals with the fractional heat conduction models and their use for determining thermal diffusivity. A brief historical overview of the authors who have dealt with the heat conduction equation is described in the introduction of the paper. The one-dimensional heat conduction models with using integer- and fractional-order derivatives are listed. Analytical and numerical methods of solution of the heat conduction models with using integer- and fractional-order derivatives are described. Individual methods have been implemented in MATLAB and the examples of simulations are listed. The proposal and experimental verification of the methods for determining thermal diffusivity using half-order derivative of temperature by time are listed at the conclusion of the paper.
Model for radial gas fraction profiles in vertical pipe flow
International Nuclear Information System (INIS)
Lucas, D.; Krepper, E.; Prasser, H.M.
2001-01-01
A one-dimensional model is presented, which predicts the radial volume fraction profiles from a given bubble size distribution. It bases on the assumption of an equilibrium of the forces acting on a bubble perpendicularly to the flow path (non drag forces). For the prediction of the flow pattern this model could be used within an procedure together with appropriate models for local bubble coalescence and break-up. (orig.)
Likelihood inference for a fractionally cointegrated vector autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Ørregård Nielsen, Morten
2012-01-01
such that the process X_{t} is fractional of order d and cofractional of order d-b; that is, there exist vectors ß for which ß'X_{t} is fractional of order d-b, and no other fractionality order is possible. We define the statistical model by 0inference when the true values satisfy b0¿1/2 and d0-b0......We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model with a restricted constant term, ¿, based on the Gaussian likelihood conditional on initial values. The model nests the I(d) VAR model. We give conditions on the parameters...... process in the parameters when errors are i.i.d. with suitable moment conditions and initial values are bounded. When the limit is deterministic this implies uniform convergence in probability of the conditional likelihood function. If the true value b0>1/2, we prove that the limit distribution of (ß...
Inter-fraction variations in respiratory motion models
Energy Technology Data Exchange (ETDEWEB)
McClelland, J R; Modat, M; Ourselin, S; Hawkes, D J [Centre for Medical Image Computing, University College London (United Kingdom); Hughes, S; Qureshi, A; Ahmad, S; Landau, D B, E-mail: j.mcclelland@cs.ucl.ac.uk [Department of Oncology, Guy' s and St Thomas' s Hospitals NHS Trust, London (United Kingdom)
2011-01-07
Respiratory motion can vary dramatically between the planning stage and the different fractions of radiotherapy treatment. Motion predictions used when constructing the radiotherapy plan may be unsuitable for later fractions of treatment. This paper presents a methodology for constructing patient-specific respiratory motion models and uses these models to evaluate and analyse the inter-fraction variations in the respiratory motion. The internal respiratory motion is determined from the deformable registration of Cine CT data and related to a respiratory surrogate signal derived from 3D skin surface data. Three different models for relating the internal motion to the surrogate signal have been investigated in this work. Data were acquired from six lung cancer patients. Two full datasets were acquired for each patient, one before the course of radiotherapy treatment and one at the end (approximately 6 weeks later). Separate models were built for each dataset. All models could accurately predict the respiratory motion in the same dataset, but had large errors when predicting the motion in the other dataset. Analysis of the inter-fraction variations revealed that most variations were spatially varying base-line shifts, but changes to the anatomy and the motion trajectories were also observed.
Fractional calculus model of electrical impedance applied to human skin.
Vosika, Zoran B; Lazovic, Goran M; Misevic, Gradimir N; Simic-Krstic, Jovana B
2013-01-01
Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and complex orders. Therefore, it adds a new dimension to understand and describe basic nature and behavior of complex systems in an improved way. Here we use the fractional calculus for modeling electrical properties of biological systems. We derived a new class of generalized models for electrical impedance and applied them to human skin by experimental data fitting. The primary model introduces new generalizations of: 1) Weyl fractional derivative operator, 2) Cole equation, and 3) Constant Phase Element (CPE). These generalizations were described by the novel equation which presented parameter [Formula: see text] related to remnant memory and corrected four essential parameters [Formula: see text] We further generalized single generalized element by introducing specific partial sum of Maclaurin series determined by parameters [Formula: see text] We defined individual primary model elements and their serial combination models by the appropriate equations and electrical schemes. Cole equation is a special case of our generalized class of models for[Formula: see text] Previous bioimpedance data analyses of living systems using basic Cole and serial Cole models show significant imprecisions. Our new class of models considerably improves the quality of fitting, evaluated by mean square errors, for bioimpedance data obtained from human skin. Our models with new parameters presented in specific partial sum of Maclaurin series also extend representation, understanding and description of complex systems electrical properties in terms of remnant memory effects.
Fractional calculus model of electrical impedance applied to human skin.
Directory of Open Access Journals (Sweden)
Zoran B Vosika
Full Text Available Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and complex orders. Therefore, it adds a new dimension to understand and describe basic nature and behavior of complex systems in an improved way. Here we use the fractional calculus for modeling electrical properties of biological systems. We derived a new class of generalized models for electrical impedance and applied them to human skin by experimental data fitting. The primary model introduces new generalizations of: 1 Weyl fractional derivative operator, 2 Cole equation, and 3 Constant Phase Element (CPE. These generalizations were described by the novel equation which presented parameter [Formula: see text] related to remnant memory and corrected four essential parameters [Formula: see text] We further generalized single generalized element by introducing specific partial sum of Maclaurin series determined by parameters [Formula: see text] We defined individual primary model elements and their serial combination models by the appropriate equations and electrical schemes. Cole equation is a special case of our generalized class of models for[Formula: see text] Previous bioimpedance data analyses of living systems using basic Cole and serial Cole models show significant imprecisions. Our new class of models considerably improves the quality of fitting, evaluated by mean square errors, for bioimpedance data obtained from human skin. Our models with new parameters presented in specific partial sum of Maclaurin series also extend representation, understanding and description of complex systems electrical properties in terms of remnant memory effects.
Discrete random walk models for space-time fractional diffusion
International Nuclear Information System (INIS)
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
2002-01-01
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order α is part of (0,2] and skewness θ (moduleθ≤{α,2-α}), and the first-order time derivative with a Caputo derivative of order β is part of (0,1]. Such evolution equation implies for the flux a fractional Fick's law which accounts for spatial and temporal non-locality. The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process that we view as a generalized diffusion process. By adopting appropriate finite-difference schemes of solution, we generate models of random walk discrete in space and time suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation
Fractional calculus phenomenology in two-dimensional plasma models
Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill
2006-10-01
Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).
Statistical properties of several models of fractional random point processes
Bendjaballah, C.
2011-08-01
Statistical properties of several models of fractional random point processes have been analyzed from the counting and time interval statistics points of view. Based on the criterion of the reduced variance, it is seen that such processes exhibit nonclassical properties. The conditions for these processes to be treated as conditional Poisson processes are examined. Numerical simulations illustrate part of the theoretical calculations.
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
S. Peiris (Shelton); M. Asai (Manabu); M.J. McAleer (Michael)
2016-01-01
textabstractIn recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility
Rayleigh scattering in coupled microcavities: theory.
Vörös, Zoltán; Weihs, Gregor
2014-12-03
In this paper we theoretically study how structural disorder in coupled semiconductor heterostructures influences single-particle scattering events that would otherwise be forbidden by symmetry. We extend the model of Savona (2007 J. Phys.: Condens. Matter 19 295208) to describe Rayleigh scattering in coupled planar microcavity structures, and find that effective filter theories can be ruled out.
Modelling nematode movement using time-fractional dynamics.
Hapca, Simona; Crawford, John W; MacMillan, Keith; Wilson, Mike J; Young, Iain M
2007-09-07
We use a correlated random walk model in two dimensions to simulate the movement of the slug parasitic nematode Phasmarhabditis hermaphrodita in homogeneous environments. The model incorporates the observed statistical distributions of turning angle and speed derived from time-lapse studies of individual nematode trails. We identify strong temporal correlations between the turning angles and speed that preclude the case of a simple random walk in which successive steps are independent. These correlated random walks are appropriately modelled using an anomalous diffusion model, more precisely using a fractional sub-diffusion model for which the associated stochastic process is characterised by strong memory effects in the probability density function.
Energy Technology Data Exchange (ETDEWEB)
Safari, Bonfils; Gasore, Jimmy [Department of Physics, National University of Rwanda, P.O. Box 117, Huye, South Province (Rwanda)
2010-12-15
A wind energy system converts the kinetic energy of the wind into mechanical or electrical energy that can be harnessed for practical uses and transform the economy of rural areas where access to water and electricity is very restricted and industry is almost nonexistent in most of the developing countries like Rwanda. Assessing wind power potential for a location is an imperative requirement before making a decision for the installation of windmills or a wind electric generator and evaluating plans for relating projects. The aim of the present study was to evaluate the potential of wind resource in Rwanda and to constitute a database for the users of the wind power. A time series of hourly daily measured wind speed and wind direction for the period between 1974 and 1993 on five main Rwandan meteorological stations was provided by the National Meteorology Department. Statistical methods applying Weibull and Rayleigh distribution were presented to evaluate the wind speed characteristics and the wind power potential at a height of 10 m above ground level using hourly monthly average data. Those characteristics were extrapolated for higher levels in altitude. The results give a global picture of the distribution of the wind potential in different locations of Rwanda. (author)
Leaky-box approximation to the fractional diffusion model
International Nuclear Information System (INIS)
Uchaikin, V V; Sibatov, R T; Saenko, V V
2013-01-01
Two models based on fractional differential equations for galactic cosmic ray diffusion are applied to the leaky-box approximation. One of them (Lagutin-Uchaikin, 2000) assumes a finite mean free path of cosmic ray particles, another one (Lagutin-Tyumentsev, 2004) uses distribution with infinite mean distance between collision with magnetic clouds, when the trajectories have form close to ballistic. Calculations demonstrate that involving boundary conditions is incompatible with spatial distributions given by the second model.
Directory of Open Access Journals (Sweden)
Kareema Abed Al-Kadim
2017-12-01
Full Text Available In this paper Rayleigh Pareto distribution have introduced denote by( R_PD. We stated some useful functions. Therefor we give some of its properties like the entropy function, mean, mode, median , variance , the r-th moment about the mean, the rth moment about the origin, reliability, hazard functions, coefficients of variation, of sekeness and of kurtosis. Finally, we estimate the parameters so the aim of this search is to introduce a new distribution
Modeling and analysis of fractional order DC-DC converter.
Radwan, Ahmed G; Emira, Ahmed A; AbdelAty, Amr M; Azar, Ahmad Taher
2017-07-11
Due to the non-idealities of commercial inductors, the demand for a better model that accurately describe their dynamic response is elevated. So, the fractional order models of Buck, Boost and Buck-Boost DC-DC converters are presented in this paper. The detailed analysis is made for the two most common modes of converter operation: Continuous Conduction Mode (CCM) and Discontinuous Conduction Mode (DCM). Closed form time domain expressions are derived for inductor currents, voltage gain, average current, conduction time and power efficiency where the effect of the fractional order inductor is found to be strongly present. For example, the peak inductor current at steady state increases with decreasing the inductor order. Advanced Design Systems (ADS) circuit simulations are used to verify the derived formulas, where the fractional order inductor is simulated using Valsa Constant Phase Element (CPE) approximation and Generalized Impedance Converter (GIC). Different simulation results are introduced with good matching to the theoretical formulas for the three DC-DC converter topologies under different fractional orders. A comprehensive comparison with the recently published literature is presented to show the advantages and disadvantages of each approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Mathematical modeling of fish burger baking using fractional calculus
Directory of Open Access Journals (Sweden)
Bainy Eduarda M.
2017-01-01
Full Text Available Tilapia (Oreochromis sp. is the most important and abundant fish species in Brazil due to its adaptability to different environments. The development of tilapia-based products could be an alternative in order to aggregate value and increase fish meat consumption. However, there is little information available on fishburger freezing and cooking in the literature. In this work, the mathematical modeling of the fish burger baking was studied. Previously to the baking process, the fishburgers were assembled in cylindrical shape of height equal to 8mm and diameter 100mm and then baked in an electrical oven with forced heat convection at 150ºC. A T-type thermocouple was inserted in the burger to obtain its temperature profile at the central position. In order to describe the temperature of the burger during the baking process, lumped-parameter models of integer and fractional order and also a nonlinear model due to heat capacity temperature dependence were considered. The burger physical properties were obtained from the literature. After proper parameter estimation tasks and statistical validation, the fractional order model could better describe the experimental temperature behavior, a value of 0.91±0.02 was obtained for the fractional order of the system with correlation coefficient of 0.99. Therefore, with the better temperature prediction, process control and economic optimization studies of the baking process can be conducted.
Recent results in Rayleigh scattering
International Nuclear Information System (INIS)
Kahane, S.; Shahal, O.; Moreh, R.; Ben-Gurion Univ. of the Negev, Beer-Sheva
1997-01-01
New measurements of Rayleigh scattering, employing neutron capture γ rays are presented. Experimental conditions are achieved such that the Rayleigh contribution is dominant and much larger than other competing coherent process. A detailed comparison with the modified relativistic form factor approximation (MRFF) is made. It is found that MRFF overestimates the true cross sections by 3-4%. (author)
QUADRO: A SUPERVISED DIMENSION REDUCTION METHOD VIA RAYLEIGH QUOTIENT OPTIMIZATION.
Fan, Jianqing; Ke, Zheng Tracy; Liu, Han; Xia, Lucy
We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method-named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization)-for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are employed to guarantee uniform convergence in estimating non-polynomially many parameters, even though only the fourth moments are assumed. Methodologically, QUADRO is based on elliptical models which allow us to formulate the Rayleigh quotient maximization as a convex optimization problem. Computationally, we propose an efficient linearized augmented Lagrangian method to solve the constrained optimization problem. Theoretically, we provide explicit rates of convergence in terms of Rayleigh quotient under both Gaussian and general elliptical models. Thorough numerical results on both synthetic and real datasets are also provided to back up our theoretical results.
Non-exponential extinction of radiation by fractional calculus modelling
International Nuclear Information System (INIS)
Casasanta, G.; Ciani, D.; Garra, R.
2012-01-01
Possible deviations from exponential attenuation of radiation in a random medium have been recently studied in several works. These deviations from the classical Beer-Lambert law were justified from a stochastic point of view by Kostinski (2001) . In his model he introduced the spatial correlation among the random variables, i.e. a space memory. In this note we introduce a different approach, including a memory formalism in the classical Beer-Lambert law through fractional calculus modelling. We find a generalized Beer-Lambert law in which the exponential memoryless extinction is only a special case of non-exponential extinction solutions described by Mittag-Leffler functions. We also justify this result from a stochastic point of view, using the space fractional Poisson process. Moreover, we discuss some concrete advantages of this approach from an experimental point of view, giving an estimate of the deviation from exponential extinction law, varying the optical depth. This is also an interesting model to understand the meaning of fractional derivative as an instrument to transmit randomness of microscopic dynamics to the macroscopic scale.
A holographic model for the fractional quantum Hall effect
Energy Technology Data Exchange (ETDEWEB)
Lippert, Matthew [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, 1090GL Amsterdam (Netherlands); Meyer, René [Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo,Kashiwa, Chiba 277-8568 (Japan); Taliotis, Anastasios [Theoretische Natuurkunde, Vrije Universiteit Brussel andThe International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium)
2015-01-08
Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a Γ{sub 0}(2) modular symmetry group commuting with the renormalization group flow and hence mapping different phases of two-dimensional electron gases into each other. Based on this insight, we construct a phenomenological holographic model which captures many features of the fractional quantum Hall effect. Using an SL(2,ℤ)-invariant Einstein-Maxwell-axio-dilaton theory capturing the important modular transformation properties of quantum Hall physics, we find dyonic diatonic black hole solutions which are gapped and have a Hall conductivity equal to the filling fraction, as expected for quantum Hall states. We also provide several technical results on the general behavior of the gauge field fluctuations around these dyonic dilatonic black hole solutions: we specify a sufficient criterion for IR normalizability of the fluctuations, demonstrate the preservation of the gap under the SL(2,ℤ) action, and prove that the singularity of the fluctuation problem in the presence of a magnetic field is an accessory singularity. We finish with a preliminary investigation of the possible IR scaling solutions of our model and some speculations on how they could be important for the observed universality of quantum Hall transitions.
A holographic model for the fractional quantum Hall effect
Lippert, Matthew; Meyer, René; Taliotis, Anastasios
2015-01-01
Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a Γ0(2) modular symmetry group commuting with the renormalization group flow and hence mapping different phases of two-dimensional electron gases into each other. Based on this insight, we construct a phenomenological holographic model which captures many features of the fractional quantum Hall effect. Using an -invariant Einstein-Maxwell-axio-dilaton theory capturing the important modular transformation properties of quantum Hall physics, we find dyonic diatonic black hole solutions which are gapped and have a Hall conductivity equal to the filling fraction, as expected for quantum Hall states. We also provide several technical results on the general behavior of the gauge field fluctuations around these dyonic dilatonic black hole solutions: we specify a sufficient criterion for IR normalizability of the fluctuations, demonstrate the preservation of the gap under the action, and prove that the singularity of the fluctuation problem in the presence of a magnetic field is an accessory singularity. We finish with a preliminary investigation of the possible IR scaling solutions of our model and some speculations on how they could be important for the observed universality of quantum Hall transitions.
Transient heat conduction in a pebble fuel applying fractional model
International Nuclear Information System (INIS)
Gomez A, R.; Espinosa P, G.
2009-10-01
In this paper we presents the equation of thermal diffusion of temporary-fractional order in the one-dimensional space in spherical coordinates, with the objective to analyze the heat transference between the fuel and coolant in a fuel element of a Pebble Bed Modular Reactor. The pebble fuel is the heterogeneous system made by microsphere constitutes by U O, pyrolytic carbon and silicon carbide mixed with graphite. To describe the heat transfer phenomena in the pebble fuel we applied a constitutive law fractional (Non-Fourier) in order to analyze the behaviour transient of the temperature distribution in the pebble fuel with anomalous thermal diffusion effects a numerical model is developed. (Author)
Phase Diagram of a Simple Model for Fractional Topological Insulator
Chen, Hua; Yang, Kun
2012-02-01
We study a simple model of two species of (or spin-1/2) fermions with short-range intra-species repulsion in the presence of opposite (effetive) magnetic field, each at filling factor 1/3. In the absence of inter-species interaction, the ground state is simply two copies of the 1/3 Laughlin state, with opposite chirality. Due to the overall time-reversal symmetry, this is a fractional topological insulator. We show this phase is stable against moderate inter-species interactions. However strong enough inter-species repulsion leads to phase separation, while strong enough inter-species attraction drives the system into a superfluid phase. We obtain the phase diagram through exact diagonalization caluclations. Nature of the fractional topological insluator-superfluid phase transition is discussed using an appropriate Chern-Simons-Ginsburg-Landau effective field theory.
Deformed Calogero-Sutherland model and fractional quantum Hall effect
Atai, Farrokh; Langmann, Edwin
2017-01-01
The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases. We show that a known collective field description of the CS model, which is based on conformal field theory (CFT), is actually a collective field description of the deformed CS model. This provides a natural application of the deformed CS model in Wen's effective field theory of the fractional quantum Hall effect (FQHE), with the two kinds of particles corresponding to electrons and quasi-hole excitations. In particular, we use known mathematical results about super-Jack polynomials to obtain simple explicit formulas for the orthonormal CFT basis proposed by van Elburg and Schoutens in the context of the FQHE.
Gaetani, G.A.; Cohen, A.L.; Wang, Z.; Crusius, John
2011-01-01
This study presents a new approach to coral thermometry that deconvolves the influence of water temperature on skeleton composition from that of “vital effects”, and has the potential to provide estimates of growth temperatures that are accurate to within a few tenths of a degree Celsius from both tropical and cold-water corals. Our results provide support for a physico-chemical model of coral biomineralization, and imply that Mg2+ substitutes directly for Ca2+ in biogenic aragonite. Recent studies have identified Rayleigh fractionation as an important influence on the elemental composition of coral skeletons. Daily, seasonal and interannual variations in the amount of aragonite precipitated by corals from each “batch” of calcifying fluid can explain why the temperature dependencies of elemental ratios in coral skeleton differ from those of abiogenic aragonites, and are highly variable among individual corals. On the basis of this new insight into the origin of “vital effects” in coral skeleton, we developed a Rayleigh-based, multi-element approach to coral thermometry. Temperature is resolved from the Rayleigh fractionation signal by combining information from multiple element ratios (e.g., Mg/Ca, Sr/Ca, Ba/Ca) to produce a mathematically over-constrained system of Rayleigh equations. Unlike conventional coral thermometers, this approach does not rely on an initial calibration of coral skeletal composition to an instrumental temperature record. Rather, considering coral skeletogenesis as a biologically mediated, physico-chemical process provides a means to extract temperature information from the skeleton composition using the Rayleigh equation and a set of experimentally determined partition coefficients. Because this approach is based on a quantitative understanding of the mechanism that produces the “vital effect” it should be possible to apply it both across scleractinian species and to corals growing in vastly different environments. Where
Influence of the void fraction in the linear reactivity model
International Nuclear Information System (INIS)
Castillo, J.A.; Ramirez, J.R.; Alonso, G.
2003-01-01
The linear reactivity model allows the multicycle analysis in pressurized water reactors in a simple and quick way. In the case of the Boiling water reactors the void fraction it varies axially from 0% of voids in the inferior part of the fuel assemblies until approximately 70% of voids to the exit of the same ones. Due to this it is very important the determination of the average void fraction during different stages of the reactor operation to predict the burnt one appropriately of the same ones to inclination of the pattern of linear reactivity. In this work a pursuit is made of the profile of power for different steps of burnt of a typical operation cycle of a Boiling water reactor. Starting from these profiles it builds an algorithm that allows to determine the voids profile and this way to obtain the average value of the same one. The results are compared against those reported by the CM-PRESTO code that uses another method to carry out this calculation. Finally, the range in which is the average value of the void fraction during a typical cycle is determined and an estimate of the impact that it would have the use of this value in the prediction of the reactivity produced by the fuel assemblies is made. (Author)
Modeling discrete and continuous entities with fractions and decimals.
Rapp, Monica; Bassok, Miriam; DeWolf, Melissa; Holyoak, Keith J
2015-03-01
When people use mathematics to model real-life situations, their use of mathematical expressions is often mediated by semantic alignment (Bassok, Chase, & Martin, 1998): The entities in a problem situation evoke semantic relations (e.g., tulips and vases evoke the functionally asymmetric "contain" relation), which people align with analogous mathematical relations (e.g., the noncommutative division operation, tulips/vases). Here we investigate the possibility that semantic alignment is also involved in the comprehension and use of rational numbers (fractions and decimals). A textbook analysis and results from two experiments revealed that both mathematic educators and college students tend to align the discreteness versus continuity of the entities in word problems (e.g., marbles vs. distance) with distinct symbolic representations of rational numbers--fractions versus decimals, respectively. In addition, fractions and decimals tend to be used with nonmetric units and metric units, respectively. We discuss the importance of the ontological distinction between continuous and discrete entities to mathematical cognition, the role of symbolic notations, and possible implications of our findings for the teaching of rational numbers. PsycINFO Database Record (c) 2015 APA, all rights reserved.
High-frequency Rayleigh-wave method
Xia, J.; Miller, R.D.; Xu, Y.; Luo, Y.; Chen, C.; Liu, J.; Ivanov, J.; Zeng, C.
2009-01-01
High-frequency (???2 Hz) Rayleigh-wave data acquired with a multichannel recording system have been utilized to determine shear (S)-wave velocities in near-surface geophysics since the early 1980s. This overview article discusses the main research results of high-frequency surface-wave techniques achieved by research groups at the Kansas Geological Survey and China University of Geosciences in the last 15 years. The multichannel analysis of surface wave (MASW) method is a non-invasive acoustic approach to estimate near-surface S-wave velocity. The differences between MASW results and direct borehole measurements are approximately 15% or less and random. Studies show that simultaneous inversion with higher modes and the fundamental mode can increase model resolution and an investigation depth. The other important seismic property, quality factor (Q), can also be estimated with the MASW method by inverting attenuation coefficients of Rayleigh waves. An inverted model (S-wave velocity or Q) obtained using a damped least-squares method can be assessed by an optimal damping vector in a vicinity of the inverted model determined by an objective function, which is the trace of a weighted sum of model-resolution and model-covariance matrices. Current developments include modeling high-frequency Rayleigh-waves in near-surface media, which builds a foundation for shallow seismic or Rayleigh-wave inversion in the time-offset domain; imaging dispersive energy with high resolution in the frequency-velocity domain and possibly with data in an arbitrary acquisition geometry, which opens a door for 3D surface-wave techniques; and successfully separating surface-wave modes, which provides a valuable tool to perform S-wave velocity profiling with high-horizontal resolution. ?? China University of Geosciences (Wuhan) and Springer-Verlag GmbH 2009.
Fractional diffusion models of transport in magnetically confined plasmas
International Nuclear Information System (INIS)
Castillo-Negrete, D. del; Carreras, B. A.; Lynch, V. E.
2005-01-01
Experimental and theoretical evidence suggests that transport in magnetically confined fusion plasmas deviates from the standard diffusion paradigm. Some examples include the confinement time scaling in L-mode plasmas, rapid pulse propagation phenomena, and inward transport in off-axis fueling experiments. The limitations of the diffusion paradigm can be traced back to the restrictive assumptions in which it is based. In particular, Fick's law, one of the cornerstones of diffusive transport, assumes that the fluxes only depend on local quantities, i. e. the spatial gradient of the field (s). another key issue is the Markovian assumption that neglects memory effects. Also, at a microscopic level, standard diffusion assumes and underlying Gaussian, uncorrelated stochastic process (i. e. a Brownian random walk) with well defined characteristic spatio-temporal scales. Motivated by the need to develop models of non-diffusive transport, we discuss here a class of transport models base on the use of fractional derivative operators. The models incorporates in a unified way non-Fickian transport, non-Markovian processes or memory effects, and non-diffusive scaling. At a microscopic level, the models describe an underlying stochastic process without characteristic spatio-temporal scales that generalizes the Brownian random walk. As a concrete case study to motivate and test the model, we consider transport of tracers in three-dimensional, pressure-gradient-driven turbulence. We show that in this system transport is non-diffusive and cannot be described in the context of the standard diffusion parading. In particular, the probability density function (pdf) of the radial displacements of tracers is strongly non-Gaussian with algebraic decaying tails, and the moments of the tracer displacements exhibit super-diffusive scaling. there is quantitative agreement between the turbulence transport calculations and the proposed fractional diffusion model. In particular, the model
A Stochastic Fractional Dynamics Model of Rainfall Statistics
Kundu, Prasun; Travis, James
2013-04-01
Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is designed to faithfully reflect the scale dependence and is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. The main restriction is the assumption that the statistics of the precipitation field is spatially homogeneous and isotropic and stationary in time. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of the radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment. Some data sets containing periods of non-stationary behavior that involves occasional anomalously correlated rain events, present a challenge for the model.
Slezak, Izabella H; Jasik-Slezak, Jolanta; Bilewicz-Wyrozumska, Teresa; Slezak, Andrzej
2006-01-01
On the basis of model equation describing the membrane potential delta psi(s) on concentration Rayleigh number (R(C)), mechanical pressure difference (deltaP), concentration polarization coefficient (zeta s) and ratio concentration of solutions separated by membrane (Ch/Cl), the characteristics delta psi(s) = f(Rc)(delta P, zeta s, Ch/Cl) for steady values of zeta s, R(C) and Ch/Cl in single-membrane system were calculated. In this system neutral and isotropic polymeric membrane oriented in horizontal plane, the non-homogeneous binary electrolytic solutions of various concentrations were separated. Nonhomogeneity of solutions is results from creations of the concentration boundary layers on both sides of the membrane. Calculations were made for the case where on a one side of the membrane aqueous solution of NaCl at steady concentration 10(-3) mol x l(-1) (Cl) was placed and on the other aqueous solutions of NaCl at concentrations from 10(-3) mol x l(-1) to 2 x 10(-2) mol x l(-1) (Ch). Their densities were greater than NaCl solution's at 10(-3) mol x l(-1). It was shown that membrane potential depends on hydrodynamic state of a complex concentration boundary layer-membrane-concentration boundary layer, what is controlled by deltaP, Ch/Cl, Rc and Zeta(s).
Murine Models of Heart Failure With Preserved Ejection Fraction
Directory of Open Access Journals (Sweden)
Maria Valero-Muñoz, PhD
2017-12-01
Full Text Available Heart failure with preserved ejection fraction (HFpEF is characterized by signs and symptoms of heart failure in the presence of a normal left ventricular ejection fraction. Despite accounting for up to 50% of all clinical presentations of heart failure, the mechanisms implicated in HFpEF are poorly understood, thus precluding effective therapy. The pathophysiological heterogeneity in the HFpEF phenotype also contributes to this disease and likely to the absence of evidence-based therapies. Limited access to human samples and imperfect animal models that completely recapitulate the human HFpEF phenotype have impeded our understanding of the mechanistic underpinnings that exist in this disease. Aging and comorbidities such as atrial fibrillation, hypertension, diabetes and obesity, pulmonary hypertension, and renal dysfunction are highly associated with HFpEF, yet the relationship and contribution between them remains ill-defined. This review discusses some of the distinctive clinical features of HFpEF in association with these comorbidities and highlights the advantages and disadvantage of commonly used murine models used to study the HFpEF phenotype.
Particle Based Modeling of Electrical Field Flow Fractionation Systems
Directory of Open Access Journals (Sweden)
Tonguc O. Tasci
2015-10-01
Full Text Available Electrical Field Flow Fractionation (ElFFF is a sub method in the field flow fractionation (FFF family that relies on an applied voltage on the channel walls to effect a separation. ElFFF has fallen behind some of the other FFF methods because of the optimization complexity of its experimental parameters. To enable better optimization, a particle based model of the ElFFF systems has been developed and is presented in this work that allows the optimization of the main separation parameters, such as electric field magnitude, frequency, duty cycle, offset, flow rate and channel dimensions. The developed code allows visualization of individual particles inside the separation channel, generation of realistic fractograms, and observation of the effects of the various parameters on the behavior of the particle cloud. ElFFF fractograms have been generated via simulations and compared with experiments for both normal and cyclical ElFFF. The particle visualizations have been used to verify that high duty cycle voltages are essential to achieve long retention times and high resolution separations. Furthermore, by simulating the particle motions at the channel outlet, it has been demonstrated that the top channel wall should be selected as the accumulation wall for cyclical ElFFF to reduce band broadening and achieve high efficiency separations. While the generated particle based model is a powerful tool to estimate the outcomes of the ElFFF experiments and visualize particle motions, it can also be used to design systems with new geometries which may lead to the design of higher efficiency ElFFF systems. Furthermore, this model can be extended to other FFF techniques by replacing the electrical field component of the model with the fields used in the other FFF techniques.
Cabra, R.; Chen, J. Y.; Dibble, R. W.; Myhrvold, T.; Karpetis, A. N.; Barlow, R. S.
2002-01-01
An experiment and numerical investigation is presented of a lifted turbulent H2/N2 jet flame in a coflow of hot, vitiated gases. The vitiated coflow burner emulates the coupling of turbulent mixing and chemical kinetics exemplary of the reacting flow in the recirculation region of advanced combustors. It also simplifies numerical investigation of this coupled problem by removing the complexity of recirculating flow. Scalar measurements are reported for a lifted turbulent jet flame of H2/N2 (Re = 23,600, H/d = 10) in a coflow of hot combustion products from a lean H2/Air flame ((empty set) = 0.25, T = 1,045 K). The combination of Rayleigh scattering, Raman scattering, and laser-induced fluorescence is used to obtain simultaneous measurements of temperature and concentrations of the major species, OH, and NO. The data attest to the success of the experimental design in providing a uniform vitiated coflow throughout the entire test region. Two combustion models (PDF: joint scalar Probability Density Function and EDC: Eddy Dissipation Concept) are used in conjunction with various turbulence models to predict the lift-off height (H(sub PDF)/d = 7,H(sub EDC)/d = 8.5). Kalghatgi's classic phenomenological theory, which is based on scaling arguments, yields a reasonably accurate prediction (H(sub K)/d = 11.4) of the lift-off height for the present flame. The vitiated coflow admits the possibility of auto-ignition of mixed fluid, and the success of the present parabolic implementation of the PDF model in predicting a stable lifted flame is attributable to such ignition. The measurements indicate a thickened turbulent reaction zone at the flame base. Experimental results and numerical investigations support the plausibility of turbulent premixed flame propagation by small scale (on the order of the flame thickness) recirculation and mixing of hot products into reactants and subsequent rapid ignition of the mixture.
Ammirati, J. B.; Alvarado, P. M.; Beck, S. L.
2014-12-01
Receiver Function (RF) analyses using teleseismic P waveforms is a technique to isolate P to S conversions from seismic discontinuities in the lithosphere. Using earthquakes with a good azimuthal distribution, RFs recorded at a three-component seismic station can be inverted to obtain detailed lithospheric velocity structures. The technique, however presents a velocity-depth trade-off, which results in a non-unique model because RFs do not depend on the absolute seismic velocities but rather on relative velocity contrasts. Unlike RF, surface wave dispersion is sensitive to the average shear-wave velocity which makes it well suited for studying long period variations of the lithospheric seismic velocities. We performed a joint inversion of RF and Rayleigh-wave phase velocity dispersion to investigate the structure beneath the SIEMBRA network, a 43-broadband-seismic-station array deployed in the Pampean flat slab region of Argentina. Our results indicate: 1) The presence of several mid-crustal discontinuities probably related with terrane accretion; 2) A high seismic velocity in the lower crust suggesting partial eclogitization; 3) A thicker crust (> 50 km) beneath the western Sierras Pampeanas with an abrupt change in the relative timing of the Moho signal indicating a thinner crust to the east; 4) The presence of the subducting oceanic crust lying at ~100 km depth. We then built a 1D regional velocity model for the flat slab region of Argentina and used it for regional moment tensor inversions for local earthquakes. This technique is notably dependent on small-scale variations of Earth structure when modeling higher frequency seismic waveforms. Eighteen regional focal mechanisms have been determined. Our solutions are in good agreement with GCMT source estimations although our solutions for deep earthquakes systematically resulted in shallower focal depths suggesting that the slab seismicity could be concentrated at the top of the subducting Nazca plate. Solutions
Fractional Gaussian noise: Prior specification and model comparison
Sø rbye, Sigrunn Holbek; Rue, Haavard
2017-01-01
Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ(symbol) of a first-order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.
Fractional Gaussian noise: Prior specification and model comparison
Sørbye, Sigrunn Holbek
2017-07-07
Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ(symbol) of a first-order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.
International Nuclear Information System (INIS)
Lim, S C; Teo, L P
2009-01-01
Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann–Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion
An approximate fractional Gaussian noise model with computational cost
Sørbye, Sigrunn H.
2017-09-18
Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood-based approach is ${\\\\mathcal O}(n^{2})$, exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to ${\\\\mathcal O}(n^{3})$. This paper presents an approximate fGn model of ${\\\\mathcal O}(n)$ computational cost, both with direct or indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive processes, fitting the parameters of the approximation to match the autocorrelation function of the fGn model. The resulting approximation is stationary despite being Markov and gives a remarkably accurate fit using only four components. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.
On the interaction of Rayleigh surface waves with structures
International Nuclear Information System (INIS)
Simpson, I.C.
1976-12-01
A two-dimensional soil-structure interaction analysis is carried out for transient Rayleigh surface waves that are incident on a structure. The structure is modelled by a three-degree of freedom rigid basemat to which is attached a flexible superstructure, modelled by a single mass-spring system. The structural responses to a given Rayleigh wave train are compared with those that would have been obtained if the free-field acceleration-time history had been applied as a normally incident body wave. The results clearly exhibit the 'frequency filtering' effects of the rigid basemat on the incident Rayleigh waves. It is shown that, if seismic excitation of a structure is, in fact, due to Rayleigh surface waves, then an analysis assuming normally incident body waves can considerably over-estimate structural response, both at basemat level for horizontal and vertical oscillations of the superstructure. However, in the examples considered here, relatively large rocking effects were induced by the Rayleigh waves, thus giving maximum horizontal accelerations in the superstructure that were of comparable magnitude for Rayleigh and normally incident body waves. (author)
Fractional Calculus in Hydrologic Modeling: A Numerical Perspective
Energy Technology Data Exchange (ETDEWEB)
David A. Benson; Mark M. Meerschaert; Jordan Revielle
2012-01-01
Fractional derivatives can be viewed either as a handy extension of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Levy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Levy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus.
Centrifugally Driven Rayleigh-Taylor Instability
Scase, Matthew; Hill, Richard
2017-11-01
The instability that develops at the interface between two fluids of differing density due to the rapid rotation of the system may be considered as a limit of high-rotation rate Rayleigh-Taylor instability. Previously the authors have considered the effect of rotation on a gravitationally dominated Rayleigh-Taylor instability and have shown that some growth modes of instability may be suppressed completely by the stabilizing effect of rotation (Phys. Rev. Fluids 2:024801, Sci. Rep. 5:11706). Here we consider the case of very high rotation rates and a negligible gravitational field. The initial condition is of a dense inner cylinder of fluid surrounded by a lighter layer of fluid. As the system is rotated about the generating axis of the cylinder, the dense inner fluid moves away from the axis and the familiar bubbles and spikes of Rayleigh-Taylor instability develop at the interface. The system may be thought of as a ``fluid-fluid centrifuge''. By developing a model based on an Orr-Sommerfeld equation, we consider the effects of viscosity, surface tension and interface diffusion on the growth rate and modes of instability. We show that under particular circumstances some modes may be stabilized. School of Mathematical Sciences.
Tunable polymeric sorbent materials for fractionation of model naphthenates.
Mohamed, Mohamed H; Wilson, Lee D; Headley, John V
2013-04-04
The sorption properties are reported for several examples of single-component carboxylic acids representing naphthenic acids (NAs) with β-cyclodextrin (β-CD) based polyurethane sorbents. Seven single-component examples of NAs were chosen with variable z values, carbon number, and chemical structure as follows: 2-hexyldecanoic acid (z = 0 and C = 16; S1), n-caprylic acid (z = 0 and C = 8; S2), trans-4-pentylcyclohexanecarboxylic acid (z = -2 and C = 12; S3), 4-methylcyclohexanecarboxylic acid (z = -2 and C = 8; S4), dicyclohexylacetic acid (z = -4; C = 14; S5), 4-pentylbicyclo[2.2.2]octane-1-carboxylic acid (z = -4; C = 14; S6), and lithocholic acid (z = -6; C = 24; S7). The copolymer sorbents were synthesized at three relative β-CD:diisocyanate mole ratios (i.e., 1:1, 1:2, and 1:3) using 4,4'-dicyclohexylmethane diisocyanate (CDI) and 4,4'-diphenylmethane diisocyanate (MDI). The sorption properties of the copolymer sorbents were characterized using equilibrium sorption isotherms in aqueous solution at pH 9.00 with electrospray ionization mass spectrometry. The equilibrium fraction of the unbound carboxylate anions was monitored in the aqueous phase. The sorption properties of the copolymer sorbents (i.e., Qm) were obtained from the Sips isotherm model. The Qm values generally decrease as the number of accessible β-CD inclusion sites in the copolymer framework decreases. The chemical structure of the adsorbates played an important role in their relative uptake, as evidenced by the adsorbate lipophilic surface area (LSA) and the involvement of hydrophobic effects. The copolymers exhibit molecular selective sorption of the single-component carboxylates in mixtures which suggests their application as sorbents for fractionation of mixtures of NAs. By comparison, granular activated carbon (GAC) and chitosan sorbents did not exhibit any significant molecular selective sorption relative to the copolymer materials; however, evidence of variable sorption capacity was
Fractional model for heat conduction in polar bear hairs
Directory of Open Access Journals (Sweden)
Wang Qing-Li
2012-01-01
Full Text Available Time-fractional differential equations can accurately describe heat conduction in fractal media, such as wool fibers, goose down and polar bear hair. The fractional complex transform is used to convert time-fractional heat conduction equations with the modified Riemann-Liouville derivative into ordinary differential equations, and exact solutions can be easily obtained. The solution process is straightforward and concise.
Modelling in Primary School: Constructing Conceptual Models and Making Sense of Fractions
Shahbari, Juhaina Awawdeh; Peled, Irit
2017-01-01
This article describes sixth-grade students' engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students…
A fractional motion diffusion model for grading pediatric brain tumors.
Karaman, M Muge; Wang, He; Sui, Yi; Engelhard, Herbert H; Li, Yuhua; Zhou, Xiaohong Joe
2016-01-01
To demonstrate the feasibility of a novel fractional motion (FM) diffusion model for distinguishing low- versus high-grade pediatric brain tumors; and to investigate its possible advantage over apparent diffusion coefficient (ADC) and/or a previously reported continuous-time random-walk (CTRW) diffusion model. With approval from the institutional review board and written informed consents from the legal guardians of all participating patients, this study involved 70 children with histopathologically-proven brain tumors (30 low-grade and 40 high-grade). Multi- b -value diffusion images were acquired and analyzed using the FM, CTRW, and mono-exponential diffusion models. The FM parameters, D fm , φ , ψ (non-Gaussian diffusion statistical measures), and the CTRW parameters, D m , α , β (non-Gaussian temporal and spatial diffusion heterogeneity measures) were compared between the low- and high-grade tumor groups by using a Mann-Whitney-Wilcoxon U test. The performance of the FM model for differentiating between low- and high-grade tumors was evaluated and compared with that of the CTRW and the mono-exponential models using a receiver operating characteristic (ROC) analysis. The FM parameters were significantly lower ( p < 0.0001) in the high-grade ( D fm : 0.81 ± 0.26, φ : 1.40 ± 0.10, ψ : 0.42 ± 0.11) than in the low-grade ( D fm : 1.52 ± 0.52, φ : 1.64 ± 0.13, ψ : 0.67 ± 0.13) tumor groups. The ROC analysis showed that the FM parameters offered better specificity (88% versus 73%), sensitivity (90% versus 82%), accuracy (88% versus 78%), and area under the curve (AUC, 93% versus 80%) in discriminating tumor malignancy compared to the conventional ADC. The performance of the FM model was similar to that of the CTRW model. Similar to the CTRW model, the FM model can improve differentiation between low- and high-grade pediatric brain tumors over ADC.
Preliminary study of Rayleigh-Taylor instability in wire-array Z-pinch
International Nuclear Information System (INIS)
He Kaihui; Feng Kaiming; Li Qiang; Gao Chunming
2000-01-01
It is important to research into the MHD Rayleigh-Taylor instability developed in Z-pinch implosion. A snowplough model of the single wire Z-pinch is presented. The perturbation amplitude of Rayleigh-Taylor instability in the wire-array Z-pinch is analyzed quantitatively. Sheared axial flow is put forward to mitigate and reduce the Rayleigh-Taylor instability. And other approaches used to mitigate MHD instability in such a super-fast process are explored
Thin stillage fractionation using ultrafiltration: resistance in series model.
Arora, Amit; Dien, Bruce S; Belyea, Ronald L; Wang, Ping; Singh, Vijay; Tumbleson, M E; Rausch, Kent D
2009-02-01
The corn based dry grind process is the most widely used method in the US for fuel ethanol production. Fermentation of corn to ethanol produces whole stillage after ethanol is removed by distillation. It is centrifuged to separate thin stillage from wet grains. Thin stillage contains 5-10% solids. To concentrate solids of thin stillage, it requires evaporation of large amounts of water and maintenance of evaporators. Evaporator maintenance requires excess evaporator capacity at the facility, increasing capital expenses, requiring plant slowdowns or shut downs and results in revenue losses. Membrane filtration is one method that could lead to improved value of thin stillage and may offer an alternative to evaporation. Fractionation of thin stillage using ultrafiltration was conducted to evaluate membranes as an alternative to evaporators in the ethanol industry. Two regenerated cellulose membranes with molecular weight cut offs of 10 and 100 kDa were evaluated. Total solids (suspended and soluble) contents recovered through membrane separation process were similar to those from commercial evaporators. Permeate flux decline of thin stillage using a resistance in series model was determined. Each of the four components of total resistance was evaluated experimentally. Effects of operating variables such as transmembrane pressure and temperature on permeate flux rate and resistances were determined and optimum conditions for maximum flux rates were evaluated. Model equations were developed to evaluate the resistance components that are responsible for fouling and to predict total flux decline with respect to time. Modeling results were in agreement with experimental results (R(2) > 0.98).
Linear-quadratic model underestimates sparing effect of small doses per fraction in rat spinal cord
International Nuclear Information System (INIS)
Shun Wong, C.; Toronto University; Minkin, S.; Hill, R.P.; Toronto University
1993-01-01
The application of the linear-quadratic (LQ) model to describe iso-effective fractionation schedules for dose fraction sizes less than 2 Gy has been controversial. Experiments are described in which the effect of daily fractionated irradiation given with a wide range of fraction sizes was assessed in rat cervical spine cord. The first group of rats was given doses in 1, 2, 4, 8 and 40 fractions/day. The second group received 3 initial 'top-up'doses of 9 Gy given once daily, representing 3/4 tolerance, followed by doses in 1, 2, 10, 20, 30 and 40 fractions/day. The fractionated portion of the irradiation schedule therefore constituted only the final quarter of the tolerance dose. The endpoint of the experiments was paralysis of forelimbs secondary to white matter necrosis. Direct analysis of data from experiments with full course fractionation up to 40 fractions/day (25.0-1.98 Gy/fraction) indicated consistency with the LQ model yielding an α/β value of 2.41 Gy. Analysis of data from experiments in which the 3 'top-up' doses were followed by up to 10 fractions (10.0-1.64 Gy/fraction) gave an α/β value of 3.41 Gy. However, data from 'top-up' experiments with 20, 30 and 40 fractions (1.60-0.55 Gy/fraction) were inconsistent with LQ model and gave a very small α/β of 0.48 Gy. It is concluded that LQ model based on data from large doses/fraction underestimates the sparing effect of small doses/fraction, provided sufficient time is allowed between each fraction for repair of sublethal damage. (author). 28 refs., 5 figs., 1 tab
Tcp and NTCP radiobiological models: conventional and hypo fractionated treatments in radiotherapy
Energy Technology Data Exchange (ETDEWEB)
Astudillo V, A.; Paredes G, L. [ININ, Carretera Mexico-Toluca s/n, Ocoyoacac 52750, Estado de Mexico (Mexico); Resendiz G, G.; Posadas V, A. [Hospital Angeles Lomas, Av. Vialidad de la Barranca s/n, Col. Valle de las Palmas, 52763 Huixquilucan de Degallado, Estado de Mexico (Mexico); Mitsoura, E. [Universidad Autonoma del Estado de Mexico, Facultad de Medicina, Paseo Tollocan, Esq. Jesus Carranza s/n, Col. Moderna de la Cruz, 50180 Toluca, Estado de Mexico (Mexico); Rodriguez L, A.; Flores C, J. M., E-mail: armando.astudillo@inin.gob.mx [Hospital Medica Sur, Puente de Piedra 150, Col. Toriello Guerra, 14050 Tlalpan, Mexico D. F. (Mexico)
2015-10-15
The hypo and conventional fractionated schedules performance were compared in terms of the tumor control and the normal tissue complications. From the records of ten patients, treated for adenocarcinoma and without mastectomy, the dose-volume histogram was used. Using radiobiological models the probabilities for tumor control and normal tissue complications were calculated. For both schedules the tumor control was approximately the same. However, the damage in the normal tissue was larger in conventional fractionated schedule. This is important because patients assistance time to their fractions (15 fractions/25 fractions) can be optimized. Thus, the hypo fractionated schedule has suitable characteristics to be implemented. (Author)
Tcp and NTCP radiobiological models: conventional and hypo fractionated treatments in radiotherapy
International Nuclear Information System (INIS)
Astudillo V, A.; Paredes G, L.; Resendiz G, G.; Posadas V, A.; Mitsoura, E.; Rodriguez L, A.; Flores C, J. M.
