Modeling of heat conduction via fractional derivatives
Fabrizio, Mauro; Giorgi, Claudio; Morro, Angelo
2017-09-01
The modeling of heat conduction is considered by letting the time derivative, in the Cattaneo-Maxwell equation, be replaced by a derivative of fractional order. The purpose of this new approach is to overcome some drawbacks of the Cattaneo-Maxwell equation, for instance possible fluctuations which violate the non-negativity of the absolute temperature. Consistency with thermodynamics is shown to hold for a suitable free energy potential, that is in fact a functional of the summed history of the heat flux, subject to a suitable restriction on the set of admissible histories. Compatibility with wave propagation at a finite speed is investigated in connection with temperature-rate waves. It follows that though, as expected, this is the case for the Cattaneo-Maxwell equation, the model involving the fractional derivative does not allow the propagation at a finite speed. Nevertheless, this new model provides a good description of wave-like profiles in thermal propagation phenomena, whereas Fourier's law does not.
State-Space Modelling of Loudspeakers using Fractional Derivatives
DEFF Research Database (Denmark)
King, Alexander Weider; Agerkvist, Finn T.
2015-01-01
This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response of a fractio......This work investigates the use of fractional order derivatives in modeling moving-coil loudspeakers. A fractional order state-space solution is developed, leading the way towards incorporating nonlinearities into a fractional order system. The method is used to calculate the response...... of a fractional harmonic oscillator, representing the mechanical part of a loudspeaker, showing the effect of the fractional derivative and its relationship to viscoelasticity. Finally, a loudspeaker model with a fractional order viscoelastic suspension and fractional order voice coil is fit to measurement data...
Analysis of Drude model using fractional derivatives without singular kernels
Directory of Open Access Journals (Sweden)
Jiménez Leonardo Martínez
2017-11-01
Full Text Available We report study exploring the fractional Drude model in the time domain, using fractional derivatives without singular kernels, Caputo-Fabrizio (CF, and fractional derivatives with a stretched Mittag-Leffler function. It is shown that the velocity and current density of electrons moving through a metal depend on both the time and the fractional order 0 < γ ≤ 1. Due to non-singular fractional kernels, it is possible to consider complete memory effects in the model, which appear neither in the ordinary model, nor in the fractional Drude model with Caputo fractional derivative. A comparison is also made between these two representations of the fractional derivatives, resulting a considered difference when γ < 0.8.
Large deflection of viscoelastic beams using fractional derivative model
International Nuclear Information System (INIS)
Bahranini, Seyed Masoud Sotoodeh; Eghtesad, Mohammad; Ghavanloo, Esmaeal; Farid, Mehrdad
2013-01-01
This paper deals with large deflection of viscoelastic beams using a fractional derivative model. For this purpose, a nonlinear finite element formulation of viscoelastic beams in conjunction with the fractional derivative constitutive equations has been developed. The four-parameter fractional derivative model has been used to describe the constitutive equations. The deflected configuration for a uniform beam with different boundary conditions and loads is presented. The effect of the order of fractional derivative on the large deflection of the cantilever viscoelastic beam, is investigated after 10, 100, and 1000 hours. The main contribution of this paper is finite element implementation for nonlinear analysis of viscoelastic fractional model using the storage of both strain and stress histories. The validity of the present analysis is confirmed by comparing the results with those found in the literature.
Epps, Brenden; Cushman-Roisin, Benoit
2017-11-01
Fluid turbulence is an outstanding unsolved problem in classical physics, despite 120+ years of sustained effort. Given this history, we assert that a new mathematical framework is needed to make a transformative breakthrough. This talk offers one such framework, based upon kinetic theory tied to the statistics of turbulent transport. Starting from the Boltzmann equation and ``Lévy α-stable distributions'', we derive a turbulence model that expresses the turbulent stresses in the form of a fractional derivative, where the fractional order is tied to the transport behavior of the flow. Initial results are presented herein, for the cases of Couette-Poiseuille flow and 2D boundary layers. Among other results, our model is able to reproduce the logarithmic Law of the Wall in shear turbulence.
Directory of Open Access Journals (Sweden)
Yang Xiao-Jun
2017-01-01
Full Text Available In this paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from mathematical view of point. The comparative results of the anomalous relaxation among the various fractional derivatives are also given. They are very efficient in description of the complex phenomenon arising in heat transfer.
Directory of Open Access Journals (Sweden)
Yang Xiao-Jun
2016-01-01
Full Text Available In this article we propose a new fractional derivative without singular kernel. We consider the potential application for modeling the steady heat-conduction problem. The analytical solution of the fractional-order heat flow is also obtained by means of the Laplace transform.
A Semianalytical Solution of the Fractional Derivative Model and Its Application in Financial Market
Directory of Open Access Journals (Sweden)
Lina Song
2018-01-01
Full Text Available Fractional differential equation has been introduced to the financial theory, which presents new ideas and tools for the theoretical researches and the practical applications. In the work, an approximate semianalytical solution of the time-fractional European option pricing model is derived using the method of combining the enhanced technique of Adomian decomposition method with the finite difference method. And then the result is introduced in China’s financial market. The work makes every effort to test the feasibility of the fractional derivative model in the actual financial market.
On a business cycle model with fractional derivative under narrow-band random excitation
International Nuclear Information System (INIS)
Lin, Zifei; Li, Jiaorui; Li, Shuang
2016-01-01
This paper analyzes the dynamics of a business cycle model with fractional derivative of order α (0 < α < 1) subject to narrow-band random excitation, in which fractional derivative describes the memory property of the economic variables. Stochastic dynamical system concepts are integrated into the business cycle model for understanding the economic fluctuation. Firstly, the method of multiple scales is applied to derive the model to obtain the approximate analytical solution. Secondly, the effect of economic policy with fractional derivative on the amplitude of the economic fluctuation and the effect on stationary probability density are studied. The results show macroeconomic regulation and control can lower the stable amplitude of economic fluctuation. While in the process of equilibrium state, the amplitude is magnified. Also, the macroeconomic regulation and control improves the stability of the equilibrium state. Thirdly, how externally stochastic perturbation affects the dynamics of the economy system is investigated.
A Semianalytical Solution of the Fractional Derivative Model and Its Application in Financial Market
Song, Lina
2018-01-01
Fractional differential equation has been introduced to the financial theory, which presents new ideas and tools for the theoretical researches and the practical applications. In the work, an approximate semianalytical solution of the time-fractional European option pricing model is derived using the method of combining the enhanced technique of Adomian decomposition method with the finite difference method. And then the result is introduced in China’s financial market. The work makes every e...
A new visco-elasto-plastic model via time-space fractional derivative
Hei, X.; Chen, W.; Pang, G.; Xiao, R.; Zhang, C.
2018-02-01
To characterize the visco-elasto-plastic behavior of metals and alloys we propose a new constitutive equation based on a time-space fractional derivative. The rheological representative of the model can be analogous to that of the Bingham-Maxwell model, while the dashpot element and sliding friction element are replaced by the corresponding fractional elements. The model is applied to describe the constant strain rate, stress relaxation and creep tests of different metals and alloys. The results suggest that the proposed simple model can describe the main characteristics of the experimental observations. More importantly, the model can also provide more accurate predictions than the classic Bingham-Maxwell model and the Bingham-Norton model.
Directory of Open Access Journals (Sweden)
Abdon Atangana
2014-01-01
Full Text Available The notion of uncertainty in groundwater hydrology is of great importance as it is known to result in misleading output when neglected or not properly accounted for. In this paper we examine this effect in groundwater flow models. To achieve this, we first introduce the uncertainties functions u as function of time and space. The function u accounts for the lack of knowledge or variability of the geological formations in which flow occur (aquifer in time and space. We next make use of Riemann-Liouville fractional derivatives that were introduced by Kobelev and Romano in 2000 and its approximation to modify the standard version of groundwater flow equation. Some properties of the modified Riemann-Liouville fractional derivative approximation are presented. The classical model for groundwater flow, in the case of density-independent flow in a uniform homogeneous aquifer is reformulated by replacing the classical derivative by the Riemann-Liouville fractional derivatives approximations. The modified equation is solved via the technique of green function and the variational iteration method.
Modelling and simulation of a dynamical system with the Atangana-Baleanu fractional derivative
Owolabi, Kolade M.
2018-01-01
In this paper, we model an ecological system consisting of a predator and two preys with the newly derived two-step fractional Adams-Bashforth method via the Atangana-Baleanu derivative in the Caputo sense. We analyze the dynamical system for correct choice of parameter values that are biologically meaningful. The local analysis of the main model is based on the application of qualitative theory for ordinary differential equations. By using the fixed point theorem idea, we establish the existence and uniqueness of the solutions. Convergence results of the new scheme are verified in both space and time. Dynamical wave phenomena of solutions are verified via some numerical results obtained for different values of the fractional index, which have some interesting ecological implications.
Modeling ramp-hold indentation measurements based on Kelvin-Voigt fractional derivative model
Zhang, Hongmei; zhe Zhang, Qing; Ruan, Litao; Duan, Junbo; Wan, Mingxi; Insana, Michael F.
2018-03-01
Interpretation of experimental data from micro- and nano-scale indentation testing is highly dependent on the constitutive model selected to relate measurements to mechanical properties. The Kelvin-Voigt fractional derivative model (KVFD) offers a compact set of viscoelastic features appropriate for characterizing soft biological materials. This paper provides a set of KVFD solutions for converting indentation testing data acquired for different geometries and scales into viscoelastic properties of soft materials. These solutions, which are mostly in closed-form, apply to ramp-hold relaxation, load-unload and ramp-load creep-testing protocols. We report on applications of these model solutions to macro- and nano-indentation testing of hydrogels, gastric cancer cells and ex vivo breast tissue samples using an atomic force microscope (AFM). We also applied KVFD models to clinical ultrasonic breast data using a compression plate as required for elasticity imaging. Together the results show that KVFD models fit a broad range of experimental data with a correlation coefficient typically R 2 > 0.99. For hydrogel samples, estimation of KVFD model parameters from test data using spherical indentation versus plate compression as well as ramp relaxation versus load-unload compression all agree within one standard deviation. Results from measurements made using macro- and nano-scale indentation agree in trend. For gastric cell and ex vivo breast tissue measurements, KVFD moduli are, respectively, 1/3-1/2 and 1/6 of the elasticity modulus found from the Sneddon model. In vivo breast tissue measurements yield model parameters consistent with literature results. The consistency of results found for a broad range of experimental parameters suggest the KVFD model is a reliable tool for exploring intrinsic features of the cell/tissue microenvironments.
DEFF Research Database (Denmark)
Zhou, H. W.; Yi, H. Y.; Mishnaevsky, Leon
2017-01-01
A modeling approach to time-dependent property of Glass Fiber Reinforced Polymers (GFRP) composites is of special interest for quantitative description of long-term behavior. An electronic creep machine is employed to investigate the time-dependent deformation of four specimens of dog-bond-shaped......A modeling approach to time-dependent property of Glass Fiber Reinforced Polymers (GFRP) composites is of special interest for quantitative description of long-term behavior. An electronic creep machine is employed to investigate the time-dependent deformation of four specimens of dog......-bond-shaped GFRP composites at various stress level. A negative exponent function based on structural changes is introduced to describe the damage evolution of material properties in the process of creep test. Accordingly, a new creep constitutive equation, referred to fractional derivative Maxwell model...... by the fractional derivative Maxwell model proposed in the paper are in a good agreement with the experimental data. It is shown that the new creep constitutive model proposed in the paper needs few parameters to represent various time-dependent behaviors....
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.
International Nuclear Information System (INIS)
Liu Yaozong; Yu Dianlong; Zhao Honggang; Wen Jihong; Wen Xisen
2008-01-01
Wave propagation in two-dimensional phononic crystals (PCs) with viscoelasticity is investigated using a finite-difference-time-domain (FDTD) method. The viscoelasticity is evaluated using the Kelvin-Voigt model with fractional derivatives (FDs) so that both the dispersion and dissipation are considered. Numerical approximation of FDs is integrated into the FDTD scheme to simulate wave propagation in such PCs. All the constituent materials are treated as isotropic and homogeneous. The gaps are substantially displaced and widened and the attenuation is noticeably enhanced due to the dispersion and dissipation of host material and the complicated multiple scattering between scatterers. These results indicate that the viscoelasticity of the damping host has significant influence on wave propagation in PCs and should be considered
Directory of Open Access Journals (Sweden)
Koca Ilknur
2017-01-01
Full Text Available Recently Hristov using the concept of a relaxation kernel with no singularity developed a new model of elastic heat diffusion equation based on the Caputo-Fabrizio fractional derivative as an extended version of Cattaneo model of heat diffusion equation. In the present article, we solve exactly the Cattaneo-Hristov model and extend it by the concept of a derivative with non-local and non-singular kernel by using the new Atangana-Baleanu derivative. The Cattaneo-Hristov model with the extended derivative is solved analytically with the Laplace transform, and numerically using the Crank-Nicholson scheme.
Generalized Fractional Derivative Anisotropic Viscoelastic Characterization
Directory of Open Access Journals (Sweden)
Harry H. Hilton
2012-01-01
Full Text Available Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated.
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
Eyuboglu, Atilla Adnan; Uysal, Cagri A; Ozgun, Gonca; Coskun, Erhan; Markal Ertas, Nilgun; Haberal, Mehmet
2018-03-01
Stasis zone is the surrounding area of the coagulation zone which is an important part determining the extent of the necrosis in burn patients. In our study we aim to salvage the stasis zone by injecting adipose derived stromal vascular fraction (ADSVF). Thermal injury was applied on dorsum of Sprague-Dawley rats (n=20) by the "comb burn" model as described previously. When the burn injury was established on Sprague-Dawley rats (30min); rat dorsum was separated into 2 equal parts consisting of 4 burn zones (3 stasis zone) on each pair. ADSVF cells harvested from inguinal fat pads of Sprague-Dawley rats (n=5) were injected on the right side while same amount of phosphate buffered saline (PBS) injected on the left side of the same animal. One week later, average vital tissue on the statis zone was determined by macroscopy, angiography and microscopy. Vascular density, inflammatory cell density, gradient of fibrosis and epithelial thickness were determined via immunohistochemical assay. Macroscopic stasis zone tissue viability (32±3.28%, 57±4.28%) (p51, 1.50±0.43) (pzone on acute burn injuries. Copyright © 2017 Elsevier Ltd and ISBI. All rights reserved.
Sales, T. P.; Marques, Flávio D.; Pereira, Daniel A.; Rade, Domingos A.
