Sulfur Isotope Fractionation in Magmatic Systems：Models of Rayleigh Distillation and Selective Flux
郑永飞
1990-01-01
The effect of Rayleigh distillation by outgassing of SO2 and H2S on the isotopic composition of sulfur remaining in silicate melts is quantitatively modelled.A threshold mole fraction of sulfur in sulfide component of the melts is reckoned to be of critical importance in shifting the δ34S of the melts mith respect to the original magmas.The partial equilibrium fractionation in a magmatic system is evaluated by assuming that a non-equilibrium flux of sulfur occurs between magmatic volatiles and the melts,while an equilibrium fractionation is approached between sulfate and sulfide within the melts.The results show that under high fo2 conditions,the sulfate/sulfide ratio in a melt entds to increase,and the δ34S value of sulfur in a solidified rock might then be shifted in the positive direction.This may either be due to Rayleigh outgassing in case the mole fraction of sulfide is less than the threshold,or due to a unidirectional increase in δ34S value of the sulfate with decreaing temperature,Conversely,at low fo2,the sulfate/sulfide ratio tends to decrease and the δ34S value of total sulfur could be driven in the negative direction,either because of the Rayleigh outgassing in case the mole fraction of sulfide is greater than the threshold,or because of a unidirectional decrease inδ34S value of the sulfide.To establish isotopic equilibrium between sulfate and sulfide,the HM,QFM or WM buffers in the magmatic system are suggested to provide the redox couple that could simultaneously reduce the sulfate and oxidize the sulfide.CaO present in the silicatte Melts is also called upon to participate in the chemical equilibrium between sulfate and sulfide,Consequently,the δ34S value of an igneous rock could considerably deviate from that of its original magma due to the influence of oxygen fugacity and temperature at the time of magma solidification.
Search for methane isotope fractionation due to Rayleigh distillation on Titan
Ádámkovics, Máté; Mitchell, Jonathan L.
2016-09-01
We search for meridional variation in the abundance of CH3D relative to CH4 on Titan using near-IR spectra obtained with NIRSPAO at Keck, which have a photon-limited signal-to-noise ratio of ∼50. Our observations can rule out a larger than 10% variation in the column of CH3D below 50 km. The preferential condensation of the heavy isotopologues will fractionate methane by reducing CH3D in the remaining vapor, and therefore these observations place limits on the amount of condensation that occurs in the troposphere. While previous estimates of CH3D fractionation on Titan have estimated an upper limit of -6‰, assuming a solid condensate, we consider more recent laboratory data for the equilibrium fractionation over liquid methane, and use a Rayleigh distillation model to calculate fractionation in an ascending parcel of air that is following a moist adiabat. We find that deep, precipitating convection can enhance the fractionation of the remaining methane vapor by -10 to -40‰, depending on the final temperature of the rising parcel. By relating fractionation of our reference parcel model to the pressure level where the moist adiabat achieves the required temperature, we argue that the measured methane fractionation constrains the outflow level for a deep convective event. Observations with a factor of at least 4-6 times larger signal-to-noise are required to detect this amount of fractionation, depending on the altitude range over which the outflow from deep convection occurs.
Search for methane isotope fractionation due to Rayleigh distillation on Titan
Ádámkovics, Máté
2016-01-01
We search for meridional variation in the abundance of CH$_3$D relative to CH$_4$ on Titan using near-IR spectra obtained with NIRSPAO at Keck, which have a photon-limited signal-to-noise ratio of $\\sim$50. Our observations can rule out a larger than 10% variation in the column of CH$_3$D below 50 km. The preferential condensation of the heavy isotopologues will fractionate methane by reducing CH$_3$D in the remaining vapor, and therefore these observations place limits on the amount of condensation that occurs in the troposphere. While previous estimates of CH$_3$D fractionation on Titan have estimated an upper limit of -6 per mil, assuming a solid condensate, we consider more recent laboratory data for the equilibrium fractionation over liquid methane, and use a Rayleigh distillation model to calculate fractionation in an ascending parcel of air that is following a moist adiabat. We find that deep, precipitating convection can enhance the fractionation of the remaining methane vapor by -10 to -40 per mil, d...
Modeling of Rayleigh wave dispersion in Iberia
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.
Response of Duffing Rayleigh system with fractional derivative under Gaussian white noise excitation
张冉冉; 徐伟; 杨贵东; 韩群
2015-01-01
In this paper, we consider the response analysis of 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 Itˆo stochastic differential equation of the system. The accuracy of the analytical results is validated by those results from the Monte Carlo simulation of original system. Moreover, the effects of different system parameters and noise intensity on the response of the system are discussed as well.
Nonlinear diffusion model for Rayleigh-Taylor mixing.
Boffetta, G; De Lillo, F; Musacchio, S
2010-01-22
The complex evolution of turbulent mixing in Rayleigh-Taylor convection is studied in terms of eddy diffusivity models for the mean temperature profile. It is found that a nonlinear model, derived within the general framework of Prandtl mixing theory, reproduces accurately the evolution of turbulent profiles obtained from numerical simulations. Our model allows us to give very precise predictions for the turbulent heat flux and for the Nusselt number in the ultimate state regime of thermal convection.
Nonlinear diffusion model for Rayleigh-Taylor mixing
Boffetta, G; Musacchio, S
2010-01-01
The complex evolution of turbulent mixing in Rayleigh-Taylor convection is studied in terms of eddy diffusiviy models for the mean temperature profile. It is found that a non-linear model, derived within the general framework of Prandtl mixing theory, reproduces accurately the evolution of turbulent profiles obtained from numerical simulations. Our model allows to give very precise predictions for the turbulent heat flux and for the Nusselt number in the ultimate state regime of thermal convection.
Fast sampling model for X-ray Rayleigh scattering
Grichine, V M
2013-01-01
A simple model for X-ray Rayleigh scattering is discussed in terms of the process total cross-section and the angular distribution of scattered X-ray photons. Comparisons with other calculations and experimental data are presented. The model is optimized for the simulation of X-ray tracking inside experimental setups with complex geometry where performance and memory volume are issues to be optimized. (C) 2013 Elsevier B.V. All rights reserved.
Gilmore, R. E.; Eagle, R.; Ries, J. B.; Tripati, A. K.
2013-05-01
The elemental composition of calcium carbonate (CaCO3) precipitated by marine invertebrates varies with the physico-chemical properties of seawater, and is thus used for reconstructing past oceanic conditions, including temperature, pH, and seawater composition. Previous studies have used a Rayleigh fractionation model to interpret elemental partitioning within a range of calcitic and aragonitic organisms, including foraminifera and corals. We present elemental ratios for 18 species of calcareous marine invertebrates, including echinoids, corals, bivalves, gastropods, calcifying algae, crustacea, and serpulid worms, which were reared at CO2-induced aragonite saturation states (±SD) of 2.5 (±0.4), 2.0 (±0.4), 1.5 (±0.3), and 0.7 (±0.2). Importantly, specimens were cultured simultaneously at the same temperature and in seawater sourced from the same reservoir, allowing comparison amongst taxa without regard to native water conditions. A combination of Inductively Coupled Plasma Mass Spectrometry (ICPMS) and Inductively Coupled Plasma Optical Emission Spectrometry (ICP-OES) were used to determine the elemental ratios. We interpret the partitioning of strontium, magnesium, barium, manganese, boron, lithium and uranium within the biogenic carbonates of these 18 invertebrates, along with data from the literature for foraminifera and coccolithophores raised under varying pCO2 and temperature conditions, within a Rayleigh fractionation framework. Application of a Rayleigh model to these systems requires constraints on elemental partitioning into inorganic CaCO3. Our survey of the literature shows that there are limited data for some elements (e.g., Mn) and that, for others (e.g., Sr, Mg), there are a wide range of values reported for a given element. Given this uncertainty, we examine the impact that varying the nominal inorganic partition coefficient has on Rayleigh-derived estimates of calcium-utilization during calcification. The elements examined in this study
Rayleigh-Lamb wave propagation on a fractional order viscoelastic plate.
Meral, F Can; Royston, Thomas J; Magin, Richard L
2011-02-01
A previous study of the authors published in this journal focused on mechanical wave motion in a viscoelastic material representative of biological tissue [Meral et al., J. Acoust. Soc. Am. 126, 3278-3285 (2009)]. Compression, shear and surface wave motion in and on a viscoelastic halfspace excited by surface and sub-surface sources were considered. It was shown that a fractional order Voigt model, where the rate-dependent damping component that is dependent on the first derivative of time is replaced with a component that is dependent on a fractional derivative of time, resulted in closer agreement with experiment as compared with conventional (integer order) models, such as those of Voigt and Zener. In the present study, this analysis is extended to another configuration and wave type: out-of-plane response of a viscoelastic plate to harmonic anti-symmetric Lamb wave excitation. Theoretical solutions are compared with experimental measurements for a polymeric tissue mimicking phantom material. As in the previous configurations the fractional order modeling assumption improves the match between theory and experiment over a wider frequency range. Experimental complexities in the present study and the reliability of the different approaches for quantifying the shear viscoelastic properties of the material are discussed.
Bayes Estimation for Inverse Rayleigh Model under Different Loss Functions
Guobing Fan
2015-04-01
Full Text Available The inverse Rayleigh distribution plays an important role in life test and reliability domain. The aim of this article is study the Bayes estimation of parameter of inverse Rayleigh distribution. Bayes estimators are obtained under squared error loss, LINEX loss and entropy loss functions on the basis of quasi-prior distribution. Comparisons in terms of risks with the estimators of parameter under three loss functions are also studied. Finally, a numerical example is used to illustrate the results.
Zernike polynomial based Rayleigh-Ritz model of a piezoelectric unimorph deformable mirror
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...
Australia's Next Top Fraction Model
Gould, Peter
2013-01-01
Peter Gould suggests Australia's next top fraction model should be a linear model rather than an area model. He provides a convincing argument and gives examples of ways to introduce a linear model in primary classrooms.
Non-Rayleigh control of upper-ocean Cd isotope fractionation in the western South Atlantic
Xie, Ruifang C.; Galer, Stephen J. G.; Abouchami, Wafa; Rijkenberg, Micha J. A.; de Baar, Hein J. W.; De Jong, Jeroen; Andreae, Meinrat O.
2017-08-01
We present seawater Cd isotopic compositions in five depth profiles and a continuous surface water transect, from 50°S to the Equator, in the western South Atlantic, sampled during GEOTRACES cruise 74JC057 (GA02 section, Leg 3), and investigate the mechanisms governing Cd isotope cycling in the upper and deep ocean. The depth profiles generally display high ε 112 / 110Cd at the surface and decrease with increasing depth toward values typical of Antarctic Bottom Water (AABW). However, at stations north of the Subantarctic Front, the decrease in ε 112 / 110Cd is interrupted by a shift to values intermediate between those of surface and bottom waters, which occurs at depths occupied by North Atlantic Deep Water (NADW). This pattern is associated with variations in Cd concentration from low surface values to a maximum at mid-depths and is attributed to preferential utilization of light Cd by phytoplankton in the surface ocean. Our new results show that in this region Cd-deficient waters do not display the extreme, highly fractionated ε 112 / 110Cd reported in some earlier studies from other oceanic regions. Instead, in the surface and subsurface southwest (SW) Atlantic, when [Cd] drops below 0.1 nmol kg-1, ε 112 / 110Cd are relatively homogeneous and cluster around a value of +3.7, in agreement with the mean value of 3.8 ± 3.3 (2SD, n = 164) obtained from a statistical evaluation of the global ocean Cd isotope dataset. We suggest that Cd-deficient surface waters may acquire their Cd isotope signature via sorption of Cd onto organic ligands, colloids or bacterial/picoplankton extracellular functional groups. Alternatively, we show that an open system, steady-state model is in good accord with the observed Cd isotope systematics in the upper ocean north of the Southern Ocean. The distribution of ε 112 / 110Cd in intermediate and deep waters is consistent with the water mass distribution, with the north-south variations reflecting changes in the mixing proportion
Assessing the viscoelasticity of chicken liver by OCE and a Rayleigh wave model
Han, Zhaolong; Liu, Chih-hao; Singh, Manmohan; Aglyamov, Salavat R.; Raghunathan, Raksha; Wu, Chen; Larin, Kirill V.
2017-02-01
This study investigates the feasibility of quantifying the viscoelasticity of soft tissues with a dynamic noncontact optical coherence elastography (OCE) technique coupled with a Rayleigh wave model. Spectral analysis of an air-pulse induced elastic wave as measured by OCE provided the elastic wave dispersion curve. The dispersion curve was fitted to an analytical solution of the Rayleigh wave model to determine the Young's modulus and shear viscosity of samples. In order to validate the method, 10% gelatin phantoms with and without different concentrations of oil were prepared and tested by OCE and mechanical testing. Results demonstrated that the elasticities as assessed by the Rayleigh wave model generally agreed well with mechanical testing, and that the viscosity in the phantom with oil samples was higher than the phantoms without oil, which is in agreement with the literature. Further, this method was applied to quantify the viscoelasticity of chicken liver. The Young's modulus was E=2.04+/-0.88 kPa and the shear viscosity was η=1.20+/-0.13 Pa·s with R2=0.96+/-0.04 between the OCE-measured dispersion curve and Rayleigh wave model analytical solution. Combining OCE and the Rayleigh wave model shows promise as an effective tool for noninvasively quantifying the viscoelasticity of soft tissues.
Toward analytic theory of the Rayleigh-Taylor instability: lessons from a toy model
Mailybaev, Alexei A
2016-01-01
In this work we suggest that a turbulent phase of the Rayleigh-Taylor instability can be explained as a universal stochastic wave traveling with constant speed in a properly renormalized system. This wave, originating from ordinary deterministic chaos in a renormalized time, has two constant limiting states at both sides. These states are related to the initial discontinuity at large scales and to stationary turbulence at small scales. The theoretical analysis is confirmed with extensive numerical simulations made for a new shell model, which features all basic properties of the phenomenological theory for the Rayleigh-Taylor instability.
Cosmological Models with Fractional Derivatives and Fractional Action Functional
V.K. Shchigolev
2011-01-01
Cosmological models of a scalar field with dynamical equations containing fractional derivatives or derived from the Einstein-Hilbert action of fractional order, are constructed. A number of exact solutions to those equations of fractional cosmological models in both eases is given.
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
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.
Lognonné, Philippe; Karakostas, Foivos; Rolland, Lucie; Nishikawa, Yasuhiro
2016-08-01
Acoustic coupling between solid Earth and atmosphere has been observed since the 1960s, first from ground-based seismic, pressure, and ionospheric sensors and since 20 years with various satellite measurements, including with global positioning system (GPS) satellites. This coupling leads to the excitation of the Rayleigh surface waves by local atmospheric sources such as large natural explosions from volcanoes, meteor atmospheric air-bursts, or artificial explosions. It contributes also in the continuous excitation of Rayleigh waves and associated normal modes by atmospheric winds and pressure fluctuations. The same coupling allows the observation of Rayleigh waves in the thermosphere most of the time through ionospheric monitoring with Doppler sounders or GPS. The authors review briefly in this paper observations made on Earth and describe the general frame of the theory enabling the computation of Rayleigh waves for models of telluric planets with atmosphere. The authors then focus on Mars and Venus and give in both cases the atmospheric properties of the Rayleigh normal modes and associated surface waves compared to Earth. The authors then conclude on the observation perspectives especially for Rayleigh waves excited by atmospheric sources on Mars and for remote ionospheric observations of Rayleigh waves excited by quakes on Venus.
A fractional model for dye removal
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.
Using McDaniel's model to represent non-Rayleigh active sonar reverberation
Gu, Ming
Reverberation in active sonar systems has often been observed to follow non-Rayleigh distributions. Current statistical models tend to be either too restrictive, leading to significant mismatch error, or too general, leading to large estimation error. McDaniel's model has shown promise as having reasonably tight representation in terms of skewness and kurtosis for reverberation from a variety of sonar systems. This dissertation intensively explores capability and effectiveness of the generalized McDaniel's model in representing non-Rayleigh reverberation when minimal data are available. Three major topics are covered in this dissertation. First, derivation and computation of the cumulative distribution function of McDaniel's model is addressed. Two approaches, one based on direct integration and the other via characteristic function inversion, are both shown to achieve adequate precision with the former leading to a closed-form solution and the latter requiring significantly less computational effort. Second, parameter estimators using both method of moments (MM) and maximum likelihood (ML) algorithms are developed. The MM estimator has the advantage of a simple and rapid implementation, but the disadvantage of a non- zero probability of a solution not existing. Bootstrap/pruning techniques are proposed to partially deal with the failure of this method. The ML estimator will always provide a solution; however, it requires multivariate optimization. The expectation-maximization (EM) algorithm iteration is also derived for obtaining the ML estimates and compared with the simplex method and quasi-Newton multivariate optimization routines. Furthermore, the ability of various statistical models to represent the probability of false alarm is evaluated as a function of sample size. It is demonstrated that when minimal data are available, McDaniel's model can more accurately represent non-Rayleigh reverberation than the K or Rayleigh mixture models. Third, detection
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.
New subgrid-scale models for large-eddy simulation of Rayleigh-Bénard convection
Dabbagh, F.; Trias, F. X.; Gorobets, A.; Oliva, A.
2016-09-01
At the crossroad between flow topology analysis and the theory of turbulence, a new eddy-viscosity model for Large-eddy simulation has been recently proposed by Trias et al.[PoF, 27, 065103 (2015)]. The S3PQR-model has the proper cubic near-wall behaviour and no intrinsic limitations for statistically inhomogeneous flows. In this work, the new model has been tested for an air turbulent Rayleigh-Benard convection in a rectangular cell of aspect ratio unity and n span-wise open-ended distance. To do so, direct numerical simulation has been carried out at two Rayleigh numbers Ra = 108 and 1010, to assess the model performance and investigate a priori the effect of the turbulent Prandtl number. Using an approximate formula based on the Taylor series expansion, the turbulent Prandtl number has been calculated and revealed a constant and Ra-independent value across the bulk region equals to 0.55. It is found that the turbulent components of eddy-viscosity and eddy-diffusivity are positively prevalent to maintain a turbulent wind essentially driven by the mean buoyant force at the sidewalls. On the other hand, the new eddy-viscosity model is preliminary tested for the case of Ra = 108 and showed overestimation of heat flux within the boundary layer but fairly good prediction of turbulent kinetics at this moderate turbulent flow.
Mathematical modelling of fractional order circuits
Moreles, Miguel Angel
2016-01-01
In this work a classical derivation of fractional order circuits models is presented. Generalized constitutive equations in terms of fractional Riemann-Liouville derivatives are introduced in the Maxwell's equations. Next the Kirchhoff voltage law is applied in a RCL circuit configuration. A fractional differential equation model is obtained with Caputo derivatives. Thus standard initial conditions apply.
Alok Dhaundiyal
2016-10-01
Full Text Available This article focuses on the influence of relevant parameters of biomass pyrolysis on the numerical solution of the isothermal nth-order distributed activation energy model (DAEM using the Rayleigh distribution as the initial distribution function F(E of the activation energies. In this study, the integral upper limit, the frequency factor, the reaction order and the scale parameters are investigated. This paper also derived the asymptotic approximation for the DAEM. The influence of these parameters is used to calculate the kinetic parameters of the isothermal nth-order DAEM with the help of thermo-analytical results of TGA/DTG analysis.
Han, Zhaolong; Li, Jiasong; Singh, Manmohan; Wu, Chen; Liu, Chih-Hao; Raghunathan, Raksha; Aglyamov, Salavat R; Vantipalli, Srilatha; Twa, Michael D; Larin, Kirill V
2017-02-01
The biomechanical properties of the cornea play a critical role in forming vision. Diseases such as keratoconus can structurally degenerate the cornea causing a pathological loss in visual acuity. UV-A/riboflavin corneal collagen crosslinking (CXL) is a clinically available treatment to stiffen the cornea and restore its healthy shape and function. However, current CXL techniques do not account for pre-existing biomechanical properties of the cornea nor the effects of the CXL treatment itself. In addition to the inherent corneal structure, the intraocular pressure (IOP) can also dramatically affect the measured biomechanical properties of the cornea. In this work, we present the details and development of a modified Rayleigh-Lamb frequency equation model for quantifying corneal biomechanical properties. After comparison with finite element modeling, the model was utilized to quantify the viscoelasticity of in situ porcine corneas in the whole eye-globe configuration before and after CXL based on noncontact optical coherence elastography measurements. Moreover, the viscoelasticity of the untreated and CXL-treated eyes was quantified at various IOPs. The results showed that the stiffness of the cornea increased after CXL and that corneal stiffness is close to linear as a function of IOP. These results show that the modified Rayleigh-Lamb wave model can provide an accurate assessment of corneal viscoelasticity, which could be used for customized CXL therapies.
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.
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.
Gagnon, Alexander C.; Adkins, Jess F.; Fernandez, Diego P.; Robinson, Laura F.
2007-09-01
Deep-sea corals are a new tool in paleoceanography with the potential to provide century long records of deep ocean change at sub-decadal resolution. Complicating the reconstruction of past deep-sea temperatures, Mg/Ca and Sr/Ca paleothermometers in corals are also influenced by non-environmental factors, termed vital effects. To determine the magnitude, pattern and mechanism of vital effects we measure detailed collocated Sr/Ca and Mg/Ca ratios, using a combination of micromilling and isotope-dilution ICP-MS across skeletal features in recent samples of Desmophyllum dianthus, a scleractinian coral that grows in the near constant environment of the deep-sea. Sr/Ca variability across skeletal features is less than 5% (2σ relative standard deviation) and variability of Sr/Ca within the optically dense central band, composed of small and irregular aragonite crystals, is significantly less than the surrounding skeleton. The mean Sr/Ca of the central band, 10.6 ± 0.1 mmol/mol (2σ standard error), and that of the surrounding skeleton, 10.58±0.09 mmol/mol, are statistically similar, and agree well with the inorganic aragonite Sr/Ca-temperature relationship at the temperature of coral growth. In the central band, Mg/Ca is greater than 3 mmol/mol, more than twice that of the surrounding skeleton, a general result observed in the relative Mg/Ca ratios of D. dianthus collected from separate oceanographic locations. This large vital effect corresponds to a ˜ 10 °C signal, when calibrated via surface coral Mg/Ca-temperature relationships, and has the potential to complicate paleoreconstructions. Outside the central band, Mg/Ca ratios increase with decreasing Sr/Ca. We explain the correlated behavior of Mg/Ca and Sr/Ca outside the central band by Rayleigh fractionation from a closed pool, an explanation that has been proposed elsewhere, but which is tested in this study by a simple and general relationship. We constrain the initial solution and effective partition
Fractional constant elasticity of variance model
Ngai Hang Chan; Chi Tim Ng
2007-01-01
This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this paper, a fractional version of the Constant Elasticity of Variance (CEV) model is developed. European option pricing formula similar to that of the classical CEV model is obtained and a volatility skew pattern is revealed.
Gol' danskii, V.I.; Krupyanskii, Yu.F.; Fleurov, V.N.
1986-06-01
Specific features of the Rayleigh Scattering of Moessbauer Radiation (RSMR) technique in the study of biological systems are described. Experimental data show that the temperature and hydration degree are the principal parameters which influence intramolecular mobility in biopolymers. Data on temperature dependencies of elastic fraction, f, and spectrum line-shape do not fit neither Debye or Einstein models of solids nor the free diffusion in liquids and demand for their explanation a multimode approximation (i.e. a wide spectrum of correlation times, at T=293 K from 10/sup -6/s to 10/sup -12/-10/sup -13/s). On the basis of RSMR, low temperature specific heat and X-ray dynamic analysis data and from the general conditions that information macromolecule must be in a non-equilibrium state (an independent confirmation of this fact comes from the kinetic model of protein folding) a glass-like dynamical model of biopolymers is formulated. A possible interpretation of RSMR data shows that fluctuatively prepared tunneling between quasiequilibrium positions (QEP) can prevail activated transitions up to a room temperature.
A trade-off between model resolution and variance with selected Rayleigh-wave data
Xia, J.; Miller, R.D.; Xu, Y.
2008-01-01
Inversion of multimode surface-wave data is of increasing interest in the near-surface geophysics community. For a given near-surface geophysical problem, it is essential to understand how well the data, calculated according to a layered-earth model, might match the observed data. A data-resolution matrix is a function of the data kernel (determined by a geophysical model and a priori information applied to the problem), not the data. A data-resolution matrix of high-frequency (??? 2 Hz) Rayleigh-wave phase velocities, therefore, offers a quantitative tool for designing field surveys and predicting the match between calculated and observed data. First, we employed a data-resolution matrix to select data that would be well predicted and to explain advantages of incorporating higher modes in inversion. The resulting discussion using the data-resolution matrix provides insight into the process of inverting Rayleigh-wave phase velocities with higher mode data to estimate S-wave velocity structure. Discussion also suggested that each near-surface geophysical target can only be resolved using Rayleigh-wave phase velocities within specific frequency ranges, and higher mode data are normally more accurately predicted than fundamental mode data because of restrictions on the data kernel for the inversion system. Second, we obtained an optimal damping vector in a vicinity of an inverted model by the singular value decomposition of a trade-off function of model resolution and variance. In the end of the paper, we used a real-world example to demonstrate that selected data with the data-resolution matrix can provide better inversion results and to explain with the data-resolution matrix why incorporating higher mode data in inversion can provide better results. We also calculated model-resolution matrices of these examples to show the potential of increasing model resolution with selected surface-wave data. With the optimal damping vector, we can improve and assess an inverted
Analytical modeling of magnetic Rayleigh-Taylor instabilities in compressible fluids
Liberatore, Stéphane; Bouquet, Serge
2008-11-01
The magnetic Rayleigh-Taylor instability (MRTI) is investigated in the case of compressible plasmas. The goal of this work is highlighting the influence of both the magnetic field and the compressibility of the material on the growth rate of the Rayleigh-Taylor instability, compared to the classical growth rate derived for incompressible fluids. Our analytical linear models are derived in the framework of the ideal magnetohydrodynamics theory. Three general dispersion relations are obtained: (1) Two for stratified fluids, including compressible (denoted CS∥ when the wave vector k is parallel to the equilibrium magnetic field B0 and CS⊥ when k ⊥B0) and incompressible (denoted IS∥ and IS⊥) and (2) one for incompressible uniform density fluids, including finite mass (denoted Ifm) and infinite (denoted IU). For k ⊥B0, Ifm, IU, and IS⊥ are unmagnetized cases. Comparisons of those various configurations are performed and several differences are pointed out. The main results are as follows: Stratification weakens the MRTI while compressibility has a destabilizing effect. The magnetic field enhances these phenomena. The CS∥ and IU configurations have an identical cutoff wave number. The upper fluid (also called heavy fluid) is more sensitive to compressibility than the light one when k ∥B0. Finally, the CS∥ case is more sensitive than the CS⊥ one to physical variations.
Particle drift model for Z-pinch-driven magneto-Rayleigh-Taylor instability
Dan, Jia Kun; Xu, Qiang; Wang, Kun Lun; Ren, Xiao Dong; Huang, Xian Bin
2016-09-01
A theoretical model of Z-pinch driven magneto-Rayleigh-Taylor instability is proposed based on the particle drift point of view, which can explain the helical instability structure observed in premagnetized imploding liner experiments. It is demonstrated that all possible drift motions, including polarization drift, gradient drift, and curvature drift, which can lead to charge separations, each will attribute to an effective gravity acceleration. Theoretical predictions given by this model are dramatically different from those given by previous theories which have been readily recovered in the theory presented here as a limiting case. The theory shows qualitative agreement with available experimental data of the pitch angle and provides certain predictions to be verified.
Benoit, M H; Nyblade, A A; Pasyanos, M E
2006-01-17
The East African and Ethiopian Plateaus have long been recognized to be part of a much larger topographic anomaly on the African Plate called the African Superswell. One of the few places within the African Superswell that exhibit elevations of less than 1 km is southeastern Sudan and northern Kenya, an area containing both Mesozoic and Cenozoic rift basins. Crustal structure and uppermost mantle velocities are investigated in this area by modeling Rayleigh wave dispersion. Modeling results indicate an average crustal thickness of 25 {+-} 5 km, some 10-15 km thinner than the crust beneath the adjacent East African and Ethiopian Plateaus. The low elevations can therefore be readily attributed to an isostatic response from crustal thinning. Low Sn velocities of 4.1-4.3 km/s also characterize this region.
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.
Fractional Order Models of Industrial Pneumatic Controllers
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.
Review of Some Promising Fractional Physical Models
Tarasov, Vasily E
2015-01-01
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and differentiation of non-integer orders, i.e., by methods of the fractional calculus. This paper is a review of physical models that look very promising for future development of fractional dynamics. We suggest a short introduction to fractional calculus as a theory of integration and differentiation of non-integer order. Some applications of integro-differentiations of fractional orders in physics are discussed. Models of discrete systems with memory, lattice with long-range inter-particle interaction, dynamics of fractal media are presented. Quantum analogs of fractional derivatives and model of open nano-system systems with memory are also discussed.
Yaohua Deng
2015-01-01
Full Text Available This paper discusses the calculation problems of bending deformation of FWP processing. Take three axis CNC machining as an example, to establish mechanics model of flexible workpiece processing process. The flexible workpiece balance equation is a two-dimensional partial differential equation, to solve the problem of flexible workpiece bending deformation using Rayleigh-Ritz method and designing the test function of bending deformation of flexible workpiece. By satisfying the minimum potential energy condition of FWP processing to work out the approximate solution of bending deformation of flexible workpiece, find out the relationship between material properties of flexible piece, acting force Fz, and deformation value. Finally, the rectangle flexible workpiece which is made up of polyurethane sponge is selected as an experiment subject. The results show that the average relative deviation between theoretical value and observed value is only 5.51%. It is proved that the bending deformation test function satisfies the actual deformation calculation requirements.
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
Aliashim Albani
2014-02-01
Full Text Available The demand for electricity in Malaysia is growing in tandem with its Gross Domestic Product (GDP growth. Malaysia is going to need even more energy as it strives to grow towards a high-income economy. Malaysia has taken steps to exploring the renewable energy (RE including wind energy as an alternative source for generating electricity. In the present study, the wind energy potential of the site is statistically analyzed based on 1-year measured hourly time-series wind speed data. Wind data were obtained from the Malaysian Meteorological Department (MMD weather stations at nine selected sites in Malaysia. The data were calculated by using the MATLAB programming to determine and generate the Weibull and Rayleigh distribution functions. Both Weibull and Rayleigh models are fitted and compared to the Field data probability distributions of year 2011. From the analysis, it was shown that the Weibull distribution is fitting the Field data better than the Rayleigh distribution for the whole year 2011. The wind power density of every site has been studied based on the Weibull and Rayleigh functions. The Weibull distribution shows a good approximation for estimation of wind power density in Malaysia.
Modelling of Rayleigh-type seam waves in disturbed coal seams and around a coal mine roadway
Essen, Katja; Bohlen, Thomas; Friederich, Wolfgang; Meier, Thomas
2007-08-01
Wave propagation in coal seams is numerically modelled in order to identify approaches towards the reconnaissance beyond the heading face of an advancing coal mine roadway. Complete synthetic wavefields including P-SV body waves and Rayleigh-type seam waves are calculated using a Green's function approach for simple, laterally homogeneous models and a parallel elastic 2-D/3-D finite difference modelling code for more realistic geometries. For a simple three-layer model the wavefield within the seam is dominated by a fundamental Rayleigh seam mode symmetrical with respect to the centre of the seam on the vertical component and antisymmetrical on the horizontal component. If the seam contains an interleaved dirt band with higher velocities and density, higher modes dominate the wave propagation, depending on the thickness of the dirt band. Wave propagation in laterally inhomogeneous coal seam models with disturbances like seam ends, faults, thinning, washouts and seam splitting is strongly influenced by the type of disturbance. Amplitudes of seam waves reflected from these disturbances strongly depend on the fault throw and the degree of thinning or washout. In some cases, conversion to higher modes can occur. In all investigated models, those Rayleigh seam wave phases are preferably reflected, which have frequencies above the fundamental mode Airy phase. Lower frequency phases are preferably transmitted. However, seam waves are not reflected from a seam splitting disturbance. Thus a detection of seam splitting with reflected seam waves appears to be impossible. FD computations for 3-D models containing an ending tunnel parallel to the seam and a source beyond the heading face of the tunnel show that seam waves are converted into Rayleigh waves at the tunnel face. They propagate along the surface of the tunnel and interfere with the seam waves propagating beside the tunnel. This effect has to be taken into account for subsequent treatment of experimental data, where
Rayleigh-Taylor finger instability mixing in hydrodynamic shell convection models
Mocak, Miroslav
2010-01-01
Mixing processes in stars driven by composition gradients as a result of the Rayleigh-Taylor instability are not anticipated. They are supported only by hydrodynamic studies of stellar convection. We find that such mixing occurs below the bottom edge of convection zones in our multidimensional hydrodynamic shell convection models. It operates at interfaces created by off-center nuclear burning, where less dense gas with higher mean molecular weight is located above denser gas with a lower mean molecular weight. We discuss the mixing under various conditions with hydrodynamic convection models based on stellar evolutionary calculations of the core helium flash in a 1.25 Msun star, the core carbon flash in a 9.3 Msun star, and of oxygen burning shell in a star with a mass of 23 Msun. We simulate the hydrodynamic behavior of shell convection during various phases of stellar evolution with the Eulerian hydrodynamics code HERAKLES in two and three spatial dimensions. Initial models for this purpose are obtained by...
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.
Multi-Fraction Bayesian Sediment Transport Model
Mark L. Schmelter
2015-09-01
Full Text Available A Bayesian approach to sediment transport modeling can provide a strong basis for evaluating and propagating model uncertainty, which can be useful in transport applications. Previous work in developing and applying Bayesian sediment transport models used a single grain size fraction or characterized the transport of mixed-size sediment with a single characteristic grain size. Although this approach is common in sediment transport modeling, it precludes the possibility of capturing processes that cause mixed-size sediments to sort and, thereby, alter the grain size available for transport and the transport rates themselves. This paper extends development of a Bayesian transport model from one to k fractional dimensions. The model uses an existing transport function as its deterministic core and is applied to the dataset used to originally develop the function. The Bayesian multi-fraction model is able to infer the posterior distributions for essential model parameters and replicates predictive distributions of both bulk and fractional transport. Further, the inferred posterior distributions are used to evaluate parametric and other sources of variability in relations representing mixed-size interactions in the original model. Successful OPEN ACCESS J. Mar. Sci. Eng. 2015, 3 1067 development of the model demonstrates that Bayesian methods can be used to provide a robust and rigorous basis for quantifying uncertainty in mixed-size sediment transport. Such a method has heretofore been unavailable and allows for the propagation of uncertainty in sediment transport applications.
Phase-field model for the Rayleigh--Taylor instability of immiscible fluids
Celani, Antonio; Muratore-Ginanneschi, Paolo; Vozella, Lara
2008-01-01
The Rayleigh--Taylor instability of two immiscible fluids in the limit of small Atwood numbers is studied by means of a phase-field description. In this method the sharp fluid interface is replaced by a thin, yet finite, transition layer where the interfacial forces vary smoothly. This is achieved by introducing an order parameter (the phase field) whose variation is continuous across the interfacial layers and is uniform in the bulk region. The phase field model obeys a Cahn--Hilliard equation and is two-way coupled to the standard Navier--Stokes equations. Starting from this system of equations we have first performed a linear analysis from which we have analytically rederived the known gravity-capillary dispersion relation in the limit of vanishing mixing energy density and capillary width. We have performed numerical simulations and identified a region of parameters in which the known properties of the linear phase (both stable and unstable) are reproduced in a very accurate way. This has been done both i...
Buogo, Silvano; Cannelli, Giovanni B
2002-06-01
The growth, collapse, and rebound of a vapor bubble generated by an underwater spark is studied by means of high-speed cinematography, simultaneously acquiring the emitted acoustic signature. Video recordings show that the growth and collapse phases are nearly symmetrical during the first two or three cycles, the bubble shape being approximately spherical. After 2-3 cycles the bubble behavior changes from a collapsing/rebounding regime with sound-emitting implosions to a pulsating regime with no implosions. The motion of the bubble wall during the first collapses was found to be consistent with the Rayleigh model of a cavity in an incompressible liquid, with the inclusion of a vapor pressure term at constant temperature within each bubble cycle. An estimate of the pressure inside the bubble is obtained measuring the collapse time and maximum radius, and the amount of energy converted into acoustical energy upon each implosion is deduced. The resulting value of acoustic efficiency was found to be in agreement with measurements based on the emitted acoustic pulse.
Fractionally Integrated Models With ARCH Errors
Hauser, Michael A.; Kunst, Robert M.
1993-01-01
Abstract: We introduce ARFIMA-ARCH models which simultaneously incorporate fractional differencing and conditional heteroskedasticity. We develop the likelihood function and a numerical estimation procedure for this model class. Two ARCH models - Engle- and Weiss-type - are explicitly treated and stationarity conditions are derived. Finite-sample properties of the estimation procedure are explored by Monte Carlo simulation. An application to the Standard & Poor 500 Index indicates existence o...
Goloviznin, V. M.; Korotkin, I. A.; Finogenov, S. A.
2016-12-01
Some numerical results for the two- and three-dimensional de Vahl Davis benchmark are presented. This benchmark describes thermal convection in a square (cubic) cavity with vertical heated walls in a wide range of Rayleigh numbers (104 to 1014), which covers both laminar and highly turbulent f lows. Turbulent f lows are usually described using a turbulence model with parameters that depend on the Rayleigh number and require adjustment. An alternative is Direct Numerical Simulation (DNS) methods, but they demand extremely large computational grids. Recently, there has been an increasing interest in DNS methods with an incomplete resolution, which, in some cases, are able to provide acceptable results without resolving Kolmogorov scales. On the basis of this approach, the so-called parameter-free computational techniques have been developed. These methods cover a wide range of Rayleigh numbers and allow computing various integral properties of heat transport on relatively coarse computational grids. In this paper, a new numerical method based on the CABARET scheme is proposed for solving the Navier-Stokes equations in the Boussinesq approximation. This technique does not involve a turbulence model or any tuning parameters and has a second-order approximation scheme in time and space on uniform and nonuniform grids with a minimal computational stencil. Testing the technique on the de Vahl Davis benchmark and a sequence of refined grids shows that the method yields integral heat f luxes with a high degree of accuracy for both laminar and highly turbulent f lows. For Rayleigh numbers up to 1014, a several percent accuracy is achieved on an extremely coarse grid consisting of 20 × 20 cells refined toward the boundary. No definite or comprehensive explanation of this computational phenomenon has been given. Cautious optimism is expressed regarding the perspectives of using the new method for thermal convection computations at low Prandtl numbers typical of liquid metals.
A Fractional Micro-Macro Model for Crowds of Pedestrians based on Fractional Mean Field Games
Cao, Ke-cai; Stuart, Dan
2016-01-01
Modeling of crowds 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 micro-macro 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.
Modeling Students' Mathematics Using Steffe's Fraction Schemes
Norton, Anderson H.; McCloskey, Andrea V.
2008-01-01
Each year, more teachers learn about the successful intervention program known as Math Recovery (USMRC 2008; Wright 2003). The program uses Steffe's whole-number schemes to model, understand, and support children's development of whole-number reasoning. Readers are probably less familiar with Steffe's fraction schemes, which have proven similarly…
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.
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.
Parametric-based brain Magnetic Resonance Elastography using a Rayleigh damping material model.
Petrov, Andrii Y; Sellier, Mathieu; Docherty, Paul D; Chase, J Geoffrey
2014-10-01
The three-parameter Rayleigh damping (RD) model applied to time-harmonic Magnetic Resonance Elastography (MRE) has potential to better characterise fluid-saturated tissue systems. However, it is not uniquely identifiable at a single frequency. One solution to this problem involves simultaneous inverse problem solution of multiple input frequencies over a broad range. As data is often limited, an alternative elegant solution is a parametric RD reconstruction, where one of the RD parameters (μI or ρI) is globally constrained allowing accurate identification of the remaining two RD parameters. This research examines this parametric inversion approach as applied to in vivo brain imaging. Overall, success was achieved in reconstruction of the real shear modulus (μR) that showed good correlation with brain anatomical structures. The mean and standard deviation shear stiffness values of the white and gray matter were found to be 3±0.11kPa and 2.2±0.11kPa, respectively, which are in good agreement with values established in the literature or measured by mechanical testing. Parametric results with globally constrained μI indicate that selecting a reasonable value for the μI distribution has a major effect on the reconstructed ρI image and concomitant damping ratio (ξd). More specifically, the reconstructed ρI image using a realistic μI=333Pa value representative of a greater portion of the brain tissue showed more accurate differentiation of the ventricles within the intracranial matter compared to μI=1000Pa, and ξd reconstruction with μI=333Pa accurately captured the higher damping levels expected within the vicinity of the ventricles. Parametric RD reconstruction shows potential for accurate recovery of the stiffness characteristics and overall damping profile of the in vivo living brain despite its underlying limitations. Hence, a parametric approach could be valuable with RD models for diagnostic MRE imaging with single frequency data. Copyright © 2014
Modeling electron fractionalization with unconventional Fock spaces
Cobanera, Emilio
2017-08-01
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 D=1,2,3,\\ldots 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.
Menke, William
2017-02-01
We prove that the problem of inverting Rayleigh wave phase velocity functions c( k ) , where k is wavenumber, for density ρ ( z ) , rigidity μ ( z ) and Lamé parameter λ ( z ) , where z is depth, is fully non-unique, at least in the highly-idealized case where the base Earth model is an isotropic half space. The model functions completely trade off. This is one special case of a common inversion scenario in which one seeks to determine several model functions from a single data function. We explore the circumstances under which this broad class of problems is unique, starting with very simple scenarios, building up to the somewhat more complicated (and common) case where data and model functions are related by convolutions, and then finally, to scale-independent problems (which include the Rayleigh wave problem). The idealized cases that we examine analytically provide insight into the kinds of nonuniqueness that are inherent in the much more complicated problems encountered in modern geophysical imaging (though they do not necessarily provide methods for solving those problems). We also define what is meant by a Backus and Gilbert resolution kernel in this kind of inversion and show under what circumstances a unique localized average of a single model function can be constructed.
Menke, William
2017-04-01
We prove that the problem of inverting Rayleigh wave phase velocity functions c( k ), where k is wavenumber, for density ρ ( z ), rigidity μ ( z ) and Lamé parameter λ ( z ), where z is depth, is fully non-unique, at least in the highly-idealized case where the base Earth model is an isotropic half space. The model functions completely trade off. This is one special case of a common inversion scenario in which one seeks to determine several model functions from a single data function. We explore the circumstances under which this broad class of problems is unique, starting with very simple scenarios, building up to the somewhat more complicated (and common) case where data and model functions are related by convolutions, and then finally, to scale-independent problems (which include the Rayleigh wave problem). The idealized cases that we examine analytically provide insight into the kinds of nonuniqueness that are inherent in the much more complicated problems encountered in modern geophysical imaging (though they do not necessarily provide methods for solving those problems). We also define what is meant by a Backus and Gilbert resolution kernel in this kind of inversion and show under what circumstances a unique localized average of a single model function can be constructed.