2015-10-01
The hypo and conventional fractionated schedules performance were compared in terms of the tumor control and the normal tissue complications. From the records of ten patients, treated for adenocarcinoma and without mastectomy, the dose-volume histogram was used. Using radiobiological models the probabilities for tumor control and normal tissue complications were calculated. For both schedules the tumor control was approximately the same. However, the damage in the normal tissue was larger in conventional fractionated schedule. This is important because patients assistance time to their fractions (15 fractions/25 fractions) can be optimized. Thus, the hypo fractionated schedule has suitable characteristics to be implemented. (Author)
A fractional Fokker-Planck model for anomalous diffusion
Energy Technology Data Exchange (ETDEWEB)
Anderson, Johan, E-mail: anderson.johan@gmail.com [Department of Earth and Space Sciences, Chalmers University of Technology, SE-412 96 Göteborg (Sweden); Kim, Eun-jin [Department of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH (United Kingdom); Moradi, Sara [Ecole Polytechnique, CNRS UMR7648, LPP, F-91128 Palaiseau (France)
2014-12-15
In this paper, we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality of the stable Lévy distribution. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.
International Nuclear Information System (INIS)
Chesskaya, T.Yu.
1998-01-01
The Rayleigh scattering spectrum of the Moessbauer radiation is plotted on the model simulating globular macromolecules. The modeling results are compared with experimental data on the spectra of the Rayleigh scattering of the Moessbauer radiation for various moisture content and hydratation dependence of the elastic scattering portion
Predictability of Rayleigh-Taylor instability
International Nuclear Information System (INIS)
Viecelli, J.A.
1986-01-01
Numerical experiments modeling the Rayleigh Taylor instability are carried out using a two-dimensional incompressible Eulerian hydrodynamic code VFTS. The method of integrating the Navier-Stokes equations including the viscous terms is similar to that described in Kim and Moin, except that Lagrange particles have been added and provision for body forces is given. The Eulerian method is 2nd order accurate in both space and time, and the Poisson equation for the effective pressure field is solved exactly at each time step using a cyclic reduction method. 3 refs., 3 figs
Nonlinear saturation of the Rayleigh Taylor instability
International Nuclear Information System (INIS)
Das, A.; Mahajan, S.; Kaw, P.; Sen, A.; Benkadda, S.; Verga, A.
1997-01-01
The problem of the nonlinear saturation of the 2 dimensional Rayleigh Taylor instability is re-examined to put various earlier results in a proper perspective. The existence of a variety of final states can be attributed to the differences in the choice of boundary conditions and initial conditions in earlier numerical modeling studies. Our own numerical simulations indicate that the RT instability saturates by the self consistent generation of shear flow even in situations (with periodic boundaries) where, in principle, an infinite amount of gravitational energy can be tapped. Such final states can be achieved for suitable values of the Prandtl number. (author)
Numerical simulation of Rayleigh-Taylor turbulent mixing layers
International Nuclear Information System (INIS)
Poujade, O.; Lardjane, N.; Peybernes, M.; Boulet, M.
2009-01-01
Accelerations in actual Rayleigh-Taylor instabilities are often variable. This article focuses on a particular class of variable accelerations where g(t) ∝ t n . A reference database is built from high resolution hydrodynamic numerical simulations. The successful comparison with a simple OD analytical model and the statistical 2SFK (2-Structure, 2-Fluid, 2-Turbulence) turbulence model is provided. Moreover, we show the difference between the mechanism at play in the Rayleigh-Taylor turbulent mixing zone and Kolmogorov's in the self similar developed turbulent regime. (authors)
Rayleigh scattering in few-mode optical fibers.
Wang, Zhen; Wu, Hao; Hu, Xiaolong; Zhao, Ningbo; Mo, Qi; Li, Guifang
2016-10-24
The extremely low loss of silica fibers has enabled the telecommunication revolution, but single-mode fiber-optic communication systems have been driven to their capacity limits. As a means to overcome this capacity crunch, space-division multiplexing (SDM) using few-mode fibers (FMF) has been proposed and demonstrated. In single-mode optical fibers, Rayleigh scattering serves as the dominant mechanism for optical loss. However, to date, the role of Rayleigh scattering in FMFs remains elusive. Here we establish and experimentally validate a general model for Rayleigh scattering in FMFs. Rayleigh backscattering not only sets the intrinsic loss limit for FMFs but also provides the theoretical foundation for few-mode optical time-domain reflectometry, which can be used to probe perturbation-induced mode-coupling dynamics in FMFs. We also show that forward inter-modal Rayleigh scattering ultimately sets a fundamental limit on inter-modal-crosstalk for FMFs. Therefore, this work not only has implications specifically for SDM systems but also broadly for few-mode fiber optics and its applications in amplifiers, lasers, and sensors in which inter-modal crosstalk imposes a fundamental performance limitation.
Rayleigh scattering in an emitter-nanofiber-coupling system
Tang, Shui-Jing; Gao, Fei; Xu, Da; Li, Yan; Gong, Qihuang; Xiao, Yun-Feng
2017-04-01
Scattering is a general process in both fundamental and applied physics. In this paper, we investigate Rayleigh scattering of a solid-state-emitter coupled to a nanofiber, by S -matrix-like theory in k -space description. Under this model, both Rayleigh scattering and dipole interaction are studied between a two-level artificial atom embedded in a nanocrystal and fiber modes (guided and radiation modes). It is found that Rayleigh scattering plays a critical role in the transport properties and quantum statistics of photons. On the one hand, Rayleigh scattering produces the transparency in the optical transmitted field of the nanofiber, accompanied by the change of atomic phase, population, and frequency shift. On the other hand, the interference between two kinds of scattering fields by Rayleigh scattering and dipole transition modifies the photon statistics (second-order autocorrelation function) of output fields, showing a strong wavelength dependence. This study provides guidance for the solid-state emitter acting as a single-photon source and can be extended to explore the scattering effect in many-body physics.
Mittag-Leffler function for discrete fractional modelling
Directory of Open Access Journals (Sweden)
Guo-Cheng Wu
2016-01-01
Full Text Available From the difference equations on discrete time scales, this paper numerically investigates one discrete fractional difference equation in the Caputo delta’s sense which has an explicit solution in form of the discrete Mittag-Leffler function. The exact numerical values of the solutions are given in comparison with the truncated Mittag-Leffler function.
Beam shaping for conformal fractionated stereotactic radiotherapy: a modeling study
International Nuclear Information System (INIS)
Hacker, Fred L.; Kooy, Hanne M.; Bellerive, Marc R.; Killoran, Joseph H.; Leber, Zachary H.; Shrieve, Dennis C.; Tarbell, Nancy J.; Loeffler, Jay S.
1997-01-01
Purpose: The patient population treated with fractionated stereotactic radiotherapy (SRT) is significantly different than that treated with stereotactic radiosurgery (SRS). Generally, lesions treated with SRT are larger, less spherical, and located within critical regions of the central nervous system; hence, they offer new challenges to the treatment planner. Here a simple, cost effective, beam shaping system has been evaluated relative to both circular collimators and an ideal dynamically conforming system for effectiveness in providing conformal therapy for these lesions. Methods and Materials: We have modeled a simple system for conformal arc therapy using four independent jaws. The jaw positions and collimator angle are changed between arcs but held fixed for the duration of each arc. Eleven previously treated SRT cases have been replanned using this system. The rectangular jaw plans were then compared to the original treatment plans which used circular collimators. The plans were evaluated with respect to tissue sparing at 100%, 80%, 50%, and 20% of the prescription dose. A plan was also done for each tumor in which the beam aperture was continuously conformed to the beams eye view projection of the tumor. This was used as an ideal standard for conformal therapy in the absence of fluence modulation. Results: For tumors with a maximum extent of over 3.5 cm the rectangular jaw plans reduced the mean volume of healthy tissue involved at the prescription dose by 57% relative to the circular collimator plans. The ideal conformal plans offered no significant further improvement at the prescription dose. The relative advantage of the rectangular jaw plans decreased at lower isodoses so that at 20% of the prescription dose tissue involvement for the rectangular jaw plans was equivalent to that for the circular collimator plans. At these isodoses the ideal conformal plans gave substantially better tissue sparing. Conclusion: A simple and economical field shaping
Effective-field-theory model for the fractional quantum Hall effect
International Nuclear Information System (INIS)
Zhang, S.C.; Hansson, T.H.; Kivelson, S.
1989-01-01
Starting directly from the microscopic Hamiltonian, we derive a field-theory model for the fractional quantum hall effect. By considering an approximate coarse-grained version of the same model, we construct a Landau-Ginzburg theory similar to that of Girvin. The partition function of the model exhibits cusps as a function of density and the Hall conductance is quantized at filling factors ν = (2k-1)/sup -1/ with k an arbitrary integer. At these fractions the ground state is incompressible, and the quasiparticles and quasiholes have fractional charge and obey fractional statistics. Finally, we show that the collective density fluctuations are massive
A representation theory for a class of vector autoregressive models for fractional processes
DEFF Research Database (Denmark)
Johansen, Søren
2008-01-01
Based on an idea of Granger (1986), we analyze a new vector autoregressive model defined from the fractional lag operator 1-(1-L)^{d}. We first derive conditions in terms of the coefficients for the model to generate processes which are fractional of order zero. We then show that if there is a un...... root, the model generates a fractional process X(t) of order d, d>0, for which there are vectors ß so that ß'X(t) is fractional of order d-b, 0...
LPV model for PV cell and fractional control of DC/DC converter for photovoltaic systems
Martínez González, Rubén; Bolea Monte, Yolanda; Grau Saldes, Antoni; Martínez García, Herminio
2011-01-01
This paper deals with the fractional modelling of a DC-DC converter, suitable in solar-powered electrical generation systems, and the design of a fractional controller for the aforementioned switching converter. A new model for PV cells is proposed in order to obtain a linear equation for V-I characteristic via scheduling dependence of temperature and irradiance. Due to the fractional nature of the ultracapacitors this kind of controller gives a suitable and good performance. Peer Reviewed
LPV model for PV cells and fractional control of DC/DC converter for photovoltaic systems
Martínez González, Rubén; Bolea Monte, Yolanda; Grau Saldes, Antoni; Martínez García, Herminio
2011-01-01
This paper deals with the fractional modelling of a DC-DC converter, suitable in solar-powered electrical generation systems, and the design of a fractional controller for the aforementioned switching converter. A new model for PV cells is proposed in order to obtain a linear equation for VI characteristic via scheduling dependence of temperature and irradiance. Due to the fractional nature of the ultracapacitors this kind of controller gives a suitable and good performance. Peer Rev...
The Rayleigh-Taylor instability in the spherical pinch
International Nuclear Information System (INIS)
Chen, H.B.; Hilko, B.; Panarella, E.
1994-01-01
The spherical pinch (SP) concept is an outgrowth of the inertial confinement model (ICF). Unlike the ICF where instabilities, especially the Rayleigh-Taylor instability, have been studied extensively, the instability study of the spherical pinch has just begun. The Raleigh-Taylor instability is investigated for the first time in the SP in the present work. By using the simple condition for the Rayleigh-Taylor instability ∇p · ∇p < O (density and pressure gradients have opposite direction), we have qualitatively identified the regions for development of instabilities in the SP. It is found that the explosion phase (central discharge) is stable and instabilities take place in the imploding phase. However, the growth rate for the instability is not in exponential form, and the appearance of the Rayleigh-Taylor instability does not prevent the main shock wave from converging to the center of the sphere
Rayleigh-Taylor instability and mixing in SN 1987A
International Nuclear Information System (INIS)
Ebisuzaki, T.; Shigeyama, T.; Nomoto, K.
1989-01-01
The stability of the supernova ejecta is compared with the Rayleigh-Taylor instability for a realistic model of SN 1987A. A linear analysis indicates that the layers around the composition interface between the hydrogen-rich and helium zones, and become Rayleigh-Taylor unstable between the helium and metal zones. In these layers, the pressure increases outward because of deceleration due to the reverse shock which forms when the blast shock hits the massive hydrogen-rich envelope. On the contrary, the density steeply decreases outward because of the preexisting nuclear burning shell. Then, these layers undergo the Raleigh-Taylor instability because of the opposite signs of the pressure and density gradients. The estimated growth rate is larger than the expansion rate of the supernova. The Rayleigh-Taylor instability near the composition interface is likely to induce mixing, which has been strongly suggested from observations of SN 1987A. 25 refs
An Investigation of Fraction Models in Early Elementary Grades: A Mixed-Methods Approach
Wilkerson, Trena L.; Cooper, Susan; Gupta, Dittika; Montgomery, Mark; Mechell, Sara; Arterbury, Kristin; Moore, Sherrie; Baker, Betty Ruth; Sharp, Pat T.
2015-01-01
This study examines the effect varying models have on student understanding of fractions. The study addressed the question of what students know and understand about fractional concepts through the use of discrete and continuous models. A sample of 54 students in kindergarten and 3rd grade were given an interview pretest, participated in…
International Nuclear Information System (INIS)
Das, S.; Sahoo, R.K.
1999-01-01
Analysis of flow and convective heat transfer in volumetrically heated porous layer has become a separate topic for research in the last twenty five years in view of its importance in various engineering applications, such as heat removal from nuclear fuel debris, heat transfer associated with storage of nuclear waste, exothermic reaction in packed-bed reactors, heat recovery from geothermal systems and particularly in the field of large storage systems of agricultural products. Here, a pressure-velocity solution for natural convection for fluid saturated heat generating porous medium in a square enclosure is analyzed by finite element method. The numerical solutions obtained for wide range of fluid Rayleigh number, Ra f , Darcy number, Da, and heat generating number, Q d . The justification for taking these non-dimensional parameters independently is to establish the effect of individual parameters on flow patterns. It has been observed that peak temperature occurs at the top central part and weaker velocity prevails near the vertical walls of the enclosure due to the heat generation parameter alone. On comparison, the modified Rayleigh number used by the earlier investigators, can not explain explicitly the effect of heat generation parameter on natural convection within an enclosure having differentially heated vertical walls. At higher Darcy number, the peak temperature and peak velocity are comparatively more, resulting in better enhancement of heat transfer rate
SOLVING FRACTIONAL-ORDER COMPETITIVE LOTKA-VOLTERRA MODEL BY NSFD SCHEMES
Directory of Open Access Journals (Sweden)
S.ZIBAEI
2016-12-01
Full Text Available In this paper, we introduce fractional-order into a model competitive Lotka- Volterra prey-predator system. We will discuss the stability analysis of this fractional system. The non-standard nite difference (NSFD scheme is implemented to study the dynamic behaviors in the fractional-order Lotka-Volterra system. Proposed non-standard numerical scheme is compared with the forward Euler and fourth order Runge-Kutta methods. Numerical results show that the NSFD approach is easy and accurate for implementing when applied to fractional-order Lotka-Volterra model.
Generalized modeling of the fractional-order memcapacitor and its character analysis
Guo, Zhang; Si, Gangquan; Diao, Lijie; Jia, Lixin; Zhang, Yanbin
2018-06-01
Memcapacitor is a new type of memory device generalized from the memristor. This paper proposes a generalized fractional-order memcapacitor model by introducing the fractional calculus into the model. The generalized formulas are studied and the two fractional-order parameter α, β are introduced where α mostly affects the fractional calculus value of charge q within the generalized Ohm's law and β generalizes the state equation which simulates the physical mechanism of a memcapacitor into the fractional sense. This model will be reduced to the conventional memcapacitor as α = 1 , β = 0 and to the conventional memristor as α = 0 , β = 1 . Then the numerical analysis of the fractional-order memcapacitor is studied. And the characteristics and output behaviors of the fractional-order memcapacitor applied with sinusoidal charge are derived. The analysis results have shown that there are four basic v - q and v - i curve patterns when the fractional order α, β respectively equal to 0 or 1, moreover all v - q and v - i curves of the other fractional-order models are transition curves between the four basic patterns.
Short Rayleigh length free electron lasers
Directory of Open Access Journals (Sweden)
W. B. Colson
2006-03-01
Full Text Available Conventional free electron laser (FEL oscillators minimize the optical mode volume around the electron beam in the undulator by making the resonator Rayleigh length about one third to one half of the undulator length. This maximizes gain and beam-mode coupling. In compact configurations of high-power infrared FELs or moderate power UV FELs, the resulting optical intensity can damage the resonator mirrors. To increase the spot size and thereby reduce the optical intensity at the mirrors below the damage threshold, a shorter Rayleigh length can be used, but the FEL interaction is significantly altered. We model this interaction using a coordinate system that expands with the rapidly diffracting optical mode from the ends of the undulator to the mirrors. Simulations show that the interaction of the strongly focused optical mode with a narrow electron beam inside the undulator distorts the optical wave front so it is no longer in the fundamental Gaussian mode. The simulations are used to study how mode distortion affects the single-pass gain in weak fields, and the steady-state extraction in strong fields.
Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System
Directory of Open Access Journals (Sweden)
Zhenhua Hu
2013-01-01
Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.
The fractional-order modeling and synchronization of electrically coupled neuron systems
Moaddy, K.
2012-11-01
In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grünwald-Letnikov discretization process which is easily implemented and reliably accurate. © 2011 Elsevier Ltd. All rights reserved.
The fractional-order modeling and synchronization of electrically coupled neuron systems
Moaddy, K.; Radwan, Ahmed G.; Salama, Khaled N.; Momani, Shaher M.; Hashim, Ishak
2012-01-01
In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grünwald-Letnikov discretization process which is easily implemented and reliably accurate. © 2011 Elsevier Ltd. All rights reserved.
Universal block diagram based modeling and simulation schemes for fractional-order control systems.
Bai, Lu; Xue, Dingyü
2017-05-08
Universal block diagram based schemes are proposed for modeling and simulating the fractional-order control systems in this paper. A fractional operator block in Simulink is designed to evaluate the fractional-order derivative and integral. Based on the block, the fractional-order control systems with zero initial conditions can be modeled conveniently. For modeling the system with nonzero initial conditions, the auxiliary signal is constructed in the compensation scheme. Since the compensation scheme is very complicated, therefore the integrator chain scheme is further proposed to simplify the modeling procedures. The accuracy and effectiveness of the schemes are assessed in the examples, the computation results testify the block diagram scheme is efficient for all Caputo fractional-order ordinary differential equations (FODEs) of any complexity, including the implicit Caputo FODEs. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Amato, Ernesto; Italiano, Antonio; Baldari, Sergio
2014-01-01
We developed a general model for the calculation of absorbed fractions in ellipsoidal volumes of soft tissue uniformly filled with alpha, beta and gamma emitting radionuclides. The approach exploited Monte Carlo simulations with the Geant4 code to determine absorbed fractions in ellipsoids characterized by a wide range of dimensions and ellipticities, for monoenergetic emissions of each radiation type. The so-obtained absorbed fractions were put in an analytical relationship with the 'general...
Directory of Open Access Journals (Sweden)
Yang Xiao-Jun
2017-01-01
Full Text Available In this paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from mathematical view of point. The comparative results of the anomalous relaxation among the various fractional derivatives are also given. They are very efficient in description of the complex phenomenon arising in heat transfer.
N'Doye, Ibrahima
2015-05-25
In this paper, a dynamical fractional viscoelastic fluids convection model in porous media is proposed and its chaotic behavior is studied. A preformed equilibrium points analysis indicates the conditions where chaotic dynamics can be observed, and show the existence of chaos. The behavior and stability analysis of the integer-order and the fractional commensurate and non-commensurate orders of a fractional viscoelastic fluids system, which exhibits chaos, are presented as well.
Rayleigh-Taylor convective overturn in stellar collapse
International Nuclear Information System (INIS)
Bruenn, S.W.; Buchler, J.R.; Livio, M.
1979-01-01
Rayleigh--Taylor convective overturn in collapsing stellar cores is modeled with a one-dimensional parametrization. The results of a numerical hydrodynamic study are very encouraging and indicate that such an overturn could well be a dominant feature in the supernova explosion mechanism
Numerical Solution of Fractional Neutron Point Kinetics Model in Nuclear Reactor
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Nowak Tomasz Karol
2014-06-01
Full Text Available This paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme in the FOMCON Toolbox in MATLAB environment. Third is the method proposed by Edwards. The impact of selected parameters on the model’s response was examined. The results for typical input were discussed and compared.
Importance sampling the Rayleigh phase function
DEFF Research Database (Denmark)
Frisvad, Jeppe Revall
2011-01-01
Rayleigh scattering is used frequently in Monte Carlo simulation of multiple scattering. The Rayleigh phase function is quite simple, and one might expect that it should be simple to importance sample it efficiently. However, there seems to be no one good way of sampling it in the literature....... This paper provides the details of several different techniques for importance sampling the Rayleigh phase function, and it includes a comparison of their performance as well as hints toward efficient implementation....
Fractional statistics in 2+1 dimensions through the Gaussian model
International Nuclear Information System (INIS)
Murthy, G.
1986-01-01
The free massless field in 2+1 dimensions is written as an ''integral'' over free massless fields in 1+1 dimensions. Taking the operators with fractional dimension in the Gaussian model as a springboard we construct operators with fractional statistics in the former theory
On the identification of fractionally cointegrated VAR models with the F(d) condition
DEFF Research Database (Denmark)
Carlini, Federico; Santucci de Magistris, Paolo
with different fractional integration and cointegration parameters. The properties of these multiple non-identified sub-models are studied and a necessary and sufficient condition for the identification of the fractional parameters of the system is provided. The condition is named F(d). The assessment of the F(d...
Directory of Open Access Journals (Sweden)
Yang Xiao-Jun
2016-01-01
Full Text Available In this article we propose a new fractional derivative without singular kernel. We consider the potential application for modeling the steady heat-conduction problem. The analytical solution of the fractional-order heat flow is also obtained by means of the Laplace transform.
SU-E-T-70: A Radiobiological Model of Reoxygenation and Fractionation Effects
Energy Technology Data Exchange (ETDEWEB)
Guerrero, M [University of Maryland School of Medicine, Baltimore, MD (United States); Carlson, DJ [Yale Univ. School of Medicine, New Haven, CT (United States)
2015-06-15
Purpose: To develop a simple reoxygenation model that fulfills the following goals:1-Quantify the reoxygenation effect in biologically effective dose (BED) and compare it to the repopulation effect.2-Model the hypoxic fraction in tumors as a function of the number of fractions.3-Develop a simple analytical expression for a reoxygenation term in BED calculations. Methods: The model considers tumor cells in two compartments: one normoxic population of cells and one hypoxic compartment including cells under a range of reduced oxygen concentrations. The surviving fraction is predicted using the linear-quadratic (LQ) model. A hypoxia reduction factor (HRF) is used to quantify reductions in radiosensitivity parameters α-A and β-A as cellular oxygen concentration decreases. The HRF is defined as the ratio of the dose at a specific level of hypoxia to the dose under fully aerobic conditions to achieve equal cell killing. The model assumes that a fraction of the hypoxic cells ( ) moves from the hypoxic to the aerobic compartment after each daily fraction. As an example, we consider standard fractionation for NSCLC (d=2Gy,n=33) versus a SBRT (n=5, d=10Gy) fractionation and compare the loss in reoxygenation biological effect with the gain in repopulation biological effect. Results: An analytic expression for the surviving fraction after n daily treatments is derived and the reoxygenation term in the biological effect is calculated. Reoxygenation and repopulation effects are the same order of magnitude for potential doubling time Td values of 2 to 5 days. The hypoxic fraction increases or decreases with n depending on the reoxygenation rate Δ. For certain combinations of parameters, the biological effect of reoxygenation goes as -(n-1)*ln(1-Δ) providing a simple expression that can be introduced in BED calculations. Conclusion: A novel radiobiological model was developed that can be used to evaluate the effect of reoxygenation in fractionated radiotherapy.
A Fractional Supervision Game Model of Multiple Stakeholders and Numerical Simulation
Directory of Open Access Journals (Sweden)
Rongwu Lu
2017-01-01
Full Text Available Considering the popular use of a certain kind of supervision management problem in many fields, we firstly build an ordinary supervision game model of multiple stakeholders. Secondly, a fractional supervision game model is set up and solved based on the theory of fractional calculus and a predictor-corrector numerical approach. Thirdly, the methods of phase diagram and time series graph were applied to simulate and analyse the dynamic process of the fractional order game model. Results of numerical solutions are given to illustrate our conclusions and referred to the practice.
The equivalent electrical permittivity of gas-solid mixtures at intermediate solid volume fractions.
Energy Technology Data Exchange (ETDEWEB)
Torczynski, John Robert; Ceccio, Steven Louis; Tortora, Paul Richard
2005-07-01
Several mixture models are evaluated for their suitability in predicting the equivalent permittivity of dielectric particles in a dielectric medium for intermediate solid volume fractions (0.4 to 0.6). Predictions of the Maxwell, Rayleigh, Bottcher and Bruggeman models are compared to computational simulations of several arrangements of solid particles in a gas and to the experimentally determined permittivity of a static particle bed. The experiment uses spherical glass beads in air, so air and glass permittivity values (1 and 7, respectively) are used with all of the models and simulations. The experimental system used to measure the permittivity of the static particle bed and its calibration are described. The Rayleigh model is found to be suitable for predicting permittivity over the entire range of solid volume fractions (0-0.6).
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
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Shelton Peiris
2017-12-01
Full Text Available This paper considers a flexible class of time series models generated by Gegenbauer polynomials incorporating the long memory in stochastic volatility (SV components in order to develop the General Long Memory SV (GLMSV model. We examine the corresponding statistical properties of this model, discuss the spectral likelihood estimation and investigate the finite sample properties via Monte Carlo experiments. We provide empirical evidence by applying the GLMSV model to three exchange rate return series and conjecture that the results of out-of-sample forecasts adequately confirm the use of GLMSV model in certain financial applications.
Hydrogen solubility measurements of analyzed tall oil fractions and a solubility model
International Nuclear Information System (INIS)
Uusi-Kyyny, Petri; Pakkanen, Minna; Linnekoski, Juha; Alopaeus, Ville
2017-01-01
Highlights: • Hydrogen solubility was measured in four tall oil fractions between 373 and 597 K. • Continuous flow synthetic isothermal and isobaric method was used. • A Henry’s law model was developed for the distilled tall oil fractions. • The complex composition of the samples was analyzed and is presented. - Abstract: Knowledge of hydrogen solubility in tall oil fractions is important for designing hydrotreatment processes of these complex nonedible biobased materials. Unfortunately measurements of hydrogen solubility into these fractions are missing in the literature. This work reports hydrogen solubility measured in four tall oil fractions between 373 and 597 K and at pressures from 5 to 10 MPa. Three of the fractions were distilled tall oil fractions their resin acids contents are respectively 2, 20 and 23 in mass-%. Additionally one fraction was a crude tall oil (CTO) sample containing sterols as the main neutral fraction. Measurements were performed using a continuous flow synthetic isothermal and isobaric method based on the visual observation of the bubble point. Composition of the flow was changed step-wise for the bubble point composition determination. We assume that the tall oil fractions did not react during measurements, based on the composition analysis performed before and after the measurements. Additionally the densities of the fractions were measured at atmospheric pressure from 293.15 to 323.15 K. A Henry’s law model was developed for the distilled tall oil fractions describing the solubility with an absolute average deviation of 2.1%. Inputs of the solubility model are temperature, total pressure and the density of the oil at 323.15 K. The solubility of hydrogen in the CTO sample can be described with the developed model with an absolute average deviation of 3.4%. The solubility of hydrogen increases both with increasing pressure and/or increasing temperature. The more dense fractions of the tall oil exhibit lower hydrogen
Underprediction of human skin erythema at low doses per fraction by the linear quadratic model
International Nuclear Information System (INIS)
Hamilton, Christopher S.; Denham, James W.; O'Brien, Maree; Ostwald, Patricia; Kron, Tomas; Wright, Suzanne; Doerr, Wolfgang
1996-01-01
Background and purpose. The erythematous response of human skin to radiotherapy has proven useful for testing the predictions of the linear quadratic (LQ) model in terms of fractionation sensitivity and repair half time. No formal investigation of the response of human skin to doses less than 2 Gy per fraction has occurred. This study aims to test the validity of the LQ model for human skin at doses ranging from 0.4 to 5.2 Gy per fraction. Materials and methods. Complete erythema reaction profiles were obtained using reflectance spectrophotometry in two patient populations: 65 patients treated palliatively with 5, 10, 12 and 20 daily treatment fractions (varying thicknesses of bolus, various body sites) and 52 patients undergoing prostatic irradiation for localised carcinoma of the prostate (no bolus, 30-32 fractions). Results and conclusions. Gender, age, site and prior sun exposure influence pre- and post-treatment erythema values independently of dose administered. Out-of-field effects were also noted. The linear quadratic model significantly underpredicted peak erythema values at doses less than 1.5 Gy per fraction. This suggests that either the conventional linear quadratic model does not apply for low doses per fraction in human skin or that erythema is not exclusively initiated by radiation damage to the basal layer. The data are potentially explained by an induced repair model
Rayleigh imaging in spectral mammography
Berggren, Karl; Danielsson, Mats; Fredenberg, Erik
2016-03-01
Spectral imaging is the acquisition of multiple images of an object at different energy spectra. In mammography, dual-energy imaging (spectral imaging with two energy levels) has been investigated for several applications, in particular material decomposition, which allows for quantitative analysis of breast composition and quantitative contrast-enhanced imaging. Material decomposition with dual-energy imaging is based on the assumption that there are two dominant photon interaction effects that determine linear attenuation: the photoelectric effect and Compton scattering. This assumption limits the number of basis materials, i.e. the number of materials that are possible to differentiate between, to two. However, Rayleigh scattering may account for more than 10% of the linear attenuation in the mammography energy range. In this work, we show that a modified version of a scanning multi-slit spectral photon-counting mammography system is able to acquire three images at different spectra and can be used for triple-energy imaging. We further show that triple-energy imaging in combination with the efficient scatter rejection of the system enables measurement of Rayleigh scattering, which adds an additional energy dependency to the linear attenuation and enables material decomposition with three basis materials. Three available basis materials have the potential to improve virtually all applications of spectral imaging.
Zhang, Shuzeng; Li, Xiongbing; Jeong, Hyunjo
2017-06-20
A theoretical model, along with experimental verification, is developed to describe the generation, propagation and reception of a Rayleigh wave using angle beam wedge transducers. The Rayleigh wave generation process using an angle beam wedge transducer is analyzed, and the actual Rayleigh wave sound source distributions are evaluated numerically. Based on the reciprocity theorem and considering the actual sound source, the Rayleigh wave beams are modeled using an area integral method. The leaky Rayleigh wave theory is introduced to investigate the reception of the Rayleigh wave using the angle beam wedge transducers, and the effects of the wave spreading in the wedge and transducer size are considered in the reception process. The effects of attenuations of the Rayleigh wave and leaky Rayleigh wave are discussed, and the received wave results with different sizes of receivers are compared. The experiments are conducted using two angle beam wedge transducers to measure the Rayleigh wave, and the measurement results are compared with the predictions using different theoretical models. It is shown that the proposed model which considers the wave spreading in both the sample and wedges can be used to interpret the measurements reasonably.
Modelling of diffuse solar fraction with multiple predictors
Energy Technology Data Exchange (ETDEWEB)
Ridley, Barbara; Boland, John [Centre for Industrial and Applied Mathematics, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, SA 5095 (Australia); Lauret, Philippe [Laboratoire de Physique du Batiment et des Systemes, University of La Reunion, Reunion (France)
2010-02-15
For some locations both global and diffuse solar radiation are measured. However, for many locations, only global radiation is measured, or inferred from satellite data. For modelling solar energy applications, the amount of radiation on a tilted surface is needed. Since only the direct component on a tilted surface can be calculated from direct on some other plane using trigonometry, we need to have diffuse radiation on the horizontal plane available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia. Boland et al. developed a validated model for Australian conditions. Boland et al. detailed our recent advances in developing the theoretical framework for the use of the logistic function instead of piecewise linear or simple nonlinear functions and was the first step in identifying the means for developing a generic model for estimating diffuse from global and other predictors. We have developed a multiple predictor model, which is much simpler than previous models, and uses hourly clearness index, daily clearness index, solar altitude, apparent solar time and a measure of persistence of global radiation level as predictors. This model performs marginally better than currently used models for locations in the Northern Hemisphere and substantially better for Southern Hemisphere locations. We suggest it can be used as a universal model. (author)
The lack of potassium-isotopic fractionation in Bishunpur chondrules
Alexander, C.M. O'D.; Grossman, J.N.; Wang, Jingyuan; Zanda, B.; Bourot-Denise, M.; Hewins, R.H.
2000-01-01
In a search for evidence of evaporation during chondrule formation, the mesostases of 11 Bishunpur chondrules and melt inclusions in olivine phenocrysts in 7 of them have been analyzed for their alkali element abundances and K-isotopic compositions. Except for six points, all areas of the chondrules that were analyzed had δ41K compositions that were normal within error (typically ±3%, 2s̀). The six “anomalous” points are probably all artifacts. Experiments have shown that free evaporation of K leads to large 41K enrichments in the evaporation residues, consistent with Rayleigh fractionation. Under Rayleigh conditions, a 3% enrichment in δ41K is produced by ∼12% loss of K. The range of L-chondrite-normalized K/Al ratios (a measure of the K-elemental fractionation) in the areas analyzed vary by almost three orders of magnitude. If all chondrules started out with L-chondrite-like K abundances and the K loss occurred via Rayleigh fractionation, the most K-depleted chondrules would have had compositions of up to δ41K ≅ 200%. Clearly, K fractionation did not occur by evaporation under Rayleigh conditions. Yet experiments and modeling indicate that K should have been lost during chondrule formation under currently accepted formation conditions (peak temperature, cooling rate, etc.). Invoking precursors with variable alkali abundances to produce the range of K/Al fractionation in chondrules does not explain the K-isotopic data because any K that was present should still have experienced sufficient loss during melting for there to have been a measurable isotopic fractionation. If K loss and isotopic fractionation was inevitable during chondrule formation, the absence of K-isotopic fractionation in Bishunpur chondrules requires that they exchanged K with an isotopically normal reservoir during or after formation. There is evidence for alkali exchange between chondrules and rim-matrix in all unequilibrated ordinary chondrites. However, melt inclusions can have
International Nuclear Information System (INIS)
Sasaki, Takehito; Kamata, Rikisaburo; Urahashi, Shingo; Yamaguchi, Tetsuji.
1993-01-01
One hundred and sixty-nine cervical lymph node-metastases from head and neck squamous cell carcinomas treated with either even fractionation or uneven fractionation regimens were analyzed in the present investigation. Logistic multivariate regression analysis indicated that: type of fractionation (even vs uneven), size of metastases, T value of primary tumors, and total dose are independent variables out of 18 variables that significantly influenced the rate of tumor clearance. The data, with statistical bias corrected by the regression equation, indicated that the uneven fractionation scheme significantly improved the rate of tumor clearance for the same size of metastases, total dose, and overall time compared to the even fractionation scheme. Further analysis by a linear-quadratic cell survival model indicated that the clinical improvement by uneven fractionation might not be explained entirely by a larger dose per fraction. It is suggested that tumor cells irradiated with an uneven fractionation regimen might repopulate more slowly, or they might be either less hypoxic or redistributed in a more radiosensitive phase in the cell cycle than those irradiated with even fractionation. This conclusion is clearly not definite, but it is suitable, pending the results of further investigation. (author)
Cusimano, N.; Gerardo-Giorda, L.
2018-06-01
Classical models of electrophysiology do not typically account for the effects of high structural heterogeneity in the spatio-temporal description of excitation waves propagation. We consider a modification of the Monodomain model obtained by replacing the diffusive term of the classical formulation with a fractional power of the operator, defined in the spectral sense. The resulting nonlocal model describes different levels of tissue heterogeneity as the fractional exponent is varied. The numerical method for the solution of the fractional Monodomain relies on an integral representation of the nonlocal operator combined with a finite element discretisation in space, allowing to handle in a natural way bounded domains in more than one spatial dimension. Numerical tests in two spatial dimensions illustrate the features of the model. Activation times, action potential duration and its dispersion throughout the domain are studied as a function of the fractional parameter: the expected peculiar behaviour driven by tissue heterogeneities is recovered.
Rayleigh-type parametric chemical oscillation
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Shyamolina; Ray, Deb Shankar, E-mail: pcdsr@iacs.res.in [Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032 (India)
2015-09-28
We consider a nonlinear chemical dynamical system of two phase space variables in a stable steady state. When the system is driven by a time-dependent sinusoidal forcing of a suitable scaling parameter at a frequency twice the output frequency and the strength of perturbation exceeds a threshold, the system undergoes sustained Rayleigh-type periodic oscillation, wellknown for parametric oscillation in pipe organs and distinct from the usual forced quasiperiodic oscillation of a damped nonlinear system where the system is oscillatory even in absence of any external forcing. Our theoretical analysis of the parametric chemical oscillation is corroborated by full numerical simulation of two well known models of chemical dynamics, chlorite-iodine-malonic acid and iodine-clock reactions.
Rayleigh-type parametric chemical oscillation.
Ghosh, Shyamolina; Ray, Deb Shankar
2015-09-28
We consider a nonlinear chemical dynamical system of two phase space variables in a stable steady state. When the system is driven by a time-dependent sinusoidal forcing of a suitable scaling parameter at a frequency twice the output frequency and the strength of perturbation exceeds a threshold, the system undergoes sustained Rayleigh-type periodic oscillation, wellknown for parametric oscillation in pipe organs and distinct from the usual forced quasiperiodic oscillation of a damped nonlinear system where the system is oscillatory even in absence of any external forcing. Our theoretical analysis of the parametric chemical oscillation is corroborated by full numerical simulation of two well known models of chemical dynamics, chlorite-iodine-malonic acid and iodine-clock reactions.
Rayleigh-Taylor instability in a visco-plastic fluid
International Nuclear Information System (INIS)
Demianov, A Yu; Doludenko, A N; Son, E E; Inogamov, N A
2010-01-01
The Rayleigh-Taylor and Richtmyer-Meshkov instabilities of a visco-plastic fluid are discussed. The Bingham model is used as an effective rheological model which takes into account plastic effects. For the purposes of numerical simulation a one-mode disturbance of the contact surface between two fluids is considered. The main goal of this work is to construct numerical 2D and 3D models and to obtain the relationship between yield stress and the development of instability.
Rayleigh-Taylor instability in a visco-plastic fluid
Demianov, A. Yu; Doludenko, A. N.; Inogamov, N. A.; Son, E. E.
2010-12-01
The Rayleigh-Taylor and Richtmyer-Meshkov instabilities of a visco-plastic fluid are discussed. The Bingham model is used as an effective rheological model which takes into account plastic effects. For the purposes of numerical simulation a one-mode disturbance of the contact surface between two fluids is considered. The main goal of this work is to construct numerical 2D and 3D models and to obtain the relationship between yield stress and the development of instability.
A Semianalytical Solution of the Fractional Derivative Model and Its Application in Financial Market
Directory of Open Access Journals (Sweden)
Lina Song
2018-01-01
Full Text Available Fractional differential equation has been introduced to the financial theory, which presents new ideas and tools for the theoretical researches and the practical applications. In the work, an approximate semianalytical solution of the time-fractional European option pricing model is derived using the method of combining the enhanced technique of Adomian decomposition method with the finite difference method. And then the result is introduced in China’s financial market. The work makes every effort to test the feasibility of the fractional derivative model in the actual financial market.
On the identification of fractionally cointegrated VAR models with the F(d) condition
DEFF Research Database (Denmark)
Carlini, Federico; Santucci de Magistris, Paolo
for any choice of the lag length, also when the true cointegration rank is known. The properties of these multiple non-identified models are studied and a necessary and sufficient condition for the identification of the fractional parameters of the system is provided. The condition is named F(d......) and it is a generalization to the fractional case of the I(1) condition in the VECM model. The assessment of the F(d) condition in the empirical analysis is relevant for the determination of the fractional parameters as well as the number of lags. The paper also illustrates the indeterminacy between the cointegration rank...
On the identification of fractionally cointegrated VAR models with the F(d) condition
DEFF Research Database (Denmark)
Santucci de Magistris, Paolo; Carlini, Federico
for any choice of the lag-length when the true cointegration rank is known. The properties of these multiple non-identified models are studied and a necessary and sufficient condition for the identification of the fractional parameters of the system is provided. The condition is named F(d......). This is a generalization of the well-known I(1) condition to the fractional case. Imposing a proper restriction on the fractional integration parameter, d, is sufficient to guarantee identification of all model parameters and the validity of the F(d) condition. The paper also illustrates the indeterminacy between...
Use of Angle Model to Understand Addition and Subtraction of Fractions
Directory of Open Access Journals (Sweden)
Muzwangowenyu Mukwambo
2018-02-01
Full Text Available Learners in lower primary and even some in upper primary grades grapple to perform mathematical operations which involve fractions. Failure to solve these mathematical operations creates a gap in the teaching and learning processes of mathematics. We opine that this is attributed to use of traditional mathematical approaches of teaching and learning (TMATL of operations of fraction. With the hope of engaging the reformed mathematical approach of teaching and learning (RMATL this study investigated the following: How can trainee teachers use the angle model in RMATL operations of fractions? What are the perceptions of trainee teachers in the use of the angle model which engages RMATL to teach the operations of fractions? With the goal to fill the mentioned gap in which learners struggle to perform operations involving fractions, we observed and analysed worksheets on operation with fractions students wrote. Observations and interviews with trainee teachers of lower primary revealed poor performance in problems related to operations with fractions. Observed patterns supported by cognitivism revealed that invented methods or strategies on which RMATL is anchored are suitable enough to engage learner–centred teaching and learning which can prevent the abstractness of the concept of operations with fractions.
On conservation laws for models in discrete, noncommutative and fractional differential calculus
International Nuclear Information System (INIS)
Klimek, M.
2001-01-01
We present the general method of derivation the explicit form of conserved currents for equations built within the framework of discrete, noncommutative or fractional differential calculus. The procedure applies to linear models with variable coefficients including also nonlinear potential part. As an example an equation on quantum plane, nonlinear Toda lattice model and homogeneous equation of fractional diffusion in 1+1 dimensions are studied
Neutron fraction and neutrino mean free path predictions in relativistic mean field models
International Nuclear Information System (INIS)
Hutauruk, P.T.P.; Williams, C.K.; Sulaksono, A.; Mart, T.
2004-01-01
The equation of state (EOS) of dense matter and neutrino mean free path (NMFP) in a neutron star have been studied by using relativistic mean field models motivated by effective field theory. It is found that the models predict too large proton fractions, although one of the models (G2) predicts an acceptable EOS. This is caused by the isovector terms. Except G2, the other two models predict anomalous NMFP's. In order to minimize the anomaly, besides an acceptable EOS, a large M* is favorable. A model with large M* retains the regularity in the NMFP even for a small neutron fraction
Stochastic fractional differential equations: Modeling, method and analysis
International Nuclear Information System (INIS)
Pedjeu, Jean-C.; Ladde, Gangaram S.
2012-01-01
By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model described by a system of multi-time scale stochastic differential equations is formulated. The classical Picard–Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this leads to the problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations of Itô–Doob type. Finally, to illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are outlined.
Transmit selection for imperfect threshold-based receive MRC in Rayleigh fading channels
Radaydeh, Redha Mahmoud Mesleh; Alouini, Mohamed-Slim
2010-01-01
experience identically distributed and non-identically distributed Rayleigh fading conditions. New closed-form expressions for the combined SNR statistics and some performance measures are presented. The system models adopted herein and the presented
Model-order reduction of lumped parameter systems via fractional calculus
Hollkamp, John P.; Sen, Mihir; Semperlotti, Fabio
2018-04-01
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach to the simulation of non-homogeneous systems dictates the use of numerical solutions and often imposes stringent compromises between accuracy and computational performance. Fractional calculus provides an alternative approach where complex dynamical systems can be modeled with compact fractional equations that not only can still guarantee analytical solutions, but can also enable high levels of order reduction without compromising on accuracy. Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting fractional differential models have both a complex and frequency-dependent order of the differential operator. The implications of this type of approach for both model order reduction and model synthesis are discussed.
RADIATIVE RAYLEIGH-TAYLOR INSTABILITIES
International Nuclear Information System (INIS)
Jacquet, Emmanuel; Krumholz, Mark R.
2011-01-01
We perform analytic linear stability analyses of an interface separating two stratified media threaded by a radiation flux, a configuration relevant in several astrophysical contexts. We develop a general framework for analyzing such systems and obtain exact stability conditions in several limiting cases. In the optically thin, isothermal regime, where the discontinuity is chemical in nature (e.g., at the boundary of a radiation pressure-driven H II region), radiation acts as part of an effective gravitational field, and instability arises if the effective gravity per unit volume toward the interface overcomes that away from it. In the optically thick a diabaticregime where the total (gas plus radiation) specific entropy of a Lagrangian fluid element is conserved, for example at the edge of radiation pressure-driven bubble around a young massive star, we show that radiation acts like a modified equation of state and derive a generalized version of the classical Rayleigh-Taylor stability condition.