2018-06-01
Nonlinear aeroelastic systems are prone to the appearance of limit cycle oscillations, bifurcations, and chaos. Such problems are of increasing concern in aircraft design since there is the need to control nonlinear instabilities and improve safety margins, at the same time as aircraft are subjected to increasingly critical operational conditions. On the other hand, in spite of the fact that viscoelastic materials have already been successfully used for the attenuation of undesired vibrations in several types of mechanical systems, a small number of research works have addressed the feasibility of exploring the viscoelastic effect to improve the behavior of nonlinear aeroelastic systems. In this context, the objective of this work is to assess the influence of viscoelastic materials on the aeroelastic features of a three-degrees-of-freedom typical section with hardening structural nonlinearities. The equations of motion are derived accounting for the presence of viscoelastic materials introduced in the resilient elements associated to each degree-of-freedom. A constitutive law based on fractional derivatives is adopted, which allows the modeling of temperature-dependent viscoelastic behavior in time and frequency domains. The unsteady aerodynamic loading is calculated based on the classical linear potential theory for arbitrary airfoil motion. The aeroelastic behavior is investigated through time domain simulations, and subsequent frequency transformations, from which bifurcations are identified from diagrams of limit cycle oscillations amplitudes versus airspeed. The influence of the viscoelastic effect on the aeroelastic behavior, for different values of temperature, is also investigated. The numerical simulations show that viscoelastic damping can increase the flutter speed and reduce the amplitudes of limit cycle oscillations. These results prove the potential that viscoelastic materials have to increase aircraft components safety margins regarding aeroelastic
Directory of Open Access Journals (Sweden)
Adailton S. Borges
Full Text Available Abstract A broad class of engineering systems can be satisfactory modeled under the assumptions of small deformations and linear material properties. However, many mechanical systems used in modern applications, like structural elements typical of aerospace and petroleum industries, have been characterized by increased slenderness and high static and dynamic loads. In such situations, it becomes indispensable to consider the nonlinear geometric effects and/or material nonlinear behavior. At the same time, in many cases involving dynamic loads, there comes the need for attenuation of vibration levels. In this context, this paper describes the development and validation of numerical models of viscoelastic slender beam-like structures undergoing large displacements. The numerical approach is based on the combination of the nonlinear Cosserat beam theory and a viscoelastic model based on Fractional Derivatives. Such combination enables to derive nonlinear equations of motion that, upon finite element discretization, can be used for predicting the dynamic behavior of the structure in the time domain, accounting for geometric nonlinearity and viscoelastic damping. The modeling methodology is illustrated and validated by numerical simulations, the results of which are compared to others available in the literature.
Directory of Open Access Journals (Sweden)
Shilei Liu
2018-04-01
Full Text Available High intensity focused ultrasound (HIFU has been proven to be promising in non-invasive therapies, in which precise prediction of the focused ultrasound field is crucial for its accurate and safe application. Although the Khokhlov–Zabolotskaya–Kuznetsov (KZK equation has been widely used in the calculation of the nonlinear acoustic field of HIFU, some deviations still exist when it comes to dispersive medium. This problem also exists as an obstacle to the Westervelt model and the Spherical Beam Equation. Considering that the KZK equation is the most prevalent model in HIFU applications due to its accurate and simple simulation algorithms, there is an urgent need to improve its performance in dispersive medium. In this work, a modified KZK (mKZK equation derived from a fractional order derivative is proposed to calculate the nonlinear acoustic field in a dispersive medium. By correcting the power index in the attenuation term, this model is capable of providing improved prediction accuracy, especially in the axial position of the focal area. Simulation results using the obtained model were further compared with the experimental results from a gel phantom. Good agreements were found, indicating the applicability of the proposed model. The findings of this work will be helpful in making more accurate treatment plans for HIFU therapies, as well as facilitating the application of ultrasound in acoustic hyperthermia therapy.
Fractional variational calculus in terms of Riesz fractional derivatives
International Nuclear Information System (INIS)
Agrawal, O P
2007-01-01
This paper presents extensions of traditional calculus of variations for systems containing Riesz fractional derivatives (RFDs). Specifically, we present generalized Euler-Lagrange equations and the transversality conditions for fractional variational problems (FVPs) defined in terms of RFDs. We consider two problems, a simple FVP and an FVP of Lagrange. Results of the first problem are extended to problems containing multiple fractional derivatives, functions and parameters, and to unspecified boundary conditions. For the second problem, we present Lagrange-type multiplier rules. For both problems, we develop the Euler-Lagrange-type necessary conditions which must be satisfied for the given functional to be extremum. Problems are considered to demonstrate applications of the formulations. Explicitly, we introduce fractional momenta, fractional Hamiltonian, fractional Hamilton equations of motion, fractional field theory and fractional optimal control. The formulations presented and the resulting equations are similar to the formulations for FVPs given in Agrawal (2002 J. Math. Anal. Appl. 272 368, 2006 J. Phys. A: Math. Gen. 39 10375) and to those that appear in the field of classical calculus of variations. These formulations are simple and can be extended to other problems in the field of fractional calculus of variations
Toufik, Mekkaoui; Atangana, Abdon
2017-10-01
Recently a new concept of fractional differentiation with non-local and non-singular kernel was introduced in order to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives. A new numerical scheme has been developed, in this paper, for the newly established fractional differentiation. We present in general the error analysis. The new numerical scheme was applied to solve linear and non-linear fractional differential equations. We do not need a predictor-corrector to have an efficient algorithm, in this method. The comparison of approximate and exact solutions leaves no doubt believing that, the new numerical scheme is very efficient and converges toward exact solution very rapidly.
Generalized fractional Schroedinger equation with space-time fractional derivatives
International Nuclear Information System (INIS)
Wang Shaowei; Xu Mingyu
2007-01-01
In this paper the generalized fractional Schroedinger equation with space and time fractional derivatives is constructed. The equation is solved for free particle and for a square potential well by the method of integral transforms, Fourier transform and Laplace transform, and the solution can be expressed in terms of Mittag-Leffler function. The Green function for free particle is also presented in this paper. Finally, we discuss the relationship between the cases of the generalized fractional Schroedinger equation and the ones in standard quantum
Joel W. Homan; Charles H. Luce; James P. McNamara; Nancy F. Glenn
2011-01-01
Describing the spatial variability of heterogeneous snowpacks at a watershed or mountain-front scale is important for improvements in large-scale snowmelt modelling. Snowmelt depletion curves, which relate fractional decreases in snowcovered area (SCA) against normalized decreases in snow water equivalent (SWE), are a common approach to scale-up snowmelt models....
Measuring memory with the order of fractional derivative
Du, Maolin; Wang, Zaihua; Hu, Haiyan
2013-12-01
Fractional derivative has a history as long as that of classical calculus, but it is much less popular than it should be. What is the physical meaning of fractional derivative? This is still an open problem. In modeling various memory phenomena, we observe that a memory process usually consists of two stages. One is short with permanent retention, and the other is governed by a simple model of fractional derivative. With the numerical least square method, we show that the fractional model perfectly fits the test data of memory phenomena in different disciplines, not only in mechanics, but also in biology and psychology. Based on this model, we find that a physical meaning of the fractional order is an index of memory.
Fractional Order Models of Industrial Pneumatic Controllers
Directory of Open Access Journals (Sweden)
Abolhassan Razminia
2014-01-01
Full Text Available This paper addresses a new approach for modeling of versatile controllers in industrial automation and process control systems such as pneumatic controllers. Some fractional order dynamical models are developed for pressure and pneumatic systems with bellows-nozzle-flapper configuration. In the light of fractional calculus, a fractional order derivative-derivative (FrDD controller and integral-derivative (FrID are remodeled. Numerical simulations illustrate the application of the obtained theoretical results in simple examples.
Generalized time fractional IHCP with Caputo fractional derivatives
International Nuclear Information System (INIS)
Murio, D A; MejIa, C E
2008-01-01
The numerical solution of the generalized time fractional inverse heat conduction problem (GTFIHCP) on a finite slab is investigated in the presence of measured (noisy) data when the time fractional derivative is interpreted in the sense of Caputo. The GTFIHCP involves the simultaneous identification of the heat flux and temperature transient functions at one of the boundaries of the finite slab together with the initial condition of the original direct problem from noisy Cauchy data at a discrete set of points on the opposite (active) boundary. A finite difference space marching scheme with adaptive regularization, using trigonometric mollification techniques and generalized cross validation is introduced. Error estimates for the numerical solution of the mollified problem and numerical examples are provided.
Coronary CT Angiography Derived Fractional Flow Reserve
DEFF Research Database (Denmark)
Nørgaard, Bjarne Linde; Jensen, Jesper Møller; Blanke, Philipp
2017-01-01
Purpose of Review: To summarize the scientific basis of CT derived fractional flow reserve (FFRCT) and present an updated review on the evidence from clinical trials and real-world observational data Recent Findings: In prospective multicenter studies of patients with stable coronary artery disea...... of patients with stable CAD. The optimal FFRCT testing interpretation strategy, as well as the relative cost-efficiency of FFRCT against standard noninvasive functional testing, need further investigation....
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
Fractional derivatives for physicists and engineers background and theory
Uchaikin, Vladimir V
2013-01-01
The first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it work, where does it lead to? The two-volume book written on high didactic level answers these questions. Fractional Derivatives for Physicists and Engineers— The first volume contains a clear introduction into such a modern branch of analysis as the fractional calculus. The second develops a wide panorama of applications of the fractional calculus to various physical problems. This book recovers new perspectives in front of the reader dealing with turbulence and semiconductors, plasma and thermodynamics, mechanics and quantum optics, nanophysics and astrophysics. The book is addressed to students, engineers and physicists, specialists in theory of probability and statistics, in mathematical modeling and numerical simulations, to everybody who doesn't wish to stay apart from the new mathematical methods becoming more and ...
THE NEW SOLUTION OF TIME FRACTIONAL WAVE EQUATION WITH CONFORMABLE FRACTIONAL DERIVATIVE DEFINITION
Çenesiz, Yücel; Kurt, Ali
2015-01-01
– In this paper, we used new fractional derivative definition, the conformable fractional derivative, for solving two and three dimensional time fractional wave equation. This definition is simple and very effective in the solution procedures of the fractional differential equations that have complicated solutions with classical fractional derivative definitions like Caputo, Riemann-Liouville and etc. The results show that conformable fractional derivative definition is usable and convenient ...
International Nuclear Information System (INIS)
Al-Mossawy, Mohammed Idrees; Demiral, Birol; Raja, D M Anwar
2013-01-01
Foam is used in enhanced oil recovery to improve the sweep efficiency by controlling the gas mobility. The surfactant-alternating-gas (SAG) foam process is used as an alternative to the water-alternating-gas (WAG) injection. In the WAG technique, the high mobility and the low density of the gas lead the gas to flow in channels through the high permeability zones of the reservoir and to rise to the top of the reservoir by gravity segregation. As a result, the sweep efficiency decreases and there will be more residual oil in the reservoir. The foam can trap the gas in liquid films and reduces the gas mobility. The fractional-flow method describes the physics of immiscible displacements in porous media. Finding the water fractional flow theoretically or experimentally as a function of the water saturation represents the heart of this method. The relative permeability function is the conventional way to derive the fractional-flow function. This study presents an improved relative permeability model to derive the fractional-flow functions for WAG and SAG foam core-floods. The SAG flow regimes are characterized into weak foam, strong foam without a shock front and strong foam with a shock front. (paper)
A Caputo fractional derivative of a function with respect to another function
Almeida, Ricardo
2017-03-01
In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor's Theorem, Fermat's Theorem, etc., are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided.
Fractional derivative and its application in mathematics and physics
International Nuclear Information System (INIS)
Namsrai, K.
2004-12-01
We propose fractional derivatives and to study those mathematical and physical consequences. It is shown that fractional derivatives possess noncommutative and nonassociative properties and within which motion of a particle, differential and integral calculuses are investigated. (author)
Fractional Hamiltonian analysis of higher order derivatives systems
International Nuclear Information System (INIS)
Baleanu, Dumitru; Muslih, Sami I.; Tas, Kenan
2006-01-01
The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives
Modelling altered fractionation schedules
International Nuclear Information System (INIS)
Fowler, J.F.
1993-01-01
The author discusses the conflicting requirements of hyperfractionation and accelerated fractionation used in radiotherapy, and the development of computer modelling to predict how to obtain an optimum of tumour cell kill without exceeding normal-tissue tolerance. The present trend is to shorten hyperfractionated schedules from 6 or 7 weeks to give overall times of 4 or 5 weeks as in new schedules by Herskovic et al (1992) and Harari (1992). Very high doses are given, much higher than can be given when ultrashort schedules such as CHART (12 days) are used. Computer modelling has suggested that optimum overall times, to yield maximum cell kill in tumours ((α/β = 10 Gy) for a constant level of late complications (α/β = 3 Gy) would be X or X-1 weeks, where X is the doubling time of the tumour cells in days (Fowler 1990). For median doubling times of about 5 days, overall times of 4 or 5 weeks should be ideal. (U.K.)
International Nuclear Information System (INIS)
He, Ji-Huan; Elagan, S.K.; Li, Z.B.
2012-01-01
The fractional complex transform is suggested to convert a fractional differential equation with Jumarie's modification of Riemann–Liouville derivative into its classical differential partner. Understanding the fractional complex transform and the chain rule for fractional calculus are elucidated geometrically. -- Highlights: ► The chain rule for fractional calculus is invalid, a counter example is given. ► The fractional complex transform is explained geometrically. ► Fractional equations can be converted into differential equations.
Subrecoil laser cooling dynamics: a fractional derivative approach
International Nuclear Information System (INIS)
Uchaikin, Vladimir V; Sibatov, Renat T
2009-01-01
The subrecoil laser cooling process is considered in the framework of a model with two states (trapping and recycling), with instantaneous transitions between them. The key point of the work is the use of a fractional exponential function for waiting time distributions. This allows us to derive a general master equation covering both important cases: those with exponential and power type tails. Their solutions are expressed through fractionally stable distributions. The pdfs of the total trapping time of an atom and the proportion of trapped atoms are found. Analytical relationships show a good agreement with numerical results from Monte Carlo simulation
Directory of Open Access Journals (Sweden)
Ping Zhou
2012-01-01
Full Text Available The unstable equilibrium points of the fractional-order Lorenz chaotic system can be controlled via fractional-order derivative, and chaos synchronization for the fractional-order Lorenz chaotic system can be achieved via fractional-order derivative. The control and synchronization technique, based on stability theory of fractional-order systems, is simple and theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed method.
Variational problems with fractional derivatives: Euler-Lagrange equations
International Nuclear Information System (INIS)
Atanackovic, T M; Konjik, S; Pilipovic, S
2008-01-01
We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these two bounds coincide, we derive a new form of Euler-Lagrange equations. We use approximations for fractional derivatives in the Lagrangian and obtain the Euler-Lagrange equations which approximate the initial Euler-Lagrange equations in a weak sense
Shilei Liu; Yanye Yang; Chenghai Li; Xiasheng Guo; Juan Tu; Dong Zhang
2018-01-01
High intensity focused ultrasound (HIFU) has been proven to be promising in non-invasive therapies, in which precise prediction of the focused ultrasound field is crucial for its accurate and safe application. Although the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation has been widely used in the calculation of the nonlinear acoustic field of HIFU, some deviations still exist when it comes to dispersive medium. This problem also exists as an obstacle to the Westervelt model and the Spherical ...
Simulation of chemical reactions using fractional derivatives
International Nuclear Information System (INIS)
Zabadal, J.; Vilhena, M.; Livotto, P.
2001-01-01
In this work a new approach to solve time-dependant Schroedinger equation for molecular systems is proposed. The method employs functional derivatives to describe the time evolution of the wave functions in reactive systems, in order to establish the mechanisms and products of the reaction. A numerical simulation is reported
Exact solutions to the time-fractional differential equations via local fractional derivatives
Guner, Ozkan; Bekir, Ahmet
2018-01-01
This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.