State-Space Modelling of Loudspeakers using Fractional Derivatives
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....... It is shown that the identified parameters can be used in a linear fractional order state-space model to simulate the loudspeakers’ time domain 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...
Schilling, Oleg; Mueschke, Nicholas; Latini, Marco; Don, Wai Sun; Andrews, Malcolm
2006-11-01
Gradient-diffusion models of turbulent transport in Rayleigh- Taylor and Richtmyer-Meshkov instability-induced mixing are assessed using direct numerical simulation (DNS) and implicit large-eddy simulation (ILES) data. Mean and fluctuating fields, defined from spatial averages over the periodic directions of the DNS, are used to construct the unclosed terms in the turbulent kinetic energy transport equation. These terms are then compared a priori with the corresponding terms modeled using the gradient-diffusion approximation to assess the validity of this approximation for these buoyancy- and shock- driven flows. Implications for two-equation turbulence modeling of Rayleigh-Taylor and Richtmyer-Meshkov instability-induced mixing are discussed. This work was performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48. This research was also sponsored by the National Nuclear Security Administration under the Stewardship Science Academic Alliances Program through DOE Research Grant No. DE-FG03- 02NA00060. UCRL-ABS-223369
Spiral defect chaos in a model of Rayleigh-Benard convection
Xi, H; Viñals, J; Xi, Hao-wen; Vinals., Jorge
1993-01-01
A numerical solution of a generalized Swift-Hohenberg equation in two dimensions reveals the existence of a spatio-temporal chaotic state comprised of a large number of rotating spirals. This state is observed for a reduced Rayleigh number $\\epsilon=0.25$. The power spectrum of the state is isotropic, and the spatial correlation function decays exponentially, with an estimated decay length $\\xi \\approx 2.5 \\lambda_{c}$, where $\\lambda_{c}$ is the critical wavelength near the onset of convection. Our study suggests that this spiral defect state occurs for low Prandtl numbers and large aspect ratios.
Asymptotic dynamics for the Cucker-Smale-type model with the Rayleigh friction
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.
Fractional Langevin model of gait variability
Latka Miroslaw
2005-08-01
Full Text Available Abstract The stride interval in healthy human gait fluctuates from step to step in a random manner and scaling of the interstride interval time series motivated previous investigators to conclude that this time series is fractal. Early studies suggested that gait is a monofractal process, but more recent work indicates the time series is weakly multifractal. Herein we present additional evidence for the weakly multifractal nature of gait. We use the stride interval time series obtained from ten healthy adults walking at a normal relaxed pace for approximately fifteen minutes each as our data set. A fractional Langevin equation is constructed to model the underlying motor control system in which the order of the fractional derivative is itself a stochastic quantity. Using this model we find the fractal dimension for each of the ten data sets to be in agreement with earlier analyses. However, with the present model we are able to draw additional conclusions regarding the nature of the control system guiding walking. The analysis presented herein suggests that the observed scaling in interstride interval data may not be due to long-term memory alone, but may, in fact, be due partly to the statistics.
Fery Gustomo
2013-09-01
Full Text Available Radar (Radio, Detection, and Ranging mampu mendeteksi target untuk mendapatkan informasi berupa jarak, azimuth, dan kecepatan. Sinyal Radar ada dua jenis, yaitu pulsa (Pulsed Radar dan gelombang kontinyu (Continuous Wave Radar. Pulsed Radar mempunyai prinsip kerja memancarkan sinyal pulsa dengan PRI (Pulse Repetition Interval dan PRF (Pulse Repetition Frequency tertentu dipancarkan dengan modulasi ke dalam sinyal sinusoidal dengan frekuensi yang lebih tinggi serta memanfaatkan delay dari setiap pulsanya untuk mendapatkan informasi dari target. Sedangkan Continuous Wave Radar mempunyai prinsip kerja memancarkan sinyal sinusoidal secara terus menerus dan memanfaatkan sinyal echo yang terdiri dari beberapa variasi frekuensi akibat adanya efek Doppler untuk mendeteksi target. Terdapat pengaruh jenis gelombang sinyal radar terhadap kemampuan deteksi radar. Model distribusi Rayleigh dipilih untuk dapat mewakili suatu kondisi lingkungan (clutter yang bergerak dan mempunyai parameter kecepatan angin. Hasil simulasi dari kedua jenis sinyal menunjukkan bahwa pada model clutter terdistribusi Rayleigh, radar CW mempunyai kemampuan deteksi yang lebih baik pada kecepatan target yang lebih tinggi, karena mampu mendeteksi target dengan kecepatan 20-60 knots. Sedangkan radar pulsa mempunyai kemampuan deteksi yang lebih baik pada kecepatan target rendah yaitu pada kecepatan 15-55 knots. Untuk Probabilitas deteksi minimum 90%, Radar CW mempunyai ketahanan yang lebih baik terhadap noise daripada radar pulsa karena kemampuan radar pulsa terbatas pada nilai SNR 20 dB. Sedangkan radar CW mampu mendeteksi target dengan baik sampai SNR bernilai 15 dB. Sedangkan untuk deteksi terhadap kecepatan target, radar CW mempunyai hasil yang lebih akurat daripada radar pulsa.
Low-dimensional model of turbulent Rayleigh-Benard convection in a Cartesian cell with square domain
Bailon-Cuba, Jorge
2011-01-01
A low-dimensional model (LDM) for turbulent Rayleigh-Benard convection in a Cartesian cell with square domain, based on the Galerkin projection of the Boussinesq equations onto a finite set of empirical eigenfunctions, is presented. The empirical eigenfunctions are obtained from a joint Proper Orthogonal Decomposition (POD) of the velocity and temperature fields using the Snapshot Method on the basis of a direct numerical simulation (DNS). The resulting LDM is a quadratic inhomogeneous system of coupled ordinary differential equations which we use to describe the long-time temporal evolution of the large-scale mode amplitudes for a Rayleigh number of 1e5 and a Prandtl number of 0.7. The truncation to a finite number of degrees of freedom, that does not exceed a number of 310 for the present, requires the additional implementation of an eddy viscosity-diffusivity to capture the missing dissipation of the small-scale modes. The magnitude of this additional dissipation mechanism is determined by requiring statis...
Discrete model of dislocations in fractional nonlocal elasticity
Tarasov, Vasily E
2016-01-01
Discrete models of dislocations in fractional nonlocal materials are suggested. The proposed models are based on fractional-order differences instead of finite differences of integer orders that are usually used...
Yi-Fei Pu
2013-01-01
Full Text Available The traditional integer-order partial differential equation-based image denoising approaches often blur the edge and complex texture detail; thus, their denoising effects for texture image are not very good. To solve the problem, a fractional partial differential equation-based denoising model for texture image is proposed, which applies a novel mathematical method—fractional calculus to image processing from the view of system evolution. We know from previous studies that fractional-order calculus has some unique properties comparing to integer-order differential calculus that it can nonlinearly enhance complex texture detail during the digital image processing. The goal of the proposed model is to overcome the problems mentioned above by using the properties of fractional differential calculus. It extended traditional integer-order equation to a fractional order and proposed the fractional Green’s formula and the fractional Euler-Lagrange formula for two-dimensional image processing, and then a fractional partial differential equation based denoising model was proposed. The experimental results prove that the abilities of the proposed denoising model to preserve the high-frequency edge and complex texture information are obviously superior to those of traditional integral based algorithms, especially for texture detail rich images.
Jung, Woo Hyun; Moriyama, Kiyofumi; Park, Hyun Sun [POSTECH, Pohang (Korea, Republic of)
2016-05-15
One of them is FCI (Fuel-Coolant Interaction) phenomenon which is resulted from RPV (Reactor Pressure Vessel) failure at high pressure and high temperature condition of molten fuel. If RPV fails, the melt is ejected to the cavity which is flooded by water as a jet form. Then, the ejected melt jet interacts with water causing massive steam generation and resulting in particulate debris bed on the basemat. As a result of FCI, the initial boundary conditions of steam explosion and debris bed coolability are determined and that is the reason why understanding exact mechanism of melt jet breakup is important in this field. That is, FCI can be said as a starting phenomenon in the ex-vessel severe accident scenario. Until now, numerous previous researchers conducted FCI experiments and numerical analysis in small scale and plant scale. In two MATE experiments, the jet breakup lengths are compared and analyzed with the visualization data. From the observation, the new jet breakup model is proposed including the multiple boundary layer stripping mechanism. Combining the existing and new models, the erosion rate fraction for total melt mass rate was obtained. The new model showed that multiple BLS mechanisms contribute approximately 30% of the total melt jet breakup resulting in the short jet breakup length observed in the MATE 00-2 experiment.
Discrete model of dislocations in fractional nonlocal elasticity
Vasily E. Tarasov
2016-01-01
Full Text Available Discrete models of dislocations in fractional nonlocal materials are suggested. The proposed models are based on fractional-order differences instead of finite differences of integer orders that are usually used. The fractional differences allow us to describe long-range interactions in materials. In continuous limit the suggested discrete models give continuum models of dislocations in nonlocal continua. Fractional generalization of the Frenkel–Kontorova model by using long-range interactions is suggested. We also propose a fractional generalization of interacting atomic chains (IAC model of dislocations by considering long-range interacting chains.
Debayle, E.; Ricard, Y. R.
2011-12-01
We present a global SV-wave tomographic model of the upper mantle, built from a new dataset of fundamental and higher mode Rayleigh waveforms. We use an extension of the automated waveform inversion approach of Debayle (1999) designed to improve the extraction of fundamental and higher mode information from a single surface wave seismogram. The improvement is shown to be significant in the transition zone structure which is constrained by the higher modes. The new approach is fully automated and can be run on a Beowulf computer to process massive surface wave dataset. It has been used to match successfully over 350 000 fundamental and higher mode Rayleigh waveforms, corresponding to about 20 millions of new measurements extracted from the seismograms. For each seismogram, we obtain a path average shear velocity and quality factor model, and a set of fundamental and higher mode dispersion and attenuation curves compatible with the recorded waveform. The set of dispersion curves provides a global database for future finite frequency inversion. Our new 3D SV-wave tomographic model takes into account the effect of azimuthal anisotropy and is constrained with a lateral resolution of several hundred kilometers and a vertical resolution of a few tens of kilometers. In the uppermost 200 km, our model shows a very strong correlation with surface tectonics. The slow velocity signature of mid-oceanic ridges extend down to ~100 km depth while the high velocity signature of cratons vanishes below 200 km depth. At depth greater than 400 km, the pattern of seismic velocities appear relatively homogeneous at large scale, except for high velocity slabs which produce broad high velocity regions within the transition zone. Although resolution is still good, the region between 200 and 400 km is associated with a complex pattern of seismic heterogeneities showing no simple correlation with the shallower or deeper structure.
Engaging Students with Multiple Models of Fractions
Zhang, Xiaofen; Clements, M. A.; Ellerton, Nerida F.
2015-01-01
An understanding of unit fractions, and especially of one-half, one-third, and one-fourth, is crucially important for elementary school children's development of number sense (CCSSI 2010). We describe multimodal activities designed to assist elementary school students in gaining a rich understanding of unit fractions. Research has shown (Zhang,…
Multiphase Rayleigh-Bénard convection
Oresta, P.; Fornarelli, F.; Prosperetti, Andrea
2014-01-01
Numerical simulations of two-phase Rayleigh-Bénard convection in a cylindrical cell with particles or vapor bubbles suspended in the fluid are described. The particles or bubbles are modeled as points, the Rayleigh number is 2×106 and the fluids considered are air, for the particle case, and
Likelihood Inference for a Nonstationary Fractional Autoregressive Model
Johansen, Søren; Nielsen, Morten Ørregaard
This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d - b; where d = b > 1/2 are parameters to be estimated. We model the data X¿, ..., X¿ given the initial...
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. ...
Modeling Persistence In Hydrological Time Series Using Fractional Differencing
Hosking, J. R. M.
1984-12-01
The class of autoregressive integrated moving average (ARIMA) time series models may be generalized by permitting the degree of differencing d to take fractional values. Models including fractional differencing are capable of representing persistent series (d > 0) or short-memory series (d = 0). The class of fractionally differenced ARIMA processes provides a more flexible way than has hitherto been available of simultaneously modeling the long-term and short-term behavior of a time series. In this paper some fundamental properties of fractionally differenced ARIMA processes are presented. Methods of simulating these processes are described. Estimation of the parameters of fractionally differenced ARIMA models is discussed, and an approximate maximum likelihood method is proposed. The methodology is illustrated by fitting fractionally differenced models to time series of streamflows and annual temperatures.
Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model
Johansen, Søren; Nielsen, Morten Ørregaard
We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X(t) to be fractional of order d and cofractional of order d-b; that is, there exist vectors ß for which ß...
Fletcher, Jon B.; Erdem, Jemile
2017-06-01
Rayleigh wave group velocities obtained from ambient noise tomography are inverted for an upper crustal model of the Central Valley, California, centered on the Sacramento/San Joaquin Delta. Two methods were tried; the first uses SURF96, a least squares routine. It provides a good fit to the data, but convergence is dependent on the starting model. The second uses a genetic algorithm, whose starting model is random. This method was tried at several nodes in the model and compared to the output from SURF96. The genetic code is run five times and the variance of the output of all five models can be used to obtain an estimate of error. SURF96 produces a more regular solution mostly because it is typically run with a smoothing constraint. Models from the genetic code are generally consistent with the SURF96 code sometimes producing lower velocities at depth. The full model, calculated using SURF96, employed a 2-pass strategy, which used a variable damping scheme in the first pass. The resulting model shows low velocities near the surface in the Central Valley with a broad asymmetrical sedimentary basin located close to the western edge of the Central Valley near 122°W longitude. At shallow depths, the Rio Vista Basin is found nestled between the Pittsburgh/Kirby Hills and Midland faults, but a significant basin also seems to exist to the west of the Kirby Hills fault. There are other possible correlations between fast and slow velocities in the Central Valley and geologic features such as the Stockton Arch, oil or gas producing regions and the fault-controlled western boundary of the Central Valley.
Lü Shu-hui; WANG Kui-hua; WU Wen-bing; C. J. LEO
2015-01-01
The dynamic response of pile in layered soil is theoretically investigated when considering the transverse inertia effect. Firstly, the fictitious soil-pile model is employed to simulate the dynamic interaction between the pile and the soil layers beneath pile toe. The dynamic interactions of adjacent soil layers along the vertical direction are simplified as distributed Voigt models. Meanwhile, the pile and fictitious soil-pile are assumed to be viscoelastic Rayleigh-Love rods, and both the radial and vertical displacement continuity conditions at the soil-pile interface are taken into consideration. On this basis, the analytical solution for dynamic response at the pile head is derived in the frequency domain and the corresponding quasi-analytical solution in the time domain is then obtained by means of the convolution theorem. Following this, the accuracy and parameter value of the hypothetical boundaries for soil-layer interfaces are discussed. Comparisons with published solution and measured data are carried out to verify the rationality of the present solution. Parametric analyses are further conducted by using the present solution to investigate the relationships between the transverse inertia effects and soil-pile parameters.
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.
Research on Modeling of Hydropneumatic Suspension Based on Fractional Order
Junwei Zhang; Sizhong Chen; Yuzhuang Zhao; Jianbo Feng; Chang Liu; Ying Fan
2015-01-01
With such excellent performance as nonlinear stiffness, adjustable vehicle height, and good vibration resistance, hydropneumatic suspension (HS) has been more and more applied to heavy vehicle and engineering vehicle. Traditional modeling methods are still confined to simple models without taking many factors into consideration. A hydropneumatic suspension model based on fractional order (HSM-FO) is built with the advantage of fractional order (FO) in viscoelastic material modeling considerin...
Fractional Differencing Modeling and Forecasting of Eurocurrency Deposit Rates
John Barkoulas; Baum, Christopher F
1996-01-01
We investigate the low frequency properties of three- and six- month rates for Eurocurrency deposits denominated in eight major currencies with specific emphasis on fractional dynamics. Using the fractional integration testing procedure suggested by Geweke and Porter-Hudak (1983), we find that several of the Eurocurrency deposit rates are fractionally integrated processes with long memory. These findings have important implications for econometric modeling, forecasting, and cointegration test...
de Lucena, Rodrigo F.; Taioli, Fabio
2014-09-01
This paper presents a study on Rayleigh wave modeling. After model implementation using Matlab software, unpublished studies were conducted of dispersion curve sensitivity to percentage changes in parameter values, including S- and P-wave velocities, substrate density, and layer thickness. The study of the sensitivity of dispersion curves demonstrated that parameters such as S-wave velocity and layer thickness cannot be ignored as inversion parameters, while P-wave velocity and density can be considered as known parameters since their influence is minimal. However, the results showed limitations that should be considered and overcome when choosing the known and unknown parameters through determining a good initial model or/and by gathering a priori information. A methodology considering the sensitivity study of dispersion curves was developed and evaluated to generate initial values (initial model) to be included in the local search inversion algorithm, clearly establishing initial favorable conditions for data inversion.
An efficient method for solving fractional Hodgkin-Huxley model
Nagy, A. M.; Sweilam, N. H.
2014-06-01
In this paper, we present an accurate numerical method for solving fractional Hodgkin-Huxley model. A non-standard finite difference method (NSFDM) is implemented to study the dynamic behaviors of the proposed model. The Grünwald-Letinkov definition is used to approximate the fractional derivatives. Numerical results are presented graphically reveal that NSFDM is easy to implement, effective and convenient for solving the proposed model.
The fractional-nonlinear robotic manipulator: Modeling and dynamic simulations
David, S. A.; Balthazar, J. M.; Julio, B. H. S.; Oliveira, C.
2012-11-01
In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional-order nonlinear dynamics equations of a two link robotic manipulator. The aformentioned equations have been simulated for several cases involving: integer and non-integer order analysis, with and without external forcing acting and some different initial conditions. The fractional nonlinear governing equations of motion are coupled and the time evolution of the angular positions 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 dynamics equations of a two link robotic manipulator have been modeled with the fractional Euler-Lagrange dynamics approach. The results reveal that the fractional-nonlinear robotic manipulator can exhibit different and curious behavior from those obtained with the standard dynamical system and can be useful for a better understanding and control of such nonlinear systems.
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.
Likelihood Inference for a Nonstationary Fractional Autoregressive Model
Johansen, Søren; Nielsen, Morten Ørregaard
values Xº-n, n = 0, 1, ..., under the assumption that the errors are i.i.d. Gaussian. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with suitable moment conditions and the initial values......This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d - b; where d = b > 1/2 are parameters to be estimated. We model the data X¿, ..., X¿ given the initial...... are bounded. We use this to prove existence and consistency of the local likelihood estimator, and to ?find the asymptotic distribution of the estimators and the likelihood ratio test of the associated fractional unit root hypothesis, which contains the fractional Brownian motion of type II...
Likelihood inference for a nonstationary fractional autoregressive model
Johansen, Søren; Nielsen, Morten Ørregaard
values X0-n, n = 0, 1,...,under the assumption that the errors are i.i.d. Gaussian. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with suitable moment conditions and the initial values......This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d-b; where d ≥ b > 1/2 are parameters to be estimated. We model the data X1,...,XT given the initial...... are bounded. We use this to prove existence and consistency of the local likelihood estimator, and to find the asymptotic distribution of the estimators and the likelihood ratio test of the associated fractional unit root hypothesis, which contains the fractional Brownian motion of type II....
Application of Integer and Fractional Models in Electrochemical Systems
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.
A Fractional Order Recovery SIR Model from a Stochastic Process.
Angstmann, C N; Henry, B I; McGann, A V
2016-03-01
Over the past several decades, there has been a proliferation of epidemiological models with ordinary derivatives replaced by fractional derivatives in an ad hoc manner. These models may be mathematically interesting, but their relevance is uncertain. Here we develop an SIR model for an epidemic, including vital dynamics, from an underlying stochastic process. We show how fractional differential operators arise naturally in these models whenever the recovery time from the disease is power-law distributed. This can provide a model for a chronic disease process where individuals who are infected for a long time are unlikely to recover. The fractional order recovery model is shown to be consistent with the Kermack-McKendrick age-structured SIR model, and it reduces to the Hethcote-Tudor integral equation SIR model. The derivation from a stochastic process is extended to discrete time, providing a stable numerical method for solving the model equations. We have carried out simulations of the fractional order recovery model showing convergence to equilibrium states. The number of infecteds in the endemic equilibrium state increases as the fractional order of the derivative tends to zero.
Seismic Rayleigh Wave Digital Processing Technology
Jie, Li
2013-04-01
In Rayleigh wave exploration, the digital processing of data plays a very important position. This directly affects the interpretation of ground effect. Therefore, the use of accurate processing software and effective method in the Rayleigh wave exploration has important theoretical and practical significance. Previously, Rayleigh wave dispersion curve obtained by the one-dimensional phase analysis. This method requires channel spacing should be less than the effective wavelength. And minimal phase error will cause great changes in the phase velocity of Rayleigh wave. Damped least square method is a local linear model. It is easy to cause that inversion objective function cannot find the global optimal solution. Therefore, the method and the technology used in the past are difficult to apply the requirements of the current Rayleigh wave exploration. This study focused on the related technologies and algorithms of F-K domain dispersion curve extraction and GA global non-linear inversion, and combined with the impact of Rayleigh wave data acquisition parameters and the characteristics. Rayleigh wave exploration data processing software design and process technology research is completed. Firstly, the article describes the theoretical basis of Rayleigh wave method. This is also part of the theoretical basis of following treatment. The theoretical proof of existence of Rayleigh wave Dispersive in layered strata. Secondly, F-K domain dispersion curve extraction tests showed that the method can overcome the one-dimensional digital processing technology deficiencies, and make full use of multi-channel Rayleigh wave data record information. GA global non-linear inversion indicated that the inversion is not easy getting into local optimal solution. Thirdly, some examples illustrate each mode Rayleigh wave dispersion curve characteristics in the X-T domain. Tests demonstrated the impact on their extraction of dispersion curves. Parameters change example (including the X
Langevin equation for the extended Rayleigh model with an asymmetric bath.
Plyukhin, Alexander V; Schofield, Jeremy
2004-02-01
In this paper a one-dimensional model of two infinite gases separated by a movable heavy piston is considered. The nonlinear Langevin equation for the motion of the piston is derived from first principles for the case when the thermodynamic parameters and/or the molecular masses of gas particles on the left and right sides of the piston are different. Microscopic expressions involving time correlation functions of the force between bath particles and the piston are obtained for all parameters appearing in the nonlinear Langevin equation. It is demonstrated that the equation has stationary solutions corresponding to directional fluctuation-induced drift in the absence of systematic forces. In the case of ideal gases interacting with the piston via a quadratic repulsive potential, the model is exactly solvable and explicit expressions for the kinetic coefficients in the nonlinear Langevin equation are derived. The transient solution of the nonlinear Langevin equation is analyzed perturbatively and it is demonstrated that previously obtained results for systems with the hard-wall interaction are recovered.
Rayleigh-Brillouin Scattering in Binary Gas Mixtures
Gu, Ziyu; van de Water, Willem; Marques, Wilson
2015-01-01
Precise measurements are performed on spectral lineshapes of spontaneous Rayleigh-Brillouin scattering in mixtures of the noble gases Ar and Kr, with He. Admixture of a light He atomic fraction results in marked changes of the spectra, although in all experiments He is merely a spectator atom: it affects the relaxation of density fluctuations of the heavy constituent, but its contribution to the scattered light intensity is negligibly small. The results are compared to a theory for the spectral lineshape without adjustable parameters, yielding excellent agreement for the case of binary mono-atomic gases, signifying a step towards modeling and understanding of light scattering in more complex molecular media.
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.
Sharma, Som; Vaishnav, Rajesh; Shukla, Krishna K.; Lal, Shyam; Chandra, Harish; Acharya, Yashwant B.
2017-07-01
General characteristics of sub-tropical middle atmospheric temperature structure over a high altitude station, Mt. Abu (24.5°N, 72.7°E, altitude 1670 m, above mean sea level (amsl)) are presented using about 150 nights observational datasets of Rayleigh Lidar. The monthly mean temperature contour plot shows two distinct maxima in the stratopause region ( 45-55 km), occurring during February-March and September-October, a seasonal dependence similar to that reported for mid- and high-latitudes respectively. Semi-Annual Oscillation (SAO) are stronger at an altitude 60 km in the mesospheric temperature in comparison to stratospheric region. A comparison with the satellite (Halogen Occultation Experiment, (HALOE)) data shows qualitative agreement, but quantitatively a significant difference is found between the observation and satellite. The derived temperatures from Lidar observations are warmer 2-3 K in the stratospheric region and 5-10 K in the mesospheric region than temperatures observed from the satellite. A comparison with the models, COSPAR International Reference Atmosphere (CIRA)-86 and Mass Spectrometer Incoherent Scatter Extended (MSISE)-90, showed differences of 3 K in the stratosphere and 5-10 K in the mesosphere, with deviations somewhat larger for CIRA-86. In most of the months and in all altitude regions model temperatures were lower than the Lidar observed temperature except in the altitude range of 40-50 km. MSISE-90 Model temperature overestimates as compared to Lidar temperature during December-February in the altitude region of 50-60 km. In the altitude region of 55-70 km both models deviate significantly, with differences exceeding 10-12 K, particularly during equinoctial periods. An average heating rate of 2.5 K/month during equinoxes and cooling rate of 4 K/month during November-December are found in altitude region of 50-70 km, relatively less heating and cooling rates are found in the altitude range of 30-50 km. The stratospheric
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 ...
An efficient method for solving fractional Hodgkin–Huxley model
Nagy, A.M., E-mail: abdelhameed_nagy@yahoo.com [Department of Mathematics, Faculty of Science, Benha University, 13518 Benha (Egypt); Sweilam, N.H., E-mail: n_sweilam@yahoo.com [Department of Mathematics, Faculty of Science, Cairo University, 12613 Giza (Egypt)
2014-06-13
In this paper, we present an accurate numerical method for solving fractional Hodgkin–Huxley model. A non-standard finite difference method (NSFDM) is implemented to study the dynamic behaviors of the proposed model. The Grünwald–Letinkov definition is used to approximate the fractional derivatives. Numerical results are presented graphically reveal that NSFDM is easy to implement, effective and convenient for solving the proposed model. - Highlights: • An accurate numerical method for solving fractional Hodgkin–Huxley model is given. • Non-standard finite difference method (NSFDM) is implemented to the proposed model. • NSFDM can solve differential equations involving derivatives of non-integer order. • NDFDM is very powerful and efficient technique for solving the proposed model.
On an Estimation Method for an Alternative Fractionally Cointegrated Model
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...
Andersen, Kurt Munk
1997-01-01
Rayleigh's principle expresses that the smallest eigenvalue of a regular Sturm-Liouville problem with regular boundary conditions is the minimum value of a certain functional, the so called Rayleigh's quotient, and that this value is attained at the corresponding eigenfunctions only. This can...... be proved by means of more advanced methods. However, it turns out that there is an elementary proof, which is presented in the report....
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 (Gibraltar arc to ~55 km depth. Low upper mantle velocities (<4.2 km/s) are observed beneath the Atlas, the northeastern end of the Betic Mountains and the Late Cenozoic volcanic fields in Iberia and Morocco, indicative of high temperatures at relatively shallow depths
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)
Atmospheric Turbulence Modeling for Aerospace Vehicles: Fractional Order Fit
Kopasakis, George (Inventor)
2015-01-01
An improved model for simulating atmospheric disturbances is disclosed. A scale Kolmogorov spectral may be scaled to convert the Kolmogorov spectral into a finite energy von Karman spectral and a fractional order pole-zero transfer function (TF) may be derived from the von Karman spectral. Fractional order atmospheric turbulence may be approximated with an integer order pole-zero TF fit, and the approximation may be stored in memory.
Hillier, Andrew; Isobe, Hiroaki; Shibata, Kazunari [Kwasan and Hida Observatories, Kyoto University, Kyoto (Japan); Berger, Thomas, E-mail: andrew@kwasan.kyoto-u.ac.jp [Lockheed Martin Solar and Astrophysics Laboratory, Palo Alto, CA (United States)
2012-02-20
The launch of the Hinode satellite led to the discovery of rising plumes, dark in chromospheric lines, that propagate from large ({approx}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-Schlueter 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{sup -1}) and a maximum plume width Almost-Equal-To 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{sup -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.
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.
Deimel, Christian; Günther, Markus; Skoda, Romuald
2014-03-01
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.
Knapmeyer-Endrun, Brigitte; Golombek, Matthew P.; Ohrnberger, Matthias
2016-10-01
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.
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
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.
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.
Microbially Mediated Kinetic Sulfur Isotope Fractionation: Reactive Transport Modeling Benchmark
Wanner, C.; Druhan, J. L.; Cheng, Y.; Amos, R. T.; Steefel, C. I.; Ajo Franklin, J. B.
2014-12-01
Microbially mediated sulfate reduction is a ubiquitous process in many subsurface systems. Isotopic fractionation is characteristic of this anaerobic process, since sulfate reducing bacteria (SRB) favor the reduction of the lighter sulfate isotopologue (S32O42-) over the heavier isotopologue (S34O42-). Detection of isotopic shifts have been utilized as a proxy for the onset of sulfate reduction in subsurface systems such as oil reservoirs and aquifers undergoing uranium bioremediation. Reactive transport modeling (RTM) of kinetic sulfur isotope fractionation has been applied to field and laboratory studies. These RTM approaches employ different mathematical formulations in the representation of kinetic sulfur isotope fractionation. In order to test the various formulations, we propose a benchmark problem set for the simulation of kinetic sulfur isotope fractionation during microbially mediated sulfate reduction. The benchmark problem set is comprised of four problem levels and is based on a recent laboratory column experimental study of sulfur isotope fractionation. Pertinent processes impacting sulfur isotopic composition such as microbial sulfate reduction and dispersion are included in the problem set. To date, participating RTM codes are: CRUNCHTOPE, TOUGHREACT, MIN3P and THE GEOCHEMIST'S WORKBENCH. Preliminary results from various codes show reasonable agreement for the problem levels simulating sulfur isotope fractionation in 1D.
A fractional diffusion equation model for cancer tumor
Iyiola, Olaniyi Samuel; Zaman, F. D.
2014-10-01
In this article, we consider cancer tumor models and investigate the need for fractional order derivative as compared to the classical first order derivative in time. Three different cases of the net killing rate are taken into account including the case where net killing rate of the cancer cells is dependent on the concentration of the cells. At first, we use a relatively new analytical technique called q-Homotopy Analysis Method on the resulting time-fractional partial differential equations to obtain analytical solution in form of convergent series with easily computable components. Our numerical analysis enables us to give some recommendations on the appropriate order (fractional) of derivative in time to be used in modeling cancer tumor.
A fractional calculus model of anomalous dispersion of acoustic waves.
Wharmby, Andrew W
2016-09-01
An empirical formula based on viscoelastic analysis techniques that employs concepts from the fractional calculus that was used to model the dielectric behavior of materials exposed to oscillating electromagnetic fields in the radiofrequency, terahertz, and infrared bands. This work adapts and applies the formula to model viscoelastic behavior of materials that show an apparent increase of phase velocity of vibration with an increase in frequency, otherwise known as anomalous dispersion. A fractional order wave equation is derived through the application of the classic elastic-viscoelastic correspondence principle whose analytical solution is used to describe absorption and dispersion of acoustic waves in the viscoelastic material displaying anomalous dispersion in a specific frequency range. A brief discussion and comparison of an alternative fractional order wave equation recently formulated is also included.
Modeling Heavy Metal Sorption Kinetics Using Fractional Calculus
V. C. Friesen
2015-01-01
Full Text Available Heavy metals are commonly regarded as environmentally aggressive and hazardous to human health. Among the different metals, lead plays an important economic role due to its large use in the automotive industry, being an essential component of batteries. Different approaches have been reported in the literature aimed at lead removal, and among them a very successful one considers the use of water hyacinths for sorption-based operation. The modeling of the metal sorption kinetics is a fundamental step towards in-depth studies and proper separation equipment design and optimization. Fractional calculus represents a novel approach and a growing research field for process modeling, which is based on the successful use of derivatives of arbitrary order. This paper reports the modeling of the kinetics of lead sorption by water hyacinths (Eichhornia crassipes using a fractional calculus. A general procedure on error analysis is also employed to prove the actual fractional nature of the proposed model by the use of parametric variance analysis, which was carried out using two different approaches (with the complete Hessian matrix and with a simplified Hessian matrix. The joint parameter confidence regions were generated, allowing to successfully show the fractional nature of the model and the sorption process.
Lithium-ion batteries modeling involving fractional differentiation
Sabatier, Jocelyn; Merveillaut, Mathieu; Francisco, Junior Mbala; Guillemard, Franck; Porcelatto, Denis
2014-09-01
With hybrid and electric vehicles development, automobile battery monitoring systems (BMS) have to meet the new requirements. These systems have to give information on state of health, state of charge, available power. To get this information, BMS often implement battery models. Accuracy of the information manipulated by the BMS thus depends on the model accuracy. This paper is within this framework and addresses lithium-ion battery modeling. The proposed fractional model is based on simplifications of an electrochemical model and on resolution of some partial differential equations used in its description. Such an approach permits to get a simple model in which electrochemical variables and parameters still appear.
Discrete random walk models for space-time fractional diffusion
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
2002-11-01
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 {alpha} is part of (0,2] and skewness {theta} (module{theta}{<=}{l_brace}{alpha},2-{alpha}{r_brace}), and the first-order time derivative with a Caputo derivative of order {beta} 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.
Research on Modeling of Hydropneumatic Suspension Based on Fractional Order
Junwei Zhang
2015-01-01
Full Text Available With such excellent performance as nonlinear stiffness, adjustable vehicle height, and good vibration resistance, hydropneumatic suspension (HS has been more and more applied to heavy vehicle and engineering vehicle. Traditional modeling methods are still confined to simple models without taking many factors into consideration. A hydropneumatic suspension model based on fractional order (HSM-FO is built with the advantage of fractional order (FO in viscoelastic material modeling considering the mechanics property of multiphase medium of HS. Then, the detailed calculation method is proposed based on Oustaloup filtering approximation algorithm. The HSM-FO is implemented in Matlab/Simulink, and the results of comparison among the simulation curve of fractional order, integral order, and the curve of real experiment prove the feasibility and validity of HSM-FO. The damping force property of the suspension system under different fractional orders is also studied. In the end of this paper, several conclusions concerning HSM-FO are drawn according to analysis of simulation.
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
Fraction Multiplication and Division Models: A Practitioner Reference Paper
Ervin, Heather K.
2017-01-01
It is well documented in literature that rational number is an important area of understanding in mathematics. Therefore, it follows that teachers and students need to have an understanding of rational number and related concepts such as fraction multiplication and division. This practitioner reference paper examines models that are important to…
Chromo-Rayleigh Interactions of Dark Matter
Bai, Yang
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.
Atmospheric Turbulence Modeling for Aero Vehicles: Fractional Order Fits
Kopasakis, George
2015-01-01
Atmospheric turbulence models are necessary for the design of both inlet/engine and flight controls, as well as for studying coupling between the propulsion and the vehicle structural dynamics for supersonic vehicles. Models based on the Kolmogorov spectrum have been previously utilized to model atmospheric turbulence. In this paper, a more accurate model is developed in its representative fractional order form, typical of atmospheric disturbances. This is accomplished by first scaling the Kolmogorov spectral to convert them into finite energy von Karman forms and then by deriving an explicit fractional circuit-filter type analog for this model. This circuit model is utilized to develop a generalized formulation in frequency domain to approximate the fractional order with the products of first order transfer functions, which enables accurate time domain simulations. The objective of this work is as follows. Given the parameters describing the conditions of atmospheric disturbances, and utilizing the derived formulations, directly compute the transfer function poles and zeros describing these disturbances for acoustic velocity, temperature, pressure, and density. Time domain simulations of representative atmospheric turbulence can then be developed by utilizing these computed transfer functions together with the disturbance frequencies of interest.
Mathematical modeling of fish burger baking using fractional calculus
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.
Rayleigh surface wave modeling by finite difference method in biphasic media%双相介质瑞雷面波有限差分正演模拟
张伟; 甘伏平; 刘伟; 郑智杰
2014-01-01
为了研究双相介质瑞雷面波的形成机制及传播规律，促进瑞雷面波资料处理方法的发展。文章根据弹性波动方程，采用交错网格有限差分算法，对二维各向同性弹性介质做解析解与数值解的对比，在此基础上，将PML吸收边界条件，改进的镜像法应用于双相介质波动方程中，并作了稳定性分析，对双相介质水平层状、起伏分界面等典型模型瑞雷面波及体波在内的全波场进行研究。结果表明：基于弹性介质解析解与数值解的对比，在误差接受范围内，研究双相介质是可行的；把稍作改进的镜像法应用于双相介质中，能够有效地处理瑞雷面波自由边界问题；通过详细分析双相介质瑞雷面波及体波在内的全波场的信息，对以双相介质为基础的地震波勘探有一定的指导作用。%In order to study the mechanism and propagation of Rayleigh surface wave in biphasic media and promote the development of data⁃processing method of Rayleigh surface wave, the authors applied finite difference method with staggered grids to simulate the 2D i⁃sotropic elastic media based on the elastic wave equation, and made a comparison between the analytical and numerical solutions. On such a basis, the PML absorbing boundary condition and improved image method can be applied to the two⁃phase medium wave equa⁃tion to simulate the typical media model including horizontal layer and undulating interface, analyze the full wave information including the Rayleigh surface wave and body wave, and make a stability analysis. The results show that, on the basis of the comparison between the numerical solution and the analytical solution of the elastic media within the acceptable range of the error, the study of biphasic me⁃dium is feasible. The slight improvement of the image method can be applied to biphasic media to deal with free boundary condition problem of the Rayleigh surface wave
Likelihood inference for a fractionally cointegrated vector autoregressive model
Johansen, Søren; Nielsen, Morten Ørregaard
We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X_{t} to be fractional of order d and cofractional of order d-b; that is, there exist vectors β for which β......′X_{t} is fractional of order d-b. The parameters d and b satisfy either d≥b≥1/2, d=b≥1/2, or d=d_{0}≥b≥1/2. Our main technical contribution is the proof of consistency of the maximum likelihood estimators on the set 1/2≤b≤d≤d_{1} for any d_{1}≥d_{0}. To this end, we consider the conditional likelihood as a stochastic...... process in the parameters, and prove that it converges in distribution when errors are i.i.d. with suitable moment conditions and initial values are bounded. We then prove that the estimator of β is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. We...
Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model
Johansen, Søren; Nielsen, Morten Ørregaard
We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X(t) to be 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. The parameters d and b satisfy either d=b=1/2, d=b=1/2, or d=d0=b=1/2. Our main technical contribution is the proof of consistency of the maximum likelihood estimators on the set 1/2=b=d=d1 for any d1=d0. To this end, we consider the conditional likelihood as a stochastic process...... in the parameters, and prove that it converges in distribution when errors are i.i.d. with suitable moment conditions and initial values are bounded. We then prove that the estimator of ß is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. We also find...
Time fractional capital-induced labor migration model
Ali Balcı, Mehmet
2017-07-01
In this study we present a new model of neoclassical economic growth by considering that workers move from regions with lower density of capital to regions with higher density of capital. Since the labor migration and capital flow involves self-similarities in long range time, we use the fractional order derivatives for the time variable. To solve this model we proposed Variational Iteration Method, and studied numerically labor migration flow data from Turkey along with other countries throughout the period of 1966-2014.
A time fractional model to represent rainfall process
Jacques GOLDER
2014-01-01
Full Text Available This paper deals with a stochastic representation of the rainfall process. The analysis of a rainfall time series shows that cumulative representation of a rainfall time series can be modeled as a non-Gaussian random walk with a log-normal jump distribution and a time-waiting distribution following a tempered α-stable probability law. Based on the random walk model, a fractional Fokker-Planck equation (FFPE with tempered α-stable waiting times was obtained. Through the comparison of observed data and simulated results from the random walk model and FFPE model with tempered α-stable waiting times, it can be concluded that the behavior of the rainfall process is globally reproduced, and the FFPE model with tempered α-stable waiting times is more efficient in reproducing the observed behavior.
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.
Intrinsic Kinetic Modeling of Thermal Dimerization of C5 Fraction
Guo Liang; Wang Tiefeng; Li Dongfeng; Wang Jinfu
2016-01-01
This work aims to investigate the intrinsic kinetics of thermal dimerization of C5 fraction in the reactive distilla-tion process. Experiments are conducted in an 1000-mL stainless steel autoclave under some selected design conditions. By means of the weighted least squares method, the intrinsic kinetics of thermal dimerization of C5 fraction is established, and the corresponding pre-exponential factor as well as the activation energy are determined. For example, the pre-exponential factor A is equal to 4.39×105 and the activation energy Ea is equal to 6.58×104 J/mol for the cyclopentadiene dimerization re-action. The comparison between the experimental and calculated results shows that the kinetics model derived in this work is accurate and reliable, which can be used in the design of reactive distillation columns.
Fractionalized Fermi liquid in a Kondo-Heisenberg model
Tsvelik, A. M.
2016-10-01
The Kondo-Heisenberg model is used as a controllable tool to demonstrate the existence of a peculiar metallic state with unbroken translational symmetry where the Fermi surface volume is not controlled by the total electron density. I use a nonperturbative approach where the strongest interactions are taken into account by means of exact solution, and corrections are controllable. In agreement with the general requirements formulated by T. Senthil et al. [Phys. Rev. Lett. 90, 216403 (2003), 10.1103/PhysRevLett.90.216403], the resulting metallic state represents a fractionalized Fermi liquid where well defined quasiparticles coexist with gapped fractionalized collective excitations. The system undergoes a phase transition to an ordered phase (charge density wave or superconducting), at the transition temperature which is parametrically small in comparison to the quasiparticle Fermi energy.
Generalized elastic model yields a fractional Langevin equation description.
Taloni, Alessandro; Chechkin, Aleksei; Klafter, Joseph
2010-04-23
Starting from a generalized elastic model which accounts for the stochastic motion of several physical systems such as membranes, (semi)flexible polymers, and fluctuating interfaces among others, we derive the fractional Langevin equation (FLE) for a probe particle in such systems, in the case of thermal initial conditions. We show that this FLE is the only one fulfilling the fluctuation-dissipation relation within a new family of fractional Brownian motion equations. The FLE for the time-dependent fluctuations of the donor-acceptor distance in a protein is shown to be recovered. When the system starts from nonthermal conditions, the corresponding FLE, which does not fulfill the fluctuation-dissipation relation, is derived.