A set for relational reasoning: Facilitation of algebraic modeling by a fraction task.
DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J
2016-12-01
Recent work has identified correlations between early mastery of fractions and later math achievement, especially in algebra. However, causal connections between aspects of reasoning with fractions and improved algebra performance have yet to be established. The current study investigated whether relational reasoning with fractions facilitates subsequent algebraic reasoning using both pre-algebra students and adult college students. Participants were first given either a relational reasoning fractions task or a fraction algebra procedures control task. Then, all participants solved word problems and constructed algebraic equations in either multiplication or division format. The word problems and the equation construction tasks involved simple multiplicative comparison statements such as "There are 4 times as many students as teachers in a classroom." Performance on the algebraic equation construction task was enhanced for participants who had previously completed the relational fractions task compared with those who completed the fraction algebra procedures task. This finding suggests that relational reasoning with fractions can establish a relational set that promotes students' tendency to model relations using algebraic expressions. Copyright © 2016 Elsevier Inc. All rights reserved.
No-arbitrage, leverage and completeness in a fractional volatility model
Vilela Mendes, R.; Oliveira, M. J.; Rodrigues, A. M.
2015-02-01
When the volatility process is driven by fractional noise one obtains a model which is consistent with the empirical market data. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions of the model are obtained with different leverage behaviors. Here, the no-arbitrage and completeness properties of the models are rigorously studied.
DEFF Research Database (Denmark)
Ørregård Nielsen, Morten
This paper proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time series models. The model is parametric and quite general, and, in particular, encompasses...... the multivariate non-cointegrated fractional ARIMA model. The novelty of the consistency result, in particular, is that it applies to a multivariate model and to an arbitrarily large set of admissible parameter values, for which the objective function does not converge uniformly in probablity, thus making...
Fractional single-phase-lagging heat conduction model for describing anomalous diffusion
Directory of Open Access Journals (Sweden)
T.N. Mishra
2016-03-01
Full Text Available The fractional single-phase-lagging (FSPL heat conduction model is obtained by combining scalar time fractional conservation equation to the single-phase-lagging (SPL heat conduction model. Based on the FSPL heat conduction model, anomalous diffusion within a finite thin film is investigated. The effect of different parameters on solution has been observed and studied the asymptotic behavior of the FSPL model. The analytical solution is obtained using Laplace transform method. The whole analysis is presented in dimensionless form. Numerical examples of particular interest have been studied and discussed in details.
Directory of Open Access Journals (Sweden)
HASHEM SABERI NAJAFI
2016-07-01
Full Text Available Generalized differential transform method (GDTM is a powerful method to solve the fractional differential equations. In this paper, a new fractional model for systems with single degree of freedom (SDOF is presented, by using the GDTM. The advantage of this method compared with some other numerical methods has been shown. The analysis of new approximations, damping and acceleration of systems are also described. Finally, by reducing damping and analysis of the errors, in one of the fractional cases, we have shown that in addition to having a suitable solution for the displacement close to the exact one, the system enjoys acceleration once crossing the equilibrium point.
Langlands, T A M; Henry, B I; Wearne, S L
2009-12-01
We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by fractional order exponents. Solutions are obtained as functions of the scaling parameters for infinite cables and semi-infinite cables with instantaneous current injections. Voltage attenuation along dendrites in response to alpha function synaptic inputs is computed. Action potential firing rates are also derived based on simple integrate and fire versions of the models. Our results show that electrotonic properties and firing rates of nerve cells are altered by anomalous subdiffusion in these models. We have suggested electrophysiological experiments to calibrate and validate the models.
Gómez-Aguilar, J. F.
2018-03-01
In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.
A model to accumulate fractionated dose in a deforming organ
International Nuclear Information System (INIS)
Yan Di; Jaffray, D.A.; Wong, J.W.
1999-01-01
Purpose: Measurements of internal organ motion have demonstrated that daily organ deformation exists throughout the course of radiation treatment. However, a method of constructing the resultant dose delivered to the organ volume remains a difficult challenge. In this study, a model to quantify internal organ motion and a method to construct a cumulative dose in a deforming organ are introduced. Methods and Materials: A biomechanical model of an elastic body is used to quantify patient organ motion in the process of radiation therapy. Intertreatment displacements of volume elements in an organ of interest is calculated by applying an finite element method with boundary conditions, obtained from multiple daily computed tomography (CT) measurements. Therefore, by incorporating also the measurements of daily setup error, daily dose delivered to a deforming organ can be accumulated by tracking the position of volume elements in the organ. Furthermore, distribution of patient-specific organ motion is also predicted during the early phase of treatment delivery using the daily measurements, and the cumulative dose distribution in the organ can then be estimated. This dose distribution will be updated whenever a new measurement becomes available, and used to reoptimize the ongoing treatment. Results: An integrated process to accumulate dosage in a daily deforming organ was implemented. In this process, intertreatment organ motion and setup error were systematically quantified, and incorporated in the calculation of the cumulative dose. An example of the rectal wall motion in a prostate treatment was applied to test the model. The displacements of volume elements in the rectal wall, as well as the resultant doses, were calculated. Conclusion: This study is intended to provide a systematic framework to incorporate daily patient-specific organ motion and setup error in the reconstruction of the cumulative dose distribution in an organ of interest. The realistic dose
International Nuclear Information System (INIS)
Dale, R.G.
1986-01-01
By extending a previously developed mathematical model based on the linear-quadratic dose-effect relationship, it is possible to examine the consequences of performing fractionated treatments for which there is insufficient time between fractions to allow complete damage repair. Equations are derived which give the relative effectiveness of such treatments in terms of tissue-repair constants (μ values) and α/β ratios, and these are then applied to some examples of treatments involving multiple fractions per day. The interplay of the various mechanisms involved (including repopulation effects) and their possible influence on treatments involving closely spaced fractions are examined. If current indications of the differences in recovery rates between early- and late-reacting normal tissues are representative, then it is shown that such differences may limit the clinical potential of accelerated fractionation regimes, where several fractions per day are given in a relatively short overall time. (author)
A Semianalytical Solution of the Fractional Derivative Model and Its Application in Financial Market
Song, Lina
2018-01-01
Fractional differential equation has been introduced to the financial theory, which presents new ideas and tools for the theoretical researches and the practical applications. In the work, an approximate semianalytical solution of the time-fractional European option pricing model is derived using the method of combining the enhanced technique of Adomian decomposition method with the finite difference method. And then the result is introduced in China’s financial market. The work makes every e...
Algorithms for testing of fractional dynamics: a practical guide to ARFIMA modelling
International Nuclear Information System (INIS)
Burnecki, Krzysztof; Weron, Aleksander
2014-01-01
In this survey paper we present a systematic methodology which demonstrates how to identify the origins of fractional dynamics. We consider three mechanisms which lead to it, namely fractional Brownian motion, fractional Lévy stable motion and an autoregressive fractionally integrated moving average (ARFIMA) process but we concentrate on the ARFIMA modelling. The methodology is based on statistical tools for identification and validation of the fractional dynamics, in particular on an ARFIMA parameter estimator, an ergodicity test, a self-similarity index estimator based on sample p-variation and a memory parameter estimator based on sample mean-squared displacement. A complete list of algorithms needed for this is provided in appendices A–F. Finally, we illustrate the methodology on various empirical data and show that ARFIMA can be considered as a universal model for fractional dynamics. Thus, we provide a practical guide for experimentalists on how to efficiently use ARFIMA modelling for a large class of anomalous diffusion data. (paper)
Stochastic Fractional Programming Approach to a Mean and Variance Model of a Transportation Problem
Directory of Open Access Journals (Sweden)
V. Charles
2011-01-01
Full Text Available In this paper, we propose a stochastic programming model, which considers a ratio of two nonlinear functions and probabilistic constraints. In the former, only expected model has been proposed without caring variability in the model. On the other hand, in the variance model, the variability played a vital role without concerning its counterpart, namely, the expected model. Further, the expected model optimizes the ratio of two linear cost functions where as variance model optimize the ratio of two non-linear functions, that is, the stochastic nature in the denominator and numerator and considering expectation and variability as well leads to a non-linear fractional program. In this paper, a transportation model with stochastic fractional programming (SFP problem approach is proposed, which strikes the balance between previous models available in the literature.
López-Sánchez, Erick J.; Romero, Juan M.; Yépez-Martínez, Huitzilin
2017-09-01
Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.
Directory of Open Access Journals (Sweden)
Bin Wang
2016-01-01
Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.
Modeling ramp-hold indentation measurements based on Kelvin-Voigt fractional derivative model
Zhang, Hongmei; zhe Zhang, Qing; Ruan, Litao; Duan, Junbo; Wan, Mingxi; Insana, Michael F.
2018-03-01
Interpretation of experimental data from micro- and nano-scale indentation testing is highly dependent on the constitutive model selected to relate measurements to mechanical properties. The Kelvin-Voigt fractional derivative model (KVFD) offers a compact set of viscoelastic features appropriate for characterizing soft biological materials. This paper provides a set of KVFD solutions for converting indentation testing data acquired for different geometries and scales into viscoelastic properties of soft materials. These solutions, which are mostly in closed-form, apply to ramp-hold relaxation, load-unload and ramp-load creep-testing protocols. We report on applications of these model solutions to macro- and nano-indentation testing of hydrogels, gastric cancer cells and ex vivo breast tissue samples using an atomic force microscope (AFM). We also applied KVFD models to clinical ultrasonic breast data using a compression plate as required for elasticity imaging. Together the results show that KVFD models fit a broad range of experimental data with a correlation coefficient typically R 2 > 0.99. For hydrogel samples, estimation of KVFD model parameters from test data using spherical indentation versus plate compression as well as ramp relaxation versus load-unload compression all agree within one standard deviation. Results from measurements made using macro- and nano-scale indentation agree in trend. For gastric cell and ex vivo breast tissue measurements, KVFD moduli are, respectively, 1/3-1/2 and 1/6 of the elasticity modulus found from the Sneddon model. In vivo breast tissue measurements yield model parameters consistent with literature results. The consistency of results found for a broad range of experimental parameters suggest the KVFD model is a reliable tool for exploring intrinsic features of the cell/tissue microenvironments.
International Nuclear Information System (INIS)
Dong, Jianping
2011-01-01
The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas-Fermi model, obtain the quantum pressure of the free electron gas. We also show the validity of the Hohenberg-Kohn theorems in the space fractional quantum mechanics and generalize the density functional theory to the fractional quantum mechanics. -- Highlights: → Thomas-Fermi model under the framework of fractional quantum mechanics is studied. → We show the validity of the HK theorems in the space fractional quantum mechanics. → The density functional theory is generalized to the fractional quantum mechanics.
International Nuclear Information System (INIS)
Gerweck, Leo E.; Dubois, Willum; Baumann, Michael; Suit, Herman D.
1995-01-01
, the rank-order correlation coefficient between the single dose hypoxic versus fractionated dose TCD50s under hypoxic or aerobic conditions was 1.0. For all 5 tumors examined, a trend for rank correlation was observed between the single dose and the fractionated dose TCD50s performed under normal or clamp hypoxic conditions (r=0.7, p=0.16 in both cases). The linear correlation coefficients were 0.83, p=0.08 and 0.72, p=0.17, respectively. Failure to attain a rank correlation of 1.0 was due to one tumor exhibiting an insignificant fractionation effect. The rank correlation between the TCD50s for fractionated treatments under normal versus the extrapolated TCD50s under clamp hypoxic conditions was 1.00; the linear correlation coefficient was 0.97 (p=0.01). Conclusions: In the tumor models examined, factors controlling the single fraction tumor control dose, also impact the response to fractionated treatments. These results suggest that laboratory estimates of intrinsic radiosensitivity and tumor clonogen number at the onset of treatment, will be of use in predicting radiocurability for fractionated treatments, as has been observed for single dose treatments
DEFF Research Database (Denmark)
Ørregård Nielsen, Morten
2015-01-01
the multivariate non-cointegrated fractional autoregressive integrated moving average (ARIMA) model. The novelty of the consistency result, in particular, is that it applies to a multivariate model and to an arbitrarily large set of admissible parameter values, for which the objective function does not converge...
Fractional order creep model for dam concrete considering degree of hydration
Huang, Yaoying; Xiao, Lei; Bao, Tengfei; Liu, Yu
2018-05-01
Concrete is a material that is an intermediate between an ideal solid and an ideal fluid. The creep of concrete is related not only to the loading age and duration, but also to its temperature and temperature history. Fractional order calculus is a powerful tool for solving physical mechanics modeling problems. Using a software element based on the generalized Kelvin model, a fractional order creep model of concrete considering the loading age and duration is established. Then, the hydration rate of cement is considered in terms of the degree of hydration, and the fractional order creep model of concrete considering the degree of hydration is established. Moreover, uniaxial tensile creep tests of dam concrete under different curing temperatures were conducted, and the results were combined with the creep test data and complex optimization method to optimize the parameters of a new creep model. The results show that the fractional tensile creep model based on hydration degree can better describe the tensile creep properties of concrete, and this model involves fewer parameters than the 8-parameter model.
Forecasting daily political opinion polls using the fractionally cointegrated VAR model
DEFF Research Database (Denmark)
Nielsen, Morten Ørregaard; Shibaev, Sergei S.
We examine forecasting performance of the recent fractionally cointegrated vector autoregressive (FCVAR) model. We use daily polling data of political support in the United Kingdom for 2010-2015 and compare with popular competing models at several forecast horizons. Our findings show that the four...... trend from the model follows the vote share of the UKIP very closely, and we thus interpret it as a measure of Euro-skepticism in public opinion rather than an indicator of the more traditional left-right political spectrum. In terms of prediction of vote shares in the election, forecasts generated...... variants of the FCVAR model considered are generally ranked as the top four models in terms of forecast accuracy, and the FCVAR model significantly outperforms both univariate fractional models and the standard cointegrated VAR (CVAR) model at all forecast horizons. The relative forecast improvement...
Energy Technology Data Exchange (ETDEWEB)
Mavroidis, Panayiotis, E-mail: mavroidis@uthscsa.edu [Department of Radiation Oncology, University of Texas Health Sciences Center, San Antonio, Texas (United States); Department of Medical Radiation Physics, Karolinska Institutet and Stockholm University, Stockholm (Sweden); Milickovic, Natasa [Department of Medical Physics and Engineering, Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Cruz, Wilbert F. [Department of Radiation Oncology, University of Texas Health Sciences Center, San Antonio, Texas (United States); Tselis, Nikolaos [Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Karabis, Andreas [Pi-Medical Ltd., Athens (Greece); Stathakis, Sotirios; Papanikolaou, Nikos [Department of Radiation Oncology, University of Texas Health Sciences Center, San Antonio, Texas (United States); Zamboglou, Nikolaos [Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Baltas, Dimos [Department of Medical Physics and Engineering, Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Nuclear and Particle Physics Section, Physics Department, University of Athens, Athens (Greece)
2014-01-01
Purpose: The aim of the present study was the investigation of different fractionation schemes to estimate their clinical impact. For this purpose, widely applied radiobiological models and dosimetric measures were used to associate their results with clinical findings. Methods and Materials: The dose distributions of 12 clinical high-dose-rate brachytherapy implants for prostate were evaluated in relation to different fractionation schemes. The fractionation schemes compared were: (1) 1 fraction of 20 Gy; (2) 2 fractions of 14 Gy; (3) 3 fractions of 11 Gy; and (4) 4 fractions of 9.5 Gy. The clinical effectiveness of the different fractionation schemes was estimated through the complication-free tumor control probability (P{sub +}), the biologically effective uniform dose, and the generalized equivalent uniform dose index. Results: For the different fractionation schemes, the tumor control probabilities were 98.5% in 1 × 20 Gy, 98.6% in 2 × 14 Gy, 97.5% in 3 × 11 Gy, and 97.8% in 4 × 9.5 Gy. The corresponding P{sub +} values were 88.8% in 1 × 20 Gy, 83.9% in 2 × 14 Gy, 86.0% in 3 × 11 Gy, and 82.3% in 4 × 9.5 Gy. With use of the fractionation scheme 4 × 9.5 Gy as reference, the isoeffective schemes regarding tumor control for 1, 2, and 3 fractions were 1 × 19.68 Gy, 2 × 13.75 Gy, and 3 × 11.05 Gy. The optimum fractionation schemes for 1, 2, 3, and 4 fractions were 1 × 19.16 Gy with a P{sub +} of 91.8%, 2 × 13.2 Gy with a P{sub +} of 89.6%, 3 × 10.6 Gy with a P{sub +} of 88.4%, and 4 × 9.02 Gy with a P{sub +} of 86.9%. Conclusions: Among the fractionation schemes 1 × 20 Gy, 2 × 14 Gy, 3 × 11 Gy, and 4 × 9.5 Gy, the first scheme was more effective in terms of P{sub +}. After performance of a radiobiological optimization, it was shown that a single fraction of 19.2 to 19.7 Gy (average 19.5 Gy) should produce at least the same benefit as that given by the 4 × 9.5 Gy scheme, and it should reduce the expected total complication probability by
Determination of bone mineral volume fraction using impedance analysis and Bruggeman model
Energy Technology Data Exchange (ETDEWEB)
Ciuchi, Ioana Veronica; Olariu, Cristina Stefania, E-mail: oocristina@yahoo.com; Mitoseriu, Liliana, E-mail: lmtsr@uaic.ro
2013-11-20
Highlights: • Mineral volume fraction of a bone sample was determined. • Dielectric properties for bone sample and for the collagen type I were determined by impedance spectroscopy. • Bruggeman effective medium approximation was applied in order to evaluate mineral volume fraction of the sample. • The computed values were compared with ones derived from a histogram test performed on SEM micrographs. -- Abstract: Measurements by impedance spectroscopy and Bruggeman effective medium approximation model were employed in order to determine the mineral volume fraction of dry bone. This approach assumes that two or more phases are present into the composite: the matrix (environment) and the other ones are inclusion phases. A fragment of femur diaphysis dense bone from a young pig was investigated in its dehydrated state. Measuring the dielectric properties of bone and its main components (hydroxyapatite and collagen) and using the Bruggeman approach, the mineral volume filling factor was determined. The computed volume fraction of the mineral volume fraction was confirmed by a histogram test analysis based on the SEM microstructures. In spite of its simplicity, the method provides a good approximation for the bone mineral volume fraction. The method which uses impedance spectroscopy and EMA modeling can be further developed by considering the conductive components of the bone tissue as a non-invasive in situ impedance technique for bone composition evaluation and monitoring.
Determination of bone mineral volume fraction using impedance analysis and Bruggeman model
International Nuclear Information System (INIS)
Ciuchi, Ioana Veronica; Olariu, Cristina Stefania; Mitoseriu, Liliana
2013-01-01
Highlights: • Mineral volume fraction of a bone sample was determined. • Dielectric properties for bone sample and for the collagen type I were determined by impedance spectroscopy. • Bruggeman effective medium approximation was applied in order to evaluate mineral volume fraction of the sample. • The computed values were compared with ones derived from a histogram test performed on SEM micrographs. -- Abstract: Measurements by impedance spectroscopy and Bruggeman effective medium approximation model were employed in order to determine the mineral volume fraction of dry bone. This approach assumes that two or more phases are present into the composite: the matrix (environment) and the other ones are inclusion phases. A fragment of femur diaphysis dense bone from a young pig was investigated in its dehydrated state. Measuring the dielectric properties of bone and its main components (hydroxyapatite and collagen) and using the Bruggeman approach, the mineral volume filling factor was determined. The computed volume fraction of the mineral volume fraction was confirmed by a histogram test analysis based on the SEM microstructures. In spite of its simplicity, the method provides a good approximation for the bone mineral volume fraction. The method which uses impedance spectroscopy and EMA modeling can be further developed by considering the conductive components of the bone tissue as a non-invasive in situ impedance technique for bone composition evaluation and monitoring
Fractionations of rare earth elements in plants and their conceptive model.
Ding, ShiMing; Liang, Tao; Yan, JunCai; Zhang, ZiLi; Huang, ZeChun; Xie, YaNing
2007-02-01
Fractionations of rare earth elements (REEs) and their mechanisms in soybean were studied through application of exogenous mixed REEs under hydroponic conditions. Significant enrichment of middle REEs (MREEs) and heavy REEs (HREEs) was observed in plant roots and leaves respectively, with slight fractionation between light REEs (LREEs) and HREEs in stems. Moreover, the tetrad effect was observed in these organs. Investigations into REE speciation in roots and in the xylem sap using X-ray absorption spectroscopy (XAS) and nanometer-sized TiO2 adsorption techniques, associated with other controlled experiments, demonstrated that REE fractionations should be dominated by fixation mechanism in roots caused by cell wall absorption and phosphate precipitation, and by the combined effects of fixation mechanism and transport mechanism in aboveground parts caused by solution complexation by intrinsic organic ligands. A conceptive model was established for REE fractionations in plants based on the above studies.
Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate
Directory of Open Access Journals (Sweden)
Adnane Boukhouima
2017-01-01
Full Text Available We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV infection. In the model, the infection transmission process is modeled by a specific functional response. First, we show that the model is mathematically and biologically well posed. Second, the local and global stabilities of the equilibria are investigated. Finally, some numerical simulations are presented in order to illustrate our theoretical results.
Short Rayleigh Length Free Electron Lasers
Crooker, P P; Armstead, R L; Blau, J
2004-01-01
Conventional free electron laser (FEL) oscillators minimize the optical mode volume around the electron beam in the undulator by making the resonator Rayleigh length about one third of the undulator length. This maximizes gain and beam-mode coupling. In compact configurations of high-power infrared FELs or moderate power UV FELs, the resulting optical intensity can damage the resonator mirrors. To increase the spot size and thereby reduce the optical intensity at the mirrors below the damage threshold, a shorter Rayleigh length can be used, but the FEL interaction is significantly altered. A new FEL interaction is described and analyzed with a Rayleigh length that is only one tenth the undulator length, or less. The effect of mirror vibration and positioning are more critical in the short Rayleigh length design, but we find that they are still within normal design tolerances.
Chemical Applications of Second Harmonic Rayleigh Scattering ...
Indian Academy of Sciences (India)
Chemical Applications of Second Harmonic Rayleigh Scattering Puspendu Kumar Das Department of Inorganic and Physical Chemistry Indian Institute of Science Bangalore 560012, India pkdas@ipc.iisc.ernet.in.
Directory of Open Access Journals (Sweden)
Salman IJAZ
2018-05-01
Full Text Available In this paper, a methodology has been developed to address the issue of force fighting and to achieve precise position tracking of control surface driven by two dissimilar actuators. The nonlinear dynamics of both actuators are first approximated as fractional order models. Based on the identified models, three fractional order controllers are proposed for the whole system. Two Fractional Order PID (FOPID controllers are dedicated to improving transient response and are designed in a position feedback configuration. In order to synchronize the actuator dynamics, a third fractional order PI controller is designed, which feeds the force compensation signal in position feedback loop of both actuators. Nelder-Mead (N-M optimization technique is employed in order to optimally tune controller parameters based on the proposed performance criteria. To test the proposed controllers according to real flight condition, an external disturbance of higher amplitude that acts as airload is applied directly on the control surface. In addition, a disturbance signal function of system states is applied to check the robustness of proposed controller. Simulation results on nonlinear system model validated the performance of the proposed scheme as compared to optimal PID and high gain PID controllers. Keywords: Aerospace, Fractional order control, Model identification, Nelder-Mead optimization, Robustness
Modelling size-fractionated primary production in the Atlantic Ocean from remote sensing
Brewin, Robert J. W.; Tilstone, Gavin H.; Jackson, Thomas; Cain, Terry; Miller, Peter I.; Lange, Priscila K.; Misra, Ankita; Airs, Ruth L.
2017-11-01
Marine primary production influences the transfer of carbon dioxide between the ocean and atmosphere, and the availability of energy for the pelagic food web. Both the rate and the fate of organic carbon from primary production are dependent on phytoplankton size. A key aim of the Atlantic Meridional Transect (AMT) programme has been to quantify biological carbon cycling in the Atlantic Ocean and measurements of total primary production have been routinely made on AMT cruises, as well as additional measurements of size-fractionated primary production on some cruises. Measurements of total primary production collected on the AMT have been used to evaluate remote-sensing techniques capable of producing basin-scale estimates of primary production. Though models exist to estimate size-fractionated primary production from satellite data, these have not been well validated in the Atlantic Ocean, and have been parameterised using measurements of phytoplankton pigments rather than direct measurements of phytoplankton size structure. Here, we re-tune a remote-sensing primary production model to estimate production in three size fractions of phytoplankton (10 μm) in the Atlantic Ocean, using measurements of size-fractionated chlorophyll and size-fractionated photosynthesis-irradiance experiments conducted on AMT 22 and 23 using sequential filtration-based methods. The performance of the remote-sensing technique was evaluated using: (i) independent estimates of size-fractionated primary production collected on a number of AMT cruises using 14C on-deck incubation experiments and (ii) Monte Carlo simulations. Considering uncertainty in the satellite inputs and model parameters, we estimate an average model error of between 0.27 and 0.63 for log10-transformed size-fractionated production, with lower errors for the small size class (10 μm), and errors generally higher in oligotrophic waters. Application to satellite data in 2007 suggests the contribution of cells 2 μm to total
Rayleigh-Taylor instability in an equal mass plasma
Energy Technology Data Exchange (ETDEWEB)
Adak, Ashish, E-mail: ashish-adak@yahoo.com [Department of Instrumentation Science, Jadavpur University, Kolkata 700 032 (India); Ghosh, Samiran, E-mail: sran-g@yahoo.com [Department of Applied Mathematics, University of Calcutta 92, Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Chakrabarti, Nikhil, E-mail: nikhil.chakrabarti@saha.ac.in [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India)
2014-09-15
The Rayleigh-Taylor (RT) instability in an inhomogeneous pair-ion plasma has been analyzed. Considering two fluid model for two species of ions (positive and negative), we obtain the possibility of the existence of RT instability. The growth rate of the RT instability as usual depends on gravity and density gradient scale length. The results are discussed in context of pair-ion plasma experiments.
Directory of Open Access Journals (Sweden)
José Francisco Gómez Aguilar
2012-07-01
Full Text Available Using the fractional calculus approach, we present the Laplace analysis of an equivalent electrical circuit for a multilayered system, which includes distributed elements of the Cole model type. The Bode graphs are obtained from the numerical simulation of the corresponding transfer functions using arbitrary electrical parameters in order to illustrate the methodology. A numerical Laplace transform is used with respect to the simulation of the fractional differential equations. From the results shown in the analysis, we obtain the formula for the equivalent electrical circuit of a simple spectrum, such as that generated by a real sample of blood tissue, and the corresponding Nyquist diagrams. In addition to maintaining consistency in adjusted electrical parameters, the advantage of using fractional differential equations in the study of the impedance spectra is made clear in the analysis used to determine a compact formula for the equivalent electrical circuit, which includes the Cole model and a simple RC model as special cases.
On a business cycle model with fractional derivative under narrow-band random excitation
International Nuclear Information System (INIS)
Lin, Zifei; Li, Jiaorui; Li, Shuang
2016-01-01
This paper analyzes the dynamics of a business cycle model with fractional derivative of order α (0 < α < 1) subject to narrow-band random excitation, in which fractional derivative describes the memory property of the economic variables. Stochastic dynamical system concepts are integrated into the business cycle model for understanding the economic fluctuation. Firstly, the method of multiple scales is applied to derive the model to obtain the approximate analytical solution. Secondly, the effect of economic policy with fractional derivative on the amplitude of the economic fluctuation and the effect on stationary probability density are studied. The results show macroeconomic regulation and control can lower the stable amplitude of economic fluctuation. While in the process of equilibrium state, the amplitude is magnified. Also, the macroeconomic regulation and control improves the stability of the equilibrium state. Thirdly, how externally stochastic perturbation affects the dynamics of the economy system is investigated.
Fractional Poisson-Nernst-Planck Model for Ion Channels I: Basic Formulations and Algorithms.
Chen, Duan
2017-11-01
In this work, we propose a fractional Poisson-Nernst-Planck model to describe ion permeation in gated ion channels. Due to the intrinsic conformational changes, crowdedness in narrow channel pores, binding and trapping introduced by functioning units of channel proteins, ionic transport in the channel exhibits a power-law-like anomalous diffusion dynamics. We start from continuous-time random walk model for a single ion and use a long-tailed density distribution function for the particle jump waiting time, to derive the fractional Fokker-Planck equation. Then, it is generalized to the macroscopic fractional Poisson-Nernst-Planck model for ionic concentrations. Necessary computational algorithms are designed to implement numerical simulations for the proposed model, and the dynamics of gating current is investigated. Numerical simulations show that the fractional PNP model provides a more qualitatively reasonable match to the profile of gating currents from experimental observations. Meanwhile, the proposed model motivates new challenges in terms of mathematical modeling and computations.
A new visco-elasto-plastic model via time-space fractional derivative
Hei, X.; Chen, W.; Pang, G.; Xiao, R.; Zhang, C.
2018-02-01
To characterize the visco-elasto-plastic behavior of metals and alloys we propose a new constitutive equation based on a time-space fractional derivative. The rheological representative of the model can be analogous to that of the Bingham-Maxwell model, while the dashpot element and sliding friction element are replaced by the corresponding fractional elements. The model is applied to describe the constant strain rate, stress relaxation and creep tests of different metals and alloys. The results suggest that the proposed simple model can describe the main characteristics of the experimental observations. More importantly, the model can also provide more accurate predictions than the classic Bingham-Maxwell model and the Bingham-Norton model.
Rayleigh-Taylor mixing in supernova experiments
International Nuclear Information System (INIS)
Swisher, N. C.; Abarzhi, S. I.; Kuranz, C. C.; Arnett, D.; Hurricane, O.; Remington, B. A.; Robey, H. F.
2015-01-01
We report a scrupulous analysis of data in supernova experiments that are conducted at high power laser facilities in order to study core-collapse supernova SN1987A. Parameters of the experimental system are properly scaled to investigate the interaction of a blast-wave with helium-hydrogen interface, and the induced Rayleigh-Taylor instability and Rayleigh-Taylor mixing of the denser and lighter fluids with time-dependent acceleration. We analyze all available experimental images of the Rayleigh-Taylor flow in supernova experiments and measure delicate features of the interfacial dynamics. A new scaling is identified for calibration of experimental data to enable their accurate analysis and comparisons. By properly accounting for the imprint of the experimental conditions, the data set size and statistics are substantially increased. New theoretical solutions are reported to describe asymptotic dynamics of Rayleigh-Taylor flow with time-dependent acceleration by applying theoretical analysis that considers symmetries and momentum transport. Good qualitative and quantitative agreement is achieved of the experimental data with the theory and simulations. Our study indicates that in supernova experiments Rayleigh-Taylor flow is in the mixing regime, the interface amplitude contributes substantially to the characteristic length scale for energy dissipation; Rayleigh-Taylor mixing keeps order
Acoustofluidic particle dynamics: Beyond the Rayleigh limit.
Baasch, Thierry; Dual, Jürg
2018-01-01
In this work a numerical model to calculate the trajectories of multiple acoustically and hydrodynamically interacting spherical particles is presented. The acoustic forces are calculated by solving the fully coupled three-dimensional scattering problem using finite element software. The method is not restricted to single re-scattering events, mono- and dipole radiation, and long wavelengths with respect to the particle diameter, thus expanding current models. High frequency surface acoustic waves have been used in the one cell per well technology to focus individual cells in a two-dimensional wave-field. Sometimes the cells started forming clumps and it was not possible to focus on individual cells. Due to a lack of existing theory, this could not be fully investigated. Here, the authors use the full dynamic simulations to identify limiting factors of the one-cell-per-well technology. At first, the authors demonstrate good agreement of the numerical model with analytical results in the Rayleigh limiting case. A frequency dependent stability exchange between the pressure and velocity was then demonstrated. The numerical formulation presented in this work is relatively general and can be used for a multitude of different high frequency applications. It is a powerful tool in the analysis of microscale acoustofluidic devices and processes.
Jones, Alan G.; Afonso, Juan Carlos; Fullea, Javier
2015-04-01
The deep mantle African Superswell is thought to cause up to 500 m of the uplift of the Southern African Plateau. We investigate this phenomenon through stochastic thermo-chemical inversion modelling of the geoid, surface heat flow, Rayleigh and Love dispersion curves and MT data, in a manner that is fully petrologically-consistent. We invert for a three layer crustal velocity, density and thermal structure, but assume the resistivity layering (based on prior inversion of the MT data alone). Inversions are performed using an improved Delayed Rejection and Adaptive Metropolis (DRAM) type Markov chain Monte Carlo (MCMC) algorithm. We demonstrate that a single layer lithosphere can fit most of the data, but not the MT responses. We further demonstrate that modelling the seismic data alone, without the constraint of requiring reasonable oxide chemistry or of fitting the geoid, permits wildly acceptable elevations and with very poorly defined lithosphere-asthenosphere boundary (LAB). We parameterise the lithosphere into three layers, and bound the permitted oxide chemistry of each layer consistent with known chemical layering. We find acceptable models, from 5 million tested in each case, that fit all responses and yield a posteriori elevation distributions centred on 900-950 m, suggesting dynamic support from the lower mantle of some 400 m.
Energy Technology Data Exchange (ETDEWEB)
Ali, Farhad, E-mail: farhadaliecomaths@yahoo.com [Department of Mathematics, City University of Science and Information Technology, Peshawar 25000 (Pakistan); Sheikh, Nadeem Ahmad [Department of Mathematics, City University of Science and Information Technology, Peshawar 25000 (Pakistan); Khan, Ilyas [Basic Engineering Sciences Department, College of Engineering Majmaah University, Majmaah 11952 (Saudi Arabia); Saqib, Muhammad [Department of Mathematics, City University of Science and Information Technology, Peshawar 25000 (Pakistan)
2017-02-01
The effects of magnetohydrodynamics on the blood flow when blood is represented as a Casson fluid, along with magnetic particles in a horizontal cylinder is studied. The flow is due to an oscillating pressure gradient. The Laplace and finite Hankel transforms are used to obtain the closed form solutions of the fractional partial differential equations. Effects of various parameters on the flow of both blood and magnetic particles are shown graphically. The analysis shows that, the model with fractional order derivatives bring a remarkable changes as compared to the ordinary model. The study highlights that applied magnetic field reduces the velocities of both the blood and magnetic particles.
International Nuclear Information System (INIS)
Ali, Farhad; Sheikh, Nadeem Ahmad; Khan, Ilyas; Saqib, Muhammad
2017-01-01
The effects of magnetohydrodynamics on the blood flow when blood is represented as a Casson fluid, along with magnetic particles in a horizontal cylinder is studied. The flow is due to an oscillating pressure gradient. The Laplace and finite Hankel transforms are used to obtain the closed form solutions of the fractional partial differential equations. Effects of various parameters on the flow of both blood and magnetic particles are shown graphically. The analysis shows that, the model with fractional order derivatives bring a remarkable changes as compared to the ordinary model. The study highlights that applied magnetic field reduces the velocities of both the blood and magnetic particles.
The role of initial values in nonstationary fractional time series models
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
We consider the nonstationary fractional model $\\Delta^{d}X_{t}=\\varepsilon _{t}$ with $\\varepsilon_{t}$ i.i.d.$(0,\\sigma^{2})$ and $d>1/2$. We derive an analytical expression for the main term of the asymptotic bias of the maximum likelihood estimator of $d$ conditional on initial values, and we...... discuss the role of the initial values for the bias. The results are partially extended to other fractional models, and three different applications of the theoretical results are given....
A mathematical model of the nine-month pregnant woman for calculating specific absorbed fractions
International Nuclear Information System (INIS)
Watson, E.E.; Stabin, M.G.
1987-01-01
Existing models which allow calculation of internal doses from radionuclide intakes by both men and women are based on a mathematical model of Reference Man. No attempt has been made to allow for the changing geometric relationships that occur during pregnancy which would affect the doses to the mother's organs and to the fetus. As pregnancy progresses, many of the mother's abdominal organs are repositioned, and their shapes may be somewhat changed. Estimation of specific absorbed fractions requires that existing mathematical models be modified to accommodate these changes. Specific absorbed fractions for Reference Woman at three, six and nine months of pregnancy should be sufficient for estimating the doses to the pregnant woman and the fetus. This report describes a model for the pregnant woman at nine months. An enlarged uterus was incorporated into a model for Reference Woman. Several abdominal organs as well as the exterior of the trunk were modified to accommodate the new uterus. This model will allow calculation of specific absorbed fractions for the fetus from photon emitters in maternal organs. Specific absorbed fractions for the repositioned maternal organs from other organs can also be calculated. 14 refs.; 2 figs
A mathematical model of the nine-month pregnant woman for calculating specific absorbed fractions
International Nuclear Information System (INIS)
Watson, E.E.; Stabin, M.G.
1986-01-01
Existing models that allow calculation of internal doses from radionuclide intakes by both men and women are based on a mathematical model of Reference Man. No attempt has been made to allow for the changing geometric relationships that occur during pregnancy which would affect the doses to the mother's organs and to the fetus. As pregnancy progresses, many of the mother's abdominal organs are repositioned, and their shapes may be somewhat changed. Estimation of specific absorbed fractions requires that existing mathematical models be modified to accommodate these changes. Specific absorbed fractions for Reference Woman at three, six, and nine months of pregnancy should be sufficient for estimating the doses to the pregnant woman and the fetus. This report describes a model for the pregnant woman at nine months. An enlarged uterus was incorporated into a model for Reference Woman. Several abdominal organs as well as the exterior of the trunk were modified to accommodate the new uterus. This model will allow calculation of specific absorbed fractions for the fetus from photon emitters in maternal organs. Specific absorbed fractions for the repositioned maternal organs from other organs can also be calculated. 14 refs., 2 figs
New phenomena in variable-density Rayleigh-Taylor turbulence
Energy Technology Data Exchange (ETDEWEB)
Livescu, D; Ristorcelli, J R; Petersen, M R; Gore, R A, E-mail: livescu@lanl.gov [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)
2010-12-15
This paper presents several issues related to mixing and turbulence structure in buoyancy-driven turbulence at low to moderate Atwood numbers, A, found from direct numerical simulations in two configurations: classical Rayleigh-Taylor instability and an idealized triply periodic Rayleigh-Taylor flow. Simulations at A up to 0.5 are used to examine the turbulence characteristics and contrast them with those obtained close to the Boussinesq approximation. The data sets used represent the largest simulations to date in each configuration. One of the more remarkable issues explored, first reported in (Livescu and Ristorcelli 2008 J. Fluid Mech. 605 145-80), is the marked difference in mixing between different density fluids as opposed to the mixing that occurs between fluids of commensurate densities, corresponding to the Boussinesq approximation. Thus, in the triply periodic configuration and the non-Boussinesq case, an initially symmetric density probability density function becomes skewed, showing that the mixing is asymmetric, with pure heavy fluid mixing more slowly than pure light fluid. A mechanism producing the mixing asymmetry is proposed and the consequences for the classical Rayleigh-Taylor configuration are discussed. In addition, it is shown that anomalous small-scale anisotropy found in the homogeneous configuration (Livescu and Ristorcelli 2008 J. Fluid Mech. 605 145-80) and Rayleigh-Taylor turbulence at A=0.5 (Livescu et al 2008 J. Turbul. 10 1-32) also occurs near the Boussinesq limit. Results pertaining to the moment closure modelling of Rayleigh-Taylor turbulence are also presented. Although the Rayleigh-Taylor mixing layer width reaches self-similar growth relatively fast, the lower-order terms in the self-similar expressions for turbulence moments have long-lasting effects and derived quantities, such as the turbulent Reynolds number, are slow to follow the self-similar predictions. Since eddy diffusivity in the popular gradient transport hypothesis
Direct numerical simulation of the Rayleigh-Taylor instability with the spectral element method
International Nuclear Information System (INIS)
Zhang Xu; Tan Duowang
2009-01-01
A novel method is proposed to simulate Rayleigh-Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier-Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh-Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh-Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh-Taylor instabilities of turbulent flows. (authors)
Two-Part Models for Fractional Responses Defined as Ratios of Integers
Directory of Open Access Journals (Sweden)
Harald Oberhofer
2014-09-01
Full Text Available This paper discusses two alternative two-part models for fractional response variables that are defined as ratios of integers. The first two-part model assumes a Binomial distribution and known group size. It nests the one-part fractional response model proposed by Papke and Wooldridge (1996 and, thus, allows one to apply Wald, LM and/or LR tests in order to discriminate between the two models. The second model extends the first one by allowing for overdispersion in the data. We demonstrate the usefulness of the proposed two-part models for data on the 401(k pension plan participation rates used in Papke and Wooldridge (1996.
Rayleigh-Taylor/gravitational instability in dense magnetoplasmas
Energy Technology Data Exchange (ETDEWEB)
Ali, S., E-mail: shahid.ali@ncp.edu.p [National Centre for Physics, Quaid-i-Azam University Campus, Islamabad (Pakistan); IPFN, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Ahmed, Z. [COMSATS Institute of Information Technology, Department of Physics, Wah Campus (Pakistan); Mirza, Arshad M. [Theoretical Plasma Physics Group, Physics Department, Quaid-i-Azam University, Islamabad 45320 (Pakistan); Ahmad, I. [COMSATS Institute of Information Technology, Department of Physics, Islamabad Campus (Pakistan)
2009-08-10
The Rayleigh-Taylor instability is investigated in a nonuniform dense quantum magnetoplasma. For this purpose, a quantum hydrodynamical model is used for the electrons whereas the ions are assumed to be cold and classical. The dispersion relation for the Rayleigh-Taylor instability becomes modified with the quantum corrections associated with the Fermi pressure law and the quantum Bohm potential force. Numerically, it is found that the quantum speed and density gradient significantly modify the growth rate of RT instability. In a dense quantum magnetoplasma case, the linear growth rate of RT instability becomes significantly higher than its classical value and the modes are found to be highly localized. The present investigation should be useful in the studies of dense astrophysical magnetoplasmas as well as in laser-produced plasmas.
Rayleigh-Taylor/gravitational instability in dense magnetoplasmas
International Nuclear Information System (INIS)
Ali, S.; Ahmed, Z.; Mirza, Arshad M.; Ahmad, I.
2009-01-01
The Rayleigh-Taylor instability is investigated in a nonuniform dense quantum magnetoplasma. For this purpose, a quantum hydrodynamical model is used for the electrons whereas the ions are assumed to be cold and classical. The dispersion relation for the Rayleigh-Taylor instability becomes modified with the quantum corrections associated with the Fermi pressure law and the quantum Bohm potential force. Numerically, it is found that the quantum speed and density gradient significantly modify the growth rate of RT instability. In a dense quantum magnetoplasma case, the linear growth rate of RT instability becomes significantly higher than its classical value and the modes are found to be highly localized. The present investigation should be useful in the studies of dense astrophysical magnetoplasmas as well as in laser-produced plasmas.
Model for the isotopic fractionation of water in the Amazon basin
International Nuclear Information System (INIS)
Dall'Olio, A.; Azevedo, C.T. de
1979-01-01
Two models on the isotopic fractionation of water are presented. In the first model. It is assumed that the only source of water vapour for the Amazon region is the Atlantic Ocean, introduced by the predominant easterly winds. The second model contains the assumption that the forest also serves as a source of water vapour contributing an equal volume of water to the regional rains as the vapour of oceanic origin. (Author) [pt
Popović, Jovan K.; Spasić, Dragan T.; Tošić, Jela; Kolarović, Jovanka L.; Malti, Rachid; Mitić, Igor M.; Pilipović, Stevan; Atanacković, Teodor M.
2015-05-01
The aim of this study is to promote a model based on the fractional differential calculus related to the pharmacokinetic individualization of high dose methotrexate treatment in children with acute lymphoblastic leukaemia, especially in high risk patients. We applied two-compartment fractional model on 8 selected cases with the largest number (4-19) of measured concentrations, among 43 pediatric patients received 24-h methotrexate 2-5 g/m2 infusions. The plasma concentrations were determined by fluorescence polarization immunoassay. Our mathematical procedure, designed by combining Post's and Newton's method, was coded in Mathematica 8.0 and performed on Fujicu Celsius M470-2 PC. Experimental data show that most of the measured values of methotrexate were in decreasing order. However, in certain treatments local maximums were detected. On the other hand, integer order compartmental models do not give values which fit well with the observed data. By the use of our model, we obtained better results, since it gives more accurate behavior of the transmission, as well as the local maximums which were recognized in methotrexate monitoring. It follows from our method that an additional test with a small methotrexate dose can be suggested for the fractional system parameter identification and the prediction of a possible pattern with a full dose in the case of high risk patients. A special feature of the fractional model is that it can also recognize and better fit an observed non-monotonic behavior. A new parameter determination procedure can be successfully used.
Dipping-interface mapping using mode-separated Rayleigh waves
Luo, Y.; Xia, J.; Xu, Y.; Zeng, C.; Miller, R.D.; Liu, Q.
2009-01-01
Multichannel analysis of surface waves (MASW) method is a non-invasive geophysical technique that uses the dispersive characteristic of Rayleigh waves to estimate a vertical shear (S)-wave velocity profile. A pseudo-2D S-wave velocity section is constructed by aligning 1D S-wave velocity profiles at the midpoint of each receiver spread that are contoured using a spatial interpolation scheme. The horizontal resolution of the section is therefore most influenced by the receiver spread length and the source interval. Based on the assumption that a dipping-layer model can be regarded as stepped flat layers, high-resolution linear Radon transform (LRT) has been proposed to image Rayleigh-wave dispersive energy and separate modes of Rayleigh waves from a multichannel record. With the mode-separation technique, therefore, a dispersion curve that possesses satisfactory accuracy can be calculated using a pair of consecutive traces within a mode-separated shot gather. In this study, using synthetic models containing a dipping layer with a slope of 5, 10, 15, 20, or 30 degrees and a real-world example, we assess the ability of using high-resolution LRT to image and separate fundamental-mode Rayleigh waves from raw surface-wave data and accuracy of dispersion curves generated by a pair of consecutive traces within a mode-separated shot gather. Results of synthetic and real-world examples demonstrate that a dipping interface with a slope smaller than 15 degrees can be successfully mapped by separated fundamental waves using high-resolution LRT. ?? Birkh??user Verlag, Basel 2009.