Fractional diffusion models of nonlocal transport
International Nuclear Information System (INIS)
Castillo-Negrete, D. del
2006-01-01
A class of nonlocal models based on the use of fractional derivatives (FDs) is proposed to describe nondiffusive transport in magnetically confined plasmas. FDs are integro-differential operators that incorporate in a unified framework asymmetric non-Fickian transport, non-Markovian ('memory') effects, and nondiffusive scaling. To overcome the limitations of fractional models in unbounded domains, we use regularized FDs that allow the incorporation of finite-size domain effects, boundary conditions, and variable diffusivities. We present an α-weighted explicit/implicit numerical integration scheme based on the Grunwald-Letnikov representation of the regularized fractional diffusion operator in flux conserving form. In sharp contrast with the standard diffusive model, the strong nonlocality of fractional diffusion leads to a linear in time response for a decaying pulse at short times. In addition, an anomalous fractional pinch is observed, accompanied by the development of an uphill transport region where the 'effective' diffusivity becomes negative. The fractional flux is in general asymmetric and, for steady states, it has a negative (toward the core) component that enhances confinement and a positive component that increases toward the edge and leads to poor confinement. The model exhibits the characteristic anomalous scaling of the confinement time, τ, with the system's size, L, τ∼L α , of low-confinement mode plasma where 1<α<2 is the order of the FD operator. Numerical solutions of the model with an off-axis source show that the fractional inward transport gives rise to profile peaking reminiscent of what is observed in tokamak discharges with auxiliary off-axis heating. Also, cold-pulse perturbations to steady sates in the model exhibit fast, nondiffusive propagation phenomena that resemble perturbative experiments
An inverse Sturm–Liouville problem with a fractional derivative
Jin, Bangti
2012-05-01
In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and numerical reconstructions of the potential with a Newton method from finite spectral data are presented. Surprisingly, it allows very satisfactory reconstructions for both smooth and discontinuous potentials, provided that the order . α∈. (1,. 2) of fractional derivative is sufficiently away from 2. © 2012 Elsevier Inc.
Directory of Open Access Journals (Sweden)
Bingqing Lu
2018-01-01
Full Text Available Fractional calculus provides efficient physical models to quantify non-Fickian dynamics broadly observed within the Earth system. The potential advantages of using fractional partial differential equations (fPDEs for real-world problems are often limited by the current lack of understanding of how earth system properties influence observed non-Fickian dynamics. This study explores non-Fickian dynamics for pollutant transport in field-scale discrete fracture networks (DFNs, by investigating how fracture and rock matrix properties influence the leading and tailing edges of pollutant breakthrough curves (BTCs. Fractured reservoirs exhibit erratic internal structures and multi-scale heterogeneity, resulting in complex non-Fickian dynamics. A Monte Carlo approach is used to simulate pollutant transport through DFNs with a systematic variation of system properties, and the resultant non-Fickian transport is upscaled using a tempered-stable fractional in time advection–dispersion equation. Numerical results serve as a basis for determining both qualitative and quantitative relationships between BTC characteristics and model parameters, in addition to the impacts of fracture density, orientation, and rock matrix permeability on non-Fickian dynamics. The observed impacts of medium heterogeneity on tracer transport at late times tend to enhance the applicability of fPDEs that may be parameterized using measurable fracture–matrix characteristics.
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.
A fractional model for dye removal
Directory of Open Access Journals (Sweden)
Ji-Huan He
2016-01-01
Full Text Available The adsorption process has a fractional property, and a fractional model is suggested to study a transport model of direct textile industry wastewater. An approximate solution of the concentration is obtained by the variational iteration method.
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. ...
International Nuclear Information System (INIS)
Jumarie, Guy
2004-01-01
There are presently two different models of fractional Brownian motions available in the literature: the Riemann-Liouville fractional derivative of white noise on the one hand, and the complex-valued Brownian motion of order n defined by using a random walk in the complex plane, on the other hand. The paper provides a comparison between these two approaches, and in addition, takes this opportunity to contribute some complements. These two models are more or less equivalent on the theoretical standpoint for fractional order between 0 and 1/2, but their practical significances are quite different. Otherwise, for order larger than 1/2, the fractional derivative model has no counterpart in the complex plane. These differences are illustrated by an example drawn from mathematical finance. Taylor expansion of fractional order provides the expression of fractional difference in terms of finite difference, and this allows us to improve the derivation of Fokker-Planck equation and Kramers-Moyal expansion, and to get more insight in their relation with stochastic differential equations of fractional order. In the case of multi-fractal systems, the Fokker-Planck equation can be solved by using path integrals, and the fractional dynamic equations of the state moments of the stochastic system can be easily obtained. By combining fractional derivative and complex white noise of order n, one obtains a family of complex-valued fractional Brownian motions which exhibits long-range dependence. The conclusion outlines suggestions for further research, mainly regarding Lorentz transformation of fractional noises
Modeling electron fractionalization with unconventional Fock spaces.
Cobanera, Emilio
2017-08-02
It is shown that certain fractionally-charged quasiparticles can be modeled on D-dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges, then this approach fractionalizes the Abelian charges only. In particular, the mth-root of a spinful fermion carries charge e/m and spin 1/2. Just like taking a root of a complex number, taking a root of a fermion yields a mildly non-unique result. As a consequence, there are several possible choices of quantum exchange statistics for fermion-root quasiparticles. These choices are tied to the dimensionality [Formula: see text] of the lattice by basic physical considerations. One particular family of fermion-root quasiparticles is directly connected to the parafermion zero-energy modes expected to emerge in certain mesoscopic devices involving fractional quantum Hall states. Hence, as an application of potential mesoscopic interest, I investigate numerically the hybridization of Majorana and parafermion zero-energy edge modes caused by fractionalizing but charge-conserving tunneling.
A fractional derivative approach to full creep regions in salt rock
DEFF Research Database (Denmark)
Zhou, H. W.; Wang, C. P.; Mishnaevsky, Leon
2013-01-01
Based on the definition of the constant-viscosity Abel dashpot, a new creep element, referred to as the variable-viscosity Abel dashpot, is proposed to characterize damage growth in salt rock samples during creep tests. Ultrasonic testing is employed to determine a formula of the variable viscosity...... coefficient, indicating that the change of the variable viscosity coefficient with the time meets a negative exponent law. In addition, by replacing the Newtonian dashpot in the classical Nishihara model with the variable-viscosity Abel dashpot, a damage-mechanism-based creep constitutive model is proposed...... on the basis of time-based fractional derivative. The analytic solution for the fractional-derivative creep constitutive model is presented. The parameters of the fractional derivative creep model are determined by the Levenberg–Marquardt method on the basis of the experimental results of creep tests on salt...
Extended Riemann-Liouville type fractional derivative operator with applications
Directory of Open Access Journals (Sweden)
Agarwal P.
2017-12-01
Full Text Available The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox’s H-function are also presented.
Non-Noether symmetries of Hamiltonian systems with conformable fractional derivatives
International Nuclear Information System (INIS)
Wang Lin-Li; Fu Jing-Li
2016-01-01
In this paper, we present the fractional Hamilton’s canonical equations and the fractional non-Noether symmetry of Hamilton systems by the conformable fractional derivative. Firstly, the exchanging relationship between isochronous variation and fractional derivatives, and the fractional Hamilton principle of the system under this fractional derivative are proposed. Secondly, the fractional Hamilton’s canonical equations of Hamilton systems based on the Hamilton principle are established. Thirdly, the fractional non-Noether symmetries, non-Noether theorem and non-Noether conserved quantities for the Hamilton systems with the conformable fractional derivatives are obtained. Finally, an example is given to illustrate the results. (paper)
Directory of Open Access Journals (Sweden)
Taohua Liu
2017-01-01
Full Text Available Fractional advection-dispersion equations, as generalizations of classical integer-order advection-dispersion equations, are used to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, we develop an implicit finite difference method for fractional advection-dispersion equations with fractional derivative boundary conditions. First-order consistency, solvability, unconditional stability, and first-order convergence of the method are proven. Then, we present a fast iterative method for the implicit finite difference scheme, which only requires storage of O(K and computational cost of O(KlogK. Traditionally, the Gaussian elimination method requires storage of O(K2 and computational cost of O(K3. Finally, the accuracy and efficiency of the method are checked with a numerical example.
Fractional-order integral and derivative controller for temperature ...
Indian Academy of Sciences (India)
ideal transfer function as a reference model, for a temperature profile tracking. ... tant, and in process industry (Tsai & Lu 1998), the most common control task is to ..... be solved for fractional order α using numerical classical approach in MATLAB. ..... discrepancy between simulation and experimental results may be due to ...
Fractional derivatives. An introduction; Derivate frazionarie. Che cosa sono, a cosa servono
Energy Technology Data Exchange (ETDEWEB)
Dattoli, G. [ENEA, Div. Fisica Applicata, Centro Ricerche Frascati, Rome (Italy)
2001-07-01
In this item is presented a brief survey of fractional calculus and of the relevant applications. In the work are discussed different points of view of the operation of fractional derivative and present a unifying definition. The role played by fractional derivatives and integrals within the framework of integral transform is analyzed. [Italian] In questo articolo si traccia un profilo del cosidetto calcolo frazionario e delle relative applicazioni a problemi di matematica pura ed applicata. Si discutono varie definizioni dell'operazione di derivata frazionaria, non tutte coincidenti fra loro, e si mostra come sia possibile proporre una definizione univoca che inglobi tutte le altre. Si analizza infine il ruolo giocato dalle derivate e dagli integrali frazionari e, piu' in generale, quello degli operatori differenziali ad esponente frazionario, nell'ambito della teoria delle rappresentazioni integrali.
Positive solutions of fractional differential equations with derivative terms
Directory of Open Access Journals (Sweden)
Cuiping Cheng
2012-11-01
Full Text Available In this article, we are concerned with the existence of positive solutions for nonlinear fractional differential equation whose nonlinearity contains the first-order derivative, $$displaylines{ D_{0^+}^{alpha}u(t+f(t,u(t,u'(t=0,quad tin (0,1,; n-1
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 ...
Finite element formulation of viscoelastic sandwich beams using fractional derivative operators
Galucio, A. C.; Deü, J.-F.; Ohayon, R.
This paper presents a finite element formulation for transient dynamic analysis of sandwich beams with embedded viscoelastic material using fractional derivative constitutive equations. The sandwich configuration is composed of a viscoelastic core (based on Timoshenko theory) sandwiched between elastic faces (based on Euler-Bernoulli assumptions). The viscoelastic model used to describe the behavior of the core is a four-parameter fractional derivative model. Concerning the parameter identification, a strategy to estimate the fractional order of the time derivative and the relaxation time is outlined. Curve-fitting aspects are focused, showing a good agreement with experimental data. In order to implement the viscoelastic model into the finite element formulation, the Grünwald definition of the fractional operator is employed. To solve the equation of motion, a direct time integration method based on the implicit Newmark scheme is used. One of the particularities of the proposed algorithm lies in the storage of displacement history only, reducing considerably the numerical efforts related to the non-locality of fractional operators. After validations, numerical applications are presented in order to analyze truncation effects (fading memory phenomena) and solution convergence aspects.
Fractional Heat Conduction Models and Thermal Diffusivity Determination
Directory of Open Access Journals (Sweden)
Monika Žecová
2015-01-01
Full Text Available The contribution deals with the fractional heat conduction models and their use for determining thermal diffusivity. A brief historical overview of the authors who have dealt with the heat conduction equation is described in the introduction of the paper. The one-dimensional heat conduction models with using integer- and fractional-order derivatives are listed. Analytical and numerical methods of solution of the heat conduction models with using integer- and fractional-order derivatives are described. Individual methods have been implemented in MATLAB and the examples of simulations are listed. The proposal and experimental verification of the methods for determining thermal diffusivity using half-order derivative of temperature by time are listed at the conclusion of the paper.
International Nuclear Information System (INIS)
Zabadal, J.; Vilhena, M.T.; Segatto, C.F.; Pazos, R.P.Ruben Panta.
2002-01-01
In this work we construct a closed-form solution for the multidimensional transport equation rewritten in integral form which is expressed in terms of a fractional derivative of the angular flux. We determine the unknown order of the fractional derivative comparing the kernel of the integral equation with the one of the Riemann-Liouville definition of fractional derivative. We report numerical simulations
Energy Technology Data Exchange (ETDEWEB)
Zabadal, J. E-mail: jorge.zabadal@ufrgs.br; Vilhena, M.T. E-mail: vilhena@mat.ufrgs.br; Segatto, C.F. E-mail: cynthia@mat.ufrgs.br; Pazos, R.P.Ruben Panta. E-mail: rpp@mat.pucrgs.br
2002-07-01
In this work we construct a closed-form solution for the multidimensional transport equation rewritten in integral form which is expressed in terms of a fractional derivative of the angular flux. We determine the unknown order of the fractional derivative comparing the kernel of the integral equation with the one of the Riemann-Liouville definition of fractional derivative. We report numerical simulations.
Discrete random walk models for space-time fractional diffusion
International Nuclear Information System (INIS)
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
2002-01-01
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order α is part of (0,2] and skewness θ (moduleθ≤{α,2-α}), and the first-order time derivative with a Caputo derivative of order β is part of (0,1]. Such evolution equation implies for the flux a fractional Fick's law which accounts for spatial and temporal non-locality. The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process that we view as a generalized diffusion process. By adopting appropriate finite-difference schemes of solution, we generate models of random walk discrete in space and time suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation
On some new properties of fractional derivatives with Mittag-Leffler kernel
Baleanu, Dumitru; Fernandez, Arran
2018-06-01
We establish a new formula for the fractional derivative with Mittag-Leffler kernel, in the form of a series of Riemann-Liouville fractional integrals, which brings out more clearly the non-locality of fractional derivatives and is easier to handle for certain computational purposes. We also prove existence and uniqueness results for certain families of linear and nonlinear fractional ODEs defined using this fractional derivative. We consider the possibility of a semigroup property for these derivatives, and establish extensions of the product rule and chain rule, with an application to fractional mechanics.
A Computational Model of Fraction Arithmetic
Braithwaite, David W.; Pyke, Aryn A.; Siegler, Robert S.
2017-01-01
Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…
Directory of Open Access Journals (Sweden)
Amal Khalaf Haydar
2016-01-01
Full Text Available The main aim in this paper is to use all the possible arrangements of objects such that r1 of them are equal to 1 and r2 (the others of them are equal to 2, in order to generalize the definitions of Riemann-Liouville and Caputo fractional derivatives (about order 0<β
Fractional-order gradient descent learning of BP neural networks with Caputo derivative.
Wang, Jian; Wen, Yanqing; Gou, Yida; Ye, Zhenyun; Chen, Hua
2017-05-01
Fractional calculus has been found to be a promising area of research for information processing and modeling of some physical systems. In this paper, we propose a fractional gradient descent method for the backpropagation (BP) training of neural networks. In particular, the Caputo derivative is employed to evaluate the fractional-order gradient of the error defined as the traditional quadratic energy function. The monotonicity and weak (strong) convergence of the proposed approach are proved in detail. Two simulations have been implemented to illustrate the performance of presented fractional-order BP algorithm on three small datasets and one large dataset. The numerical simulations effectively verify the theoretical observations of this paper as well. Copyright © 2017 Elsevier Ltd. All rights reserved.
A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics
Lei, Dong; Liang, Yingjie; Xiao, Rui
2018-01-01
We develop a fractional model to describe the thermomechanical behavior of amorphous thermoplastics. The fractional model is composed of two parallel fractional Maxwell elements. The first fractional Maxwell model is used to describe the glass transition, while the second component is aimed at describing the viscous flow. We further derive the analytical solutions for the stress relaxation modulus and complex modulus through Laplace transform. We then demonstrate the model is able to describe the master curves of the stress relaxation modulus, storage modulus and loss modulus, which all show two distinct transition regions. The obtained parameters show that the modulus of the two fractional Maxwell elements differs in 2-3 orders of magnitude, while the relaxation time differs in 7-9 orders of magnitude. Finally, we apply the model to describe the stress response of constant strain rate tests. The model, together with the parameters obtained from fitting the master curve of stress relaxation modulus, can accurately predict the temperature and strain rate dependent stress response.