Correlations in a generalized elastic model: fractional Langevin equation approach.
Taloni, Alessandro; Chechkin, Aleksei; Klafter, Joseph
2010-12-01
The generalized elastic model (GEM) provides the evolution equation which governs the stochastic motion of several many-body systems in nature, such as polymers, membranes, and growing interfaces. On the other hand a probe (tracer) particle in these systems performs a fractional Brownian motion due to the spatial interactions with the other system's components. The tracer's anomalous dynamics can be described by a fractional Langevin equation (FLE) with a space-time correlated noise. We demonstrate that the description given in terms of GEM coincides with that furnished by the relative FLE, by showing that the correlation functions of the stochastic field obtained within the FLE framework agree with the corresponding quantities calculated from the GEM. Furthermore we show that the Fox H -function formalism appears to be very convenient to describe the correlation properties within the FLE approach.
Transient heat conduction in a pebble fuel applying fractional model
Gomez A, R.; Espinosa P, G. [Universidad Autonoma Metropolitana, Unidad Iztapalapa, Area de Ingenieria en Recursos Energeticos, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 Mexico D. F. (Mexico)], e-mail: gepe@xanum.uam.mx
2009-10-15
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)
Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model
Johansen, Søren; Nielsen, Morten Ørregaard
2012-01-01
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......likelihood estimators. To this end we prove weak convergence of the conditional likelihood as a continuous stochastic...... 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...
On fractional order composite model reference adaptive control
Wei, Yiheng; Sun, Zhenyuan; Hu, Yangsheng; Wang, Yong
2016-08-01
This paper presents a novel composite model reference adaptive control approach for a class of fractional order linear systems with unknown constant parameters. The method is extended from the model reference adaptive control. The parameter estimation error of our method depends on both the tracking error and the prediction error, whereas the existing method only depends on the tracking error, which makes our method has better transient performance in the sense of generating smooth system output. By the aid of the continuous frequency distributed model, stability of the proposed approach is established in the Lyapunov sense. Furthermore, the convergence property of the model parameters estimation is presented, on the premise that the closed-loop control system is stable. Finally, numerical simulation examples are given to demonstrate the effectiveness of the proposed schemes.
Fractional Langevin model of memory in financial markets.
Picozzi, Sergio; West, Bruce J
2002-10-01
The separation of the microscopic and macroscopic time scales is necessary for the validity of ordinary statistical physics and the dynamical description embodied in the Langevin equation. When the microscopic time scale diverges, the differential equations on the macroscopic level are no longer valid and must be replaced with fractional differential equations of motion; in particular, we obtain a fractional-differential stochastic equation of motion. After decades of statistical analysis of financial time series certain "stylized facts" have emerged, including the statistics of stock price fluctuations having "fat tails" and their linear correlations in time being exceedingly short lived. On the other hand, the magnitude of these fluctuations and other such measures of market volatility possess temporal correlations that decay as an inverse power law. One explanation of this long-term memory is that it is a consequence of the time-scale separation between "microscopic" and "macroscopic" economic variables. We propose a fractional Langevin equation as a dynamical model of the observed memory in financial time series.
Universality of energy spectrum in turbulent Rayleigh-Benard convection
Bai, Kunlun; Hoeller, Judith; Brown, Eric
2016-11-01
We present study of energy spectrum in turbulent Rayleigh-Benard convection, in both cylindrical and cubic containers, tilting and non-tilting conditions, and with Rayleigh number ranging from 0 . 5 ×109 to 1 ×1010 . For these different conditions of geometry, tilt, and Rayleigh number, the temperature spectra measured on the system side walls are significantly different from each other. Even for the same condition, the spectrum varies depending on whether the sensors locate in the path of large-scale circulations. However, quite interestingly, once the signals of large-scale circulations are subtracted from the raw temperature, all spectra display a universal shape, regardless of system geometry, tilt, Rayleigh number, and location of sensors. It suggests that one could model the large-scale circulations and small-scale fluctuations separately in turbulent Rayleigh-Benard convection.
Phase noise and jitter modeling for fractional-N PLLs
S. A. Osmany; Herzel, F.; Schmalz, K; Winkler, W.
2007-01-01
We present an analytical phase noise model for fractional-N phase-locked loops (PLL) with emphasis on integrated RF synthesizers in the GHz range. The noise of the crystal reference, the voltage-controlled oscillator (VCO), the loop filter, the charge pump, and the sigma-delta modulator (SDM) is filtered by the PLL operation. We express the rms phase error (jitter) in terms of phase noise of the reference, the VCO phase noise and the third-order loop filter parameters. In addition, we conside...
A mathematical model on fractional Lotka-Volterra equations.
Das, S; Gupta, P K
2011-05-21
The article presents the solutions of Lotka-Volterra equations of fractional-order time derivatives with the help of analytical method of nonlinear problem called the homotopy perturbation method (HPM). By using initial values, the explicit solutions of predator and prey populations for different particular cases have been derived. The numerical solutions show that only a few iterations are needed to obtain accurate approximate solutions. The method performs extremely well in terms of efficiency and simplicity to solve this historical biological model. Copyright © 2011 Elsevier Ltd. All rights reserved.
On the use of fractional order PK-PD models
Ionescu, Clara; Copot, Dana
2017-01-01
Quantifying and controlling depth of anesthesia is a challenging process due to lack of measurement technology for direct effects of drug supply into the body. Efforts are being made to develop new sensor techniques and new horizons are explored for modeling this intricate process. This paper introduces emerging tools available on the ‘engineering market’ imported from the area of fractional calculus. A novel interpretation of the classical drug-effect curve is given, enabling linear control. This enables broadening the horizon of signal processing and control techniques and suggests future research lines.
Schilling, Oleg
2016-11-01
Two-, three- and four-equation, single-velocity, multicomponent Reynolds-averaged Navier-Stokes (RANS) models, based on the turbulent kinetic energy dissipation rate or lengthscale, are used to simulate At = 0 . 5 Rayleigh-Taylor turbulent mixing with constant and complex accelerations. The constant acceleration case is inspired by the Cabot and Cook (2006) DNS, and the complex acceleration cases are inspired by the unstable/stable and unstable/neutral cases simulated using DNS (Livescu, Wei & Petersen 2011) and the unstable/stable/unstable case simulated using ILES (Ramaprabhu, Karkhanis & Lawrie 2013). The four-equation models couple equations for the mass flux a and negative density-specific volume correlation b to the K- ɛ or K- L equations, while the three-equation models use a two-fluid algebraic closure for b. The lengthscale-based models are also applied with no buoyancy production in the L equation to explore the consequences of neglecting this term. Predicted mixing widths, turbulence statistics, fields, and turbulent transport equation budgets are compared among these models to identify similarities and differences in the turbulence production, dissipation and diffusion physics represented by the closures used in these models. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
First-principles models of equilibrium tellurium isotope fractionation
Haghnegahdar, M. A.; Schauble, E. A.; Fornadel, A. P.; Spry, P. G.
2013-12-01
In this study, equilibrium mass-dependent isotopic fractionation among representative Te-bearing species is estimated with first-principles thermodynamic calculations. Tellurium is a group 16 element (along with O, S, and Se) with eight stable isotopes ranging in mass from 120Te to 130Te, and six commonly-occurring oxidation states: -II, -I, 0, +II, +IV, and +VI. In its reduced form, Te(-II), tellurium has a unique crystal-chemical role as a bond partner for gold and silver in epithermal and orogenic gold deposits, which likely form when oxidized Te species (e.g., H2TeO3, TeO32-) or perhaps polytellurides (e.g., Te22-) interact with precious metals in hydrothermal solution. Te(IV) is the most common oxidation state at the Earth's surface, including surface outcrops of telluride ore deposits, where tellurite and tellurate minerals form by oxidation. In the ocean, dissolved tellurium tends to be scavenged by particulate matter. Te(VI) is more abundant than Te(IV) in the ocean water (1), even though it is thought to be less stable thermodynamically. This variety of valence states in natural systems and range of isotopic masses suggest that tellurium could exhibit geochemically useful isotope abundance variations. Tellurium isotope fractionations were determined for representative molecules and crystals of varying complexity and chemistry. Gas-phase calculations are combined with supermolecular cluster models of aqueous and solid species. These in turn are compared with plane-wave density functional theory calculations with periodic boundary conditions. In general, heavyTe/lightTe is predicted to be higher for more oxidized species, and lower for reduced species, with 130Te/125Te fractionations as large as 4‰ at 100οC between coexisting Te(IV) and Te(-II) or Te(0) compounds. This is a much larger fractionation than has been observed in naturally occurring redox pairs (i.e., Te (0) vs. Te(IV) species) so far, suggesting that disequilibrium processes may control
The linear-quadratic model is inappropriate to model high dose per fraction effects in radiosurgery.
Kirkpatrick, John P; Meyer, Jeffrey J; Marks, Lawrence B
2008-10-01
The linear-quadratic (LQ) model is widely used to model the effect of total dose and dose per fraction in conventionally fractionated radiotherapy. Much of the data used to generate the model are obtained in vitro at doses well below those used in radiosurgery. Clinically, the LQ model often underestimates tumor control observed at radiosurgical doses. The underlying mechanisms implied by the LQ model do not reflect the vascular and stromal damage produced at the high doses per fraction encountered in radiosurgery and ignore the impact of radioresistant subpopulations of cells. The appropriate modeling of both tumor control and normal tissue toxicity in radiosurgery requires the application of emerging understanding of molecular-, cellular-, and tissue-level effects of high-dose/fraction-ionizing radiation and the role of cancer stem cells.
Phase noise and jitter modeling for fractional-N PLLs
S. A. Osmany
2007-06-01
Full Text Available We present an analytical phase noise model for fractional-N phase-locked loops (PLL with emphasis on integrated RF synthesizers in the GHz range. The noise of the crystal reference, the voltage-controlled oscillator (VCO, the loop filter, the charge pump, and the sigma-delta modulator (SDM is filtered by the PLL operation. We express the rms phase error (jitter in terms of phase noise of the reference, the VCO phase noise and the third-order loop filter parameters. In addition, we consider OFDM systems, where the PLL phase noise is reduced by digital signal processing after down-conversion of the RF signal to baseband. The rms phase error is discussed as a function of the loop parameters. Our model drastically simplifies the noise optimization of the PLL loop dynamics.
Modelling heat transfer in heterogeneous media using fractional calculus.
Sierociuk, Dominik; Dzielinski, Andrzej; Sarwas, Grzegorz; Petras, Ivo; Podlubny, Igor; Skovranek, Tomas
2013-05-13
This paper presents the results of modelling the heat transfer process in heterogeneous media with the assumption that part of the heat flux is dispersed in the air around the beam. The heat transfer process in a solid material (beam) can be described by an integer order partial differential equation. However, in heterogeneous media, it can be described by a sub- or hyperdiffusion equation which results in a fractional order partial differential equation. Taking into consideration that part of the heat flux is dispersed into the neighbouring environment we additionally modify the main relation between heat flux and the temperature, and we obtain in this case the heat transfer equation in a new form. This leads to the transfer function that describes the dependency between the heat flux at the beginning of the beam and the temperature at a given distance. This article also presents the experimental results of modelling real plant in the frequency domain based on the obtained transfer function.
Phase noise and jitter modeling for fractional-N PLLs
Osmany, S. A.; Herzel, F.; Schmalz, K.; Winkler, W.
2007-06-01
We present an analytical phase noise model for fractional-N phase-locked loops (PLL) with emphasis on integrated RF synthesizers in the GHz range. The noise of the crystal reference, the voltage-controlled oscillator (VCO), the loop filter, the charge pump, and the sigma-delta modulator (SDM) is filtered by the PLL operation. We express the rms phase error (jitter) in terms of phase noise of the reference, the VCO phase noise and the third-order loop filter parameters. In addition, we consider OFDM systems, where the PLL phase noise is reduced by digital signal processing after down-conversion of the RF signal to baseband. The rms phase error is discussed as a function of the loop parameters. Our model drastically simplifies the noise optimization of the PLL loop dynamics.
Modeling the fractional magnetic states of magnetostructural transformations
Della Torre, Edward [Department of Electrical and Computer Engineering, The George Washington University, Washington, DC 20052 (United States); ElBidweihy, Hatem, E-mail: hatem@gwmail.gwu.edu [Department of Electrical and Computer Engineering, The George Washington University, Washington, DC 20052 (United States); Provenzano, Virgil [National Institute for Standards and Technology, Gaithersburg, MD 20899 (United States); Bennett, Lawrence H. [Department of Electrical and Computer Engineering, The George Washington University, Washington, DC 20052 (United States)
2014-02-15
The large inverse magnetocaloric effect (MCE) in the off-stoichiometric Heusler alloys occurs at a critical temperature near room temperature. At this temperature, the material is in a mixed-state and can have a variable ratio of two stable magnetic crystallographic-states; a high magnetization state (HM) and a low magnetization state (LM). The field-induced thermal hysteresis in the virgin curve of Ni{sub 50}Mn{sub 35}In{sub 15} and the virgin first-order reversal curves (VFORC) are presented. A model is introduced to describe the descending branches of these curves based on the different magnetic fields of conversion (from HM to LM). Using limited measurements, the model is used as a tool to determine the fractions of the two crystallographic-states within the mixed-state region.
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.
Bagheri, Amirhossein; Greenhalgh, Stewart; Khojasteh, Ali; Rahimian, Mohammad
2015-10-01
The dispersion of interface waves is studied theoretically in a model consisting of a liquid layer of finite thickness overlying a transversely isotropic solid layer which is itself underlain by a transversely isotropic solid of dissimilar elastic properties. The method of potential functions and Hankel transformation was utilized to solve the equations of motion. Two frequency equations were developed: one for Love waves and the other for the remaining surface and interface waves. Numerical group and phase velocity dispersion curves were computed for four different classes of model, in which the substratum is stiffer or weaker than the overlying layer, and for various thickness combinations of the layers. Dispersion curves are presented for generalized Rayleigh, Scholte, Stoneley and Love waves, each of which are possible in all proposed models. They show the dependence of the velocity on layer thicknesses and material properties (elastic constants). Special cases involving zero thickness for the water layer or the solid layer, and/or isotropic material properties for the solid exhibit interesting features and agree favourably with previously published results for these simpler cases, thus validating the new formulation.
When does 1/2 = 1/3?: Modelling with Wet Fractions
Fitzallen, Noleine
2015-01-01
Many fraction activities rely on the use of area models for developing partitioning skills. These models, however, are limited in their ability to assist students to visualise a fraction of an object when the whole changes. This article describes a fraction modelling activity that requires the transfer of water from one container to another. The…
Rayleigh scattering in the atmospheres of hot stars
Fišák, Jakub; Munzar, Dominik; Kubát, Jiří
2016-01-01
Rayleigh scattering is a result of an interaction of photons with bound electrons. Rayleigh scattering is mostly neglected in calculations of hot star model atmospheres because most of the hydrogen atoms are ionized and the heavier elements have a lower abundance than hydrogen. In atmospheres of some chemically peculiar stars, helium overabundant regions containing singly ionized helium are present and Rayleigh scattering can be a significant opacity source. We evaluate the contribution of Rayleigh scattering by neutral hydrogen and singly ionized helium in the atmospheres of hot stars with solar composition and in the atmospheres of helium overabundant stars. We computed several series of model atmospheres using the TLUSTY code and emergent fluxes using the SYNSPEC code. These models describe atmospheres of main sequence B-type stars with different helium abundance. We used an existing grid of models for atmospheres with solar chemical composition and we calculated an additional grid for helium-rich stars wi...
Gaetani, G.A.; Cohen, A.L.; Wang, Z.; Crusius, J.
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
Dynamical Models to Infer the Core Mass Fraction of Venus
Quintana, Elisa V.; Barclay, Thomas
2016-10-01
The uncompressed density of Venus is just a few percent lower than Earth's, however the nature of the interior core structure of Venus remains unclear. Employing state-of-the-art dynamical formation models that allow both accretion and collisional fragmentation, we perform hundreds of simulations of terrestrial planet growth around the Sun in the presence of the giant planets. For both Earth and Venus analogs, we quantify the iron-silicate ratios, water/volatile abundances and specific impact energies of all collisions that lead to their formation. Preliminary results suggest that the distributions of core mass fraction and water content are comparable among the Earth and Venus analogs, suggesting that Earth and Venus may indeed have formed with similar structures and compositions.
Fractional Calculus in Hydrologic Modeling: A Numerical Perspective
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.
Fractional calculus in hydrologic modeling: A numerical perspective.
Benson, David A; Meerschaert, Mark M; Revielle, Jordan
2013-01-01
Fractional derivatives can be viewed either as handy extensions 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 Lévy 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 Lévy) 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.
Hillier, Andrew; Isobe, Hiroaki; Shibata, Kazunari [Kwasan and Hida Observatories, Kyoto University, Kyoto (Japan); Berger, Thomas [Lockheed Martin Solar and Astrophysics Laboratory, Palo Alto, CA (United States)
2012-09-10
The launch of the Hinode satellite has allowed high-resolution observations of supersonic bright downflows in quiescent prominences, known as prominence knots. We present observations in the Ca II H spectral line using the Solar Optical Telescope on board the Hinode satellite of a descending plasma knot of size {approx}900 km. The knot initially undergoes ballistic motion before undergoing impulsive accelerations at the same time as experiencing increases in intensity. We also present a subset of our three-dimensional magnetohydrodynamic simulations, performed to investigate the nonlinear stability of the Kippenhahn-Shlueter prominence model to the magnetic Rayleigh-Taylor instability in which interchange reconnection occurs. The interchange reconnection in the model breaks the force balance along the field lines which initiates the downflows. The downflows propagate with a downward fluid velocity of {approx}15 km s{sup -1} and a characteristic size of {approx}700 km. We conclude that the observed plasma blob and the simulated downflow are driven by the breaking of the force balance along the magnetic field as a result of a change in magnetic topology caused by reconnection of the magnetic field.
High-Frequency Rayleigh-Wave Method
Jianghai Xia; Richard D Millerg; Xu Yixian; Luo Yinhe; Chen Chao; Liu Jiangping; Julian Ivanov; Chong Zeng
2009-01-01
High-frequency (≥2 Hz) Rayleigh-wave data acquired with a multichannei recording sys-tem 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 tech-niques 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 nou-iuvasive 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.
Electroviscoelasticity of liquid/liquid interfaces: fractional-order model.
Spasic, Aleksandar M; Lazarevic, Mihailo P
2005-02-01
A number of theories that describe the behavior of liquid-liquid interfaces have been developed and applied to various dispersed systems, e.g., Stokes, Reiner-Rivelin, Ericksen, Einstein, Smoluchowski, and Kinch. A new theory of electroviscoelasticity describes the behavior of electrified liquid-liquid interfaces in fine dispersed systems and is based on a new constitutive model of liquids. According to this model liquid-liquid droplet or droplet-film structure (collective of particles) is considered as a macroscopic system with internal structure determined by the way the molecules (ions) are tuned (structured) into the primary components of a cluster configuration. How the tuning/structuring occurs depends on the physical fields involved, both potential (elastic forces) and nonpotential (resistance forces). All these microelements of the primary structure can be considered as electromechanical oscillators assembled into groups, so that excitation by an external physical field may cause oscillations at the resonant/characteristic frequency of the system itself (coupling at the characteristic frequency). Up to now, three possible mathematical formalisms have been discussed related to the theory of electroviscoelasticity. The first is the tension tensor model, where the normal and tangential forces are considered, only in mathematical formalism, regardless of their origin (mechanical and/or electrical). The second is the Van der Pol derivative model, presented by linear and nonlinear differential equations. Finally, the third model presents an effort to generalize the previous Van der Pol equation: the ordinary time derivative and integral are now replaced with the corresponding fractional-order time derivative and integral of order p<1.
Haitao Qi; Hui Jin
2006-01-01
The fractional calculus is used in the constitutive relationship model of viscoelastic fluid.A generalized Maxwell model with fractional calculus is considered.Based on the flow conditions described,two flow cases are solved and the exact solutions are obtained by using the Weber transform and the Laplace transform for fractional calculus.
Mathematical Models Arising in the Fractal Forest Gap via Local Fractional Calculus
Chun-Ying Long
2014-01-01
Full Text Available The forest new gap models via local fractional calculus are investigated. The JABOWA and FORSKA models are extended to deal with the growth of individual trees defined on Cantor sets. The local fractional growth equations with local fractional derivative and difference are discussed. Our results are first attempted to show the key roles for the nondifferentiable growth of individual trees.
Formal modeling and verification of fractional order linear systems.
Zhao, Chunna; Shi, Likun; Guan, Yong; Li, Xiaojuan; Shi, Zhiping
2016-05-01
This paper presents a formalization of a fractional order linear system in a higher-order logic (HOL) theorem proving system. Based on the formalization of the Grünwald-Letnikov (GL) definition, we formally specify and verify the linear and superposition properties of fractional order systems. The proof provides a rigor and solid underpinnings for verifying concrete fractional order linear control systems. Our implementation in HOL demonstrates the effectiveness of our approach in practical applications.
Fractional model for heat conduction in polar bear hairs
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…
Fractional Moment Bounds and Disorder Relevance for Pinning Models
Derrida, Bernard; Giacomin, Giambattista; Lacoin, Hubert; Toninelli, Fabio Lucio
2009-05-01
We study the critical point of directed pinning/wetting models with quenched disorder. The distribution K(·) of the location of the first contact of the (free) polymer with the defect line is assumed to be of the form K( n) = n - α-1 L( n), with α ≥ 0 and L(·) slowly varying. The model undergoes a (de)-localization phase transition: the free energy (per unit length) is zero in the delocalized phase and positive in the localized phase. For α 1, then quenched and annealed critical points differ whenever disorder is present, and we give the scaling form of their difference for small disorder. In agreement with the so-called Harris criterion, disorder is therefore relevant in this case. In the marginal case α = 1/2, under the assumption that L(·) vanishes sufficiently fast at infinity, we prove that the difference between quenched and annealed critical points, which is smaller than any power of the disorder strength, is positive: disorder is marginally relevant. Again, the case considered in [12,17] is out of our analysis and remains open. The results are achieved by setting the parameters of the model so that the annealed system is localized, but close to criticality, and by first considering a quenched system of size that does not exceed the correlation length of the annealed model. In such a regime we can show that the expectation of the partition function raised to a suitably chosen power {γ in (0, 1)} is small. We then exploit such an information to prove that the expectation of the same fractional power of the partition function goes to zero with the size of the system, a fact that immediately entails that the quenched system is delocalized.
A note on fractional linear pure birth and pure death processes in epidemic models
Garra, Roberto; 10.1016/j.physa.2011.06.005
2011-01-01
In this note we highlight the role of fractional linear birth and linear death processes recently studied in \\citet{sakhno} and \\citet{pol}, in relation to epidemic models with empirical power law distribution of the events. Taking inspiration from a formal analogy between the equation of self consistency of the epidemic type aftershock sequences (ETAS) model, and the fractional differential equation describing the mean value of fractional linear growth processes, we show some interesting applications of fractional modelling to study \\textit{ab initio} epidemic processes without the assumption of any empirical distribution. We also show that, in the frame of fractional modelling, subcritical regimes can be linked to linear fractional death processes and supercritical regimes to linear fractional birth processes. Moreover we discuss a simple toy model to underline the possible application of these stochastic growth models to more general epidemic phenomena such as tumoral growth.
Rayleigh scattering in the atmospheres of hot stars
Fišák, J.; Krtička, J.; Munzar, D.; Kubát, J.
2016-05-01
Context. Rayleigh scattering is a result of an interaction of photons with bound electrons. Rayleigh scattering is mostly neglected in calculations of hot star model atmospheres because most of the hydrogen atoms are ionized and the heavier elements have a lower abundance than hydrogen. In atmospheres of some chemically peculiar stars, helium overabundant regions containing singly ionized helium are present and Rayleigh scattering can be a significant opacity source. Aims: We evaluate the contribution of Rayleigh scattering by neutral hydrogen and singly ionized helium in the atmospheres of hot stars with solar composition and in the atmospheres of helium overabundant stars. Methods: We computed several series of model atmospheres using the TLUSTY code and emergent fluxes using the SYNSPEC code. These models describe atmospheres of main sequence B-type stars with different helium abundance. We used an existing grid of models for atmospheres with solar chemical composition and we calculated an additional grid for helium-rich stars with N(He)/N(H) = 10. Results: Rayleigh scattering by neutral hydrogen can be neglected in atmospheres of hot stars, while Rayleigh scattering by singly ionized helium can be a non-negligible opacity source in some hot stars, especially in helium-rich stars.
Animal models of heart failure with preserved ejection fraction
G. Conceição; I. Heinonen (Ilkka); A.P. Lourenço; D.J.G.M. Duncker (Dirk); I. Falcão-Pires
2016-01-01
textabstractHeart failure with preserved ejection fraction (HFpEF) constitutes a clinical syndrome in which the diagnostic criteria of heart failure are not accompanied by gross disturbances of systolic function, as assessed by ejection fraction. In turn, under most circumstances, diastolic function
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).
A Fractional Fokker-Planck Model for Anomalous Diffusion
anderson, Johan; Moradi, Sara
2014-01-01
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 observing the transition from a Gaussian distribution to a L\\'evy distribution. The statistical properties of the distribution functions are assessed by a generalized 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.
Tcp and NTCP radiobiological models: conventional and hypo fractionated treatments in radiotherapy
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)
Numerical simulation for SI model with variable-order fractional
mohamed mohamed
2016-04-01
Full Text Available In this paper numerical studies for the variable-order fractional delay differential equations are presented. Adams-Bashforth-Moulton algorithm has been extended to study this problem, where the derivative is defined in the Caputo variable-order fractional sense. Special attention is given to prove the error estimate of the proposed method. Numerical test examples are presented to demonstrate utility of the method. Chaotic behaviors are observed in variable-order one dimensional delayed systems.
Animal models of heart failure with preserved ejection fraction
Conceição, G.; Heinonen, I.; Lourenço, A. P.; Duncker, D. J.; Falcão-Pires, I.
2016-01-01
Heart failure with preserved ejection fraction (HFpEF) constitutes a clinical syndrome in which the diagnostic criteria of heart failure are not accompanied by gross disturbances of systolic function, as assessed by ejection fraction. In turn, under most circumstances, diastolic function is impaired. Although it now represents over 50 % of all patients with heart failure, the mechanisms of HFpEF remain understood, precluding effective therapy. Understanding the pathophysiology of HFpEF has be...
Regression model for tuning the PID controller with fractional order time delay system
S.P. Agnihotri; Laxman Madhavrao Waghmare
2014-01-01
In this paper a regression model based for tuning proportional integral derivative (PID) controller with fractional order time delay system is proposed. The novelty of this paper is that tuning parameters of the fractional order time delay system are optimally predicted using the regression model. In the proposed method, the output parameters of the fractional order system are used to derive the regression function. Here, the regression model depends on the weights of the exponential function...
2016-01-01
In recent days, fractional calculus (FC) has been accepted as a novel modeling tool that can extend the descriptive power of the traditional calculus. Fractional-order descriptiveness can increase the flexibility and degrees of freedom of the model by means of fractional parameters. Based on the fact that real capacitors and inductors are “intrinsic” fractional order, fractional calculus is introduced into the modeling process to establish a fractional-order state-space averaging model of the...
Jan Freundlich
2013-01-01
Full Text Available The paper presents vibration analysis of a simply supported beam with a fractional order viscoelastic material model. The Bernoulli-Euler beam model is considered. The beam is excited by the supports movement. The Riemann – Liouville fractional derivative of order 0 α ⩽ 1 is applied. In the first stage, the steady-state vibrations of the beam are analyzed and therefore the Riemann – Liouville fractional derivative with lower terminal at −∞ is assumed. This assumption simplifies solution of the fractional differential equations and enables us to directly obtain amplitude-frequency characteristics of the examined system. The characteristics are obtained for various values of fractional derivative of order α and values of the Voigt material model parameters. The studies show that the selection of appropriate damping coefficients and fractional derivative order of damping model enables us to fit more accurately dynamic characteristic of the beam in comparison with using integer order derivative damping model.
Mittag-Leffler function for discrete fractional modelling
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.
A representation theory for a class of vector autoregressive models for fractional processes
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 unit...... 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...
Human intake fraction of toxic pollutants: a model comparison between caltox and uses-lca
Huijbregts, Mark A J; Geelen, Loes M.J.; Edgar G. Hertwich; McKone, Thomas E.; Meent, Dik van de
2004-01-01
In Life Cycle Assessment and Comparative Risk Assessment potential human exposure to toxic pollutants can be expressed as the human intake fraction (iF), representing the fraction of the quantity emitted that enters the human population. To assess model uncertainty in the human intake fraction, ingestion and inhalation iFs of 367 substances emitted to air and freshwater were calculated with two commonly applied multi-media fate and exposure models, CalTOX and USES-LCA. Comparison of the ...
On a fractal LC-electric circuit modeled by local fractional calculus
Yang, Xiao-Jun; Machado, J. A. Tenreiro; Cattani, Carlo; Gao, Feng
2017-06-01
A non-differentiable model of the LC-electric circuit described by a local fractional differential equation of fractal dimensional order is addressed in this article. From the fractal electrodynamics point of view, the relaxation oscillator, defined on Cantor sets in LC-electric circuit, and its exact solution using the local fractional Laplace transform are obtained. Comparative results among local fractional derivative, Riemann-Liouville fractional derivative and conventional derivative are discussed. Local fractional calculus is proposed as a new tool suitable for the study of a large class of electric circuits.
A proposed fractional-order Gompertz model and its application to tumour growth data.
Bolton, Larisse; Cloot, Alain H J J; Schoombie, Schalk W; Slabbert, Jacobus P
2015-06-01
A fractional-order Gompertz model of orders between 0 and 2 is proposed. The main purpose of this investigation is to determine whether the ordinary or proposed fractional Gompertz model would best fit our experimental dataset. The solutions for the proposed model are obtained using fundamental concepts from fractional calculus. The closed-form equations of both the proposed model and the ordinary Gompertz model are calibrated using an experimental dataset containing tumour growth volumes of a Rhabdomyosarcoma tumour in a mouse. With regard to the proposed model, the order, within the interval mentioned, that resulted in the best fit to the data was used in a further investigation into the prediction capability of the model. This was compared to the prediction capability of the ordinary Gompertz model. The result of the investigation was that a fractional-order Gompertz model of order 0.68 produced a better fit to our experimental dataset than the well-known ordinary Gompertz model.
Rayleigh--Taylor spike evaporation
Schappert, G. T.; Batha, S. H.; Klare, K. A.; Hollowell, D. E.; Mason, R. J.
2001-09-01
Laser-based experiments have shown that Rayleigh--Taylor (RT) growth in thin, perturbed copper foils leads to a phase dominated by narrow spikes between thin bubbles. These experiments were well modeled and diagnosed until this '' spike'' phase, but not into this spike phase. Experiments were designed, modeled, and performed on the OMEGA laser [T. R. Boehly, D. L. Brown, R. S. Craxton , Opt. Commun. 133, 495 (1997)] to study the late-time spike phase. To simulate the conditions and evolution of late time RT, a copper target was fabricated consisting of a series of thin ridges (spikes in cross section) 150 {mu}m apart on a thin flat copper backing. The target was placed on the side of a scale-1.2 hohlraum with the ridges pointing into the hohlraum, which was heated to 190 eV. Side-on radiography imaged the evolution of the ridges and flat copper backing into the typical RT bubble and spike structure including the '' mushroom-like feet'' on the tips of the spikes. RAGE computer models [R. M. Baltrusaitis, M. L. Gittings, R. P. Weaver, R. F. Benjamin, and J. M. Budzinski, Phys. Fluids 8, 2471 (1996)] show the formation of the '' mushrooms,'' as well as how the backing material converges to lengthen the spike. The computer predictions of evolving spike and bubble lengths match measurements fairly well for the thicker backing targets but not for the thinner backings.
Cognitive Models: The Missing Link to Learning Fraction Multiplication and Division
de Castro, Belinda V.
2008-01-01
This quasi-experimental study aims to streamline cognitive models on fraction multiplication and division that contain the most worthwhile features of other existing models. Its exploratory nature and its approach to proof elicitation can be used to help establish its effectiveness in building students' understanding of fractions as compared to…
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…
Conceptual Mis(understandings) of Fractions: From Area Models to Multiple Embodiments
Zhang, Xiaofen; Clements, M. A.; Ellerton, Nerida F.
2015-01-01
Area-model representations seem to have been dominant in the teaching and learning of fractions, especially in primary school mathematics curricula. In this study, we investigated 40 fifth grade children's understandings of the unit fractions, 1/2, 1/3, and 1/4, represented through a variety of different models. Analyses of pre-teaching test and…
Ripesi, P; Schifano, S F; Tripiccione, R
2014-01-01
We study the turbulent evolution originated from a system subjected to a Rayleigh-Taylor instability with a double density at high resolution in a 2 dimensional geometry using a highly optimized thermal Lattice Boltzmann code for GPUs. The novelty of our investigation stems from the initial condition, given by the superposition of three layers with three different densities, leading to the development of two Rayleigh-Taylor fronts that expand upward and downward and collide in the middle of the cell. By using high resolution numerical data we highlight the effects induced by the collision of the two turbulent fronts in the long time asymptotic regime. We also provide details on the optimized Lattice-Boltzmann code that we have run on a cluster of GPUs
Deriving pedotransfer functions for soil quartz fraction in southern France from reverse modeling
Calvet, Jean-Christophe; Fritz, Noureddine; Berne, Christine; Piguet, Bruno; Maurel, William; Meurey, Catherine
2016-12-01
The quartz fraction in soils is a key parameter of soil thermal conductivity models. Because it is difficult to measure the quartz fraction in soils, this information is usually unavailable. This source of uncertainty impacts the simulation of sensible heat flux, evapotranspiration and land surface temperature in numerical simulations of the Earth system. Improving the estimation of soil quartz fraction is needed for practical applications in meteorology, hydrology and climate modeling. This paper investigates the use of long time series of routine ground observations made in weather stations to retrieve the soil quartz fraction. Profile soil temperature and water content were monitored at 21 weather stations in southern France. Soil thermal diffusivity was derived from the temperature profiles. Using observations of bulk density, soil texture, and fractions of gravel and soil organic matter, soil heat capacity and thermal conductivity were estimated. The quartz fraction was inversely estimated using an empirical geometric mean thermal conductivity model. Several pedotransfer functions for estimating quartz content from gravimetric or volumetric fractions of soil particles (e.g., sand) were analyzed. The soil volumetric fraction of quartz (fq) was systematically better correlated with soil characteristics than the gravimetric fraction of quartz. More than 60 % of the variance of fq could be explained using indicators based on the sand fraction. It was shown that soil organic matter and/or gravels may have a marked impact on thermal conductivity values depending on which predictor of fq is used. For the grassland soils examined in this study, the ratio of sand-to-soil organic matter fractions was the best predictor of fq, followed by the gravimetric fraction of sand. An error propagation analysis and a comparison with independent data from other tested models showed that the gravimetric fraction of sand is the best predictor of fq when a larger variety of soil types
Rayleigh-Taylor Instability in a Relativistic Fireball on a Moving Computational Grid
Duffell, Paul C
2013-01-01
We numerically calculate the growth and saturation of the Rayleigh-Taylor instability caused by the deceleration of relativistic outflows with Lorentz factor \\Gamma = 10, 30, and 100. The instability generates turbulence whose scale exhibits strong dependence on Lorentz factor, as only modes within the causality scale \\Delta \\theta ~ 1/\\Gamma can grow. We develop a simple diagnostic to measure the fraction of energy in turbulent eddies and use it to estimate magnetic field amplification by the instability. We estimate a magnetic energy fraction ~ 0.01 due to Rayleigh-Taylor turbulence in a shock-heated region behind the forward shock. The instability completely disrupts the contact discontinuity between the ejecta and the swept up circumburst medium. The reverse shock is stable, but is impacted by the Rayleigh-Taylor instability, which strengthens the reverse shock and pushes it away from the forward shock. The forward shock front is unaffected by the instability, but Rayleigh-Taylor fingers can penetrate abo...
Coexisting Raman- and Rayleigh-Enhanced Four-Wave Mixing in Femtosecond Polarization Beats
NIE Zhi-Qiang; ZHAO Yan; ZHANG Yan-Peng; GAN Chen-Li; ZHENG Huai-Sin; LI Chang-Biao; LU Ke-Qing
2009-01-01
Based on the polarization interference of Raman- and Rayleigh-enhanced four-wave mixing processes,heterodyne detection of the Raman,Rayleigh and coexisting Raman and Rayleigh femtosecond difference-frequency polarization beats is investigated in the cw and the three Markovian stochastic models,respectively.These two processes exhibit asymmetric and symmetric spectra,respectively,and the thermal effect in them can be suppressed by a field-correlation method.Such studies of coexisting Raman- and Rayleigh-enhanced four-wave mixing processes can have important applications in coherence quantum control,and quantum information processing.
Numerical simulation of Martian historical dynamo: Impact of the Rayleigh number on the dynamo state
WANG TianYuan; KUANG WeiJia; MA ShiZhuang
2009-01-01
The observed Mars remnant magnetism suggests that there was an active dynamo in the Martian core.We use the MoSST core dynamics model to simulate the Martian historical dynamo,focusing on the variation of the dynamo states with the Rayleigh number Ra (a non-dimensional parameter describing the buoyancy force in the core).Our numerical results show that the mean field length scale does not vary monotonically with the Rayleigh number,and the field morphology at the core mantle boundary changes with Rayleigh number.In particular,it drifts westward with a speed decreasing with Rayleigh number.
Numerical simulation of Martian historical dynamo:Impact of the Rayleigh number on the dynamo state
无
2009-01-01
The observed Mars remnant magnetism suggests that there was an active dynamo in the Martian core. We use the MoSST core dynamics model to simulate the Martian historical dynamo, focusing on the variation of the dynamo states with the Rayleigh number Ra (a non-dimensional parameter describing the buoyancy force in the core). Our numerical results show that the mean field length scale does not vary monotonically with the Rayleigh number, and the field morphology at the core mantle boundary changes with Rayleigh number. In particular, it drifts westward with a speed decreasing with Rayleigh number.
PLANE SURFACE SUDDENLY SET IN MOTION IN A VISCOELASTIC FLUID WITH FRACTIONAL MAXWELL MODEL
谭文长; 徐明瑜
2002-01-01
The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak.
Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model
Wenchang, Tan; Mingyu, Xu
2002-08-01
The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak.
SOLVING FRACTIONAL-ORDER COMPETITIVE LOTKA-VOLTERRA MODEL BY NSFD SCHEMES
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.
Banquet Speech Some Sketches Of Rayleigh
Howard, John N.
1985-11-01
Several short sketches are presented of Lord Rayleigh, to show his method of working and his interaction with his fellow scientists. The topics discussed are: his research on the blue of the sky (Rayleigh scattering); his rescue of Waterston from near-oblivion; his research on surface acoustic waves (Rayleigh waves); his collaboration with Agnes Pockels; his research on blackbody radiation (the Rayleigh-Jeans Law).
Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System
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.
Blue Skies, Coffee Creamer, and Rayleigh Scattering
Liebl, Michael
2010-01-01
The first physical explanation of Earths blue sky was fashioned in 1871 by Lord Rayleigh. Many discussions of Rayleigh scattering and approaches to studying it both in and out of the classroom are available. Rayleigh scattering accounts for the blue color of the sky and the orange/red color of the Sun near sunset and sunrise, and a number of…
Blue Skies, Coffee Creamer, and Rayleigh Scattering
Liebl, Michael
2010-01-01
The first physical explanation of Earths blue sky was fashioned in 1871 by Lord Rayleigh. Many discussions of Rayleigh scattering and approaches to studying it both in and out of the classroom are available. Rayleigh scattering accounts for the blue color of the sky and the orange/red color of the Sun near sunset and sunrise, and a number of…
Modelling viscosity and mass fraction of bitumen - diluent mixtures
Miadonye, A.; Latour, N.; Puttagunta, V.R. [Lakehead Univ., Thunder Bay, ON (Canada)
1999-07-01
In recovery of bitumen in oil sands extraction, the reduction of the viscosity is important above and below ground. The addition of liquid diluent breaks down or weakens the intermolecular forces that create a high viscosity in bitumen. The addition of even 5% of diluent can cause a viscosity reduction in excess of 8%, thus facilitating the in situ recovery and pipeline transportation of bitumen. Knowledge of bitumen - diluent viscosity is highly important because without it, determination of upgrading processes, in situ recovery, well simulation, heat transfer, fluid flow and a variety of other engineering problems would be difficult or impossible to solve. The development of a simple correlation to predict the viscosity of binary mixtures of bitumen - diluent in any proportion is described. The developed correlation used to estimate the viscosities and mass fractions of bitumen - diluent mixtures was within acceptable limits of error. For the prediction of mixture viscosities, the developed correlation gave the best results with an overall average absolute deviation of 12% compared to those of Chironis (17%) and Cragoe (23%). Predictions of diluent mass fractions yielded a much better result with an overall average absolute deviation of 5%. The unique features of the correlation include its computational simplicity, its applicability to mixtures at temperatures other than 30 degrees C, and the fact that only the bitumen and diluent viscosities are needed to make predictions. It is the only correlation capable of predicting viscosities of mixtures, as well as diluent mass fractions required to reduce bitumen viscosity to pumping viscosities. The prediction of viscosities at 25, 60.3, and 82.6 degrees C produced excellent results, particularly at high temperatures with an average absolute deviation of below 10%. 11 refs., 3 figs., 8 tabs.
Zheng Yongai, E-mail: zhengyongai@163.co [Department of Computer, Yangzhou University, Yangzhou, 225009 (China); Nian Yibei [School of Energy and Power Engineering, Yangzhou University, Yangzhou, 225009 (China); Wang Dejin [Department of Computer, Yangzhou University, Yangzhou, 225009 (China)
2010-12-01
In this Letter, a kind of novel model, called the generalized Takagi-Sugeno (T-S) fuzzy model, is first developed by extending the conventional T-S fuzzy model. Then, a simple but efficient method to control fractional order chaotic systems is proposed using the generalized T-S fuzzy model and adaptive adjustment mechanism (AAM). Sufficient conditions are derived to guarantee chaos control from the stability criterion of linear fractional order systems. The proposed approach offers a systematic design procedure for stabilizing a large class of fractional order chaotic systems from the literature about chaos research. The effectiveness of the approach is tested on fractional order Roessler system and fractional order Lorenz system.
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.
Numerical Solution of Fractional Neutron Point Kinetics Model in Nuclear Reactor
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.