Fractional-order mathematical model of an irrigation main canal pool
Directory of Open Access Journals (Sweden)
Shlomi N. Calderon-Valdez
2015-09-01
Full Text Available In this paper a fractional order model for an irrigation main canal is proposed. It is based on the experiments developed in a laboratory prototype of a hydraulic canal and the application of a direct system identification methodology. The hydraulic processes that take place in this canal are equivalent to those that occur in real main irrigation canals and the results obtained here can therefore be easily extended to real canals. The accuracy of the proposed fractional order model is compared by deriving two other integer-order models of the canal of a complexity similar to that proposed here. The parameters of these three mathematical models have been identified by minimizing the Integral Square Error (ISE performance index existing between the models and the real-time experimental data obtained from the canal prototype. A comparison of the performances of these three models shows that the fractional-order model has the lowest error and therefore the higher accuracy. Experiments showed that our model outperformed the accuracy of the integer-order models by about 25%, which is a significant improvement as regards to capturing the canal dynamics.
An in vitro lung model to assess true shunt fraction by multiple inert gas elimination.
Directory of Open Access Journals (Sweden)
Balamurugan Varadarajan
Full Text Available The Multiple Inert Gas Elimination Technique, based on Micropore Membrane Inlet Mass Spectrometry, (MMIMS-MIGET has been designed as a rapid and direct method to assess the full range of ventilation-to-perfusion (V/Q ratios. MMIMS-MIGET distributions have not been assessed in an experimental setup with predefined V/Q-distributions. We aimed (I to construct a novel in vitro lung model (IVLM for the simulation of predefined V/Q distributions with five gas exchange compartments and (II to correlate shunt fractions derived from MMIMS-MIGET with preset reference shunt values of the IVLM. Five hollow-fiber membrane oxygenators switched in parallel within a closed extracorporeal oxygenation circuit were ventilated with sweep gas (V and perfused with human red cell suspension or saline (Q. Inert gas solution was infused into the perfusion circuit of the gas exchange assembly. Sweep gas flow (V was kept constant and reference shunt fractions (IVLM-S were established by bypassing one or more oxygenators with perfusate flow (Q. The derived shunt fractions (MM-S were determined using MIGET by MMIMS from the retention data. Shunt derived by MMIMS-MIGET correlated well with preset reference shunt fractions. The in vitro lung model is a convenient system for the setup of predefined true shunt fractions in validation of MMIMS-MIGET.
Fractional Modeling of the AC Large-Signal Frequency Response in Magnetoresistive Current Sensors
Directory of Open Access Journals (Sweden)
Sergio Iván Ravelo Arias
2013-12-01
Full Text Available Fractional calculus is considered when derivatives and integrals of non-integer order are applied over a specific function. In the electrical and electronic domain, the transfer function dependence of a fractional filter not only by the filter order n, but additionally, of the fractional order α is an example of a great number of systems where its input-output behavior could be more exactly modeled by a fractional behavior. Following this aim, the present work shows the experimental ac large-signal frequency response of a family of electrical current sensors based in different spintronic conduction mechanisms. Using an ac characterization set-up the sensor transimpedance function is obtained considering it as the relationship between sensor output voltage and input sensing current,[PLEASE CHECK FORMULA IN THE PDF]. The study has been extended to various magnetoresistance sensors based in different technologies like anisotropic magnetoresistance (AMR, giant magnetoresistance (GMR, spin-valve (GMR-SV and tunnel magnetoresistance (TMR. The resulting modeling shows two predominant behaviors, the low-pass and the inverse low-pass with fractional index different from the classical integer response. The TMR technology with internal magnetization offers the best dynamic and sensitivity properties opening the way to develop actual industrial applications.
Monbouquette, H G
1987-06-01
Intrinsic models, which take into account biomass volume fraction, must be formulated for adequate simulation of high-biomass-density fermentations with cell recycle. Through comparison of corresponding intrinsic and non-intrinsic models in dimensionless form, constraints for non-intrinsic model usage in terms of biokinetic and fermenter operating parameters can be identified a priori. Analysis of a simple product-inhibition model indicates that the non-intrinsic approach is suitable only when the attainable biomass volume fraction in the fermentation broth is less than about 0.10. Inappropriate application of a non-intrinsic model can lead to gross errors in calculated substrate and product concentrations, substrate conversion, and volumetric productivity.
Models for high cell density bioreactors must consider biomass volume fraction: cell recycle example
Energy Technology Data Exchange (ETDEWEB)
Monbouquette, H.G.
1987-06-01
Intrinsic models, which take into account biomass volume fraction, must be formulated for adequate simulation of high-biomass-density fermentations with cell recycle. Through comparison of corresponding intrinsic and non-intrinsic models in dimensionless form, constraints for non-intrinsic model usage in terms of biokinetic and fermenter operating parameters can be identified a priori. Analysis of a simple product-inhibition model indicates that the non-intrinsic approach is suitable only when the attainable biomass volume fraction in the fermentation broth is less than about 0.10. Inappropriate application of a non-intrinsic model can lead to gross errors in calculated substrate and product concentrations, substrate conversion, and volumetric productivity. (Refs. 14).
Directory of Open Access Journals (Sweden)
Rafał Stanisławski
2016-01-01
Full Text Available This paper presents new results on modeling and analysis of dynamics of fractional-order discrete-time linear time-invariant single-input single-output (LTI SISO systems by means of new, two-layer, “fractional-order discrete-time Laguerre filters.” It is interesting that the fractionality of the filters at the upper system dynamics layer is directly projected from the lower Laguerre-based approximation layer for the Grünwald-Letnikov difference. A new stability criterion for discrete-time fractional-order Laguerre-based LTI SISO systems is introduced and supplemented with a stability preservation analysis. Both the stability criterion and the stability preservation analysis bring up rather surprising results, which is illustrated with simulation examples.
Fractional poisson--a simple dose-response model for human norovirus.
Messner, Michael J; Berger, Philip; Nappier, Sharon P
2014-10-01
This study utilizes old and new Norovirus (NoV) human challenge data to model the dose-response relationship for human NoV infection. The combined data set is used to update estimates from a previously published beta-Poisson dose-response model that includes parameters for virus aggregation and for a beta-distribution that describes variable susceptibility among hosts. The quality of the beta-Poisson model is examined and a simpler model is proposed. The new model (fractional Poisson) characterizes hosts as either perfectly susceptible or perfectly immune, requiring a single parameter (the fraction of perfectly susceptible hosts) in place of the two-parameter beta-distribution. A second parameter is included to account for virus aggregation in the same fashion as it is added to the beta-Poisson model. Infection probability is simply the product of the probability of nonzero exposure (at least one virus or aggregate is ingested) and the fraction of susceptible hosts. The model is computationally simple and appears to be well suited to the data from the NoV human challenge studies. The model's deviance is similar to that of the beta-Poisson, but with one parameter, rather than two. As a result, the Akaike information criterion favors the fractional Poisson over the beta-Poisson model. At low, environmentally relevant exposure levels (Poisson model; however, caution is advised because no subjects were challenged at such a low dose. New low-dose data would be of great value to further clarify the NoV dose-response relationship and to support improved risk assessment for environmentally relevant exposures. © 2014 Society for Risk Analysis Published 2014. This article is a U.S. Government work and is in the public domain for the U.S.A.
DEFF Research Database (Denmark)
Nielsen, Kræn Vodder; Blanke, Mogens; Eriksson, Lars
2016-01-01
the behavior of the scavenge oxygen fraction well over the entire envelope of load and blower speed range that are relevant for EGR. The simplicity of the new model makes it suitable for observer and control design, which are essential steps to meet the emission requirements for marine diesel engines that take...
Wang, Xiao-Tian; Wu, Min; Zhou, Ze-Min; Jing, Wei-Shu
2012-02-01
This paper deals with the problem of discrete time option pricing using the fractional long memory stochastic volatility model with transaction costs. Through the 'anchoring and adjustment' argument in a discrete time setting, a European call option pricing formula is obtained.
Using Semiotic Resources to Build Images When Teaching the Part-Whole Model of Fractions
Mildenhall, Paula
2013-01-01
This paper reports an exploration into the use of a combination of semiotic resources when teaching the part-whole model of fractions. The study involved a single case study of one class teacher and six students in an Australian primary classroom. Using video as the predominate research tool it was possible to describe how gesture and language…
Hopf bifurcations in a fractional reaction–diffusion model for the ...
African Journals Online (AJOL)
The phenomenon of hopf bifurcation has been well-studied and applied to many physical situations to explain behaviour of solutions resulting from differential and partial differential equations. This phenomenon is applied to a fractional reaction diffusion model for tumor invasion and development. The result suggests that ...
Modelling of stable isotope fractionation by methane oxidation and diffusion in landfill cover soils
International Nuclear Information System (INIS)
Mahieu, Koenraad; De Visscher, Alex; Vanrolleghem, Peter A.; Van Cleemput, Oswald
2008-01-01
A technique to measure biological methane oxidation in landfill cover soils that is gaining increased interest is the measurement of stable isotope fractionation in the methane. Usually to quantify methane oxidation, only fractionation by oxidation is taken into account. Recently it was shown that neglecting the isotope fractionation by diffusion results in underestimation of the methane oxidation. In this study a simulation model was developed that describes gas transport and methane oxidation in landfill cover soils. The model distinguishes between 12 CH 4 , 13 CH 4 , and 12 CH 3 D explicitly, and includes isotope fractionation by diffusion and oxidation. To evaluate the model, the simulations were compared with column experiments from previous studies. The predicted concentration profiles and isotopic profiles match the measured ones very well, with a root mean square deviation (RMSD) of 1.7 vol% in the concentration and a RMSD of 0.8 per mille in the δ 13 C value, with δ 13 C the relative 13 C abundance as compared to an international standard. Overall, the comparison shows that a model-based isotope approach for the determination of methane oxidation efficiencies is feasible and superior to existing isotope methods
Sharp, Emily; Shih Dennis, Minyi
2017-01-01
This study used a multiple probe across participants design to examine the effects of a model drawing strategy (MDS) intervention package on fraction comparing and ordering word problem-solving performance of three Grade 4 students. MDS is a form of cognitive strategy instruction for teaching word problem solving that includes explicit instruction…
Fractional dosing of yellow fever vaccine to extend supply: a modelling study.
Wu, Joseph T; Peak, Corey M; Leung, Gabriel M; Lipsitch, Marc
2016-12-10
The ongoing yellow fever epidemic in Angola strains the global vaccine supply, prompting WHO to adopt dose sparing for its vaccination campaign in Kinshasa, Democratic Republic of the Congo, in July-August, 2016. Although a 5-fold fractional-dose vaccine is similar to standard-dose vaccine in safety and immunogenicity, efficacy is untested. There is an urgent need to ensure the robustness of fractional-dose vaccination by elucidation of the conditions under which dose fractionation would reduce transmission. We estimate the effective reproductive number for yellow fever in Angola using disease natural history and case report data. With simple mathematical models of yellow fever transmission, we calculate the infection attack rate (the proportion of population infected over the course of an epidemic) with various levels of transmissibility and 5-fold fractional-dose vaccine efficacy for two vaccination scenarios, ie, random vaccination in a hypothetical population that is completely susceptible, and the Kinshasa vaccination campaign in July-August, 2016, with different age cutoff for fractional-dose vaccines. We estimate the effective reproductive number early in the Angola outbreak was between 5·2 and 7·1. If vaccine action is all-or-nothing (ie, a proportion of vaccine recipients receive complete protection [VE] and the remainder receive no protection), n-fold fractionation can greatly reduce infection attack rate as long as VE exceeds 1/n. This benefit threshold becomes more stringent if vaccine action is leaky (ie, the susceptibility of each vaccine recipient is reduced by a factor that is equal to the vaccine efficacy). The age cutoff for fractional-dose vaccines chosen by WHO for the Kinshasa vaccination campaign (2 years) provides the largest reduction in infection attack rate if the efficacy of 5-fold fractional-dose vaccines exceeds 20%. Dose fractionation is an effective strategy for reduction of the infection attack rate that would be robust with a
Fractional Dosing of Yellow Fever Vaccine to Extend Supply: A Modeling Study
Peak, Corey M.; Leung, Gabriel M.
2016-01-01
Background The ongoing yellow fever (YF) epidemic in Angola strains the global vaccine supply, prompting WHO to adopt dose sparing for its vaccination campaign in Kinshasa in July–August 2016. Although a 5-fold fractional-dose vaccine is similar to standard-dose vaccine in safety and immunogenicity, efficacy is untested. There is an urgent need to ensure the robustness of fractional-dose vaccination by elucidating the conditions under which dose fractionation would reduce transmission. Methods We estimate the effective reproductive number for YF in Angola using disease natural history and case report data. With simple mathematical models of YF transmission, we calculate the infection attack rate (IAR, the proportion of population infected over the course of an epidemic) under varying levels of transmissibility and five-fold fractional-dose vaccine efficacy for two vaccination scenarios: (i) random vaccination in a hypothetical population that is completely susceptible; (ii) the Kinshasa vaccination campaign in July–August 2016 with different age cutoff for fractional-dose vaccines. Findings We estimate the effective reproductive number early in the Angola outbreak was between 5·2 and 7·1. If vaccine action is all-or-nothing (i.e. a proportion VE of vaccinees receives complete and the remainder receive no protection), n-fold fractionation can dramatically reduce IAR as long as efficacy VE exceeds 1/n. This benefit threshold becomes more stringent if vaccine action is leaky (i.e. the susceptibility of each vaccinee is reduced by a factor that is equal to the vaccine efficacy VE). The age cutoff for fractional-dose vaccines chosen by the WHO for the Kinshasa vaccination campaign (namely, 2 years) provides the largest reduction in IAR if the efficacy of five-fold fractional-dose vaccines exceeds 20%. Interpretation Dose fractionation is a very effective strategy for reducing infection attack rate that would be robust with a large margin for error in case
Directory of Open Access Journals (Sweden)
Petráš Ivo
2011-01-01
Full Text Available This paper deals with the fractional-order linear and nonlinear models used in bioengineering applications and an effective method for their numerical solution. The proposed method is based on the power series expansion of a generating function. Numerical solution is in the form of the difference equation, which can be simply applied in the Matlab/Simulink to simulate the dynamics of system. Several illustrative examples are presented, which can be widely used in bioengineering as well as in the other disciplines, where the fractional calculus is often used.
Computing diffuse fraction of global horizontal solar radiation: A model comparison.
Dervishi, Sokol; Mahdavi, Ardeshir
2012-06-01
For simulation-based prediction of buildings' energy use or expected gains from building-integrated solar energy systems, information on both direct and diffuse component of solar radiation is necessary. Available measured data are, however, typically restricted to global horizontal irradiance. There have been thus many efforts in the past to develop algorithms for the derivation of the diffuse fraction of solar irradiance. In this context, the present paper compares eight models for estimating diffuse fraction of irradiance based on a database of measured irradiance from Vienna, Austria. These models generally involve mathematical formulations with multiple coefficients whose values are typically valid for a specific location. Subsequent to a first comparison of these eight models, three better performing models were selected for a more detailed analysis. Thereby, the coefficients of the models were modified to account for Vienna data. The results suggest that some models can provide relatively reliable estimations of the diffuse fractions of the global irradiance. The calibration procedure could only slightly improve the models' performance.
Modelling the spread of Ebola virus with Atangana-Baleanu fractional operators
Koca, Ilknur
2018-03-01
The model of Ebola spread within a targeted population is extended to the concept of fractional differentiation and integration with non-local and non-singular fading memory introduced by Atangana and Baleanu. It is expected that the proposed model will show better approximation than the models established before. The existence and uniqueness of solutions for the spread of Ebola disease model is given via the Picard-Lindelof method. Finally, numerical solutions for the model are given by using different parameter values.
Plume structure in high-Rayleigh-number convection
Puthenveettil, Baburaj A.; Arakeri, Jaywant H.
2005-10-01
Near-wall structures in turbulent natural convection at Rayleigh numbers of 10^{10} to 10^{11} at A Schmidt number of 602 are visualized by a new method of driving the convection across a fine membrane using concentration differences of sodium chloride. The visualizations show the near-wall flow to consist of sheet plumes. A wide variety of large-scale flow cells, scaling with the cross-section dimension, are observed. Multiple large-scale flow cells are seen at aspect ratio (AR)= 0.65, while only a single circulation cell is detected at AR= 0.435. The cells (or the mean wind) are driven by plumes coming together to form columns of rising lighter fluid. The wind in turn aligns the sheet plumes along the direction of shear. the mean wind direction is seen to change with time. The near-wall dynamics show plumes initiated at points, which elongate to form sheets and then merge. Increase in rayleigh number results in a larger number of closely and regularly spaced plumes. The plume spacings show a common log normal probability distribution function, independent of the rayleigh number and the aspect ratio. We propose that the near-wall structure is made of laminar natural-convection boundary layers, which become unstable to give rise to sheet plumes, and show that the predictions of a model constructed on this hypothesis match the experiments. Based on these findings, we conclude that in the presence of a mean wind, the local near-wall boundary layers associated with each sheet plume in high-rayleigh-number turbulent natural convection are likely to be laminar mixed convection type.
Magin, Richard L.; Li, Weiguo; Velasco, M. Pilar; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.
2011-01-01
We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena (T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter (α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for microstructural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues. PMID:21498095
Stochastic modeling for neural spiking events based on fractional superstatistical Poisson process
Directory of Open Access Journals (Sweden)
Hidetoshi Konno
2018-01-01
Full Text Available In neural spike counting experiments, it is known that there are two main features: (i the counting number has a fractional power-law growth with time and (ii the waiting time (i.e., the inter-spike-interval distribution has a heavy tail. The method of superstatistical Poisson processes (SSPPs is examined whether these main features are properly modeled. Although various mixed/compound Poisson processes are generated with selecting a suitable distribution of the birth-rate of spiking neurons, only the second feature (ii can be modeled by the method of SSPPs. Namely, the first one (i associated with the effect of long-memory cannot be modeled properly. Then, it is shown that the two main features can be modeled successfully by a class of fractional SSPP (FSSPP.
Stochastic modeling for neural spiking events based on fractional superstatistical Poisson process
Konno, Hidetoshi; Tamura, Yoshiyasu
2018-01-01
In neural spike counting experiments, it is known that there are two main features: (i) the counting number has a fractional power-law growth with time and (ii) the waiting time (i.e., the inter-spike-interval) distribution has a heavy tail. The method of superstatistical Poisson processes (SSPPs) is examined whether these main features are properly modeled. Although various mixed/compound Poisson processes are generated with selecting a suitable distribution of the birth-rate of spiking neurons, only the second feature (ii) can be modeled by the method of SSPPs. Namely, the first one (i) associated with the effect of long-memory cannot be modeled properly. Then, it is shown that the two main features can be modeled successfully by a class of fractional SSPP (FSSPP).
Eluru, Naveen; Chakour, Vincent; Chamberlain, Morgan; Miranda-Moreno, Luis F
2013-10-01
Vehicle operating speed measured on roadways is a critical component for a host of analysis in the transportation field including transportation safety, traffic flow modeling, roadway geometric design, vehicle emissions modeling, and road user route decisions. The current research effort contributes to the literature on examining vehicle speed on urban roads methodologically and substantively. In terms of methodology, we formulate a new econometric model framework for examining speed profiles. The proposed model is an ordered response formulation of a fractional split model. The ordered nature of the speed variable allows us to propose an ordered variant of the fractional split model in the literature. The proposed formulation allows us to model the proportion of vehicles traveling in each speed interval for the entire segment of roadway. We extend the model to allow the influence of exogenous variables to vary across the population. Further, we develop a panel mixed version of the fractional split model to account for the influence of site-specific unobserved effects. The paper contributes substantively by estimating the proposed model using a unique dataset from Montreal consisting of weekly speed data (collected in hourly intervals) for about 50 local roads and 70 arterial roads. We estimate separate models for local roads and arterial roads. The model estimation exercise considers a whole host of variables including geometric design attributes, roadway attributes, traffic characteristics and environmental factors. The model results highlight the role of various street characteristics including number of lanes, presence of parking, presence of sidewalks, vertical grade, and bicycle route on vehicle speed proportions. The results also highlight the presence of site-specific unobserved effects influencing the speed distribution. The parameters from the modeling exercise are validated using a hold-out sample not considered for model estimation. The results indicate
Gao, Feng-Yin; Kang, Yan-Mei; Chen, Xi; Chen, Guanrong
2018-05-01
This paper reveals the effect of fractional Gaussian noise with Hurst exponent H ∈(1 /2 ,1 ) on the information capacity of a general nonlinear neuron model with binary signal input. The fGn and its corresponding fractional Brownian motion exhibit long-range, strong-dependent increments. It extends standard Brownian motion to many types of fractional processes found in nature, such as the synaptic noise. In the paper, for the subthreshold binary signal, sufficient conditions are given based on the "forbidden interval" theorem to guarantee the occurrence of stochastic resonance, while for the suprathreshold binary signal, the simulated results show that additive fGn with Hurst exponent H ∈(1 /2 ,1 ) could increase the mutual information or bits count. The investigation indicated that the synaptic noise with the characters of long-range dependence and self-similarity might be the driving factor for the efficient encoding and decoding of the nervous system.
International Nuclear Information System (INIS)
Reis, Arlene A. dos; Cardoso, Joaquim C.S.; Lourenco, Maria Cristina
2005-01-01
The Publication 66 of International Commission of Radiological Protection (ICRP, 1994) presented the Human Respiratory tract Model that simulates the deposition and translocation of radioactive material in the air that penetrates in the body by inhalation. The main objective of this study is to evaluate the variation in fractional activity absorbed into blood when physiological and morphological parameters from Brazilian population are applied in the deposition model. The clearance model was implemented in the software Excel (version 2000) using a system of differential equations to solve simultaneous process of translocation and absorption of material deposited. After implementation were applied in the model fractional deposition calculated by deposition model using physiological and morphological parameters from Brazilian population. The results show that the variation in the clearance model depends on the material dissolution. For materials of rapid absorption, the variations calculated are not significant. Materials of moderate and slow absorption, presented variation greater than 20% in fractional activity absorbed into blood, depending on levels of exercise. (author)
Analysis of two colliding fractionally damped spherical shells in modelling blunt human head impacts
Rossikhin, Yury A.; Shitikova, Marina V.
2013-06-01
The collision of two elastic or viscoelastic spherical shells is investigated as a model for the dynamic response of a human head impacted by another head or by some spherical object. Determination of the impact force that is actually being transmitted to bone will require the model for the shock interaction of the impactor and human head. This model is indended to be used in simulating crash scenarios in frontal impacts, and provide an effective tool to estimate the severity of effect on the human head and to estimate brain injury risks. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. It is assumed that the viscoelastic features of the shells are exhibited only in the contact domain, while the remaining parts retain their elastic properties. In this case, the contact spot is assumed to be a plane disk with constant radius, and the viscoelastic features of the shells are described by the fractional derivative standard linear solid model. In the case under consideration, the governing differential equations are solved analytically by the Laplace transform technique. It is shown that the fractional parameter of the fractional derivative model plays very important role, since its variation allows one to take into account the age-related changes in the mechanical properties of bone.
Long-range transport and global fractionation of POPs: insights from multimedia modeling studies
International Nuclear Information System (INIS)
Scheringer, M.; Salzmann, M.; Stroebe, M.; Wegmann, F.; Fenner, K.; Hungerbuehler, K.
2004-01-01
The long-range transport of persistent organic pollutants (POPs) is investigated with two multimedia box models of the global system. ChemRange is a purely evaluative, one-dimensional steady-state (level III) model; CliMoChem is a two-dimensional model with different temperatures, land/water ratios and vegetation types in different latitudinal zones. Model results are presented for three case studies: (i) the effect of atmospheric aerosol particles on the long-range transport of POPs, (ii) the effect of oceanic deposition on the long-range transport of different PCB congeners, (iii) the global fractionation of different PCB congeners. The model results for these case studies show: (i) the low atmospheric half-lives estimated for several organochlorine pesticides are likely to be inconsistent with the observed long-range transport of these compounds; (ii) export to the deep sea reduces the potential for long-range transport of highly hydrophobic compounds (but does not remove these chemicals from the biosphere); (iii) there are different meanings of the term global fractionation that refer to different aspects of the fractionation process and need to be distinguished. The case-study results further indicate that the influences of varying environmental conditions on the physicochemical properties and the degradation rate constants of POPs need to be determined. - Multimedia box models are applied to case studies of the behavior of POPs
Energy Technology Data Exchange (ETDEWEB)
Julia, J; Nyblade, A; Hansen, S; Rodgers, A; Matzel, E
2009-07-06
In this project, we are developing models of lithospheric structure for a wide variety of tectonic regions throughout Eurasia and the Middle East by regionalizing 1D velocity models obtained by jointly inverting P-wave and S-wave receiver functions with Rayleigh wave group and phase velocities. We expect the regionalized velocity models will improve our ability to predict travel-times for local and regional phases, such as Pg, Pn, Sn and Lg, as well as travel-times for body-waves at upper mantle triplication distances in both seismic and aseismic regions of Eurasia and the Middle East. We anticipate the models will help inform and strengthen ongoing and future efforts within the NNSA labs to develop 3D velocity models for Eurasia and the Middle East, and will assist in obtaining model-based predictions where no empirical data are available and for improving locations from sparse networks using kriging. The codes needed to conduct the joint inversion of P-wave receiver functions (PRFs), S-wave receiver functions (SRFs), and dispersion velocities have already been assembled as part of ongoing research on lithospheric structure in Africa. The methodology has been tested with synthetic 'data' and case studies have been investigated with data collected at an open broadband stations in South Africa. PRFs constrain the size and S-P travel-time of seismic discontinuities in the crust and uppermost mantle, SRFs constrain the size and P-S travel-time of the lithosphere-asthenosphere boundary, and dispersion velocities constrain average S-wave velocity within frequency-dependent depth-ranges. Preliminary results show that the combination yields integrated 1D velocity models local to the recording station, where the discontinuities constrained by the receiver functions are superimposed to a background velocity model constrained by the dispersion velocities. In our first year of this project we will (i) generate 1D velocity models for open broadband seismic stations
Longhi, J.
1977-01-01
A description is presented of an empirical model of fractional crystallization which predicts that slightly modified versions of certain of the proposed whole moon compositions can reproduce the major-element chemistry and mineralogy of most of the primitive highland rocks through equilibrium and fractional crystallization processes combined with accumulation of crystals and trapping of residual liquids. These compositions contain sufficient Al to form a plagioclase-rich crust 60 km thick on top of a magma ocean that was initially no deeper than about 300 km. Implicit in the model are the assumptions that all cooling and crystallization take place at low pressure and that there are no compositional or thermal gradients in the liquid. Discussions of the cooling and crystallization of the proposed magma ocean show these assumptions to be disturbingly naive when applied to the ocean as a whole. However, the model need not be applied to the whole ocean, but only to layers of cooling liquid near the surface.
Frequency dependence of complex moduli of brain tissue using a fractional Zener model
International Nuclear Information System (INIS)
Kohandel, M; Sivaloganathan, S; Tenti, G; Darvish, K
2005-01-01
Brain tissue exhibits viscoelastic behaviour. If loading times are substantially short, static tests are not sufficient to determine the complete viscoelastic behaviour of the material, and dynamic test methods are more appropriate. The concept of complex modulus of elasticity is a powerful tool for characterizing the frequency domain behaviour of viscoelastic materials. On the other hand, it is well known that classical viscoelastic models can be generalized by means of fractional calculus to describe more complex viscoelastic behaviour of materials. In this paper, the fractional Zener model is investigated in order to describe the dynamic behaviour of brain tissue. The model is fitted to experimental data of oscillatory shear tests of bovine brain tissue to verify its behaviour and to obtain the material parameters
Doubly 15N-substituted diazenylium: THz laboratory spectra and fractionation models
Dore, L.; Bizzocchi, L.; Wirström, E. S.; Degli Esposti, C.; Tamassia, F.; Charnley, S. B.
2017-07-01
Context. Isotopic fractionation in dense molecular cores has been suggested as a possible origin of large 14N/15N ratio variations in solar system materials. While chemical models can explain some observed variations with different fractionation patterns for molecules with -NH or -CN functional groups, they fail to reproduce the observed ratios in diazenylium (N2H+). Aims: Observations of doubly 15N-substituted species could provide important constraints and insights for theoretical chemical models of isotopic fractionation. However, spectroscopic data are very scarce. Methods: The rotational spectra of the fully 15N-substituted isopologues of the diazenylium ion, 15N2H+ and 15N2D+, have been investigated in the laboratory well into the THz region by using a source-modulation microwave spectrometer equipped with a negative glow discharge cell. An extended chemical reaction network has been used to estimate what ranges of 15N fractionation in doubly 15N-substituted species could be expected in the interstellar medium (ISM). Results: For each isotopologue of the H- and D-containing pair, nine rotational transitions were accurately measured in the frequency region 88 GHz-1.2 THz. The analysis of the spectrum provided very precise rest frequencies at millimeter and sub-millimeter wavelengths, useful for the radioastronomical identification of the rotational lines of 15N2H+ and 15N2D+ in the ISM.
Lubrication pressure and fractional viscous damping effects on the spring-block model of earthquakes
Tanekou, G. B.; Fogang, C. F.; Kengne, R.; Pelap, F. B.
2018-04-01
We examine the dynamical behaviours of the "single mass-spring" model for earthquakes considering lubrication pressure effects on pre-existing faults and viscous fractional damping. The lubrication pressure supports a part of the load, thereby reducing the normal stress and the associated friction across the gap. During the co-seismic phase, all of the strain accumulated during the inter-seismic duration does not recover; a fraction of this strain remains as a result of viscous relaxation. Viscous damping friction makes it possible to study rocks at depth possessing visco-elastic behaviours. At increasing depths, rock deformation gradually transitions from brittle to ductile. The fractional derivative is based on the properties of rocks, including information about previous deformation events ( i.e., the so-called memory effect). Increasing the fractional derivative can extend or delay the transition from stick-slip oscillation to a stable equilibrium state and even suppress it. For the single block model, the interactions of the introduced lubrication pressure and viscous damping are found to give rise to oscillation death, which corresponds to aseismic fault behaviour. Our result shows that the earthquake occurrence increases with increases in both the damping coefficient and the lubrication pressure. We have also revealed that the accumulation of large stresses can be controlled via artificial lubrication.
Bivariate Rayleigh Distribution and its Properties
Directory of Open Access Journals (Sweden)
Ahmad Saeed Akhter
2007-01-01
Full Text Available Rayleigh (1880 observed that the sea waves follow no law because of the complexities of the sea, but it has been seen that the probability distributions of wave heights, wave length, wave induce pitch, wave and heave motions of the ships follow the Rayleigh distribution. At present, several different quantities are in use for describing the state of the sea; for example, the mean height of the waves, the root mean square height, the height of the “significant waves” (the mean height of the highest one-third of all the waves the maximum height over a given interval of the time, and so on. At present, the ship building industry knows less than any other construction industry about the service conditions under which it must operate. Only small efforts have been made to establish the stresses and motions and to incorporate the result of such studies in to design. This is due to the complexity of the problem caused by the extensive variability of the sea and the corresponding response of the ships. Although the problem appears feasible, yet it is possible to predict service conditions for ships in an orderly and relatively simple manner Rayleigh (1980 derived it from the amplitude of sound resulting from many independent sources. This distribution is also connected with one or two dimensions and is sometimes referred to as “random walk” frequency distribution. The Rayleigh distribution can be derived from the bivariate normal distribution when the variate are independent and random with equal variances. We try to construct bivariate Rayleigh distribution with marginal Rayleigh distribution function and discuss its fundamental properties.
Dipierro, Serena; Valdinoci, Enrico
2018-07-01
Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of hyperbolic equations, which typically exhibit shocks and discontinuities. In this paper, we show how a simple toy-model of a highly ramified structure, somehow inspired by that of the Purkinje cells, may produce a fractional diffusion via the superposition of travelling waves that solve a hyperbolic equation. This could suggest that the high ramification of the Purkinje cells might have provided an evolutionary advantage of "smoothing" the transmission of signals and avoiding shock propagations (at the price of slowing a bit such transmission). Although an experimental confirmation of the possibility of such evolutionary advantage goes well beyond the goals of this paper, we think that it is intriguing, as a mathematical counterpart, to consider the time fractional diffusion as arising from the superposition of delayed travelling waves in highly ramified transmission media. The case of a travelling concave parabola with sufficiently small curvature is explicitly computed. The new link that we propose between time fractional diffusion and hyperbolic equation also provides a novelty with respect to the usual paradigm relating time fractional diffusion with parabolic equations in the limit. This paper is written in such a way as to be of interest to both biologists and mathematician alike. In order to accomplish this aim, both complete explanations of the objects considered and detailed lists of references are provided.
Cheong, Chin Wen
2008-02-01
This article investigated the influences of structural breaks on the fractionally integrated time-varying volatility model in the Malaysian stock markets which included the Kuala Lumpur composite index and four major sectoral indices. A fractionally integrated time-varying volatility model combined with sudden changes is developed to study the possibility of structural change in the empirical data sets. Our empirical results showed substantial reduction in fractional differencing parameters after the inclusion of structural change during the Asian financial and currency crises. Moreover, the fractionally integrated model with sudden change in volatility performed better in the estimation and specification evaluations.
Attractors of the periodically forced Rayleigh system
Directory of Open Access Journals (Sweden)
Petre Bazavan
2011-07-01
Full Text Available The autonomous second order nonlinear ordinary differential equation(ODE introduced in 1883 by Lord Rayleigh, is the equation whichappears to be the closest to the ODE of the harmonic oscillator withdumping.In this paper we present a numerical study of the periodic andchaotic attractors in the dynamical system associated with the generalized Rayleigh equation. Transition between periodic and quasiperiodic motion is also studied. Numerical results describe the system dynamics changes (in particular bifurcations, when the forcing frequency is varied and thus, periodic, quasiperiodic or chaotic behaviour regions are predicted.
Fernández-Manso, O.; Fernández-Manso, A.; Quintano, C.
2014-09-01
Aboveground biomass (AGB) estimation from optical satellite data is usually based on regression models of original or synthetic bands. To overcome the poor relation between AGB and spectral bands due to mixed-pixels when a medium spatial resolution sensor is considered, we propose to base the AGB estimation on fraction images from Linear Spectral Mixture Analysis (LSMA). Our study area is a managed Mediterranean pine woodland (Pinus pinaster Ait.) in central Spain. A total of 1033 circular field plots were used to estimate AGB from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) optical data. We applied Pearson correlation statistics and stepwise multiple regression to identify suitable predictors from the set of variables of original bands, fraction imagery, Normalized Difference Vegetation Index and Tasselled Cap components. Four linear models and one nonlinear model were tested. A linear combination of ASTER band 2 (red, 0.630-0.690 μm), band 8 (short wave infrared 5, 2.295-2.365 μm) and green vegetation fraction (from LSMA) was the best AGB predictor (Radj2=0.632, the root-mean-squared error of estimated AGB was 13.3 Mg ha-1 (or 37.7%), resulting from cross-validation), rather than other combinations of the above cited independent variables. Results indicated that using ASTER fraction images in regression models improves the AGB estimation in Mediterranean pine forests. The spatial distribution of the estimated AGB, based on a multiple linear regression model, may be used as baseline information for forest managers in future studies, such as quantifying the regional carbon budget, fuel accumulation or monitoring of management practices.
A New Model of the Fractional Order Dynamics of the Planetary Gears
Directory of Open Access Journals (Sweden)
Vera Nikolic-Stanojevic
2013-01-01
Full Text Available A theoretical model of planetary gears dynamics is presented. Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. In the paper, it has been indicated that even the small disturbance in design realizations of this gear cause nonlinear properties of dynamics which are the source of vibrations and noise in the gear transmission. Dynamic model of the planetary gears with four degrees of freedom is used. Applying the basic principles of analytical mechanics and taking the initial and boundary conditions into consideration, it is possible to obtain the system of equations representing physical meshing process between the two or more gears. This investigation was focused to a new model of the fractional order dynamics of the planetary gear. For this model analytical expressions for the corresponding fractional order modes like one frequency eigen vibrational modes are obtained. For one planetary gear, eigen fractional modes are obtained, and a visualization is presented. By using MathCAD the solution is obtained.
Shear flow stabilization of the hydromagnetic Rayleigh-Taylor instability
International Nuclear Information System (INIS)
Roderick, N.F.; Shumlak, U.; Douglas, M.; Peterkin, R.E. Jr.; Ruden, E.
1997-01-01
Numerical simulations have indicated that shear flow may help stabilize the hydromagnetic Rayleigh-Taylor instability in imploding plasma z-pinches. A simple extension to a model presented in Chandrasekhar has been developed to study the linear stability of incompressible plasma subjected to both a shear flow and acceleration. The model has been used to investigate the stability plasma implosion schemes using externally imposed velocity shear which develops from the plasma flow itself. Specific parameters were chosen to represent plasma implosions driven by the Saturn and PBFA-Z, pulsed power generators at Sandia National Laboratories. Results indicate a high shear is necessary to stabilize the z-pinch implosions studied
DEFF Research Database (Denmark)
Stegmann, Mikkel Bille; Pedersen, Dorthe
2005-01-01
in four-dimensional MRI. The theoretical foundation of our work is the generative two-dimensional Active Appearance Models by Cootes et al., here extended to bi-temporal, three-dimensional models. Further issues treated include correction of respiratory induced slice displacements, systole detection......, and a texture model pruning strategy. Cross-validation carried out on clinical-quality scans of twelve volunteers indicates that ejection fraction and cardiac blood pool volumes can be estimated automatically and rapidly with accuracy on par with typical inter-observer variability....
Epps, Brenden; Cushman-Roisin, Benoit
2017-11-01
Fluid turbulence is an outstanding unsolved problem in classical physics, despite 120+ years of sustained effort. Given this history, we assert that a new mathematical framework is needed to make a transformative breakthrough. This talk offers one such framework, based upon kinetic theory tied to the statistics of turbulent transport. Starting from the Boltzmann equation and ``Lévy α-stable distributions'', we derive a turbulence model that expresses the turbulent stresses in the form of a fractional derivative, where the fractional order is tied to the transport behavior of the flow. Initial results are presented herein, for the cases of Couette-Poiseuille flow and 2D boundary layers. Among other results, our model is able to reproduce the logarithmic Law of the Wall in shear turbulence.
On the continuing relevance of Mandelbrot's non-ergodic fractional renewal models of 1963 to 1967
Watkins, Nicholas W.
2017-12-01
The problem of "1/f" noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot's fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, and their links to the CTRW, I present preliminary results of my research into the history of Mandelbrot's very little known work in that area from 1963 to 1967. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, "1/f" noise and LRD, concepts which are often treated as equivalent. Contribution to the "Topical Issue: Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Structural analysis of gluten-free doughs by fractional rheological model
Orczykowska, Magdalena; Dziubiński, Marek; Owczarz, Piotr
2015-02-01
This study examines the effects of various components of tested gluten-free doughs, such as corn starch, amaranth flour, pea protein isolate, and cellulose in the form of plantain fibers on rheological properties of such doughs. The rheological properties of gluten-free doughs were assessed by using the rheological fractional standard linear solid model (FSLSM). Parameter analysis of the Maxwell-Wiechert fractional derivative rheological model allows to state that gluten-free doughs present a typical behavior of viscoelastic quasi-solid bodies. We obtained the contribution dependence of each component used in preparations of gluten-free doughs (either hard-gel or soft-gel structure). The complicate analysis of the mechanical structure of gluten-free dough was done by applying the FSLSM to explain quite precisely the effects of individual ingredients of the dough on its rheological properties.
Modelling and simulation of a dynamical system with the Atangana-Baleanu fractional derivative
Owolabi, Kolade M.
2018-01-01
In this paper, we model an ecological system consisting of a predator and two preys with the newly derived two-step fractional Adams-Bashforth method via the Atangana-Baleanu derivative in the Caputo sense. We analyze the dynamical system for correct choice of parameter values that are biologically meaningful. The local analysis of the main model is based on the application of qualitative theory for ordinary differential equations. By using the fixed point theorem idea, we establish the existence and uniqueness of the solutions. Convergence results of the new scheme are verified in both space and time. Dynamical wave phenomena of solutions are verified via some numerical results obtained for different values of the fractional index, which have some interesting ecological implications.
Modelling the fine and coarse fraction of Pb, Cd, As and Ni air concentration in Spain
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, M. A.; Vivanco, M. G.
2015-07-01
Lead, cadmium, arsenic and nickel are present in the air due to natural and anthropogenic emissions, normally joined to particles. Human health and ecosystems can be damaged by high atmospheric levels of these metals, since they can be introduced in organisms via inhalation or ingestion. Small particles are inhaled and embebed in lungs and alveolus more easily than coarse particles. The CHIMERE model is a eulerian air quality model extensively used in air quality modelling. Metals have been recently included in this model in a special version developed in the CIEMAT modelling group (Madrid, Spain). Vivanco et al. (2011) and Gonzalez et al. (2012) showed an evaluation of the model performance for some metals in Spain and Europe. In these studies, metals were considered as fine particles. Nevertheless there is some observational evidence of the presence of some metals also in the coarse fraction. For this reason, a new attempt of modelling metals considering a fine (<2.5 μm) and coarse (2.5-10 μm) fraction has been done. Measurements of metal concentration in PM10, PM2.5 and PM1 recorded in Spain were used to obtain the new metal particle distribution size. On the other hand, natural emissions, not considered in the above mentioned studies, were implemented in the model, by considering metal emissions associated to dust resuspensiont. An evaluation of the new version is presented and discussed for two domains in Spain, centered on Barcelona and Huelva respectively. (Author)
Modelling the fine and coarse fraction of Pb, Cd, As and Ni air concentration in Spain
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, M.A.; Vivanco, M.
2015-07-01
Lead, cadmium, arsenic and nickel are present in the air due to natural and anthropogenic emissions, normally joined to particles. Human health and ecosystems can be damaged by high atmospheric levels of these metals, since they can be introduced in organisms via inhalation or ingestion. Small particles are inhaled and embebed in lungs and alveolus more easily than coarse particles. The CHIMERE model is a eulerian air quality model extensively used in air quality modelling. Metals have been recently included in this model in a special version developed in the CIEMAT modelling group (Madrid, Spain). Vivanco et al. (2011) and González et al. (2012) showed an evaluation of the model performance for some metals in Spain and Europe. In these studies, metals were considered as fine particles. Nevertheless there is some observational evidence of the presence of some metals also in the coarse fraction. For this reason, a new attempt of modelling metals considering a fine (<2.5 μm) and coarse (2.5-10 μm) fraction has been done. Measurements of metal concentration in PM10, PM2.5 and PM1 recorded in Spain were used to obtain the new metal particle distribution size. On the other hand, natural emissions, not considered in the above mentioned studies, were implemented in the model, by considering metal emissions associated to dust resuspensiont. An evaluation of the new version is presented and discussed for two domains in Spain, centered on Barcelona and Huelva respectively. (Author)
Modelling the fine and coarse fraction of Pb, Cd, As and Ni air concentration in Spain
International Nuclear Information System (INIS)
Gonzalez, M. A.; Vivanco, M. G.
2015-01-01
Lead, cadmium, arsenic and nickel are present in the air due to natural and anthropogenic emissions, normally joined to particles. Human health and ecosystems can be damaged by high atmospheric levels of these metals, since they can be introduced in organisms via inhalation or ingestion. Small particles are inhaled and embebed in lungs and alveolus more easily than coarse particles. The CHIMERE model is a eulerian air quality model extensively used in air quality modelling. Metals have been recently included in this model in a special version developed in the CIEMAT modelling group (Madrid, Spain). Vivanco et al. (2011) and Gonzalez et al. (2012) showed an evaluation of the model performance for some metals in Spain and Europe. In these studies, metals were considered as fine particles. Nevertheless there is some observational evidence of the presence of some metals also in the coarse fraction. For this reason, a new attempt of modelling metals considering a fine (<2.5 μm) and coarse (2.5-10 μm) fraction has been done. Measurements of metal concentration in PM10, PM2.5 and PM1 recorded in Spain were used to obtain the new metal particle distribution size. On the other hand, natural emissions, not considered in the above mentioned studies, were implemented in the model, by considering metal emissions associated to dust resuspensiont. An evaluation of the new version is presented and discussed for two domains in Spain, centered on Barcelona and Huelva respectively. (Author)
Directory of Open Access Journals (Sweden)
Ernesto Amato
2014-03-01
Full Text Available We developed a general model for the calculation of absorbed fractions in ellipsoidal volumes of soft tissue uniformly filled with alpha, beta and gamma emitting radionuclides. The approach exploited Monte Carlo simulations with the Geant4 code to determine absorbed fractions in ellipsoids characterized by a wide range of dimensions and ellipticities, for monoenergetic emissions of each radiation type. The so-obtained absorbed fractions were put in an analytical relationship with the 'generalized radius', calculated as 3V/S, where V is the ellipsoid volume and S its surface. Radiation-specific parametric functions were obtained in order to calculate the absorbed fraction of a given radiation in a generic ellipsoidal volume. The dose from a generic radionuclide can be calculated through a process of summation and integration over the whole radionuclide emission spectrum, profitably implemented in an electronic spreadsheet. We compared the results of our analytical calculation approach with those obtained from the OLINDA/EXM computer software, finding a good agreement in a wide range of sphere radii, for the high-energy pure beta emitter 90Y, the commonly employed beta-gamma emitter 131I, and the pure alpha emitter 213Po. The generality of our approach makes it useful an easy to implement in clinical dosimetry calculations as well as in radiation safety estimations when doses from internal radionuclide uptake are to be taken into account.
Wildschut, J.; Arentz, J.; Rasrendra, C. B.; Venderbosch, R. H.; Heeres, H. J.
2009-01-01
Fast pyrolysis oil can be upgraded by a catalytic hydrotreatment (250-400 degrees C, 100-200 bar) using heterogeneous catalysts such as Ru/C to hydrocarbon-like products that can serve as liquid transportation fuels. Insight into the complex reaction pathways of the various component fractions during hydrotreatment is desirable to reduce the formation of by-products such as char and gaseous components. This paper deals with the catalytic hydrotreatment of representative model components for t...