Memory regeneration phenomenon in dielectrics: the fractional derivative approach
International Nuclear Information System (INIS)
Uchaikin, V; Sibatov, R; Uchaikin, D
2009-01-01
Classical theory predicts that a capacitor's charging current obeys the first-order differential equation and hence follows the exponential Debye law. However, there are many experimental results confirming the inverse-power Curie-von Schweidler law of the charging current. The principal difference between the Curie-von Schweidler law and the Debye law is the presence of memory: the process depends not only on initial conditions but also on the whole prehistory. We constructed and investigated the capacitor model that extends the fractional Westerlund model by accounting for the resistance of the capacitor. To follow the transition to classical Debye theory, we investigated the solution of the fractional equation for the order α close to 1. The calculations show that the solution obeys the exponential law up to some point of time independently of the prehistory and then changes its behavior to the inverse power law depending on the prehistory. Comparison with experimental data confirmed the existence of this effect. We named it the regenerated memory effect.
Safdar, Rabia; Imran, M.; Khalique, Chaudry Masood
2018-06-01
Exact solutions for velocity field and tangential stress for rotational flow of a generalized Burgers' fluid within an infinite circular pipe are derived by using the methods of Laplace and finite Hankel transformations. Firstly we take the position of fluid at rest and then the fluid flow due to the rotation of the pipe around the axis of flow having time dependant angular velocity. The exact solutions are presented in terms of the generalized Ga,b,c (., t) -functions. The corresponding results can be freely specified for the same results of Burgers', Oldroyd B, Maxwell, second grade and Newtonian fluids (performing the same motion) as particular cases of the results obtained earlier. The impact of the different parameters, individually and in comparison, are represented by graphical demonstrations. Secondly the numerical solutions for velocity and stress are also obtained with the help of Laplace transformation, Gaver Stehfest's algorithm and MATHCAD. Finally a comparison of both methods for the same problem is done and shows the consistency of results.
Directory of Open Access Journals (Sweden)
Ai-Min Yang
2014-01-01
Full Text Available The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.
Coronary Computed Tomography Angiography Derived Fractional Flow Reserve and Plaque Stress
DEFF Research Database (Denmark)
Nørgaard, Bjarne Linde; Leipsic, Jonathon; Koo, Bon-Kwon
2016-01-01
Fractional flow reserve (FFR) measured during invasive coronary angiography is an independent prognosticator in patients with coronary artery disease and the gold standard for decision making in coronary revascularization. The integration of computational fluid dynamics and quantitative anatomic...... and physiologic modeling now enables simulation of patient-specific hemodynamic parameters including blood velocity, pressure, pressure gradients, and FFR from standard acquired coronary computed tomography (CT) datasets. In this review article, we describe the potential impact on clinical practice...... and the science behind noninvasive coronary computed tomography (CT) angiography derived fractional flow reserve (FFRCT) as well as future applications of this technology in treatment planning and quantifying forces on atherosclerotic plaques....
Spatial Rotation of the Fractional Derivative in Two-Dimensional Space
Directory of Open Access Journals (Sweden)
Ehab Malkawi
2015-01-01
Full Text Available The transformations of the partial fractional derivatives under spatial rotation in R2 are derived for the Riemann-Liouville and Caputo definitions. These transformation properties link the observation of physical quantities, expressed through fractional derivatives, with respect to different coordinate systems (observers. It is the hope that such understanding could shed light on the physical interpretation of fractional derivatives. Also it is necessary to be able to construct interaction terms that are invariant with respect to equivalent observers.
Comparative study of void fraction models
International Nuclear Information System (INIS)
Borges, R.C.; Freitas, R.L.
1985-01-01
Some models for the calculation of void fraction in water in sub-cooled boiling and saturated vertical upward flow with forced convection have been selected and compared with experimental results in the pressure range of 1 to 150 bar. In order to know the void fraction axial distribution it is necessary to determine the net generation of vapour and the fluid temperature distribution in the slightly sub-cooled boiling region. It was verified that the net generation of vapour was well represented by the Saha-Zuber model. The selected models for the void fraction calculation present adequate results but with a tendency to super-estimate the experimental results, in particular the homogeneous models. The drift flux model is recommended, followed by the Armand and Smith models. (F.E.) [pt
Saad, K. M.
2018-03-01
In this work we extend the standard model for a cubic isothermal auto-catalytic chemical system (CIACS) to a new model of a fractional cubic isothermal auto-catalytic chemical system (FCIACS) based on Caputo (C), Caputo-Fabrizio (CF) and Atangana-Baleanu in the Liouville-Caputo sense (ABC) fractional time derivatives, respectively. We present approximate solutions for these extended models using the q -homotopy analysis transform method ( q -HATM). We solve the FCIACS with the C derivative and compare our results with those obtained using the CF and ABC derivatives. The ranges of convergence of the solutions are found and the optimal values of h , the auxiliary parameter, are derived. Finally, these solutions are compared with numerical solutions of the various models obtained using finite differences and excellent agreement is found.
Analysis of the cable equation with non-local and non-singular kernel fractional derivative
Karaagac, Berat
2018-02-01
Recently a new concept of differentiation was introduced in the literature where the kernel was converted from non-local singular to non-local and non-singular. One of the great advantages of this new kernel is its ability to portray fading memory and also well defined memory of the system under investigation. In this paper the cable equation which is used to develop mathematical models of signal decay in submarine or underwater telegraphic cables will be analysed using the Atangana-Baleanu fractional derivative due to the ability of the new fractional derivative to describe non-local fading memory. The existence and uniqueness of the more generalized model is presented in detail via the fixed point theorem. A new numerical scheme is used to solve the new equation. In addition, stability, convergence and numerical simulations are presented.
Likelihood inference for a nonstationary fractional autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Ørregård Nielsen, Morten
2010-01-01
This paper discusses model-based inference in an autoregressive model for fractional processes which allows the process to be fractional of order d or d-b. Fractional differencing involves infinitely many past values and because we are interested in nonstationary processes we model the data X1......,...,X_{T} given the initial values X_{-n}, n=0,1,..., as is usually done. The initial values are not modeled but assumed to be bounded. This represents a considerable generalization relative to all previous work where it is assumed that initial values are zero. For the statistical analysis we assume...... the conditional Gaussian likelihood and for the probability analysis we also condition on initial values but assume that the errors in the autoregressive model are i.i.d. with suitable moment conditions. We analyze the conditional likelihood and its derivatives as stochastic processes in the parameters, including...
Fractional calculus model of electrical impedance applied to human skin.
Vosika, Zoran B; Lazovic, Goran M; Misevic, Gradimir N; Simic-Krstic, Jovana B
2013-01-01
Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and complex orders. Therefore, it adds a new dimension to understand and describe basic nature and behavior of complex systems in an improved way. Here we use the fractional calculus for modeling electrical properties of biological systems. We derived a new class of generalized models for electrical impedance and applied them to human skin by experimental data fitting. The primary model introduces new generalizations of: 1) Weyl fractional derivative operator, 2) Cole equation, and 3) Constant Phase Element (CPE). These generalizations were described by the novel equation which presented parameter [Formula: see text] related to remnant memory and corrected four essential parameters [Formula: see text] We further generalized single generalized element by introducing specific partial sum of Maclaurin series determined by parameters [Formula: see text] We defined individual primary model elements and their serial combination models by the appropriate equations and electrical schemes. Cole equation is a special case of our generalized class of models for[Formula: see text] Previous bioimpedance data analyses of living systems using basic Cole and serial Cole models show significant imprecisions. Our new class of models considerably improves the quality of fitting, evaluated by mean square errors, for bioimpedance data obtained from human skin. Our models with new parameters presented in specific partial sum of Maclaurin series also extend representation, understanding and description of complex systems electrical properties in terms of remnant memory effects.
Fractional calculus model of electrical impedance applied to human skin.
Directory of Open Access Journals (Sweden)
Zoran B Vosika
Full Text Available Fractional calculus is a mathematical approach dealing with derivatives and integrals of arbitrary and complex orders. Therefore, it adds a new dimension to understand and describe basic nature and behavior of complex systems in an improved way. Here we use the fractional calculus for modeling electrical properties of biological systems. We derived a new class of generalized models for electrical impedance and applied them to human skin by experimental data fitting. The primary model introduces new generalizations of: 1 Weyl fractional derivative operator, 2 Cole equation, and 3 Constant Phase Element (CPE. These generalizations were described by the novel equation which presented parameter [Formula: see text] related to remnant memory and corrected four essential parameters [Formula: see text] We further generalized single generalized element by introducing specific partial sum of Maclaurin series determined by parameters [Formula: see text] We defined individual primary model elements and their serial combination models by the appropriate equations and electrical schemes. Cole equation is a special case of our generalized class of models for[Formula: see text] Previous bioimpedance data analyses of living systems using basic Cole and serial Cole models show significant imprecisions. Our new class of models considerably improves the quality of fitting, evaluated by mean square errors, for bioimpedance data obtained from human skin. Our models with new parameters presented in specific partial sum of Maclaurin series also extend representation, understanding and description of complex systems electrical properties in terms of remnant memory effects.
Exact solutions of a class of fractional Hamiltonian equations involving Caputo derivatives
Energy Technology Data Exchange (ETDEWEB)
Baleanu, Dumitru [Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Ankara 06530 (Turkey); Trujillo, Juan J [Departamento de Analisis Matematico, University of La Laguna, 38271 La Laguna, Tenerife (Spain)], E-mail: dumitru@cankaya.edu.tr, E-mail: JTrujill@ullmat.es, E-mail: baleanu@venus.nipne.ro
2009-11-15
The fractional Hamiltonian equations corresponding to the Lagrangians of constrained systems within Caputo derivatives are investigated. The fractional phase space is obtained and the exact solutions of some constrained systems are obtained.
Investigation of the Dirac Equation by Using the Conformable Fractional Derivative
Mozaffari, F. S.; Hassanabadi, H.; Sobhani, H.; Chung, W. S.
2018-05-01
In this paper,the Dirac equation is constructed using the conformable fractional derivative so that in its limit for the fractional parameter, the normal version is recovered. Then, the Cornell potential is considered as the interaction of the system. In this case, the wave function and the energy eigenvalue equation are derived with the aim of the bi-confluent Heun functions. use of the conformable fractional derivative is proven to lead to a branching treatment for the energy of the system. Such a treatment is obvious for small values of the fractional parameter, and a united value as the fractional parameter approaches unity.
Energy Technology Data Exchange (ETDEWEB)
Machida, M.; Ono, S. [Idemitsu Kosan Co. Ltd., Tokyo (Japan); Hattori, H. [Hokkaido University, Sapporo (Japan). Center for Advanced Research of Energy Technology
1997-09-01
The improvement in hydrodenitrogenation (HDN) of coal-derived liquids by co-refining with a petroleum fraction results principally from lowering the nitrogen content of the feedstock (coal-derived liquid) by blending with a nitrogen-free petroleum fraction. Effects of different fractions of coal-derived liquids on HDN and hydrodeoxygenation (HDO) were also examined. The HDN improvement by co-refining could be interpreted in terms of Langmuir-Hinshelwood mechanism. 38 refs., 3 figs., 3 tabs.
Fractional virus epidemic model on financial networks
Directory of Open Access Journals (Sweden)
Balci Mehmet Ali
2016-01-01
Full Text Available In this study, we present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets. Since the long time series have a global memory effect, we represent our model by using the fractional calculus. This model operates on a network, where vertices are the stock markets and edges are constructed by the correlation distances. Thereafter, we find an analytical solution to commensurate system and use the well-known differential transform method to obtain the solution of incommensurate system of fractional differential equations. Our findings are confirmed and complemented by the data set of the relevant stock markets between 2006 and 2016. Rather than the hypothetical values, we use the Hurst Exponent of each time series to approximate the fraction size and graph theoretical concepts to obtain the variables.
Yang, YongGe; Xu, Wei; Yang, Guidong
2018-04-01
To the best of authors' knowledge, little work was referred to the study of a noisy vibro-impact oscillator with a fractional derivative. Stochastic bifurcations of a vibro-impact oscillator with two kinds of fractional derivative elements driven by Gaussian white noise excitation are explored in this paper. We can obtain the analytical approximate solutions with the help of non-smooth transformation and stochastic averaging method. The numerical results from Monte Carlo simulation of the original system are regarded as the benchmark to verify the accuracy of the developed method. The results demonstrate that the proposed method has a satisfactory level of accuracy. We also discuss the stochastic bifurcation phenomena induced by the fractional coefficients and fractional derivative orders. The important and interesting result we can conclude in this paper is that the effect of the first fractional derivative order on the system is totally contrary to that of the second fractional derivative order.
An inverse Sturm–Liouville problem with a fractional derivative
Jin, Bangti; Rundell, William
2012-01-01
In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and numerical
A Fractional Micro-Macro Model for Crowds of Pedestrians Based on Fractional Mean Field Games
Institute of Scientific and Technical Information of China (English)
Kecai Cao; Yang Quan Chen; Daniel Stuart
2016-01-01
Modeling a crowd of pedestrians has been considered in this paper from different aspects. Based on fractional microscopic model that may be much more close to reality, a fractional macroscopic model has been proposed using conservation law of mass. Then in order to characterize the competitive and cooperative interactions among pedestrians, fractional mean field games are utilized in the modeling problem when the number of pedestrians goes to infinity and fractional dynamic model composed of fractional backward and fractional forward equations are constructed in macro scale. Fractional micromacro model for crowds of pedestrians are obtained in the end.Simulation results are also included to illustrate the proposed fractional microscopic model and fractional macroscopic model,respectively.
Directory of Open Access Journals (Sweden)
Venkat M Ramakrishnan
Full Text Available Human adipose-derived stromal vascular fraction (hSVF cells are an easily accessible, heterogeneous cell system that can spontaneously self-assemble into functional microvasculatures in vivo. However, the mechanisms underlying vascular self-assembly and maturation are poorly understood, therefore we utilized an in vitro model to identify potential in vivo regulatory mechanisms. We utilized passage one (P1 hSVF because of the rapid UEA1+ endothelium (EC loss at even P2 culture. We exposed hSVF cells to a battery of angiogenesis inhibitors and found that the pan-Wnt inhibitor IWP2 produced the most significant hSVF-EC networking decrease (~25%. To determine which Wnt isoform(s and receptor(s may be involved, hSVF was screened by PCR for isoforms associated with angiogenesis, with only WNT5A and its receptor, FZD4, being expressed for all time points observed. Immunocytochemistry confirmed Wnt5a protein expression by hSVF. To see if Wnt5a alone could restore IWP2-induced EC network inhibition, recombinant human Wnt5a (0-150 ng/ml was added to IWP2-treated cultures. The addition of rhWnt5a significantly increased EC network area and significantly decreased the ratio of total EC network length to EC network area compared to untreated controls. To determine if Wnt5a mediates in vivo microvascular self-assembly, 3D hSVF constructs containing an IgG isotype control, anti-Wnt5a neutralizing antibody or rhWnt5a were implanted subcutaneously for 2w in immune compromised mice. Compared to IgG controls, anti-Wnt5a treatment significantly reduced vessel length density by ~41%, while rhWnt5a significantly increased vessel length density by ~62%. However, anti-Wnt5a or rhWnt5a did not significantly affect the density of segments and nodes, both of which measure vascular complexity. Taken together, this data demonstrates that endogenous Wnt5a produced by hSVF plays a regulatory role in microvascular self-assembly in vivo. These findings also suggest that
Modelling nematode movement using time-fractional dynamics.