Imaging Rayleigh wave attenuation with USArray
Bao, Xueyang; Dalton, Colleen A.; Jin, Ge; Gaherty, James B.; Shen, Yang
2016-07-01
The EarthScope USArray provides an opportunity to obtain detailed images of the continental upper mantle at an unprecedented scale. The majority of mantle models derived from USArray data to date contain spatial variations in seismic-wave speed; however, in many cases these data sets do not by themselves allow a non-unique interpretation. Joint interpretation of seismic attenuation and velocity models can improve upon the interpretations based only on velocity and provide important constraints on the temperature, composition, melt content, and volatile content of the mantle. The surface wave amplitudes that constrain upper-mantle attenuation are sensitive to factors in addition to attenuation, including the earthquake source excitation, focusing and defocusing by elastic structure, and local site amplification. Because of the difficulty of isolating attenuation from these other factors, little is known about the attenuation structure of the North American upper mantle. In this study, Rayleigh wave traveltime and amplitude in the period range 25-100 s are measured using an interstation cross-correlation technique, which takes advantage of waveform similarity at nearby stations. Several estimates of Rayleigh wave attenuation and site amplification are generated at each period, using different approaches to separate the effects of attenuation and local site amplification on amplitude. It is assumed that focusing and defocusing effects can be described by the Laplacian of the traveltime field. All approaches identify the same large-scale patterns in attenuation, including areas where the attenuation values are likely contaminated by unmodelled focusing and defocusing effects. Regionally averaged attenuation maps are constructed after removal of the contaminated attenuation values, and the variations in intrinsic shear attenuation that are suggested by these Rayleigh wave attenuation maps are explored.
Deliyianni, Eleni; Gagatsis, Athanasios; Elia, Iliada; Panaoura, Areti
2016-01-01
The aim of this study was to propose and validate a structural model in fraction and decimal number addition, which is founded primarily on a synthesis of major theoretical approaches in the field of representations in Mathematics and also on previous research on the learning of fractions and decimals. The study was conducted among 1,701 primary…
The Role of the Mittag-Leffler Function in Fractional Modeling
Sergei Rogosin
2015-05-01
Full Text Available This is a survey paper illuminating the distinguished role of the Mittag-Leffler function and its generalizations in fractional analysis and fractional modeling. The content of the paper is connected to the recently published monograph by Rudolf Gorenflo, Anatoly Kilbas, Francesco Mainardi and Sergei Rogosin.
Deliyianni, Eleni; Gagatsis, Athanasios; Elia, Iliada; Panaoura, Areti
2016-01-01
The aim of this study was to propose and validate a structural model in fraction and decimal number addition, which is founded primarily on a synthesis of major theoretical approaches in the field of representations in Mathematics and also on previous research on the learning of fractions and decimals. The study was conducted among 1,701 primary…
Dividing Fractions Using an Area Model: A Look at In-Service Teachers' Understanding
Lamberg, Teruni; Wiest, Lynda R.
2015-01-01
The paper reports an investigation into how a group of elementary and middle school teachers collectively attempted to solve and understand a fraction division problem using an area model. Solving the word problem required that teachers determine how many two-thirds fit into three-fourths. The teachers struggled to conceptualise fraction division,…
A Verilog-A Based Fractional Frequency Synthesizer Model for Fast and Accurate Noise Assessment
V. R. Gonzalez-Diaz
2016-04-01
Full Text Available This paper presents a new strategy to simulate fractional frequency synthesizer behavioral models with better performance and reduced simulation time. The models are described in Verilog-A with accurate phase noise predictions and they are based on a time jitter to power spectral density transformation of the principal noise sources in a synthesizer. The results of a fractional frequency synthesizer simulation is compared with state of the art Verilog-A descriptions showing a reduction of nearly 20 times. In addition, experimental results of a fractional frequency synthesizer are compared to the simulation results to validate the proposed model.
A COMPARATIVE STUDY UNDER PROGRESSIVELY FIRST FAILURE CENSORED RAYLEIGH DATA
Gyan Prakash
2015-06-01
Full Text Available A comparative study presented in this article for two different asymmetric loss functions is based on simulation. Two-parameter Rayleigh model is considered here as the underline model for evaluating the properties of Bayes estimators under progressive first failure censored data. Known and unknown both cases of location parameter are considered here for Bayes estimation of scale parameter.
Wei, Song; Chen, Wen; Hon, Y. C.
2016-11-01
This paper investigates the temporal effects in the modeling of flows through porous media and particles transport. Studies will be made among the time fractional diffusion model and two classical nonlinear diffusion models. The effects of the parameters upon the mentioned models have been studied. By simulating the sub-diffusion processes and comparing the numerical results of these models under different boundary conditions, we can conclude that the time fractional diffusion model is more suitable for simulating the sub-diffusion with steady diffusion rate; whereas the nonlinear models are more appropriate for depicting the sub-diffusion under changing diffusion rate.
Rayleigh scattering in few-mode optical fibers
Wang, Zhen; Wu, Hao; Hu, Xiaolong; Zhao, Ningbo; Mo, Qi; Li, Guifang
2016-01-01
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. PMID:27775003
Rayleigh scattering in few-mode optical fibers
Wang, Zhen; Wu, Hao; Hu, Xiaolong; Zhao, Ningbo; Mo, Qi; Li, Guifang
2016-10-01
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.
Aromatization of light naphtha fractions on zeolites 1: Kinetic model
Rovenskaja Svetlana A.
2003-01-01
Full Text Available On the basis of analyzing kinetic experimental data performed in laboratory integral reactors a lumping kinetic model of the "Zeoforming" process was developed. A reaction scheme of the lumped components was proposed, that was adapted to the technological requirements. The reaction rate constants and activation energies were estimated, that are valid for certain feed compositions. The model is intended for further modeling and optimization of the process.
Mendoza, Carlos I; Santamaría-Holek, I
2009-01-28
We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuum-medium description based on a recursive-differential method where correlations between the spheres are introduced through an effective volume fraction. In contrast to other differential methods, the introduction of the effective volume fraction as the integration variable implicitly considers interactions between the spheres of the same recursive stage. The final expression for the viscosity scales with this effective volume fraction, which allows constructing a master curve that contains all the experimental situations considered. The agreement of our expression for the viscosity with experiments at low- and high-shear rates and in the high-frequency limit is remarkable for all volume fractions.
Rotating Rayleigh-Taylor turbulence
Boffetta, G.; Mazzino, A.; Musacchio, S.
2016-09-01
The turbulent Rayleigh-Taylor system in a rotating reference frame is investigated by direct numerical simulations within the Oberbeck-Boussinesq approximation. On the basis of theoretical arguments, supported by our simulations, we show that the Rossby number decreases in time, and therefore the Coriolis force becomes more important as the system evolves and produces many effects on Rayleigh-Taylor turbulence. We find that rotation reduces the intensity of turbulent velocity fluctuations and therefore the growth rate of the temperature mixing layer. Moreover, in the presence of rotation the conversion of potential energy into turbulent kinetic energy is found to be less effective, and the efficiency of the heat transfer is reduced. Finally, during the evolution of the mixing layer we observe the development of a cyclone-anticyclone asymmetry.
Liu, Zhongxian; Liang, Jianwen; Wu, Chengqing
2016-06-01
Two dimensional diffraction of Rayleigh waves by a fluid-saturated poroelastic alluvial valley of arbitrary shape in a poroelastic half-space is investigated using the method of fundamental solutions (MFS). To satisfy the free surface boundary conditions exactly, Green's functions of compressional (PI and PII) and shear (SV) wave sources buried in a fluid-saturated poroelastic half-space are adopted. Next, the procedure for solving the scattering wave field is presented. It is verified that the MFS is of excellent accuracy and numerical stability. Numerical results illustrate that the dynamic response strongly depends on such factors as the incident frequency, the porosity of alluvium, the boundary drainage condition, and the valley shape. There is a significant difference between the diffraction of Rayleigh waves for the saturated soil case and for the corresponding dry soil case. The wave focusing effect both on the displacement and pore pressure can be observed inside the alluvial valley and the amplification effect seems most obvious in the case of higher porosity and lower frequency. Additionally, special attention should also be paid to the concentration of pore pressure, which is closely related to the site liquefaction in earthquakes.
Numerical Solution of Fractional Diffusion Equation Model for Freezing in Finite Media
R. S. Damor
2013-01-01
Full Text Available Phase change problems play very important role in engineering sciences including casting of nuclear waste materials, vivo freezing of biological tissues, solar collectors and so forth. In present paper, we propose fractional diffusion equation model for alloy solidification. A transient heat transfer analysis is carried out to study the anomalous diffusion. Finite difference method is used to solve the fractional differential equation model. The temperature profiles, the motion of interface, and interface velocity have been evaluated for space fractional diffusion equation.
The equivalent electrical permittivity of gas-solid mixtures at intermediate solid volume fractions.
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).
A review of inhalability fraction models: discussion and recommendations.
Millage, Kyle K; Bergman, Josh; Asgharian, Bahman; McClellan, Gene
2010-02-01
The first step in mathematically modeling the mechanics of respiratory deposition of particles is to estimate the ability of a particle to enter the head, either through the mouth or nose. Models of the biological effects from inhaled particles are commonly, albeit incorrectly, simplified by making an assumption that the only particles of concern are those that can readily penetrate to the pulmonary region of the lung: typically particles less than 5microm in aerodynamic diameter. Inhalability for particles of this size is effectively 100%, so there is little need to develop a mathematical representation of the phenomenon. However, chemical irritants, biological agents, or radioactive material, in the form of large particles or droplets, can cause adverse biological responses by simply being taken into the head and depositing in the extrathoracic area. As a result, it is important to understand the inhalability of both small and large particles. The concept of particle inhalability received little consideration until the 1970s; since then it has been the subject of many experiments with a fairly wide disparity of results, in part due to the variety of dependent variables and the difficulty in adequate measurement methods. This article describes the currently utilized models of inhalability, recommends specific methods for implementing inhalability into mathematical models of respiratory deposition, and identifies outstanding issues and limitations. In this article, we describe inhalability as it applies to particulate matter and liquid droplets; modeling the inhalability of fibers is a work in progress and is not addressed.
Neuronal spike timing adaptation described with a fractional leaky integrate-and-fire model.
Wondimu Teka
2014-03-01
Full Text Available The voltage trace of neuronal activities can follow multiple timescale dynamics that arise from correlated membrane conductances. Such processes can result in power-law behavior in which the membrane voltage cannot be characterized with a single time constant. The emergent effect of these membrane correlations is a non-Markovian process that can be modeled with a fractional derivative. A fractional derivative is a non-local process in which the value of the variable is determined by integrating a temporal weighted voltage trace, also called the memory trace. Here we developed and analyzed a fractional leaky integrate-and-fire model in which the exponent of the fractional derivative can vary from 0 to 1, with 1 representing the normal derivative. As the exponent of the fractional derivative decreases, the weights of the voltage trace increase. Thus, the value of the voltage is increasingly correlated with the trajectory of the voltage in the past. By varying only the fractional exponent, our model can reproduce upward and downward spike adaptations found experimentally in neocortical pyramidal cells and tectal neurons in vitro. The model also produces spikes with longer first-spike latency and high inter-spike variability with power-law distribution. We further analyze spike adaptation and the responses to noisy and oscillatory input. The fractional model generates reliable spike patterns in response to noisy input. Overall, the spiking activity of the fractional leaky integrate-and-fire model deviates from the spiking activity of the Markovian model and reflects the temporal accumulated intrinsic membrane dynamics that affect the response of the neuron to external stimulation.
Critical exponents of O(N) models in fractional dimensions
Codello, A; D'Odorico, G
2014-01-01
We compute critical exponents of O(N) models in fractal dimensions between two and four, and for continuos values of the number of field components N, in this way completing the RG classification of universality classes for these models. In d=2 the N-dependence of the correlation length critical exponent gives us the last piece of information needed to establish a RG derivation of the Mermin-Wagner theorem. We also report critical exponents for multi-critical universality classes in the cases N>1 and N=0. Finally, in the large-N limit our critical exponents correctly approach those of the spherical model, allowing us to set N~100 as threshold for the quantitative validity of leading order large-N estimates.
Tian, Li-Ping; Liu, Lizhi; Wu, Fang-Xiang
2010-01-01
Derived from biochemical principles, molecular biological systems can be described by a group of differential equations. Generally these differential equations contain fractional functions plus polynomials (which we call improper fractional model) as reaction rates. As a result, molecular biological systems are nonlinear in both parameters and states. It is well known that it is challenging to estimate parameters nonlinear in a model. However, in fractional functions both the denominator and numerator are linear in the parameters while polynomials are also linear in parameters. Based on this observation, we develop an iterative linear least squares method for estimating parameters in biological systems modeled by improper fractional functions. The basic idea is to transfer optimizing a nonlinear least squares objective function into iteratively solving a sequence of linear least squares problems. The developed method is applied to the estimation of parameters in a metabolism system. The simulation results show the superior performance of the proposed method for estimating parameters in such molecular biological systems.
Magnetization direction in the Heisenberg model exhibiting fractional Brownian motion
Zhang, Zhengping; Mouritsen, Ole G.; Zuckermann, Martin J.
1993-01-01
The temporal magnetization-direction fluctuations in the three-dimensional classical ferromagnetic Heisenberg model have been generated by Monte Carlo simulation and analyzed by the rescaled-range method to yield the Hurst exponent H. A value of H congruent-to 1 has been found to apply...
Gianni Pagnini
2012-01-01
inhomogeneity and nonstationarity properties of the medium. For instance, when this superposition is applied to the time-fractional diffusion process, the resulting Master Equation emerges to be the governing equation of the Erdélyi-Kober fractional diffusion, that describes the evolution of the marginal distribution of the so-called generalized grey Brownian motion. This motion is a parametric class of stochastic processes that provides models for both fast and slow anomalous diffusion: it is made up of self-similar processes with stationary increments and depends on two real parameters. The class includes the fractional Brownian motion, the time-fractional diffusion stochastic processes, and the standard Brownian motion. In this framework, the M-Wright function (known also as Mainardi function emerges as a natural generalization of the Gaussian distribution, recovering the same key role of the Gaussian density for the standard and the fractional Brownian motion.
Short Rayleigh length free electron lasers
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.
Likelihood inference for a nonstationary fractional autoregressive model
Johansen, Søren; Ørregård Nielsen, Morten
2010-01-01
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...... d and b, and prove that they converge in distribution. We use the results to prove consistency of the maximum likelihood estimator for d,b in a large compact subset of {1/2...
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.
Nicy Sebastian
2015-08-01
Full Text Available The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral, one can list out almost all of the extended densities for the pathway parameter q < 1 and q → 1. Here, we bring out the idea of thicker- or thinner-tailed models associated with a gamma-type distribution as a limiting case of the pathway operator. Applications of this extended gamma model in statistical mechanics, input-output models, solar spectral irradiance modeling, etc., are established.
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.
Analysis of the Keller–Segel Model with a Fractional Derivative without Singular Kernel
Abdon Atangana
2015-06-01
Full Text Available Using some investigations based on information theory, the model proposed by Keller and Segel was extended to the concept of fractional derivative using the derivative with fractional order without singular kernel recently proposed by Caputo and Fabrizio. We present in detail the existence of the coupled-solutions using the fixed-point theorem. A detailed analysis of the uniqueness of the coupled-solutions is also presented. Using an iterative approach, we derive special coupled-solutions of the modified system and we present some numerical simulations to see the effect of the fractional order.
Shimabukuro, Yosio Edemir; Smith, James A.
1991-01-01
Constrained-least-squares and weighted-least-squares mixing models for generating fraction images derived from remote sensing multispectral data are presented. An experiment considering three components within the pixels-eucalyptus, soil (understory), and shade-was performed. The generated fraction images for shade (shade image) derived from these two methods were compared by considering the performance and computer time. The derived shade images are related to the observed variation in forest structure, i.e., the fraction of inferred shade in the pixel is related to different eucalyptus ages.
Fractional supersymmetric Liouville theory and the multi-cut matrix models
Irie, Hirotaka
2009-01-01
We argue that the non-critical version of the k-fractional superstring theory can be described with the k-cut critical points of the matrix models. In particular we show that, from the spectrum structure of fractional super-Liouville theory, (p,q) minimal fractional superstrings live in the Z_k-symmetry breaking critical points of the k-cut two-matrix models, and that the operator contents and string susceptibility coincide in both sides. By using this correspondence, we also propose the set of primary operators of the fractional superconformal ghost system which consistently gives the correct gravitational scaling critical exponents of the on-shell vertex operators.
Fractional supersymmetric Liouville theory and the multi-cut matrix models
Irie, Hirotaka
2009-10-01
We point out that the non-critical version of the k-fractional superstring theory can be described by k-cut critical points of the matrix models. In particular, in comparison with the spectrum structure of fractional super-Liouville theory, we show that (p,q) minimal fractional superstring theories appear in the Z-symmetry breaking critical points of the k-cut two-matrix models and the operator contents and string susceptibility coincide on both sides. By using this correspondence, we also propose a set of primary operators of the fractional superconformal ghost system which consistently produces the correct gravitational scaling critical exponents of the on-shell vertex operators.
A New Empirical Model for Estimation of sp3 Fraction in Diamond-Like Carbon Films
DAI Hai-Yang; WANG Li-Wu; JIANG Hui; HUANG Ning-Kang
2007-01-01
A new empirical model to estimate the content of sp3 in diamond-like carbon (DLC) films is presented, based on the conventional Raman spectra excited by 488nm or 514nm visible light for different carbons. It is found that bandwidth of the G peak is related to the sp3 fraction. A wider bandwidth of the G peak shows a higher sp3 fraction in DLC films.
Exact Solution of Unsteady Flow of Viscoelastic Fluid in a Pipe with Fractional Maxwell Model
无
2007-01-01
The unsteady flow of viscoelastic fluid in a cylindrical pipe was investigated using the fractional Maxwell model. Two special cases of unsteady pipe flow were expressed. The first is start-up flow, and the second is oscillating flow. The exact solution of start-up flow under a constant pressure gradient was obtained by using the theories of Laplace transform and Fourier-Bessel series for fractional derivatives. The exact solution of oscillating flow was obtained by utilizing the separation of variables.
Cure fraction estimation from the mixture cure models for grouped survival data.
Yu, Binbing; Tiwari, Ram C; Cronin, Kathleen A; Feuer, Eric J
2004-06-15
Mixture cure models are usually used to model failure time data with long-term survivors. These models have been applied to grouped survival data. The models provide simultaneous estimates of the proportion of the patients cured from disease and the distribution of the survival times for uncured patients (latency distribution). However, a crucial issue with mixture cure models is the identifiability of the cure fraction and parameters of kernel distribution. Cure fraction estimates can be quite sensitive to the choice of latency distributions and length of follow-up time. In this paper, sensitivity of parameter estimates under semi-parametric model and several most commonly used parametric models, namely lognormal, loglogistic, Weibull and generalized Gamma distributions, is explored. The cure fraction estimates from the model with generalized Gamma distribution is found to be quite robust. A simulation study was carried out to examine the effect of follow-up time and latency distribution specification on cure fraction estimation. The cure models with generalized Gamma latency distribution are applied to the population-based survival data for several cancer sites from the Surveillance, Epidemiology and End Results (SEER) Program. Several cautions on the general use of cure model are advised.
Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms
Yu, Yue; Perdikaris, Paris; Karniadakis, George Em
2016-10-01
We develop efficient numerical methods for fractional order PDEs, and employ them to investigate viscoelastic constitutive laws for arterial wall mechanics. Recent simulations using one-dimensional models [1] have indicated that fractional order models may offer a more powerful alternative for modeling the arterial wall response, exhibiting reduced sensitivity to parametric uncertainties compared with the integer-calculus-based models. Here, we study three-dimensional (3D) fractional PDEs that naturally model the continuous relaxation properties of soft tissue, and for the first time employ them to simulate flow structure interactions for patient-specific brain aneurysms. To deal with the high memory requirements and in order to accelerate the numerical evaluation of hereditary integrals, we employ a fast convolution method [2] that reduces the memory cost to O (log (N)) and the computational complexity to O (Nlog (N)). Furthermore, we combine the fast convolution with high-order backward differentiation to achieve third-order time integration accuracy. We confirm that in 3D viscoelastic simulations, the integer order models strongly depends on the relaxation parameters, while the fractional order models are less sensitive. As an application to long-time simulations in complex geometries, we also apply the method to modeling fluid-structure interaction of a 3D patient-specific compliant cerebral artery with an aneurysm. Taken together, our findings demonstrate that fractional calculus can be employed effectively in modeling complex behavior of materials in realistic 3D time-dependent problems if properly designed efficient algorithms are employed to overcome the extra memory requirements and computational complexity associated with the non-local character of fractional derivatives.
Tsai, C.; Yeh, G.
2011-12-01
In this investigation, newly proposed constitutive retentions are implemented to a fractional-flow based compressible multiphase-phase flow model. With the new model, a compressible three-phase (water, non-aqueous phase liquid (NAPL) and air) flow problem is simulated. In fractional-flow approaches, the three mass balance equations written in terms of three phase pressures are transformed to those in terms of the total pressure, saturation of water, and saturation of total liquid. These three governing equations are discretized with the Galerkin finite element method (FEM). The resulted matrix equation is solved with Bi-CGSTAB. Several numerical experiments are presented to examine the accuracy and robustness of the proposed model. The results show the presented fractional-flow based multiphase flow model is feasible and yields physically realistic solutions for compressible three-phase flow problems in porous media.
J. E. Macías-Díaz
2017-01-01
Full Text Available We depart from the well-known one-dimensional Fisher’s equation from population dynamics and consider an extension of this model using Riesz fractional derivatives in space. Positive and bounded initial-boundary data are imposed on a closed and bounded domain, and a fully discrete form of this fractional initial-boundary-value problem is provided next using fractional centered differences. The fully discrete population model is implicit and linear, so a convenient vector representation is readily derived. Under suitable conditions, the matrix representing the implicit problem is an inverse-positive matrix. Using this fact, we establish that the discrete population model is capable of preserving the positivity and the boundedness of the discrete initial-boundary conditions. Moreover, the computational solubility of the discrete model is tackled in the closing remarks.
Asymptotic Rayleigh instantaneous unit hydrograph
Troutman, B.M.; Karlinger, M.R.
1988-01-01
The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude, N, tends asymptotically, as N grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor, {Mathematical expression}, where ?? is a mean link wave travel time. ?? 1988 Springer-Verlag.
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.
A fractional model for time-variant non-Newtonian flow
Yang Xu
2017-01-01
Full Text Available This work applies a fractional flow model to describe a time-variant behavior of non-Newtonian substances. Specifically, we model the physical mechanism underlying the thixotropic and anti-thixotropic phenomena of non-Newtonian flow. This study investigates the behaviors of cellulose suspensions and SMS pastes under constant shear rate. The results imply that the presented model with only two parameters is adequate to fit experimental data. Moreover, the parameter of fractional order is an appropriate index to characterize the state of given substances. Its value indicates the extent of thixotropy and anti-thixotropy with positive and negative order respectively.
Attenuation of Rayleigh Surface Waves in a Porous Material
DEBBOUB Salima; BOUMA(I)ZA Youcef; BOUDOUR Amar; TAHRAOUI Tarek
2012-01-01
Using acoustic microscopy at higher frequency,we show the velocity evolutions of surface acoustic waves,in particular Rayleigh waves that depend on porosity for a mesoporous silicon layer.The velocities are obtained from different V(z) curves,which are determined experimentally at a frequency of 600MHz.The analysis of V(z) data yields attenuation that is directly dependent on porosity.On the other hand,αN attenuation has been modeled and allows us to investigate its influence on the velocity VR of the propagation for Rayleigh waves.%Using acoustic microscopy at higher frequency, we show the velocity evolutions of surface acoustic waves, in particular Rayleigh waves that depend on porosity for a mesoporous silicon layer. The velocities are obtained from different V(z) curves, which are determined experimentally at a frequency of 600 MHz. The analysis of V(z) data yields attenuation that is directly dependent on porosity. On the other hand, αN attenuation has been modeled and allows us to investigate its influence on the velocity VR of the propagation for Rayleigh waves.
叶昆; 李黎; 唐家祥
2003-01-01
Viscoelastic dampers, as supplementary energy dissipation devices, have been used in building structures under seismic excitation or wind loads. Different analytical models have been proposed to describe their dynamic force deformation characteristics. Among these analytical models, the fractional derivative models have attracted more attention as they can capture the frequency dependence of the material stiffness and damping properties observed from tests very well. In this paper, a Fourier-transform-based technique is presented to obtain the fractional unit impulse function and the response of structures with added viscoelastic dampers whose force-deformation relationship is described by a fractional derivative model. Then, a Duhamel integral-type expression is suggested for the response analysis of a fractional damped dynamic system subjected to deterministic or random excitation. Through numerical verification, it is shown that viscoelastic dampers are effective in reducing structural responses over a wide frequency range, and the proposed schemes can be used to accurately predict the stochastic seismic response of structures with added viscoelastic dampers described by a Kelvin model with fractional derivative.
Human intake fraction of toxic pollutants: a model comparison between caltox and uses-lca
Huijbregts, Mark A.J.; Geelen, Loes M.J.; Hertwich, Edgar G.; McKone, Thomas E.; van de Meent, Dik
2004-01-06
In Life Cycle Assessment and Comparative Risk Assessment potential human exposure to toxic pollutants can be expressed as the human intake fraction (iF), representing the fraction of the quantity emitted that enters the human population. To assess model uncertainty in the human intake fraction, ingestion and inhalation iFs of 367 substances emitted to air and freshwater were calculated with two commonly applied multi-media fate and exposure models, CalTOX and USES-LCA. Comparison of the model outcomes reveal that uncertainty in the ingestion iFs was up to a factor of 70. The uncertainty in the inhalation iFs was up to a factor of 865,000. The comparison showed that relatively few model differences account for the uncertainties found. An optimal model structure in the calculation of human intake fractions can be achieved by including (1) rain and no-rain scenarios, (2) a continental sea water compartment, (3) drinking water purification, (4) pH-correction of chemical properties, and (5) aerosol-associated deposition on plants. Finally, vertical stratification of the soil compartment combined with a chemical-dependent soil depth may be considered in future intake fraction calculations.
Retrieval of Rayleigh Wave Ellipticity from Ambient Vibration Recordings
Maranò, Stefano; Hobiger, Manuel; Fäh, Donat
2017-01-01
The analysis of ambient vibrations is a useful tool in microzonation and geotechnical investigations. Ambient vibrations are composed to a large part of surface waves, both Love and Rayleigh waves. One reason to analyse surface waves is that they carry information about the subsurface. The dispersion curve of Rayleigh waves and Love waves can be retrieved using array processing techniques. The Rayleigh wave ellipticity, including the sense of rotation of the particle motion, can also be retrieved using array techniques. These quantities are used in an inversion procedure aimed at obtaining a structural model of the subsurface. The focus of this work is the retrieval of Rayleigh wave ellipticity. We show applications of the (ML) method presented in Maranó et al. (2012) to a number of sites in Switzerland. The sites examined are chosen to reflect a wide range of soil conditions that are of interest in microzonation studies. Using a synthetic wavefield with known structural model, we compare our results with theoretical ellipticity curves and we show the accuracy of the considered algorithm. The sense of rotation of the particle motion (prograde vs. retrograde) is also estimated. In addition, we show that by modelling the presence of both Love and Rayleigh waves it is possible to mitigate the disruptive influence of Love waves on the estimation of Rayleigh wave ellipticity. Using recordings from several real sites, we show that it is possible to retrieve the ellipticity curve over a broad range of frequencies. Fundamental modes and higher modes are retrieved. Singularities of the ellipticity, corresponding to a change of the sense of rotation from prograde to retrograde (or vice versa), are detected with great accuracy. Knowledge of Rayleigh wave ellipticity, including the sense of rotation, is useful in several ways. The ellipticity angle allows us to pinpoint accurately the frequency of singularities (i.e., peaks and zeros of the H/V representation of the
Tapiero, Charles S.; Vallois, Pierre
2016-11-01
The premise of this paper is that a fractional probability distribution is based on fractional operators and the fractional (Hurst) index used that alters the classical setting of random variables. For example, a random variable defined by its density function might not have a fractional density function defined in its conventional sense. Practically, it implies that a distribution's granularity defined by a fractional kernel may have properties that differ due to the fractional index used and the fractional calculus applied to define it. The purpose of this paper is to consider an application of fractional calculus to define the fractional density function of a random variable. In addition, we provide and prove a number of results, defining the functional forms of these distributions as well as their existence. In particular, we define fractional probability distributions for increasing and decreasing functions that are right continuous. Examples are used to motivate the usefulness of a statistical approach to fractional calculus and its application to economic and financial problems. In conclusion, this paper is a preliminary attempt to construct statistical fractional models. Due to the breadth and the extent of such problems, this paper may be considered as an initial attempt to do so.
Forecasting daily political opinion polls using the fractionally cointegrated VAR model
Nielsen, Morten Ørregaard; Shibaev, Sergei S.
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......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...... 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...
Shiqian Nie
2017-01-01
Full Text Available The fractional advection-diffusion equation (fADE model is a new approach to describe the vertical distribution of suspended sediment concentration in steady turbulent flow. However, the advantages and parameter definition of the fADE model in describing the sediment suspension distribution are still unclear. To address this knowledge gap, this study first reviews seven models, including the fADE model, for the vertical distribution of suspended sediment concentration in steady turbulent flow. The fADE model, among others, describes both Fickian and non-Fickian diffusive characteristics of suspended sediment, while the other six models assume that the vertical diffusion of suspended sediment follows Fick’s first law. Second, this study explores the sensitivity of the fractional index of the fADE model to the variation of particle sizes and sediment settling velocities, based on experimental data collected from the literatures. Finally, empirical formulas are developed to relate the fractional derivative order to particle size and sediment settling velocity. These formulas offer river engineers a substitutive way to estimate the fractional derivative order in the fADE model.
Ørregård Nielsen, Morten
2015-01-01
This article 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...
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...
Atangana Abdon
2016-01-01
Full Text Available In this manuscript we proposed a new fractional derivative with non-local and no-singular kernel. We presented some useful properties of the new derivative and applied it to solve the fractional heat transfer model.
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
Tuning algorithms for fractional order internal model controllers for time delay processes
Muresan, Cristina I.; Dutta, Abhishek; Dulf, Eva H.; Pinar, Zehra; Maxim, Anca; Ionescu, Clara M.
2016-03-01
This paper presents two tuning algorithms for fractional-order internal model control (IMC) controllers for time delay processes. The two tuning algorithms are based on two specific closed-loop control configurations: the IMC control structure and the Smith predictor structure. In the latter, the equivalency between IMC and Smith predictor control structures is used to tune a fractional-order IMC controller as the primary controller of the Smith predictor structure. Fractional-order IMC controllers are designed in both cases in order to enhance the closed-loop performance and robustness of classical integer order IMC controllers. The tuning procedures are exemplified for both single-input-single-output as well as multivariable processes, described by first-order and second-order transfer functions with time delays. Different numerical examples are provided, including a general multivariable time delay process. Integer order IMC controllers are designed in each case, as well as fractional-order IMC controllers. The simulation results show that the proposed fractional-order IMC controller ensures an increased robustness to modelling uncertainties. Experimental results are also provided, for the design of a multivariable fractional-order IMC controller in a Smith predictor structure for a quadruple-tank system.
Sarah Malec
2015-09-01
Full Text Available Soil erosion can be linked to relative fractional cover of photosynthetic-active vegetation (PV, non-photosynthetic-active vegetation (NPV and bare soil (BS, which can be integrated into erosion models as the cover-management C-factor. This study investigates the capability of EnMAP imagery to map fractional cover in a region near San Jose, Costa Rica, characterized by spatially extensive coffee plantations and grazing in a mountainous terrain. Simulated EnMAP imagery is based on airborne hyperspectral HyMap data. Fractional cover estimates are derived in an automated fashion by extracting image endmembers to be used with a Multiple End-member Spectral Mixture Analysis approach. The C-factor is calculated based on the fractional cover estimates determined independently for EnMAP and HyMap. Results demonstrate that with EnMAP imagery it is possible to extract quality endmember classes with important spectral features related to PV, NPV and soil, and be able to estimate relative cover fractions. This spectral information is critical to separate BS and NPV which greatly can impact the C-factor derivation. From a regional perspective, we can use EnMAP to provide good fractional cover estimates that can be integrated into soil erosion modeling.
Isotropic model of fractional transport in two-dimensional bounded domains.
Kullberg, A; del-Castillo-Negrete, D; Morales, G J; Maggs, J E
2013-05-01
A two-dimensional fractional Laplacian operator is derived and used to model nonlocal, nondiffusive transport. This integro-differential operator appears in the long-wavelength, fluid description of quantities undergoing non-Brownian random walks without characteristic length scale. To study bounded domains, a mask function is introduced that modifies the kernel in the fractional Laplacian and removes singularities at the boundary. Green's function solutions to the fractional diffusion equation are presented for the unbounded domain and compared to the one-dimensional Cartesian approximations. A time-implicit numerical integration scheme is presented to study fractional diffusion in a circular disk with azimuthal symmetry. Numerical studies of steady-state reveal temperature profiles in which the heat flux and temperature gradient are in the same direction, i.e., uphill transport. The response to off-axis heating, scaling of confinement time with system size, and propagation of cold pulses are investigated.
Fractionations of rare earth elements in plants and their conceptive model
2007-01-01
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.
The Rayleigh-Stokes problem for an edge in a generalized Oldroyd-B fluid
Fetecau, Corina; Jamil, Muhammad; Fetecau, Constantin; Vieru, Dumitru
2009-09-01
The velocity field corresponding to the Rayleigh-Stokes problem for an edge, in an incompressible generalized Oldroyd-B fluid has been established by means of the double Fourier sine and Laplace transforms. The fractional calculus approach is used in the constitutive relationship of the fluid model. The obtained solution, written in terms of the generalized G-functions, is presented as a sum of the Newtonian solution and the corresponding non-Newtonian contribution. The solution for generalized Maxwell fluids, as well as those for ordinary Maxwell and Oldroyd-B fluids, performing the same motion, is obtained as a limiting case of the present solution. This solution can be also specialized to give the similar solution for generalized second grade fluids. However, for simplicity, a new and simpler exact solution is established for these fluids. For β → 1, this last solution reduces to a previous solution obtained by a different technique.
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.
Sudden spreading of infections in an epidemic model with a finite seed fraction
Hasegawa, Takehisa
2016-01-01
We study a simple case of the susceptible-weakened-infected-removed model in regular random graphs in a situation where an epidemic starts from a finite fraction of initially infected nodes (seeds). Previous studies have shown that, assuming a single seed, this model exhibits a kind of discontinuous transition at a certain value of infection rate. Performing Monte Carlo simulations and evaluating approximate master equations, we find that the present model has two critical infection rates with a finite seed fraction. At the first critical rate the system shows a percolation transition of clusters composed of removed nodes, and at the second critical rate, which is larger than the first one, a giant cluster suddenly grows and the order parameter jumps even though it has been already rising. Numerical evaluation of the master equations shows that such sudden epidemic spreading does occur if the degree of the underlying network is large and the seed fraction is small.
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.
A fractional order model for lead-acid battery crankability estimation
Sabatier, J.; Cugnet, M.; Laruelle, S.; Grugeon, S.; Sahut, B.; Oustaloup, A.; Tarascon, J. M.
2010-05-01
With EV and HEV developments, battery monitoring systems have to meet the new requirements of car industry. This paper deals with one of them, the battery ability to start a vehicle, also called battery crankability. A fractional order model obtained by system identification is used to estimate the crankability of lead-acid batteries. Fractional order modelling permits an accurate simulation of the battery electrical behaviour with a low number of parameters. It is demonstrated that battery available power is correlated to the battery crankability and its resistance. Moreover, the high-frequency gain of the fractional model can be used to evaluate the battery resistance. Then, a battery crankability estimator using the battery resistance is proposed. Finally, this technique is validated with various battery experimental data measured on test rigs and vehicles.
Model for computation of solar fraction in a single-slope solar still
Madhlopa, A.; Johnstone, C. [Energy Systems Research Unit, Department of Mechanical Engineering, University of Strathclyde, 75 Montrose Street, Glasgow G1 1XJ (United Kingdom)
2009-06-15
A new model that calculates the distribution of solar radiation inside a single-slope solar still has been proposed. In this model, the solar fraction on a vertical surface is divided into beam and diffuse parts and the optical view factors of surfaces inside the still are taken into account. To validate the model, outdoor tests of a conventional solar still were conducted under different weather conditions at the University of Strathclyde. The proposed model is compared with the previous one. It is found that the beam solar fraction is affected by both the geometry of the solar still and position of the sun in the sky. In contrast, the diffuse solar fraction is only dependent on the geometry of the solar distiller. The present model exhibited a lower root mean square error than that of the previous model. It appears that splitting the solar fraction into beam and diffuse parts improves the accuracy of modelling the performance of a single-slope solar still. (author)
Kaur, A; Takhar, P S; Smith, D M; Mann, J E; Brashears, M M
2008-10-01
A fractional differential equations (FDEs)-based theory involving 1- and 2-term equations was developed to predict the nonlinear survival and growth curves of foodborne pathogens. It is interesting to note that the solution of 1-term FDE leads to the Weibull model. Nonlinear regression (Gauss-Newton method) was performed to calculate the parameters of the 1-term and 2-term FDEs. The experimental inactivation data of Salmonella cocktail in ground turkey breast, ground turkey thigh, and pork shoulder; and cocktail of Salmonella, E. coli, and Listeria monocytogenes in ground beef exposed at isothermal cooking conditions of 50 to 66 degrees C were used for validation. To evaluate the performance of 2-term FDE in predicting the growth curves-growth of Salmonella typhimurium, Salmonella Enteritidis, and background flora in ground pork and boneless pork chops; and E. coli O157:H7 in ground beef in the temperature range of 22.2 to 4.4 degrees C were chosen. A program was written in Matlab to predict the model parameters and survival and growth curves. Two-term FDE was more successful in describing the complex shapes of microbial survival and growth curves as compared to the linear and Weibull models. Predicted curves of 2-term FDE had higher magnitudes of R(2) (0.89 to 0.99) and lower magnitudes of root mean square error (0.0182 to 0.5461) for all experimental cases in comparison to the linear and Weibull models. This model was capable of predicting the tails in survival curves, which was not possible using Weibull and linear models. The developed model can be used for other foodborne pathogens in a variety of food products to study the destruction and growth behavior.
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-type parametric chemical oscillation
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.
Anelastic Rayleigh-Taylor mixing layers
Schneider, N.; Gauthier, S.
2016-07-01
Anelastic Rayleigh-Taylor mixing layers for miscible fluids are investigated with a recently built model (Schneider and Gauthier 2015 J. Eng. Math. 92 55-71). Four Chebyshev-Fourier-Fourier direct numerical simulations are analyzed. They use different values for the compressibility parameters: Atwood number (the dimensionless difference of the heavy and light fluid densities) and stratification (accounts for the vertical variation of density due to gravity). For intermediate Atwood numbers and finite stratification, compressibility effects quickly occurs. As a result only nonlinear behaviours are reached. The influence of the compressibility parameters on the growth speed of the RTI is discussed. The 0.1—Atwood number/0.4—stratification configuration reaches a turbulent regime. This turbulent mixing layer is analyzed with statistical tools such as moments, PDFs, anisotropy indicators and spectra.
HYGROSCOPIC MOISTURE SORPTION KINETICS MODELING OF CORN STOVER AND ITS FRACTIONS
Igathinathane, C. [Mississippi State University (MSU); Pordesimo, L. O. [Mississippi State University (MSU); Womac, A.R. [University of Tennessee; Sokhansanj, Shahabaddine [ORNL
2009-01-01
Corn stover, a major crop-based lignocellulosic biomass feedstock, is required to be at an optimum moisture content for efficient bioconversion processes. Environmental conditions surrounding corn stover, as in storage facilities, affect its moisture due to hygroscopic sorption or desorption. The measurement and modeling of sorption characteristics of corn stover and its leaf, husk, and stalk fractions are useful from utilization and storage standpoints, hence investigated in this article. A benchtop low-temperature humidity chamber provided the test environments of 20 C, 30 C, and 40 C at a constant 95% relative humidity. Measured sorption characteristics with three replications for each fraction were obtained from instantaneous sample masses and initial moisture contents. Observed sorption characteristics were fitted using exponential, Page, and Peleg models. Corn stover fractions displayed a rapid initial moisture uptake followed by a slower sorption rates and eventually becoming almost asymptotic after 25 h. Sorption characteristics of all corn stover fractions were significantly different (P < 0.0001) but not the effect of temperature (P > 0.05) on these fractions. The initial 30 min of sorption was found to be critical due to peak rates of sorption from storage, handling, and processing standpoints. The Page and Peleg models had comparable performance fitting the sorption curves (R2 = 0.995), however the exponential model (R2 = 0.91) was not found suitable because of patterned residuals. The Arrhenius type relationship (P < 0.05; R2 = 0.80) explained the temperature variation of the fitted sorption model parameters. The Peleg model fitted constants, among the sorption models studied, had the best fit (R2 = 0.93) with the Arrhenius relationship. A developed method of mass proportion, involving individual corn stover fraction dry matter ratios, predicted the whole corn stover sorption characteristics from that of its individual fractions. Sorption
Ali, Farhad; Sheikh, Nadeem Ahmad; Khan, Ilyas; Saqib, Muhammad
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.
Comlekoglu, T.; Weinberg, S. H.
2017-09-01
Cardiac memory is the dependence of electrical activity on the prior history of one or more system state variables, including transmembrane potential (Vm), ionic current gating, and ion concentrations. While prior work has represented memory either phenomenologically or with biophysical detail, in this study, we consider an intermediate approach of a minimal three-variable cardiomyocyte model, modified with fractional-order dynamics, i.e., a differential equation of order between 0 and 1, to account for history-dependence. Memory is represented via both capacitive memory, due to fractional-order Vm dynamics, that arises due to non-ideal behavior of membrane capacitance; and ionic current gating memory, due to fractional-order gating variable dynamics, that arises due to gating history-dependence. We perform simulations for varying Vm and gating variable fractional-orders and pacing cycle length and measure action potential duration (APD) and incidence of alternans, loss of capture, and spontaneous activity. In the absence of ionic current gating memory, we find that capacitive memory, i.e., decreased Vm fractional-order, typically shortens APD, suppresses alternans, and decreases the minimum cycle length (MCL) for loss of capture. However, in the presence of ionic current gating memory, capacitive memory can prolong APD, promote alternans, and increase MCL. Further, we find that reduced Vm fractional order (typically less than 0.75) can drive phase 4 depolarizations that promote spontaneous activity. Collectively, our results demonstrate that memory reproduced by a fractional-order model can play a role in alternans formation and pacemaking, and in general, can greatly increase the range of electrophysiological characteristics exhibited by a minimal model.