Robertson, Andy; Schipanski, Meagan; Sherrod, Lucretia; Ma, Liwang; Ahuja, Lajpat; McNamara, Niall; Smith, Pete; Davies, Christian
2016-04-01
Agriculture, covering more than 30% of global land area, has an exciting opportunity to help combat climate change by effectively managing its soil to promote increased C sequestration. Further, newly sequestered soil carbon (C) through agriculture needs to be stored in more stable forms in order to have a lasting impact on reducing atmospheric CO2 concentrations. While land uses in different climates and soils require different management strategies, the fundamental mechanisms that regulate C sequestration and stabilisation remain the same. These mechanisms are used by a number of different systems models to simulate C dynamics, and thus assess the impacts of change in management or climate. To evaluate the accuracy of these model simulations, our research uses a multidirectional approach to compare C stocks of physicochemical soil fractions collected at two long-term agricultural sites. Carbon stocks for a number of soil fractions were measured at two sites (Lincoln, UK; Colorado, USA) over 8 and 12 years, respectively. Both sites represent managed agricultural land but have notably different climates and levels of disturbance. The measured soil fractions act as proxies for varying degrees of stability, with C contained within these fractions relatable to the C simulated within the soil pools of mechanistic systems models1. Using stable isotope techniques at the UK site, specific turnover times of C within the different fractions were determined and compared with those simulated in the pools of 3 different models of varying complexity (RothC, DayCent and RZWQM2). Further, C dynamics and N-mineralisation rates of the measured fractions at the US site were assessed and compared to results of the same three models. The UK site saw a significant increase in C stocks within the most stable fractions, with topsoil (0-30cm) sequestration rates of just over 0.3 tC ha-1 yr-1 after only 8 years. Further, the sum of all fractions reported C sequestration rates of nearly 1
Fractional calculus model of articular cartilage based on experimental stress-relaxation
Smyth, P. A.; Green, I.
2015-05-01
Articular cartilage is a unique substance that protects joints from damage and wear. Many decades of research have led to detailed biphasic and triphasic models for the intricate structure and behavior of cartilage. However, the models contain many assumptions on boundary conditions, permeability, viscosity, model size, loading, etc., that complicate the description of cartilage. For impact studies or biomimetic applications, cartilage can be studied phenomenologically to reduce modeling complexity. This work reports experimental results on the stress-relaxation of equine articular cartilage in unconfined loading. The response is described by a fractional calculus viscoelastic model, which gives storage and loss moduli as functions of frequency, rendering multiple advantages: (1) the fractional calculus model is robust, meaning that fewer constants are needed to accurately capture a wide spectrum of viscoelastic behavior compared to other viscoelastic models (e.g., Prony series), (2) in the special case where the fractional derivative is 1/2, it is shown that there is a straightforward time-domain representation, (3) the eigenvalue problem is simplified in subsequent dynamic studies, and (4) cartilage stress-relaxation can be described with as few as three constants, giving an advantage for large-scale dynamic studies that account for joint motion or impact. Moreover, the resulting storage and loss moduli can quantify healthy, damaged, or cultured cartilage, as well as artificial joints. The proposed characterization is suited for high-level analysis of multiphase materials, where the separate contribution of each phase is not desired. Potential uses of this analysis include biomimetic dampers and bearings, or artificial joints where the effective stiffness and damping are fundamental parameters.
First measurement of the Rayleigh cross section
Naus, H.; Ubachs, W.
2000-01-01
Rayleigh cross section for N2, Ar and SF6 was performed using the technique of cavity ring-down spectroscopy (CRDS). The experiment was based on the assumption that scattering cross section is equal to the extinction in the absence of absorption. The theory explains the molecular origin of
Development of a three dimensional circulation model based on fractional step method
Directory of Open Access Journals (Sweden)
Mazen Abualtayef
2010-03-01
Full Text Available A numerical model was developed for simulating a three-dimensional multilayer hydrodynamic and thermodynamic model in domains with irregular bottom topography. The model was designed for examining the interactions between flow and topography. The model was based on the three-dimensional Navier-Stokes equations and was solved using the fractional step method, which combines the finite difference method in the horizontal plane and the finite element method in the vertical plane. The numerical techniques were described and the model test and application were presented. For the model application to the northern part of Ariake Sea, the hydrodynamic and thermodynamic results were predicted. The numerically predicted amplitudes and phase angles were well consistent with the field observations.
Directory of Open Access Journals (Sweden)
J.-P. Lhomme
1999-01-01
Full Text Available In many experimental conditions, the evaporative fraction, defined as the ratio between evaporation and available energy, has been found stable during daylight hours. This constancy is investigated over fully covering vegetation by means of a land surface scheme coupled with a mixed-layer model, which accounts for entrainment of overlying air. The evaporation rate follows the Penman-Monteith equation and the surface resistance is given by a Jarvis type parameterization involving solar radiation, saturation deficit and leaf water potential. The diurnal course of the evaporative fraction is examined, together with the influence of environmental factors (soil water availability, solar radiation input, wind velocity, saturation deficit above the well-mixed layer. In conditions of fair weather, the curves representing the diurnal course of the evaporative fraction have a typical concave-up shape. Around midday (solar time these curves appear as relatively constant, but always lower that the daytime mean value. Evaporative fraction decreases when soil water decreases or when solar energy increases. An increment of saturation deficit above the mixed-layer provokes only a slight increase of evaporative fraction, and wind velocity has almost no effect. The possibility of estimation daytime evaporation from daytime available energy multiplied by the evaporative fraction at a single time of the day is also investigated. It appears that it is possible to obtain fairly good estimates of daytime evaporation by choosing adequately the time of the measurement of the evaporative fraction. The central hours of the day, and preferably about 3 hr before or after noon, are the most appropriate to provide good estimates. The estimation appears also to be much better when soil water availability (or evaporation is high than when it is low.
Energy Technology Data Exchange (ETDEWEB)
Ludden, J.N.; Thompson, G.; Bryan, W.B.; Frey, F.A.
1980-08-10
Ferrobasalts from DSDP sites 214 and 216 on the Ninetyeast Ridge are characterized by high absolute iron (FeO>12.9 wt %), FeO/MgO>1.9, and TiO/sub 2/>2.0 wt %. Their trace element abundances indicate a tholeiitic affinity; however, they are distinct from midocean ridge incompatible element-depleted tholeiites owing to higher contents of Ba, Zr, and Sr and flat to slightly light-REE-enriched, chondrite-normalized REE patterns. Calculations using major and trace element abundances and phase compositions are generally consistent with a model relating most major elements and phase compositions in site 214 and 216 ferrobasalts by fractionation of clinopyroxene and plagio-class. However, some incompatible element abundances for site 216 basalts are not consistent with the fractional crystallization models. Baslats from site 214 can be related to andesitic rocks from the same site by fractionating clinopyroxene, plagioclase and titanomagnetite. Site 254 basalts, at the southern end of the Ninetyeast Ridge, and island tholeiites in the southern Indian Ocean (Amsterdam-St. Paul or Kerguelen-Heard volcanic provinces) possibly represent the most recent activity associated with a hot spot forming the Ninetyeast Ridge. These incompatible-element-enriched tholeiites have major element compositions consistent with those expected for a parental liquid for the site 214 and 216 ferrobasalts. However, differences in the trace element contents of the basalts from the Ninetyeast Ridge sites are not consistent with simple fractional crystallization derivation but require either a complex melting model or a heterogeneous mantle source.
Simons, J.-P.; Hilst, R.D. van der; Montagner, F.J.,; Zielhuis, A.
2002-01-01
We present an azimuthally anisotropic 3-D shear-wave speed model of the Australian upper mantle obtained from the dispersion of fundamental and higher modes of Rayleigh waves.We compare two tomographic techniques to map path-average earth models into a 3-D model for heterogeneity and azimuthal
Fractional Generalizations of Maxwell and Kelvin-Voigt Models for Biopolymer Characterization.
Directory of Open Access Journals (Sweden)
Bertrand Jóźwiak
Full Text Available The paper proposes a fractional generalization of the Maxwell and Kelvin-Voigt rheological models for a description of dynamic behavior of biopolymer materials. It was found that the rheological models of Maxwell-type do not work in the case of modeling of viscoelastic solids, and the model which significantly better describes the nature of changes in rheological properties of such media is the modified fractional Kelvin-Voigt model with two built-in springpots (MFKVM2. The proposed model was used to describe the experimental data from the oscillatory and creep tests of 3% (w/v kuzu starch pastes, and to determine the values of their rheological parameters as a function of pasting time. These parameters provide a lot of additional information about structure and viscoelastic properties of the medium in comparison to the classical analysis of dynamic curves G' and G" and shear creep compliance J(t. It allowed for a comprehensive description of a wide range of properties of kuzu starch pastes, depending on the conditions of pasting process.
A stochastic fractional dynamics model of space-time variability of rain
Kundu, Prasun K.; Travis, James E.
2013-09-01
varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, which allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and time scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and on the Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to fit the second moment statistics of radar data at the smaller spatiotemporal scales. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well at these scales without any further adjustment.
International Nuclear Information System (INIS)
Pors Nielsen, S.; Baerenholdt, O.; Munck, O.
1975-01-01
By application of a power function model, fractional intestinal calcium absorption was investigated with a new technique involving whole-body counting after successive oral and intravenous administration of standard doses of 47 Ca. The fractional calcium retention 7 days after the oral load of 47 Ca was also measured. Fractional calcium retention averaged 30.3% in normal subjects and 11.5% in 11 patients with intestinal malabsorption. In the same groups fractional calcium absorption averaged 46.6% and 16.4%, respectively. Fractional calcium retention and intestinal calcium absorption were significantly correlated to body surface area, and there was a well-defined relation between fractional retention and absorption of calcium. These studies demonstrate that measurements of fractional retention and fractional intestinal absorption of calcium can be combined by the use of a whole-body counter, that fractional retention and intestinal absorption are proportional to total body surface area and therefore probably also to the total bone mass, and that fractional retention and absorption are so closely interrelated that frational absorption can be estimated from fractional retention with reasonable accuracy in normal subjects. (auth.)
On Lamb and Rayleigh wave convergence in viscoelastic tissues
Energy Technology Data Exchange (ETDEWEB)
Nenadic, Ivan Z; Urban, Matthew W; Aristizabal, Sara; Mitchell, Scott A; Humphrey, Tye C; Greenleaf, James F, E-mail: Nenadic.Ivan@mayo.edu [Department of Biomedical Engineering, Mayo Clinic College of Medicine, Rochester, MN, 55905 (United States)
2011-10-21
Characterization of the viscoelastic material properties of soft tissue has become an important area of research over the last two decades. Our group has been investigating the feasibility of using a shear wave dispersion ultrasound vibrometry (SDUV) method to excite Lamb waves in organs with plate-like geometry to estimate the viscoelasticity of the medium of interest. The use of Lamb wave dispersion ultrasound vibrometry to quantify the mechanical properties of viscoelastic solids has previously been reported. Two organs, the heart wall and the spleen, can be readily modeled using plate-like geometries. The elasticity of these two organs is important because they change in pathological conditions. Diastolic dysfunction is the inability of the left ventricle (LV) of the heart to supply sufficient stroke volumes into the systemic circulation and is accompanied by the loss of compliance and stiffening of the LV myocardium. It has been shown that there is a correlation between high splenic stiffness in patients with chronic liver disease and strong correlation between spleen and liver stiffness. Here, we investigate the use of the SDUV method to quantify the viscoelasticity of the LV free-wall myocardium and spleen by exciting Rayleigh waves on the organ's surface and measuring the wave dispersion (change of wave velocity as a function of frequency) in the frequency range 40-500 Hz. An equation for Rayleigh wave dispersion due to cylindrical excitation was derived by modeling the excised myocardium and spleen with a homogenous Voigt material plate immersed in a nonviscous fluid. Boundary conditions and wave potential functions were solved for the surface wave velocity. Analytical and experimental convergence between the Lamb and Rayleigh waves is reported in a finite element model of a plate in a fluid of similar density, gelatin plate and excised porcine spleen and left-ventricular free-wall myocardium.
Analysis of tin-ore samples by the ratio of Rayleigh to Compton backscattering
International Nuclear Information System (INIS)
Ao Qi; Cao Liguo; Ding Yimin
1990-01-01
The relationship between the ratio of gamma-ray Rayleigh to Compton backscattering intensities (R/C) and the weight fraction of heavy element in light matrixes were investigated. An improved (R/C) eff analytical technique for tin-ore samples was described. The technique can be regarded as a substitute for the XRF method in which the self-absorption process worsens the analytical accuracy of heavy elements
Directory of Open Access Journals (Sweden)
Abdon Atangana
2014-01-01
Full Text Available The notion of uncertainty in groundwater hydrology is of great importance as it is known to result in misleading output when neglected or not properly accounted for. In this paper we examine this effect in groundwater flow models. To achieve this, we first introduce the uncertainties functions u as function of time and space. The function u accounts for the lack of knowledge or variability of the geological formations in which flow occur (aquifer in time and space. We next make use of Riemann-Liouville fractional derivatives that were introduced by Kobelev and Romano in 2000 and its approximation to modify the standard version of groundwater flow equation. Some properties of the modified Riemann-Liouville fractional derivative approximation are presented. The classical model for groundwater flow, in the case of density-independent flow in a uniform homogeneous aquifer is reformulated by replacing the classical derivative by the Riemann-Liouville fractional derivatives approximations. The modified equation is solved via the technique of green function and the variational iteration method.
Recoilless fractions calculated with the nearest-neighbour interaction model by Kagan and Maslow
Kemerink, G. J.; Pleiter, F.
1986-08-01
The recoilless fraction is calculated for a number of Mössbauer atoms that are natural constituents of HfC, TaC, NdSb, FeO, NiO, EuO, EuS, EuSe, EuTe, SnTe, PbTe and CsF. The calculations are based on a model developed by Kagan and Maslow for binary compounds with rocksalt structure. With the exception of SnTe and, to a lesser extent, PbTe, the results are in reasonable agreement with the available experimental data and values derived from other models.
Analytical evaluation of atomic form factors: Application to Rayleigh scattering
Energy Technology Data Exchange (ETDEWEB)
Safari, L., E-mail: laleh.safari@ist.ac.at [IST Austria (Institute of Science and Technology Austria), Am Campus 1, 3400 Klosterneuburg (Austria); Department of Physics, University of Oulu, Box 3000, FI-90014 Oulu (Finland); Santos, J. P. [Laboratório de Instrumentação, Engenharia Biomédica e Física da Radiação (LIBPhys-UNL), Departamento de Física, Faculdade de Ciências e Tecnologia, FCT, Universidade Nova de Lisboa, 2829-516 Caparica (Portugal); Amaro, P. [Laboratório de Instrumentação, Engenharia Biomédica e Física da Radiação (LIBPhys-UNL), Departamento de Física, Faculdade de Ciências e Tecnologia, FCT, Universidade Nova de Lisboa, 2829-516 Caparica (Portugal); Physikalisches Institut, Universität Heidelberg, D-69120 Heidelberg (Germany); Jänkälä, K. [Department of Physics, University of Oulu, Box 3000, FI-90014 Oulu (Finland); Fratini, F. [Department of Physics, University of Oulu, Box 3000, FI-90014 Oulu (Finland); Institute of Atomic and Subatomic Physics, TU Wien, Stadionallee 2, 1020 Wien (Austria); Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, MG (Brazil)
2015-05-15
Atomic form factors are widely used for the characterization of targets and specimens, from crystallography to biology. By using recent mathematical results, here we derive an analytical expression for the atomic form factor within the independent particle model constructed from nonrelativistic screened hydrogenic wave functions. The range of validity of this analytical expression is checked by comparing the analytically obtained form factors with the ones obtained within the Hartee-Fock method. As an example, we apply our analytical expression for the atomic form factor to evaluate the differential cross section for Rayleigh scattering off neutral atoms.
Statistical approach of weakly nonlinear ablative Rayleigh-Taylor instability
International Nuclear Information System (INIS)
Garnier, J.; Masse, L.
2005-01-01
A weakly nonlinear model is proposed for the Rayleigh-Taylor instability in presence of ablation and thermal transport. The nonlinear effects for a single-mode disturbance are computed, included the nonlinear correction to the exponential growth of the fundamental modulation. Mode coupling in the spectrum of a multimode disturbance is thoroughly analyzed by a statistical approach. The exponential growth of the linear regime is shown to be reduced by the nonlinear mode coupling. The saturation amplitude is around 0.1λ for long wavelengths, but higher for short instable wavelengths in the ablative regime
Fitting the Fractional Polynomial Model to Non-Gaussian Longitudinal Data
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Ji Hoon Ryoo
2017-08-01
Full Text Available As in cross sectional studies, longitudinal studies involve non-Gaussian data such as binomial, Poisson, gamma, and inverse-Gaussian distributions, and multivariate exponential families. A number of statistical tools have thus been developed to deal with non-Gaussian longitudinal data, including analytic techniques to estimate parameters in both fixed and random effects models. However, as yet growth modeling with non-Gaussian data is somewhat limited when considering the transformed expectation of the response via a linear predictor as a functional form of explanatory variables. In this study, we introduce a fractional polynomial model (FPM that can be applied to model non-linear growth with non-Gaussian longitudinal data and demonstrate its use by fitting two empirical binary and count data models. The results clearly show the efficiency and flexibility of the FPM for such applications.
Zhang, Hongmei; Wang, Yue; Fatemi, Mostafa; Insana, Michael F.
2017-03-01
Kelvin-Voigt fractional derivative (KVFD) model parameters have been used to describe viscoelastic properties of soft tissues. However, translating model parameters into a concise set of intrinsic mechanical properties related to tissue composition and structure remains challenging. This paper begins by exploring these relationships using a biphasic emulsion materials with known composition. Mechanical properties are measured by analyzing data from two indentation techniques—ramp-stress relaxation and load-unload hysteresis tests. Material composition is predictably correlated with viscoelastic model parameters. Model parameters estimated from the tests reveal that elastic modulus E 0 closely approximates the shear modulus for pure gelatin. Fractional-order parameter α and time constant τ vary monotonically with the volume fraction of the material’s fluid component. α characterizes medium fluidity and the rate of energy dissipation, and τ is a viscous time constant. Numerical simulations suggest that the viscous coefficient η is proportional to the energy lost during quasi-static force-displacement cycles, E A . The slope of E A versus η is determined by α and the applied indentation ramp time T r. Experimental measurements from phantom and ex vivo liver data show close agreement with theoretical predictions of the η -{{E}A} relation. The relative error is less than 20% for emulsions 22% for liver. We find that KVFD model parameters form a concise features space for biphasic medium characterization that described time-varying mechanical properties. The experimental work was carried out at the Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. Methodological development, including numerical simulation and all data analysis, were carried out at the school of Life Science and Technology, Xi’an JiaoTong University, 710049, China.
Krieter, Detlef H; Lange, Florian; Lemke, Horst-Dieter; Bonn, Florian; Wanner, Christoph
2018-04-01
Technical problems during clinical lipid apheresis interfere with fractionator performance. Therefore, a large animal model was established to characterize a new plasma fractionation membrane. Four sheep were randomized, controlled, and crossover subjected to double ofiltration lipoprotein apheresis with three specimens of FractioPES R having slightly different HDL sieving coefficients (S K ) (FPESa, 0.30, FPESb, 0.26, and FPESc, 0.22) versus a control fractionator (EVAL). S K and reduction ratios were determined for LDL, HDL, fibrinogen, IgG, and albumin. Compared to EVAL (0.42 ± 0.04 to 0.74 ± 0.08) and FPESa (0.36 ± 0.06 to 0.64 ± 0.04), S K for HDL were lower (P < 0.05) with FPESc (0.30 ± 0.04 to 0.49 ± 0.10). Fibrinogen S K were higher (P < 0.05) with EVAL (0.02 ± 0.01 to 0.40 ± 0.08) compared to FPESb (0.05 ± 0.02 to 0.26 ± 0.34) and FPESc (0.01 ± 0.01 to 0.21 ± 0.16). No further differences were determined. The animal model distinguished between minor differences in fractionation membrane permeability, demonstrating equivalent sieving of FPESa and EVAL and slightly inferior permeability of FPESb and FPESc. © 2018 International Society for Apheresis, Japanese Society for Apheresis, and Japanese Society for Dialysis Therapy.
Generalised and Fractional Langevin Equations-Implications for Energy Balance Models
Watkins, N. W.; Chapman, S. C.; Chechkin, A.; Ford, I.; Klages, R.; Stainforth, D. A.
2017-12-01
Energy Balance Models (EBMs) have a long heritage in climate science, including their use in modelling anomalies in global mean temperature. Many types of EBM have now been studied, and this presentation concerns the stochastic EBMs, which allow direct treatment of climate fluctuations and noise. Some recent stochastic EBMs (e.g. [1]) map on to Langevin's original form of his equation, with temperature anomaly replacing velocity, and other corresponding replacements being made. Considerable sophistication has now been reached in the application of multivariate stochastic Langevin modelling in many areas of climate. Our work is complementary in intent and investigates the Mori-Kubo "Generalised Langevin Equation" (GLE) which incorporates non-Markovian noise and response in a univariate framework, as a tool for modelling GMT [2]. We show how, if it is present, long memory simplifies the GLE to a fractional Langevin equation (FLE). Evidence for long range memory in global temperature, and the success of fractional Gaussian noise in its prediction [5] has already motivated investigation of a power law response model [3,4,5]. We go beyond this work to ask whether an EBM of FLE-type exists, and what its solutions would be. [l] Padilla et al, J. Climate (2011); [2] Watkins, GRL (2013); [3] Rypdal, JGR (2012); [4] Rypdal and Rypdal, J. Climate (2014); [5] Lovejoy et al, ESDD (2015).
DEFF Research Database (Denmark)
Zhou, H. W.; Yi, H. Y.; Mishnaevsky, Leon
2017-01-01
A modeling approach to time-dependent property of Glass Fiber Reinforced Polymers (GFRP) composites is of special interest for quantitative description of long-term behavior. An electronic creep machine is employed to investigate the time-dependent deformation of four specimens of dog-bond-shaped......A modeling approach to time-dependent property of Glass Fiber Reinforced Polymers (GFRP) composites is of special interest for quantitative description of long-term behavior. An electronic creep machine is employed to investigate the time-dependent deformation of four specimens of dog......-bond-shaped GFRP composites at various stress level. A negative exponent function based on structural changes is introduced to describe the damage evolution of material properties in the process of creep test. Accordingly, a new creep constitutive equation, referred to fractional derivative Maxwell model...... by the fractional derivative Maxwell model proposed in the paper are in a good agreement with the experimental data. It is shown that the new creep constitutive model proposed in the paper needs few parameters to represent various time-dependent behaviors....
Rayleigh scattering and nonlinear inversion of elastic waves
Energy Technology Data Exchange (ETDEWEB)
Gritto, Roland [Univ. of California, Berkeley, CA (United States)
1995-12-01
Rayleigh scattering of elastic waves by an inclusion is investigated and the limitations determined. In the near field of the inhomogeneity, the scattered waves are up to a factor of 300 stronger than in the far field, excluding the application of the far field Rayleigh approximation for this range. The investigation of the relative error as a function of parameter perturbation shows a range of applicability broader than previously assumed, with errors of 37% and 17% for perturbations of -100% and +100%, respectively. The validity range for the Rayleigh limit is controlled by large inequalities, and therefore, the exact limit is determined as a function of various parameter configurations, resulting in surprisingly high values of up to k_{p}R = 0.9. The nonlinear scattering problem can be solved by inverting for equivalent source terms (moments) of the scatterer, before the elastic parameters are determined. The nonlinear dependence between the moments and the elastic parameters reveals a strong asymmetry around the origin, which will produce different results for weak scattering approximations depending on the sign of the anomaly. Numerical modeling of cross hole situations shows that near field terms are important to yield correct estimates of the inhomogeneities in the vicinity of the receivers, while a few well positioned sources and receivers considerably increase the angular coverage, and thus the model resolution of the inversion parameters. The pattern of scattered energy by an inhomogeneity is complicated and varies depending on the object, the wavelength of the incident wave, and the elastic parameters involved. Therefore, it is necessary to investigate the direction of scattered amplitudes to determine the best survey geometry.
Rahimi, Zaher; Sumelka, Wojciech; Yang, Xiao-Jun
2017-11-01
The application of fractional calculus in fractional models (FMs) makes them more flexible than integer models inasmuch they can conclude all of integer and non-integer operators. In other words FMs let us use more potential of mathematics to modeling physical phenomena due to the use of both integer and fractional operators to present a better modeling of problems, which makes them more flexible and powerful. In the present work, a new fractional nonlocal model has been proposed, which has a simple form and can be used in different problems due to the simple form of numerical solutions. Then the model has been used to govern equations of the motion of the Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT). Next, free vibration of the Timoshenko and Euler-Bernoulli simply-supported (S-S) beam has been investigated. The Galerkin weighted residual method has been used to solve the non-linear governing equations.
Physics of the Kitaev Model: Fractionalization, Dynamic Correlations, and Material Connections
Hermanns, M.; Kimchi, I.; Knolle, J.
2018-03-01
Quantum spin liquids have fascinated condensed matter physicists for decades because of their unusual properties such as spin fractionalization and long-range entanglement. Unlike conventional symmetry breaking, the topological order underlying quantum spin liquids is hard to detect experimentally. Even theoretical models are scarce for which the ground state is established to be a quantum spin liquid. The Kitaev honeycomb model and its generalizations to other tricoordinated lattices are chief counterexamples - they are exactly solvable, harbor a variety of quantum spin liquid phases, and are also relevant for certain transition metal compounds including the polymorphs of (Na,Li)2IrO3 iridates and RuCl3. In this review, we give an overview of the rich physics of the Kitaev model, including two-dimensional and three-dimensional fractionalization as well as dynamic correlations and behavior at finite temperatures. We discuss the different materials and argue how the Kitaev model physics can be relevant even though most materials show magnetic ordering at low temperatures.
A predictor-corrector algorithm to estimate the fractional flow in oil-water models
International Nuclear Information System (INIS)
Savioli, Gabriela B; Berdaguer, Elena M Fernandez
2008-01-01
We introduce a predictor-corrector algorithm to estimate parameters in a nonlinear hyperbolic problem. It can be used to estimate the oil-fractional flow function from the Buckley-Leverett equation. The forward model is non-linear: the sought- for parameter is a function of the solution of the equation. Traditionally, the estimation of functions requires the selection of a fitting parametric model. The algorithm that we develop does not require a predetermined parameter model. Therefore, the estimation problem is carried out over a set of parameters which are functions. The algorithm is based on the linearization of the parameter-to-output mapping. This technique is new in the field of nonlinear estimation. It has the advantage of laying aside parametric models. The algorithm is iterative and is of predictor-corrector type. We present theoretical results on the inverse problem. We use synthetic data to test the new algorithm.
Energy Technology Data Exchange (ETDEWEB)
Fiorino, Claudio, E-mail: fiorino.claudio@hsr.it [Department of Medical Physics, San Raffaele Scientific Institute, Milan (Italy); Cozzarini, Cesare [Department of Radiotherapy, San Raffaele Scientific Institute, Milan (Italy); Rancati, Tiziana [Prostate Cancer Program, Fondazione Istituto di Ricovero e Cura a Carattere Scientifico Istituto Nazionale dei Tumori, Milan (Italy); Briganti, Alberto [Department of Urology, San Raffaele Scientific Institute, Milan (Italy); Cattaneo, Giovanni Mauro; Mangili, Paola [Department of Medical Physics, San Raffaele Scientific Institute, Milan (Italy); Di Muzio, Nadia Gisella [Department of Radiotherapy, San Raffaele Scientific Institute, Milan (Italy); Calandrino, Riccardo [Department of Medical Physics, San Raffaele Scientific Institute, Milan (Italy)
2014-12-01
Purpose: To fit urinary toxicity data of patients treated with postprostatectomy radiation therapy with the linear quadratic (LQ) model with/without introducing a time factor. Methods and Materials: Between 1993 and 2010, 1176 patients were treated with conventional fractionation (1.8 Gy per fraction, median 70.2 Gy, n=929) or hypofractionation (2.35-2.90 Gy per fraction, n=247). Data referred to 2004-2010 (when all schemes were in use, n=563; conventional fractionation: 316; hypofractionation: 247) were fitted as a logit function of biological equivalent dose (BED), according to the LQ model with/without including a time factor γ (fixing α/β = 5 Gy). The 3-year risks of severe urethral stenosis, incontinence, and hematuria were considered as endpoints. Best-fit parameters were derived, and the resulting BEDs were taken in multivariable backward logistic models, including relevant clinical variables, considering the whole population. Results: The 3-year incidences of severe stenosis, incontinence, and hematuria were, respectively, 6.6%, 4.8%, and 3.3% in the group treated in 2004-2010. The best-fitted α/β values were 0.81 Gy and 0.74 Gy for incontinence and hematuria, respectively, with the classic LQ formula. When fixing α/β = 5 Gy, best-fit values for γ were, respectively, 0.66 Gy/d and 0.85 Gy/d. Sensitivity analyses showed reasonable values for γ (0.6-1.0 Gy/d), with comparable goodness of fit for α/β values between 3.5 and 6.5 Gy. Likelihood ratio tests showed that the fits with/without including γ were equivalent. The resulting multivariable backward logistic models in the whole population included BED, pT4, and use of antihypertensives (area under the curve [AUC] = 0.72) for incontinence and BED, pT4, and year of surgery (AUC = 0.80) for hematuria. Stenosis data could not be fitted: a 4-variable model including only clinical factors (acute urinary toxicity, pT4, year of surgery, and use of antihypertensives) was suggested (AUC
International Nuclear Information System (INIS)
Fiorino, Claudio; Cozzarini, Cesare; Rancati, Tiziana; Briganti, Alberto; Cattaneo, Giovanni Mauro; Mangili, Paola; Di Muzio, Nadia Gisella; Calandrino, Riccardo
2014-01-01
Purpose: To fit urinary toxicity data of patients treated with postprostatectomy radiation therapy with the linear quadratic (LQ) model with/without introducing a time factor. Methods and Materials: Between 1993 and 2010, 1176 patients were treated with conventional fractionation (1.8 Gy per fraction, median 70.2 Gy, n=929) or hypofractionation (2.35-2.90 Gy per fraction, n=247). Data referred to 2004-2010 (when all schemes were in use, n=563; conventional fractionation: 316; hypofractionation: 247) were fitted as a logit function of biological equivalent dose (BED), according to the LQ model with/without including a time factor γ (fixing α/β = 5 Gy). The 3-year risks of severe urethral stenosis, incontinence, and hematuria were considered as endpoints. Best-fit parameters were derived, and the resulting BEDs were taken in multivariable backward logistic models, including relevant clinical variables, considering the whole population. Results: The 3-year incidences of severe stenosis, incontinence, and hematuria were, respectively, 6.6%, 4.8%, and 3.3% in the group treated in 2004-2010. The best-fitted α/β values were 0.81 Gy and 0.74 Gy for incontinence and hematuria, respectively, with the classic LQ formula. When fixing α/β = 5 Gy, best-fit values for γ were, respectively, 0.66 Gy/d and 0.85 Gy/d. Sensitivity analyses showed reasonable values for γ (0.6-1.0 Gy/d), with comparable goodness of fit for α/β values between 3.5 and 6.5 Gy. Likelihood ratio tests showed that the fits with/without including γ were equivalent. The resulting multivariable backward logistic models in the whole population included BED, pT4, and use of antihypertensives (area under the curve [AUC] = 0.72) for incontinence and BED, pT4, and year of surgery (AUC = 0.80) for hematuria. Stenosis data could not be fitted: a 4-variable model including only clinical factors (acute urinary toxicity, pT4, year of surgery, and use of antihypertensives) was suggested (AUC
International Nuclear Information System (INIS)
Fakir, Hatim; Hlatky, Lynn; Li, Huamin; Sachs, Rainer
2013-01-01
Purpose: Optimal treatment planning for fractionated external beam radiation therapy requires inputs from radiobiology based on recent thinking about the “five Rs” (repopulation, radiosensitivity, reoxygenation, redistribution, and repair). The need is especially acute for the newer, often individualized, protocols made feasible by progress in image guided radiation therapy and dose conformity. Current stochastic tumor control probability (TCP) models incorporating tumor repopulation effects consider “stem-like cancer cells” (SLCC) to be independent, but the authors here propose that SLCC-SLCC interactions may be significant. The authors present a new stochastic TCP model for repopulating SLCC interacting within microenvironmental niches. Our approach is meant mainly for comparing similar protocols. It aims at practical generalizations of previous mathematical models. Methods: The authors consider protocols with complete sublethal damage repair between fractions. The authors use customized open-source software and recent mathematical approaches from stochastic process theory for calculating the time-dependent SLCC number and thereby estimating SLCC eradication probabilities. As specific numerical examples, the authors consider predicted TCP results for a 2 Gy per fraction, 60 Gy protocol compared to 64 Gy protocols involving early or late boosts in a limited volume to some fractions. Results: In sample calculations with linear quadratic parameters α = 0.3 per Gy, α/β = 10 Gy, boosting is predicted to raise TCP from a dismal 14.5% observed in some older protocols for advanced NSCLC to above 70%. This prediction is robust as regards: (a) the assumed values of parameters other than α and (b) the choice of models for intraniche SLCC-SLCC interactions. However, α = 0.03 per Gy leads to a prediction of almost no improvement when boosting. Conclusions: The predicted efficacy of moderate boosts depends sensitively on α. Presumably, the larger values of α are
Fakir, Hatim; Hlatky, Lynn; Li, Huamin; Sachs, Rainer
2013-12-01
Optimal treatment planning for fractionated external beam radiation therapy requires inputs from radiobiology based on recent thinking about the "five Rs" (repopulation, radiosensitivity, reoxygenation, redistribution, and repair). The need is especially acute for the newer, often individualized, protocols made feasible by progress in image guided radiation therapy and dose conformity. Current stochastic tumor control probability (TCP) models incorporating tumor repopulation effects consider "stem-like cancer cells" (SLCC) to be independent, but the authors here propose that SLCC-SLCC interactions may be significant. The authors present a new stochastic TCP model for repopulating SLCC interacting within microenvironmental niches. Our approach is meant mainly for comparing similar protocols. It aims at practical generalizations of previous mathematical models. The authors consider protocols with complete sublethal damage repair between fractions. The authors use customized open-source software and recent mathematical approaches from stochastic process theory for calculating the time-dependent SLCC number and thereby estimating SLCC eradication probabilities. As specific numerical examples, the authors consider predicted TCP results for a 2 Gy per fraction, 60 Gy protocol compared to 64 Gy protocols involving early or late boosts in a limited volume to some fractions. In sample calculations with linear quadratic parameters α = 0.3 per Gy, α∕β = 10 Gy, boosting is predicted to raise TCP from a dismal 14.5% observed in some older protocols for advanced NSCLC to above 70%. This prediction is robust as regards: (a) the assumed values of parameters other than α and (b) the choice of models for intraniche SLCC-SLCC interactions. However, α = 0.03 per Gy leads to a prediction of almost no improvement when boosting. The predicted efficacy of moderate boosts depends sensitively on α. Presumably, the larger values of α are the ones appropriate for individualized
Anticonvulsant activity of DNS II fraction in the acute seizure models.
Raza, Muhammad Liaquat; Zeeshan, Mohammad; Ahmad, Manzoor; Shaheen, Farzana; Simjee, Shabana U
2010-04-21
Delphinium nordhagenii belongs to family Ranunculaceae, it is widely found in tropical areas of Pakistan. Other species of Delphinium are reported as anticonvulsant and are traditionally used in the treatment of epilepsy. Delphinium nordhagenii is used by local healer in Pakistan but never used for scientific investigation as anticonvulsant. Thus, Delphinium nordhagenii was subjected to bioassay-guided fractionation and the most active fraction, i.e. DNS II acetone was chosen for further testing in the acute seizure models of epilepsy to study the antiepileptic potential in male mice. Different doses (60, 65 and 70mg/kg, i.p.) of DNS II acetone fraction of Delphinium nordhagenii was administered 30min prior the chemoconvulsant's injection in the male mice. Convulsive doses of chemoconvulsants (pentylenetetrazole 90mg/kg, s.c. and picrotoxin 3.15mg/kg, s.c.) were used. The mice were observed 45-90min for the presence of seizures. Moreover, four different doses of DNS II (60, 65, 70 and 100mg/kg, i.p.) were tested in the MES test. The DNS II acetone fraction of Delphinium nordhagenii has exhibited the anticonvulsant actions by preventing the seizures against PTZ- and picrotoxin-induced seizure as well as 100% seizure protection in MES test. The results are comparable with standard AEDs (diazepam 7.5mg/kg, i.p. and phenytoin 20mg/kg, i.p.). These findings suggest that the Delphinium nordhagenii possesses the anticonvulsant activity. Further analysis is needed to confirm the structure and target the extended activity profile. Copyright 2010 Elsevier Ireland Ltd. All rights reserved.
International Nuclear Information System (INIS)
Pitkaenen, Maunu.
1986-04-01
X-ray induced changes in rat and human bone and bone marrow vasculature and in rat brain vasculature were measured as a function of time after irradiation and absorbed dose. The absorbed dose in the organ varied from 5 to 25 Gy for single dose irradiations and from 19 to 58 Gy for fractionated irradiations.The number of fractions varied from 3 to 10 for the rats and from 12 to 25 for the human. Blood flow changes were measured using an ''1''2''5I antipyrine or ''8''6RbCl extraction technique. The red blood cell (RBC) volume was examined by ''5''1Cr labelled red cells. Different fractionation models have been compared. Radiation induced reduction of bone and bone marrow blood flow were both time and dose dependent. Reduced blood flow 3 months after irradiation would seem to be an important factor in the subsequent atrophy of bones. With a single dose of 10 Gy the bone marrow blood flow returned to the control level by 7 months after irradiation. In the irradiated bone the RBC volume was about same as that in the control side but in bone marrow the reduction was from 32 to 59%. The dose levels predicted by the nominal standard dose (NSD) formula produced about the same damage to the rat femur seven months after irradiation when the extraction of ''8''6Rb chloride and the dry weight were concerned as the end points. However, the results suggest that the NSB formula underestimates the late radiation damage in bone marrow when a small number of large fractions are used. In the irradiated brains of the rats the blood flow was on average 20.4% higher compared to that in the control group. There was no significant difference in brain blood flow between different fractionation schemes. The value of 0.42 for the exponent of N corresponds to the average value for central nervous system tolerance in the literature. The model used may be sufficiently accurate for clinical work provided the treatment schemes used do not depart too radically from standard practice
Financial analysis of technology acquisition using fractionated lasers as a model.
Jutkowitz, Eric; Carniol, Paul J; Carniol, Alan R
2010-08-01
Ablative fractional lasers are among the most advanced and costly devices on the market. Yet, there is a dearth of published literature on the cost and potential return on investment (ROI) of such devices. The objective of this study was to provide a methodological framework for physicians to evaluate ROI. To facilitate this analysis, we conducted a case study on the potential ROI of eight ablative fractional lasers. In the base case analysis, a 5-year lease and a 3-year lease were assumed as the purchase option with a $0 down payment and 3-month payment deferral. In addition to lease payments, service contracts, labor cost, and disposables were included in the total cost estimate. Revenue was estimated as price per procedure multiplied by total number of procedures in a year. Sensitivity analyses were performed to account for variability in model assumptions. Based on the assumptions of the model, all lasers had higher ROI under the 5-year lease agreement compared with that for the 3-year lease agreement. When comparing results between lasers, those with lower operating and purchase cost delivered a higher ROI. Sensitivity analysis indicates the model is most sensitive to purchase method. If physicians opt to purchase the device rather than lease, they can significantly enhance ROI. ROI analysis is an important tool for physicians who are considering making an expensive device acquisition. However, physicians should not rely solely on ROI and must also consider the clinical benefits of a laser. (c) Thieme Medical Publishers.
Directory of Open Access Journals (Sweden)
Ana Paula Delowski Ciniello
Full Text Available Abstract The present paper aims at presenting a methodology for characterizing viscoelastic materials in time domain, taking into account the fractional Zener constitutive model and the influence of temperature through Williams, Landel, and Ferry’s model. To that effect, a set of points obtained experimentally through uniaxial tensile tests with different constant strain rates is considered. The approach is based on the minimization of the quadratic relative distance between the experimental stress-strain curves and the corresponding ones given by the theoretical model. In order to avoid the local minima in the process of optimization, a hybrid technique based on genetic algorithms and non-linear programming techniques is used. The methodology is applied in the characterization of two different commercial viscoelastic materials. The results indicate that the proposed methodology is effective in identifying thermorheologically simple viscoelastic materials.
Model of chromosomal loci dynamics in bacteria as fractional diffusion with intermittent transport
Gherardi, Marco; Calabrese, Ludovico; Tamm, Mikhail; Cosentino Lagomarsino, Marco
2017-10-01
The short-time dynamics of bacterial chromosomal loci is a mixture of subdiffusive and active motion, in the form of rapid relocations with near-ballistic dynamics. While previous work has shown that such rapid motions are ubiquitous, we still have little grasp on their physical nature, and no positive model is available that describes them. Here, we propose a minimal theoretical model for loci movements as a fractional Brownian motion subject to a constant but intermittent driving force, and compare simulations and analytical calculations to data from high-resolution dynamic tracking in E. coli. This analysis yields the characteristic time scales for intermittency. Finally, we discuss the possible shortcomings of this model, and show that an increase in the effective local noise felt by the chromosome associates to the active relocations.
Directory of Open Access Journals (Sweden)
Luciano Mescia
2017-11-01
Full Text Available Electromagnetic fields are involved in several therapeutic and diagnostic applications such as hyperthermia and electroporation. For these applications, pulsed electric fields (PEFs and transient phenomena are playing a key role for understanding the biological response due to the exposure to non-ionizing wideband pulses. To this end, the PEF propagation in the six-layered planar structure modeling the human head has been studied. The electromagnetic field and the specific absorption rate (SAR have been calculated through an accurate finite-difference time-domain (FDTD dispersive modeling based on the fractional derivative operator. The temperature rise inside the tissues due to the electromagnetic field exposure has been evaluated using both the non-thermoregulated and thermoregulated Gagge’s two-node models. Moreover, additional parametric studies have been carried out with the aim to investigate the thermal response by changing the amplitude and duration of the electric pulses.
Directory of Open Access Journals (Sweden)
Yunfeng Jiang
2016-07-01
Full Text Available A fractional derivative system identification approach for modeling battery dynamics is presented in this paper, where fractional derivatives are applied to approximate non-linear dynamic behavior of a battery system. The least squares-based state-variable filter (LSSVF method commonly used in the identification of continuous-time models is extended to allow the estimation of fractional derivative coefficents and parameters of the battery models by monitoring a charge/discharge demand signal and a power storage/delivery signal. In particular, the model is combined by individual fractional differential models (FDMs, where the parameters can be estimated by a least-squares algorithm. Based on experimental data, it is illustrated how the fractional derivative model can be utilized to predict the dynamics of the energy storage and delivery of a lithium iron phosphate battery (LiFePO 4 in real-time. The results indicate that a FDM can accurately capture the dynamics of the energy storage and delivery of the battery over a large operating range of the battery. It is also shown that the fractional derivative model exhibits improvements on prediction performance compared to standard integer derivative model, which in beneficial for a battery management system.
International Nuclear Information System (INIS)
Craiem, Damian; Magin, Richard L
2010-01-01
New lumped-element models of red blood cell mechanics can be constructed using fractional order generalizations of springs and dashpots. Such 'spring-pots' exhibit a fractional order viscoelastic behavior that captures a wide spectrum of experimental results through power-law expressions in both the time and frequency domains. The system dynamics is fully described by linear fractional order differential equations derived from first order stress–strain relationships using the tools of fractional calculus. Changes in the composition or structure of the membrane are conveniently expressed in the fractional order of the model system. This approach provides a concise way to describe and quantify the biomechanical behavior of membranes, cells and tissues. (perspective)
Directory of Open Access Journals (Sweden)
Olaniyi Samuel Iyiola
2014-09-01
Full Text Available In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation using q-Homotopy Analysis Method (q-HAM. Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.
Craiem, Damian; Magin, Richard L
2010-01-20
New lumped-element models of red blood cell mechanics can be constructed using fractional order generalizations of springs and dashpots. Such 'spring-pots' exhibit a fractional order viscoelastic behavior that captures a wide spectrum of experimental results through power-law expressions in both the time and frequency domains. The system dynamics is fully described by linear fractional order differential equations derived from first order stress-strain relationships using the tools of fractional calculus. Changes in the composition or structure of the membrane are conveniently expressed in the fractional order of the model system. This approach provides a concise way to describe and quantify the biomechanical behavior of membranes, cells and tissues.
Muserere, Simon Takawira; Hoko, Zvikomborero; Nhapi, Innocent
Varying conditions are required for different species of microorganisms for the complex biological processes taking place within the activated sludge treatment system. It is against the requirement to manage this complex dynamic system that computer simulators were developed to aid in optimising activated sludge treatment processes. These computer simulators require calibration with quality data input that include wastewater fractionation among others. Thus, this research fractionated raw sewage, at Firle Sewage Treatment Works (STW), for calibration of the BioWin simulation model. Firle STW is a 3-stage activated sludge system. Wastewater characteristics of importance for activated sludge process design can be grouped into carbonaceous, nitrogenous and phosphorus compounds. Division of the substrates and compounds into their constituent fractions is called fractionation and is a valuable tool for process assessment. Fractionation can be carried out using bioassay methods or much simpler physico-chemical methods. The bioassay methods require considerable experience with experimental activated sludge systems and associated measurement techniques while the physico-chemical methods are straight forward. Plant raw wastewater fractionation was carried out through two 14-day campaign periods, the first being from 3 to 16 July 2013 and the second was from 1 to 14 October 2013. According to the Zimbabwean Environmental Management Act, and based on the sensitivity of its catchment, Firle STW effluent discharge regulatory standards in mg/L are COD (<60), TN (<10), ammonia (<0.2), and TP (<1). On the other hand Firle STW Unit 4 effluent quality results based on City of Harare records in mg/L during the period of study were COD (90 ± 35), TN (9.0 ± 3.0), ammonia (0.2 ± 0.4) and TP (3.0 ± 1.0). The raw sewage parameter concentrations measured during the study in mg/L and fractions for raw sewage respectively were as follows total COD (680 ± 37), slowly biodegradable COD
Chemical Applications of Second Harmonic Rayleigh Scattering ...
Indian Academy of Sciences (India)
Chemical Applications of Second Harmonic Rayleigh Scattering Puspendu Kumar Das Department of Inorganic and Physical Chemistry Indian Institute of Science Bangalore 560012, India pkdas@ipc.iisc.ernet.in · Slide 2 · Slide 3 · Slide 4 · Slide 5 · Slide 6 · Slide 7 · Slide 8 · Slide 9 · Slide 10 · Slide 11 · Slide 12 · Slide 13.