Hapca, Simona; Crawford, John W; MacMillan, Keith; Wilson, Mike J; Young, Iain M
2007-09-07
We use a correlated random walk model in two dimensions to simulate the movement of the slug parasitic nematode Phasmarhabditis hermaphrodita in homogeneous environments. The model incorporates the observed statistical distributions of turning angle and speed derived from time-lapse studies of individual nematode trails. We identify strong temporal correlations between the turning angles and speed that preclude the case of a simple random walk in which successive steps are independent. These correlated random walks are appropriately modelled using an anomalous diffusion model, more precisely using a fractional sub-diffusion model for which the associated stochastic process is characterised by strong memory effects in the probability density function.
International Nuclear Information System (INIS)
Dong Jianping; Xu Mingyu
2008-01-01
The space fractional Schroedinger equation with a finite square potential, periodic potential, and delta-function potential is studied in this paper. We find that the continuity or discontinuity condition of a fractional derivative of the wave functions should be considered to solve the fractional Schroedinger equation in fractional quantum mechanics. More parity states than those given by standard quantum mechanics for the finite square potential well are obtained. The corresponding energy equations are derived and then solved by graphical methods. We show the validity of Bloch's theorem and reveal the energy band structure for the periodic potential. The jump (discontinuity) condition for the fractional derivative of the wave function of the delta-function potential is given. With the help of the jump condition, we study some delta-function potential fields. For the delta-function potential well, an alternate expression of the wave function (the H function form of it was given by Dong and Xu [J. Math. Phys. 48, 072105 (2007)]) is obtained. The problems of a particle penetrating through a delta-function potential barrier and the fractional probability current density of the particle are also discussed. We study the Dirac comb and show the energy band structure at the end of the paper
Revised models of interstellar nitrogen isotopic fractionation
Wirström, E. S.; Charnley, S. B.
2018-03-01
Nitrogen-bearing molecules in cold molecular clouds exhibit a range of isotopic fractionation ratios and these molecules may be the precursors of 15N enrichments found in comets and meteorites. Chemical model calculations indicate that atom-molecular ion and ion-molecule reactions could account for most of the fractionation patterns observed. However, recent quantum-chemical computations demonstrate that several of the key processes are unlikely to occur in dense clouds. Related model calculations of dense cloud chemistry show that the revised 15N enrichments fail to match observed values. We have investigated the effects of these reaction rate modifications on the chemical model of Wirström et al. (2012) for which there are significant physical and chemical differences with respect to other models. We have included 15N fractionation of CN in neutral-neutral reactions and also updated rate coefficients for key reactions in the nitrogen chemistry. We find that the revised fractionation rates have the effect of suppressing 15N enrichment in ammonia at all times, while the depletion is even more pronounced, reaching 14N/15N ratios of >2000. Taking the updated nitrogen chemistry into account, no significant enrichment occurs in HCN or HNC, contrary to observational evidence in dark clouds and comets, although the 14N/15N ratio can still be below 100 in CN itself. However, such low CN abundances are predicted that the updated model falls short of explaining the bulk 15N enhancements observed in primitive materials. It is clear that alternative fractionating reactions are necessary to reproduce observations, so further laboratory and theoretical studies are urgently needed.
Directory of Open Access Journals (Sweden)
Waleed M. Abd-Elhameed
2016-09-01
Full Text Available Herein, two numerical algorithms for solving some linear and nonlinear fractional-order differential equations are presented and analyzed. For this purpose, a novel operational matrix of fractional-order derivatives of Fibonacci polynomials was constructed and employed along with the application of the tau and collocation spectral methods. The convergence and error analysis of the suggested Fibonacci expansion were carefully investigated. Some numerical examples with comparisons are presented to ensure the efficiency, applicability and high accuracy of the proposed algorithms. Two accurate semi-analytic polynomial solutions for linear and nonlinear fractional differential equations are the result.
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.
Fractional diffusion equation with distributed-order material derivative. Stochastic foundations
International Nuclear Information System (INIS)
Magdziarz, M; Teuerle, M
2017-01-01
In this paper, we present the stochastic foundations of fractional dynamics driven by the fractional material derivative of distributed-order type. Before stating our main result, we present the stochastic scenario which underlies the dynamics given by the fractional material derivative. Then we introduce the Lévy walk process of distributed-order type to establish our main result, which is the scaling limit of the considered process. It appears that the probability density function of the scaling limit process fulfills, in a weak sense, the fractional diffusion equation with the material derivative of distributed-order type. (paper)
Cuahutenango-Barro, B.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.
2017-12-01
Analytical solutions of the wave equation with bi-fractional-order and frictional memory kernel of Mittag-Leffler type are obtained via Caputo-Fabrizio fractional derivative in the Liouville-Caputo sense. Through the method of separation of variables and Laplace transform method we derive closed-form solutions and establish fundamental solutions. Special cases with homogeneous Dirichlet boundary conditions and nonhomogeneous initial conditions, as well as for the external force are considered. Numerical simulations of the special solutions were done and novel behaviors are obtained.
International Nuclear Information System (INIS)
Scalliet, P.; Schueren, E. van der; Erfmann, R.K.L.; Landuyt, W.
1988-01-01
The authors present a method for the derivation of the time constant of repair from fractionated and protracted irradiations, using formulae based on those derived by Dale (1985) and Liversage (1969) establishing the correlation between the biological effects of low dose rate and acute fractionated irradiation. (UK)
Leigh, Annballaw Bridget; Cheung, Ho Pan; Lin, Li-Zhu; Ng, Tzi Bun; Lao, Lixing; Zhang, Yanbo; Zhang, Zhang-Jin; Tong, Yao; Sze, Stephen Cho Wing
2017-09-01
The Chinese medicine formula Tian Xian Liquid (TXL) has been used clinically for cancer therapy in China for more than 25 years. However, the comprehensive and holistic effects of its bioactive fractions for various antitumor therapeutic effects have not been unraveled. This is the first study to scientifically elucidate the holistic effect of Chinese medicine formula for treating colon cancer, hence allowing a better understanding of the essence of Chinese medicine formula, through the comparison of the actions of TXL and its functional constituent fractions, including ethyl acetate (EA), butanol (BU), and aqueous (WA) fractions. Tissue-specific proliferative/antiproliferative effects of these fractions on human colorectal carcinoma HT-29 cells and splenocytes were studied by using the MTT assay. Their modulations on the expression of markers of antiproliferation, antimetastasis, reversion of multidrug resistance in treated HT-29 cells were examined with real-time polymerase chain reaction and Western blot analysis, and their modulations in a xenografted nude mouse model were examined by Western blot analysis. Results revealed that EA fraction slightly inhibited the proliferation of HT-29 cells, but tissue-specifically exerted the most potent antiproliferative effect on splenocytes. On the contrary, only TXL and BU fraction tissue-specifically contributed to the proliferation of splenocytes, but inhibited the proliferation of HT-29 cells. WA fraction exerted the most potent antiproliferative effect on HT-29 cells and also the strongest inhibitory action on tumor size in the nude mouse model in our previous study. In the HT-29 model, TXL and WA fraction exerted the most pronounced effect on upregulation of p21 mRNA and protein; TXL, and EA and WA fractions exerted the effect on downregulation of G1 phase cell cycle protein, cyclin D1 mRNA and protein; EA and BU fractions exerted the most prominent anti-invasive effect on anti-invasion via downregulation of MMP-1 m
Fractional derivative of the Hurwitz ζ-function and chaotic decay to zero
Directory of Open Access Journals (Sweden)
C. Cattani
2016-01-01
Full Text Available In this paper the fractional order derivative of a Dirichlet series, Hurwitz zeta function and Riemann zeta function is explicitly computed using the Caputo fractional derivative in the Ortigueira sense. It is observed that the obtained results are a natural generalization of the integer order derivative. Some interesting properties of the fractional derivative of the Riemann zeta function are also investigated to show that there is a chaotic decay to zero (in the Gaussian plane and a promising expression as a complex power series.
Modeling and analysis of fractional order DC-DC converter.
Radwan, Ahmed G; Emira, Ahmed A; AbdelAty, Amr M; Azar, Ahmad Taher
2017-07-11
Due to the non-idealities of commercial inductors, the demand for a better model that accurately describe their dynamic response is elevated. So, the fractional order models of Buck, Boost and Buck-Boost DC-DC converters are presented in this paper. The detailed analysis is made for the two most common modes of converter operation: Continuous Conduction Mode (CCM) and Discontinuous Conduction Mode (DCM). Closed form time domain expressions are derived for inductor currents, voltage gain, average current, conduction time and power efficiency where the effect of the fractional order inductor is found to be strongly present. For example, the peak inductor current at steady state increases with decreasing the inductor order. Advanced Design Systems (ADS) circuit simulations are used to verify the derived formulas, where the fractional order inductor is simulated using Valsa Constant Phase Element (CPE) approximation and Generalized Impedance Converter (GIC). Different simulation results are introduced with good matching to the theoretical formulas for the three DC-DC converter topologies under different fractional orders. A comprehensive comparison with the recently published literature is presented to show the advantages and disadvantages of each approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Ghosh, Uttam; Banerjee, Joydip; Sarkar, Susmita; Das, Shantanu
2018-06-01
Klein-Gordon equation is one of the basic steps towards relativistic quantum mechanics. In this paper, we have formulated fractional Klein-Gordon equation via Jumarie fractional derivative and found two types of solutions. Zero-mass solution satisfies photon criteria and non-zero mass satisfies general theory of relativity. Further, we have developed rest mass condition which leads us to the concept of hidden wave. Classical Klein-Gordon equation fails to explain a chargeless system as well as a single-particle system. Using the fractional Klein-Gordon equation, we can overcome the problem. The fractional Klein-Gordon equation also leads to the smoothness parameter which is the measurement of the bumpiness of space. Here, by using this smoothness parameter, we have defined and interpreted the various cases.
Directory of Open Access Journals (Sweden)
Mehdi Behfar
2011-11-01
Full Text Available Tendon never restores the complete biological and mechanical properties after healing. Bone marrow and recently adipose tissue have been used as the sources of mesenchymal stem cells, which have been proven to enhance tendon healing. Stromal vascular fraction (SVF, derived from adipose tissue by an enzymatic digestion, represents an alternative source of multipotent cells, which undergo differentiation into multiple lineages to be used in regenerative medicine. In the present study, we investigated potentials of this source on tendon healing. Twenty rabbits were divided into control and treatment groups. Five rabbits were used as donors of adipose tissue. The injury model was unilateral complete transection through the middle one third of deep digital flexor tendon. Immediately after suture repair, either fresh stromal vascular fraction from enzymatic digestion of adipose tissue or placebo was intratendinously injected into the suture site in treatments and controls, respectively. Cast immobilization was continued for two weeks after surgery. Animals were sacrificed at the third week and tendons underwent histological, immunohistochemical, and mechanical evaluations. By histology, improved fibrillar organization and remodeling of neotendon were observed in treatment group. Immunohistochemistry revealed an insignificant increase in collagen type III and I expression in treatments over controls. Mechanical testing showed significant increase in maximum load and energy absorption in SVF treated tendons. The present study showed that intratendinous injection of uncultured adipose derived stromal vascular fraction improved structural and mechanical properties of repaired tendon and it could be an effective modality for treating tendon laceration.
Inter-fraction variations in respiratory motion models
Energy Technology Data Exchange (ETDEWEB)
McClelland, J R; Modat, M; Ourselin, S; Hawkes, D J [Centre for Medical Image Computing, University College London (United Kingdom); Hughes, S; Qureshi, A; Ahmad, S; Landau, D B, E-mail: j.mcclelland@cs.ucl.ac.uk [Department of Oncology, Guy' s and St Thomas' s Hospitals NHS Trust, London (United Kingdom)
2011-01-07
Respiratory motion can vary dramatically between the planning stage and the different fractions of radiotherapy treatment. Motion predictions used when constructing the radiotherapy plan may be unsuitable for later fractions of treatment. This paper presents a methodology for constructing patient-specific respiratory motion models and uses these models to evaluate and analyse the inter-fraction variations in the respiratory motion. The internal respiratory motion is determined from the deformable registration of Cine CT data and related to a respiratory surrogate signal derived from 3D skin surface data. Three different models for relating the internal motion to the surrogate signal have been investigated in this work. Data were acquired from six lung cancer patients. Two full datasets were acquired for each patient, one before the course of radiotherapy treatment and one at the end (approximately 6 weeks later). Separate models were built for each dataset. All models could accurately predict the respiratory motion in the same dataset, but had large errors when predicting the motion in the other dataset. Analysis of the inter-fraction variations revealed that most variations were spatially varying base-line shifts, but changes to the anatomy and the motion trajectories were also observed.
Parameter estimation in fractional diffusion models
Kubilius, Kęstutis; Ralchenko, Kostiantyn
2017-01-01
This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides s...
Cadmium isotope fractionation of materials derived from various industrial processes
Energy Technology Data Exchange (ETDEWEB)
Martinková, Eva, E-mail: eva.cadkova@geology.cz [Czech Geological Survey, Geologická 6, 152 00 Prague 5 (Czech Republic); Chrastný, Vladislav, E-mail: chrastny@fzp.czu.cz [Faculty of Environmental Sciences, Czech University of Life Sciences Prague, Kamýcká 129, 165 21 Prague 6 (Czech Republic); Francová, Michaela, E-mail: michaela.francova@fzp.czu.cz [Faculty of Environmental Sciences, Czech University of Life Sciences Prague, Kamýcká 129, 165 21 Prague 6 (Czech Republic); Šípková, Adéla, E-mail: adela.sipkova@geology.cz [Czech Geological Survey, Geologická 6, 152 00 Prague 5 (Czech Republic); Čuřík, Jan, E-mail: jan.curik@geology.cz [Czech Geological Survey, Geologická 6, 152 00 Prague 5 (Czech Republic); Myška, Oldřich, E-mail: oldrich.myska@geology.cz [Czech Geological Survey, Geologická 6, 152 00 Prague 5 (Czech Republic); Mižič, Lukáš, E-mail: lukas.mizic@geology.cz [Czech Geological Survey, Geologická 6, 152 00 Prague 5 (Czech Republic)
2016-01-25
Highlights: • All studied industrial processes were accompanied by Cd isotope fractionation. • ϵ{sup 114/110} Cd values of the waste materials were discernible from primary sources. • Technology in use plays an important role in Cd isotope fractionation. - Abstract: Our study represents ϵ{sup 114/110} Cd {sub NIST3108} values of materials resulting from anthropogenic activities such as coal burning, smelting, refining, metal coating, and the glass industry. Additionally, primary sources (ore samples, pigment, coal) processed in the industrial premises were studied. Two sphalerites, galena, coal and pigment samples exhibited ϵ{sup 114/110} Cd{sub NIST3108} values of 1.0 ± 0.2, 0.2 ± 0.2, 1.3 ± 0.1, −2.3 ± 0.2 and −0.1 ± 0.3, respectively. In general, all studied industrial processes were accompanied by Cd isotope fractionation. Most of the industrial materials studied were clearly distinguishable from the samples used as a primary source based on ϵ{sup 114/110} Cd {sub NIST3108} values. The heaviest ϵ{sup 114/110} Cd{sub NIST3108} value of 58.6 ± 0.9 was found for slag resulting from coal combustion, and the lightest ϵ{sup 114/110} Cd{sub NIST3108} value of −23 ± 2.5 was observed for waste material after Pb refinement. It is evident that ϵ{sup 114/110} Cd {sub NIST3108} values depend on technological processes, and in case of incomplete Cd transfer from source to final waste material, every industrial activity creates differences in Cd isotope composition. Our results show that Cd isotope analysis is a promising tool to track the origins of industrial waste products.