Emile Franc Doungmo Goufo
2014-01-01
Full Text Available Until now, classical models of clusters’ fission remain unable to fully explain strange phenomena like the phenomenon of shattering (Ziff and McGrady, 1987 and the sudden appearance of infinitely many particles in some systems having initial finite number of particles. That is why there is a need to extend classical models to models with fractional derivative order and use new and various techniques to analyze them. In this paper, we prove the existence of strongly continuous solution operators for nonlocal fragmentation models with Michaud time derivative of fractional order (Samko et al., 1993. We focus on the case where the splitting rate is dependent on size and position and where new particles generating from fragmentation are distributed in space randomly according to some probability density. In the analysis, we make use of the substochastic semigroup theory, the subordination principle for differential equations of fractional order (Prüss, 1993, Bazhlekova, 2000, the analogy of Hille-Yosida theorem for fractional model (Prüss, 1993, and useful properties of Mittag-Leffler relaxation function (Berberan-Santos, 2005. We are then able to show that the solution operator to the full model is positive and contractive.
Bo Yu
2013-01-01
Full Text Available The authors present a fractional anomalous diffusion model to describe the uptake of sodium ions across the epithelium of gastrointestinal mucosa and their subsequent diffusion in the underlying blood capillaries using fractional Fick’s law. A heterogeneous two-phase model of the gastrointestinal mucosa is considered, consisting of a continuous extracellular phase and a dispersed cellular phase. The main mode of uptake is considered to be a fractional anomalous diffusion under concentration gradient and potential gradient. Appropriate partial differential equations describing the variation with time of concentrations of sodium ions in both the two phases across the intestinal wall are obtained using Riemann-Liouville space-fractional derivative and are solved by finite difference methods. The concentrations of sodium ions in the interstitial space and in the cells have been studied as a function of time, and the mean concentration of sodium ions available for absorption by the blood capillaries has also been studied. Finally, numerical results are presented graphically for various values of different parameters. This study demonstrates that fractional anomalous diffusion model is appropriate for describing the uptake of sodium ions across the epithelium of gastrointestinal mucosa.
Importance sampling the Rayleigh phase function
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. Thi....... 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.......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...
A comparative analysis of radiobiological models for cell surviving fractions at high doses.
Andisheh, B; Edgren, M; Belkić, Dž; Mavroidis, P; Brahme, A; Lind, B K
2013-04-01
For many years the linear-quadratic (LQ) model has been widely used to describe the effects of total dose and dose per fraction at low-to-intermediate doses in conventional fractionated radiotherapy. Recent advances in stereotactic radiosurgery (SRS) and stereotactic radiotherapy (SRT) have increased the interest in finding a reliable cell survival model, which will be accurate at high doses, as well. Different models have been proposed for improving descriptions of high dose survival responses, such as the Universal Survival Curve (USC), the Kavanagh-Newman (KN) and several generalizations of the LQ model, e.g. the Linear-Quadratic-Linear (LQL) model and the Pade Linear Quadratic (PLQ) model. The purpose of the present study is to compare a number of models in order to find the best option(s) which could successfully be used as a fractionation correction method in SRT. In this work, six independent experimental data sets were used: CHOAA8 (Chinese hamster fibroblast), H460 (non-small cell lung cancer, NSLC), NCI-H841 (small cell lung cancer, SCLC), CP3 and DU145 (human prostate carcinoma cell lines) and U1690 (SCLC). By detailed comparisons with these measurements, the performance of nine different radiobiological models was examined for the entire dose range, including high doses beyond the shoulder of the survival curves. Using the computed and measured cell surviving fractions, comparison of the goodness-of-fit for all the models was performed by means of the reduced χ (2)-test with a 95% confidence interval. The obtained results indicate that models with dose-independent final slopes and extrapolation numbers generally represent better choices for SRT. This is especially important at high doses where the final slope and extrapolation numbers are presently found to play a major role. The PLQ, USC and LQL models have the least number of shortcomings at all doses. The extrapolation numbers and final slopes of these models do not depend on dose. Their asymptotes
Coil fraction-dependent phase behaviour of a model globular protein–polymer diblock copolymer
Thomas, Carla S. [MIT (Massachusetts Inst. of Technology), Cambridge, MA (United States); Olsen, Bradley D. [MIT (Massachusetts Inst. of Technology), Cambridge, MA (United States)
2014-01-01
The self-assembly of the model globular protein–polymer block copolymer mCherry-b-poly(N-isopropyl acrylamide) is explored across a range of polymer coil fractions from 0.21 to 0.82 to produce a phase diagram for these materials as a function of molecular composition. Overall, four types of morphologies were observed: hexagonally packed cylinders, perforated lamellae, lamellae, and disordered nanostructures. Across all coil fractions and morphologies, a lyotropic re-entrant order–disorder transition in water was observed, with disordered structures below 30 wt% and above 70 wt% and well-ordered morphologies at intermediate concentrations. Solid state samples prepared by solvent evaporation show moderately ordered structures similar to those observed in 60 wt% solutions, suggesting that bulk structures result from kinetic trapping of morphologies which appear at lower concentrations. While highly ordered cylindrical nanostructures are observed around a bioconjugate polymer volume fraction of 0.3 and well-ordered lamellae are seen near a volume fraction of 0.6, materials at lower or higher coil fractions become increasingly disordered. Notable differences between the phase behaviour of globular protein–polymer block copolymers and coil–coil diblock copolymers include the lack of spherical nanostructures at either high or low polymer coil fractions as well as shifted phase boundaries between morphologies which result in an asymmetric phase diagram.
Juraske, R; Antón, A; Castells, F; Huijbregts, M A J
2007-04-01
Human intake due to pesticide residues in food commodities can be much higher than those related to water consumption and air inhalation, stressing the importance to correctly estimate pesticide uptake into plants and predict subsequent intake by humans. We calculated the human intake fraction of captan via tomato consumption taking into account the time between pesticide application and harvest, the time between harvest and consumption, the absorption of spray deposit on plant surfaces, transfer properties through the cuticle, degradation inside the plant and loss due to food processing. Human population intake fractions due to ingestion were calculated for complete, washed and peeled tomatoes. The calculated intake fractions were compared with measurements derived from an experimental setup in a Mediterranean greenhouse. The fraction of captan applied in the greenhouse as plant treatment that eventually is ingested by the human population is on average 10(-2)-10(-5), depending on the time between pesticide application and ingestion of tomatoes and the processing step considered. Model and experimentally derived intake fractions deviated less than a factor of 2 for complete and washed tomatoes and a factor of 3 for peeled tomatoes. Intake fractions due to air inhalation and consumption of drinking water are expected to be significantly lower (5-9 orders of magnitude) than those induced by the intake of tomatoes in this case study.
Andrew McAloon
2011-12-01
Full Text Available An economical and environmentally friendly whey protein fractionation process was developed using supercritical carbon dioxide (sCO2 as an acid to produce enriched fractions of α-lactalbumin (α-LA and β-lactoglobulin (β-LG from a commercial whey protein isolate (WPI containing 20% α-LA and 55% β-LG, through selective precipitation of α-LA. Pilot-scale experiments were performed around the optimal parameter range (T = 60 to 65 °C, P = 8 to 31 MPa, C = 5 to 15% (w/w WPI to quantify the recovery rates of the individual proteins and the compositions of both fractions as a function of processing conditions. Mass balances were calculated in a process flow-sheet to design a large-scale, semi-continuous process model using SuperproDesigner® software. Total startup and production costs were estimated as a function of processing parameters, product yield and purity. Temperature, T, pressure, P, and concentration, C, showed conflicting effects on equipment costs and the individual precipitation rates of the two proteins, affecting the quantity, quality, and production cost of the fractions considerably. The highest α-LA purity, 61%, with 80% α-LA recovery in the solid fraction, was obtained at T = 60 °C, C = 5% WPI, P = 8.3 MPa, with a production cost of $8.65 per kilogram of WPI treated. The most profitable conditions resulted in 57%-pure α-LA, with 71% α-LA recovery in the solid fraction and 89% β-LG recovery in the soluble fraction, and production cost of $5.43 per kilogram of WPI treated at T = 62 °C, C = 10% WPI and P = 5.5 MPa. The two fractions are ready-to-use, new food ingredients with a pH of 6.7 and contain no residual acid or chemical contaminants.
Effective-field-theory model for the fractional quantum Hall effect
Zhang, S. C.; Hansson, T. H.; Kivelson, S.
1989-01-01
Starting directly from the microscopic Hamiltonian, a field-theory model is derived for the fractional quantum Hall effect. By considering an approximate coarse-grained version of the same model, a Landau-Ginzburg theory similar to that of Girvin (1986) is constructed. The partition function of the model exhibits cusps as a function of density. It is shown that the collective density fluctuations are massive.
Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media
Wenwen Zhong
2013-01-01
Full Text Available Numerical simulation of two-phase flow in fractured porous media is an important topic in the subsurface flow, environmental problems, and petroleum reservoir engineering. The conventional model does not work well in many cases since it lacks the memory property of fracture media. In this paper, we develop a new numerical formulation with fractional time derivative for two-phase flow in fractured porous media. In the proposed formulation, the different fractional time derivatives are applied to fracture and matrix regions since they have different memory properties. We further develop a two-level time discrete method, which uses a large time step for the pressure and a small time step size for the saturation. The pressure equation is solved implicitly in each large time step, while the saturation is updated by an explicit fractional time scheme in each time substep. Finally, the numerical tests are carried out to demonstrate the effectiveness of the proposed numerical model.
Fractional-order mathematical model of an irrigation main canal pool
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.
Development of a three dimensional circulation model based on fractional step method
Abualtayef, Mazen; Kuroiwa, Masamitsu; Seif, Ahmed Khaled; Matsubara, Yuhei; Aly, Ahmed M.; Sayed, Ahmed A.; Sambe, Alioune Nar
2010-03-01
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.
Fractional Modeling of the AC Large-Signal Frequency Response in Magnetoresistive Current Sensors
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.
Bayesian bivariate generalized Lindley model for survival data with a cure fraction.
Martinez, Edson Z; Achcar, Jorge A
2014-11-01
The cure fraction models have been widely used to analyze survival data in which a proportion of the individuals is not susceptible to the event of interest. In this article, we introduce a bivariate model for survival data with a cure fraction based on the three-parameter generalized Lindley distribution. The joint distribution of the survival times is obtained by using copula functions. We consider three types of copula function models, the Farlie-Gumbel-Morgenstern (FGM), Clayton and Gumbel-Barnett copulas. The model is implemented under a Bayesian framework, where the parameter estimation is based on Markov Chain Monte Carlo (MCMC) techniques. To illustrate the utility of the model, we consider an application to a real data set related to an invasive cervical cancer study.
Jazia, Abderrahmin Ben; Bellis, Cédric
2013-01-01
This study focuses on the numerical modeling of wave propagation in fractionally-dissipative media. These viscoelastic models are such that the attenuation is frequency dependent and follows a power law with non-integer exponent. As a prototypical example, the Andrade model is chosen for its simplicity and its satisfactory fits of experimental flow laws in rocks and metals. The corresponding constitutive equation features a fractional derivative in time, a non-local term that can be expressed as a convolution product which direct implementation bears substantial memory cost. To circumvent this limitation, a diffusive representation approach is deployed, replacing the convolution product by an integral of a function satisfying a local time-domain ordinary differential equation. An associated quadrature formula yields a local-in-time system of partial differential equations, which is then proven to be well-posed. The properties of the resulting model are also compared to those of the original Andrade model. The...
Su, Qian; Tan, Chao; Dong, Feng
2017-03-01
When measuring the phase fraction of oil–water two-phase flow with the ultrasound attenuation, the phase distribution and fraction have direct influence on the attenuation coefficient. Therefore, the ultrasound propagation at various phase fractions and distributions were investigated. Mechanism models describing phase fraction with the ultrasound attenuation coefficient were established by analyzing the interaction between ultrasound and two-phase flow by considering the scattering, absorption and diffusion effect. Experiments were performed to verify the theoretical analysis, and the test results gave good agreement with the theoretical analysis. When the dispersed phase fraction is low, the relationship between ultrasound attenuation coefficient and phase fraction is of monotonic linearity; at higher dispersed phase fraction, ultrasound attenuation coefficient presents an irregular response to the dispersed phase fraction. The presented mechanism models give reasonable explanations about the trend of ultrasound attenuation.
DEVELOPMENT OF A POPULATION BALANCE MODEL TO SIMULATE FRACTIONATION OF GROUND SWITCHGRASS
Naimi, L.J. [University of British Columbia, Vancouver; Bi, X.T. [University of British Columbia, Vancouver; Lau, A.K. [University of British Columbia, Vancouver; Sokhansanj, Shahabaddine [ORNL; Womac, A.R. [University of Tennessee, Knoxville (UTK); Igathinathane, C. [North Dakota State University; Sowlati, T. [University of British Columbia, Vancouver; Melin, Staffan [Delta Research Corporation; Emami, M. [University of British Columbia, Vancouver; Afzal, M [University of New Brunswick
2011-01-01
The population balance model represents a time-dependent formulation of mass conservation for a ground biomass that flows through a set of sieves. The model is suitable for predicting the change in size and distribution of ground biomass while taking into account the flow rate processes of particles through a grinder. This article describes the development and application of this model to a switchgrass grinding operation. The mass conservation formulation of the model contains two parameters: breakage rate and breakage ratio. A laboratory knife mill was modified to act as a batch or flow-through grinder. The ground switchgrass was analyzed over a set of six Tyler sieves with apertures ranging from 5.66 mm (top sieve) to 1 mm (bottom sieve). The breakage rate was estimated from the sieving tests. For estimating the breakage ratio, each of the six fractions was further ground and sieved to 11 fractions on a set of sieves with apertures ranging from 5.66 to 0.25 mm (and pan). These data formed a matrix of values for determining the breakage ratio. Using the two estimated parameters, the transient population balance model was solved numerically. Results indicated that the population balance model generally underpredicted the fractions remaining on sieves with 5.66, 4.00, and 2.83 mm apertures and overpredicted fractions remaining on sieves with 2.00, 1.41, and 1.00 mm apertures. These trends were similar for both the batch and flow-through grinder configurations. The root mean square of residuals (RSE), representing the difference between experimental and simulated mass of fractions, was 0.32 g for batch grinding and 0.1 g for flow-through grinding. The breakage rate exhibited a linear function of the logarithm of particle size, with a regression coefficient of 0.99.
Freed, Alan D.; Diethelm, Kai; Gray, Hugh R. (Technical Monitor)
2002-01-01
Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.
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…
The role of initial values in nonstationary fractional time series models
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...
The Solution of Modified Fractional Bergman’s Minimal Blood Glucose-Insulin Model
Badr S. Alkahtani
2017-05-01
Full Text Available In the present paper, we use analytical techniques to solve fractional nonlinear differential equations systems that arise in Bergman’s minimal model, used to describe blood glucose and insulin metabolism, after intravenous tolerance testing. We also discuss the stability and uniqueness of the solution.
Longère, Patrice; Dragon, A. André
2008-01-01
Evaluation of the inelastic heat fraction in the context of microstructure supported dynamic plasticity modelling correspondence: Corresponding author. (Longere, Patrice) (Longere, Patrice) (Dragon, A. Andre) Laboratoire de Genie Mecanique et Materiaux ? Universite de Bretagne Sud ? Rue de Saint-Maude - BP 92116--> , 56321 LORIENT Cedex--> - FRANCE (Longere, Patrice)...
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…
Asymptotic Solution to the Rayleigh Problem of Dynamic Soaring
Bousquet, Gabriel D; Slotine, Jean-Jacques E
2015-01-01
It is believed that albatrosses power their flight through dynamic soaring, a technique where energy is extracted from horizontally blowing shear winds. The Rayleigh model of dynamic soaring, also called the two layer model, makes a 2-dimensional approximation of the wind field and glider trajectory. This note considers the "Rayleigh problem" of finding the minimum wind necessary for the existence of energy neutral gliding cycles. We utilize a 3-degree of freedom glider model with quadratic drag. Asymptotic solutions in the limit of large glide ratios are obtained. The optimal motion is a traveling trajectory constituted of a succession of small partial turns. It is over 50% more efficient at preserving airspeed than full half-turn based trajectories.
Momentum Fractions carried by quarks and gluons in models of proton structure functions at small $x$
Choudhury, D K; Kalita, K
2016-01-01
The paper reports analysis of momentum fractions carried by quarks and gluons in models of Proton structure functions at small $x$. First, we analyze the model proposed by Lastovicka based on self-similarity sometime back. We then make a similar analysis for a second model based on the same notion which is also free from singularity in $x$ : $0
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.
Mao, Haidan; Du, Xinyue; Chen, Linfei; Zhao, Daomu
2011-06-01
On the basis of the fact that a hard-edged aperture function can be expressed as finite matrices with different weighting coefficients, we obtain the analytical formula for the propagation of the broadband gaussian Schell-model (BGSM) beam through the apertured fractional Fourier transformation (AFrFT) system. It is shown by numerical examples that the intensity distribution in the plane of a small fractional order is obviously influenced by the bandwidth when the BGSM beams propagate through the AFrFT system. Further extensions are also pointed out.
Impact of Model and Observation Error on Assimilating Snow Cover Fraction Observations
Arsenault, Kristi R.
Accurately modeling or observing snow cover fraction (SCF) estimates, which represent fractional snow cover area within a gridcell, can help with better understanding earth system dynamics, improving weather and climate prediction, and providing end-use water solutions. Seeking to obtain more accurate snowpack estimates, high resolution snow cover fraction observations are assimilated with different data assimilation (DA) methods within a land surface model (LSM). The LSM simulates snowpack states, snow water equivalent and snow depth, to obtain improved snowpack estimates known as the analysis. Data assimilation experiments are conducted for two mountainous areas where high spatial snow variability occurs, which can impact realistic snowpack representation for different hydrological and meteorological applications. Consequently, the experiments are conducted at higher model resolutions to better capture this variability. This study focuses on four key aspects of how assimilating SCF observations may improve snowpack estimates and impact the LSM overall. These include investigating the role of data assimilation method complexity, evaluating the impact of model and observational errors on snow state analysis estimates, improving the model's SCF representation for assimilation using observation operators, and examining subsequent model state and flux impacts when SCF observations are assimilated. A simpler direct insertion (DI) and a more complex ensemble Kalman filter (EnKF) data assimilation method were applied. The more complex method proved to be superior to the simpler one; however, this method required accounting for more realistic observational and model errors. Also, the EnKF method required an ensemble of model forecasts, in which bias in the ensemble generation was found and removed. Reducing this bias improved the model snowpack estimates. Detection and geolocation errors in the satellite-based snow cover fraction observations also contributed to degrading
Fractional order Buck-Boost converter in CCM: modelling, analysis and simulations
Wang, Faqiang; Ma, Xikui
2014-12-01
In this paper, the modelling, analysis and the power electronics simulator (PSIM) simulations of the fractional order Buck-Boost converter operating in continuous conduction mode (CCM) operation are investigated. Based on the three-terminal switch device method, the average circuit model of the fractional order Buck-Boost converter is established, and the corresponding DC equivalent circuit model and AC small signal equivalent circuit model are presented. And then, the equilibrium point and the transfer functions are derived. It is found that the equilibrium point is not influenced by the inductor's or the capacitor's order, but both these orders are included in the derived transfer functions. Finally, the comparisons between the theoretical analysis and the PSIM simulations are given for confirmation.
Bouchard, D; Höhener, P; Hunkeler, D; 10.1016/j.jconhyd.2010.09.006
2011-01-01
Analytical models were developed that simulate stable isotope ratios of volatile organic compounds (VOCs) near a point source contamination in the unsaturated zone. The models describe diffusive transport of VOCs, biodegradation and source ageing. The mass transport is governed by Fick's law for diffusion, and the equation for reactive transport of VOCs in the soil gas phase was solved for different source geometries and for different boundary conditions. Model results were compared to experimental data from a one-dimensional laboratory column and a radial-symmetric field experiment, and the comparison yielded a satisfying agreement. The model results clearly illustrate the significant isotope fractionation by gas-phase diffusion under transient state conditions. This leads to an initial depletion of heavy isotopes with increasing distance from the source. The isotope evolution of the source is governed by the combined effects of isotope fractionation due to vaporization, diffusion and biodegradation. The net...
Zhou, H. W.; Yi, H. Y.; Mishnaevsky, Leon
2016-01-01
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 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....
POLYNOMIAL MODEL BASED FAST FRACTIONAL PIXEL SEARCH ALGORITHM FOR H.264/AVC
Xi Yinglai; Hao Chongyang; Lai Changcai
2006-01-01
This paper proposed a novel fast fractional pixel search algorithm based on polynomial model.With the analysis of distribution characteristics of motion compensation error surface inside fractional pixel searching window, the matching error is fitted with parabola along horizontal and vertical direction respectively. The proposed searching strategy needs to check only 6 points rather than 16 or 24 points, which are used in the Hierarchical Fractional Pel Search algorithm (HFPS) for 1/4-pel and 1/8-pel Motion Estimation (ME). The experimental results show that the proposed algorithm shows very good capability in keeping the rate distortion performance while reduces computation load to a large extent compared with HFPS algorithm.
Treeby, Bradley E; Cox, B T
2010-05-01
The efficient simulation of wave propagation through lossy media in which the absorption follows a frequency power law has many important applications in biomedical ultrasonics. Previous wave equations which use time-domain fractional operators require the storage of the complete pressure field at previous time steps (such operators are convolution based). This makes them unsuitable for many three-dimensional problems of interest. Here, a wave equation that utilizes two lossy derivative operators based on the fractional Laplacian is derived. These operators account separately for the required power law absorption and dispersion and can be efficiently incorporated into Fourier based pseudospectral and k-space methods without the increase in memory required by their time-domain fractional counterparts. A framework for encoding the developed wave equation using three coupled first-order constitutive equations is discussed, and the model is demonstrated through several one-, two-, and three-dimensional simulations.
Modular Data and Verlinde Formulae for Fractional Level WZW Models I
Creutzig, Thomas
2012-01-01
The modular properties of fractional level affine sl(2)-theories and, in particular, the application of the Verlinde formula, have a long and checkered history in conformal field theory. Recent advances in logarithmic conformal field theory have led to the realisation that problems with fractional level models stem from trying to build the theory with an insufficiently rich category of representations. In particular, the appearance of negative fusion coefficients for admissible highest weight representations is now completely understood. Here, the modular story for certain fractional level theories is completed. Modular transformations are derived for the complete set of admissible irreducible representations when the level is k=-1/2 or k=-4/3. The S-matrix data and Verlinde formula are then checked against the known fusion rules with complete agreement. Finally, an infinite set of modular invariant partition functions is constructed in each case.
Maneesha Gupta
2013-01-01
Full Text Available Second and third order digital integrators (DIs have been optimized first using Particle Swarm Optimization (PSO with minimized error fitness function obtained by registering mean, median, and standard deviation values in different random iterations. Later indirect discretization using Continued Fraction Expansion (CFE has been used to ascertain a better fitting of proposed integer order optimized DIs into their corresponding fractional counterparts by utilizing their refined properties, now restored in them due to PSO algorithm. Simulation results for the comparisons of the frequency responses of proposed 2nd and 3rd order optimized DIs and proposed discretized mathematical models of half integrators based on them, with their respective existing operators, have been presented. Proposed integer order PSO optimized integrators as well as fractional order integrators (FOIs have been observed to outperform the existing recently published operators in their respective domains reasonably well in complete range of Nyquist frequency.
Global Existence of Weak Solutions to a Fractional Model in Magnetoelastic Interactions
Idriss Ellahiani
2016-01-01
Full Text Available The paper deals with global existence of weak solutions to a one-dimensional mathematical model describing magnetoelastic interactions. The model is described by a fractional Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We prove global existence by using Faedo-Galerkin/penalty method. Some commutator estimates are used to prove the convergence of nonlinear terms.
Ningning Yang
2016-01-01
Full Text Available In recent days, fractional calculus (FC has been accepted as a novel modeling tool that can extend the descriptive power of the traditional calculus. Fractional-order descriptiveness can increase the flexibility and degrees of freedom of the model by means of fractional parameters. Based on the fact that real capacitors and inductors are “intrinsic” fractional order, fractional calculus is introduced into the modeling process to establish a fractional-order state-space averaging model of the Buck-Boost converter in pseudo-continuous conduction mode (PCCM. Orders of the model are considered as extra parameters, and these parameters have significant influences on the performance of the model. The inductor current, the inductor current ripple, the amplitude of the output voltage, and the transfer functions of the fractional-order model are all related to orders. The contrast simulation experiments are conducted to investigate the performance of integer-order and fractional-order Buck-Boost converters in PCCM. Results of numerical and circuit simulations demonstrate that the proposed theoretical analysis is effective; the fractional-order model of the Buck-Boost converter in PCCM has certain theoretical and practical significance for modeling and performance analysis of other electrical or electronic equipment.
Zhou, H. W.; Yi, H. Y.; Mishnaevsky, L.; Wang, R.; Duan, Z. Q.; Chen, Q.
2016-08-01
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 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, is suggested to characterize the time-dependent behavior of GFRP composites by replacing Newtonian dashpot with the Abel dashpot in the classical Maxwell model. The analytic solution for the fractional derivative Maxwell model is given and the relative parameters are determined. The results estimated 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.
Gabor-based kernel PCA with fractional power polynomial models for face recognition.
Liu, Chengjun
2004-05-01
This paper presents a novel Gabor-based kernel Principal Component Analysis (PCA) method by integrating the Gabor wavelet representation of face images and the kernel PCA method for face recognition. Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. The kernel PCA method is then extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semidefinite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semidefinite Gram matrix either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. In order to derive real kernel PCA features, we apply only those kernel PCA eigenvectors that are associated with positive eigenvalues. The feasibility of the Gabor-based kernel PCA method with fractional power polynomial models has been successfully tested on both frontal and pose-angled face recognition, using two data sets from the FERET database and the CMU PIE database, respectively. The FERET data set contains 600 frontal face images of 200 subjects, while the PIE data set consists of 680 images across five poses (left and right profiles, left and right half profiles, and frontal view) with two different facial expressions (neutral and smiling) of 68 subjects. The effectiveness of the Gabor-based kernel PCA method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the PCA method, the kernel PCA method with polynomial kernels, the kernel PCA method with fractional power
Theoretical Analysis of Rayleigh Backscattering Noise in Fiber Raman Amplifiers
无
2005-01-01
In this paper, a new theoretical model for Rayleigh backscattering (RB) analysis of fiber Raman amplifiers is proposed. The model includes all the interactions among the pumps, signals, and all orders of RB. The results show that the higher order RB has a negligible influence on the performance of the amplifier. The co-propagating and counterpropagating RB power of the signal grow quadratically with the net-gain of the amplifier. The signal to double Rayleigh backscattering noise ratio (OSNRDRB ) of backward-pumped FRAs is better than that of the forward-pumped ones at high net-gain level (＞ 13 dB), while at low net-gain level the OSNRDrb of the forward-pumped FRAs is slightly better than that of the backward-pumped ones.
Initial versus tangent stiffness-based Rayleigh damping in inelastic time history seismic analyses
Jehel, Pierre; Ibrahimbegovic, Adnan
2013-01-01
In the inelastic time history analyses of structures in seismic motion, part of the seismic energy that is imparted to the structure is absorbed by the inelastic structural model, and Rayleigh damping is commonly used in practice as an additional energy dissipation source. It has been acknowledged that Rayleigh damping models lack physical consistency and that, in turn, it must be carefully used to avoid encountering unintended consequences as the appearance of artificial damping. There are concerns raised by the mass proportional part of Rayleigh damping, but they are not considered in this paper. As far as the stiffness proportional part of Rayleigh damping is concerned, either the initial structural stiffness or the updated tangent stiffness can be used. The objective of this paper is to provide a comprehensive comparison of these two types of Rayleigh damping models so that a practitioner (i) can objectively choose the type of Rayleigh damping model that best fits her/his needs and (ii) is provided with u...
Frequency dependence of complex moduli of brain tissue using a fractional Zener model
Kohandel, M [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Sivaloganathan, S [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Tenti, G [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Darvish, K [Center for Applied Biomechanics, University of Virginia, Charlottesville, VA (United States)
2005-06-21
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.
Linear Regression Model of the Ash Mass Fraction and Electrical Conductivity for Slovenian Honey
Mojca Jamnik
2008-01-01
Full Text Available Mass fraction of ash is a quality criterion for determining the botanical origin of honey. At present, this parameter is generally being replaced by the measurement of electrical conductivity (κ. The value κ depends on the ash and acid content of honey; the higher their content, the higher the resulting conductivity. A linear regression model for the relationship between ash and electrical conductivity has been established for Slovenian honey by analysing 290 samples of Slovenian honey (including acacia, lime, chestnut, spruce, fir, multifloral and mixed forest honeydew honey. The obtained model differs from the one proposed by the International Honey Commission (IHC in the slope, but not in the section part of the relation formula. Therefore, the Slovenian model is recommended when calculating the ash mass fraction from the results of electrical conductivity in samples of Slovenian honey.
A model to determine the petroleum pressure in a well using fractional differential equations
Brito Martinez, Beatriz; Brambila Paz, Fernando; Fuentes Ruiz, Carlos
2016-11-01
A noninvasive method was used to determine the pressure of petroleum leaving a well. The mathematical model is based on nonlinear fractional differential equations. This model comes from the fractal dimension of the porous medium. The problem is solved in three stages. In the first stage the fractal dimension of the porous medium is determined. We show that microwaves reflected and transmitted through soil have a fractal dimension which is correlated with the fractal dimension of the porous medium. The fractal signature of microwave scattering correlates with certain physical and mechanical properties of soils (porosity, permeability, conductivity, etc.). In the second stage we use three partial fractional equations as a mathematical model to study the diffusion inside the porous medium. In this model sub-diffusive phenomenon occurs if fractal derivative is between zero and one and supra-diffusive occurs if the derivative is greater than 1 and less than 2. Finally in the third stage the mathematical model is used to determinate the petroleum pressure output in a Mexican oil field, which contains three partial fractional equations with triple porosity and permeability.
Rayleigh-Ritz variation method and connected-moments expansions
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)], E-mail: fernande@quimica.unlp.edu.ar
2009-11-15
We compare the connected-moments expansion (CMX) with the Rayleigh-Ritz variational method in the Krylov space (RRK). As a benchmark model we choose the same two-dimensional anharmonic oscillator already treated earlier by means of the CMX. Our results show that the RRK converges more smoothly than the CMX. We also discuss the fact that the CMX is size consistent while the RRK is not.
Eliazar, Iddo I., E-mail: eliazar@post.tau.ac.il [Holon Institute of Technology, P.O. Box 305, Holon 58102 (Israel); Shlesinger, Michael F., E-mail: mike.shlesinger@navy.mil [Office of Naval Research, Code 30, 875 N. Randolph St., Arlington, VA 22203 (United States)
2013-06-10
Brownian motion is the archetypal model for random transport processes in science and engineering. Brownian motion displays neither wild fluctuations (the “Noah effect”), nor long-range correlations (the “Joseph effect”). The quintessential model for processes displaying the Noah effect is Lévy motion, the quintessential model for processes displaying the Joseph effect is fractional Brownian motion, and the prototypical model for processes displaying both the Noah and Joseph effects is fractional Lévy motion. In this paper we review these four random-motion models–henceforth termed “fractional motions” –via a unified physical setting that is based on Langevin’s equation, the Einstein–Smoluchowski paradigm, and stochastic scaling limits. The unified setting explains the universal macroscopic emergence of fractional motions, and predicts–according to microscopic-level details–which of the four fractional motions will emerge on the macroscopic level. The statistical properties of fractional motions are classified and parametrized by two exponents—a “Noah exponent” governing their fluctuations, and a “Joseph exponent” governing their dispersions and correlations. This self-contained review provides a concise and cohesive introduction to fractional motions.
High Prandtl number effect on Rayleigh-Bénard convection heat transfer at high Rayleigh number
Ma, Li; Li, Jing; Ji, Shui; Chang, Huajian
2017-02-01
This paper represents results of the Rayleigh-Bénard convection heat transfer in silicon oil confined by two horizontal plates, heated from below, and cooled from above. The Prandtl numbers considered as 100-10,000 corresponding to three types of silicon oil. The experiments covered a range of Rayleigh numbers from 2.14·109 to 2.27·1013. The data points that the Nusselt number dependents on the Rayleigh number, which is asymptotic to a 0.248 power. Furthermore, the experiment results can fit the data in low Rayleigh number well.
Overview of Rayleigh-Taylor instability
Sharp, D.H.
1983-01-01
The aim of this talk is to survey Rayleigh-Taylor instability, describing the phenomenology that occurs at a Taylor unstable interface, and reviewing attempts to understand these phenomena quantitatively.
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.
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.
Fractional Brownian motion, the Matérn process, and stochastic modeling of turbulent dispersion
Lilly, Jonathan M.; Sykulski, Adam M.; Early, Jeffrey J.; Olhede, Sofia C.
2017-08-01
Stochastic processes exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm), with the spectral slope at high frequencies being associated with the degree of small-scale roughness or fractal dimension. However, a broad class of real-world signals have a high-frequency slope, like fBm, but a plateau in the vicinity of zero frequency. This low-frequency plateau, it is shown, implies that the temporal integral of the process exhibits diffusive behavior, dispersing from its initial location at a constant rate. Such processes are not well modeled by fBm, which has a singularity at zero frequency corresponding to an unbounded rate of dispersion. A more appropriate stochastic model is a much lesser-known random process called the Matérn process, which is shown herein to be a damped version of fractional Brownian motion. This article first provides a thorough introduction to fractional Brownian motion, then examines the details of the Matérn process and its relationship to fBm. An algorithm for the simulation of the Matérn process in O(NlogN) operations is given. Unlike fBm, the Matérn process is found to provide an excellent match to modeling velocities from particle trajectories in an application to two-dimensional fluid turbulence.
A New Model of the Fractional Order Dynamics of the Planetary Gears
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.
Rayleigh-Taylor mixing in supernova experiments
Swisher, N. C.; Abarzhi, S. I., E-mail: snezhana.abarzhi@gmail.com [Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (United States); Kuranz, C. C. [University of Michigan, Ann Arbor, Michigan 48109 (United States); Arnett, D. [University of Arizona, Tucson, Arizona 85721 (United States); Hurricane, O.; Remington, B. A.; Robey, H. F. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States)
2015-10-15
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.
Direct Numerical Simulation of the Rayleigh-Taylor Instability with the Spectral Element Method
ZHANG Xu; TAN Duo-Wang
2009-01-01
A novel method is proposed to simulate Rayleigh-Taylor instabilities using a specially-developed unsteady threedimensional 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 instabjJjties are studied using this three-dimensional unsteady code,inducling instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers.These results indicate that turbulent structures ofRayleigh-Taylor instabilities are strongly dependent on the initial conditions.The results also suggest that a high-order numerical method should provide the capability of sir.ulating small scale fluctuations of Rayleigh-Taylor instabilities of turbulent flows.
STELLAR LOCI II. A MODEL-FREE ESTIMATE OF THE BINARY FRACTION FOR FIELD FGK STARS
Yuan, Haibo; Liu, Xiaowei [Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871 (China); Xiang, Maosheng; Huang, Yang; Chen, Bingqiu [Department of Astronomy, Peking University, Beijing 100871 (China); Wu, Yue [Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012 (China); Hou, Yonghui; Zhang, Yong, E-mail: yuanhb4861@pku.edu.cn, E-mail: x.liu@pku.edu.cn [Nanjing Institute of Astronomical Optics and Technology, National Astronomical Observatories, Chinese Academy of Sciences, Nanjing 210042 (China)
2015-02-01
We propose a stellar locus outlier (SLOT) method to determine the binary fraction of main-sequence stars statistically. The method is sensitive to neither the period nor mass ratio distributions of binaries and is able to provide model-free estimates of binary fraction for large numbers of stars of different populations in large survey volumes. We have applied the SLOT method to two samples of stars from the Sloan Digital Sky Survey (SDSS) Stripe 82, constructed by combining the recalibrated SDSS photometric data with the spectroscopic information from the SDSS and LAMOST surveys. For the SDSS spectroscopic sample, we find an average binary fraction for field FGK stars of 41% ± 2%. The fractions decrease toward late spectral types and are 44% ± 5%, 43% ± 3%, 35% ± 5%, and 28% ± 6% for stars with g – i colors in the range 0.3-0.6 mag, 0.6-0.9 mag, 0.9-1.2 mag, and 1.2-1.6 mag, respectively. A modest metallicity dependence is also found. The fraction decreases with increasing metallicity. For stars with [Fe/H] between –0.5 and 0.0 dex, –1.0 and –0.5 dex, –1.5 and –1.0 dex, and –2.0 and –1.5 dex, the inferred binary fractions are 37% ± 3%, 39% ± 3%, 50% ± 9%, and 53% ± 20%, respectively. We have further divided the sample into stars from the thin disk, the thick disk, the transition zone between them, and the halo. The results suggest that the Galactic thin and thick disks have comparable binary fractions, whereas the Galactic halo contains a significantly larger fraction of binaries. Applying the method to the LAMOST spectroscopic sample yields consistent results. Finally, other potential applications and future work with the method are discussed.
Analytical expressions for maximum wind turbine average power in a Rayleigh wind regime
Carlin, P.W.
1996-12-01
Average or expectation values for annual power of a wind turbine in a Rayleigh wind regime are calculated and plotted as a function of cut-out wind speed. This wind speed is expressed in multiples of the annual average wind speed at the turbine installation site. To provide a common basis for comparison of all real and imagined turbines, the Rayleigh-Betz wind machine is postulated. This machine is an ideal wind machine operating with the ideal Betz power coefficient of 0.593 in a Rayleigh probability wind regime. All other average annual powers are expressed in fractions of that power. Cases considered include: (1) an ideal machine with finite power and finite cutout speed, (2) real machines operating in variable speed mode at their maximum power coefficient, and (3) real machines operating at constant speed.
Xiao-Kang Zheng; Long-Hua Chen; Xiao Yan; Hong-Mei Wang
2005-01-01
AIM: To explore the impact of prolonged fraction dosedelivery time modeling intensity-modulated radiation therapy (IMRT) on cell killing of human hepatocellular carcinoma (HCC) HepG2 and Hep3B cell lines.METHODS: The radiobiological characteristics of human HCC HepG2 and Hep3b cell lines were studied with standard clonogenic assays, using standard linear-quadratic model and incomplete repair model to fit the dose-survival curves. The identical methods were also employed to investigate the biological effectiveness of irradiation protocols modeling clinical conventional fractionated external beam radiotherapy (EBRT, fraction delivery time 3 min) and IMRT with different prolonged fraction delivery time (15, 30, and 45 min). The differences of cell surviving fraction irradiated with different fraction delivery time were tested with paired t-test. Factors determining the impact of prolonged fraction delivery time on cell killing were analyzed.RESULTS: The α/β and repair half-time (T1/2) of HepG2and Hep3b were 3.1 and 7.4 Gy, and 22 and 19 min respectively. The surviving fraction of HepG2 irradiated modeling IMRT with different fraction delivery time was significantly higher than irradiated modeling EBRT and the cell survival increased more pronouncedly with the fraction delivery time prolonged from 15 to 45 min,while no significant differences of cell survival in Hep3b were found between different fraction delivery time protocols.CONCLUSION: The prolonged fraction delivery time modeling IMRT significantly decreased the cell killing in HepG2 but not in Hep3b. The capability of sub-lethal damage repair was the predominant factor determining the cell killing decrease. These effects, if confirmed by clinical studies, should be considered in designing IMRT treatments for HCC.
Diagnosing ΛHDE model with statefinder hierarchy and fractional growth parameter
Zhou, LanJun; Wang, Shuang
2016-07-01
Recently, a new dark energy model called ΛHDE was proposed. In this model, dark energy consists of two parts: cosmological constant Λ and holographic dark energy (HDE). Two key parameters of this model are the fractional density of cosmological constant ΩΛ0, and the dimensionless HDE parameter c. Since these two parameters determine the dynamical properties of DE and the destiny of universe, it is important to study the impacts of different values of ΩΛ0 and c on the ΛHDE model. In this paper, we apply various DE diagnostic tools to diagnose ΛHDE models with different values of ΩΛ0 and c; these tools include statefinder hierarchy {S 3 (1) , S 4 (1) }, fractional growth parameter ɛ, and composite null diagnostic (CND), which is a combination of {S 3 (1) , S 4 (1) } and ɛ. We find that: (1) adopting different values of ΩΛ0 only has quantitative impacts on the evolution of the ΛHDE model, while adopting different c has qualitative impacts; (2) compared with S 3 (1) , S 4 (1) can give larger differences among the cosmic evolutions of the ΛHDE model associated with different ΩΛ0 or different c; (3) compared with the case of using a single diagnostic, adopting a CND pair has much stronger ability to diagnose the ΛHDE model.
Modelling the fine and coarse fraction of Pb, Cd, As and Ni air concentration in Spain
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
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)
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.
Richard MT Webb; David L. Parkhurst
2016-01-01
The U.S. Geological Surveyâs (USGS) Water, Energy, and Biogeochemical ModelÂ (WEBMOD) was used to simulate hydrology, weathering, and isotopic fractionation in theÂ Andrews Creek watershed in Rocky Mountain National Park, Colorado and the Icacos RiverÂ watershed in the Luquillo Experimental Forest, Puerto Rico. WEBMOD includes hydrologicÂ modules derived from the USGS...
Gencoglu, Muharrem Tuncay; Baskonus, Haci Mehmet; Bulut, Hasan
2017-01-01
The main aim of this manuscript is to obtain numerical solutions for the nonlinear model of interpersonal relationships with time fractional derivative. The variational iteration method is theoretically implemented and numerically conducted only to yield the desired solutions. Numerical simulations of desired solutions are plotted by using Wolfram Mathematica 9. The authors would like to thank the reviewers for their comments that help improve the manuscript.
Watkins, N. W.; Rosenberg, S.; Sanchez, R.; Chapman, S. C.; Credgington, D.
2008-12-01
Since the 1960s Mandelbrot has advocated the use of fractals for the description of the non-Euclidean geometry of many aspects of nature. In particular he proposed two kinds of model to capture persistence in time (his Joseph effect, common in hydrology and with fractional Brownian motion as the prototype) and/or prone to heavy tailed jumps (the Noah effect, typical of economic indices, for which he proposed Lévy flights as an exemplar). Both effects are now well demonstrated in space plasmas, notably in the turbulent solar wind. Models have, however, typically emphasised one of the Noah and Joseph parameters (the Lévy exponent μ and the temporal exponent β) at the other's expense. I will describe recent work in which we studied a simple self-affine stable model-linear fractional stable motion, LFSM, which unifies both effects and present a recently-derived diffusion equation for LFSM. This replaces the second order spatial derivative in the equation of fBm with a fractional derivative of order μ, but retains a diffusion coefficient with a power law time dependence rather than a fractional derivative in time. I will also show work in progress using an LFSM model and simple analytic scaling arguments to study the problem of the area between an LFSM curve and a threshold. This problem relates to the burst size measure introduced by Takalo and Consolini into solar-terrestrial physics and further studied by Freeman et al [PRE, 2000] on solar wind Poynting flux near L1. We test how expressions derived by other authors generalise to the non-Gaussian, constant threshold problem. Ongoing work on extension of these LFSM results to multifractals will also be discussed.