Modelling the fine and coarse fraction of heavy metals in Spain
García Vivanco, Marta; González, M. Angeles
2014-05-01
Heavy metals, such as cadmium, lead, nickel, arsenic, copper, chrome, zinc and selenium, are present in the air due to natural and anthropogenic emissions, normally joined to particles. These metals can affect life organisms via inhalation or ingestion, causing damages in human health and ecosystems. Small particles are inhaled and embebed in lungs and alveolus more easily than coarse particles. The CHIMERE model is a eulerian air quality model extensively used in air quality modelling. Metals have been recently included in this model in a special version developed in the CIEMAT (Madrid, Spain) modelling group. Vivanco et al. (2011) and González et al. (2012) showed the model performance for some metals in Spain and Europe. However, in these studies, metals were considered as fine particles. Some studies based on observed heavy metals air concentration indicate the presence of metals also in the coarse fraction, in special for Cu and Zn. For this reason, a new attempt of modelling metals considering a fine (Arsenic, Lead, Cadmium and Nickel Ambient Air Concentrations in Spain, 2011. Proceedings of the 11 th International Conference on Computational Science and Its Applications (ICCSA 11) 243-246 - González, Ma Vivanco, Marta; Palomino, Inmaculada; Garrido, Juan; Santiago, Manuel; Bessagnet, Bertrand Modelling Some Heavy Metals Air Concentration in Europe. // Water, Air & Soil Pollution;Sep2012, Vol. 223 Issue 8, p5227
Phase dispersion of Raman and Rayleigh-enhanced four-wave mixings in femtosecond polarization beats
International Nuclear Information System (INIS)
Yan, Zhao; Zhi-Qiang, Nie; Chang-Biao, Li; Yan-Peng, Zhang; Chen-Li, Gan; Huai-Bin, Zheng; Yuan-Yuan, Li; Ke-Qing, Lu
2009-01-01
Based on color-locking noisy field correlation in three Markovian stochastic models, phase dispersions of the Raman- and Rayleigh-enhanced four-wave mixing (FWM) have been investigated. The phase dispersions are modified by both linewidth and time delay for negative time delay, but only by linewidth for positive time delay. Moreover, the results under narrowband condition are close to the nonmodified nonlinear dispersion and absorption of the material. Homodyne and heterodyne detections of the Raman, the Rayleigh and the mixing femtosecond difference-frequency polarization beats have also been investigated, separately
Ultimate regime of high Rayleigh number convection in a porous medium.
Hewitt, Duncan R; Neufeld, Jerome A; Lister, John R
2012-06-01
Well-resolved direct numerical simulations of 2D Rayleigh-Bénard convection in a porous medium are presented for Rayleigh numbers Ra≤4×10(4) which reveal that, contrary to previous indications, the linear classical scaling for the Nusselt number, Nu~Ra, is attained asymptotically. The flow dynamics are analyzed, and the interior of the vigorously convecting system is shown to be increasingly well described as Ra→∞ by a simple columnar "heat-exchanger" model with a single horizontal wave number k and a linear background temperature field. The numerical results are approximately fitted by k~Ra(0.4).
Dynamics of single-bubble sonoluminescence. An alternative approach to the Rayleigh-Plesset equation
de Barros, Ana L. F.; Nogueira, Álvaro L. M. A.; Paschoal, Ricardo C.; Portes, Dirceu, Jr.; Rodrigues, Hilario
2018-03-01
Sonoluminescence is the phenomenon in which acoustic energy is (partially) transformed into light as a bubble of gas collapses inside a liquid medium. One particular model used to explain the motion of the bubble’s wall forced by acoustic pressure is expressed by the Rayleigh-Plesset equation, which can be obtained from the Navier-Stokes equation. In this article, we describe an alternative approach to derive the Rayleigh-Plesset equation based on Lagrangian mechanics. This work is addressed mainly to undergraduate students and teachers. It requires knowledge of calculus and of many concepts from various fields of physics at the intermediate level.
M. M. Clark; T. H. Fletcher; R. R. Linn
2010-01-01
The chemical processes of gas phase combustion in wildland fires are complex and occur at length-scales that are not resolved in computational fluid dynamics (CFD) models of landscape-scale wildland fire. A new approach for modelling fire chemistry in HIGRAD/FIRETEC (a landscape-scale CFD wildfire model) applies a mixtureâ fraction model relying on thermodynamic...
Energy Technology Data Exchange (ETDEWEB)
Choi, A. S.; Flach, G. P.; Martino, C. J.; Zamecnik, J. R.; Harris, M. K.; Wilmarth, W. R.; Calloway, T. B.
2005-03-23
In order to accelerate waste treatment and disposal of Hanford tank waste by 2028, the Department of Energy (DOE) and CH2M Hill Hanford Group (CHG), Inc. are evaluating alternative technologies which will be used in conjunction with the Waste Treatment Plant (WTP) to safely pretreat and immobilize the tank waste. Several technologies (Bulk Vitrification and Steam Reforming) are currently being evaluated for immobilizing the pretreated waste. Since the WTP does not have sufficient capacity to pretreat all the waste going to supplemental treatment by the 2028 milestone, two technologies (Selective Dissolution and Fractional Crystallization) are being considered for pretreatment of salt waste. The scope of this task was to: (1) evaluate the recent Savannah River Site (SRS) Tank 41 dissolution campaign and other literature to provide a more complete understanding of selective dissolution, (2) provide an update on the progress of salt dissolution and modeling activities at SRS, (3) investigate SRS experience and outside literature sources on industrial equipment and experimental results of previous fractional crystallization processes, and (4) evaluate recent Hanford AP104 boildown experiments and modeling results and recommend enhancements to the Environmental Simulation Program (ESP) to improve its predictive capabilities. This report provides a summary of this work and suggested recommendations.
Skovbølling Haak, Christina; Illes, Monica; Paasch, Uwe; Hædersdal, Merete
2011-07-01
Ablative fractional resurfacing (AFR) represents a new treatment potential for various skin conditions and new laser devices are being introduced. It is important to gain information about the impact of laser settings on the dimensions of the created laser channels for obtaining a safe and efficient treatment outcome. The aim of this study was to establish a standard model to document the histological tissue damage profiles after AFR and to test a new laser device at diverse settings. Ex vivo abdominal pig skin was treated with a MedArt 620, prototype fractional carbon dioxide (CO(2)) laser (Medart, Hvidovre, Denmark) delivering single microbeams (MB) with a spot size of 165 μm. By using a constant pulse duration of 2 ms, intensities of 1-18 W, single and 2-4 stacked pulses, energies were delivered in a range from 2-144 mJ/MB. Histological evaluations included 3-4 high-quality histological measurements for each laser setting (n = 28). AFR created cone-shaped laser channels. Ablation depths varied from reaching the superficial dermis (2 mJ, median 41 μm) to approaching the subcutaneous fat (144 mJ, median 1,943 μm) and correlated to the applied energy levels in an approximate linear relation (r(2) = 0.84, p skin model to characterize AFR laser channels histologically.
Directory of Open Access Journals (Sweden)
Lazarević Mihailo P.
2013-01-01
Full Text Available In this paper, the applications of biologically inspired modeling and control of (biomechanical (nonredundant mechanisms are presented, as well as newly obtained results of author in mechanics which are based on using fractional calculus. First, it is proposed to use biological analog-synergy due to existence of invariant features in the execution of functional motion. Second, the model of (biomechanical system may be obtained using another biological concept called distributed positioning (DP, which is based on the inertial properties and actuation of joints of considered mechanical system. In addition, it is proposed to use other biological principles such as: principle of minimum interaction, which takes a main role in hierarchical structure of control and self-adjusting principle (introduce local positive/negative feedback on control with great amplifying, which allows efficiently realization of control based on iterative natural learning. Also, new, recently obtained results of the author in the fields of stability, electroviscoelasticity, and control theory are presented which are based on using fractional calculus (FC. [Projekat Ministarstva nauke Republike Srbije, br. 35006
Energy Technology Data Exchange (ETDEWEB)
Morais, A. P. [Biomedical Engineering Program, COPPE, Rio de Janeiro (Brazil); Salgado de Oliveira University, Marechal Deodoro Street, 217 – Centro, Niterói, Rio de Janeiro (Brazil); Pino, A. V. [Biomedical Engineering Program, COPPE, Rio de Janeiro (Brazil); Souza, M. N. [Biomedical Engineering Program, COPPE, Rio de Janeiro (Brazil); Electronics Department at Polytechnic School, Federal University of Rio de Janeiro, Centro de Tecnologia Bloco H sala 217, Ilha do Fundão, Rio de Janeiro (Brazil)
2016-08-15
This in vitro study evaluated the diagnostic performance of an alternative electric bioimpedance spectroscopy technique (BIS-STEP) detect questionable occlusal carious lesions. Six specialists carried out the visual (V), radiography (R), and combined (VR) exams of 57 sound or non-cavitated occlusal carious lesion teeth classifying the occlusal surfaces in sound surface (H), enamel caries (EC), and dentinal caries (DC). Measurements were based on the current response to a step voltage excitation (BIS-STEP). A fractional electrical model was used to predict the current response in the time domain and to estimate the model parameters: Rs and Rp (resistive parameters), and C and α (fractional parameters). Histological analysis showed caries prevalence of 33.3% being 15.8% hidden caries. Combined examination obtained the best traditional diagnostic results with specificity = 59.0%, sensitivity = 70.9%, and accuracy = 60.8%. There were statistically significant differences in bioimpedance parameters between the H and EC groups (p = 0.016) and between the H and DC groups (Rs, p = 0.006; Rp, p = 0.022, and α, p = 0.041). Using a suitable threshold for the Rs, we obtained specificity = 60.7%, sensitivity = 77.9%, accuracy = 73.2%, and 100% of detection for deep lesions. It can be concluded that BIS-STEP method could be an important tool to improve the detection and management of occlusal non-cavitated primary caries and pigmented sites.
International Nuclear Information System (INIS)
Morais, A. P.; Pino, A. V.; Souza, M. N.
2016-01-01
This in vitro study evaluated the diagnostic performance of an alternative electric bioimpedance spectroscopy technique (BIS-STEP) detect questionable occlusal carious lesions. Six specialists carried out the visual (V), radiography (R), and combined (VR) exams of 57 sound or non-cavitated occlusal carious lesion teeth classifying the occlusal surfaces in sound surface (H), enamel caries (EC), and dentinal caries (DC). Measurements were based on the current response to a step voltage excitation (BIS-STEP). A fractional electrical model was used to predict the current response in the time domain and to estimate the model parameters: Rs and Rp (resistive parameters), and C and α (fractional parameters). Histological analysis showed caries prevalence of 33.3% being 15.8% hidden caries. Combined examination obtained the best traditional diagnostic results with specificity = 59.0%, sensitivity = 70.9%, and accuracy = 60.8%. There were statistically significant differences in bioimpedance parameters between the H and EC groups (p = 0.016) and between the H and DC groups (Rs, p = 0.006; Rp, p = 0.022, and α, p = 0.041). Using a suitable threshold for the Rs, we obtained specificity = 60.7%, sensitivity = 77.9%, accuracy = 73.2%, and 100% of detection for deep lesions. It can be concluded that BIS-STEP method could be an important tool to improve the detection and management of occlusal non-cavitated primary caries and pigmented sites.
The fractional diffusion limit of a kinetic model with biochemical pathway
Perthame, Benoît; Sun, Weiran; Tang, Min
2018-06-01
Kinetic-transport equations that take into account the intracellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathematical studies have shown their interest and their relations to more standard models. Macroscopic equations of Keller-Segel type have been derived using parabolic scaling. Due to the randomness of receptor methylation or intracellular chemical reactions, noise occurs in the signaling pathways and affects the tumbling rate. Then comes the question to understand the role of an internal noise on the behavior of the full population. In this paper we consider a kinetic model for chemotaxis which includes biochemical pathway with noises. We show that under proper scaling and conditions on the tumbling frequency as well as the form of noise, fractional diffusion can arise in the macroscopic limits of the kinetic equation. This gives a new mathematical theory about how long jumps can be due to the internal noise of the bacteria.
Fractional Response Models - A Replication Exercise of Papke and Wooldridge (1996
Directory of Open Access Journals (Sweden)
Harald Oberhofer
2012-09-01
Full Text Available This paper replicates the estimates of a fractional response model for share data reported in the seminal paper of Leslie E. Papke and Jeffrey M. Wooldridge published in the Journal of Applied Econometrics 11(6, 1996, pp.619-632. We have been able to replicate all of the reported estimation results concerning the determinants of employee participation rates in 401(k pension plans using the standard routines provided in Stata. As an alternative, we estimate a two-part model that is capable of coping with the excessive number of boundary values equalling one in the data. The estimated marginal effects are similar to those derived in the paper. A small-scale Monte Carlo simulation exercise suggests that the RESET tests proposed by Papke and Wooldridge in their robust form are useful for detecting neglected non-linearities in small samples.
Evidence of a fractional quantum Hall nematic phase in a microscopic model
Regnault, N.; Maciejko, J.; Kivelson, S. A.; Sondhi, S. L.
2017-07-01
At small momenta, the Girvin-MacDonald-Platzman (GMP) mode in the fractional quantum Hall (FQH) effect can be identified with gapped nematic fluctuations in the isotropic FQH liquid. This correspondence would be exact as the GMP mode softens upon approach to the putative point of a quantum phase transition to a FQH nematic. Motivated by these considerations as well as by suggestive evidence of an FQH nematic in tilted field experiments, we have sought evidence of such a nematic FQHE in a microscopic model of interacting electrons in the lowest Landau level at filling factor 1/3. Using a family of anisotropic Laughlin states as trial wave functions, we find a continuous quantum phase transition between the isotropic Laughlin liquid and the FQH nematic. Results of numerical exact diagonalization also suggest that rotational symmetry is spontaneously broken, and that the phase diagram of the model contains both a nematic and a stripe phase.
Directory of Open Access Journals (Sweden)
Jagdev Singh
2017-07-01
Full Text Available In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM, to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotopy analysis method and homotopy polynomials that makes the calculation very easy. To compare the results obtained by using q-HASTM, we solve the same nonlinear problem by Adomian’s decomposition method (ADM. The convergence of the q-HASTM series solution for the model is adapted and controlled by auxiliary parameter ℏ and asymptotic parameter n. The numerical results are demonstrated graphically and in tabular form. The result obtained by employing the proposed scheme reveals that the approach is very accurate, effective, flexible, simple to apply and computationally very nice.
Druhan, J. L.; Giannetta, M.; Sanford, R. A.
2017-12-01
, resulting in model behavior which is, in effect, a microbial redox analog to the variable observed fractionation factor resulting from a transition state theory rate law as derived by DePaolo (2011).
Numerically pricing American options under the generalized mixed fractional Brownian motion model
Chen, Wenting; Yan, Bowen; Lian, Guanghua; Zhang, Ying
2016-06-01
In this paper, we introduce a robust numerical method, based on the upwind scheme, for the pricing of American puts under the generalized mixed fractional Brownian motion (GMFBM) model. By using portfolio analysis and applying the Wick-Itô formula, a partial differential equation (PDE) governing the prices of vanilla options under the GMFBM is successfully derived for the first time. Based on this, we formulate the pricing of American puts under the current model as a linear complementarity problem (LCP). Unlike the classical Black-Scholes (B-S) model or the generalized B-S model discussed in Cen and Le (2011), the newly obtained LCP under the GMFBM model is difficult to be solved accurately because of the numerical instability which results from the degeneration of the governing PDE as time approaches zero. To overcome this difficulty, a numerical approach based on the upwind scheme is adopted. It is shown that the coefficient matrix of the current method is an M-matrix, which ensures its stability in the maximum-norm sense. Remarkably, we have managed to provide a sharp theoretic error estimate for the current method, which is further verified numerically. The results of various numerical experiments also suggest that this new approach is quite accurate, and can be easily extended to price other types of financial derivatives with an American-style exercise feature under the GMFBM model.
A novel patient-specific model to compute coronary fractional flow reserve.
Kwon, Soon-Sung; Chung, Eui-Chul; Park, Jin-Seo; Kim, Gook-Tae; Kim, Jun-Woo; Kim, Keun-Hong; Shin, Eun-Seok; Shim, Eun Bo
2014-09-01
The fractional flow reserve (FFR) is a widely used clinical index to evaluate the functional severity of coronary stenosis. A computer simulation method based on patients' computed tomography (CT) data is a plausible non-invasive approach for computing the FFR. This method can provide a detailed solution for the stenosed coronary hemodynamics by coupling computational fluid dynamics (CFD) with the lumped parameter model (LPM) of the cardiovascular system. In this work, we have implemented a simple computational method to compute the FFR. As this method uses only coronary arteries for the CFD model and includes only the LPM of the coronary vascular system, it provides simpler boundary conditions for the coronary geometry and is computationally more efficient than existing approaches. To test the efficacy of this method, we simulated a three-dimensional straight vessel using CFD coupled with the LPM. The computed results were compared with those of the LPM. To validate this method in terms of clinically realistic geometry, a patient-specific model of stenosed coronary arteries was constructed from CT images, and the computed FFR was compared with clinically measured results. We evaluated the effect of a model aorta on the computed FFR and compared this with a model without the aorta. Computationally, the model without the aorta was more efficient than that with the aorta, reducing the CPU time required for computing a cardiac cycle to 43.4%. Copyright © 2014. Published by Elsevier Ltd.
Kumar, Dinesh; Rai, K N
2017-07-01
In this paper, we investigated the thermal behavior in living biological tissues using time fractional dual-phase-lag bioheat transfer (DPLBHT) model subjected to Dirichelt boundary condition in presence of metabolic and electromagnetic heat sources during thermal therapy. We solved this bioheat transfer model using finite element Legendre wavelet Galerkin method (FELWGM) with help of block pulse function in sense of Caputo fractional order derivative. We compared the obtained results from FELWGM and exact method in a specific case, and found a high accuracy. Results are interpreted in the form of standard and anomalous cases for taking different order of time fractional DPLBHT model. The time to achieve hyperthermia position is discussed in both cases as standard and time fractional order derivative. The success of thermal therapy in the treatment of metastatic cancerous cell depends on time fractional order derivative to precise prediction and control of temperature. The effect of variability of parameters such as time fractional derivative, lagging times, blood perfusion coefficient, metabolic heat source and transmitted power on dimensionless temperature distribution in skin tissue is discussed in detail. The physiological parameters has been estimated, corresponding to the value of fractional order derivative for hyperthermia treatment therapy. Copyright © 2017 Elsevier Ltd. All rights reserved.
Rayleigh-Taylor mixing with time-dependent acceleration
Abarzhi, Snezhana
2016-10-01
We extend the momentum model to describe Rayleigh-Taylor (RT) mixing driven by a time-dependent acceleration. The acceleration is a power-law function of time, similarly to astrophysical and plasma fusion applications. In RT flow the dynamics of a fluid parcel is driven by a balance per unit mass of the rates of momentum gain and loss. We find analytical solutions in the cases of balanced and imbalanced gains and losses, and identify their dependence on the acceleration exponent. The existence is shown of two typical regimes of self-similar RT mixing-acceleration-driven Rayleigh-Taylor-type and dissipation-driven Richtymer-Meshkov-type with the latter being in general non-universal. Possible scenarios are proposed for transitions from the balanced dynamics to the imbalanced self-similar dynamics. Scaling and correlations properties of RT mixing are studied on the basis of dimensional analysis. Departures are outlined of RT dynamics with time-dependent acceleration from canonical cases of homogeneous turbulence as well as blast waves with first and second kind self-similarity. The work is supported by the US National Science Foundation.
Rayleigh-Taylor mixing with space-dependent acceleration
Abarzhi, Snezhana
2016-11-01
We extend the momentum model to describe Rayleigh-Taylor (RT) mixing driven by a space-dependent acceleration. The acceleration is a power-law function of space coordinate, similarly to astrophysical and plasma fusion applications. In RT flow the dynamics of a fluid parcel is driven by a balance per unit mass of the rates of momentum gain and loss. We find analytical solutions in the cases of balanced and imbalanced gains and losses, and identify their dependence on the acceleration exponent. The existence is shown of two typical sub-regimes of self-similar RT mixing - the acceleration-driven Rayleigh-Taylor-type mixing and dissipation-driven Richtymer-Meshkov-type mixing with the latter being in general non-universal. Possible scenarios are proposed for transitions from the balanced dynamics to the imbalanced self-similar dynamics. Scaling and correlations properties of RT mixing are studied on the basis of dimensional analysis. Departures are outlined of RT dynamics with space-dependent acceleration from canonical cases of homogeneous turbulence as well as blast waves with first and second kind self-similarity. The work is supported by the US National Science Foundation.
Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad
2017-07-01
This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two numerical schemes namely an iterative scheme based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report numerical simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. Numerical experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative scheme.
N'Doye, Ibrahima; Laleg-Kirati, Taous-Meriem
2015-01-01
, and show the existence of chaos. The behavior and stability analysis of the integer-order and the fractional commensurate and non-commensurate orders of a fractional viscoelastic fluids system, which exhibits chaos, are presented as well.
Mathematical modelling of the mass-spring-damper system - A fractional calculus approach
Directory of Open Access Journals (Sweden)
Jesus Bernal Alvarado
2012-08-01
Full Text Available In this paper the fractional differential equation for the mass-spring-damper system in terms of the fractional time derivatives of the Caputo type is considered. In order to be consistent with the physical equation, a new parameter is introduced. This parameter characterizes the existence of fractional components in the system. A relation between the fractional order time derivative and the new parameter is found. Different particular cases are analyzed
Black holes in multi-fractional and Lorentz-violating models
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [CSIC, Instituto de Estructura de la Materia, Madrid (Spain); Rodriguez Fernandez, David [Universidad de Oviedo, Department of Physics, Oviedo (Spain); Ronco, Michele [Universita di Roma ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); INFN, Rome (Italy)
2017-05-15
We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length l{sub *}. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to l{sub *}. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models. (orig.)
Modeling of radial gas fraction profiles for bubble flow in vertical pipes
Energy Technology Data Exchange (ETDEWEB)
Lucas, D.; Krepper, E.; Prasser, H.-M. [Forschungszentrum Rossendorf e.V., Institute of Safety Research, Dresden (Germany)
2001-07-01
The paper presents a method for the prediction of radial gas fraction profiles from a given bubble size distribution. The method is based on the assumption of the equilibrium of the forces acting on a bubble perpendicularly to the flow direction. Assuming a large number of bubble size classes radial distributions are calculated separately for all bubble classes. The sum of these distributions is the radial profile of the gas fraction. The results of the model are compared with experimental data for a number of gas and liquid volume flow rates. The experiments were performed at a vertical test loop (inner diameter 50 mm) in FZ-Rossendorf using a wire mesh sensor. The sensor enables the determination of void distributions in the cross section of the loop. A special evaluation procedure supplies bubble size distributions as well as local distributions of bubbles within a predefined interval of bubble sizes. There is a good agreement between experimental and calculated data. In particular the change from wall peaking to core peaking is well predicted. (authors)
Black holes in multi-fractional and Lorentz-violating models
International Nuclear Information System (INIS)
Calcagni, Gianluca; Rodriguez Fernandez, David; Ronco, Michele
2017-01-01
We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length l_*. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to l_*. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models. (orig.)
Modeling of radial gas fraction profiles for bubble flow in vertical pipes
International Nuclear Information System (INIS)
Lucas, D.; Krepper, E.; Prasser, H.-M.
2001-01-01
The paper presents a method for the prediction of radial gas fraction profiles from a given bubble size distribution. The method is based on the assumption of the equilibrium of the forces acting on a bubble perpendicularly to the flow direction. Assuming a large number of bubble size classes radial distributions are calculated separately for all bubble classes. The sum of these distributions is the radial profile of the gas fraction. The results of the model are compared with experimental data for a number of gas and liquid volume flow rates. The experiments were performed at a vertical test loop (inner diameter 50 mm) in FZ-Rossendorf using a wire mesh sensor. The sensor enables the determination of void distributions in the cross section of the loop. A special evaluation procedure supplies bubble size distributions as well as local distributions of bubbles within a predefined interval of bubble sizes. There is a good agreement between experimental and calculated data. In particular the change from wall peaking to core peaking is well predicted. (authors)
Black holes in multi-fractional and Lorentz-violating models.
Calcagni, Gianluca; Rodríguez Fernández, David; Ronco, Michele
2017-01-01
We study static and radially symmetric black holes in the multi-fractional theories of gravity with q -derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length [Formula: see text]. In the q -derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to [Formula: see text]. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q -derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models.
An actual load forecasting methodology by interval grey modeling based on the fractional calculus.
Yang, Yang; Xue, Dingyü
2017-07-17
The operation processes for thermal power plant are measured by the real-time data, and a large number of historical interval data can be obtained from the dataset. Within defined periods of time, the interval information could provide important information for decision making and equipment maintenance. Actual load is one of the most important parameters, and the trends hidden in the historical data will show the overall operation status of the equipments. However, based on the interval grey parameter numbers, the modeling and prediction process is more complicated than the one with real numbers. In order not lose any information, the geometric coordinate features are used by the coordinates of area and middle point lines in this paper, which are proved with the same information as the original interval data. The grey prediction model for interval grey number by the fractional-order accumulation calculus is proposed. Compared with integer-order model, the proposed method could have more freedom with better performance for modeling and prediction, which can be widely used in the modeling process and prediction for the small amount interval historical industry sequence samples. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Fayssal, Iyad A; Moukalled, Fadl; Alam, Samir; Isma'eel, Hussain
2018-04-01
This paper reports on a new boundary condition formulation to model the total coronary myocardial flow and resistance characteristics of the myocardial vascular bed for any specific patient when considered for noninvasive diagnosis of ischemia. The developed boundary condition model gives an implicit representation of the downstream truncated coronary bed. Further, it is based on incorporating patient-specific physiological parameters that can be noninvasively extracted to account for blood flow demand to the myocardium at rest and hyperemic conditions. The model is coupled to a steady three-dimensional (3D) collocated pressure-based finite volume flow solver and used to characterize the "functional significance" of a patient diseased coronary artery segment without the need for predicting the hemodynamics of the entire arterial system. Predictions generated with this boundary condition provide a deep understanding of the inherent challenges behind noninvasive image-based diagnostic techniques when applied to human diseased coronary arteries. The overall numerical method and formulated boundary condition model are validated via two computational-based procedures and benchmarked with available measured data. The newly developed boundary condition is used via a designed computational methodology to (a) confirm the need for incorporating patient-specific physiological parameters when modeling the downstream coronary resistance, (b) explain the discrepancies presented in the literature between measured and computed fractional flow reserve (FFRCT), and (c) discuss the current limitations and future challenges in shifting to noninvasive assessment of ischemia.
Energy Technology Data Exchange (ETDEWEB)
Sabzikar, Farzad, E-mail: sabzika2@stt.msu.edu [Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823 (United States); Meerschaert, Mark M., E-mail: mcubed@stt.msu.edu [Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823 (United States); Chen, Jinghua, E-mail: cjhdzdz@163.com [School of Sciences, Jimei University, Xiamen, Fujian, 361021 (China)
2015-07-15
Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.
Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua
2015-07-01
Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.
International Nuclear Information System (INIS)
Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua
2015-01-01
Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series
Rayleigh wave effects in an elastic half-space.
Aggarwal, H. R.
1972-01-01
Consideration of Rayleigh wave effects in a homogeneous isotropic linearly elastic half-space subject to an impulsive uniform disk pressure loading. An approximate formula is obtained for the Rayleigh wave effects. It is shown that the Rayleigh waves near the center of loading arise from the portion of the dilatational and shear waves moving toward the axis, after they originate at the edge of the load disk. A study is made of the vertical displacement due to Rayleigh waves at points on the axis near the surface of the elastic half-space.
Directory of Open Access Journals (Sweden)
Fuqiang Zhao
2017-01-01
Full Text Available In the current study, a numerical technique for solving one-dimensional fractional nonsteady heat transfer model is presented. We construct the second kind Chebyshev wavelet and then derive the operational matrix of fractional-order integration. The operational matrix of fractional-order integration is utilized to reduce the original problem to a system of linear algebraic equations, and then the numerical solutions obtained by our method are compared with those obtained by CAS wavelet method. Lastly, illustrated examples are included to demonstrate the validity and applicability of the technique.
Modeling anomalous diffusion by a subordinated fractional Lévy-stable process
International Nuclear Information System (INIS)
Teuerle, Marek; Wyłomańska, Agnieszka; Sikora, Grzegorz
2013-01-01
Two phenomena that can be discovered in systems with anomalous diffusion are long-range dependence and trapping events. The first effect concerns events that are arbitrarily distant but still influence each other exceptionally strongly, which is characteristic for anomalous regimes. The second corresponds to the presence of constant values of the underlying process. Motivated by the relatively poor class of models that can cover these two phenomena, we introduce subordinated fractional Lévy-stable motion with tempered stable waiting times. We present in detail its main properties, propose a simulation scheme and give an estimation procedure for its parameters. The last part of the paper is a presentation, via the Monte Carlo approach, of the effectiveness of the estimation of the parameters. (paper)
International Nuclear Information System (INIS)
Liu Yaozong; Yu Dianlong; Zhao Honggang; Wen Jihong; Wen Xisen
2008-01-01
Wave propagation in two-dimensional phononic crystals (PCs) with viscoelasticity is investigated using a finite-difference-time-domain (FDTD) method. The viscoelasticity is evaluated using the Kelvin-Voigt model with fractional derivatives (FDs) so that both the dispersion and dissipation are considered. Numerical approximation of FDs is integrated into the FDTD scheme to simulate wave propagation in such PCs. All the constituent materials are treated as isotropic and homogeneous. The gaps are substantially displaced and widened and the attenuation is noticeably enhanced due to the dispersion and dissipation of host material and the complicated multiple scattering between scatterers. These results indicate that the viscoelasticity of the damping host has significant influence on wave propagation in PCs and should be considered
Space-fractional model for the spreading of matter in heterogeneous porous media
International Nuclear Information System (INIS)
Krepysheva, N.; Neel, M.Ch.
2005-01-01
In very heterogeneous porous media (like the soil, or an aquifer, for instance), experimental results showed that mass transport sometimes does not obey Fourier's law. Continuous Time Random Walks in the form of L y Flights provide a small scale model for super diffusive spreading of a tracer plume, dissolved in a fluid, itself enclosed in a porous medium. In an infinite medium, the corresponding behavior of the concentration of solute is known to obey a variant of Fourier's law, with a Riesz-Feller operator in place of the Laplacian. Here we show that with some modifications the result extends to semi infinite media. A numerical method allowing for the simulation of fractional derivatives is adapted to semi infinite media, with special attention to convective terms, associated to a possibly non zero global trough flow. (authors)
Space-fractional model for the spreading of matter in heterogeneous porous media
Energy Technology Data Exchange (ETDEWEB)
Krepysheva, N. [Institut National de Recherches Agronomiques (INRA), UMRA Climat-Sol-Environnement, 84 - Avignon (France); Neel, M.Ch. [Universite d' Avignon, Faculte des Sciences, UMRA Climat-Sol-Environnement, 84 - Avignon (France)
2005-07-01
In very heterogeneous porous media (like the soil, or an aquifer, for instance), experimental results showed that mass transport sometimes does not obey Fourier's law. Continuous Time Random Walks in the form of L y Flights provide a small scale model for super diffusive spreading of a tracer plume, dissolved in a fluid, itself enclosed in a porous medium. In an infinite medium, the corresponding behavior of the concentration of solute is known to obey a variant of Fourier's law, with a Riesz-Feller operator in place of the Laplacian. Here we show that with some modifications the result extends to semi infinite media. A numerical method allowing for the simulation of fractional derivatives is adapted to semi infinite media, with special attention to convective terms, associated to a possibly non zero global trough flow. (authors)
Hypo-fractionated treatment in radiotherapy: radio-biological models Tcp and NTCP
International Nuclear Information System (INIS)
Astudillo V, A. J.; Mitsoura, E.; Paredes G, L.; Resendiz G, G.
2014-08-01
At the present time the breast cancer in Mexico has the first place of incidence of the malignant neoplasia s in the women, and represents 11.34% of all the cancer cases. On the other hand, the treatments for cancer by means of ionizing radiations have been dominated under the approaches of the medical radio-oncologists which have been based on test and error by many years. The radio-biological models, as the Tcp, NTCP and dosimetric variables, for their clinical application in the conventional radiotherapy with hypo-fractionation have as purpose predicting personalized treatment plans that they present most probability of tumor control and minor probability of late reactions, becoming this way support tools in the decisions taking for the patient treatments planning of Medical Physicists and Radio-oncologists. (Author)
International Nuclear Information System (INIS)
Wennberg, Berit M.; Baumann, Pia; Gagliardi, Giovanna
2011-01-01
Background. In SBRT of lung tumours no established relationship between dose-volume parameters and the incidence of lung toxicity is found. The aim of this study is to compare the LQ model and the universal survival curve (USC) to calculate biologically equivalent doses in SBRT to see if this will improve knowledge on this relationship. Material and methods. Toxicity data on radiation pneumonitis grade 2 or more (RP2+) from 57 patients were used, 10.5% were diagnosed with RP2+. The lung DVHs were corrected for fractionation (LQ and USC) and analysed with the Lyman- Kutcher-Burman (LKB) model. In the LQ-correction α/β = 3 Gy was used and the USC parameters used were: α/β = 3 Gy, D 0 = 1.0 Gy, n = 10, α 0.206 Gy-1 and d T = 5.8 Gy. In order to understand the relative contribution of different dose levels to the calculated NTCP the concept of fractional NTCP was used. This might give an insight to the questions of whether 'high doses to small volumes' or 'low doses to large volumes' are most important for lung toxicity. Results and Discussion. NTCP analysis with the LKB-model using parameters m = 0.4, D50 = 30 Gy resulted for the volume dependence parameter (n) with LQ correction n = 0.87 and with USC correction n = 0.71. Using parameters m = 0.3, D 50 = 20 Gy n = 0.93 with LQ correction and n 0.83 with USC correction. In SBRT of lung tumours, NTCP modelling of lung toxicity comparing models (LQ,USC) for fractionation correction, shows that low dose contribute less and high dose more to the NTCP when using the USC-model. Comparing NTCP modelling of SBRT data and data from breast cancer, lung cancer and whole lung irradiation implies that the response of the lung is treatment specific. More data are however needed in order to have a more reliable modelling
Rayleigh-Bénard turbulence modified by two-way coupled inertial, nonisothermal particles
Park, Hyungwon John; O'Keefe, Kevin; Richter, David H.
2018-03-01
Direct numerical simulation (DNS) combined with the Lagrangian point particle model is used to study Rayleigh-Bénard convection in order to understand modifications due to the interaction of inertial, nonisothermal particles with buoyancy-driven turbulence. In this system, turbulence can be altered through direct momentum coupling, as well as through buoyancy modification via thermal coupling between phases. We quantify the effect of the dispersed phase by changes to the total integrated turbulent kinetic energy (TKE) and Nusselt number (Nu). The dispersed particles experience gravitational settling and are introduced at the lower wall so that turbulence must overcome the settling velocity for the particles to vertically distribute throughout the domain. We focus primarily on particle inertia, settling velocity, mass fraction, and the ratio of the particle to fluid specific heat. Furthermore, individual contributions by the momentum coupling and thermal coupling are studied to see which most significantly changes Nu and TKE. Our results show that particles with Stokes number of order unity maximize Nu, corresponding to a peak of clustering and attenuation of TKE. Increased mass fractions lead to a linear increase of Nu and decrease of TKE. With varying specific heat ratio, Nu and TKE exhibit monotonic behaviors, where in the high limit particles become isothermal and depend upon the initialized particle temperature. It is also shown that particles two-way coupled only through momentum attenuate Nu and weaken TKE, while thermal-only coupling also weakens TKE but enhances Nu. When both couplings are present, however, thermal coupling overwhelms the momentum coupling attenuation, and the net result is an enhancement of Nu.
A simple proposal for Rayleigh's scaterring experiment
Directory of Open Access Journals (Sweden)
Adriano José Ortiz
2010-03-01
Full Text Available This work presents an alternative proposal for Rayleigh's scattering experiment presented and discussed in Krapas and Santos (2002 in this journal. Besides being simple and low-cost, the proposal suggested here is also proposing to demonstrate experimentally other physical phenomena such as polarization of light from the sky, the rainbow and reflection on non-conductive surfaces, as well as determine the direction of these biases. The polarization will be observed with the aid of Polaroid obtained from liquid crystal displays taken from damaged electronic devices and the Polaroid polarization direction will be established by the observation of Brewester's angle in reflection experiment.
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Yu Zhang
2015-10-01
Full Text Available In this article, we begin with the non-homogeneous model for the non-differentiable heat flow, which is described using the local fractional vector calculus, from the first law of thermodynamics in fractal media point view. We employ the local fractional variational iteration algorithm II to solve the fractal heat equations. The obtained results show the non-differentiable behaviors of temperature fields of fractal heat flow defined on Cantor sets.
Fractional-order leaky integrate-and-fire model with long-term memory and power law dynamics.
Teka, Wondimu W; Upadhyay, Ranjit Kumar; Mondal, Argha
2017-09-01
Pyramidal neurons produce different spiking patterns to process information, communicate with each other and transform information. These spiking patterns have complex and multiple time scale dynamics that have been described with the fractional-order leaky integrate-and-Fire (FLIF) model. Models with fractional (non-integer) order differentiation that generalize power law dynamics can be used to describe complex temporal voltage dynamics. The main characteristic of FLIF model is that it depends on all past values of the voltage that causes long-term memory. The model produces spikes with high interspike interval variability and displays several spiking properties such as upward spike-frequency adaptation and long spike latency in response to a constant stimulus. We show that the subthreshold voltage and the firing rate of the fractional-order model make transitions from exponential to power law dynamics when the fractional order α decreases from 1 to smaller values. The firing rate displays different types of spike timing adaptation caused by changes on initial values. We also show that the voltage-memory trace and fractional coefficient are the causes of these different types of spiking properties. The voltage-memory trace that represents the long-term memory has a feedback regulatory mechanism and affects spiking activity. The results suggest that fractional-order models might be appropriate for understanding multiple time scale neuronal dynamics. Overall, a neuron with fractional dynamics displays history dependent activities that might be very useful and powerful for effective information processing. Copyright © 2017 Elsevier Ltd. All rights reserved.
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Wei Wang
2013-01-01
Full Text Available The precipitation of wax/solid paraffin during production, transportation, and processing of crude oil is a serious problem. It is essential to have a reliable model to predict the wax appearance temperature and the amount of solid precipitated at different conditions. This paper presents a work to predict the solid precipitation based on solid-liquid equilibrium with regular solution-molecular thermodynamic theory and characterization of the crude oil plus fraction. Due to the differences of solubility characteristics between solid and liquid phase, the solubility parameters of liquid and solid phase are calculated by a modified model. The heat capacity change between solid and liquid phase is considered and estimated in the thermodynamic model. An activity coefficient based thermodynamic method combined with two characteristic methods to calculate wax precipitation in crude oil, especially heavy oil, has been tested with experimental data. The results show that the wax appearance temperature and the amount of weight precipitated can be predicted well with the experimental data.
NMR signals within the generalized Langevin model for fractional Brownian motion
Lisý, Vladimír; Tóthová, Jana
2018-03-01
The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard memoryless Langevin description of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spin-bearing particles in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in an exceedingly simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues. The effect of the trap is demonstrated by introducing a simple model for the generalized diffusion coefficient of the particle.
The effect of pressure on spontaneous Rayleigh-Brillouin scattering spectrum in nitrogen
Yang, Chuanyin; Wu, Tao; Shang, Jingcheng; Zhang, Xinyi; Hu, Rongjing; He, XingDao
2018-05-01
In order to study the effect of gas pressure on spontaneous Rayleigh-Brillouin scattering spectrum and verify the validity of Tenti S6 model at pressures up to 8 atm, the spontaneous Rayleigh-Brillouin scattering experiment in nitrogen was performed for a wavelength of 532 nm at the constant room temperature of 296 K and a 90° scattering angle. By comparing the experimental spectrum with the theoretical spectrum, the normalized root mean square deviation was calculated and found less than 2.2%. It is verified that Tenti S6 model can be applied to the spontaneous Rayleigh-Brillion scattering of nitrogen under higher pressures. The results of the experimental data analysis demonstrate that pressure has more effect on Brillouin peak intensity and has negligible effect on Brillouin frequency shift, and pressure retrieval based on spontaneous Rayleigh-Brillouin scattering profile is a promising method for remote of pressure, such as harsh environment applications. Some factors that caused experiment deviations are also discussed.
Bentil, Sarah A; Dupaix, Rebecca B
2014-02-01
The ability of the fractional Zener constitutive model to predict the behavior of postmortem swine brain tissue was examined in this work. Understanding tissue behavior attributed to degradation is invaluable in many fields such as the forensic sciences or cases where only cadaveric tissue is available. To understand how material properties change with postmortem age, the fractional Zener model was considered as it includes parameters to describe brain stiffness and also the parameter α, which quantifies the viscoelasticity of a material. The relationship between the viscoelasticity described by α and tissue degradation was examined by fitting the model to data collected in a previous study (Bentil, 2013). This previous study subjected swine neural tissue to in vitro unconfined compression tests using four postmortem age groups (week). All samples were compressed to a strain level of 10% using two compressive rates: 1mm/min and 5mm/min. Statistical analysis was used as a tool to study the influence of the fractional Zener constants on factors such as tissue degradation and compressive rate. Application of the fractional Zener constitutive model to the experimental data showed that swine neural tissue becomes less stiff with increased postmortem age. The fractional Zener model was also able to capture the nonlinear viscoelastic features of the brain tissue at low strain rates. The results showed that the parameter α was better correlated with compressive rate than with postmortem age. © 2013 Published by Elsevier Ltd.
Maggi, F.; Riley, W. J.
2009-12-01
The composition and location of 15N atoms on N2O isotopomers and isotopologues during isotope speciation has been used to characterize soil biological N cycling and N2O surface emissions. Although there exist few experimental observations, no attempt has been made to model N2O isotopomer speciation. The mathematical treatment of biological kinetic reactions in isotopic applications normally makes use of first-order and quasi steady-state complexation assumptions without taking into account changes in enzyme concentration, reaction stoichiometry, and isotopologue and isotopomer speciation. When multiatomic isotopically-labeled reactants are used in a multi-molecurar reaction, these assumptions may fail since they always lead to a constant fractionation factor and cannot describe speciation of isotopologues and isotopomers. We have developed a mathematical framework that is capable of describing isotopologue and isotopmer speciation and fractionation under the assumption of non-steady complexation during biological kinetic reactions that overcome the limitations mentioned above. This framework was applied to a case study of non-steady (variable and inverse) isotopic effects observed during N2O production and consumption in soils. Our mathematical treatment has led to generalized kinetic equations which replicate experimental observations with high accuracy and help interpret non-steady isotopic effects and isotopologue and isotopomer speciation. The kinetic equations introduced and applied here have general validity in describing isotopic effects in any biochemical reactions by considering: changing enzyme concentrations, mass and isotope conservation, and reaction stoichiometry. The equations also describe speciation of any isotopologue and isotopomer product from any isotopologue and isotopmer reactant.
Maggi, Federico; Riley, William J.
2009-12-01
The theoretical formulation of biological kinetic isotope fractionation often assumes first-order or Michaelis-Menten kinetics, the latter solved under the quasi-steady state assumption. Both formulations lead to a constant isotope fractionation factor, therefore they may return incorrect estimations of isotopic effects and misleading interpretations of isotopic signatures when fractionation is not a steady process. We have analyzed the isotopic signature of denitrification in biogeochemical soil systems by Menyailo and Hungate (2006) in which high and variable 15N-N2O enrichment during N2O production and inverse isotope fractionation during N2O consumption could not be explained with first-order kinetics and the Rayleigh equation, or with Michaelis-Menten kinetics. When Michaelis-Menten kinetics were coupled to Monod kinetics to describe biomass and enzyme dynamics, and the quasi-steady state assumption was relaxed, transient Michaelis-Menten-Monod kinetics accurately reproduced the observed concentrations, and variable and inverse isotope fractionations. These results imply a substantial revision in modeling isotopic effects, suggesting that steady state kinetics such as first-order, Rayleigh, and classic Michaelis-Menten kinetics should be superseded by transient kinetics in conjunction with biomass and enzyme dynamics.
Universality in quasiperiodic Rayleigh-Benard convection
International Nuclear Information System (INIS)
Ecke, R.E.; Mainieri, R.; Sullivan, T.S.
1991-01-01
We study universal scaling properties of quasiperiodic Rayleigh-Benard convection in a 3 He--superfluid- 4 He mixture. The critical line is located in a parameter space of Rayleigh and Prandtl numbers using a transient-Poincare-section technique to identify transitions from nodal periodic points to spiral periodic points within resonance horns. We measure the radial and angular contraction rates and extract the linear-stability eigenvalues (Flouquet multipliers) of the periodic point. At the crossings of the critical line with the lines of fixed golden-mean-tail winding number we determine the universality class of our experimental dynamics using f(α) and trajectory-scaling-function analyses. A technique is used to obtain a robust five-scale approximation to the universal trajectory scaling function. Different methods of multifractal analysis are employed and an understanding of statistical and systematic errors in these procedures is developed. The power law of the inflection point of the map, determined for three golden-mean-tail winding numbers, is 2.9±0.3, corresponding to the universality class of the sine map
Penetrative convection at high Rayleigh numbers
Toppaladoddi, Srikanth; Wettlaufer, John S.
2018-04-01
We study penetrative convection of a fluid confined between two horizontal plates, the temperatures of which are such that a temperature of maximum density lies between them. The range of Rayleigh numbers studied is Ra=[0.01 ,4 ]106,108 and the Prandtl numbers are Pr=1 and 11.6. An evolution equation for the growth of the convecting region is obtained through an integral energy balance. We identify a new nondimensional parameter, Λ , which is the ratio of temperature difference between the stable and unstable regions of the flow; larger values of Λ denote increased stability of the upper stable layer. We study the effects of Λ on the flow field using well-resolved lattice Boltzmann simulations and show that the characteristics of the flow depend sensitively upon it. For the range Λ = , we find that for a fixed Ra the Nusselt number, Nu, increases with decreasing Λ . We also investigate the effects of Λ on the vertical variation of convective heat flux and the Brunt-Väisälä frequency. Our results clearly indicate that in the limit Λ →0 the problem reduces to that of the classical Rayleigh-Bénard convection.