Fractional-moment Capital Asset Pricing model
International Nuclear Information System (INIS)
Li Hui; Wu Min; Wang Xiaotian
2009-01-01
In this paper, we introduce the definition of the 'α-covariance' and present the fractional-moment versions of Capital Asset Pricing Model,which can be used to price assets when asset return distributions are likely to be stable Levy (or Student-t) distribution during panics and stampedes in worldwide security markets in 2008. Furthermore, if asset returns are truly governed by the infinite-variance stable Levy distributions, life is fundamentally riskier than in a purely Gaussian world. Sudden price movements like the worldwide security market crash in 2008 turn into real-world possibilities.
Fractional Calculus in Hydrologic Modeling: A Numerical Perspective
Energy Technology Data Exchange (ETDEWEB)
David A. Benson; Mark M. Meerschaert; Jordan Revielle
2012-01-01
Fractional derivatives can be viewed either as a handy extension of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Levy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Levy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus.
International Nuclear Information System (INIS)
Fan Hongyi; Hao Ren; Lu Hailiang
2008-01-01
Based on our previous paper (Commun. Theor. Phys. 39 (2003) 417) we derive the convolution theorem of fractional Fourier transformation in the context of quantum mechanics, which seems a convenient and neat way. Generalization of this method to the complex fractional Fourier transformation case is also possible
Directory of Open Access Journals (Sweden)
Erkinjon Karimov
2017-10-01
Full Text Available In this work we discuss higher order multi-term partial differential equation (PDE with the Caputo-Fabrizio fractional derivative in time. Using method of separation of variables, we reduce fractional order partial differential equation to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.
Erkinjon Karimov; Sardor Pirnafasov
2017-01-01
In this work we discuss higher order multi-term partial differential equation (PDE) with the Caputo-Fabrizio fractional derivative in time. Using method of separation of variables, we reduce fractional order partial differential equation to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.
Evaluating derived vegetation indices and cover fraction to estimate ...
African Journals Online (AJOL)
Nahom
This study was conducted to assess satellite data for quantifying and mapping the ... aboveground biomass using regression models of the sample aboveground ... especially in the context of drought, land degradation risk assessment and.
Cheraghali, A M; Aboofazeli, R
2009-12-01
In Iran all transfusion services are concentrated under authority of one public and centralized transfusion organization which has created the opportunity of using plasma produced in its blood centers for fractionation. In 2008 voluntary and non remunerated Iranian donors donated 1.8 million units of blood. This indicates a 25/1000 donation index. After responding to the needs for fresh plasma and cryoprecipitate each year about 150000 L of recovered plasma are reserved for fractionation. In an attempt to improve both blood safety profile and availability and affordability of plasma derived medicines, Iran's national transfusion service has entered into a contract fractionation agreement for surplus of plasma produced from donated blood by voluntary non remunerated donors. In order to ensure safety of product produced, Iran has chosen to collaborate with international fractionators based in highly regulated countries. The main objective of this study was to evaluate the impact of contract plasma fractionation on the affordability of the plasma derived medicines in Iran. During 2006-2008, Iran's contract fractionation project was able to produce 46%, 18% and 6% of IVIG, Albumin and FVIII consumed in Iran's market, respectively. In contrary to IVIG and Albumin, due to fairly high consumption of FVIII in Iran, the role of fractionation project in meeting the needs to FVIII was not substantial. However, Iran's experience has shown that contract plasma fractionation, through direct and indirect effects on price of plasma derived medicines, could substantially improve availability and affordability of such products in national health care system.
Directory of Open Access Journals (Sweden)
Lihong Zhang
2017-11-01
Full Text Available In this article, a family of nonlinear diffusion equations involving multi-term Caputo-Fabrizio time fractional derivative is investigated. Some maximum principles are obtained. We also demonstrate the application of the obtained results by deriving some estimation for solution to reaction-diffusion equations.
Abdullah, M.; Butt, Asma Rashid; Raza, Nauman; Alshomrani, Ali Saleh; Alzahrani, A. K.
2018-01-01
The magneto hydrodynamic blood flow in the presence of magnetic particles through a circular cylinder is investigated. To calculate the impact of externally applied uniform magnetic field, the blood is electrically charged. Initially the fluid and circular cylinder is at rest but at time t =0+ , the cylinder starts to oscillate along its axis with velocity fsin (Ωt) . To obtain the mathematical model of blood flow with fractional derivatives Caputo fractional operator is employed. The solutions for the velocities of blood and magnetic particles are procured semi analytically by using Laplace transformation method. The inverse Laplace transform has been calculated numerically by using MATHCAD computer software. The obtained results of velocities are presented in Laplace domain in terms of modified Bessel function I0 (·) . The obtained results satisfied all imposed initial and boundary conditions. The hybrid technique that is employed here less computational effort and time cost as compared to other techniques used in literature. As the limiting cases of our results the solutions of the flow model with ordinary derivatives has been procured. Finally, the impact of Reynolds number Re, fractional parameter α and Hartmann number Ha is analyzed and portrayed through graphs. It is worthy to pointing out that fractional derivatives brings remarkable differences as compared to ordinary derivatives. It also has been observed that velocity of blood and magnetic particles is weaker under the effect of transverse magnetic field.
Directory of Open Access Journals (Sweden)
Gesiane Ribeiro
2013-12-01
Full Text Available The objective of this study was to evaluate the culture of equine bone marrow mononuclear fraction and adipose tissue - derived stromal vascular fraction cells in two different cell culture media. Five adult horses were submitted to bone marrow aspiration from the sternum, and then from the adipose tissue of the gluteal region near the base of the tail. Mononuclear fraction and stromal vascular fraction were isolated from the samples and cultivated in DMEM medium supplemented with 10% fetal bovine serum or in AIM-V medium. The cultures were observed once a week with an inverted microscope, to perform a qualitative analysis of the morphology of the cells as well as the general appearance of the cell culture. Colony-forming units (CFU were counted on days 5, 15 and 25 of cell culture. During the first week of culture, differences were observed between the samples from the same source maintained in different culture media. The number of colonies was significantly higher in samples of bone marrow in relation to samples of adipose tissue.
Non-exponential extinction of radiation by fractional calculus modelling
International Nuclear Information System (INIS)
Casasanta, G.; Ciani, D.; Garra, R.
2012-01-01
Possible deviations from exponential attenuation of radiation in a random medium have been recently studied in several works. These deviations from the classical Beer-Lambert law were justified from a stochastic point of view by Kostinski (2001) . In his model he introduced the spatial correlation among the random variables, i.e. a space memory. In this note we introduce a different approach, including a memory formalism in the classical Beer-Lambert law through fractional calculus modelling. We find a generalized Beer-Lambert law in which the exponential memoryless extinction is only a special case of non-exponential extinction solutions described by Mittag-Leffler functions. We also justify this result from a stochastic point of view, using the space fractional Poisson process. Moreover, we discuss some concrete advantages of this approach from an experimental point of view, giving an estimate of the deviation from exponential extinction law, varying the optical depth. This is also an interesting model to understand the meaning of fractional derivative as an instrument to transmit randomness of microscopic dynamics to the macroscopic scale.
Effective-field-theory model for the fractional quantum Hall effect
International Nuclear Information System (INIS)
Zhang, S.C.; Hansson, T.H.; Kivelson, S.
1989-01-01
Starting directly from the microscopic Hamiltonian, we derive a field-theory model for the fractional quantum hall effect. By considering an approximate coarse-grained version of the same model, we construct a Landau-Ginzburg theory similar to that of Girvin. The partition function of the model exhibits cusps as a function of density and the Hall conductance is quantized at filling factors ν = (2k-1)/sup -1/ with k an arbitrary integer. At these fractions the ground state is incompressible, and the quasiparticles and quasiholes have fractional charge and obey fractional statistics. Finally, we show that the collective density fluctuations are massive
A representation theory for a class of vector autoregressive models for fractional processes
DEFF Research Database (Denmark)
Johansen, Søren
2008-01-01
Based on an idea of Granger (1986), we analyze a new vector autoregressive model defined from the fractional lag operator 1-(1-L)^{d}. We first derive conditions in terms of the coefficients for the model to generate processes which are fractional of order zero. We then show that if there is a un...... root, the model generates a fractional process X(t) of order d, d>0, for which there are vectors ß so that ß'X(t) is fractional of order d-b, 0...
Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System
Directory of Open Access Journals (Sweden)
Zhenhua Hu
2013-01-01
Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.
New method dynamically models hydrocarbon fractionation
Energy Technology Data Exchange (ETDEWEB)
Kesler, M.G.; Weissbrod, J.M.; Sheth, B.V. [Kesler Engineering, East Brunswick, NJ (United States)
1995-10-01
A new method for calculating distillation column dynamics can be used to model time-dependent effects of independent disturbances for a range of hydrocarbon fractionation. It can model crude atmospheric and vacuum columns, with relatively few equilibrium stages and a large number of components, to C{sub 3} splitters, with few components and up to 300 equilibrium stages. Simulation results are useful for operations analysis, process-control applications and closed-loop control in petroleum, petrochemical and gas processing plants. The method is based on an implicit approach, where the time-dependent variations of inventory, temperatures, liquid and vapor flows and compositions are superimposed at each time step on the steady-state solution. Newton-Raphson (N-R) techniques are then used to simultaneously solve the resulting finite-difference equations of material, equilibrium and enthalpy balances that characterize distillation dynamics. The important innovation is component-aggregation and tray-aggregation to contract the equations without compromising accuracy. This contraction increases the N-R calculations` stability. It also significantly increases calculational speed, which is particularly important in dynamic simulations. This method provides a sound basis for closed-loop, supervisory control of distillation--directly or via multivariable controllers--based on a rigorous, phenomenological column model.
Linking the fractional derivative and the Lomnitz creep law to non-Newtonian time-varying viscosity
Pandey, Vikash; Holm, Sverre
2016-09-01
Many of the most interesting complex media are non-Newtonian and exhibit time-dependent behavior of thixotropy and rheopecty. They may also have temporal responses described by power laws. The material behavior is represented by the relaxation modulus and the creep compliance. On the one hand, it is shown that in the special case of a Maxwell model characterized by a linearly time-varying viscosity, the medium's relaxation modulus is a power law which is similar to that of a fractional derivative element often called a springpot. On the other hand, the creep compliance of the time-varying Maxwell model is identified as Lomnitz's logarithmic creep law, making this possibly its first direct derivation. In this way both fractional derivatives and Lomnitz's creep law are linked to time-varying viscosity. A mechanism which yields fractional viscoelasticity and logarithmic creep behavior has therefore been found. Further, as a result of this linking, the curve-fitting parameters involved in the fractional viscoelastic modeling, and the Lomnitz law gain physical interpretation.
Energy Technology Data Exchange (ETDEWEB)
Sabzikar, Farzad, E-mail: sabzika2@stt.msu.edu [Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823 (United States); Meerschaert, Mark M., E-mail: mcubed@stt.msu.edu [Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823 (United States); Chen, Jinghua, E-mail: cjhdzdz@163.com [School of Sciences, Jimei University, Xiamen, Fujian, 361021 (China)
2015-07-15
Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.
Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua
2015-07-01
Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.
International Nuclear Information System (INIS)
Sabzikar, Farzad; Meerschaert, Mark M.; Chen, Jinghua
2015-01-01
Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered fractional difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series
Jin, Jie; Sun, Ke; Liu, Wei; Li, Shiwei; Peng, Xianqiang; Yang, Yan; Han, Lanfang; Du, Ziwen; Wang, Xiangke
2018-05-01
Chemical composition and pollutant sorption of biochar-derived organic matter fractions (BDOMs) are critical for understanding the long-term environmental significance of biochar. Phenanthrene (PHE) sorption by the humic acid-like (HAL) fractions isolated from plant straw- (PLABs) and animal manure-based (ANIBs) biochars, and the residue materials (RES) after HAL extraction was investigated. The HAL fraction comprised approximately 50% of organic carbon (OC) of the original biochars. Results of XPS and 13 C NMR demonstrated that the biochar-derived HAL fractions mainly consisted of aromatic clusters substituted by carboxylic groups. The CO 2 cumulative surface area of BDOMs excluding PLAB-derived RES fractions was obviously lower than that of corresponding biochars. The sorption nonlinearity of PHE by the fresh biochars was significantly stronger than that of the BDOM fractions, implying that the BDOM fractions were more chemically homogeneous. The BDOMs generally exhibited comparable or higher OC-normalized distribution coefficients (K oc ) of PHE than the original biochars. The PHE logK oc values of the fresh biochars correlated negatively with the micropore volumes due to steric hindrance effect. In contrast, a positive relationship between the sorption coefficients (K d ) of BDOMs and the micropore volumes was observed in this study, suggesting that pore filling could dominate PHE sorption by the BDOMs. The positive correlation between the PHE logK oc values of the HAL fractions and the aromatic C contents indicates that PHE sorption by the HAL fractions was regulated by aromatic domains. The findings of this study improve our knowledge of the evolution of biochar properties after application and its potential environmental impacts. Copyright © 2018 Elsevier Ltd. All rights reserved.
Fractional model for heat conduction in polar bear hairs
Directory of Open Access Journals (Sweden)
Wang Qing-Li
2012-01-01
Full Text Available Time-fractional differential equations can accurately describe heat conduction in fractal media, such as wool fibers, goose down and polar bear hair. The fractional complex transform is used to convert time-fractional heat conduction equations with the modified Riemann-Liouville derivative into ordinary differential equations, and exact solutions can be easily obtained. The solution process is straightforward and concise.
Directory of Open Access Journals (Sweden)
B. Kuldeep
2015-06-01
Full Text Available Fractional calculus has recently been identified as a very important mathematical tool in the field of signal processing. Digital filters designed by fractional derivatives give more accurate frequency response in the prescribed frequency region. Digital filters are most important part of multi-rate filter bank systems. In this paper, an improved method based on fractional derivative constraints is presented for the design of two-channel quadrature mirror filter (QMF bank. The design problem is formulated as minimization of L2 error of filter bank transfer function in passband, stopband interval and at quadrature frequency, and then Lagrange multiplier method with fractional derivative constraints is applied to solve it. The proposed method is then successfully applied for the design of two-channel QMF bank with higher order filter taps. Performance of the QMF bank design is then examined through study of various parameters such as passband error, stopband error, transition band error, peak reconstruction error (PRE, stopband attenuation (As. It is found that, the good design can be obtained with the change of number and value of fractional derivative constraint coefficients.