Synchronous Generator Model with Fractional Order Voltage Regulator PIbDa
Dariusz Spałek
2015-06-01
Full Text Available Synchronous generator together with excitation circuit, voltage controller and system stabilizer constitute nonlinear ordinary differential equations set. The nonlinearity of differential equations set results from magnetic circuits saturation. One of the most important, from the electric energy distribution point of view, is the influence of voltage control applied on the generator voltage. There could be applied regulator either classical PID or fractional of type PIbDa which bases on the so-called fractional derivative idea. Numerical solutions of nonlinear differential equations set, that takes into account both magnetic circuits saturation and fractional regulator PIbDa, lead to decisions either to accept or to reject the chosen parameters. The sensibility of generator work on chosen fractional regulator parameters is the main aim of this paper. With the help of C++ program provided the most important states of work (short–circuit, setting voltage change, reactive power rejection can be analyzed basing on the accepted model of synchronous generator such as (1,1, (2,2 or (3,3.
Fractional brownian functions as mathematical models of natural rhythm in architecture.
Cirovic, Ivana M
2014-10-01
Carl Bovill suggested and described a method of generating rhythm in architecture with the help of fractional Brownian functions, as they are mathematical models of natural rhythm. A relationship established in the stated procedure between fractional Brownian functions as models of rhythm, and the observed group of architectural elements, is recognized as an analogical relationship, and the procedure of generating rhythm as a process of analogical transfer from the natural domain to the architectural domain. Since analogical transfer implies relational similarity of two domains, and the establishment of one-to-one correspondence, this paper is trying to determine under which conditions such correspondence could be established. For example, if the values of the observed visual feature of architectural elements are not similar to each other in a way in which they can form a monotonically increasing, or a monotonically decreasing bounded sequence, then the structural alignment and the one-to-one correspondence with a single fractional Brownian function cannot be established, hence, this function is deemed inappropriate as a model for the architectural rhythm. In this case we propose overlapping of two or more functions, so that each of them is an analog for one subset of mutually similar values of the visual feature of architectural elements.
Fractional Brownian motion, the Matern process, and stochastic modeling of turbulent dispersion
Lilly, J M; Early, J J; Olhede, S C
2016-01-01
Stochastic process exhibiting power-law slopes in the frequency domain are frequently well modeled by fractional Brownian motion (fBm). In particular, the spectral slope at high frequencies is associated with the degree of small-scale roughness or fractal dimension. However, a broad class of real-world signals have a high-frequency slope, like fBm, but a plateau in the vicinity of zero frequency. This low-frequency plateau, it is shown, implies that the temporal integral of the process exhibits diffusive behavior, dispersing from its initial location at a constant rate. Such processes are not well modeled by fBm, which has a singularity at zero frequency corresponding to an unbounded rate of dispersion. A more appropriate stochastic model is a much lesser-known random process called the Matern process, which is shown herein to be a damped version of fractional Brownian motion. This article first provides a thorough introduction to fractional Brownian motion, then examines the details of the Matern process and...
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
Tanimoto, Toshiro; Hadziioannou, Céline; Igel, Heiner; Wassermann, Joachim; Schreiber, Ulrich; Gebauer, André; Chow, Bryant
2016-04-01
Monthly variations in the ratio of Rayleigh-to-Love waves in the secondary microseism are obtained from a colocated ring laser and an STS-2 seismograph at Wettzell, Germany. Two main conclusions are derived for the Rayleigh-to-Love wave kinetic energy ratios in the secondary microseism; first, the energy ratio is in the range 0.8-0.9 (Love wave energy is larger than Rayleigh wave energy most of the year by about 10-20%. Second, this ratio suddenly increases to 1.0-1.2 in June and July, indicating a larger fraction of Rayleigh wave energy. This change suggests that the locations and behaviors of excitation sources are different in these months.
Li, Zheng; Wang, Hong; Yang, Danping
2017-10-01
We present a space-time fractional Allen-Cahn phase-field model that describes the transport of the fluid mixture of two immiscible fluid phases. The space and time fractional order parameters control the sharpness and the decay behavior of the interface via a seamless transition of the parameters. Although they are shown to provide more accurate description of anomalous diffusion processes and sharper interfaces than traditional integer-order phase-field models do, fractional models yield numerical methods with dense stiffness matrices. Consequently, the resulting numerical schemes have significantly increased computational work and memory requirement. We develop a lossless fast numerical method for the accurate and efficient numerical simulation of the space-time fractional phase-field model. Numerical experiments shows the utility of the fractional phase-field model and the corresponding fast numerical method.
Nielsen, Kræn Vodder; Blanke, Mogens; Eriksson, Lars
2016-01-01
therefore focus on deriving and validating a mean-value model of a large two-stroke crosshead diesel engines with EGR. The model introduces a number of amendments and extensions to previous, complex models and shows in theory and practice that a simplified nonlinear model captures all essential dynamics...... 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......Exhaust gas recirculation (EGR) systems have been introduced to large marine engines in order to reduce NOx formation. Adequate modelling for control design is one of the bottlenecks to design EGR control that also meets emission requirements during transient loading conditions. This paper...
Hamiltonian analysis of gauged $CP^1$ model, with or without Hopf term, and fractional spin
Chakraborty, B
1997-01-01
Recently it has been shown by Cho and Kimm that the gauged $CP^1$ model, obtained by gauging the global SU(2) group of $CP^1$ model and adding a corresponding Chern-Simons term, has got its own soliton. These solitons are somewhat distinct from those of pure $CP^1$ model, as they cannot always be characterised by $\\pi_2(CP^1)=Z$. In this paper, we first carry out the Hamiltonian analysis of this gauged $CP^1$ model. Then we couple the Hopf term, associated to these solitons and again carry out its Hamiltonian analysis. The symplectic structures, along with the structures of the constraints, of these two models (with or without Hopf term) are found to be essentially the same. The model with Hopf term, is then shown to have fractional spin, which however depends not only on the soliton number $N$ but also on the nonabelian charge.
Development of a three dimensional circulation model based on fractional step method
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.
Yang, Ning-Ning; Liu, Chong-Xin; Wu, Chao-Jun
2012-08-01
In this paper, the fractional-order mathematical model and the fractional-order state-space averaging model of the Buck—Boost converter in continuous conduction mode (CCM) are established based on the fractional calculus and the Adomian decomposition method. Some dynamical properties of the current-mode controlled fractional-order Buck—Boost converter are analysed. The simulation is accomplished by using SIMULINK. Numerical simulations are presented to verify the analytical results and we find that bifurcation points will be moved backward as α and β vary. At the same time, the simulation results show that the converter goes through different routes to chaos.
Xuefang, L.; Liu, Y.
2015-12-01
Huang et al (2010) found that Fe, Ca and Mg isotope fractionations of high-temperature silicate melts are only associated with the temperature gradients in thermal diffusion processes and are independent of compositions and mean temperatures [1]. Richter et al (2010) doubted that the existing data are sufficient to obtain such conclusion [2]. A few theoretical models have been proposed for explaining isotopic fractionations in these processes under high temperatures [3, 4]. However, molecular-level mechanisms and theoretical treatments of these processes are still under debating. Here we provide a unified theory based on the local thermodynamic equilibrium treatment (LTE) of statistical mechanics for evaluating thermal isotopic fractionations under a wide range of temperatures. Under high temperatures, our theory however can be reasonably approximated to this equation: where A and B are constants which are related to specific isotope systems and chemical compositions of silicate melts. If the thermal gradient is not very large and the mean temperature is high, the second part of the above equation can be safely neglected and obtain an extremely simple equation which is linearly depended on temperatures, agreeing with what Huang et al (2010) concluded. Based on this terse equation, we can not only easily provide isotope fractionation data for almost all kinds of isotope systems, but also can provide the mechanisms of isotope fractionation in thermal diffusion processes. [1] Huang et al (2010) Nature 464, 396-400. [2] Richter et al (2010) Nature 472, E1-E1. [3] Dominguez et al (2011) Nature 473, 70-73.
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.
Fractional Generalizations of Maxwell and Kelvin-Voigt Models for Biopolymer Characterization.
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.
2013-01-01
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 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. 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 radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment.
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.
Application of fractional calculus to modeling transient combustion of solid propellants
Kulish, Vladimir; Horák, Vladimír; Duc, Linh Do; Lukáč, Tomáš
2017-01-01
It was Zel'dovich, who first considered the transient combustion problem of solid propellants. Some more detailed models of that process have been developed afterwards. However, until today, numerical methods remain the prevailing tool for modeling unsteady combustion processes. In this work, it has been demonstrated that at least one of the problems of the unsteady combustion theory, which previously investigated numerically, can be treated analytically by means of fractional calculus. The solution for the unsteady speed of combustion thus derived is then compared with the solution obtained by numerical means in previous studies. The comparison shows a good agreement between those results, especially for small values of time.
Fractional snow cover mapping from MODIS data using wavelet-artificial intelligence hybrid models
Moosavi, Vahid; Malekinezhad, Hossein; Shirmohammadi, Bagher
2014-04-01
This study was carried out to evaluate the wavelet-artificial intelligence hybrid models to produce fractional snow cover maps. At first, cloud cover was removed from MODIS data and cloud free images were produced. SVM-based binary classified ETM+ imagery were then used as reference maps in order to obtain train and test data for sub-pixel classification models. ANN and ANFIS-based modeling were performed using raw data (without wavelet-based preprocessing). In the next step, several mother wavelets and levels were used in order to decompose the original data to obtain wavelet coefficients. Then, the decomposed data were used for further modeling processes. ANN, ANFIS, wavelet-ANN and wavelet-ANFIS models were compared to evaluate the effect of wavelet transformation on the ability of artificial intelligence models. It was demonstrated that wavelet transformation as a preprocessing approach can significantly enhance the performance of ANN and ANFIS models. This study indicated an overall accuracy of 92.45% for wavelet-ANFIS model, 86.13% for wavelet-ANN, 72.23% for ANFIS model and 66.78% for ANN model. In fact, hybrid wavelet-artificial intelligence models can extract the characteristics of the original signals (i.e. model inputs) accurately through decomposing the non-stationary and complex signals into several stationary and simpler signals. The positive effect of fuzzification as well as wavelet transformation in the wavelet-ANFIS model was also confirmed.
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.
Fractional Diffusion Based Modelling and Prediction of Human Brain Response to External Stimuli
Hamidreza Namazi
2015-01-01
Full Text Available Human brain response is the result of the overall ability of the brain in analyzing different internal and external stimuli and thus making the proper decisions. During the last decades scientists have discovered more about this phenomenon and proposed some models based on computational, biological, or neuropsychological methods. Despite some advances in studies related to this area of the brain research, there were fewer efforts which have been done on the mathematical modeling of the human brain response to external stimuli. This research is devoted to the modeling and prediction of the human EEG signal, as an alert state of overall human brain activity monitoring, upon receiving external stimuli, based on fractional diffusion equations. The results of this modeling show very good agreement with the real human EEG signal and thus this model can be used for many types of applications such as prediction of seizure onset in patient with epilepsy.
A model-independent determination of the inclusive semileptonic decay fraction of B mesons
Albrecht, H.; Ehrlichmann, H.; Hamacher, T.; Hofmann, R. P.; Kirchhoff, T.; Nau, A.; Nowak, S.; Schröder, H.; Schulz, H. D.; Walter, M.; Wurth, R.; Hast, C.; Kolanoski, H.; Kosche, A.; Lange, A.; Lindner, A.; Mankel, R.; Schieber, M.; Siegmund, T.; Spaan, B.; Thurn, H.; Töpfer, D.; Wegener, D.; Bittner, M.; Eckstein, P.; Paulini, M.; Reim, K.; Wegener, H.; Eckmann, R.; Mundt, R.; Oest, T.; Reiner, R.; Schmidt-Parzefall, W.; Funk, W.; Stiewe, J.; Werner, S.; Ehret, K.; Hofmann, W.; Hüpper, A.; Khan, S.; Knöpfle, K. T.; Seeger, M.; Spengler, J.; Britton, D. I.; Charlesworth, C. E. K.; Edwards, K. W.; Hyatt, E. R. F.; Kapitza, H.; Krieger, P.; Macfarlane, D. B.; Patel, P. M.; Prentice, J. D.; Saull, P. R. B.; Tzamariudaki, K.; van de Water, R. G.; Yoon, T.-S.; Reßing, D.; Schmidtler, M.; Schneider, M.; Schubert, K. R.; Strahl, K.; Waldi, R.; Weseler, S.; Kernel, G.; Križnič, P.; Podobnik, T.; Živko, T.; Balagura, V.; Belyaev, I.; Chechelnitsky, S.; Danilov, M.; Droutskoy, A.; Gershtein, Yu.; Golutvin, A.; Kostina, G.; Litvintsev, D.; Lubimov, V.; Pakhlov, P.; Ratnikov, F.; Semenov, S.; Snizhko, A.; Soloshenko, V.; Tichomirov, I.; Zaitsev, Yu.; Argus Collaboration
1993-12-01
With the ARGUS detector at the e +e - storage ring DORIS II, we have determined decay fraction and electron momentum spectrum of the inclusive decay mode B → eνX. Usinng lepton tags from the second B meson. in 209 000 γ(4 S) → BoverlineB decays, we could determine the spectrum for all electron momenta pe > 0.6 GeV/ c. Including the small extrapolation to pe > 0, we find the model-independent decay fraction B(B → eνX) = (9.6 ± 0.5 ± 0.4)%. Adding D meson tags, our result is (9.7 ± 0.5 ± 0.4)%.
Nonlethal Fraction of Virus Population in Evolution Models with Lethal Mutations
Yakushkina, Tatiana; Saakian, David B.
2017-03-01
Lethal mutations are very common in asexual evolution, both in RNA viruses and in the clonal evolution of cancer cells. In a special case of lethal mutations (truncated selection), after a critical total number of mutations the replicator (the virus or the cell) has no offspring. We consider the Eigen and Crow-Kimura models with truncated fitness landscapes, and calculate the fraction of viable replicators (that do have offspring) in the population. We derive a formula for the fraction of the population with nonlethal replicators for the case of a uniform distribution of lethal sequences in the sequence space. We assume that our results can be applied to the origin of life and cancer biology.
Yong Zhang
2013-01-01
Full Text Available Heterogeneous media consisting of segregated flow regions are fractional-order systems, where the regional-scale anomalous diffusion can be described by the fractional derivative model (FDM. The standard FDM, however, first, cannot characterize the Darcy-scale dispersion through repacked sand columns, and second, the link between medium properties and model parameters remains unknown. To fill these two knowledge gaps, this study applies a tempered fractional derivative model (TFDM to capture bromide transport through laboratory repacked sand. Column transport experiments are conducted first, where glass beads and silica sand with different diameters are repacked individually. Late-time tails are observed in the breakthrough curves (BTC of bromide even in relatively homogeneous glass beads. The TFDM can capture the observed subdiffusion, especially the late-time BTC with a transient declining rate. Results also show that both the size distribution of repacked sand and the magnitude of fluid velocity can affect subdiffusion. In particular, a wider sand size distribution or a smaller flow rate can enhance the subdiffusion, leading to a smaller time index and a higher truncation parameter in the TFDM. Therefore, the Darcy-scale dispersion follows the tempered stable law, and the model parameters might be related to the soil size and flow conditions.
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.
Dörr, Aaron; Mehdizadeh, Amirfarhang
2012-01-01
Based on the notion of a construction process consisting of the stepwise addition of particles to the pure fluid, a discrete model for the apparent viscosity as well as for the maximum packing fraction of polydisperse suspensions of spherical, non-colloidal particles is derived. The model connects the approaches by Bruggeman and Farris and is valid for large size ratios of consecutive particle classes during the construction process. Furthermore, a new general form of the well-known Krieger equation allowing for the choice of a second-order Taylor coefficient for the volume fraction is proposed and then applied as a monodisperse reference equation in the course of polydisperse modeling. By applying the polydisperse viscosity model to two different particle size distributions (Rosin-Rammler and uniform distribution), the influence of polydispersity on the apparent viscosity is examined. The extension of the model to the case of small size ratios as well as to the inclusion of shear rate effects is left for fut...
Diagnosing $\\Lambda$HDE model with statefinder hierarchy and fractional growth parameter
Zhou, Lanjun
2016-01-01
Recently, a new dark energy model called $\\Lambda$HDE was proposed. In this model, dark energy consists of two parts: cosmological constant $\\Lambda$ and holographic dark energy (HDE). Two key parameters of this model are the fractional density of cosmological constant $\\Omega_{\\Lambda0}$, and the dimensionless HDE parameter $c$. Since these two parameters determine the dynamical properties of DE and the destiny of universe, it is important to study the impacts of different values of $\\Omega_{\\Lambda0}$ and $c$ on the $\\Lambda$HDE model. In this paper, we apply various DE diagnostic tools to diagnose $\\Lambda$HDE models with different values of $\\Omega_{\\Lambda0}$ and $c$; these tools include statefinder hierarchy \\{$S_3^{(1)}, S_4^{(1)}$\\}, fractional growth parameter $\\epsilon$, and composite null diagnostic (CND), which is a combination of \\{$S_3^{(1)}, S_4^{(1)}$\\} and $\\epsilon$. We find that: (1) adopting different values of $\\Omega_{\\Lambda0}$ only has quantitative impacts on the evolution of the $\\Lam...
Optical switching by stimulated thermal Rayleigh scattering
Peterson, Lauren M.
1986-06-01
Preliminary experiments were conducted whose ultimate goal is to develop all-optical control functions useful in an all-optical or optical-electronic hybrid digital computer or for optical interconnects. Stimulated thermal Rayleigh scattering (STRS) based upon generator experiments was pursued for scattering angles of 90 deg and 180 deg (backscattering). A pulsed nitrogen laser pumped dye laser served as the radiation source and the interaction medium was a liquid to which an absorbing dye was added. STRS amplifier experiments were successful and gain was observed and studied parametrically using eosine dye in ethanol. The gain was found to increase (although the gain coefficient decreased) with increasing pump power and the gain was found to be a maximum at an absorption coefficient of about 2.6 per cm. The generator experiments did not lead to stimulated scattering due to the limited output power of the laser and its multi-longitudinal spectral mode content. These studies will be continued along with analytical modeling in order to characterize the interaction and to enable the optimization of the scattering process.
Tenreiro Machado, J. A.
2015-08-01
This paper addresses the matrix representation of dynamical systems in the perspective of fractional calculus. Fractional elements and fractional systems are interpreted under the light of the classical Cole-Cole, Davidson-Cole, and Havriliak-Negami heuristic models. Numerical simulations for an electrical circuit enlighten the results for matrix based models and high fractional orders. The conclusions clarify the distinction between fractional elements and fractional systems.
Blockhuys, S; Vanhoecke, B; Paelinck, L; Bracke, M; DeWagter, C
2009-03-01
We present different in vitro experimental models which allow us to evaluate the effect of spatially fractionated dose distributions on metabolic activity. We irradiated a monolayer of MCF-7/6 human breast cancer cells with a steep and a smooth 6 MV x-ray dose gradient. In the steep gradient model, we irradiated the cells with three separate small fields. We also developed two smooth gradient models. In the first model, the cells are cultured in a T25 flask and irradiated with a smooth dose gradient over the length of the flask, while in the second one, the cells are cultured in a 96-well plate and also irradiated over the length of the plate. In an attempt to correlate the spatially fractionated dose distributions with metabolic activity, the effect of irradiation was evaluated by means of the MTT assay. This assay is used to determine the metabolic activity by measuring the amount of formazan formed after the conversion of MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) by cellular dehydrogenases. The results obtained with our different models suggest a dose-specific effect on metabolic activity, characterized by an increased formazan optical density occurring in the dose range 1.0-4.0 Gy in the steep dose gradient model and in the dose ranges 4.2-6.5 Gy and 2.3-5.1 Gy in the two smooth dose gradient models. The corresponding times for maximal formazan accumulation were 5-7 days in the steep dose gradient model and day 9-13 and day 9-11 in the smooth dose gradient models. Altogether, our results suggest that the MTT assay may be used as a biological dose-response meter to monitor the radiotherapeutic effectiveness.
Blockhuys, S; Vanhoecke, B; Bracke, M [Laboratory Experimental Cancer Research, Ghent University Hospital, De Pintelaan 185, B-9000 Gent (Belgium); Paelinck, L; De Wagter, C [Department of Radiotherapy, Ghent University Hospital, De Pintelaan 185, B-9000 Gent (Belgium)], E-mail: Stephanie.Blockhuys@ugent.be
2009-03-21
We present different in vitro experimental models which allow us to evaluate the effect of spatially fractionated dose distributions on metabolic activity. We irradiated a monolayer of MCF-7/6 human breast cancer cells with a steep and a smooth 6 MV x-ray dose gradient. In the steep gradient model, we irradiated the cells with three separate small fields. We also developed two smooth gradient models. In the first model, the cells are cultured in a T25 flask and irradiated with a smooth dose gradient over the length of the flask, while in the second one, the cells are cultured in a 96-well plate and also irradiated over the length of the plate. In an attempt to correlate the spatially fractionated dose distributions with metabolic activity, the effect of irradiation was evaluated by means of the MTT assay. This assay is used to determine the metabolic activity by measuring the amount of formazan formed after the conversion of MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) by cellular dehydrogenases. The results obtained with our different models suggest a dose-specific effect on metabolic activity, characterized by an increased formazan optical density occurring in the dose range 1.0-4.0 Gy in the steep dose gradient model and in the dose ranges 4.2-6.5 Gy and 2.3-5.1 Gy in the two smooth dose gradient models. The corresponding times for maximal formazan accumulation were 5-7 days in the steep dose gradient model and day 9-13 and day 9-11 in the smooth dose gradient models. Altogether, our results suggest that the MTT assay may be used as a biological dose-response meter to monitor the radiotherapeutic effectiveness.
Ying Li
Full Text Available Vegetation is an important part of ecosystem and estimation of fractional vegetation cover is of significant meaning to monitoring of vegetation growth in a certain region. With Landsat TM images and HJ-1B images as data source, an improved selective endmember linear spectral mixture model (SELSMM was put forward in this research to estimate the fractional vegetation cover in Huangfuchuan watershed in China. We compared the result with the vegetation coverage estimated with linear spectral mixture model (LSMM and conducted accuracy test on the two results with field survey data to study the effectiveness of different models in estimation of vegetation coverage. Results indicated that: (1 the RMSE of the estimation result of SELSMM based on TM images is the lowest, which is 0.044. The RMSEs of the estimation results of LSMM based on TM images, SELSMM based on HJ-1B images and LSMM based on HJ-1B images are respectively 0.052, 0.077 and 0.082, which are all higher than that of SELSMM based on TM images; (2 the R2 of SELSMM based on TM images, LSMM based on TM images, SELSMM based on HJ-1B images and LSMM based on HJ-1B images are respectively 0.668, 0.531, 0.342 and 0.336. Among these models, SELSMM based on TM images has the highest estimation accuracy and also the highest correlation with measured vegetation coverage. Of the two methods tested, SELSMM is superior to LSMM in estimation of vegetation coverage and it is also better at unmixing mixed pixels of TM images than pixels of HJ-1B images. So, the SELSMM based on TM images is comparatively accurate and reliable in the research of regional fractional vegetation cover estimation.
Li, Ying; Wang, Hong; Li, Xiao Bing
2015-01-01
Vegetation is an important part of ecosystem and estimation of fractional vegetation cover is of significant meaning to monitoring of vegetation growth in a certain region. With Landsat TM images and HJ-1B images as data source, an improved selective endmember linear spectral mixture model (SELSMM) was put forward in this research to estimate the fractional vegetation cover in Huangfuchuan watershed in China. We compared the result with the vegetation coverage estimated with linear spectral mixture model (LSMM) and conducted accuracy test on the two results with field survey data to study the effectiveness of different models in estimation of vegetation coverage. Results indicated that: (1) the RMSE of the estimation result of SELSMM based on TM images is the lowest, which is 0.044. The RMSEs of the estimation results of LSMM based on TM images, SELSMM based on HJ-1B images and LSMM based on HJ-1B images are respectively 0.052, 0.077 and 0.082, which are all higher than that of SELSMM based on TM images; (2) the R2 of SELSMM based on TM images, LSMM based on TM images, SELSMM based on HJ-1B images and LSMM based on HJ-1B images are respectively 0.668, 0.531, 0.342 and 0.336. Among these models, SELSMM based on TM images has the highest estimation accuracy and also the highest correlation with measured vegetation coverage. Of the two methods tested, SELSMM is superior to LSMM in estimation of vegetation coverage and it is also better at unmixing mixed pixels of TM images than pixels of HJ-1B images. So, the SELSMM based on TM images is comparatively accurate and reliable in the research of regional fractional vegetation cover estimation.
A predictor-corrector algorithm to estimate the fractional flow in oil-water models
Savioli, Gabriela B [Laboratorio de IngenierIa de Reservorios, IGPUBA and Departamento de IngenierIa Quimica, Facultad de IngenierIa, Universidad de Buenos Aires, Av. Las Heras 2214 Piso 3 C1127AAR Buenos Aires (Argentina); Berdaguer, Elena M Fernandez [Instituto de Calculo, Facultad de Ciencias Exactas y Naturales, UBA-CONICET and Departamento de Matematica, Facultad de IngenierIa, Universidad de Buenos Aires, 1428 Buenos Aires (Argentina)], E-mail: gsavioli@di.fcen.uba.ar, E-mail: efernan@ic.fcen.uba.ar
2008-11-01
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.
Fractional Black-Scholes Model and Technical Analysis of Stock Price
Song Xu
2013-01-01
Full Text Available In the stock market, some popular technical analysis indicators (e.g., Bollinger bands, RSI, ROC, etc. are widely used to forecast the direction of prices. The validity is shown by observed relative frequency of certain statistics, using the daily (hourly, weekly, etc. stock prices as samples. However, those samples are not independent. In earlier research, the stationary property and the law of large numbers related to those observations under Black-Scholes stock price model and stochastic volatility model have been discussed. Since the fitness of both Black-Scholes model and short-range dependent process has been questioned, we extend the above results to fractional Black-Scholes model with Hurst parameter H>1/2, under which the stock returns follow a kind of long-range dependent process. We also obtain the rate of convergence.
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
Cheng Xu
2015-01-01
Full Text Available In this manuscript, the local fractional arbitrary Euler-Lagrange formula are utilized to address the diffusion model of fractal heat and mass transfer in a fluidized bed based on the Fick's law with local fractional vector calculus. This article has been corrected. Link to the correction 10.2298/TSCI150923149E
Zanetti, Massimo; Bovolo, Francesca; Bruzzone, Lorenzo
2015-12-01
The problem of estimating the parameters of a Rayleigh-Rice mixture density is often encountered in image analysis (e.g., remote sensing and medical image processing). In this paper, we address this general problem in the framework of change detection (CD) in multitemporal and multispectral images. One widely used approach to CD in multispectral images is based on the change vector analysis. Here, the distribution of the magnitude of the difference image can be theoretically modeled by a Rayleigh-Rice mixture density. However, given the complexity of this model, in applications, a Gaussian-mixture approximation is often considered, which may affect the CD results. In this paper, we present a novel technique for parameter estimation of the Rayleigh-Rice density that is based on a specific definition of the expectation-maximization algorithm. The proposed technique, which is characterized by good theoretical properties, iteratively updates the parameters and does not depend on specific optimization routines. Several numerical experiments on synthetic data demonstrate the effectiveness of the method, which is general and can be applied to any image processing problem involving the Rayleigh-Rice mixture density. In the CD context, the Rayleigh-Rice model (which is theoretically derived) outperforms other empirical models. Experiments on real multitemporal and multispectral remote sensing images confirm the validity of the model by returning significantly higher CD accuracies than those obtained by using the state-of-the-art approaches.
A rational fraction polynomials model to study vertical dynamic wheel-rail interaction
Correa, N.; Vadillo, E. G.; Santamaria, J.; Gómez, J.
2012-04-01
This paper presents a model designed to study vertical interactions between wheel and rail when the wheel moves over a rail welding. The model focuses on the spatial domain, and is drawn up in a simple fashion from track receptances. The paper obtains the receptances from a full track model in the frequency domain already developed by the authors, which includes deformation of the rail section and propagation of bending, elongation and torsional waves along an infinite track. Transformation between domains was secured by applying a modified rational fraction polynomials method. This obtains a track model with very few degrees of freedom, and thus with minimum time consumption for integration, with a good match to the original model over a sufficiently broad range of frequencies. Wheel-rail interaction is modelled on a non-linear Hertzian spring, and consideration is given to parametric excitation caused by the wheel moving over a sleeper, since this is a moving wheel model and not a moving irregularity model. The model is used to study the dynamic loads and displacements emerging at the wheel-rail contact passing over a welding defect at different speeds.
Fractional charge separation in the hard-core Bose Hubbard Model on the Kagome Lattice
Zhang, Xue Feng; Eggert, Sebastian
2013-03-01
We consider the hard core Bose Hubbard Model on a Kagome lattice with fixed (open) boundary conditions on two edges. We find that the fixed boundary conditions lift the degeneracy and freeze the system at 1/3 and 2/3 filling at small hopping. At larger hopping strengths, fractional charges spontaneously separate and are free to move to the edges of the system, which leads to a novel compressible phase with solid order. The compressibility is due to excitations on the edge which display a chrial symmetry breaking that is reminiscent of the quantum Hall effect. Large scale Monte Carlo simulations confirm the analytical calculations.
Quantifying Arsenic Leaching from Soils Using a Fractional-Derivative Model
Lu, B.; Zhang, Y.; LU, B.
2015-12-01
Arsenic leaching from soils can exhibit multiple-rate kinetics due to the heterogeneity nature of the medium, motivating the development of a fractional-order derivative model (FDM). The sorption-desorption process in saturated natural soils may not be limited to be a single rate or can reach equilibrium quickly, even at the laboratory scale. Applications of the FDM show that the multi-rate mass transfer quantifies the multi-stage desorption in Arsenic leaching characterized by the heavy late-time tailing behavior.
Unsteady flow of viscoelastic fluid between two cylinders using fractional Maxwell model
Muhammad Jamil; Constantin Fetecau; Corina Fetecau
2012-01-01
The unsteady flow of an incompressible fractional Maxwell fluid between two infinite coaxial cylinders is studied by means of integral transforms.The motion of the fluid is due to the inner cylinder that applies a time dependent torsional shear to the fluid.The exact solutions for velocity and shear stress are presented in series form in terms of some generalized functions.They can easily be particularized to give similar solutions for Maxwell and Newtonian fluids.Finally,the influence of pertinent parameters on the fluid motion,as well as a comparison between models,is highlighted by graphical illustrations.
Bivariate Rayleigh Distribution and its Properties
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.
Ruedig, Elizabeth; Caffrey, Emily; Hess, Catherine; Higley, Kathryn
2014-08-01
Simple, ellipsoidal geometries have long been the standard for estimating radiation dose rates in non-human biota (NHB). With the introduction of a regulatory protection standard that emphasizes protection of NHB as its own end point, there has been interest in improved models for the calculation of dose rates in NHB. Here, we describe the creation of a voxelized model for a rainbow trout (Oncorhynchus mykiss), a freshwater aquatic salmonid. Absorbed fractions (AFs) for both photon and electron sources were tabulated at electron energies of 0.1, 0.2, 0.4, 0.5, 0.7, 1.0, 1.5, 2.0, and 4.0 MeV and photon energies of 0.01, 0.015, 0.02, 0.03, 0.05, 0.1, 0.2, 0.5, 1.0, 1.5, 2.0, and 4.0 MeV. A representative set of the data is made available in this publication; the entire set of absorbed fractions is available as electronic supplementary materials. These results are consistent with previous voxelized models and reinforce the well-understood relationship between the AF and the target's mass and location, as well as the energy of the incident radiation.
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.
DePaolo, D.
2010-10-15
A surface reaction kinetic model is developed for predicting Ca isotope fractionation and metal/Ca ratios of calcite as a function of rate of precipitation from aqueous solution. The model is based on the requirements for dynamic equilibrium; i.e. proximity to equilibrium conditions is determined by the ratio of the net precipitation rate (R{sub p}) to the gross forward precipitation rate (R{sub f}), for conditions where ionic transport to the growing crystal surface is not rate-limiting. The value of R{sub p} has been experimentally measured under varying conditions, but the magnitude of R{sub f} is not generally known, and may depend on several factors. It is posited that, for systems with no trace constituents that alter the surface chemistry, R{sub f} can be estimated from the bulk far-from-equilibrium dissolution rate of calcite (R{sub b} or k{sub b}), since at equilibrium R{sub f} = R{sub b}, and R{sub p} = 0. Hence it can be inferred that R{sub f} {approx} R{sub p} + R{sub b}. The dissolution rate of pure calcite is measureable and is known to be a function of temperature and pH. At given temperature and pH, equilibrium precipitation is approached when R{sub p} (= R{sub f} - R{sub b}) << R{sub b}. For precipitation rates high enough that R{sub p} >> R{sub b}, both isotopic and trace element partitioning are controlled by the kinetics of ion attachment to the mineral surface, which tend to favor more rapid incorporation of the light isotopes of Ca and discriminate weakly between trace metals and Ca. With varying precipitation rate, a transition region between equilibrium and kinetic control occurs near R{sub p} {approx} R{sub b} for Ca isotopic fractionation. According to this model, Ca isotopic data can be used to estimate R{sub f} for calcite precipitation. Mechanistic models for calcite precipitation indicate that the molecular exchange rate is not constant at constant T and pH, but rather is dependent also on solution saturation state and hence R{sub p
Exact results for spin dynamics and fractionalization in the Kitaev Model.
Baskaran, G; Mandal, Saptarshi; Shankar, R
2007-06-15
We present certain exact analytical results for dynamical spin correlation functions in the Kitaev Model. It is the first result of its kind in nontrivial quantum spin models. The result is also novel: in spite of the presence of gapless propagating Majorana fermion excitations, dynamical two spin correlation functions are identically zero beyond nearest neighbor separation. This shows existence of a gapless but short range spin liquid. An unusual, all energy scale fractionalization of a spin-flip quanta, into two infinitely massive pi fluxes and a dynamical Majorana fermion, is shown to occur. As the Kitaev Model exemplifies topological quantum computation, our result presents new insights into qubit dynamics and generation of topological excitations.
Biot-JKD model: simulation of 1D transient poroelastic waves with fractional derivatives
Blanc, Emilie; Lombard, Bruno
2012-01-01
A time-domain numerical modeling of Biot poroelastic waves is presented. The viscous dissipation occurring in the pores is described using the dynamic permeability model developed by Johnson-Koplik-Dashen (JKD). Some of the coefficients in the Biot-JKD model are proportional to the square root of the frequency: in the time-domain, these coefficients introduce order 1/2 shifted fractional derivatives involving a convolution product. Based on a diffusive representation, the convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations. Thanks to the dispersion relation, the coefficients in the diffusive representation are obtained by performing an optimization procedure in the frequency range of interest. A splitting strategy is then applied numerically: the propagative part of Biot-JKD equations is discretized using a fourth-order ADER scheme on a Cartesian grid, whereas the diffusive part is solved exactly. Comparisons with analytical solution...
HU Zhen-qi; HE Fen-qin; YIN Jian-zhong; LU Xia; TANG Shi-lu; WANG Lin-lin; LI Xiao-jing
2007-01-01
The objective of this paper is to improve the monitoring speed and precision of fractional vegetation cover (fc). It mainly focuses onfc estimation when fcmax andfcmin are not approximately equal to 100% and 0%, respectively due to using remote sensing image with medium or low spatial resolution. Meanwhile, we present a new method offc estimation based on a random set offc maximum and minimum values from digital camera (DC) survey data and a dimidiate pixel model. The results show that this is a convenient, efficient and accurate method forfc monitoring, with the maximum error -0.172 and correlation coefficient of 0.974 between DC survey data and the estimated value of the remote sensing model. The remaining DC survey data can be used as verification data for the precision of thefc estimation. In general, the estimation offc based on DC survey data and a remote sensing model is a brand-new development trend and deserves further extensive utilization.
Reflectometry using longitudinal, shear and Rayleigh waves.
Chen, W; Wu, J
2000-09-01
A new technique of reflectometry using longitudinal, shear and Rayleigh waves is presented. Reflection coefficient as a function of angle incidence of an ultrasound beam with a finite beamwidth was measured for water-aluminum, water-brass, and water-glass interfaces. The measured values have matched very favorably with the results of numerical calculations based on the angular spectrum of waves method. It has been shown that the speeds of longitudinal, shear and Rayleigh waves of a solid can be determined very accurately by measuring a spectacularly reflected signal versus angle of incidence.
Optical results with Rayleigh quotient discrimination filters
Juday, Richard D.; Rollins, John M.; Monroe, Stanley E., Jr.; Morelli, Michael V.
1999-03-01
We report experimental laboratory results using filters that optimize the Rayleigh quotient [Richard D. Juday, 'Generalized Rayleigh quotient approach to filter optimization,' JOSA-A 15(4), 777-790 (April 1998)] for discriminating between two similar objects. That quotient is the ratio of the correlation responses to two differing objects. In distinction from previous optical processing methods it includes the phase of both objects -- not the phase of only the 'accept' object -- in the computation of the filter. In distinction from digital methods it is explicitly constrained to optically realizable filter values throughout the optimization process.
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.
Yang, Qingxia; Xu, Jun; Cao, Binggang; Li, Xiuqing
2017-01-01
Identification of internal parameters of lithium-ion batteries is a useful tool to evaluate battery performance, and requires an effective model and algorithm. Based on the least square genetic algorithm, a simplified fractional order impedance model for lithium-ion batteries and the corresponding parameter identification method were developed. The simplified model was derived from the analysis of the electrochemical impedance spectroscopy data and the transient response of lithium-ion batteries with different states of charge. In order to identify the parameters of the model, an equivalent tracking system was established, and the method of least square genetic algorithm was applied using the time-domain test data. Experiments and computer simulations were carried out to verify the effectiveness and accuracy of the proposed model and parameter identification method. Compared with a second-order resistance-capacitance (2-RC) model and recursive least squares method, small tracing voltage fluctuations were observed. The maximum battery voltage tracing error for the proposed model and parameter identification method is within 0.5%; this demonstrates the good performance of the model and the efficiency of the least square genetic algorithm to estimate the internal parameters of lithium-ion batteries. PMID:28212405
Yang, Qingxia; Xu, Jun; Cao, Binggang; Li, Xiuqing
2017-01-01
Identification of internal parameters of lithium-ion batteries is a useful tool to evaluate battery performance, and requires an effective model and algorithm. Based on the least square genetic algorithm, a simplified fractional order impedance model for lithium-ion batteries and the corresponding parameter identification method were developed. The simplified model was derived from the analysis of the electrochemical impedance spectroscopy data and the transient response of lithium-ion batteries with different states of charge. In order to identify the parameters of the model, an equivalent tracking system was established, and the method of least square genetic algorithm was applied using the time-domain test data. Experiments and computer simulations were carried out to verify the effectiveness and accuracy of the proposed model and parameter identification method. Compared with a second-order resistance-capacitance (2-RC) model and recursive least squares method, small tracing voltage fluctuations were observed. The maximum battery voltage tracing error for the proposed model and parameter identification method is within 0.5%; this demonstrates the good performance of the model and the efficiency of the least square genetic algorithm to estimate the internal parameters of lithium-ion batteries.
Tan, Cheng; Liang, Zhi-Shan
2016-03-01
In this paper, based on the fact that the inductors and capacitors are of fractional order in nature, the four-order mathematical model of the fractional order quadratic Boost converter in type I and type II discontinuous conduction mode (DCM) — DCM is established by using fractional calculus theory. Direct current (DC) analysis is conducted by using the DC equivalent model and the transfer functions are derived from the corresponding alternating current (AC) equivalent model. The DCM-DCM regions of type I and type II are obtained and the relations between the regions and the orders are found. The influence of the orders on the performance of the quadratic Boost converter in DCM-DCM is verified by numerical and circuit simulations. Simulation results demonstrate the correctness of the fractional order model and the efficiency of the proposed theoretical analysis.
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.
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.
Muñiz-Lerma, Jose Alberto; Paliwal, Manas; Jung, In-Ho; Brochu, Mathieu
2017-04-01
A one-dimensional numerical solidification model has been developed to predict the recovery and refining efficiency of fractional crystallization applied to a blend of aircraft Al scraps with variations of Fe and Si. The model incorporates the effective partition coefficient depending on the degree of melt stirring. Moreover, the kinetic factors that affect the formation of primary Al FCC during fractional crystallization such as solidification velocity, thermal gradient, cooling rate, and solute back-diffusion are taken into account. The simulation results suggest that the optimum solidification velocities that are able to yield the highest refining can be ranged between 1.0 × 10-6 and 1.0 × 10-5 m/s with medium to high stirring levels. The maximum recovery of refined Al has been estimated to be 31 wt pct of the initial scrap when the process is carried out at 1 × 10-6 m/s and the initial concentrations of Fe and Si are 1 and 2 pct, respectively.
Emergent chiral spin liquid: fractional quantum Hall effect in a kagome Heisenberg model.
Gong, Shou-Shu; Zhu, Wei; Sheng, D N
2014-09-10
The fractional quantum Hall effect (FQHE) realized in two-dimensional electron systems under a magnetic field is one of the most remarkable discoveries in condensed matter physics. Interestingly, it has been proposed that FQHE can also emerge in time-reversal invariant spin systems, known as the chiral spin liquid (CSL) characterized by the topological order and the emerging of the fractionalized quasiparticles. A CSL can naturally lead to the exotic superconductivity originating from the condense of anyonic quasiparticles. Although CSL was highly sought after for more than twenty years, it had never been found in a spin isotropic Heisenberg model or related materials. By developing a density-matrix renormalization group based method for adiabatically inserting flux, we discover a FQHE in a spin-½ isotropic kagome Heisenberg model. We identify this FQHE state as the long-sought CSL with a uniform chiral order spontaneously breaking time reversal symmetry, which is uniquely characterized by the half-integer quantized topological Chern number protected by a robust excitation gap. The CSL is found to be at the neighbor of the previously identified Z2 spin liquid, which may lead to an exotic quantum phase transition between two gapped topological spin liquids.