Joel W. Homan; Charles H. Luce; James P. McNamara; Nancy F. Glenn
2011-01-01
Describing the spatial variability of heterogeneous snowpacks at a watershed or mountain-front scale is important for improvements in large-scale snowmelt modelling. Snowmelt depletion curves, which relate fractional decreases in snowcovered area (SCA) against normalized decreases in snow water equivalent (SWE), are a common approach to scale-up snowmelt models....
DEFF Research Database (Denmark)
Nielsen, Joakim Refslund; Dellwik, Ebba; Hahmann, Andrea N.
2014-01-01
A method is presented for development of satellite green vegetation fraction (GVF) time series for use in the Weather Research and Forecasting (WRF) model. The GVF data is in the WRF model used to describe the temporal evolution of many land surface parameters, in addition to the evolution of veg...
DEFF Research Database (Denmark)
Manfredi, Simone; Tonini, Davide; Christensen, Thomas Højlund
2011-01-01
and environmental factors involved, including energy generation from landfill gas and storage of biogenic carbon. Leachate and gas emissions associated to each individual waste fraction have been estimated by means of a mathematical modelling. This approach towards landfilling emissions allows for a more precise...... quantification of the landfill impacts when comparing management options for selected waste fractions.Results from the life-cycle impact assessment (LCIA) show that the environmental performance estimated for landfilling with energy recovery of the fractions “organics” and “recyclable paper” is comparable...... with composting (for “organics”) and incineration (for “recyclable paper”). This however requires high degree of control over gas and leachate emissions, high gas collection efficiency and extensive gas utilization at the landfill. For the other waste fractions, recycling and incineration are favourable, although...
Lisý, Vladimír; Tóthová, Jana
2018-02-01
Nuclear magnetic resonance is often used to study random motion of spins in different systems. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard Langevin theory of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spins in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in a simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues.
Directory of Open Access Journals (Sweden)
Pietro Bia
2016-01-01
Full Text Available The interaction of electromagnetic fields and biological tissues has become a topic of increasing interest for new research activities in bioelectrics, a new interdisciplinary field combining knowledge of electromagnetic theory, modeling, and simulations, physics, material science, cell biology, and medicine. In particular, the feasibility of pulsed electromagnetic fields in RF and mm-wave frequency range has been investigated with the objective to discover new noninvasive techniques in healthcare. The aim of this contribution is to illustrate a novel Finite-Difference Time-Domain (FDTD scheme for simulating electromagnetic pulse propagation in arbitrary dispersive biological media. The proposed method is based on the fractional calculus theory and a general series expansion of the permittivity function. The spatial dispersion effects are taken into account, too. The resulting formulation is explicit, it has a second-order accuracy, and the need for additional storage variables is minimal. The comparison between simulation results and those evaluated by using an analytical method based on the Fourier transformation demonstrates the accuracy and effectiveness of the developed FDTD model. Five numerical examples showing the plane wave propagation in a variety of dispersive media are examined.
Supporting Students’ Reasoning About Multiplication of Fractions by Constructing an Array Model
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Ronal Rifandi
2017-08-01
Full Text Available The aim of the research is to support students in constructing an array model as a bridge from their informal knowledge to the formal one in understanding the part-whole relation concept. The part-whole relation concept is important for students to reason about multiplication of fractions. Realistic Mathematics Education which is in Indonesia adapted as Pendidikan Matematika Realistik Indonesia (PMRI is used as an approach in designing a series of lessons. For this purpose, hypothetical learning trajectory (HLT became the base for conducting a teaching experiment and designing its learning materials. The research was conducted in the fifth grade of SD Al Hikmah Surabaya, an elementary school in Indonesia, with five students as the participants. The collected data were qualitative data in the form of students’ written works and the transcript of video recording during the lesson. The data were analyzed retrospectively by confronting the conjecture of students’ thinking in the HLT with the fact in the teaching experiment. The result of the research shows that most students could use the contextual problem in promoting their ability on constructing their own array model to reason about part-whole relation.
Rayleigh-Taylor analysis in a laser-induced plasma
International Nuclear Information System (INIS)
Marin, R A; Gonzales, C A; Riascos, H
2012-01-01
We report the conditions (plasma parameters) under which the Rayleigh-Taylor Instability (RTI) develops in an Al plasma produced by a Nd:Yag pulsed laser with a fluence range of 1 to 4 J/cm 2 , wavelength of 1064nm and 10Hz repetition rate. The used data correspond to different pressure values of the ambient N atmosphere. From previous works, we took the RTI growth rate form. From the perturbation theory the instability amplitude is proportional to e -ηt . Using the drag model, we calculated the plume dynamics equations integrating the instability term and plotted the instability growth profile with the delay time values to get critical numbers for it, in order to show under which conditions the RTI appears.
Size invariance of the granular Rayleigh-Taylor instability.
Vinningland, Jan Ludvig; Johnsen, Øistein; Flekkøy, Eirik G; Toussaint, Renaud; Måløy, Knut Jørgen
2010-04-01
The size scaling behavior of the granular Rayleigh-Taylor instability [J. L. Vinningland, Phys. Rev. Lett. 99, 048001 (2007)] is investigated experimentally, numerically, and theoretically. An upper layer of grains displaces a lower gap of air by organizing into dense fingers of falling grains separated by rising bubbles of air. The dependence of these structures on the system and grain sizes is investigated. A spatial measurement of the finger structures is obtained by the Fourier power spectrum of the wave number k. As the size of the grains increases the wave number decreases accordingly which leaves the dimensionless product of wave number and grain diameter, dk, invariant. A theoretical interpretation of the invariance, based on the scaling properties of the model equations, suggests a gradual breakdown of the invariance for grains smaller than approximately 70 microm or greater than approximately 570 microm in diameter.
Numerical simulation of anisotropic preheating ablative Rayleigh-Taylor instability
International Nuclear Information System (INIS)
Wang Lifeng; Ye Wenhua; Li Yingjun
2010-01-01
The linear growth rate of the anisotropic preheating ablative Rayleigh-Taylor instability (ARTI) is studied by numerical simulations. The preheating model κ(T)=κ SH [1+f(T)] is applied, where f(T) is the preheating function interpreting the preheating tongue effect in the cold plasma ahead of the ablative front. An arbitrary coefficient D is introduced in the energy equation to study the influence of transverse thermal conductivity on the growth of the ARTI. We find that enhancing diffusion in a plane transverse to the mean longitudinal flow can strongly reduce the growth of the instability. Numerical simulations exhibit a significant stabilization of the ablation front by improving the transverse thermal conduction. Our results are in general agreement with the theory analysis and numerical simulations by Masse. (authors)
Front propagation in Rayleigh-Taylor systems with reaction
International Nuclear Information System (INIS)
Scagliarini, A; Biferale, L; Sbragaglia, M; Mantovani, F; Pivanti, M; Schifano, S F; Tripiccione, R; Pozzati, F; Toschi, F
2011-01-01
A special feature of Rayleigh-Taylor systems with chemical reactions is the competition between turbulent mixing and the 'burning processes', which leads to a highly non-trivial dynamics. We studied the problem performing high resolution numerical simulations of a 2d system, using a thermal lattice Boltzmann (LB) model. We spanned the various regimes emerging at changing the relative chemical/turbulent time scales, from slow to fast reaction; in the former case we found numerical evidence of an enhancement of the front propagation speed (with respect to the laminar case), providing a phenomenological argument to explain the observed behaviour. When the reaction is very fast, instead, the formation of sharp fronts separating patches of pure phases, leads to an increase of intermittency in the small scale statistics of the temperature field.
Rho, a Fraction From Rhodiola crenulate, Ameliorates Hepatic Steatosis in Mice Models
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Qin Yi
2018-03-01
Full Text Available The prevalence of non-alcoholic fatty liver disease (NAFLD, which is developed from hepatic steatosis, is increasing worldwide. However, no specific drugs for NAFLD have been approved yet. To observe the effects of Rho, a fraction from Rhodiola crenulate, on non-alcoholic hepatic steatosis, three mouse models with characteristics of NAFLD were used including high-fat diet (HFD-induced obesity (DIO mice, KKAy mice, and HFD combined with tetracycline stimulated Model-T mice. Hepatic lipid accumulation was determined via histopathological analysis and/or hepatic TG determination. The responses to insulin were evaluated by insulin tolerance test (ITT, glucose tolerance test (GTT, and hyperinsulinemic-euglycemic clamp, respectively. The pathways involved in hepatic lipid metabolism were observed via western-blot. Furthermore, the liver microcirculation was observed by inverted microscopy. The HPLC analysis indicated that the main components of Rho were flavan polymers. The results of histopathological analysis showed that Rho could ameliorate hepatic steatosis in DIO, KKAy, and Model-T hepatic steatosis mouse models, respectively. After Rho treatment in DIO mice, insulin resistance was improved with increasing glucose infusion rate (GIR in hyperinsulinemic-euglycemic clamp, and decreasing areas under the blood glucose-time curve (AUC in both ITT and GTT; the pathways involved in fatty acid uptake and de novo lipogenesis were both down-regulated, respectively. However, the pathways involved in beta-oxidation and VLDL-export on hepatic steatosis were not changed significantly. The liver microcirculation disturbances were also improved by Rho in DIO mice. These results suggest that Rho is a lead nature product for hepatic steatosis treatment. The mechanism is related to enhancing insulin sensitivity, suppressing fatty acid uptake and inhibiting de novo lipogenesis in liver.
Ice-vapor equilibrium fractionation factor of hydrogen and oxygen isotopes
DEFF Research Database (Denmark)
Ellehøj, Mads Dam; Steen-Larsen, Hans Christian; Johnsen, Sigfus Johann
2013-01-01
RATIONALE: The equilibrium fractionation factors govern the relative change in the isotopic composition during phase transitions of water. The commonly used results, which were published more than 40 years ago, are limited to a minimum temperature of -33 degrees C. This limits the reliability...... values, with a temperature dependency in accordance with theory for equilibrium fractionation. We obtain the following expressions for the temperature dependency of the fractionation coefficients: ln(alpha(delta 2H)) = 0.2133 - 203.10/T + 48888/T-2 ln(alpha(delta 18O)) = 0.0831 - 49.192/T + 8312.5/T2...... Compared with previous experimental work, a significantly larger for H-2 is obtained while, for O-18, is larger for temperatures below -20 degrees C and slightly lower for temperatures above this. CONCLUSIONS: Using the new values for alpha, a Rayleigh distillation model shows significant changes in both...
Energy Technology Data Exchange (ETDEWEB)
Cimpan, Emil
2004-09-15
water fraction. The model intended to employ existent formulas of the medium parameters worked out by Maxwell, Bruggeman and Ramu and Rao. However, to calculate the loss due to the induced eddy currents within the medium in the particular case of the oil continuous phase, other mathematical models expressing (equivalent) medium conductivity and permittivity were required and developed in this work. Although the resonance frequency of the coil was decreasing with increasing medium conductivity, this variation was not as significant as the variation of the coil impedance. This raised the question as to whether coils having the same self-resonance frequency in different media could be constructed. This was worth investigating because it could simplify the mathematical modelling. This was indeed the case and coils featuring approximately the same resonance frequency in different media were made. Concluding, the measuring device based on the HFMFT, which was constructed, investigated and described in this work can be developed into a practical instrument for monitoring the water fraction in multiphase flows. The overall measurement accuracy when using this technique would depend on the analytical models expressing the medium parameters and circumscribing the HFMFT itself. When the mathematical modelling of the HFMFT was finalised, it was understood that many other applications of the technique were also possible. Some of these applications, which might be of interest such as a conductivity meter and a three-component ratio meter, are briefly discussed.
Study on Rayleigh Wave Inversion for Estimating Shear-wave Velocity Profile
Directory of Open Access Journals (Sweden)
T.A. Sanny
2003-05-01
Full Text Available Rayleigh wave or ground roll is a noise in seismic body waves. However, how to use this noise for soil characterization is very interesting since Rayleigh wave phase velocity is a function of compression-wave velocity, shear-wave velocity, density and layer thickness. In layered-medium Rayleigh wave velocity also depends on wavelength or frequency, and this phenomenon is called dispersion. Inversion procedure to get shear-wave velocity profile needs a priori information about the solution of the problem to limit the unknown parameters. The Lagrange multiplier method was used to solve the constrained optimization problems or well known as a smoothing parameter in inversion problems. The advantage of our inversion procedure is that it can guarantee the convergence of solution even though the field data is incomplete, insufficient, and inconsistent. The addition of smoothing parameter can reduce the time to converge. Beside numerical stability, the statistical stability is also involved in inversion procedure. In field experiment we extracted ground roll data from seismic refraction record. The dispersion curves had been constructed by applying f-k analysis and f-k dip filtering. The dispersion curves show the dependence of Rayleigh wave phase velocities in layered media to frequency. The synthetic models also demonstrate the stability and the speed of inversion procedure.
Una versión de la distribución Rayleigh generalizada transmutada
Directory of Open Access Journals (Sweden)
Yuri A. Iriarte
2015-06-01
Full Text Available La calidad de los procedimientos utilizados en un análisis estadístico depende en gran medida del modelo o las distribuciones de probabilidad que se emplean. Debido a esto, diversos autores han realizado un esfuerzo considerable en generalizar o extender distribuciones de probabilidad presentes en la literatura estadística. En este contexto, Vodă en [13] introduce la distribución de probabilidad Rayleigh generalizada; esta distribución es bastante utilizada en el análisis estadístico de confiabilidad. En este artículo extendemos la distribución Rayleigh generalizada usando el mapa de transmutación de rango cuadrático estudiado por Shaw y Buckley en [12]. Estudiamos las principales propiedades del nuevo modelo, realizamos inferencia estadística y mostramos una aplicación con datos reales. Finalmente, se presentan las principales conclusiones del artículo. Abstract. Statistical analysis procedures’s quality depends on the proper use of the probability distributions. For that reason, many probability distributions have been generalized. For example, Vodă in [13] introduced the generalized Rayleigh distribution, a model widely used in reliability analysis. In this article, we introduce an extension of the generalized Rayleigh distribution using the quadratic rank transmutation map studied by Shaw and Buckley in [12]. We study t
Large-scale patterns in Rayleigh-Benard convection
International Nuclear Information System (INIS)
Hardenberg, J. von; Parodi, A.; Passoni, G.; Provenzale, A.; Spiegel, E.A.
2008-01-01
Rayleigh-Benard convection at large Rayleigh number is characterized by the presence of intense, vertically moving plumes. Both laboratory and numerical experiments reveal that the rising and descending plumes aggregate into separate clusters so as to produce large-scale updrafts and downdrafts. The horizontal scales of the aggregates reported so far have been comparable to the horizontal extent of the containers, but it has not been clear whether that represents a limitation imposed by domain size. In this work, we present numerical simulations of convection at sufficiently large aspect ratio to ascertain whether there is an intrinsic saturation scale for the clustering process when that ratio is large enough. From a series of simulations of Rayleigh-Benard convection with Rayleigh numbers between 10 5 and 10 8 and with aspect ratios up to 12π, we conclude that the clustering process has a finite horizontal saturation scale with at most a weak dependence on Rayleigh number in the range studied
DEFF Research Database (Denmark)
Jala, Ram Chandra Reddy; Guo, Zheng; Bjerring, Thomas
2010-01-01
A multi-stage temperature-programmed fractionating crystallization process was carried out to examine the effects of the presence of stearic acid (SA), oleic acid (OA), and linoleic acid (LA) on the separation of elaidic acid (EA). The results showed that the efficiency of fractionating...
Asphaltene self-association: Modeling and effect of fractionation with a polar solvent
DEFF Research Database (Denmark)
Garcia, Daniel Merino; Murgich, J; Andersen, Simon Ivar
2004-01-01
of DeltaH(a) obtained suggest that a fraction of asphaltenes is not active in the calorimetric experiments. Asphaltenes from Venezuela (LM1) and Mexico (KU) have been fractionated by precipitation with a mixture of acetone and toluene. It is considered that the most polar compounds are collected...
An economical and environmentally friendly whey protein fractionation process was developed using supercritical carbon dioxide (sCO2) as an acid to produce enriched fractions of alpha-lactalbumin (alpha-La) and beta-lactoglobulin (beta-Lg) from a commercial whey protein isolate (WPI) containing 55% ...
DEFF Research Database (Denmark)
Christensen, Bent Jesper; Kruse, Robinson; Sibbertsen, Philipp
We consider hypothesis testing in a general linear time series regression framework when the possibly fractional order of integration of the error term is unknown. We show that the approach suggested by Vogelsang (1998a) for the case of integer integration does not apply to the case of fractional...
Unstable Titan-generated Rayleigh-Taylor Lakes Impact Ice
Umurhan, O. M.; Korycansky, D. G.; Zahnle, K. J.
2014-12-01
The evolution of surface morphology on Titan, Triton, and other worlds is strongly influenced by the interplay of various fluid dynamical processes. Specifically, overturning instabilities can easily arise due to the special circumstances of landform evolution that probably occurred on these worlds. On Titan, large impacts that formed basins like Menrva crater (and possibly Hotei Regio) would have generated impact-melt ice lakes unstably arranged over less dense ice. Cantaloupe terrains, for example as seen on Triton, may be the result of condensation of volatiles (methane, nitrogen) leading to unstably stratified layers of different compositions and densities. In each of these cases, Rayleigh-Taylor instabilities leading to large scale diapirism may be at play. In addition to the dynamics of these instabilities, other physical effects (e.g. heat diffusion, freezing/melting, porosity, temperature dependent viscosity) likely play an important role in the evolution of these features. In this ongoing study, we examine the properties of unstably stratified fluids in which the lower less-dense ice has a temperature dependent viscosity. Surprisingly, we find that there exists an optimal disturbance length scale corresponding to the fastest growth of the Rayleigh-Taylor instability. For unstably stratified layers of water (low viscosity heavy liquid lying above an ice whose viscosity increases with depth) the fastest growing mode corresponds to 40-60 km scales with overturn times of approximately 100 days. We present a detailed numerical stability analysis in a corresponding Boussinessq model (in the creeping flow limit) incorporating thermal conduction and latent heat release and we examine the stability properties surveying a variety of parameters. We have also developed a two-dimensional numerical code (a hybrid spectral/compact-differencing scheme) to model the evolution of such systems for which we shall present preliminary numerical results depicting the outcome of
Direct numerical simulations of type Ia supernovae flames II: The Rayleigh-Taylor instability
International Nuclear Information System (INIS)
Bell, J.B.; Day, M.S.; Rendleman, C.A.; Woosley, S.E.; Zingale, M.
2004-01-01
A Type Ia supernova explosion likely begins as a nuclear runaway near the center of a carbon-oxygen white dwarf. The outward propagating flame is unstable to the Landau-Darrieus, Rayleigh-Taylor, and Kelvin-Helmholtz instabilities, which serve to accelerate it to a large fraction of the speed of sound. We investigate the Rayleigh-Taylor unstable flame at the transition from the flamelet regime to the distributed-burning regime, around densities of 10e7 gm/cc, through detailed, fully resolved simulations. A low Mach number, adaptive mesh hydrodynamics code is used to achieve the necessary resolution and long time scales. As the density is varied, we see a fundamental change in the character of the burning--at the low end of the density range the Rayleigh-Taylor instability dominates the burning, whereas at the high end the burning suppresses the instability. In all cases, significant acceleration of the flame is observed, limited only by the size of the domain we are able to study. We discuss the implications of these results on the potential for a deflagration to detonation transition
Kochunov, P; Chiappelli, J; Hong, L E
2013-01-01
Diffusion tensor imaging (DTI) assumes a single pool of anisotropically diffusing water to calculate fractional anisotropy (FA) and is commonly used to ascertain white matter (WM) deficits in schizophrenia. At higher b-values, diffusion-signal decay becomes bi-exponential, suggesting the presence of two, unrestricted and restricted, water pools. Theoretical work suggests that semi-permeable cellular membrane rather than the presence of two physical compartments is the cause. The permeability-diffusivity (PD) parameters measured from bi-exponential modeling may offer advantages, over traditional DTI-FA, in identifying WM deficits in schizophrenia. Imaging was performed in N = 26/26 patients/controls (age = 20-61 years, average age = 40.5 ± 12.6). Imaging consisted of fifteen b-shells: b = 250-3800 s/mm(2) with 30 directions/shell, covering seven slices of mid-sagittal corpus callosum (CC) at 1.7 × 1.7 × 4.6 mm. 64-direction DTI was also collected. Permeability-diffusivity-index (PDI), the ratio of restricted to unrestricted apparent diffusion coefficients, and the fraction of unrestricted compartment (Mu) were calculated for CC and cingulate gray matter (GM). FA values for CC were calculated using tract-based-spatial-statistics. Patients had significantly reduced PDI in CC (p ≅ 10(- 4)) and cingulate GM (p = 0.002), while differences in CC FA were modest (p ≅ .03). There was no group-related difference in Mu. Additional theoretical-modeling analysis suggested that reduced PDI in patients may be caused by reduced cross-membrane water molecule exchanges. PDI measurements for cerebral WM and GM yielded more robust patient-control differences than DTI-FA. Theoretical work offers an explanation that patient-control PDI differences should implicate abnormal active membrane permeability. This would implicate abnormal activities in ion-channels that use water as substrate for ion exchange, in cerebral tissues of schizophrenia patients.
Dou, Ruifeng; Phillion, A. B.
2016-08-01
Hot tearing susceptibility is commonly assessed using a pressure drop equation in the mushy zone that includes the effects of both tensile deformation perpendicular to the thermal gradient as well as shrinkage feeding. In this study, a Pore Fraction hot tearing model, recently developed by Monroe and Beckermann (JOM 66:1439-1445, 2014), is extended to additionally include the effect of strain rate parallel to the thermal gradient. The deformation and shrinkage pore fractions are obtained on the basis of the dimensionless Niyama criterion and a scaling variable method. First, the model is applied to the binary Al-Cu system under conditions of directional solidification. It is shown that for the same Niyama criterion, a decrease in the cooling rate increases both the deformation and shrinkage pore fractions because of an increase in the time spent in the brittle temperature region. Second, the model is applied to the industrial aluminum alloy AA5182 as part of a finite element simulation of the Direct Chill (DC) casting process. It is shown that an increase in the casting speed during DC casting increases the deformation and shrinkage pore fractions, causing the maximum point of pore fraction to move towards the base of the casting. These results demonstrate that including the strain rate parallel to the thermal gradient significantly improves the predictive quality of hot tearing criteria based on the pressure drop equation.
Experimental studies and model analysis of noble gas fractionation in porous media
Ding, Xin; Kennedy, B. Mack.; Evans, William C.; Stonestrom, David A.
2016-01-01
The noble gases, which are chemically inert under normal terrestrial conditions but vary systematically across a wide range of atomic mass and diffusivity, offer a multicomponent approach to investigating gas dynamics in unsaturated soil horizons, including transfer of gas between saturated zones, unsaturated zones, and the atmosphere. To evaluate the degree to which fractionation of noble gases in the presence of an advective–diffusive flux agrees with existing theory, a simple laboratory sand column experiment was conducted. Pure CO2 was injected at the base of the column, providing a series of constant CO2 fluxes through the column. At five fixed sampling depths within the system, samples were collected for CO2 and noble gas analyses, and ambient pressures were measured. Both the advection–diffusion and dusty gas models were used to simulate the behavior of CO2 and noble gases under the experimental conditions, and the simulations were compared with the measured depth-dependent concentration profiles of the gases. Given the relatively high permeability of the sand column (5 ´ 10−11 m2), Knudsen diffusion terms were small, and both the dusty gas model and the advection–diffusion model accurately predicted the concentration profiles of the CO2 and atmospheric noble gases across a range of CO2 flux from ?700 to 10,000 g m−2 d−1. The agreement between predicted and measured gas concentrations demonstrated that, when applied to natural systems, the multi-component capability provided by the noble gases can be exploited to constrain component and total gas fluxes of non-conserved (CO2) and conserved (noble gas) species or attributes of the soil column relevant to gas transport, such as porosity, tortuosity, and gas saturation.
Alvarez-Zaldívar, Pablo; Imfeld, Gwenaël; Maier, Uli; Centler, Florian; Thullner, Martin
2013-04-01
In recent years, the use of (constructed) wetlands has gained significant attention for the in situ remediation of groundwater contaminated with (chlorinated) organic hydrocarbons. Although many sophisticated experimental methods exist for the assessment of contaminant removal in such wetlands the understanding how changes in wetland hydrochemistry affect the removal processes is still limited. This knowledge gap might be reduced by the use of biogeochemical reactive transport models. This study presents the reactive transport simulation of a small-scale constructed wetland treated with groundwater containing cis-1,2-dichloroethene (cDCE). Simulated processes consider different cDCE biodegradation pathways and the associated carbon isotope fractionation, a set of further (bio)geochemical processes as well as the activity of the plant roots. Spatio-temporal hydrochemical and isotope data from a long-term constructed wetland experiment [1] are used to constrain the model. Simulation results for the initial oxic phase of the wetland experiment indicate carbon isotope enrichment factors typical for cometabolic DCE oxidation, which suggests that aerobic treatment of cDCE is not an optimal remediation strategy. For the later anoxic phase of the experiment model derived enrichment factors indicate reductive dechlorination pathways. This degradation is promoted at all wetland depths by a sufficient availability of electron donor and carbon sources from root exudates, which makes the anoxic treatment of groundwater in such wetlands an effective remediation strategy. In combination with the previous experimental data results from this study suggest that constructed wetlands are viable remediation means for the treatment of cDCE contaminated groundwater. Reactive transport models can improve the understanding of the factors controlling chlorinated ethenes removal, and the used model approach would also allow for an optimization of the wetland operation needed for a complete
Yang, Chen; Liu, Ying
2017-08-01
A two-dimensional depth-integrated numerical model is refined in this paper to simulate the hydrodynamics, graded sediment transport process and the fate of faecal bacteria in estuarine and coastal waters. The sediment mixture is divided into several fractions according to the grain size. A bed evolution model is adopted to simulate the processes of the bed elevation change and sediment grain size sorting. The faecal bacteria transport equation includes enhanced source and sink terms to represent bacterial kinetic transformation and disappearance or reappearance due to sediment deposition or re-suspension. A novel partition ratio and dynamic decay rates of faecal bacteria are adopted in the numerical model. The model has been applied to the turbid water environment in the Bristol Channel and Severn estuary, UK. The predictions by the present model are compared with field data and those by non-fractionated model.
Abdulhameed, M.; Vieru, D.; Roslan, R.
2017-10-01
This paper investigates the electro-magneto-hydrodynamic flow of the non-Newtonian behavior of biofluids, with heat transfer, through a cylindrical microchannel. The fluid is acted by an arbitrary time-dependent pressure gradient, an external electric field and an external magnetic field. The governing equations are considered as fractional partial differential equations based on the Caputo-Fabrizio time-fractional derivatives without singular kernel. The usefulness of fractional calculus to study fluid flows or heat and mass transfer phenomena was proven. Several experimental measurements led to conclusion that, in such problems, the models described by fractional differential equations are more suitable. The most common time-fractional derivative used in Continuum Mechanics is Caputo derivative. However, two disadvantages appear when this derivative is used. First, the definition kernel is a singular function and, secondly, the analytical expressions of the problem solutions are expressed by generalized functions (Mittag-Leffler, Lorenzo-Hartley, Robotnov, etc.) which, generally, are not adequate to numerical calculations. The new time-fractional derivative Caputo-Fabrizio, without singular kernel, is more suitable to solve various theoretical and practical problems which involve fractional differential equations. Using the Caputo-Fabrizio derivative, calculations are simpler and, the obtained solutions are expressed by elementary functions. Analytical solutions of the biofluid velocity and thermal transport are obtained by means of the Laplace and finite Hankel transforms. The influence of the fractional parameter, Eckert number and Joule heating parameter on the biofluid velocity and thermal transport are numerically analyzed and graphic presented. This fact can be an important in Biochip technology, thus making it possible to use this analysis technique extremely effective to control bioliquid samples of nanovolumes in microfluidic devices used for biological
GRAVITATIONALLY UNSTABLE FLAMES: RAYLEIGH-TAYLOR STRETCHING VERSUS TURBULENT WRINKLING
International Nuclear Information System (INIS)
Hicks, E. P.; Rosner, R.
2013-01-01
In this paper, we provide support for the Rayleigh-Taylor-(RT)-based subgrid model used in full-star simulations of deflagrations in Type Ia supernovae explosions. We use the results of a parameter study of two-dimensional direct numerical simulations of an RT unstable model flame to distinguish between the two main types of subgrid models (RT or turbulence dominated) in the flamelet regime. First, we give scalings for the turbulent flame speed, the Reynolds number, the viscous scale, and the size of the burning region as the non-dimensional gravity (G) is varied. The flame speed is well predicted by an RT-based flame speed model. Next, the above scalings are used to calculate the Karlovitz number (Ka) and to discuss appropriate combustion regimes. No transition to thin reaction zones is seen at Ka = 1, although such a transition is expected by turbulence-dominated subgrid models. Finally, we confirm a basic physical premise of the RT subgrid model, namely, that the flame is fractal, and thus self-similar. By modeling the turbulent flame speed, we demonstrate that it is affected more by large-scale RT stretching than by small-scale turbulent wrinkling. In this way, the RT instability controls the flame directly from the large scales. Overall, these results support the RT subgrid model.
Pseudo Phase Plane and Fractional Calculus modeling of western global economic downturn
Tenreiro Machado, J. A.; Mata, Maria Eugénia
2015-05-01
This paper applies Pseudo Phase Plane (PPP) and Fractional Calculus (FC) mathematical tools for modeling world economies. A challenging global rivalry among the largest international economies began in the early 1970s, when the post-war prosperity declined. It went on, up to now. If some worrying threatens may exist actually in terms of possible ambitious military aggression, invasion, or hegemony, countries' PPP relative positions can tell something on the current global peaceful equilibrium. A global political downturn of the USA on global hegemony in favor of Asian partners is possible, but can still be not accomplished in the next decades. If the 1973 oil chock has represented the beginning of a long-run recession, the PPP analysis of the last four decades (1972-2012) does not conclude for other partners' global dominance (Russian, Brazil, Japan, and Germany) in reaching high degrees of similarity with the most developed world countries. The synergies of the proposed mathematical tools lead to a better understanding of the dynamics underlying world economies and point towards the estimation of future states based on the memory of each time series.
Eyuboglu, Atilla Adnan; Uysal, Cagri A; Ozgun, Gonca; Coskun, Erhan; Markal Ertas, Nilgun; Haberal, Mehmet
2018-03-01
Stasis zone is the surrounding area of the coagulation zone which is an important part determining the extent of the necrosis in burn patients. In our study we aim to salvage the stasis zone by injecting adipose derived stromal vascular fraction (ADSVF). Thermal injury was applied on dorsum of Sprague-Dawley rats (n=20) by the "comb burn" model as described previously. When the burn injury was established on Sprague-Dawley rats (30min); rat dorsum was separated into 2 equal parts consisting of 4 burn zones (3 stasis zone) on each pair. ADSVF cells harvested from inguinal fat pads of Sprague-Dawley rats (n=5) were injected on the right side while same amount of phosphate buffered saline (PBS) injected on the left side of the same animal. One week later, average vital tissue on the statis zone was determined by macroscopy, angiography and microscopy. Vascular density, inflammatory cell density, gradient of fibrosis and epithelial thickness were determined via immunohistochemical assay. Macroscopic stasis zone tissue viability (32±3.28%, 57±4.28%) (p51, 1.50±0.43) (pzone on acute burn injuries. Copyright © 2017 Elsevier Ltd and ISBI. All rights reserved.
Model-Based Normalization of a Fractional-Crystal Collimator for Small-Animal PET Imaging.
Li, Yusheng; Matej, Samuel; Karp, Joel S; Metzler, Scott D
2017-05-01
Previously, we proposed to use a coincidence collimator to achieve fractional-crystal resolution in PET imaging. We have designed and fabricated a collimator prototype for a small-animal PET scanner, A-PET. To compensate for imperfections in the fabricated collimator prototype, collimator normalization, as well as scanner normalization, is required to reconstruct quantitative and artifact-free images. In this study, we develop a normalization method for the collimator prototype based on the A-PET normalization using a uniform cylinder phantom. We performed data acquisition without the collimator for scanner normalization first, and then with the collimator from eight different rotation views for collimator normalization. After a reconstruction without correction, we extracted the cylinder parameters from which we generated expected emission sinograms. Single scatter simulation was used to generate the scattered sinograms. We used the least-squares method to generate the normalization coefficient for each LOR based on measured, expected and scattered sinograms. The scanner and collimator normalization coefficients were factorized by performing two normalizations separately. The normalization methods were also verified using experimental data acquired from A-PET with and without the collimator. In summary, we developed a model-base collimator normalization that can significantly reduce variance and produce collimator normalization with adequate statistical quality within feasible scan time.
Directory of Open Access Journals (Sweden)
Jorge A. Orrego-Ruiz
2014-06-01
Full Text Available In this work, prediction models of Saturates, Aromatics, Resins and Asphaltenes fractions (SARA from thirty-seven vacuum residues of representative Colombian crudes and eighteen fractions of molecular distillation process were obtained. Mid-Infrared (MIR Attenuated Total Reflection (ATR spectroscopy in combination with partial least squares (PLS regression analysis was used to estimate accurately SARA analysis in these kind of samples. Calibration coefficients of prediction models were for saturates, aromatics, resins and asphaltenes fractions, 0.99, 0.96, 0.97 and 0.99, respectively. This methodology permits to control the molecular distillation process since small differences in chemical composition can be detected. Total time elapsed to give the SARA analysis per sample is 10 minutes.
Rayleigh's hypothesis and the geometrical optics limit.
Elfouhaily, Tanos; Hahn, Thomas
2006-09-22
The Rayleigh hypothesis (RH) is often invoked in the theoretical and numerical treatment of rough surface scattering in order to decouple the analytical form of the scattered field. The hypothesis stipulates that the scattered field away from the surface can be extended down onto the rough surface even though it is formed by solely up-going waves. Traditionally this hypothesis is systematically used to derive the Volterra series under the small perturbation method which is equivalent to the low-frequency limit. In this Letter we demonstrate that the RH also carries the high-frequency or the geometrical optics limit, at least to first order. This finding has never been explicitly derived in the literature. Our result comforts the idea that the RH might be an exact solution under some constraints in the general case of random rough surfaces and not only in the case of small-slope deterministic periodic gratings.
Directory of Open Access Journals (Sweden)
Xin Lu
2018-03-01
Full Text Available In recent years, the fractional order model has been employed to state of charge (SOC estimation. The non integer differentiation order being expressed as a function of recursive factors defining the fractality of charge distribution on porous electrodes. The battery SOC affects the fractal dimension of charge distribution, therefore the order of the fractional order model varies with the SOC at the same condition. This paper proposes a new method to estimate the SOC. A fractional continuous variable order model is used to characterize the fractal morphology of charge distribution. The order identification results showed that there is a stable monotonic relationship between the fractional order and the SOC after the battery inner electrochemical reaction reaches balanced. This feature makes the proposed model particularly suitable for SOC estimation when the battery is in the resting state. Moreover, a fast iterative method based on the proposed model is introduced for SOC estimation. The experimental results showed that the proposed iterative method can quickly estimate the SOC by several iterations while maintaining high estimation accuracy.
Directory of Open Access Journals (Sweden)
Adailton S. Borges
Full Text Available Abstract A broad class of engineering systems can be satisfactory modeled under the assumptions of small deformations and linear material properties. However, many mechanical systems used in modern applications, like structural elements typical of aerospace and petroleum industries, have been characterized by increased slenderness and high static and dynamic loads. In such situations, it becomes indispensable to consider the nonlinear geometric effects and/or material nonlinear behavior. At the same time, in many cases involving dynamic loads, there comes the need for attenuation of vibration levels. In this context, this paper describes the development and validation of numerical models of viscoelastic slender beam-like structures undergoing large displacements. The numerical approach is based on the combination of the nonlinear Cosserat beam theory and a viscoelastic model based on Fractional Derivatives. Such combination enables to derive nonlinear equations of motion that, upon finite element discretization, can be used for predicting the dynamic behavior of the structure in the time domain, accounting for geometric nonlinearity and viscoelastic damping. The modeling methodology is illustrated and validated by numerical simulations, the results of which are compared to others available in the literature.
Xin, X.; Li, F.; Peng, Z.; Qinhuo, L.
2017-12-01
Land surface heterogeneities significantly affect the reliability and accuracy of remotely sensed evapotranspiration (ET), and it gets worse for lower resolution data. At the same time, temporal scale extrapolation of the instantaneous latent heat flux (LE) at satellite overpass time to daily ET are crucial for applications of such remote sensing product. The purpose of this paper is to propose a simple but efficient model for estimating daytime evapotranspiration considering heterogeneity of mixed pixels. In order to do so, an equation to calculate evapotranspiration fraction (EF) of mixed pixels was derived based on two key assumptions. Assumption 1: the available energy (AE) of each sub-pixel equals approximately to that of any other sub-pixels in the same mixed pixel within acceptable margin of bias, and as same as the AE of the mixed pixel. It's only for a simpification of the equation, and its uncertainties and resulted errors in estimated ET are very small. Assumption 2: EF of each sub-pixel equals to the EF of the nearest pure pixel(s) of same land cover type. This equation is supposed to be capable of correcting the spatial scale error of the mixed pixels EF and can be used to calculated daily ET with daily AE data.The model was applied to an artificial oasis in the midstream of Heihe River. HJ-1B satellite data were used to estimate the lumped fluxes at the scale of 300 m after resampling the 30-m resolution datasets to 300 m resolution, which was used to carry on the key step of the model. The results before and after correction were compare to each other and validated using site data of eddy-correlation systems. Results indicated that the new model is capable of improving accuracy of daily ET estimation relative to the lumped method. Validations at 12 sites of eddy-correlation systems for 9 days of HJ-1B overpass showed that the R² increased to 0.82 from 0.62; the RMSE decreased to 1.60 MJ/m² from 2.47MJ/m²; the MBE decreased from 1.92 MJ/m² to 1
Experimental investigation of turbulent mixing by Rayleigh-Taylor instability
International Nuclear Information System (INIS)
Youngs, D.L.
1992-01-01
A key feature of compressible turbulent mixing is the generation of vorticity via the ∇px ∇(1/ρ) term. This source of vorticity is also present in incompressible flows involving the mixing of fluids of different density, for example Rayleigh-Taylor unstable flows. This paper gives a summary of an experimental investigation of turbulent mixing at a plane boundary between two fluids, of densities ρ 1 , and ρ 2 . (ρ 1 > ρ 2 ) due to Rayleigh-Taylor instability. The two fluids are near incompressible and mixing occurs when an approximately constant acceleration, g, is applied normal to the interface with direction from fluid 2 to fluid 1. Full details of the experimental programme are given in a set of three reports. Some of the earlier experiments are also described by Read. Previous experimental work and much of the theoretical research has concentrated on studying the growth of the instability from a single wavelength perturbation rather than turbulent mixing. Notable exceptions are published in the Russian literature. A related process, turbulent mixing induced by the passage of shock waves though an interface between fluids of different density is described by Andronov et al. The major purpose of the experiments described here was to study the evolution of the instability from small random perturbations where it is found that large and larger structures appear as time proceeds. A novel technique was used to provide the desired acceleration. The two fluids were enclosed in a rectangular tank, the lighter fluid 2 initially resting on top of the denser fluid 1. One or more rocket motors were then used to drive the tank vertically downwards. The aim of the experimental programme is to provide data for the calibration of a turbulence model used to predict mixing in real situations
The mitigation effect of sheared axial flow on the rayleigh-taylor instability in Z-pinch plasma
International Nuclear Information System (INIS)
Zhang Yang
2005-01-01
A magnetohydrodynamic formulation is derived to investigate the mitigation effects of the sheared axial flow on the Rayleigh-Taylor (RT) instability in Z-pinch plasma. The dispersion relation of the compressible model is given. The mitigation effects of sheared axial flow on the Rayleigh-Taylor instability of Z-pinch plasma in the compressible and incompressible models are compared respectively, and the effect of compressible on the instability of system with sheared axial flow is discussed. It is found that, compressibility effects can stabilize the Rayleigh-Taylor/Kelvin-Helmholtz (RT/KH) instability, and this allows the sheared axial flow mitigate the RT instability far more effectively. The authors also find that, at the early stage of the implosion, if the temperature of the plasma is not very high, the compressible model is much more suitable to describing the state of system than the incompressible one. (author)
Tamrat, Yohannes; Nedi, Teshome; Assefa, Solomon; Teklehaymanot, Tilahun; Shibeshi, Workineh
2017-09-29
Many people still experience pain and inflammation regardless of the available drugs for treatments. In addition, the available drugs have many side effects, which necessitated a quest for new drugs from several sources in which medicinal plants are the major one. This study evaluated the analgesic and anti- inflammatory activity of the solvent fractions of Moringa stenopetala in rodent models of pain and inflammation. Successive soxhlet and maceration were used as methods of extractions using solvents of increasing polarity; chloroform, methanol and water. Swiss albino mice models were used in radiant tail flick latency, acetic acid induced writhing and carrageenan induced paw edema to assess the analgesic and anti-inflammatory activities. The test groups received different doses (100 mg/kg, 200 mg/kg and 400 mg/kg) of the three fractions (chloroform, methanol and aqueous). The positive control groups received morphine (20 mg/kg) or aspirin (100 mg/kg or 150 mg/kg) based on the respective models. The negative control groups received the 10 ml/kg of vehicles (distilled water or 2% Tween 80). In all models, the chloroform fraction had protections only at a dose of 400 mg/kg. However, the methanol and aqueous fraction at all doses have shown significant central and peripheral analgesic activities with a comparable result to the standards. The aqueous and methanol fractions significantly reduced carrageenan induced inflammation in a dose dependent manner, in which the highest reduction of inflammation was observed in aqueous fraction at 400 mg/kg. This study provided evidence on the traditionally claimed uses of the plant in pain and inflammatory diseases, and Moringa stenopetala could be potential source for development of new analgesic and anti-inflammatory drugs.
Rayleigh scatter in kilovoltage x-ray imaging: is the independent atom approximation good enough?
Poludniowski, G; Evans, PM; Webb, S
2009-01-01
Monte Carlo simulation is the gold standard method for modelling scattering processes in medical x-ray imaging. General-purpose Monte Carlo codes, however, typically use the independent atom approximation (IAA). This is known to be inaccurate for Rayleigh scattering, for many materials, in the forward direction. This work addresses whether the IAA is sufficient for the typical modelling tasks in medical kilovoltage x-ray imaging. As a means of comparison, we incorporate a more realistic 'inte...
Nonlinear spectrum of the ablative Rayleigh-Taylor instability in laser-accelerated planar plasmas
International Nuclear Information System (INIS)
Keskinen, M. J.; Schmitt, A.
2007-01-01
A model for the nonlinear spectrum of the ablative Rayleigh-Taylor instability in laser-accelerated planar plasmas has been developed for a wide range of Froude numbers and scale sizes. It is found that the spectrum can be characterized by an inverse power law with spectral index of approximately 2 in the limit of small-wavenumber spectrum cutoffs and small-scale density gradient scale lengths. Comparison of the model spectrum with recent experimental observations is made with good agreement
International Nuclear Information System (INIS)
Bastin, Kenneth; Mehta, Minesh
1997-01-01
Purpose/Objective: To develop a rabbit model enabling single or fractionated optic nerve irradiation, measure post-irradiation visual evoked potentials (VEP), fundoscopic and histopathologic changes, and relate different radiation dosing fractions to these measurable physiologic changes. Materials and Methods: Forty male New Zealand white rabbits underwent surgical right orbital prolapse with template-guided optic nerve irradiation using an iridium-192 high dose rate afterloader. Rabbits were randomized into single fraction groups (0 (control), 10, 12.5, 15, 20, and 30 Gy (3 per group); or two fraction groups of 0 (control) 5, 7.5, 10, 15, and 20 Gy (3 per group); or three fractions groups of 10 and 15 Gy (2 per group). Bilateral fundoscopy and pattern-reversal VEPs (0.5 and 1 c/deg, 1 hertz) were performed at 6 and 12 months (mos) following scheduled irradiation. VEP peaks (P1) were measured. Sacrifice and necropsy followed 12 month evaluation, allowing for histological changes. Results: Excluding deaths from anesthesia (2), CNS mite infection (2), sepsis, pyothorax, 'undetermined' and technically non-analyzable VEP recordings, 24 complete rabbit data sets were evaluated. Fundoscopy demonstrated no gross changes at any dose. Histopathology demonstrated generalized optic nerve atrophy without radiation dose correlation. Among single fraction groups, VEP showed a 6 mos post-irradiation P1 prolongation only in the 20 and 30 Gy groups (maximum 67%). At 12 mos lower dose single fraction groups had a prolonged P1 peak. All fractionated groups above 5 Gy x 2 had P1 prolongation times at 6 mos (maximum 46% in the 15 Gy x 3 data set) but by 12 mos these groups had non-measurable, deteriorated VEPs. Correlating VEP P1 latency with the calculated linear quadratic formula (LQM) biologically equivalent dose (BED,α/β=3) for each group demonstrated a general correlation (t-Test P<.001) as shown: Conclusion: Using a rabbit model for selective optic nerve irradiation we conclude
Use of Angle Model to Understand Addition and Subtraction of Fractions
Muzwangowenyu Mukwambo; Kenneth Ngcoza; Lineo Florence Ramasike
2018-01-01
Learners in lower primary and even some in upper primary grades grapple to perform mathematical operations which involve fractions. Failure to solve these mathematical operations creates a gap in the teaching and learning processes of mathematics. We opine that this is attributed to use of traditional mathematical approaches of teaching and learning (TMATL) of operations of fraction. With the hope of engaging the reformed mathematical approach of teaching and learning (RMATL) this study inves...