International Nuclear Information System (INIS)
Yang Yong-Ge; Xu Wei; Sun Ya-Hui; Gu Xu-Dong
2016-01-01
This paper aims to investigate the stochastic response of the van der Pol (VDP) oscillator with two kinds of fractional derivatives under Gaussian white noise excitation. First, the fractional VDP oscillator is replaced by an equivalent VDP oscillator without fractional derivative terms by using the generalized harmonic balance technique. Then, the stochastic averaging method is applied to the equivalent VDP oscillator to obtain the analytical solution. Finally, the analytical solutions are validated by numerical results from the Monte Carlo simulation of the original fractional VDP oscillator. The numerical results not only demonstrate the accuracy of the proposed approach but also show that the fractional order, the fractional coefficient and the intensity of Gaussian white noise play important roles in the responses of the fractional VDP oscillator. An interesting phenomenon we found is that the effects of the fractional order of two kinds of fractional derivative items on the fractional stochastic systems are totally contrary. (paper)
On a system of differential equations with fractional derivatives arising in rod theory
International Nuclear Information System (INIS)
Atanackovic, Teodor M; Stankovic, Bogoljub
2004-01-01
We study a system of equations with fractional derivatives, that arises in the analysis of the lateral motion of an elastic column fixed at one end and loaded by a concentrated follower force at the other end. We assume that the column is positioned on a viscoelastic foundation described by a constitutive equation of fractional derivative type. The stability boundary is determined. It is shown that as in the case of an elastic (Winkler) type of foundation the stability boundary remains the same as for the column without a foundation! Thus, with the solution analysed here, the column exhibits the so-called Hermann-Smith paradox
Yu, Minda; He, Xiaosong; Liu, Jiaomei; Wang, Yuefeng; Xi, Beidou; Li, Dan; Zhang, Hui; Yang, Chao
2018-04-14
Understanding the heterogeneous evolution characteristics of dissolved organic matter fractions derived from compost is crucial to exploring the composting biodegradation process and the possible applications of compost products. Herein, two-dimensional correlation spectroscopy integrated with reversed-phase high performance liquid chromatography and size exclusion chromatography were utilized to obtain the molecular weight (MW) and polarity evolution characteristics of humic acid (HA), fulvic acid (FA), and the hydrophilic (HyI) fractions during composting. The high-MW humic substances and building blocks in the HA fraction degraded faster during composting than polymers, proteins, and organic colloids. Similarly, the low MW acid FA factions transformed faster than the low weight neutral fractions, followed by building blocks, and finally polymers, proteins, and organic colloids. The evolutions of HyI fractions during composting occurred first for building blocks, followed by low MW acids, and finally low weight neutrals. With the progress of composting, the hydrophobic properties of the HA and FA fractions were enhanced. The degradation/humification process of the hydrophilic and transphilic components was faster than that of the hydrophobic component. Compared with the FA and HyI fractions, the HA fraction exhibited a higher MW and increased hydrophobicity. Copyright © 2018 Elsevier B.V. All rights reserved.
Numerical Solution of Fractional Neutron Point Kinetics Model in Nuclear Reactor
Directory of Open Access Journals (Sweden)
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.
Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative
Directory of Open Access Journals (Sweden)
José Francisco Gómez Aguilar
2014-01-01
Full Text Available An alternative construction for the space-time fractional diffusion-advection equation for the sedimentation phenomena is presented. The order of the derivative is considered as 0<β, γ≤1 for the space and time domain, respectively. The fractional derivative of Caputo type is considered. In the spatial case we obtain the fractional solution for the underdamped, undamped, and overdamped case. In the temporal case we show that the concentration has amplitude which exhibits an algebraic decay at asymptotically large times and also shows numerical simulations where both derivatives are taken in simultaneous form. In order that the equation preserves the physical units of the system two auxiliary parameters σx and σt are introduced characterizing the existence of fractional space and time components, respectively. A physical relation between these parameters is reported and the solutions in space-time are given in terms of the Mittag-Leffler function depending on the parameters β and γ. The generalization of the fractional diffusion-advection equation in space-time exhibits anomalous behavior.
Ali Abro, Kashif; Hussain, Mukkarum; Mahmood Baig, Mirza
2017-10-01
The significance of the different shapes of molybdenum disulfide nanoparticles contained in ethylene glycol has recently attracted researchers, because of the numerical or experimental analyses on the shapes of molybdenum disulfide and the lack of fractionalized analytic approaches. This work is dedicated to examining the shape impacts of molybdenum disulfide nanofluids in the mixed convection flow with magnetic field and a porous medium. Ethylene glycol is chosen as the base fluid in which molybdenum disulfide nanoparticles are suspended. Non-spherically shaped molybdenum disulfide nanoparticles, namely, platelet, blade, cylinder and brick, are utilized in this analysis. The modeling of the problem is characterized by employing the modern approach of Atangana-Baleanu fractional derivatives and the governing partial differential equations are solved via Laplace transforms with inversion. Solutions are obtained for temperature distribution and velocity field and expressed in terms of compact form of M-function, Mba(T) . In the end, a figures are drawn to compare the different non-spherically shaped molybdenum disulfide nanoparticles. Furthermore, the Atangana-Baleanu fractional derivatives model has been compared with ordinary derivatives models and discussed graphically by setting various rheological parameters.
DEFF Research Database (Denmark)
Møller Jensen, Jesper; Erik Bøtker, Hans; Norling Mathiassen, Ole
2017-01-01
Aims: To assess the use of downstream coronary angiography (ICA) and short-term safety of frontline coronary CT angiography (CTA) with selective CT-derived fractional flow reserve (FFRCT) testing in stable patients with typical angina pectoris. Methods and results: Between 1 January 2016 and 30 J...... of safe cancellation of planned ICAs....
Nonlinear analysis and analog simulation of a piezoelectric buckled beam with fractional derivative
Mokem Fokou, I. S.; Buckjohn, C. Nono Dueyou; Siewe Siewe, M.; Tchawoua, C.
2017-08-01
In this article, an analog circuit for implementing fractional-order derivative and a harmonic balance method for a vibration energy harvesting system under pure sinusoidal vibration source is proposed in order to predict the system response. The objective of this paper is to discuss the performance of the system with fractional derivative and nonlinear damping (μb). Bifurcation diagram, phase portrait and power spectral density (PSD) are provided to deeply characterize the dynamics of the system. These results are corroborated by the 0-1 test. The appearance of the chaotic vibrations reduces the instantaneous voltage. The pre-experimental investigation is carried out through appropriate software electronic circuit (Multisim). The corresponding electronic circuit is designed, exhibiting periodic and chaotic behavior, in accord with numerical simulations. The impact of fractional derivative and nonlinear damping is presented with detail on the output voltage and power of the system. The agreement between numerical and analytical results justifies the efficiency of the analytical technique used. In addition, by combining the harmonic excitation with the random force, the stochastic resonance phenomenon occurs and improves the harvested energy. It emerges from these results that the order of fractional derivative μ and nonlinear damping μb play an important role in the response of the system.
A new fractional derivative and its application to explanation of polar bear hairs
Directory of Open Access Journals (Sweden)
Ji-Huan He
2016-04-01
Full Text Available A new fractional derivative is defined through the variational iteration method, and its application in explaining the excellent thermal protection of polar bear hairs is elucidated. The fractal porosity of its inner structure makes a polar bear mathematically adapted for living in a harsh Arctic region.
A new fractional derivative and its application to explanation of polar bear hairs
Ji-Huan He; Zheng-Biao Li; Qing-li Wang
2016-01-01
A new fractional derivative is defined through the variational iteration method, and its application in explaining the excellent thermal protection of polar bear hairs is elucidated. The fractal porosity of its inner structure makes a polar bear mathematically adapted for living in a harsh Arctic region.
Table-sized matrix model in fractional learning
Soebagyo, J.; Wahyudin; Mulyaning, E. C.
2018-05-01
This article provides an explanation of the fractional learning model i.e. a Table-Sized Matrix model in which fractional representation and its operations are symbolized by the matrix. The Table-Sized Matrix are employed to develop problem solving capabilities as well as the area model. The Table-Sized Matrix model referred to in this article is used to develop an understanding of the fractional concept to elementary school students which can then be generalized into procedural fluency (algorithm) in solving the fractional problem and its operation.
The fractional-order modeling and synchronization of electrically coupled neuron systems
Moaddy, K.
2012-11-01
In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grünwald-Letnikov discretization process which is easily implemented and reliably accurate. © 2011 Elsevier Ltd. All rights reserved.
The fractional-order modeling and synchronization of electrically coupled neuron systems
Moaddy, K.; Radwan, Ahmed G.; Salama, Khaled N.; Momani, Shaher M.; Hashim, Ishak
2012-01-01
In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grünwald-Letnikov discretization process which is easily implemented and reliably accurate. © 2011 Elsevier Ltd. All rights reserved.
Fractional diffusion models of transport in magnetically confined plasmas
International Nuclear Information System (INIS)
Castillo-Negrete, D. del; Carreras, B. A.; Lynch, V. E.
2005-01-01
Experimental and theoretical evidence suggests that transport in magnetically confined fusion plasmas deviates from the standard diffusion paradigm. Some examples include the confinement time scaling in L-mode plasmas, rapid pulse propagation phenomena, and inward transport in off-axis fueling experiments. The limitations of the diffusion paradigm can be traced back to the restrictive assumptions in which it is based. In particular, Fick's law, one of the cornerstones of diffusive transport, assumes that the fluxes only depend on local quantities, i. e. the spatial gradient of the field (s). another key issue is the Markovian assumption that neglects memory effects. Also, at a microscopic level, standard diffusion assumes and underlying Gaussian, uncorrelated stochastic process (i. e. a Brownian random walk) with well defined characteristic spatio-temporal scales. Motivated by the need to develop models of non-diffusive transport, we discuss here a class of transport models base on the use of fractional derivative operators. The models incorporates in a unified way non-Fickian transport, non-Markovian processes or memory effects, and non-diffusive scaling. At a microscopic level, the models describe an underlying stochastic process without characteristic spatio-temporal scales that generalizes the Brownian random walk. As a concrete case study to motivate and test the model, we consider transport of tracers in three-dimensional, pressure-gradient-driven turbulence. We show that in this system transport is non-diffusive and cannot be described in the context of the standard diffusion parading. In particular, the probability density function (pdf) of the radial displacements of tracers is strongly non-Gaussian with algebraic decaying tails, and the moments of the tracer displacements exhibit super-diffusive scaling. there is quantitative agreement between the turbulence transport calculations and the proposed fractional diffusion model. In particular, the model
A Stochastic Fractional Dynamics Model of Rainfall Statistics
Kundu, Prasun; Travis, James
2013-04-01
Rainfall varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, that allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is designed to faithfully reflect the scale dependence and is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and times scales. The main restriction is the assumption that the statistics of the precipitation field is spatially homogeneous and isotropic and stationary in time. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and in Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to the second moment statistics of the radar data. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well without any further adjustment. Some data sets containing periods of non-stationary behavior that involves occasional anomalously correlated rain events, present a challenge for the model.
On conservation laws for models in discrete, noncommutative and fractional differential calculus
International Nuclear Information System (INIS)
Klimek, M.
2001-01-01
We present the general method of derivation the explicit form of conserved currents for equations built within the framework of discrete, noncommutative or fractional differential calculus. The procedure applies to linear models with variable coefficients including also nonlinear potential part. As an example an equation on quantum plane, nonlinear Toda lattice model and homogeneous equation of fractional diffusion in 1+1 dimensions are studied
Universal block diagram based modeling and simulation schemes for fractional-order control systems.
Bai, Lu; Xue, Dingyü
2017-05-08
Universal block diagram based schemes are proposed for modeling and simulating the fractional-order control systems in this paper. A fractional operator block in Simulink is designed to evaluate the fractional-order derivative and integral. Based on the block, the fractional-order control systems with zero initial conditions can be modeled conveniently. For modeling the system with nonzero initial conditions, the auxiliary signal is constructed in the compensation scheme. Since the compensation scheme is very complicated, therefore the integrator chain scheme is further proposed to simplify the modeling procedures. The accuracy and effectiveness of the schemes are assessed in the examples, the computation results testify the block diagram scheme is efficient for all Caputo fractional-order ordinary differential equations (FODEs) of any complexity, including the implicit Caputo FODEs. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases
Directory of Open Access Journals (Sweden)
Fazal Haq
2017-01-01
Full Text Available The fractional order Susceptible-Infected-Recovered (SIR epidemic model of childhood disease is considered. Laplace–Adomian Decomposition Method is used to compute an approximate solution of the system of nonlinear fractional differential equations. We obtain the solutions of fractional differential equations in the form of infinite series. The series solution of the proposed model converges rapidly to its exact value. The obtained results are compared with the classical case.
Spiking and bursting patterns of fractional-order Izhikevich model
Teka, Wondimu W.; Upadhyay, Ranjit Kumar; Mondal, Argha
2018-03-01
Bursting and spiking oscillations play major roles in processing and transmitting information in the brain through cortical neurons that respond differently to the same signal. These oscillations display complex dynamics that might be produced by using neuronal models and varying many model parameters. Recent studies have shown that models with fractional order can produce several types of history-dependent neuronal activities without the adjustment of several parameters. We studied the fractional-order Izhikevich model and analyzed different kinds of oscillations that emerge from the fractional dynamics. The model produces a wide range of neuronal spike responses, including regular spiking, fast spiking, intrinsic bursting, mixed mode oscillations, regular bursting and chattering, by adjusting only the fractional order. Both the active and silent phase of the burst increase when the fractional-order model further deviates from the classical model. For smaller fractional order, the model produces memory dependent spiking activity after the pulse signal turned off. This special spiking activity and other properties of the fractional-order model are caused by the memory trace that emerges from the fractional-order dynamics and integrates all the past activities of the neuron. On the network level, the response of the neuronal network shifts from random to scale-free spiking. Our results suggest that the complex dynamics of spiking and bursting can be the result of the long-term dependence and interaction of intracellular and extracellular ionic currents.
Analytical Solution for Fractional Derivative Gas-Flow Equation in Porous Media
El-Amin, Mohamed; Radwan, Ahmed G.; Sun, Shuyu
2017-01-01
In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space.
Directory of Open Access Journals (Sweden)
S. Das
2013-12-01
Full Text Available In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error with the proper choices of parameters are calculated numerically and presented through graphs and tables for different particular cases.
Analytical Solution for Fractional Derivative Gas-Flow Equation in Porous Media
El-Amin, Mohamed
2017-07-06
In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space.
Generalized modeling of the fractional-order memcapacitor and its character analysis
Guo, Zhang; Si, Gangquan; Diao, Lijie; Jia, Lixin; Zhang, Yanbin
2018-06-01
Memcapacitor is a new type of memory device generalized from the memristor. This paper proposes a generalized fractional-order memcapacitor model by introducing the fractional calculus into the model. The generalized formulas are studied and the two fractional-order parameter α, β are introduced where α mostly affects the fractional calculus value of charge q within the generalized Ohm's law and β generalizes the state equation which simulates the physical mechanism of a memcapacitor into the fractional sense. This model will be reduced to the conventional memcapacitor as α = 1 , β = 0 and to the conventional memristor as α = 0 , β = 1 . Then the numerical analysis of the fractional-order memcapacitor is studied. And the characteristics and output behaviors of the fractional-order memcapacitor applied with sinusoidal charge are derived. The analysis results have shown that there are four basic v - q and v - i curve patterns when the fractional order α, β respectively equal to 0 or 1, moreover all v - q and v - i curves of the other fractional-order models are transition curves between the four basic patterns.
A fractional Fokker-Planck model for anomalous diffusion
Energy Technology Data Exchange (ETDEWEB)
Anderson, Johan, E-mail: anderson.johan@gmail.com [Department of Earth and Space Sciences, Chalmers University of Technology, SE-412 96 Göteborg (Sweden); Kim, Eun-jin [Department of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH (United Kingdom); Moradi, Sara [Ecole Polytechnique, CNRS UMR7648, LPP, F-91128 Palaiseau (France)
2014-12-15
In this paper, we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality of the stable Lévy distribution. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy in terms of Tsallis statistical mechanics. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior.
The fractional volatility model: An agent-based interpretation
Vilela Mendes, R.