Muñiz-Lerma, Jose Alberto; Paliwal, Manas; Jung, In-Ho; Brochu, Mathieu
2017-01-01
A one-dimensional numerical solidification model has been developed to predict the recovery and refining efficiency of fractional crystallization applied to a blend of aircraft Al scraps with variations of Fe and Si. The model incorporates the effective partition coefficient depending on the degree of melt stirring. Moreover, the kinetic factors that affect the formation of primary Al FCC during fractional crystallization such as solidification velocity, thermal gradient, cooling rate, and solute back-diffusion are taken into account. The simulation results suggest that the optimum solidification velocities that are able to yield the highest refining can be ranged between 1.0 × 10-6 and 1.0 × 10-5 m/s with medium to high stirring levels. The maximum recovery of refined Al has been estimated to be 31 wt pct of the initial scrap when the process is carried out at 1 × 10-6 m/s and the initial concentrations of Fe and Si are 1 and 2 pct, respectively.
Morais, A. P.; Pino, A. V.; Souza, M. N.
2016-08-01
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.
Hamiltonian Analysis of Gauged $CP^{1}$ Model, the Hopf term, and fractional spin
Chakraborty, B
1998-01-01
Recently it was shown by Cho and Kimm that the gauged $CP^1$ model, obtained by gauging the global $SU(2)$ group and adding a corresponding Chern-Simons term, has got its own soliton. These solitons are somewhat distinct from those of pure $CP^1$ model as they cannot always be characterised by $\\pi_2(CP^1)=Z$. In this paper, we first carry out a detailed Hamiltonian analysis of this gauged $CP^1$ model. This reveals that the model has only $SU(2)$ as the gauge invariance, rather than $SU(2) \\times U(1)$. The $U(1)$ gauge invariance of the original (ungauged) $CP^1$ model is actually contained in the $SU(2)$ group itself. Then we couple the Hopf term associated to these solitons and again carry out its Hamiltonian analysis. The symplectic structures, along with the structures of the constraints of these two models (with or without Hopf term) are found to be essentially the same. The model with a Hopf term is shown to have fractional spin which, when computed in the radiation gauge, is found to depend not only ...
TAN Wenchang; XU Mingyu
2004-01-01
The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced. Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus. The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates. In addition, the solutions of the shear stresses at the plates are also determined.
Lee, Geum Seon; Yim, Dongsool; Cheong, Jae Hoon; Kang, Tae Jin
2012-12-01
Our previous report showed that Hydnocarpi Semen (HS) extract has wound repair activity at ulcer lesion in diabetic mice. In this study, fractions of n-Hexane, ethylacetate (EtOAc), and butanol (BuOH) from HS crude extract were evaluated for their wound healing activity by using in vivo diabetic ulcer models and in vitro acute inflammation model. Although n-Hexane and EtOAc fractions promote wound healing in mice with ulcer, the BuOH fraction exhibited the most potent wound healing activity and the wound area score significantly decreased after treatment of BuOH fraction even at dose of 2 mg/kg. BuOH fraction stimulated macrophages to increase the production of nitric oxide (NO) and TNF-α. The BuOH fraction also enhanced the production of TGF-β and VEGF, which were involved in fibroblast activation and angiogenesis. The mRNA expression and activation of MMP-9 were increased by three fractions and the activity was higher in BuOH fraction-treated group compared to the other groups. The mechanism that the HS helps to promote healing of diabetic ulcer is possibly associated with the production of TNF-α, a proinflammatory cytokine, as well as the secretion of VEGF, TGF-β, and MMP-9, which were involved in proliferation of capillaries and fibroblasts. These results suggest that HS can be a new candidate material for the treatment of wound in skin ulcer.
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.
Fractional Response Models - A Replication Exercise of Papke and Wooldridge (1996
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.
Choi, Seo-Woo; Kim, Soree; Jung, YounJoon, E-mail: yjjung@snu.ac.kr [Department of Chemistry, Seoul National University, Seoul 151-747 (Korea, Republic of)
2015-06-28
Kinetically constrained models have gained much interest as models that assign the origins of interesting dynamic properties of supercooled liquids to dynamical facilitation mechanisms that have been revealed in many experiments and numerical simulations. In this work, we investigate the dynamic heterogeneity in the fragile-to-strong liquid via Monte Carlo method using the model that linearly interpolates between the strong liquid-like behavior and the fragile liquid-like behavior by an asymmetry parameter b. When the asymmetry parameter is sufficiently small, smooth fragile-to-strong transition is observed both in the relaxation time and the diffusion constant. Using these physical quantities, we investigate fractional Stokes-Einstein relations observed in this model. When b is fixed, the system shows constant power law exponent under the temperature change, and the exponent has the value between that of the Frederickson-Andersen model and the East model. Furthermore, we investigate the dynamic length scale of our systems and also find the crossover relation between the relaxation time. We ascribe the competition between energetically favored symmetric relaxation mechanism and entropically favored asymmetric relaxation mechanism to the fragile-to-strong crossover behavior.
Berezowski, Tomasz; Chormański, Jarosław; Nossent, Jiri; Batelaan, Okke
2014-05-01
Distributed hydrological models enhance the analysis and explanation of environmental processes. As more spatial input data and time series become available, more analysis is required of the sensitivity of the data on the simulations. Most research so far focussed on the sensitivity of precipitation data in distributed hydrological models. However, these results can not be compared until a universal approach to quantify the sensitivity of a model to spatial data is available. The frequently tested and used remote sensing data for distributed models is snow cover. Snow cover fraction (SCF) remote sensing products are easily available from the internet, e.g. MODIS snow cover product MOD10A1 (daily snow cover fraction at 500m spatial resolution). In this work a spatial sensitivity analysis (SA) of remotely sensed SCF from MOD10A1 was conducted with the distributed WetSpa model. The aim is to investigate if the WetSpa model is differently subjected to SCF uncertainty in different areas of the model domain. The analysis was extended to look not only at SA quantities but also to relate them to the physical parameters and processes in the study area. The study area is the Biebrza River catchment, Poland, which is considered semi natural catchment and subject to a spring snow melt regime. Hydrological simulations are performed with the distributed WetSpa model, with a simulation period of 2 hydrological years. For the SA the Latin-Hypercube One-factor-At-a-Time (LH-OAT) algorithm is used, with a set of different response functions in regular 4 x 4 km grid. The results show that the spatial patterns of sensitivity can be easily interpreted by co-occurrence of different landscape features. Moreover, the spatial patterns of the SA results are related to the WetSpa spatial parameters and to different physical processes. Based on the study results, it is clear that spatial approach of SA can be performed with the proposed algorithm and the MOD10A1 SCF is spatially sensitive in
On Lamb and Rayleigh wave convergence in viscoelastic tissues
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.
On Lamb and Rayleigh Wave Convergence in Viscoelastic Tissues
Nenadic, Ivan Z.; Urban, Matthew W.; Aristizabal, Sara; Mitchell, Scott A.; Humphrey, Tye C.; Greenleaf, James F.
2012-01-01
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 Shearwave 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 (LDUV) to quantify 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 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. PMID:21970846
On Lamb and Rayleigh wave convergence in viscoelastic tissues.
Nenadic, Ivan Z; Urban, Matthew W; Aristizabal, Sara; Mitchell, Scott A; Humphrey, Tye C; Greenleaf, James F
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.
Sun, Hong-xiang; Zhang, Shu-yi; Xia, Jian-ping
2015-06-01
The propagation characteristics of laser-generated Rayleigh waves in coating-substrate structures with anisotropic and viscoelastic properties have been investigated quantitatively. Based on the plane strain theory, finite element models for simulating laser-generated Rayleigh waves in coating-substrate structures are established, in which the carbon fiber-reinforced epoxy matrix composite and aluminum are used as the coating and/or the substrate alternately. The numerical results exhibit that the characteristics of the laser-generated Rayleigh waves, including attenuation, velocity, and dispersion, are mainly and closely related to the anisotropic and viscoelastic properties of the composite in the coating-substrate structures.
Phenomenological Theory for Spatiotemporal Chaos in Rayleigh-Benard Convection
Li, Xiao-jun; Xi, Hao-wen; Gunton, J. D.
1997-01-01
We present a phenomenological theory for spatiotemporal chaos (STC) in Rayleigh-Benard convection, based on the generalized Swift-Hohenberg model. We apply a random phase approximation to STC and conjecture a scaling form for the structure factor $S(k)$ with respect to the correlation length $\\xi_2$. We hence obtain analytical results for the time-averaged convective current $J$ and the time-averaged vorticity current $\\Omega$. We also define power-law behaviors such as $J \\sim \\epsilon^\\mu$,...
Analytical evaluation of atomic form factors: application to Rayleigh scattering
Safari, L; Amaro, P; Jänkälä, K; Fratini, F
2014-01-01
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 wavefunctions. 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.
Turbo Detection in Rayleigh flat fading channel with unknown statistics
Paul Fortier
2010-11-01
Full Text Available The turbo detection of turbo coded symbols over correlated Rayleigh flat fading channels generatedaccording to Jakes’ model is considered in this paper. We propose a method to estimate the channelsignal-to-noise ratio (SNR and the maximum Doppler frequency. These statistics are required bythe linear minimum mean squared error (LMMSE channel estimator. To improve the system convergence,we redefine the channel reliability factor by taking into account the channel estimationerror statistics. Simulation results for rate 1=3 turbo code and two different normalized fading ratesshow that the use of the new reliability factor greatly improves the performance. The improvementis more substantial when channel statistics are unknown.
Tan, Qihua; Thomassen, Mads; Hjelmborg, Jacob V B
2011-01-01
among fractional polynomial models with power terms from a set of fixed values that offer a wide range of curve shapes and suggests a best fitting model. After a limited simulation study, the model has been applied to our human in vivo irritated epidermis data with missing observations to investigate......-course pattern in a gene by gene manner. We introduce a growth curve model with fractional polynomials to automatically capture the various time-dependent expression patterns and meanwhile efficiently handle missing values due to incomplete observations. For each gene, our procedure compares the performances...... time-dependent transcriptional responses to a chemical irritant. Our method was able to identify the various nonlinear time-course expression trajectories. The integration of growth curves with fractional polynomials provides a flexible way to model different time-course patterns together with model...
Modelling groundwater fractal flow with fractional differentiation via Mittag-Leffler law
Ahokposi, D. P.; Atangana, Abdon; Vermeulen, D. P.
2017-04-01
Modelling the flow of groundwater within a network of fractures is perhaps one of the most difficult exercises within the field of geohydrology. This physical problem has attracted the attention of several scientists across the globe. Already two different types of differentiations have been used to attempt modelling this problem including the classical and the fractional differentiation. In this paper, we employed the most recent concept of differentiation based on the non-local and non-singular kernel called the generalized Mittag-Leffler function, to reshape the model of groundwater fractal flow. We presented the existence of positive solution of the new model. Using the fixed-point approach, we established the uniqueness of the positive solution. We solve the new model with three different numerical schemes including implicit, explicit and Crank-Nicholson numerical methods. Experimental data collected from four constant discharge tests conducted in a typical fractured crystalline rock aquifer of the Northern Limb (Bushveld Complex) in the Limpopo Province (South Africa) are compared with the numerical solutions. It is worth noting that the four boreholes (BPAC1, BPAC2, BPAC3, and BPAC4) are located on Faults.
Black holes in multi-fractional and Lorentz-violating models
Calcagni, Gianluca; Rodríguez Fernández, David; Ronco, Michele
2017-05-01
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.
Black holes in multi-fractional and Lorentz-violating models
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.)
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.
Fdez-Güelfo, L A; Álvarez-Gallego, C; Sales Márquez, D; Romero García, L I
2011-01-01
Solid retention time (SRT) is a very important operational variable in continuous and semicontinuous waste treatment processes since the organic matter removal efficiency--expressed in terms of percentage of Dissolved Organic Carbon (% DOC) or Volatile Solids (% VS) removed--and the biogas or methane production are closely related with the SRT imposed. Optimum SRT is depending on the waste characteristics and the microorganisms involved in the process and, hence, it should be determined specifically in each case. In this work a series of experiments were carried out to determine the effect of SRT, from 40 to 8 days, on the performance of the dry (30% Total Solids) thermophilic (55°C) anaerobic digestion of organic fraction of Municipal Solid Wastes (OFMSW) operating at semicontinuous regime of feeding. The experimental results show than 15days is the optimum SRT (the best between all proved) for this process. Besides, data of organic matter concentration and methane production versus SRT have been used to obtain the kinetic parameters of the kinetic model of Romero García (1991): the maximum specific growth rate of the microorganisms (μmax=0.580 days(-1)) and the fraction of substrate non-biodegradable (α=0.268).
Wille, Marie-Luise; Langton, Christian M
2016-02-01
The acceptance of broadband ultrasound attenuation (BUA) for the assessment of osteoporosis suffers from a limited understanding of both ultrasound wave propagation through cancellous bone and its exact dependence upon the material and structural properties. It has recently been proposed that ultrasound wave propagation in cancellous bone may be described by a concept of parallel sonic rays; the transit time of each ray defined by the proportion of bone and marrow propagated. A Transit Time Spectrum (TTS) describes the proportion of sonic rays having a particular transit time, effectively describing the lateral inhomogeneity of transit times over the surface aperture of the receive ultrasound transducer. The aim of this study was to test the hypothesis that the solid volume fraction (SVF) of simplified bone:marrow replica models may be reliably estimated from the corresponding ultrasound transit time spectrum. Transit time spectra were derived via digital deconvolution of the experimentally measured input and output ultrasonic signals, and compared to predicted TTS based on the parallel sonic ray concept, demonstrating agreement in both position and amplitude of spectral peaks. Solid volume fraction was calculated from the TTS; agreement between true (geometric calculation) with predicted (computer simulation) and experimentally-derived values were R(2)=99.9% and R(2)=97.3% respectively. It is therefore envisaged that ultrasound transit time spectroscopy (UTTS) offers the potential to reliably estimate bone mineral density and hence the established T-score parameter for clinical osteoporosis assessment.
Fractional Market Model and its Verification on the Warsaw STOCK Exchange
Kozłowska, Marzena; Kasprzak, Andrzej; Kutner, Ryszard
We analyzed the rising and relaxation of the cusp-like local peaks superposed with oscillations which were well defined by the Warsaw Stock Exchange index WIG in a daily time horizon. We found that the falling paths of all index peaks were described by a generalized exponential function or the Mittag-Leffler (ML) one superposed with various types of oscillations. However, the rising paths (except the first one of WIG which rises exponentially and the most important last one which rises again according to the ML function) can be better described by bullish anti-bubbles or inverted bubbles.2-4 The ML function superposed with oscillations is a solution of the nonhomogeneous fractional relaxation equation which defines here our Fractional Market Model (FMM) of index dynamics which can be also called the Rheological Model of Market. This solution is a generalized analog of an exactly solvable fractional version of the Standard or Zener Solid Model of viscoelastic materials commonly used in modern rheology.5 For example, we found that the falling paths of the index can be considered to be a system in the intermediate state lying between two complex ones, defined by short and long-time limits of the Mittag-Leffler function; these limits are given by the Kohlrausch-Williams-Watts (KWW) law for the initial times, and the power-law or the Nutting law for asymptotic time. Some rising paths (i.e., the bullish anti-bubbles) are a kind of log-periodic oscillations of the market in the bullish state initiated by a crash. The peaks of the index can be viewed as precritical or precrash ones since: (i) the financial market changes its state too early from the bullish to bearish one before it reaches a scaling region (defined by the diverging power-law of return per unit time), and (ii) they are affected by a finite size effect. These features could be a reminiscence of a significant risk aversion of the investors and their finite number, respectively. However, this means that the
Rayleigh scattering and nonlinear inversion of elastic waves
Gritto, R.
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 {minus}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{sub 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.
Dauser, T.; García, J.; Walton, , D. J.; Eikmann, W.; Kallman, T.; McClintock, J.; Wilms, J.
2016-05-01
Aims: The only relativistic reflection model that implements a parameter relating the intensity incident on an accretion disk to the observed intensity is relxill. The parameter used in earlier versions of this model, referred to as the reflection strength, is unsatisfactory; it has been superseded by a parameter that provides insight into the accretion geometry, namely the reflection fraction. The reflection fraction is defined as the ratio of the coronal intensity illuminating the disk to the coronal intensity that reaches the observer. Methods: The relxill model combines a general relativistic ray-tracing code and a photoionization code to compute the component of radiation reflected from an accretion that is illuminated by an external source. The reflection fraction is a particularly important parameter for relativistic models with well-defined geometry, such as the lamp post model, which is a focus of this paper. Results: Relativistic spectra are compared for three inclinations and for four values of the key parameter of the lamp post model, namely the height above the black hole of the illuminating, on-axis point source. In all cases, the strongest reflection is produced for low source heights and high spin. A low-spin black hole is shown to be incapable of producing enhanced relativistic reflection. Results for the relxill model are compared to those obtained with other models and a Monte Carlo simulation. Conclusions: Fitting data by using the relxill model and the recently implemented reflection fraction, the geometry of a system can be constrained. The reflection fraction is independent of system parameters such as inclination and black hole spin. The reflection-fraction parameter was implemented with the name refl_frac in all flavours of the relxill model, and the non-relativistic reflection model xillver, in v0.4a (18 January 2016).
Feng Hou
2016-01-01
Full Text Available The triaxial creep tests of frozen silty clay mixed with sands were performed under different pressures, and the test results demonstrated that, under the low confining pressure, when the shear stress is lower than the long-term strength, the test specimen exhibits an attenuation creep because the strengthening effect is greater than the weakening effect. When the shear stress is higher than the long-term strength, the test specimen exhibits a nonattenuation creep due to the level of the strengthening and weakening effects change in different stages. As the confining pressure increases, the test specimens only exhibit an attenuation creep because of the enhancing strengthening effect. Both the hardening parameter and the damage variable were introduced to describe the strengthening and weakening effects, respectively, and a new creep constitutive model for frozen soil considering these effects was put forward based on the theory of elastoviscoplastic and the fractional derivative. Finally, the model parameters were analyzed and their determination method was also provided to reveal the trend of parameters according to the triaxial test results. The calculated results of the constitutive model show that the proposed model can describe the whole creep process of frozen soil well.
Modeling the Process of Particle Fractionation in a Pneumatic Centrifugal Apparatus
Shvab, A. V.; Evseev, N. S.
2016-07-01
The present investigation pertains to simulation of the aerodynamics of a two-phase nonisothermal twisted turbulent flow in the vortex chamber of an air-centrifugal classifier. The gas phase dynamics was determined with the aid of Reynolds equations whose closure was based on the Wilcox turbulence model. The motion of the solid phase of an ultradisperse powder is simulated by a combination of calculations of the motion trajectories of particular particles in a Lagrangian coordinate system. The influence of turbulent diffusion of particles and of other factors on the efficiency of the segregation of particle fractions by size is shown. The reliability of the results obtained is confirmed by test studies and by comparing numerical results with well-known experimental data.
Shock-Wave Heating Model for Chondrule Formation: Prevention of Isotopic Fractionation
Miura, H; Miura, Hitoshi; Nakamoto, Taishi
2006-01-01
Chondrules are considered to have much information on dust particles and processes in the solar nebula. It is naturally expected that protoplanetary disks observed in present star forming regions have similar dust particles and processes, so study of chondrule formation may provide us great information on the formation of the planetary systems. Evaporation during chondrule melting may have resulted in depletion of volatile elements in chondrules. However, no evidence for a large degree of heavy-isotope enrichment has been reported in chondrules. In order to meet this observed constraint, the rapid heating rate at temperatures below the silicate solidus is required to suppress the isotopic fractionation. We have developed a new shock-wave heating model taking into account the radiative transfer of the dust thermal continuum emission and the line emission of gas molecules and calculated the thermal history of chondrules. We have found that optically-thin shock waves for the thermal continuum emission from dust ...
Haptic feedback control in medical robots through fractional viscoelastic tissue model.
Kobayashi, Yo; Moreira, Pedro; Liu, Chao; Poignet, Philippe; Zemiti, Nabil; Fujie, Masakatsu G
2011-01-01
In this paper, we discuss the design of an adaptive control system for robot-assisted surgery with haptic feedback. Through a haptic device, the surgeon teleoperates the medical instrument in free space, fixed on a remote robot or in contact. In free space, the surgeon feels the motion of the robot. In the present paper, we evaluated the performance of the controller on viscoelastic tissue, modeled by a fractional derivative equation. In addition, we propose a novel controller using an integer formalization process that is suitable for these tissue properties. The simulation results suggested that performance, in terms of force control and telepresence, became poorer when the conventional controller, which was designed for elastic target object, was applied to the viscoelastic tissues. In contrast, the results suggested that our proposed controller maintained its performance on the viscoelastic tissues.
A novel crowd flow model based on linear fractional stable motion
Wei, Juan; Zhang, Hong; Wu, Zhenya; He, Junlin; Guo, Yangyong
2016-03-01
For the evacuation dynamics in indoor space, a novel crowd flow model is put forward based on Linear Fractional Stable Motion. Based on position attraction and queuing time, the calculation formula of movement probability is defined and the queuing time is depicted according to linear fractal stable movement. At last, an experiment and simulation platform can be used for performance analysis, studying deeply the relation among system evacuation time, crowd density and exit flow rate. It is concluded that the evacuation time and the exit flow rate have positive correlations with the crowd density, and when the exit width reaches to the threshold value, it will not effectively decrease the evacuation time by further increasing the exit width.
Density-driven free-convection model for isotopically fractionated geogenic nitrate in sabkha brine
Wood, Warren W.; Böhlke, John Karl
2017-01-01
Subsurface brines with high nitrate (NO3−) concentration are common in desert environments as atmospheric nitrogen is concentrated by the evaporation of precipitation and little nitrogen uptake. However, in addition to having an elevated mean concentration of ∼525 mg/L (as N), NO3− in the coastal sabkhas of Abu Dhabi is enriched in 15N (mean δ15N ∼17‰), which is an enigma. A NO3− solute mass balance analysis of the sabkha aquifer system suggests that more than 90% of the nitrogen is from local atmospheric deposition and the remainder from ascending brine. In contrast, isotopic mass balances based on Δ17O, δ15N, and δ18O data suggest approximately 80 to 90% of the NO3− could be from ascending brine. As the sabkha has essentially no soil, no vegetation, and no anthropogenic land or water use, we propose to resolve this apparent contradiction with a density-driven free-convection transport model. In this conceptual model, the density of rain is increased by solution of surface salts, transporting near-surface oxygenated NO3− bearing water downward where it encounters reducing conditions and mixes with oxygen-free ascending geologic brines. In this environment, NO3− is partially reduced to nitrogen gas (N2), thus enriching the remaining NO3− in heavy isotopes. The isotopically fractionated NO3− and nitrogen gas return to the near-surface oxidizing environment on the upward displacement leg of the free-convection cycle, where the nitrogen gas is released to the atmosphere and new NO3− is added to the system from atmospheric deposition. This recharge/recycling process has operated over many cycles in the 8000-year history of the shallow aquifer, progressively concentrating and isotopically fractionating the NO3−.
Yang Ning-Ning; Liu Chong-Xin; Wu Chao-Jun
2012-01-01
In this paper,the fractional-order mathematical model and the fractional-order state-space averaging model of the Buck-Boost converter in continuous conduction mode (CCM) are established based on the fractional calculus and the Adomian decomposition method.Some dynamical properties of the current-mode controlled fractional-order BuckBoost converter are analysed.The simulation is accomplished by using SIMULINK.Numerical simulations are presented to verify the analytical results and we find that bifurcation points will be moved backward as α and β vary.At the same time,the simulation results show that the converter goes through different routes to chaos.
Wennberg, Berit M.; Baumann, Pia; Gagliardi, Giovanna (Dept. of Medical Physics, Karolinska Univ. Hospital and the Karolinska Inst., Stockholm (Sweden)), e-mail: berit.wennberg@karolinska.se (and others)
2011-05-15
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 alpha/beta = 3 Gy was used and the USC parameters used were: alpha/beta = 3 Gy, D{sub 0} = 1.0 Gy, n = 10, alpha 0.206 Gy-1 and d{sub 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{sub 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 surface waves, phonon mode conversion, and thermal transport in nanostructures
Maurer, Leon; Knezevic, Irena
We study the effects of phonon mode conversion and Rayleigh (surface) waves on thermal transport in nanostructures. We present a technique to calculate thermal conductivity in the elastic-solid approximation: a finite-difference time-domain (FDTD) solution of the elastic or scalar wave equations combined with the Green-Kubo formula. The technique is similar to an equilibrium molecular dynamics simulation, captures phonon wave behavior, and scales well to nanostructures that are too large to simulate with many other techniques. By imposing fixed or free boundary conditions, we can selectively turn off mode conversion and Rayleigh waves to study their effects. In the example case of graphenelike nanoribbons with rough edges, we find that mode conversion among bulk modes has little effect on thermal transport, but that conversion between bulk and Rayleigh waves can significantly reduce thermal conductivity. With increasing surface disorder, Rayleigh waves readily become trapped by the disorder and draw energy away from the propagating bulk modes, which lowers thermal conductivity. We discuss the implications on the accuracy of popular phonon-surface scattering models that stem from scalar wave equations and cannot capture mode conversion to Rayleigh waves.
Rayleigh wave inversion using heat-bath simulated annealing algorithm
Lu, Yongxu; Peng, Suping; Du, Wenfeng; Zhang, Xiaoyang; Ma, Zhenyuan; Lin, Peng
2016-11-01
The dispersion of Rayleigh waves can be used to obtain near-surface shear (S)-wave velocity profiles. This is performed mainly by inversion of the phase velocity dispersion curves, which has been proven to be a highly nonlinear and multimodal problem, and it is unsuitable to use local search methods (LSMs) as the inversion algorithm. In this study, a new strategy is proposed based on a variant of simulated annealing (SA) algorithm. SA, which simulates the annealing procedure of crystalline solids in nature, is one of the global search methods (GSMs). There are many variants of SA, most of which contain two steps: the perturbation of model and the Metropolis-criterion-based acceptance of the new model. In this paper we propose a one-step SA variant known as heat-bath SA. To test the performance of the heat-bath SA, two models are created. Both noise-free and noisy synthetic data are generated. Levenberg-Marquardt (LM) algorithm and a variant of SA, known as the fast simulated annealing (FSA) algorithm, are also adopted for comparison. The inverted results of the synthetic data show that the heat-bath SA algorithm is a reasonable choice for Rayleigh wave dispersion curve inversion. Finally, a real-world inversion example from a coal mine in northwestern China is shown, which proves that the scheme we propose is applicable.
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.
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.
The role of fractional calculus in modeling biological phenomena: A review
Ionescu, C.; Lopes, A.; Copot, D.; Machado, J. A. T.; Bates, J. H. T.
2017-10-01
This review provides the latest developments and trends in the application of fractional calculus (FC) in biomedicine and biology. Nature has often showed to follow rather simple rules that lead to the emergence of complex phenomena as a result. Of these, the paper addresses the properties in respiratory lung tissue, whose natural solutions arise from the midst of FC in the form of non-integer differ-integral solutions and non-integer parametric models. Diffusion of substances in human body, e.g. drug diffusion, is also a phenomena well known to be captured with such mathematical models. FC has been employed in neuroscience to characterize the generation of action potentials and spiking patters but also in characterizing bio-systems (e.g. vegetable tissues). Despite the natural complexity, biological systems belong as well to this class of systems, where FC has offered parsimonious yet accurate models. This review paper is a collection of results and literature reports who are essential to any versed engineer with multidisciplinary applications and bio-medical in particular.
The emergence of nonuniform spatiotemporal fractionation schemes within the standard BED model
Unkelbach, Jan, E-mail: junkelbach@mgh.harvard.edu; Papp, Dávid [Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114 (United States)
2015-05-15
Purpose: Nonuniform spatiotemporal radiotherapy fractionation schemes, i.e., delivering distinct dose distributions in different fractions can potentially improve the therapeutic ratio. This is possible if the dose distributions are designed such that similar doses are delivered to normal tissues (exploit the fractionation effect) while hypofractionating subregions of the tumor. In this paper, the authors develop methodology for treatment planning with nonuniform fractions and demonstrate this concept in the context of intensity-modulated proton therapy (IMPT). Methods: Treatment planning is performed by simultaneously optimizing (possibly distinct) IMPT dose distributions for multiple fractions. This is achieved using objective and constraint functions evaluated for the cumulative biologically equivalent dose (BED) delivered at the end of treatment. BED based treatment planning formulations lead to nonconvex optimization problems, such that local gradient based algorithms require adequate starting positions to find good local optima. To that end, the authors develop a combinatorial algorithm to initialize the pencil beam intensities. Results: The concept of nonuniform spatiotemporal fractionation schemes is demonstrated for a spinal metastasis patient treated in two fractions using stereotactic body radiation therapy. The patient is treated with posterior oblique beams with the kidneys being located in the entrance region of the beam. It is shown that a nonuniform fractionation scheme that hypofractionates the central part of the tumor allows for a skin and kidney BED reduction of approximately 10%–20%. Conclusions: Nonuniform spatiotemporal fractionation schemes represent a novel approach to exploit fractionation effects that deserves further exploration for selected disease sites.
Analysis of Rayleigh waves with circular wavefront: a maximum likelihood approach
Maranò, Stefano; Hobiger, Manuel; Bergamo, Paolo; Fäh, Donat
2017-09-01
Analysis of Rayleigh waves is an important task in seismology and geotechnical investigations. In fact, properties of Rayleigh waves such as velocity and polarization are important observables that carry information about the structure of the subsoil. Applications analysing Rayleigh waves include active and passive seismic surveys. In active surveys, there is a controlled source of seismic energy and the sensors are typically placed near the source. In passive surveys, there is not a controlled source, rather, seismic waves from ambient vibrations are analysed and the sources are assumed to be far outside the array, simplifying the analysis by the assumption of plane waves. Whenever the source is in the proximity of the array of sensors or even within the array it is necessary to model the wave propagation accounting for the circular wavefront. In addition, it is also necessary to model the amplitude decay due to geometrical spreading. This is the case of active seismic surveys in which sensors are located near the seismic source. In this work, we propose a maximum likelihood (ML) approach for the analysis of Rayleigh waves generated at a near source. Our statistical model accounts for the curvature of the wavefront and amplitude decay due to geometrical spreading. Using our method, we show applications on real data of the retrieval of Rayleigh wave dispersion and ellipticity. We employ arrays with arbitrary geometry. Furthermore, we show how it is possible to combine active and passive surveys. This enables us to enlarge the analysable frequency range and therefore the depths investigated. We retrieve properties of Rayleigh waves from both active and passive surveys and show the excellent agreement of the results from the two surveys. In our approach we use the same array of sensors for both the passive and the active survey. This greatly simplifies the logistics necessary to perform a survey.
Rayleigh-maximum-likelihood bilateral filter for ultrasound image enhancement.
Li, Haiyan; Wu, Jun; Miao, Aimin; Yu, Pengfei; Chen, Jianhua; Zhang, Yufeng
2017-04-17
Ultrasound imaging plays an important role in computer diagnosis since it is non-invasive and cost-effective. However, ultrasound images are inevitably contaminated by noise and speckle during acquisition. Noise and speckle directly impact the physician to interpret the images and decrease the accuracy in clinical diagnosis. Denoising method is an important component to enhance the quality of ultrasound images; however, several limitations discourage the results because current denoising methods can remove noise while ignoring the statistical characteristics of speckle and thus undermining the effectiveness of despeckling, or vice versa. In addition, most existing algorithms do not identify noise, speckle or edge before removing noise or speckle, and thus they reduce noise and speckle while blurring edge details. Therefore, it is a challenging issue for the traditional methods to effectively remove noise and speckle in ultrasound images while preserving edge details. To overcome the above-mentioned limitations, a novel method, called Rayleigh-maximum-likelihood switching bilateral filter (RSBF) is proposed to enhance ultrasound images by two steps: noise, speckle and edge detection followed by filtering. Firstly, a sorted quadrant median vector scheme is utilized to calculate the reference median in a filtering window in comparison with the central pixel to classify the target pixel as noise, speckle or noise-free. Subsequently, the noise is removed by a bilateral filter and the speckle is suppressed by a Rayleigh-maximum-likelihood filter while the noise-free pixels are kept unchanged. To quantitatively evaluate the performance of the proposed method, synthetic ultrasound images contaminated by speckle are simulated by using the speckle model that is subjected to Rayleigh distribution. Thereafter, the corrupted synthetic images are generated by the original image multiplied with the Rayleigh distributed speckle of various signal to noise ratio (SNR) levels and
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.
Can a Time Fractional-Derivative Model Capture Scale-Dependent Dispersion in Saturated Soils?
Garrard, Rhiannon M; Zhang, Yong; Wei, Song; Sun, HongGuang; Qian, Jiazhong
2017-07-10
Time nonlocal transport models such as the time fractional advection-dispersion equation (t-fADE) were proposed to capture well-documented non-Fickian dynamics for conservative solutes transport in heterogeneous media, with the underlying assumption that the time nonlocality (which means that the current concentration change is affected by previous concentration load) embedded in the physical models can release the effective dispersion coefficient from scale dependency. This assumption, however, has never been systematically examined using real data. This study fills this historical knowledge gap by capturing non-Fickian transport (likely due to solute retention) documented in the literature (Huang et al. 1995) and observed in our laboratory from small to intermediate spatial scale using the promising, tempered t-fADE model. Fitting exercises show that the effective dispersion coefficient in the t-fADE, although differing subtly from the dispersion coefficient in the standard advection-dispersion equation, increases nonlinearly with the travel distance (varying from 0.5 to 12 m) for both heterogeneous and macroscopically homogeneous sand columns. Further analysis reveals that, while solute retention in relatively immobile zones can be efficiently captured by the time nonlocal parameters in the t-fADE, the motion-independent solute movement in the mobile zone is affected by the spatial evolution of local velocities in the host medium, resulting in a scale-dependent dispersion coefficient. The same result may be found for the other standard time nonlocal transport models that separate solute retention and jumps (i.e., displacement). Therefore, the t-fADE with a constant dispersion coefficient cannot capture scale-dependent dispersion in saturated porous media, challenging the application for stochastic hydrogeology methods in quantifying real-world, preasymptotic transport. Hence improvements on time nonlocal models using, for example, the novel subordination
Fractional-order elastic models of cartilage: A multi-scale approach
Magin, Richard L.; Royston, Thomas J.
2010-03-01
The objective of this research is to develop new quantitative methods to describe the elastic properties (e.g., shear modulus, viscosity) of biological tissues such as cartilage. Cartilage is a connective tissue that provides the lining for most of the joints in the body. Tissue histology of cartilage reveals a multi-scale architecture that spans a wide range from individual collagen and proteoglycan molecules to families of twisted macromolecular fibers and fibrils, and finally to a network of cells and extracellular matrix that form layers in the connective tissue. The principal cells in cartilage are chondrocytes that function at the microscopic scale by creating nano-scale networks of proteins whose biomechanical properties are ultimately expressed at the macroscopic scale in the tissue's viscoelasticity. The challenge for the bioengineer is to develop multi-scale modeling tools that predict the three-dimensional macro-scale mechanical performance of cartilage from micro-scale models. Magnetic resonance imaging (MRI) and MR elastography (MRE) provide a basis for developing such models based on the nondestructive biomechanical assessment of cartilage in vitro and in vivo. This approach, for example, uses MRI to visualize developing proto-cartilage structure, MRE to characterize the shear modulus of such structures, and fractional calculus to describe the dynamic behavior. Such models can be extended using hysteresis modeling to account for the non-linear nature of the tissue. These techniques extend the existing computational methods to predict stiffness and strength, to assess short versus long term load response, and to measure static versus dynamic response to mechanical loads over a wide range of frequencies (50-1500 Hz). In the future, such methods can perhaps be used to help identify early changes in regenerative connective tissue at the microscopic scale and to enable more effective diagnostic monitoring of the onset of disease.
Rayleigh reflections and nonlinear acoustics of solids
Breazeale, M. A.
1980-10-01
Schlierken studies of ultrasonic waves, and nonlinear acoustics of solids are addressed. A goniometer for use in a Schlieren system for visualization of ultrasonic waves in liquids is described. The goniometer is used to obtain Schlieren photographs of leaky Rayleigh waves excited on an Al2O3 layer on a stainless steel reflector immersed in water, showing that the Rayleigh wave velocity in this case is less than that of either a water Al203 layer or a water stainless steel layer. Also investigated are: (1) nonlinearity parameters and third order elastic constants of copper between 300 and 3 K; (2) measurement of nonlinearity parameters in small solid samples by the harmonic generation technique; (3) relationship between solid nonlinearity parameters and thermodynamic Gruneisen parameters; and (4) quantum mechanical theory of nonlinear interaction of ultrasonic waves.
Modulational instability arising from collective Rayleigh scattering.
Robb, G R M; McNeil, B W J
2003-02-01
It is shown that under certain conditions a collection of dielectric Rayleigh particles suspended in a viscous medium and enclosed in a bidirectional ring cavity pumped by a strong laser field can produce a new modulational instability transverse to the wave-propagation direction. The source of the instability is collective Rayleigh scattering i.e., the spontaneous formation of periodic longitudinal particle-density modulations and a backscattered optical field. Using a linear stability analysis a dispersion relation is derived which determines the region of parameter space in which modulational instability of the backscattered field and the particle distribution occurs. In the linear regime the pump is modulationally stable. A numerical analysis is carried out to observe the dynamics of the interaction in the nonlinear regime. In the nonlinear regime the pump field also becomes modulationally unstable and strong pump depletion occurs.
ALE simulation of Rayleigh-Taylor instability
Anbarlooei, H.R. [Univ. of Science and Technology, Dept. of Mechanical Engineering, Tehran (Iran, Islamic Republic of); Mazaheri, K. [Univ. of Tarbiyat Modares, Dept. of Mechanical Engineering, Tehran, (Iran, Islamic Republic of)]. E-mail: Kiumars@modares.ac.ir; Bidabadi, M. [Univ. of Science and Technology, Dept. of Mechanical Engineering, Tehran (Iran, Islamic Republic of)
2004-07-01
This paper investigates the use of an Arbitrary Lagrangian-Eulerian (ALE) technique for the simulation of a single mode Rayleigh-Taylor instability. A compatible Lagrangian algorithm is used on a simply connected quadrilateral grid in Lagrangian Phase. This algorithm includes subzonal pressures, which are used to control spurious grid motion, and an edge centered artificial viscosity. We use Reference Jacobians optimization based rezone algorithm in the rezoning phase of ALE method. Also a second order sign preserving method is used for remapping. To force monotonocity in remapping phase a Repair algorithm is used. Finally, for remapping of nodal variables we used a second order transformer to transfer these data to cell centers. It is shown that the usage of these algorithms for an ALE method can improve the simulation of a single mode Rayleigh-Taylor Instability. (author)
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...
Tavakoli-Kakhki, Mahsan; Haeri, Mohammad
2011-07-01
Fractional order PI and PID controllers are the most common fractional order controllers used in practice. In this paper, a simple analytical method is proposed for tuning the parameters of these controllers. The proposed method is useful in designing fractional order PI and PID controllers for control of complicated fractional order systems. To achieve the goal, at first a reduction technique is presented for approximating complicated fractional order models. Then, based on the obtained reduced models some analytical rules are suggested to determine the parameters of fractional order PI and PID controllers. Finally, numerical results are given to show the efficiency of the proposed tuning algorithm.
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 crystalli......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...
Large-eddy-simulation of 3-dimensional Rayleigh-Taylor instability in incompressible fluids
WANG; Lili
2002-01-01
., Stratocumulus-capped mixed layers derived from a three-dimensional model, Boundary Layer Meteorology, 18: 295-527.［15］Read, K. I., Experimental investigation of turbulent mixing by Rayleigh-Taylor instability, Physica D, 1984, 12: 45-58.［16］Youngs, D. L., Numerical simulation of turbulent mixing by Rayleigh-Taylor instability, Physica D, 1984, 12: 32-44.［17］Youngs, D. L., Modeling turbulent mixing by Rayleigh-Taylor instability, Physica D, 1989, 37: 270-287.［18］Moeng, G. H., A large eddy simulation model for the study of planetary boundary layer turbulence, J. Atmos. Sci., 1984, 41(13): 2052-2062.［19］Lesieur, M., Metais, Q., New trends in large-eddy simulations of turbulence, Annu. Rev. Fluid Mech., 1996, 28: 45-82.［20］Metais, Q., Lesieur, M., Spectral large-eddy simulations of isotropic and stably-stratified turbulence, J. Fluid Mech., 1992, 239: 157-194.
Manfredi, Simone; Tonini, Davide; Christensen, Thomas Højlund
2011-01-01
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......, by means of LCA-modelling, aims at comparing the environmental performance of three major management options (landfilling, recycling and incineration or composting) for a number of individual waste fractions. The landfilling option is here approached comprehensively, accounting for all technical...... 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...
Akram, Ghazala; Batool, Fiza
2017-05-01
The (G'/G) -expansion method is utilized for a reliable treatment of space-time fractional biological population model. The method has been applied in the sense of the Jumarie's modified Riemann-Liouville derivative. Three classes of exact traveling wave solutions, hyperbolic, trigonometric and rational solutions of the associated equation are characterized with some free parameters. A generalized fractional complex transform is applied to convert the fractional equations to ordinary differential equations which subsequently resulted in number of exact solutions. It should be mentioned that the (G'/G) -expansion method is very effective and convenient for solving nonlinear partial differential equations of fractional order whose balancing number is a negative integer.
Akram, Ghazala; Batool, Fiza
2017-10-01
The (G'/G)-expansion method is utilized for a reliable treatment of space-time fractional biological population model. The method has been applied in the sense of the Jumarie's modified Riemann-Liouville derivative. Three classes of exact traveling wave solutions, hyperbolic, trigonometric and rational solutions of the associated equation are characterized with some free parameters. A generalized fractional complex transform is applied to convert the fractional equations to ordinary differential equations which subsequently resulted in number of exact solutions. It should be mentioned that the (G'/G)-expansion method is very effective and convenient for solving nonlinear partial differential equations of fractional order whose balancing number is a negative integer.
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.
Grünwald-Letnikov operators for fractional relaxation in Havriliak-Negami models
Garrappa, Roberto
2016-09-01
Several classes of differential and integral operators of non integer order have been proposed in the past to model systems exhibiting anomalous and hereditary properties. A wide range of complex and heterogeneous systems are described in terms of laws of Havriliak-Negami type involving a special fractional relaxation whose behavior in the time-domain can not be represented by any of the existing operators. In this work we introduce new integral and differential operators for the description of Havriliak-Negami models in the time-domain. In particular we propose a formulation of Grünwald-Letnikov type which turns out to be effective not only to provide a theoretical characterization of the operators associated to Havriliak-Negami systems but also for computational purposes. We study some properties of the new operators and, by means of some numerical experiments, we present their use in practical computation and we show the superiority with respect to the few other approaches previously proposed in literature.
Mvogo, Alain; Tambue, Antoine; Ben-Bolie, Germain H.; Kofané, Timoléon C.