Directory of Open Access Journals (Sweden)
Kangning Xu
Full Text Available The loss and injury of neurons play an important role in the onset of various neurodegenerative diseases, while both microgliosis and astrocyte loss or dysfunction are significant causes of neuronal degeneration. Previous studies have suggested that an extract enriched panaxadiol saponins from ginseng has more neuroprotective potential than the total saponins of ginseng. The present study investigated whether a fraction of highly purified panaxadiol saponins (termed as Rb fraction was protective for both glia and neurons, especially GABAergic interneurons, against kainic acid (KA-induced excitotoxicity in rats. Rats received Rb fraction at 30 mg/kg (i.p., 40 mg/kg (i.p. or saline followed 40 min later by an intracerebroventricular injection of KA. Acute hippocampal injury was determined at 48 h after KA, and impairment of hippocampus-dependent learning and memory as well as delayed neuronal injury was determined 16 to 21 days later. KA injection produced significant acute hippocampal injuries, including GAD67-positive GABAergic interneuron loss in CA1, paralbumin (PV-positive GABAergic interneuron loss, pyramidal neuron degeneration and astrocyte damage accompanied with reactive microglia in both CA1 and CA3 regions of the hippocampus. There was also a delayed loss of GAD67-positive interneurons in CA1, CA3, hilus and dentate gyrus. Microgliosis also became more severe 21 days later. Accordingly, KA injection resulted in hippocampus-dependent spatial memory impairment. Interestingly, the pretreatment with Rb fraction at 30 or 40 mg/kg significantly protected the pyramidal neurons and GABAergic interneurons against KA-induced acute excitotoxicity and delayed injury. Rb fraction also prevented memory impairments and protected astrocytes from KA-induced acute excitotoxicity. Additionally, microglial activation, especially the delayed microgliosis, was inhibited by Rb fraction. Overall, this study demonstrated that Rb fraction protected both
Isolated hepatocytes and liver S9 fractions have been used to collect in vitro biotransformation data for fish as a means of improving modeled estimates of chemical bioaccumulation. To date, however, there have been few direct comparisons of these two methods. In the present st...
International Nuclear Information System (INIS)
Simon, M.; Scherzer, R.; Enge, W.
1977-01-01
In cosmic ray propagation calculations one can usually assume a homogeneous distribution of interstellar matter. The crucial astrophysical parameters in these models are: The path length distribution, the age of the cosmic ray particles and the interstellar matter density. These values are interrelated. The surviving fraction of radioactive cosmic ray isotopes is often used to determine a mean matter density of that region, where the cosmic ray particles may mainly reside. Using a Monte Carlo Propagation Program we calculated the change in the surviving fraction quantitatively assuming a region around the sources with higher matter density. (author)
Wang, Zhen; Wang, Xiaohong; Li, Yuxia; Huang, Xia
2017-12-01
In this paper, the problems of stability and Hopf bifurcation in a class of fractional-order complex-valued single neuron model with time delay are addressed. With the help of the stability theory of fractional-order differential equations and Laplace transforms, several new sufficient conditions, which ensure the stability of the system are derived. Taking the time delay as the bifurcation parameter, Hopf bifurcation is investigated and the critical value of the time delay for the occurrence of Hopf bifurcation is determined. Finally, two representative numerical examples are given to show the effectiveness of the theoretical results.
DEFF Research Database (Denmark)
Huang, Sunhua; Zhou, Bin; Li, Canbing
2018-01-01
represent complex dynamic behaviours with chaotic and unstable states on the energy conservation, carbon emissions, economic growth, and renewable energy development, and have a great impact on the formulation of government energy policies. Furthermore, based on the fractional Lyapunov stability and robust......, and the fractional-order model of the energy-saving and emission-reduction system (FOESERS) is formulated. With the proposed FOESERS, all of the equilibrium points and the corresponding eigenvalues are obtained, and the instability region and the state trajectories of FOESERS are also given. The FOESERS can...
International Nuclear Information System (INIS)
Song, William; Battista, Jerry; Van Dyk, Jake
2004-01-01
The convolution method can be used to model the effect of random geometric uncertainties into planned dose distributions used in radiation treatment planning. This is effectively done by linearly adding infinitesimally small doses, each with a particular geometric offset, over an assumed infinite number of fractions. However, this process inherently ignores the radiobiological dose-per-fraction effect since only the summed physical dose distribution is generated. The resultant potential error on predicted radiobiological outcome [quantified in this work with tumor control probability (TCP), equivalent uniform dose (EUD), normal tissue complication probability (NTCP), and generalized equivalent uniform dose (gEUD)] has yet to be thoroughly quantified. In this work, the results of a Monte Carlo simulation of geometric displacements are compared to those of the convolution method for random geometric uncertainties of 0, 1, 2, 3, 4, and 5 mm (standard deviation). The α/β CTV ratios of 0.8, 1.5, 3, 5, and 10 Gy are used to represent the range of radiation responses for different tumors, whereas a single α/β OAR ratio of 3 Gy is used to represent all the organs at risk (OAR). The analysis is performed on a four-field prostate treatment plan of 18 MV x rays. The fraction numbers are varied from 1-50, with isoeffective adjustments of the corresponding dose-per-fractions to maintain a constant tumor control, using the linear-quadratic cell survival model. The average differences in TCP and EUD of the target, and in NTCP and gEUD of the OAR calculated from the convolution and Monte Carlo methods reduced asymptotically as the total fraction number increased, with the differences reaching negligible levels beyond the treatment fraction number of ≥20. The convolution method generally overestimates the radiobiological indices, as compared to the Monte Carlo method, for the target volume, and underestimates those for the OAR. These effects are interconnected and attributed
Directory of Open Access Journals (Sweden)
S. L. Heck
2012-02-01
Full Text Available There is a widely recognized need to improve our understanding of biosphere-atmosphere carbon exchanges in areas of complex terrain including the United States Mountain West. CO2 fluxes over mountainous terrain are often difficult to measure due to unusual and complicated influences associated with atmospheric transport. Consequently, deriving regional fluxes in mountain regions with carbon cycle inversion of atmospheric CO2 mole fraction is sensitive to filtering of observations to those that can be represented at the transport model resolution. Using five years of CO2 mole fraction observations from the Regional Atmospheric Continuous CO2 Network in the Rocky Mountains (Rocky RACCOON, five statistical filters are used to investigate a range of approaches for identifying regionally representative CO2 mole fractions. Test results from three filters indicate that subsets based on short-term variance and local CO2 gradients across tower inlet heights retain nine-tenths of the total observations and are able to define representative diel variability and seasonal cycles even for difficult-to-model sites where the influence of local fluxes is much larger than regional mole fraction variations. Test results from two other filters that consider measurements from previous and following days using spline fitting or sliding windows are overly selective. Case study examples showed that these windowing-filters rejected measurements representing synoptic changes in CO2, which suggests that they are not well suited to filtering continental CO2 measurements. We present a novel CO2 lapse rate filter that uses CO2 differences between levels in the model atmosphere to select subsets of site measurements that are representative on model scales. Our new filtering techniques provide guidance for novel approaches to assimilating mountain-top CO2 mole fractions in carbon cycle inverse models.
Effects of shock waves on Rayleigh-Taylor instability
International Nuclear Information System (INIS)
Zhang Yongtao; Shu Chiwang; Zhou Ye
2006-01-01
A numerical simulation of two-dimensional compressible Navier-Stokes equations using a high-order weighted essentially nonoscillatory finite difference shock capturing scheme is carried out in this paper, to study the effect of shock waves on the development of Rayleigh-Taylor instability. Shocks with different Mach numbers are introduced ahead or behind the Rayleigh-Taylor interface, and their effect on the transition to instability is demonstrated and compared. It is observed that shock waves can speed up the transition to instability for the Rayleigh-Taylor interface significantly. Stronger shocks are more effective in this speed-up process
Sales, T. P.; Marques, Flávio D.; Pereira, Daniel A.; Rade, Domingos A.
2018-06-01
Nonlinear aeroelastic systems are prone to the appearance of limit cycle oscillations, bifurcations, and chaos. Such problems are of increasing concern in aircraft design since there is the need to control nonlinear instabilities and improve safety margins, at the same time as aircraft are subjected to increasingly critical operational conditions. On the other hand, in spite of the fact that viscoelastic materials have already been successfully used for the attenuation of undesired vibrations in several types of mechanical systems, a small number of research works have addressed the feasibility of exploring the viscoelastic effect to improve the behavior of nonlinear aeroelastic systems. In this context, the objective of this work is to assess the influence of viscoelastic materials on the aeroelastic features of a three-degrees-of-freedom typical section with hardening structural nonlinearities. The equations of motion are derived accounting for the presence of viscoelastic materials introduced in the resilient elements associated to each degree-of-freedom. A constitutive law based on fractional derivatives is adopted, which allows the modeling of temperature-dependent viscoelastic behavior in time and frequency domains. The unsteady aerodynamic loading is calculated based on the classical linear potential theory for arbitrary airfoil motion. The aeroelastic behavior is investigated through time domain simulations, and subsequent frequency transformations, from which bifurcations are identified from diagrams of limit cycle oscillations amplitudes versus airspeed. The influence of the viscoelastic effect on the aeroelastic behavior, for different values of temperature, is also investigated. The numerical simulations show that viscoelastic damping can increase the flutter speed and reduce the amplitudes of limit cycle oscillations. These results prove the potential that viscoelastic materials have to increase aircraft components safety margins regarding aeroelastic
Directory of Open Access Journals (Sweden)
Andrea Sorzia
2016-01-01
Full Text Available A tensile test until breakage and a creep and relaxation test on a polypropylene fibre are carried out and the resulting creep and stress relaxation curves are fit by a model adopting a fraction-exponential kernel in the viscoelastic operator. The models using fraction-exponential functions are simpler than the complex ones obtained from combination of dashpots and springs and, furthermore, are suitable for fitting experimental data with good approximation allowing, at the same time, obtaining inverse Laplace transform in closed form. Therefore, the viscoelastic response of polypropylene fibres can be modelled straightforwardly through analytical methods. Addition of polypropylene fibres greatly improves the tensile strength of composite materials with concrete matrix. The proposed analytical model can be employed for simulating the mechanical behaviour of composite materials with embedded viscoelastic fibres.
International Nuclear Information System (INIS)
Storb, R.; Raff, R.F.; Graham, T.; Appelbaum, F.R.; Deeg, H.J.; Schuening, F.G.; Shulman, H.; Pepe, M.
1993-01-01
The authors explored in dogs the marrow toxicity of single dose total body irradiation delivered from two opposing 60 Co sources at a rate of 10 cGy/min and compared results to those seen with total body irradiation administered in 100 cGy fractions with minimum interfraction intervals of 6 hr. Dogs were not given marrow transplants. They found that 200 cGy single dose total body irradiation was sublethal, with 12 of 13 dogs showing hematopoietic recovery and survival. Seven of 21 dogs given 300 cGy single dose total body irradiation survived compared to 6 of 10 dogs given 300 cGy fractionated total body irradiation. One of 28 dogs given 400 cGy single dose total body irradiation survived compared to none of six given fractionated radiation. With granulocyte colony stimulating factor (GCSF) administered from day 0-21 after 400 cGy total body irradiation, most dogs survived with hematological recovery. Because of the almost uniform success with GCSF after 400 cGy single dose total body irradiation, a study of GCSF after 400 cGy fractionated total body irradiation was deemed not to be informative and, thus, not carried out. Additional comparisons between single dose and fractionated total body irradiation were carried out with GCSF administered after 500 and 600 cGy of total body irradiation. As with lower doses of total body irradiation, no significant survival differences were seen between the two modes of total body irradiation, and only 3 of 26 dogs studied survived with complete hematological recovery. Overall, therefore, survival among dogs given single dose total body irradiation was not different from that of dogs given fractionated total body irradiation (p = .67). Similarly, the slopes of the postirradiation declines of granulocyte and platelet counts and the rates of their recovery in surviving dogs given equal total doses of single versus fractionated total body irradiation were indistinguishable. 24 refs., 3 figs., 2 tabs
A survival model for fractionated radiotherapy with an application to prostate cancer
Energy Technology Data Exchange (ETDEWEB)
Zaider, Marco [Department of Medical Physics, Memorial Sloan-Kettering Cancer Center, New York, NY (United States)]. E-mail: Zaiderm@mskcc.org; Zelefsky, Michael J.; Leibel, Steven A. [Department of Radiation Oncology, Memorial Sloan-Kettering Cancer Center, New York, NY (United States); Hanin, Leonid G. [Department of Mathematics, Idaho State University, Pocatello, ID (United States); Tsodikov, Alexander D.; Yakovlev, Andrei Y. [Department of Oncological Sciences, Huntsman Cancer Institute, University of Utah, Salt Lake City, UT (United States)
2001-10-01
This paper explores the applicability of a mechanistic survival model, based on the distribution of clonogens surviving a course of fractionated radiation therapy, to clinical data on patients with prostate cancer. The study was carried out using data on 1100 patients with clinically localized prostate cancer who were treated with three-dimensional conformal radiation therapy. The patients were stratified by radiation dose (group 1: <67.5 Gy; group 2: 67.5-72.5 Gy; group 3: 72.5-77.5 Gy; group 4: 77.5-87.5 Gy) and prognosis category (favourable, intermediate and unfavourable as defined by pre-treatment PSA and Gleason score). A relapse was recorded when tumour recurrence was diagnosed or when three successive prostate specific antigen (PSA) elevations were observed from a post-treatment nadir PSA level. PSA relapse-free survival was used as the primary end point. The model, which is based on an iterated Yule process, is specified in terms of three parameters: the mean number of tumour clonogens that survive the treatment, the mean of the progression time of post-treatment tumour development and its standard deviation. The model parameters were estimated by the maximum likelihood method. The fact that the proposed model provides an excellent description both of the survivor function and of the hazard rate is prima facie evidence of the validity of the model because closeness of the two survivor functions (empirical and model-based) does not generally imply closeness of the corresponding hazard rates. The estimated cure probabilities for the favourable group are 0.80, 0.74 and 0.87 (for dose groups 1-3, respectively); for the intermediate group: 0.25, 0.51, 0.58 and 0.78 (for dose groups 1-4, respectively) and for the unfavourable group: 0.0, 0.27, 0.33 and 0.64 (for dose groups 1-4, respectively). The distribution of progression time to tumour relapse was found to be independent of prognosis group but dependent on dose. As the dose increases the mean progression
Fractional Dynamics and Control
Machado, José; Luo, Albert
2012-01-01
Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science. Discusses how fractional dynamics and control can be used to solve nonlinear science and complexity issues Shows how fractional differential equations and models can be used to solve turbulence and wave equations in mechanics and gravity theories and Schrodinger’s equation Presents factional relaxation modeling of dielectric materials and wave equations for dielectrics Develops new methods for control and synchronization of...
Directory of Open Access Journals (Sweden)
Koca Ilknur
2017-01-01
Full Text Available Recently Hristov using the concept of a relaxation kernel with no singularity developed a new model of elastic heat diffusion equation based on the Caputo-Fabrizio fractional derivative as an extended version of Cattaneo model of heat diffusion equation. In the present article, we solve exactly the Cattaneo-Hristov model and extend it by the concept of a derivative with non-local and non-singular kernel by using the new Atangana-Baleanu derivative. The Cattaneo-Hristov model with the extended derivative is solved analytically with the Laplace transform, and numerically using the Crank-Nicholson scheme.
DEFF Research Database (Denmark)
Hattel, Jesper Henri; Pryds, Nini
2006-01-01
the atomisation stage taking thermal coupling into consideration and the deposition of the droplets at the surface of the billet taking geometrical aspects such as shading into account. The coupling between these two models is accomplished by ensuring that the total droplet size distribution of the spray......In this paper, the relationship between the Gas to Melt Ratio (GMR) and the solid fraction of an evolving billet surface is investigated numerically. The basis for the analysis is a recently developed integrated procedure for modelling the entire spray forming process. This model includes...... is the summation of “local” droplet size distributions along the r-axis of the spray cone. The criterion for a successful process has been a predefined process window characterised by a desired solid fraction range at a certain distance from the atomizer. Inside this process window, the gas and melt flows have...
International Nuclear Information System (INIS)
Todo, A.S.
1980-01-01
Presently, the estimates of specific absorbed fractions in various organs of a heterogeneous phantom are based on Monte Carlo calculation for monoenergetic photons uniformly distributed in the organs of an adult phantom. But, it is known that the kidney and some other organs (for example the skeleton) do not retain the radionuclides in an uniform manner in its internal region. So, we developed a model for the kidney including the cortex, medulla and collecting region. This model was utilized to estimate the specific absorbed fractions, for monoenergetic photons or electrons, in various organs of a heterogeneous phantom, when sources were uniformly distributed in each region of the kidney. All results obtained in this work were compared with those using a homogeneous model for the kidney as presented in ORNL-5000. (Author) [pt
Filtered Rayleigh Scattering Measurements in a Buoyant Flow Field
National Research Council Canada - National Science Library
Meents, Steven M
2008-01-01
Filtered Rayleigh Scattering (FRS) is a non-intrusive, laser-based flow characterization technique that consists of a narrow linewidth laser, a molecular absorption filter, and a high resolution camera behind the filter to record images...
Rayleigh scattering and depolarization ratio in linear alkylbenzene
International Nuclear Information System (INIS)
Liu, Qian; Zhou, Xiang; Huang, Wenqian; Zhang, Yuning; Wu, Wenjie; Luo, Wentai; Yu, Miao; Zheng, Yangheng; Zhou, Li; Cao, Jun; Wang, Yifang
2015-01-01
It is planned to use linear alkylbenzene (LAB) as the organic solvent for the Jiangmen Underground Neutrino Observatory (JUNO) liquid scintillator detectors, due to its ultra-transparency. However, the current Rayleigh scattering length calculation for LAB disagrees with the experimental measurement. This paper reports for the first time that the Rayleigh scattering of LAB is anisotropic, with a depolarization ratio of 0.31±0.01(stat.)±0.01(sys.). We use an indirect method for Rayleigh scattering measurement with the Einstein–Smoluchowski–Cabannes formula, and the Rayleigh scattering length of LAB is determined to be 28.2±1.0 m at 430 nm
Higher fractions theory of fractional hall effect
International Nuclear Information System (INIS)
Kostadinov, I.Z.; Popov, V.N.
1985-07-01
A theory of fractional quantum Hall effect is generalized to higher fractions. N-particle model interaction is used and the gap is expressed through n-particles wave function. The excitation spectrum in general and the mean field critical behaviour are determined. The Hall conductivity is calculated from first principles. (author)
A numerical and analytical investigation of Rayleigh-Taylor instability in a solid tungsten plate
International Nuclear Information System (INIS)
Robinson, A.C.; Swegle, J.W.
1987-07-01
The Rayleigh-Taylor instability response of an elastic-plastic tungsten plate is investigated by numerical experiments and an approximate modal analysis. The so-called ''minimum amplitude'' instability criteria derived from plasticity analyses is shown to be incomplete as a general indicator of instability or stability at very large driving pressures. Model equations are derived which are able to reproduce the basic qualitative features of the observed instability response given by the numerical calculations. 11 refs., 29 figs
Transmuted of Rayleigh Distribution with Estimation and Application on Noise Signal
Ahmed, Suhad; Qasim, Zainab
2018-05-01
This paper deals with transforming one parameter Rayleigh distribution, into transmuted probability distribution through introducing a new parameter (λ), since this studied distribution is necessary in representing signal data distribution and failure data model the value of this transmuted parameter |λ| ≤ 1, is also estimated as well as the original parameter (⊖) by methods of moments and maximum likelihood using different sample size (n=25, 50, 75, 100) and comparing the results of estimation by statistical measure (mean square error, MSE).
Breakup of an accelerated shell owing to Rayleigh--Taylor instability
International Nuclear Information System (INIS)
Suydam, B.R.
1978-06-01
A simplified model for the Rayleigh-Taylor instability of an accelerated shell is examined, and it is found that the most dangerous wavelength to be about that of the shell thickness. The shell material is assumed to be an inviscid, incompressible fluid. Effects of finite compressibility and of surface tension are found to be negligible, but the effects of viscosity are shown to be very large. The need for better knowledge of viscosity at high pressure is pointed out
Taori, A.; Jayaraman, A.; Raghunath, K.; Kamalakar, V.
2012-01-01
The vertical temperature profiles in a typical Rayleigh lidar system depends on the backscatter photon counts and the CIRA-86 model inputs. For the first time, we show that, by making simultaneous measurements of Rayleigh lidar and upper mesospheric O2 temperatures, the lidar capability can be enhanced to obtain mesospheric temperature profile up to about 95 km altitudes. The obtained results are compared with instantaneous space-borne SABER measurements for a validation.
Energy Technology Data Exchange (ETDEWEB)
Taori, A.; Jayaraman, A.; Raghunath, K. [National Atmospheric Research Laboratory, Gadanki (India); Kamalakar, V. [S.V. Univ., Tirupati (India). Dept. of Physics
2012-07-01
The vertical temperature profiles in a typical Rayleigh lidar system depends on the backscatter photon counts and the CIRA-86 model inputs. For the first time, we show that, by making simultaneous measurements of Rayleigh lidar and upper mesospheric O{sub 2} temperatures, the lidar capability can be enhanced to obtain mesospheric temperature profile up to about 95 km altitudes. The obtained results are compared with instantaneous space-borne SABER measurements for a validation. (orig.)
Rayleigh scattering under light-atom coherent interaction
Takamizawa, Akifumi; Shimoda, Koichi
2012-01-01
Semi-classical calculation of an oscillating dipole induced in a two-level atom indicates that spherical radiation from the dipole under coherent interaction, i.e., Rayleigh scattering, has a power level comparable to that of spontaneous emission resulting from an incoherent process. Whereas spontaneous emission is nearly isotropic and has random polarization generally, Rayleigh scattering is strongly anisotropic and polarized in association with incident light. In the case where Rabi frequen...
Use of Angle Model to Understand Addition and Subtraction of Fractions
Mukwambo, Muzwangowenyu; Ngcoza, Kenneth; Ramasike, Lineo Florence
2018-01-01
Learners in lower primary and even some in upper primary grades grapple to perform mathematical operations which involve fractions. Failure to solve these mathematical operations creates a gap in the teaching and learning processes of mathematics. We opine that this is attributed to use of traditional mathematical approaches of teaching and…
DEFF Research Database (Denmark)
Olesen, Mikkel Vestergaard; Needham, Esther Kjær; Pakkenberg, Bente
2017-01-01
present the optical fractionator in conjunction with BrdU immunohistochemistry to estimate the production and survival of newly-formed neurons in the granule cell layer (including the sub-granular zone) of the rat hippocampus following electroconvulsive stimulation, which is among the most potent...
Wildschut, J.; Arentz, J.; Rasrendra, C. B.; Venderbosch, R. H.; Heeres, H. J.
2009-01-01
Fast pyrolysis oil can be upgraded by a catalytic hydrotreatment (250-400 degrees C, 100-200 bar) using heterogeneous catalysts such as Ru/C to hydrocarbon-like products that can serve as liquid transportation fuels. Insight into the complex reaction pathways of the various component fractions
A No-Arbitrage Fractional Cointegration Model for Futures and Spot Daily Ranges
DEFF Research Database (Denmark)
Rossi, Eduardo; Santucci de Magistris, Paolo
2013-01-01
The no-arbitrage relation between futures and spot prices implies an analogous relation between futures and spot daily ranges. The long-memory features of the range-based volatility estimators are analyzed, and fractional cointegration is tested in a semi-parametric framework. In particular, the no...
Kinetic simulations of Rayleigh-Taylor instabilities
International Nuclear Information System (INIS)
Sagert, Irina; Bauer, Wolfgang; Colbry, Dirk; Howell, Jim; Staber, Alec; Strother, Terrance
2014-01-01
We report on an ongoing project to develop a large scale Direct Simulation Monte Carlo code. The code is primarily aimed towards applications in astrophysics such as simulations of core-collapse supernovae. It has been tested on shock wave phenomena in the continuum limit and for matter out of equilibrium. In the current work we focus on the study of fluid instabilities. Like shock waves these are routinely used as test-cases for hydrodynamic codes and are discussed to play an important role in the explosion mechanism of core-collapse supernovae. As a first test we study the evolution of a single-mode Rayleigh-Taylor instability at the interface of a light and a heavy fluid in the presence of a gravitational acceleration. To suppress small-wavelength instabilities caused by the irregularity in the separation layer we use a large particle mean free path. The latter leads to the development of a diffusion layer as particles propagate from one fluid into the other. For small amplitudes, when the instability is in the linear regime, we compare its position and shape to the analytic prediction. Despite the broadening of the fluid interface we see a good agreement with the analytic solution. At later times we observe the development of a mushroom like shape caused by secondary Kelvin-Helmholtz instabilities as seen in hydrodynamic simulations and consistent with experimental observations.
Manipulating Rayleigh-Taylor Growth Using Adjoints
Kord, Ali; Capecelatro, Jesse
2017-11-01
It has been observed that initial interfacial perturbations affect the growth of Rayleigh-Taylor (RT) instabilities. However, it remains to be seen to what extent the perturbations alter the RT growth rate. Direct numerical simulations (DNS) provide a powerful means for studying the effects of initial conditions (IC) on the growth rate. However, a brute-force approach for identifying optimal initial perturbations is not practical via DNS. In addition, identifying sensitivity of the RT growth to the large number of parameters used in defining the IC is computationally expensive. A discrete adjoint is formulated to measure sensitivities of multi-mode RT growth to ICs in a high-order finite difference framework. The sensitivity is used as a search direction for adjusting the initial perturbations to both maximize and suppress the RT growth rate during its non-linear regime. The modes that contribute the greatest sensitivity are identified, and optimized perturbation energy spectrum are reported. PhD Student, Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI.
Ablation front rayleigh taylor dispersion curve in indirect drive
International Nuclear Information System (INIS)
Budil, K.S.; Lasinski, B.; Edwards, M.J.; Wan, A.S.; Remington, B.A.; Weber, S.V.; Glendinning, S.G.; Suter, L.; Stry, P.
2000-01-01
The Rayleigh-Taylor (RT) instability, which occurs when a lower-density fluid accelerates a higher-density layer, is common in nature. At an ablation front a sharp reduction in the growth rate of the instability at short wave-lengths can occur, in marked contrast to the classical case where growth rates are highest at the shortest wavelengths. Theoretical and numerical investigations of the ablative RT instability are numerous and differ considerably on the level of stabilization expected. We present here the results of a series of laser experiments designed to probe the roll-over and cutoff region of the ablation-front RT dispersion curve in indirect drive. Aluminum foils with imposed sinusoidal perturbations ranging in wavelength from 10 to 70 pm were ablatively accelerated with a radiation drive generated in a gold cylindrical hohlraum. A strong shock wave compresses the package followed by an ∼2 ns period of roughly constant acceleration and the experiment is diagnosed via face-on radiography. Perturbations with wavelengths (ge) 20 (micro)m experienced substantial growth during the acceleration phase while shorter wavelengths showed a sharp drop off in overall growth. These experimental results compared favorably to calculations with a 2-D radiation-hydrodynamics code, however, the growth is significantly affected by the rippled shock launched by the drive. We performed numerical simulations to elucidate the influence of the rippled shock wave on the eventual growth of the perturbations, allowing comparisons to the analytic model developed by Betti et al. This combination of experiments, simulations and analytic modeling illustrates the qualitative simplicity yet quantitative complexity of the compressible RT instability. We have measured the Rayleigh-Taylor (RT) dispersion curve for a radiatively-driven sample in a series of experiments on the Nova laser facility. Planar aluminum foils were ablatively-accelerated and the subsequent perturbation growth was
Bae, Jung Min; Jung, Han Mi; Goo, Boncheol; Park, Young Min
2015-07-01
Alopecia is one of the most common dermatological problems in the elderly; however, current therapies for it are limited by low efficacy and undesirable side effects. Although clinical reports on fractional laser treatment for various alopecia types are increasing, the exact mechanism remains to be clarified. The purposes of this study were to demonstrate the effect of ablative fractional laser treatment on hair follicle regrowth in vivo and investigate the molecular mechanism after laser treatment. Ablative CO2 fractional laser was applied to the shaved dorsal skin of 7-week-old C57BL/6 mice whose hair was in the telogen stage. After 12 mice were treated at various energy (10-40 mJ/spot) and density (100-400 spots/cm(2) ) settings to determine the proper dosage for maximal effect. Six mice were then treated at the decided dosage and skin specimens were sequentially obtained by excision biopsy from the dorsal aspect of each mouse. Tissue samples were used for the immunohistochemistry and reverse transcription polymerase chain reaction assays to examine hair follicle status and their related molecules. The most effective dosage was the 10 mJ/spot and 300 spots/cm(2) setting. The anagen conversion of hair was observed in the histopathological examination, while Wnt/β-catenin expression was associated with hair regrowth in the immunohistochemistry and molecular studies. Ablative fractional lasers appear to be effective for inducing hair regrowth via activation of the Wnt/β-catenin pathway in vivo. Our findings indicate that fractional laser treatment can potentially be developed as new treatment options for stimulating hair regrowth. © 2015 Wiley Periodicals, Inc.
Energy Technology Data Exchange (ETDEWEB)
Adams, Colin Stuart [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States); Univ. of Washington, Seattle, WA (United States)
2015-01-15
The Rayleigh-Taylor instability causes mixing in plasmas throughout the universe, from micron-scale plasmas in inertial confinement fusion implosions to parsec-scale supernova remnants. The evolution of this interchange instability in a plasma is influenced by the presence of viscosity and magnetic fields, both of which have the potential to stabilize short-wavelength modes. Very few experimental observations of Rayleigh-Taylor growth in plasmas with stabilizing mechanisms are reported in the literature, and those that are reported are in sub-millimeter scale plasmas that are difficult to diagnose. Experimental observations in well-characterized plasmas are important for validation of computational models used to make design predictions for inertial confinement fusion efforts. This dissertation presents observations of instability growth during the interaction between a high Mach-number, initially un-magnetized plasma jet and a stagnated, magnetized plasma. A multi-frame fast camera captures Rayleigh-Taylor-instability growth while interferometry, spectroscopy, photodiode, and magnetic probe diagnostics are employed to estimate plasma parameters in the vicinity of the collision. As the instability grows, an evolution to longer mode wavelength is observed. Comparisons of experimental data with idealized magnetohydrodynamic simulations including a physical viscosity model suggest that the observed instability evolution is consistent with both magnetic and viscous stabilization. These data provide the opportunity to benchmark computational models used in astrophysics and fusion research.
Spontaneous Rayleigh-Brillouin scattering spectral analysis based on the Wiener filter
Directory of Open Access Journals (Sweden)
Tao Wu
2018-01-01
Full Text Available In this paper, a spontaneous Rayleigh-Brillouin scattering spectrometer is developed to measure the gaseous spontaneous Rayleigh-Brillouin scattering profiles over the pressure range from 1 to 5 atm for a wavelength of 532nm at a constant room temperature of 296K and a 90o scattering angle. In order to make a direct comparison between the experimentally obtained spectrum and the theoretical spectrum calculated from the Tenti S6 model, the measured spontaneous Rayleigh-Brillouin scattering signal is deconvolved by the Wiener filtering. The purpose is to remove the effect on the spectrum by the transmission function of the Fabry-Perrot scanning interferometer. The results of the comparison show that the deconvolved spectra are consistent with the theoretical spectra calculated from the Tenti S6 model, and thus confirm that the deconvolution based on the Wiener filter is able to process the measured spectra and improve the spectral resolution. Some factors that influence the accuracy of deconvolution are analyzed and discussed. At the same time, another comparison between the raw experimentally obtained spectra and the theoretical spectra calculated by convolving the Tenti S6 model with instrument function of the measurement system is performed in the same experimental condition. The results of the two comparisons show that, compared with the raw experimentally obtained spectrum, the deconvolved spectrum matches the theoretically calculated spectrum more accurately under lower pressure (≤2atm than under relative higher pressure (>2atm.
International Nuclear Information System (INIS)
Casner, A.; Masse, L.; Liberatore, S.; Delorme, B.; Jacquet, L.; Loiseau, P.; Smalyuk, V. A.; Martinez, D.; Remington, B. A.
2012-01-01
As the control of the development of Rayleigh-Taylor-type hydrodynamic instabilities is crucial to achieve efficient implosions on the Laser Megajoule, and as the complexity of these instabilities requires an experimental validation of theoretical models and of the associated numerical simulations, the authors briefly present a proposition of experiments aimed at studying the strongly non linear Rayleigh-Taylor instability on the National Ignition Facility (NIF). This should allow a regime of competition between bubbles to be achieved for the first time in direct attack. They evoke the first experiment performed in March 2013
International Nuclear Information System (INIS)
Kopainsky, J.
1975-01-01
In weakly ionized plasmas the scattering of electromagnetic waves on free electrons (Thompson scattering) can be neglected as compared with the scattering on bound electrons (Rayleigh scattering). If the scattering process can be described by a fluid dynamical model it is caused by sound waves which are generated or annihilated by the incident electromagnetic wave. The propagation of sound waves results in a shift of the scattered line whereas their absorption within the plasma produces the broadening of the scattered line. The theory of propagation of sound in weakly ionized plasmas is developed and extended to Rayleigh scattering. The results are applied to laser scattering in a weakly ionized hydrogen plasma. (Auth.)
Guetschow, H. A.; Nelson, B. K.
2002-12-01
Depth of crystal fractionation influences the chemical evolution of ocean island basalts and has significant implications for the physical structures of these volcanoes. In contrast to dominantly shallow systems such as Hawaii, a range of fractionation depths have been reported for Canary Islands lavas. Magmas erupted on La Palma preserve fluid- and melt-inclusion evidence for high-pressure (> 10 kbar) crystallization (Klügel et al., 1998; Hansteen et al., 1998; Nikogosian et al., 2002). If high-pressure fractional crystallization were an early and dominant process, it would generate specific patterns in rock and phase chemistry of eruptive sequences. Alkalic basalts from Taburiente volcano display coherent major element trends consistent with evolution dominated by fractional crystallization while their phenocryst compositions, trace elements, and isotopic trends require mixing between multiple sources. The current model confirms the importance of both fractionation and mixing to achieve the full range of lavas observed. A low-pressure (1 kbar) thermodynamic fractional crystallization model performed with the MELTS (Ghiorso and Sack, 1995) software closely reproduces major element trends from two stratigraphic sequences. This model also predicts the observed sequence of groundmass clinopyroxene compositions and phenocryst zoning reversals. In all low pressure simulations, olivine remains a modally significant liquidus phase during the first 20% and last 30% of the crystallization sequence, resulting in a negative correlation between the CaO and Fo content of olivine. These results are consistent with the presence of olivine phenocrysts that bear petrographic evidence of early crystallization, as well as observed compositional trends of groundmass olivine and clinopyroxene in Taburiente lavas. MELTS models that include an initial period of high pressure (12 kbar) clinopyroxene fractionation produce major element trends comparable to the low pressure model, but
Julien, Maxime; Gilbert, Alexis; Yamada, Keita; Robins, Richard J; Höhener, Patrick; Yoshida, Naohiro; Remaud, Gérald S
2018-01-01
The enrichment factor (ε) is a common way to express Isotope Effects (IEs) associated with a phenomenon. Many studies determine ε using a Rayleigh-plot, which needs multiple data points. More recent articles describe an alternative method using the Rayleigh equation that allows the determination of ε using only one experimental point, but this method is often subject to controversy. However, a calculation method using two points (one experimental point and one at t 0 ) should lead to the same results because the calculation is derived from the Rayleigh equation. But, it is frequently asked "what is the valid domain of use of this two point calculation?" The primary aim of the present work is a systematic comparison of results obtained with these two methodologies and the determination of the conditions required for the valid calculation of ε. In order to evaluate the efficiency of the two approaches, the expanded uncertainty (U) associated with determining ε has been calculated using experimental data from three published articles. The second objective of the present work is to describe how to determine the expanded uncertainty (U) associated with determining ε. Comparative methodologies using both Rayleigh-plot and two point calculation are detailed and it is clearly demonstrated that calculation of ε using a single data point can give the same result as a Rayleigh-plot provided one strict condition is respected: that the experimental value is measured at a small fraction of unreacted substrate (f < 30%). This study will help stable isotope users to present their results in a more rigorous expression: ε ± U and therefore to define better the significance of an experimental results prior interpretation. Capsule: Enrichment factor can be determined through two different methods and the calculation of associated expanded uncertainty allows checking its significance. Copyright © 2017 Elsevier B.V. All rights reserved.
DEFF Research Database (Denmark)
Cavaliere, Giuseppe; Nielsen, Morten Ørregaard; Taylor, Robert
We consider the problem of conducting estimation and inference on the parameters of univariate heteroskedastic fractionally integrated time series models. We first extend existing results in the literature, developed for conditional sum-of squares estimators in the context of parametric fractional...... time series models driven by conditionally homoskedastic shocks, to allow for conditional and unconditional heteroskedasticity both of a quite general and unknown form. Global consistency and asymptotic normality are shown to still obtain; however, the covariance matrix of the limiting distribution...... of the estimator now depends on nuisance parameters derived both from the weak dependence and heteroskedasticity present in the shocks. We then investigate classical methods of inference based on the Wald, likelihood ratio and Lagrange multiplier tests for linear hypotheses on either or both of the long and short...
Zeng, C.; Xia, J.; Miller, R.D.; Tsoflias, G.P.
2011-01-01
Conventional surface wave inversion for shallow shear (S)-wave velocity relies on the generation of dispersion curves of Rayleigh waves. This constrains the method to only laterally homogeneous (or very smooth laterally heterogeneous) earth models. Waveform inversion directly fits waveforms on seismograms, hence, does not have such a limitation. Waveforms of Rayleigh waves are highly related to S-wave velocities. By inverting the waveforms of Rayleigh waves on a near-surface seismogram, shallow S-wave velocities can be estimated for earth models with strong lateral heterogeneity. We employ genetic algorithm (GA) to perform waveform inversion of Rayleigh waves for S-wave velocities. The forward problem is solved by finite-difference modeling in the time domain. The model space is updated by generating offspring models using GA. Final solutions can be found through an iterative waveform-fitting scheme. Inversions based on synthetic records show that the S-wave velocities can be recovered successfully with errors no more than 10% for several typical near-surface earth models. For layered earth models, the proposed method can generate one-dimensional S-wave velocity profiles without the knowledge of initial models. For earth models containing lateral heterogeneity in which case conventional dispersion-curve-based inversion methods are challenging, it is feasible to produce high-resolution S-wave velocity sections by GA waveform inversion with appropriate priori information. The synthetic tests indicate that the GA waveform inversion of Rayleigh waves has the great potential for shallow S-wave velocity imaging with the existence of strong lateral heterogeneity. ?? 2011 Elsevier B.V.
The Rayleigh-Taylor instability in a self-gravitating two-layer viscous sphere
Mondal, Puskar; Korenaga, Jun
2018-03-01
The dispersion relation of the Rayleigh-Taylor instability in the spherical geometry is of profound importance in the context of the Earth's core formation. Here we present a complete derivation of this dispersion relation for a self-gravitating two-layer viscous sphere. Such relation is, however, obtained through the solution of a complex transcendental equation, and it is difficult to gain physical insights directly from the transcendental equation itself. We thus also derive an empirical formula to compute the growth rate, by combining the Monte Carlo sampling of the relevant model parameter space with linear regression. Our analysis indicates that the growth rate of Rayleigh-Taylor instability is most sensitive to the viscosity of inner layer in a physical setting that is most relevant to the core formation.
Energy Technology Data Exchange (ETDEWEB)
Torello, David [GW Woodruff School of Mechanical Engineering, Georgia Tech (United States); Kim, Jin-Yeon [School of Civil and Environmental Engineering, Georgia Tech (United States); Qu, Jianmin [Department of Civil and Environmental Engineering, Northwestern University (United States); Jacobs, Laurence J. [School of Civil and Environmental Engineering, Georgia Tech and GW Woodruff School of Mechanical Engineering, Georgia Tech (United States)
2015-03-31
This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.
Aman, Sidra; Khan, Ilyas; Ismail, Zulkhibri; Salleh, Mohd Zuki; Tlili, I.
2018-06-01
In this article the idea of Caputo time fractional derivatives is applied to MHD mixed convection Poiseuille flow of nanofluids with graphene nanoparticles in a vertical channel. The applications of nanofluids in solar energy are argued for various solar thermal systems. It is argued in the article that using nanofluids is an alternate source to produce solar energy in thermal engineering and solar energy devices in industries. The problem is modelled in terms of PDE's with initial and boundary conditions and solved analytically via Laplace transform method. The obtained solutions for velocity, temperature and concentration are expressed in terms of Wright's function. These solutions are significantly controlled by the variations of parameters including thermal Grashof number, Solutal Grashof number and nanoparticles volume fraction. Expressions for skin-friction, Nusselt and Sherwood numbers are also determined on left and right walls of the vertical channel with important numerical results in tabular form. It is found that rate of heat transfer increases with increasing nanoparticles volume fraction and Caputo time fractional parameters.
Verma, Neeraj; Singh, Anil P; Amresh, G; Sahu, P K; Rao, Ch V
2011-05-01
To evaluate the hepatoprotective potential of ethyl acetate fraction of Rhododendron arboreum (Family: Ericaceae) in Wistar rats against carbon tetrachloride (CCl(4))-induced liver damage in preventive and curative models. Fraction at a dose of 100, 200, and 400 mg/kg was administered orally once daily for 14 days in CCl(4)-treated groups (II, III, IV, V and VI). The serum levels of glutamic oxaloacetic transaminase (SGOT), glutamate pyruvate transaminase (SGPT), alkaline phosphatase (SALP), γ-glutamyltransferase (γ -GT), and bilirubin were estimated along with activities of glutathione S-transferase (GST), glutathione reductase, hepatic malondialdehyde formation, and glutathione content. The substantially elevated serum enzymatic activities of SGOT, SGPT, SALP, γ-GT, and bilirubin due to CCl(4) treatment were restored toward normal in a dose-dependent manner. Meanwhile, the decreased activities of GST and glutathione reductase were also restored toward normal. In addition, ethyl acetate fraction also significantly prevented the elevation of hepatic malondialdehyde formation and depletion of reduced glutathione content in the liver of CCl(4)-intoxicated rats in a dose-dependent manner. Silymarin used as standard reference also exhibited significant hepatoprotective activity on post-treatment against CCl(4)-induced hepatotoxicity in rats. The biochemical observations were supplemented with histopathological examination of rat liver sections. The results of this study strongly indicate that ethyl acetate fraction has a potent hepatoprotective action against CCl(4)-induced hepatic damage in rats.
Q-balls of quasi-particles in a (2,0)-theory model of the fractional quantum Hall effect
Ganor, O.J.; Hong, Y.P.; Moore, N.; Sun, H.Y.; Tan, H.S.; Torres-Chicon, N.R.
2015-01-01
A toy model of the fractional quantum Hall effect appears as part of the low-energy description of the Coulomb branch of the A(1) (2, 0)-theory formulated on (S-1 x R-2)/Z(k), where the generator of Z(k) acts as a combination of translation on S-1 and rotation by 2 pi/k on R-2. At low energy the
Maria Klimikova
2010-01-01
Understanding the reasons of the present financial problems lies In understanding the substance of fractional reserve banking. The substance of fractional banking is in lending more money than the bankers have. Banking of partial reserves is an alternative form which links deposit banking and credit banking. Fractional banking is causing many unfavorable economic impacts in the worldwide system, specifically an inflation.
Analytical modeling for fractional multi-dimensional diffusion equations by using Laplace transform
Directory of Open Access Journals (Sweden)
Devendra Kumar
2015-01-01
Full Text Available In this paper, we propose a simple numerical algorithm for solving multi-dimensional diffusion equations of fractional order which describes density dynamics in a material undergoing diffusion by using homotopy analysis transform method. The fractional derivative is described in the Caputo sense. This homotopy analysis transform method is an innovative adjustment in Laplace transform method and makes the calculation much simpler. The technique is not limited to the small parameter, such as in the classical perturbation method. The scheme gives an analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive.
An Empirical Model Of Fractionally Cointegrated Daily High And Low Stock Market Prices
Czech Academy of Sciences Publication Activity Database
Baruník, Jozef; Dvořáková, S.
2015-01-01
Roč. 45, č. 1 (2015), s. 193-206 ISSN 0264-9993 R&D Projects: GA ČR(CZ) GBP402/12/G097 Keywords : fractional cointegration * long memory * range * volatility * daily high and low prices Subject RIV: AH - Economics Impact factor: 0.997, year: 2015 http://library.utia.cas.cz/separaty/2014/E/barunik-0434888.pdf
International Nuclear Information System (INIS)
Skigin, Diana C; Lester, Marcelo
2014-01-01
We analyze the enhanced transmission phenomenon in subwavelength slit structures near a dielectric interface. In particular, we investigate the influence of Rayleigh anomalies in the spectral position as well as in the bandwidth of Fabry–Perot resonances excited on such structures. We consider the cases of propagating and evanescent incidence, i.e., when the metallic structure is illuminated from the dielectric medium side with an incidence angle larger than the critical angle. We show that Rayleigh anomalies strongly interact with Fabry–Perot resonances, and make them deviate from the spectral positions predicted by the infinitely thin slit model. To get physical insight into this problem, we develop a simplified electromagnetic model and show that there is a close correspondence between the transmitted response of the structure and the behavior of certain function that depends on the geometrical and the illumination parameters. Our results suggest that Rayleigh anomalies strongly modify the electromagnetic response of the structure due to the existence of surface waves that modify the coupling condition between the fields inside and outside the slits. Besides, we show that even in absence of Fabry–Perot resonances, it is possible to produce enhanced transmission by taking advantage of the pseudoperiodicity condition of the fields. (paper)
Directory of Open Access Journals (Sweden)
Anupam Pathak
2014-11-01
Full Text Available Abstract: Problem Statement: The two-parameter exponentiated Rayleigh distribution has been widely used especially in the modelling of life time event data. It provides a statistical model which has a wide variety of application in many areas and the main advantage is its ability in the context of life time event among other distributions. The uniformly minimum variance unbiased and maximum likelihood estimation methods are the way to estimate the parameters of the distribution. In this study we explore and compare the performance of the uniformly minimum variance unbiased and maximum likelihood estimators of the reliability function R(t=P(X>t and P=P(X>Y for the two-parameter exponentiated Rayleigh distribution. Approach: A new technique of obtaining these parametric functions is introduced in which major role is played by the powers of the parameter(s and the functional forms of the parametric functions to be estimated are not needed. We explore the performance of these estimators numerically under varying conditions. Through the simulation study a comparison are made on the performance of these estimators with respect to the Biasness, Mean Square Error (MSE, 95% confidence length and corresponding coverage percentage. Conclusion: Based on the results of simulation study the UMVUES of R(t and ‘P’ for the two-parameter exponentiated Rayleigh distribution found to be superior than MLES of R(t and ‘P’.