2016-10-01
We investigate localized wave solutions in a network of Hindmarsh-Rose neural model taking into account the long-range diffusive couplings. We show by a specific analytical technique that the model equations in the infrared limit (wave number k → 0) can be governed by the complex fractional Ginzburg-Landau (CFGL) equation. According to the stiffness of the system, we propose both the semi and the linearly implicit Riesz fractional finite-difference schemes to solve efficiently the CFGL equation. The obtained fractional numerical solutions for the nerve impulse reveal localized short impulse properties. We also show the equivalence between the continuous CFGL and the discrete Hindmarsh-Rose models for relatively large network.
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.
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...
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% ...
Spinal cord tolerance to reirradiation with single-fraction radiosurgery: a swine model.
Medin, P.M.; Foster, R.D.; Kogel, A.J. van der; Sayre, J.W.; McBride, W.H.; Solberg, T.D.
2012-01-01
PURPOSE: This study was performed to determine swine spinal cord tolerance to single-fraction, partial-volume irradiation 1 year after receiving uniform irradiation to 30 Gy in 10 fractions. METHODS AND MATERIALS: A 10-cm length of spinal cord (C3-T1) was uniformly irradiated to 30 Gy in 10 consecut
Hattel, Jesper Henri; Pryds, Nini
2006-01-01
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...
Gonzalez, C. M.; Sanchez, D. A.; Yuen, D. A.; Wright, G. B.; Barnett, G. A.
2010-12-01
As computational modeling became prolific throughout the physical sciences community, newer and more efficient ways of processing large amounts of data needed to be devised. One particular method for processing such large amounts of data arose in the form of using a graphics processing unit (GPU) for calculations. Computational scientists were attracted to the GPU as a computational tool as the performance, growth, and availability of GPUs over the past decade increased. Scientists began to utilize the GPU as the sole workhorse for their brute force calculations and modeling. The GPUs, however, were not originally designed for this style of use. As a result, difficulty arose when trying to find a use for the GPU from a scientific standpoint. A lack of parallel programming routines was the main culprit behind the difficulty in programming with a GPU, but with time and a rise in popularity, NVIDIA released a proprietary architecture named Fermi. The Fermi architecture, when used in conjunction with development tools such as CUDA, allowed the programmer easier access to routines that made parallel programming with the NVIDIA GPUs an ease. This new architecture enabled the programmer full access to faster memory, double-precision support, and large amounts of global memory at their fingertips. Our model was based on using a second-order, spatially correct finite difference method and a third order Runge-Kutta time-stepping scheme for studying the 2D Rayleigh-Benard code. The code extensively used the CUBLAS routines to do the heavy linear algebra calculations. The calculations themselves were completed using a single GPU, the NVDIA C2070 Fermi, which boasts 6 GB of global memory. The overall scientific goal of our work was to apply the Tesla C2070's computing potential to achieve an onset of flow reversals as a function of increasing large Rayleigh numbers. Previous investigations were successful using a smaller grid size of 1000x1999 and a Rayleigh number of 10^9. The
Transient growth in Rayleigh-B\\'enard-Poiseuille/Couette convection
Jerome, J John Soundar; Huerre, Patrick
2016-01-01
An investigation of the effect of a destabilizing cross-stream temperature gradient on the transient growth phenomenon of plane Poiseuille flow and plane Couette flow is presented. Only the streamwise-uniform and nearly streamwise-uniform disturbances are highly influenced by the Rayleigh number Ra and Prandtl number Pr. The maximum optimal transient growth G max of streamwise-uniform disturbances increases slowly with increasing Ra and decreasing Pr. For all Ra and Pr, at moderately large Reynolds numbersRe, the supremum of G max is always attained for streamwise-uniform perturbations (or nearly streamwise-uniform perturbations, in the case of plane Couette flow) which produce large streamwise streaks and Rayleigh-B\\'enard convection rolls (RB). The optimal growth curves retain the same large-Reynolds-number scaling as in pure shear flow. A 3D vector model of the governing equations demonstrates that the short-time behavior is governed by the classical lift-up mechanism and that the influence of Ra on this m...
Experimental and theoretical study of Rayleigh-Lamb wave propagation
Rogers, Wayne P.; Datta, Subhendu K.; Ju, T. H.
1990-01-01
Many space structures, such as the Space Station Freedom, contain critical thin-walled components. The structural integrity of thin-walled plates and shells can be monitored effectively using acoustic emission and ultrasonic testing in the Rayleigh-Lamb wave frequency range. A new PVDF piezoelectric sensor has been developed that is well suited to remote, inservice nondestructive evaluation of space structures. In the present study the new sensor was used to investigate Rayleigh-Lamb wave propagation in a plate. The experimental apparatus consisted of a glass plate (2.3 m x 25.4 mm x 5.6 mm) with PVDF sensor (3 mm diam.) mounted at various positions along its length. A steel ball impact served as a simulated acoustic emission source, producing surface waves, shear waves and longitudinal waves with dominant frequencies between 1 kHz and 200 kHz. The experimental time domain wave-forms were compared with theoretical predictions of the wave propagation in the plate. The model uses an analytical solution for the Green's function and the measured response at a single position to predict response at any other position in the plate. Close agreement was found between the experimental and theoretical results.
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.
Microsegregation and Rayleigh number variation during the solidification of superalloy Inconel 718
Ling Wang; Jianxin Dong; Yuliang Tian; Lei Zhang
2008-01-01
The microstructure and composition of the residual liquid at different temperatures were investigated by scanning electron microscopy (SEM) and energy dispersive X-ray spectrometer (EDX) associated with the Thermo-calc software calculation of the equilibrium phase diagrams of Inconel 718 and segregated liquid. The liquid density difference and Rayleigh number variation dur-ing solidification were estimated as well. It is found that the heavy segregation of Nb in liquid prompts the precipitation of δ and Laves phase directly from liquid and the resultant quenched liquid microstructure consists of pro-eutectic γ+eutectic, or complete eutectic according to the content of Nb from low to high. The liquid density increases with decreasing temperature during the solidi-fication of Inconel 718 and the liquid density difference is positive. The largest relative Rayleigh number occurs at 1320℃ when the liquid fraction is about 40vol%.
Study on Electrohydrodynamic Rayleigh-Taylor Instability with Heat and Mass Transfer
Mukesh Kumar Awasthi
2014-01-01
Full Text Available The linear analysis of Rayleigh-Taylor instability of the interface between two viscous and dielectric fluids in the presence of a tangential electric field has been carried out when there is heat and mass transfer across the interface. In our earlier work, the viscous potential flow analysis of Rayleigh-Taylor instability in presence of tangential electric field was studied. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer coefficient, and vapour fraction on the stability of the system. It has been observed that heat transfer and electric field both have stabilizing effect on the stability of the system.
Kumar, Arvind; Dutta, Pradip [Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012 (India)], E-mail: pradip@mecheng.iisc.ernet.in
2008-08-07
Movement of solid crystals in the form of dendrite fragments causes severe macro-segregation in solidified products. Dendrite fragmentation in the developing mushy zone occurs as a result of remelting (causing dissolution) and subsequent breakage of dendritic side arms from the dendritic stalks. An understanding of the mechanisms of dendrite fragmentation is essential for predicting the transport of fragmented solid crystals for possible control of macro-segregation. In this work, a Rayleigh number based fragmentation criterion is developed for detachment of dendrites from the developing mushy zone, which determines the conditions favourable for fragmentation of dendrites. The Rayleigh number, defined in this paper, measures the ratio of the driving buoyancy force for the flow in the mushy zone to the retarding frictional force associated with the permeability of the mush. The criterion developed is a function of the concentration difference, liquid fraction, permeability, growth rate of mushy layer and thermophysical properties of the material.
Hiniker, Susan M; Modlin, Leslie A; Choi, Clara Y; Atalar, Banu; Seiger, Kira; Binkley, Michael S; Harris, Jeremy P; Liao, Yaping Joyce; Fischbein, Nancy; Wang, Lei; Ho, Anthony; Lo, Anthony; Chang, Steven D; Harsh, Griffith R; Gibbs, Iris C; Hancock, Steven L; Li, Gordon; Adler, John R; Soltys, Scott G
2016-04-01
Patients with tumors adjacent to the optic nerves and chiasm are frequently not candidates for single-fraction stereotactic radiosurgery (SRS) due to concern for radiation-induced optic neuropathy. However, these patients have been successfully treated with hypofractionated SRS over 2-5 days, though dose constraints have not yet been well defined. We reviewed the literature on optic tolerance to radiation and constructed a dose-response model for visual pathway tolerance to SRS delivered in 1-5 fractions. We analyzed optic nerve and chiasm dose-volume histogram (DVH) data from perioptic tumors, defined as those within 3mm of the optic nerves or chiasm, treated with SRS from 2000-2013 at our institution. Tumors with subsequent local progression were excluded from the primary analysis of vision outcome. A total of 262 evaluable cases (26 with malignant and 236 with benign tumors) with visual field and clinical outcomes were analyzed. Median patient follow-up was 37 months (range: 2-142 months). The median number of fractions was 3 (1 fraction n = 47, 2 fraction n = 28, 3 fraction n = 111, 4 fraction n = 10, and 5 fraction n = 66); doses were converted to 3-fraction equivalent doses with the linear quadratic model using α/β = 2Gy prior to modeling. Optic structure dose parameters analyzed included Dmin, Dmedian, Dmean, Dmax, V30Gy, V25Gy, V20Gy, V15Gy, V10Gy, V5Gy, D50%, D10%, D5%, D1%, D1cc, D0.50cc, D0.25cc, D0.20cc, D0.10cc, D0.05cc, D0.03cc. From the plan DVHs, a maximum-likelihood parameter fitting of the probit dose-response model was performed using DVH Evaluator software. The 68% CIs, corresponding to one standard deviation, were calculated using the profile likelihood method. Of the 262 analyzed, 2 (0.8%) patients experienced common terminology criteria for adverse events grade 4 vision loss in one eye, defined as vision of 20/200 or worse in the affected eye. One of these patients had received 2 previous courses of radiotherapy to the optic structures
Internally heated convection and Rayleigh-Bénard convection
Goluskin, David
2016-01-01
This Brief describes six basic models of buoyancy-driven convection in a fluid layer: three configurations of internally heated convection and three configurations of Rayleigh-Bénard convection. The author discusses the main quantities that characterize heat transport in each model, along with the constraints on these quantities. This presentation is the first to place the various models in a unified framework, and similarities and differences between the cases are highlighted. Necessary and sufficient conditions for convective motion are given. For the internally heated cases only, parameter-dependent lower bounds on the mean fluid temperature are proven, and results of past simulations and laboratory experiments are summarized and reanalyzed. The author poses several open questions for future study.
DSMC simulation of Rayleigh-Brillouin scattering in binary mixtures
Bruno, Domenico; Frezzotti, Aldo; Ghiroldi, Gian Pietro
2016-11-01
Rayleigh-Brillouin scattering spectra (RBS) in dilute gas mixtures have been simulated by the Direct Simulation Monte Carlo method (DSMC). Different noble gas binary mixtures have been considered and the spectra have been simulated adopting the hard sphere collision model. It is suggested that DSMC simulations can be used in the interpretation of light scattering experiments in place of approximate kinetic models. Actually, the former have a firmer physical ground and can be readily extended to treat gas mixtures of arbitrary complexity. The results obtained confirm the capability of DSMC to predict experimental spectra and clears the way towards the simulation of polyatomic gas mixtures of interest for actual application (notably, air) where tractable kinetic model equations are still lacking.
Breakup of diminutive Rayleigh jets
van Hoeve, Wim; Snoeijer, Jacco H; Versluis, Michel; Brenner, Michael P; Lohse, Detlef
2010-01-01
Discharging a liquid from a nozzle at sufficient large velocity leads to a continuous jet that due to capillary forces breaks up into droplets. Here we investigate the formation of microdroplets from the breakup of micron-sized jets with ultra high-speed imaging. The diminutive size of the jet implies a fast breakup time scale $\\tau_\\mathrm{c} = \\sqrt{\\rho r^3 / \\gamma}$ of the order of 100\\,ns{}, and requires imaging at 14 million frames per second. We directly compare these experiments with a numerical lubrication approximation model that incorporates inertia, surface tension, and viscosity [Eggers and Dupont, J. Fluid Mech. 262, 205 (1994); Shi, Brenner, and Nagel, Science 265, 219 (1994)]. The lubrication model allows to efficiently explore the parameter space to investigate the effect of jet velocity and liquid viscosity on the formation of satellite droplets. In the phase diagram we identify regions where the formation of satellite droplets is suppressed. We compare the shape of the droplet at pinch-off...
Wilms, Matthias; Werner, René; Yamamoto, Tokihiro; Handels, Heinz; Ehrhardt, Jan
2017-06-26
Correspondence modelling between low-dimensional breathing signals and internal organ motion is a prerequisite for application of advanced techniques in radiotherapy of moving targets. Patient-specific correspondence models can, for example, be built prior to treatment based on a planning 4D CT and simultaneously acquired breathing signals. Reliability of pre-treatment-built models depends, however, on the degree of patient-specific inter-fraction motion variations. This study investigates whether motion estimation accuracy in the presence of inter-fraction motion variations can be improved using correspondence models that incorporate motion information from different patients. The underlying assumption is that inter-patient motion variations resemble patient-specific inter-fraction motion variations for subpopulations of patients with similar breathing characteristics. The hypothesis is tested by integrating a sparse manifold clustering approach into a regression-based correspondence modelling framework that allows for automated identification of patient subpopulations. The evaluation is based on a total of 73 lung 4D CT data sets, including two cohorts of patients with repeat 4D CT scans (cohort 1: 14 patients; cohort 2: ten patients). The results are consistent for both cohorts: The subpopulation-based modelling approach outperforms general population modelling (models built on all data sets available) as well as pre-treatment-built models trained on only the patient-specific motion information. The results thereby support the hypothesis and illustrate the potential of subpopulation-based correspondence modelling.
Beresh, Steven Jay; Grasser, Thomas W.; Kearney, Sean Patrick; Schefer, Robert W.
2004-01-01
Simulation-based life-cycle-engineering and the ASCI program have resulted in models of unprecedented size and fidelity. The validation of these models requires high-resolution, multi-parameter diagnostics. Within the thermal-fluids disciplines, the need for detailed, high-fidelity measurements exceeds the limits of current engineering sciences capabilities and severely tests the state of the art. The focus of this LDRD is the development and application of filtered Rayleigh scattering (FRS) for high-resolution, nonintrusive measurement of gas-phase velocity and temperature. With FRS, the flow is laser-illuminated and Rayleigh scattering from naturally occurring sources is detected through a molecular filter. The filtered transmission may be interpreted to yield point or planar measurements of three-component velocities and/or thermodynamic state. Different experimental configurations may be employed to obtain compromises between spatial resolution, time resolution, and the quantity of simultaneously measured flow variables. In this report, we present the results of a three-year LDRD-funded effort to develop FRS combustion thermometry and Aerosciences velocity measurement systems. The working principles and details of our FRS opto-electronic system are presented in detail. For combustion thermometry we present 2-D, spatially correlated FRS results from nonsooting premixed and diffusion flames and from a sooting premixed flame. The FRS-measured temperatures are accurate to within {+-}50 K (3%) in a premixed CH4-air flame and within {+-}100 K for a vortex-strained diluted CH4-air diffusion flame where the FRS technique is severely tested by large variation in scattering cross section. In the diffusion flame work, FRS has been combined with Raman imaging of the CH4 fuel molecule to correct for the local light scattering properties of the combustion gases. To our knowledge, this is the first extension of FRS to nonpremixed combustion and the first use of joint FRS
Free vibrations of a taut cable with a general viscoelastic damper modeled by fractional derivatives
Sun, Limin; Chen, Lin
2015-01-01
This study extends dynamic understanding of a taut cable with a viscous damper at arbitrary location to that with a general linear viscoelastic (VE) damper portrayed by a five-parameter fractional derivative model (FDM). The FDM is able to describe a generalized relationship between force and deformation of viscoelastic dampers (material) in a wide frequency range, which can simulate a practical damper including its support condition or a secondary tie between neighboring cables. Free vibrations of the passively controlled cable system have then been formulated analytically through complex modal analysis. For the restricted case that the FDM is installed close to one cable anchorage, asymptotic solutions for the system complex frequency and modal damping are presented; explicit formulas have also been derived to determine the maximal attainable damping and corresponding optimum FDM parameters, based on which effects of frequency-dependent damper properties are appreciated. Considering the FDM located at arbitrary location, the three distinct regimes of frequency evolutions observed for a cable with a viscous damper have been generalized to that with a VE damper; also, new characteristics of the regime diagram and the frequency evolution in each regime are observed.
Liang Cui
2015-07-01
Full Text Available Irrigation water management is crucial for agricultural production and livelihood security in many regions and countries throughout the world. In this study, a two-stage stochastic fractional programming (TSFP method is developed for planning an agricultural water resources management system under uncertainty. TSFP can provide an effective linkage between conflicting economic benefits and the associated penalties; it can also balance conflicting objectives and maximize the system marginal benefit with per unit of input under uncertainty. The developed TSFP method is applied to a real case of agricultural water resources management of the Zhangweinan River Basin China, which is one of the main food and cotton producing regions in north China and faces serious water shortage. The results demonstrate that the TSFP model is advantageous in balancing conflicting objectives and reflecting complicated relationships among multiple system factors. Results also indicate that, under the optimized irrigation target, the optimized water allocation rate of Minyou Channel and Zhangnan Channel are 57.3% and 42.7%, respectively, which adapts the changes in the actual agricultural water resources management problem. Compared with the inexact two-stage water management (ITSP method, TSFP could more effectively address the sustainable water management problem, provide more information regarding tradeoffs between multiple input factors and system benefits, and help the water managers maintain sustainable water resources development of the Zhangweinan River Basin.
Fractional derivative and hereditary combined model for memory effects on flexible polyurethane foam
Elfarhani, Makram; Jarraya, Abdessalem; Abid, Said; Haddar, Mohamed
2016-06-01
In a quasi-static regime with cyclic loading, the force-displacement curve of flexible polyurethane exhibits complicated behavior: nonlinearity, visco-elasticity, hysteresis, residual force, etc. Beside nonlinearity and visco-elasticity, this material displays high dependence on the displacement rate and past loading history. Its dependence on compression rate helps to appropriately identify the force-displacement curve. Based on the new curve identification, the overall foam response is assumed to be a composite of a nonlinear elastic component and a visco-elastic component. The elastic component is expressed as a polynomial function in displacement, while the visco-elastic one is formulated according to the hereditary approach to represent the foam visco-elastic damping force during the loading phase and according to the fractional derivative approach during unloading to represent the visco-elastic residual force in the material. The focus of this study was to develop mathematical formulations and identification parameters to faithfully characterize the visco-elastic behavior of flexible polyurethane foam under multi-cycle compressive tests. A parameter calibration methodology based on the separation of the measurement data of each component force was established. This optimization process helps to avoid the parameter values admixture problem during the phase of numeric calculations of the same component force. The validity of the model results is checked according to the simulation accuracy, the physical significance of results and their agreement with the obtained force-displacement curve identification.
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.
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
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.
Stevens, Adam H.; Patel, Manish R.; Lewis, Stephen R.
2017-01-01
We calculate transport timescales of martian methane and investigate the effect of potential release mechanisms into the atmosphere using a numerical model that includes both Fickian and Knudsen diffusion. The incorporation of Knudsen diffusion, which improves on a Fickian description of transport given the low permeability of the martian regolith, means that transport timescales from sources collocated with a putative martian water table are very long, up to several million martian years. Transport timescales also mean that any temporally varying source process, even in the shallow subsurface, would not result in a significant, observable variation in atmospheric methane concentration since changes resulting from small variations in flux would be rapidly obscured by atmospheric transport. This means that a short-lived 'plume' of methane, as detected by Mumma et al. (2009) and Webster et al. (2014), cannot be reconciled with diffusive transport from any reasonable depth and instead must invoke alternative processes such as fracturing or convective plumes. It is shown that transport through the martian regolith will cause a significant change in the isotopic composition of the gas, meaning that methane release from depth will produce an isotopic signature in the atmosphere that could be significantly different than the source composition. The deeper the source, the greater the change, and the change in methane composition in both δ13C and δD approaches -1000 ‰ for sources at a depth greater than around 1 km. This means that signatures of specific sources, in particular the methane produced by biogenesis that is generally depleted in 13CH4 and CH3D, could be obscured. We find that an abiogenic source of methane could therefore display an isotopic fractionation consistent with that expected for biogenic source processes if the source was at sufficient depth. The only unambiguous inference that can be made from measurements of methane isotopes alone is a measured
HE Hailun; SONG Jinbao; Patrick J. Lynett; LI Shuang
2009-01-01
Fractional energy losses of waves due to wave breaking when passing over a submerged bar are studied systematically using a modified numerical code that is based on the high-order Boussinesq-type equations. The model is first tested by the additional experimental data, and the model's capability of simulating the wave transformation over both gentle slope and steep slope is demonstrated. Then, the model's breaking index is replaced and tested. The new breaking index, which is optimized from the several breaking indices, is not sensitive to the spatial grid length and includes the bottom slopes. Numerical tests show that the modified model with the new breaking index is more stable and efficient for the shallow-water wave breaking. Finally, the modified model is used to study the fractional energy losses for the regular waves propagating and breaking over a submerged bar. Our results have revealed that how the nonlinearity and the dispersion of the incident waves as well as the dimensionless bar height (normalized by water depth) dominate the fractional energy losses. It is also found that the bar slope (limited to gentle slopes that less than 1:10) and the dimensionless bar length (normalized by incident wave length) have negligible effects on the fractional energy losses.
IMPROVEMENT OF BUBBLE MODEL FOR CAVITATING FLOW SIMULATIONS
TAMURA Y.; MATSUMOTO Y.
2009-01-01
In the present research,a bubble dynamics based model for cavitating flow simulations is extended to higher void fraction region for wider range of applications.The present bubble model is based on the so-called Rayleigh-Plesset equation that calculates a temporal bubble radius with the surrounding liquid pressure and is considered to be valid in an area below a certain void fraction.The solution algorithm is modified so that the Rayleigh-Plesset equation is no more solved once the bubble radius(or void fraction)reaches at a certain value till the liquid pressure recovers above the vapor pressure in order to overcome this problem.This procedure is expected to stabilize the numerical calculation.The results of simple two-dimensional flow field are presented compared with the existing bubble model.
In situ Characterization of Nanoparticles Using Rayleigh Scattering
Biswajit Santra; Shneider, Mikhail N; Roberto Car
2017-01-01
We report a theoretical analysis showing that Rayleigh scattering could be used to monitor the growth of nanoparticles under arc discharge conditions. We compute the Rayleigh scattering cross sections of the nanoparticles by combining light scattering theory for gas-particle mixtures with calculations of the dynamic electronic polarizability of the nanoparticles. We find that the resolution of the Rayleigh scattering probe is adequate to detect nanoparticles as small as C60 at the expected co...
FE FORMULATION FOR THE VISCOELASTIC BODY MODELED BY FRACTIONAL CONSTITUTIVE LAW
Zhang Wei(张卫); Nobuyuki Shimizu
2001-01-01
This paper presents finite element (FE) fornulation of the viscoelastic materials described by fractional constitutive law. The time-domain threedimensional constitutive equation is constructed. The FE equations are set up by treating the fractional operator as a special case of the hereditary integration. The equations are solved by numerical integration method. The numerical algorithm de veloped by the authors for Liouville-Riemann's fractional derivative was adopted to formulate FE procedures and extended to solve the more general case of the hereditary integration. The numerical examples were given to show the correctness and effectiveness of the integration algorithm.
G. I. Vasilieva
2010-01-01
Full Text Available The article presents experimental data on regulatory effect of neutrophilokine helper fractions on the macrophage (Mph functional activity in the course of antiplague immunity formation. It has revealed that these fractions content biologically active, low-molecular weight peptides. They stimulate Mph killing activity by increasing phagosome-lysosome fusion, thus boosting transformation of monocytes to Mph, and causing redistribution of macrophage subpopulations in the total cellular pool. The helper effect of neutrophilokine fractions upon functional activity of MPh is more pronounced during secondary immune response.
HUANG; Guanhua; HUANG; Quanzhong; ZHAN; Hongbin
2005-01-01
The newly developed Fractional Advection-Dispersion Equation (FADE), which is FADE was extended and used in this paper for modelling adsorbing contaminant transport by adding an adsorbing term. A parameter estimation method and its corresponding FORTRAN based program named FADEMain were developed on the basis of Nonlinear Least Square Algorithm and the analytical solution for one-dimensional FADE under the conditions of step input and steady state flow. Data sets of adsorbing contaminants Cd and NH4+-N transport in short homogeneous soil columns and conservative solute NaCI transport in a long homogeneous soil column, respectively were used to estimate the transport parameters both by FADEMain and the advection-dispersion equation (ADE) based program CXTFIT2.1. Results indicated that the concentration simulated by FADE agreed well with the measured data. Compared to the ADE model, FADE can provide better simulation for the concentration in the initial lower concentration part and the late higher concentration part of the breakthrough curves for both adsorbing contaminants. The dispersion coefficients for ADE were from 0.13 to 7.06 cm2/min, while the dispersion coefficients for FADE ranged from 0.119 to 3.05 cm1.856/min for NaCI transport in the long homogeneous soil column. We found that the dispersion coefficient of FADE increased with the transport distance, and the relationship between them can be quantified with an exponential function. Less scale-dependent was also found for the dispersion coefficient of FADE with respect to ADE.
Gerstenfeld, Edward P; Lavi, Nimrod; Bazan, Victor; Gojraty, Sattar; Kim, Steven J; Michele, John
2011-07-01
Complex fractionated atrial electrograms (CFEs) have been described as a target during atrial fibrillation (AF) ablation; however, the mechanism leading to CFEs is poorly understood. We used noncontact mapping in a canine model of AF to determine the activation patterns in areas of CFEs. Sustained AF was induced in 10 canines with 10-12 weeks of atrial tachy-pacing at 440 ppm. A roving mapping catheter and noncontact multielectrode array (MEA) were deployed in the left atrium (LA). NavX software was used to construct a contact bipolar CFE LA map. The MEA was then used to reconstruct wavefront propagation in proximity to CFE regions. Wavefront propagation was assessed during three separate recording segments for each site. There were 34 CFE regions identified (3.4/dog) and 102 noncontact CFE regional activation sequences studied. The CFE regions were stereotypically located at the junctions of (1) the left pulmonary vein (PV)/posterior LA, (2) right inferior PV/posterior LA, (3) right superior PV/anterior LA, and (4) the LA roof. The majority (47%) of CFE recordings were characterized by wavefront collision, usually between circulating LA wavefronts and entry/exit from the PVs. Thirty-eight (38%) CFE recordings were noted to be the central functional barrier of a reentrant wavefront. Ablation through CFE regions due to reentry led to AF termination and noninducibility in 3/5 animals. In this pacing-induced AF model, common causes of CFEs include: (1) wavefront collision, (2) conduction through channels of functional block, (3) reentry. The vast majority of these CFE regions were caused by wavefront collision rather than true "drivers" of AF. ©2011, The Authors. Journal compilation ©2011 Wiley Periodicals, Inc.
Ruilan Dong
Full Text Available The objectives of this trial were to develop multiple linear regression (MLR models and three-layer Levenberg-Marquardt back propagation (BP3 neural network models using the Cornell Net Carbohydrate and Protein System (CNCPS carbohydrate fractions as dietary variables for predicting in vitro rumen volatile fatty acid (VFA production and further compare MLR and BP3 models. Two datasets were established for the trial, of which the first dataset containing 45 feed mixtures with concentrate/roughage ratios of 10∶90, 20∶80, 30∶70, 40∶60, and 50∶50 were used for establishing the models and the second dataset containing 10 feed mixtures with the same concentrate/roughage ratios with the first dataset were used for testing the models. The VFA production of feed samples was determined using an in vitro incubation technique. The CNCPS carbohydrate fractions (g, i.e. CA (sugars, CB1 (starch and pectin, CB2 (available cell wall of feed samples were calculated based on chemical analysis. The performance of MLR models and BP3 models were compared using a paired t-test, the determination coefficient (R2 and the root mean square prediction error (RMSPE between observed and predicted values. Statistical analysis indicated that VFA production (mmol was significantly correlated with CNCPS carbohydrate fractions (g CA, CB1, and CB2 in a multiple linear pattern. Compared with MLR models, BP3 models were more accurate in predicting acetate, propionate, and total VFA production while similar in predicting butyrate production. The trial indicated that both MLR and BP3 models were suitable for predicting in vitro rumen VFA production of feed mixtures using CNCPS carbohydrate fractions CA, CB1, and CB2 as input dietary variables while BP3 models showed greater accuracy for prediction.
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
Xu, Kangning; Zhang, Yufen; Wang, Yan; Ling, Peng; Xie, Xin; Jiang, Chenyao; Zhang, Zhizhen; Lian, Xiao-Yuan
2014-01-01
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 astrocytes and neurons
Performance of Multicarrier CDMA Rake System over Rayleigh Fading Channel
SONG Li-xin; HUANG Tian-shu; DING Yao-ming
2005-01-01
Based on the theory of multicarrier (MC) technique and the Rake receiver, a multicarrier DSCDMA Rake system is proposed, where a data sequence multiplied by a spreading sequence modulates multiple carriers. The receiver provides a Rake for each subcarrier, and the outputs of the Rakes are combined by a maximal-ratio combiner. The average probability of error of the system is derived from an uncorrelated subcarrier and frequency-selective fading channel model. The system performances are evaluated over Rayleigh fading channel with an exponential multipath intensity profile(MIP) and with a rectangular MIP, respectively,when multipath interference is present. It is found that this kind of model has larger superiority in an exponential MIP than in a rectangular MIP.
Rayleigh-Taylor stabilization by material strength at Mbar pressures
Remington, Bruce; Park, Hye-Sook; Lorenz, Thomas; Cavallo, Robert; Pollaine, Stephen; Prisbrey, Shon; Rudd, Robert; Becker, Richard; Bernier, Joel
2009-11-01
We present experiments on the Rayleigh-Taylor (RT) instability in the plastic flow regime of solid-state vanadium (V) foils at 1 Mbar pressures and strain rates of 1.e6-1.e8 1/s, using a laser based, ramped-pressure acceleration technique. High pressure material strength causes strong stabilization of the RT instability at short wavelengths. Comparisons with 2D simulations utilizing models of high pressure strength show that the V strength increases by factors of 3-4 at peak pressure, compared to its ambient strength. An effective lattice viscosity of 400 poise would have a similar effect. [1] Constitutive models, and theoretical implications of these experiments will be discussed. [1] H.S. Park, B.A. Remington et al., submitted for publication (July, 2009).
Shahbari, Juhaina Awawdeh; Peled, Irit
2015-01-01
This study investigates the effect of using a realistic situation with modeling characteristics in creating and resolving a cognitive conflict to promote understanding of a changing reference in fraction calculations. The study was conducted among 96 seventh graders divided into 2 experimental groups and 1 control group. The experimental groups…
Shahbari, Juhaina Awawdeh; Peled, Irit
2015-01-01
This study investigates the effect of using a realistic situation with modeling characteristics in creating and resolving a cognitive conflict to promote understanding of a changing reference in fraction calculations. The study was conducted among 96 seventh graders divided into 2 experimental groups and 1 control group. The experimental groups…
Davijani, Nafiseh Zare; Jahanfarnia, Gholamreza; Abharian, Amir Esmaeili
2017-01-01
One of the most important issues with respect to nuclear reactors is power control. In this study, we designed a fractional-order sliding mode controller based on a nonlinear fractional-order model of the reactor system in order to track the reference power trajectory and overcome uncertainties and external disturbances. Since not all of the variables in an operating reactor are measurable or specified in the control law, we propose a reduced-order fractional neutron point kinetic (ROFNPK) model based on measurable variables. In the design, we assume the differences between the approximated model and the real system is limited. We use the obtained model in the controller design process and use the Lyapunov method to perform a stability analysis of the closed-loop system. We simulate the proposed reduced-order fractional-order sliding mode controller (ROFOSMC) using Matlab/Simulink, and its performance is compared with that of a reduced order integer-order sliding mode controller (ROIOSMC). Our simulation results indicate an acceptable performance of the proposed approach in tracking the reference power trajectory with respect to ROIOSMC because of faster response of control effort signal and the smaller tracking error. Moreover, the results illustrate the capability of the controller in rejection of the disturbance and the noise signals and the robustness of controller against uncertainty.
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...
Leaky Rayleigh wave investigation on mortar samples.
Neuenschwander, J; Schmidt, Th; Lüthi, Th; Romer, M
2006-12-01
Aggressive mineralized ground water may harm the concrete cover of tunnels and other underground constructions. Within a current research project mortar samples are used to study the effects of sulfate interaction in accelerated laboratory experiments. A nondestructive test method based on ultrasonic surface waves was developed to investigate the topmost layer of mortar samples. A pitch and catch arrangement is introduced for the generation and reception of leaky Rayleigh waves in an immersion technique allowing the measurement of their propagation velocity. The technique has been successfully verified for the reference materials aluminium, copper, and stainless steel. First measurements performed on mortar specimens demonstrate the applicability of this new diagnostic tool.
Global study of Rayleigh-Duffing oscillators
Chen, Hebai; Zou, Lan
2016-04-01
In this paper we investigate the global dynamics of Rayleigh-Duffing oscillators with global parameters, including equilibria at both finity and infinity, existences and coexistence of limit cycles and homoclinic loops. In fact, this oscillator will occur Hopf bifurcations, homoclinic bifurcations and double limit cycle bifurcations. Moreover, we find that the homoclinic bifurcation of this oscillator is special which is a gluing bifurcation. The global bifurcation diagram and all phase portrait are given, and numerical simulations are shown to verify our analysis finally.
Decoherence due to elastic rayleigh scattering
Uys, H
2010-11-01
Full Text Available in this manuscript now enables an accurate calculation of Rayleigh decoherence for these low-field trapped ion as well as other coherent-control experiments. We thank W.M. Itano, J. P. Britton, D. Hanneke, and M. J. Holland for useful suggestions.M. J. B.... acknowledges support from Georgia Tech and IARPA. D.M. is supported by NSF. This work was supported by the DARPA OLE program and by IARPA. This manuscript is the contribution of NIST and is not subject to U.S. copyright. *huys@csir.co.za †john...
Lechleitner, Franziska A.; Jamieson, Robert A.; McIntyre, Cameron; Baldini, Lisa M.; Baldini, James U. L.; Eglinton, Timothy I.
2015-04-01
Over the past two decades, speleothems have become one of the most versatile and promising archives for the study of past continental climate. Very precise absolute dating is often possible using the U-Th method, resulting in paleoclimate records of exceptional resolution and accuracy. However, not all speleothems are amenable to this dating method for a variety of reasons (e.g. low U concentrations, high detrital Th etc). This has lead researchers to exclude many otherwise suitable speleothems and cave sites from further investigation. 14C-dating of speleothems has so far not been applicable, due to the 'dead carbon' problem. As drip water percolates through the karst, dissolving CaCO3, a variable amount of 14C-dead carbon is added to the solution. This results in a temporally variable and site-specific reservoir effect, ultimately undermining the development of speleothem 14C -chronologies. However, a number of recent studies have shown a clear link between karst hydrology and associated proxies (e.g., Mg/Ca and δ13C) and this 'dead carbon fraction' (DCF). We take advantage of this relationship to model DCF and its changes using Mg/Ca, δ13C and 14C data from published speleothem records. Using one record for calibration purposes, we build a transfer function for the DCF in relation to δ13C and Mg/Ca, which we then apply to other 14C records. Initial model results are promising; we are able to reconstruct general long-term average DCF within uncertainties of the calculated DCF from the U-Th chronology. Large shifts in DCF related to hydrology are also often detected. In a second step, we apply the model to a speleothem from southern Poland, which so far could not be dated, due to very low U-concentrations. To construct a 14C chronology, the stalagmite was sampled at 5 mm intervals. CaCO3 powders were graphitized and measured by Accelerator Mass Spectrometry (MICADAS) at ETH Zurich. Additional high-resolution (0.1 mm/sample) 14C measurements were performed on
Khalansky, D.; Popova, E.; Gladyshev, P.; Dushanov, E.; Kholmurodov, Kh.
2014-12-01
Aqueous electrolyte solutions play an important role in many electrophysical and chemical processes in aerospace technology and industrial applications. As noncovalent interactions, the interactions between ions are crucially important for biomolecular structures as well (protein structure folding, molecular level processes followed by ionic pair correlations, the formation of flexible hydrate shells, and so on). Specifically, ions (cations and anions with the same valence charges) can form stable pairs if their sizes match. The formation of ionic pairs can substantially affect the thermodynamic stabilities of proteins in the alkali salts physiologically present in the human body. Research aims and problems impose severe demands on readjustments of the ionic force fields and potential parameters developed to describe aqueous solutions and electrolytic systems. Ionic solutions and their interaction with biomolecules have been observed for over 100 years [1], but the behavior of such solutions remains poorly studied today. New data obtained in this work deals with parameterization strategies and adjustments for the ionic force fields of the alkali cations and halide anions that should be helpful in biomolecular research. Using molecular dynamics (MD) models, four electrolytic systems (HCl-H2O, LiCl-H2O, NaCl-H2O, and KCl-H2O) are investigated as binary mixtures of water and cations and anions, respectively. The intermolecular interaction parameters are varied for two of the four model electrolytes (HCl-H2O and NaCl-H2O) to simulate the possibility of different ionic shells forming during interaction with water. It is found that varying the potential parameters strongly affects the dynamic and structural characteristics of electrolyte systems. MD simulations are performed in the temperature range of 300 to 600 K with a step of 50 K. MD simulations for all electrolyte models (HCl-H2O, LiCl-H2O, NaCl-H2O, KCl-H2O) are also conducted for different molar fractions of
Bahatdin Daşbaşı
2017-06-01
Full Text Available In this study, it is described the general forms of fractional-order differential equations and asymtotic stability of their system’s equilibria. In addition that, the stability analysis of equilibrium points of the local bacterial infection model which is fractional-order differential equation system, is made. Results of this analysis are supported via numerical simulations drawn by datas obtained from literature for mycobacterium tuberculosis and the antibiotics isoniazid (INH, rifampicin (RIF, streptomycin (SRT and pyrazinamide (PRZ used against this bacterial infection.
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.
Das, Saptarshi
2014-01-01
In this paper, an incommensurate fractional order (FO) model has been proposed to generate ECG like waveforms. Earlier investigation of ECG like waveform generation is based on two identical Van-der Pol (VdP) family of oscillators which are coupled by time delays and gains. In this paper, we suitably modify the three state equations corresponding to the nonlinear cross-product of states, time delay coupling of the two oscillators and low-pass filtering, using the concept of fractional derivatives. Our results show that a wide variety of ECG like waveforms can be simulated from the proposed generalized models, characterizing heart conditions under different physiological conditions. Such generalization of the modelling of ECG waveforms may be useful to understand the physiological process behind ECG signal generation in normal and abnormal heart conditions. Along with the proposed FO models, an optimization based approach is also presented to estimate the VdP oscillator parameters for representing a realistic ...
Impact of Fractionation and Dose in a Multivariate Model for Radiation-Induced Chest Wall Pain
Din, Shaun U. [Department of Radiation Oncology, Memorial Sloan Kettering Cancer Center, New York, New York (United States); Williams, Eric L.; Jackson, Andrew [Department of Medical Physics, Memorial Sloan Kettering Cancer Center, New York, New York (United States); Rosenzweig, Kenneth E. [Department of Radiation Oncology, Mount Sinai Medical Center, New York, New York (United States); Wu, Abraham J.; Foster, Amanda [Department of Radiation Oncology, Memorial Sloan Kettering Cancer Center, New York, New York (United States); Yorke, Ellen D. [Department of Medical Physics, Memorial Sloan Kettering Cancer Center, New York, New York (United States); Rimner, Andreas, E-mail: rimnera@mskcc.org [Department of Radiation Oncology, Memorial Sloan Kettering Cancer Center, New York, New York (United States)
2015-10-01
Purpose: To determine the role of patient/tumor characteristics, radiation dose, and fractionation using the linear-quadratic (LQ) model to predict stereotactic body radiation therapy–induced grade ≥2 chest wall pain (CWP2) in a larger series and develop clinically useful constraints for patients treated with different fraction numbers. Methods and Materials: A total of 316 lung tumors in 295 patients were treated with stereotactic body radiation therapy in 3 to 5 fractions to 39 to 60 Gy. Absolute dose–absolute volume chest wall (CW) histograms were acquired. The raw dose-volume histograms (α/β = ∞ Gy) were converted via the LQ model to equivalent doses in 2-Gy fractions (normalized total dose, NTD) with α/β from 0 to 25 Gy in 0.1-Gy steps. The Cox proportional hazards (CPH) model was used in univariate and multivariate models to identify and assess CWP2 exposed to a given physical and NTD. Results: The median follow-up was 15.4 months, and the median time to development of CWP2 was 7.4 months. On a univariate CPH model, prescription dose, prescription dose per fraction, number of fractions, D83cc, distance of tumor to CW, and body mass index were all statistically significant for the development of CWP2. Linear-quadratic correction improved the CPH model significance over the physical dose. The best-fit α/β was 2.1 Gy, and the physical dose (α/β = ∞ Gy) was outside the upper 95% confidence limit. With α/β = 2.1 Gy, V{sub NTD99Gy} was most significant, with median V{sub NTD99Gy} = 31.5 cm{sup 3} (hazard ratio 3.87, P<.001). Conclusion: There were several predictive factors for the development of CWP2. The LQ-adjusted doses using the best-fit α/β = 2.1 Gy is a better predictor of CWP2 than the physical dose. To aid dosimetrists, we have calculated the physical dose equivalent corresponding to V{sub NTD99Gy} = 31.5 cm{sup 3} for the 3- to 5-fraction groups.
Ducros, F.
1996-06-12
Here is a study about fluid flows (the hydrodynamic part of codes modeling the plasma dynamics) showing great gradients and unsteady flows (Rayleigh-Taylor, Richtmyer-Meshkov). The numerical resolution of these problems needs codes able to simulate the transition at the turbulence. The code exposed here (NSMP), tries to answer to these demands by the resolution of Navier-Stokes equations. After the resolution of these equations are presented the consequences of the discretization of continuous equations of fluids mechanics and then a modeling of turbulence is introduced. The two last chapters are devoted to the simulation of Rayleigh-Taylor instabilities. (N.C.). 34 refs., 39 figs., 8 colour plates.
Wang, Xiao-Tian; Yan, Hai-Gang; Tang, Ming-Ming; Zhu, En-Hui
2010-02-01
A model for option pricing of fractional version of the Merton model with ‘Hurst exponent’ H being in [1/2,1) is established with transaction costs. In particular, for H∈(1/2,1) the minimal price Cmin(t,St) of an option under transaction costs is obtained, which displays that the timestep δt and the ‘Hurst exponent’ H play an important role in option pricing with transaction costs.
A survival model for fractionated radiotherapy with an application to prostate cancer
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