2008-06-01
Based on the criteria of mathematical simplicity and consistency with empirical market data, a model with volatility driven by fractional noise has been constructed which provides a fairly accurate mathematical parametrization of the data. Here, some features of the model are reviewed and extended to account for leverage effects. Using agent-based models, one tries to find which agent strategies and (or) properties of the financial institutions might be responsible for the features of the fractional volatility model.
Langlands, T A M; Henry, B I; Wearne, S L
2009-12-01
We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by fractional order exponents. Solutions are obtained as functions of the scaling parameters for infinite cables and semi-infinite cables with instantaneous current injections. Voltage attenuation along dendrites in response to alpha function synaptic inputs is computed. Action potential firing rates are also derived based on simple integrate and fire versions of the models. Our results show that electrotonic properties and firing rates of nerve cells are altered by anomalous subdiffusion in these models. We have suggested electrophysiological experiments to calibrate and validate the models.
Gómez-Aguilar, J. F.
2018-03-01
In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.
General solution of the Bagley-Torvik equation with fractional-order derivative
Wang, Z. H.; Wang, X.
2010-05-01
This paper investigates the general solution of the Bagley-Torvik equation with 1/2-order derivative or 3/2-order derivative. This fractional-order differential equation is changed into a sequential fractional-order differential equation (SFDE) with constant coefficients. Then the general solution of the SFDE is expressed as the linear combination of fundamental solutions that are in terms of α-exponential functions, a kind of functions that play the same role of the classical exponential function. Because the number of fundamental solutions of the SFDE is greater than 2, the general solution of the SFDE depends on more than two free (independent) constants. This paper shows that the general solution of the Bagley-Torvik equation involves actually two free constants only, and it can be determined fully by the initial displacement and initial velocity.
Talib, Imran; Belgacem, Fethi Bin Muhammad; Asif, Naseer Ahmad; Khalil, Hammad
2017-01-01
In this research article, we derive and analyze an efficient spectral method based on the operational matrices of three dimensional orthogonal Jacobi polynomials to solve numerically the mixed partial derivatives type multi-terms high dimensions generalized class of fractional order partial differential equations. We transform the considered fractional order problem to an easily solvable algebraic equations with the aid of the operational matrices. Being easily solvable, the associated algebraic system leads to finding the solution of the problem. Some test problems are considered to confirm the accuracy and validity of the proposed numerical method. The convergence of the method is ensured by comparing our Matlab software simulations based obtained results with the exact solutions in the literature, yielding negligible errors. Moreover, comparative results discussed in the literature are extended and improved in this study.
Subharmonic Resonance of Van Der Pol Oscillator with Fractional-Order Derivative
Directory of Open Access Journals (Sweden)
Yongjun Shen
2014-01-01
Full Text Available The subharmonic resonance of van der Pol (VDP oscillator with fractional-order derivative is studied by the averaging method. At first, the first-order approximate solutions are obtained by the averaging method. Then the definitions of equivalent linear damping coefficient (ELDC and equivalent linear stiffness coefficient (ELSC for subharmonic resonance are established, and the effects of the fractional-order parameters on the ELDC, the ELSC, and the dynamical characteristics of system are also analysed. Moreover, the amplitude-frequency equation and phase-frequency equation of steady-state solution for subharmonic resonance are established. The corresponding stability condition is presented based on Lyapunov theory, and the existence condition for subharmonic resonance (ECSR is also obtained. At last, the comparisons of the fractional-order and the traditional integer-order VDP oscillator are fulfilled by the numerical simulation. The effects of the parameters in fractional-order derivative on the steady-state amplitude, the amplitude-frequency curves, and the system stability are also studied.
International Nuclear Information System (INIS)
Zhang Ran-Ran; Xu Wei; Yang Gui-Dong; Han Qun
2015-01-01
In this paper, we consider the response analysis of a Duffing–Rayleigh system with fractional derivative under Gaussian white noise excitation. A stochastic averaging procedure for this system is developed by using the generalized harmonic functions. First, the system state is approximated by a diffusive Markov process. Then, the stationary probability densities are derived from the averaged Itô stochastic differential equation of the system. The accuracy of the analytical results is validated by the results from the Monte Carlo simulation of the original system. Moreover, the effects of different system parameters and noise intensity on the response of the system are also discussed. (paper)
Pirnapasov, Sardor; Karimov, Erkinjon
2017-01-01
In the present work we discuss higher order multi-term partial differential equation (PDE) with the Caputo-Fabrizio fractional derivative in time. We investigate a boundary value problem for fractional heat equation involving higher order Caputo-Fabrizio derivatives in time-variable. Using method of separation of variables and integration by parts, we reduce fractional order PDE to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.
A void fraction model for annular two-phase flow
Energy Technology Data Exchange (ETDEWEB)
Tandon, T.N.; Gupta, C.P.; Varma, H.K.
1985-01-01
An analytical model has been developed for predicting void fraction in two-phase annular flow. In the analysis, the Lockhart-Martinelli method has been used to calculate two-phase frictional pressure drop and von Karman's universal velocity profile is used to represent the velocity distribution in the annular liquid film. Void fractions predicted by the proposed model are generally in good agreement with a available experimental data. This model appears to be as good as Smith's correlation and better than the Wallis and Zivi correlations for computing void fraction.
A variable-order fractal derivative model for anomalous diffusion
Directory of Open Access Journals (Sweden)
Liu Xiaoting
2017-01-01
Full Text Available This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the above mentioned anomalous diffusion (or transport processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior and heavy tail phenomena of the new model and variable-order fractional derivative model are also offered.
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.
Directory of Open Access Journals (Sweden)
Pirson Chris
2012-06-01
Full Text Available Abstract Mycobacterial lipids have long been known to modulate the function of a variety of cells of the innate immune system. Here, we report the extraction and characterisation of polar and apolar free lipids from Mycobacterium bovis AF 2122/97 and identify the major lipids present in these fractions. Lipids found included trehalose dimycolate (TDM and trehalose monomycolate (TMM, the apolar phthiocerol dimycocersates (PDIMs, triacyl glycerol (TAG, pentacyl trehalose (PAT, phenolic glycolipid (PGL, and mono-mycolyl glycerol (MMG. Polar lipids identified included glucose monomycolate (GMM, diphosphatidyl glycerol (DPG, phenylethanolamine (PE and a range of mono- and di-acylated phosphatidyl inositol mannosides (PIMs. These lipid fractions are capable of altering the cytokine profile produced by fresh and cultured bovine monocytes as well as monocyte derived dendritic cells. Significant increases in the production of IL-10, IL-12, MIP-1β, TNFα and IL-6 were seen after exposure of antigen presenting cells to the polar lipid fraction. Phenotypic characterisation of the cells was performed by flow cytometry and significant decreases in the expression of MHCII, CD86 and CD1b were found after exposure to the polar lipid fraction. Polar lipids also significantly increased the levels of CD40 expressed by monocytes and cultured monocytes but no effect was seen on the constitutively high expression of CD40 on MDDC or on the levels of CD80 expressed by any of the cells. Finally, the capacity of polar fraction treated cells to stimulate alloreactive lymphocytes was assessed. Significant reduction in proliferative activity was seen after stimulation of PBMC by polar fraction treated cultured monocytes whilst no effect was seen after lipid treatment of MDDC. These data demonstrate that pathogenic mycobacterial polar lipids may significantly hamper the ability of the host APCs to induce an appropriate immune response to an invading pathogen.
Directory of Open Access Journals (Sweden)
Yunfeng Jiang
2016-07-01
Full Text Available A fractional derivative system identification approach for modeling battery dynamics is presented in this paper, where fractional derivatives are applied to approximate non-linear dynamic behavior of a battery system. The least squares-based state-variable filter (LSSVF method commonly used in the identification of continuous-time models is extended to allow the estimation of fractional derivative coefficents and parameters of the battery models by monitoring a charge/discharge demand signal and a power storage/delivery signal. In particular, the model is combined by individual fractional differential models (FDMs, where the parameters can be estimated by a least-squares algorithm. Based on experimental data, it is illustrated how the fractional derivative model can be utilized to predict the dynamics of the energy storage and delivery of a lithium iron phosphate battery (LiFePO 4 in real-time. The results indicate that a FDM can accurately capture the dynamics of the energy storage and delivery of the battery over a large operating range of the battery. It is also shown that the fractional derivative model exhibits improvements on prediction performance compared to standard integer derivative model, which in beneficial for a battery management system.
International Nuclear Information System (INIS)
Chvetsov, A; Schwartz, J; Mayr, N; Yartsev, S
2014-01-01
Purpose: To show that a distribution of cell surviving fractions S 2 in a heterogeneous group of patients can be derived from tumor-volume variation curves during radiotherapy for non-small cell lung cancer. Methods: Our analysis was based on two data sets of tumor-volume variation curves for heterogeneous groups of 17 patients treated for nonsmall cell lung cancer with conventional dose fractionation. The data sets were obtained previously at two independent institutions by using megavoltage (MV) computed tomography (CT). Statistical distributions of cell surviving fractions S 2 and cell clearance half-lives of lethally damaged cells T1/2 have been reconstructed in each patient group by using a version of the two-level cell population tumor response model and a simulated annealing algorithm. The reconstructed statistical distributions of the cell surviving fractions have been compared to the distributions measured using predictive assays in vitro. Results: Non-small cell lung cancer presents certain difficulties for modeling surviving fractions using tumor-volume variation curves because of relatively large fractional hypoxic volume, low gradient of tumor-volume response, and possible uncertainties due to breathing motion. Despite these difficulties, cell surviving fractions S 2 for non-small cell lung cancer derived from tumor-volume variation measured at different institutions have similar probability density functions (PDFs) with mean values of 0.30 and 0.43 and standard deviations of 0.13 and 0.18, respectively. The PDFs for cell surviving fractions S 2 reconstructed from tumor volume variation agree with the PDF measured in vitro. Comparison of the reconstructed cell surviving fractions with patient survival data shows that the patient survival time decreases as the cell surviving fraction increases. Conclusion: The data obtained in this work suggests that the cell surviving fractions S 2 can be reconstructed from the tumor volume variation curves measured
Tempered fractional time series model for turbulence in geophysical flows
Meerschaert, Mark M.; Sabzikar, Farzad; Phanikumar, Mantha S.; Zeleke, Aklilu
2014-09-01
We propose a new time series model for velocity data in turbulent flows. The new model employs tempered fractional calculus to extend the classical 5/3 spectral model of Kolmogorov. Application to wind speed and water velocity in a large lake are presented, to demonstrate the practical utility of the model.
Tempered fractional time series model for turbulence in geophysical flows
International Nuclear Information System (INIS)
Meerschaert, Mark M; Sabzikar, Farzad; Phanikumar, Mantha S; Zeleke, Aklilu
2014-01-01
We propose a new time series model for velocity data in turbulent flows. The new model employs tempered fractional calculus to extend the classical 5/3 spectral model of Kolmogorov. Application to wind speed and water velocity in a large lake are presented, to demonstrate the practical utility of the model. (paper)
Seng, G. T.; Otterson, D. A.
1983-01-01
Two high performance liquid chromatographic (HPLC) methods have been developed for the determination of saturates, olefins and aromatics in petroleum and shale derived mid-distillate fuels. In one method the fuel to be analyzed is reacted with sulfuric acid, to remove a substantial portion of the aromatics, which provides a reacted fuel fraction for use in group type quantitation. The second involves the removal of a substantial portion of the saturates fraction from the HPLC system to permit the determination of olefin concentrations as low as 0.3 volume percent, and to improve the accuracy and precision of olefins determinations. Each method was evaluated using model compound mixtures and real fuel samples.
Application of Integer and Fractional Models in Electrochemical Systems
Directory of Open Access Journals (Sweden)
Isabel S. Jesus
2012-01-01
Full Text Available This paper describes the use of integer and fractional electrical elements, for modelling two electrochemical systems. A first type of system consists of botanical elements and a second type is implemented by electrolyte processes with fractal electrodes. Experimental results are analyzed in the frequency domain, and the pros and cons of adopting fractional-order electrical components for modelling these systems are compared.
Directory of Open Access Journals (Sweden)
Ahmet Bekir
2014-09-01
Full Text Available In this paper, the fractional partial differential equations are defined by modified Riemann–Liouville fractional derivative. With the help of fractional derivative and traveling wave transformation, these equations can be converted into the nonlinear nonfractional ordinary differential equations. Then G′G-expansion method is applied to obtain exact solutions of the space-time fractional Burgers equation, the space-time fractional KdV-Burgers equation and the space-time fractional coupled Burgers’ equations. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. These results reveal that the proposed method is very effective and simple in performing a solution to the fractional partial differential equation.
Fractional dynamical model for neurovascular coupling
Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem
2014-01-01
The neurovascular coupling is a key mechanism linking the neural activity to the hemodynamic behavior. Modeling of this coupling is very important to understand the brain function but it is at the same time very complex due to the complexity
SU-E-T-70: A Radiobiological Model of Reoxygenation and Fractionation Effects
Energy Technology Data Exchange (ETDEWEB)
Guerrero, M [University of Maryland School of Medicine, Baltimore, MD (United States); Carlson, DJ [Yale Univ. School of Medicine, New Haven, CT (United States)
2015-06-15
Purpose: To develop a simple reoxygenation model that fulfills the following goals:1-Quantify the reoxygenation effect in biologically effective dose (BED) and compare it to the repopulation effect.2-Model the hypoxic fraction in tumors as a function of the number of fractions.3-Develop a simple analytical expression for a reoxygenation term in BED calculations. Methods: The model considers tumor cells in two compartments: one normoxic population of cells and one hypoxic compartment including cells under a range of reduced oxygen concentrations. The surviving fraction is predicted using the linear-quadratic (LQ) model. A hypoxia reduction factor (HRF) is used to quantify reductions in radiosensitivity parameters α-A and β-A as cellular oxygen concentration decreases. The HRF is defined as the ratio of the dose at a specific level of hypoxia to the dose under fully aerobic conditions to achieve equal cell killing. The model assumes that a fraction of the hypoxic cells ( ) moves from the hypoxic to the aerobic compartment after each daily fraction. As an example, we consider standard fractionation for NSCLC (d=2Gy,n=33) versus a SBRT (n=5, d=10Gy) fractionation and compare the loss in reoxygenation biological effect with the gain in repopulation biological effect. Results: An analytic expression for the surviving fraction after n daily treatments is derived and the reoxygenation term in the biological effect is calculated. Reoxygenation and repopulation effects are the same order of magnitude for potential doubling time Td values of 2 to 5 days. The hypoxic fraction increases or decreases with n depending on the reoxygenation rate Δ. For certain combinations of parameters, the biological effect of reoxygenation goes as -(n-1)*ln(1-Δ) providing a simple expression that can be introduced in BED calculations. Conclusion: A novel radiobiological model was developed that can be used to evaluate the effect of reoxygenation in fractionated radiotherapy.
International Nuclear Information System (INIS)
Dale, R.G.
1986-01-01
By extending a previously developed mathematical model based on the linear-quadratic dose-effect relationship, it is possible to examine the consequences of performing fractionated treatments for which there is insufficient time between fractions to allow complete damage repair. Equations are derived which give the relative effectiveness of such treatments in terms of tissue-repair constants (μ values) and α/β ratios, and these are then applied to some examples of treatments involving multiple fractions per day. The interplay of the various mechanisms involved (including repopulation effects) and their possible influence on treatments involving closely spaced fractions are examined. If current indications of the differences in recovery rates between early- and late-reacting normal tissues are representative, then it is shown that such differences may limit the clinical potential of accelerated fractionation regimes, where several fractions per day are given in a relatively short overall time. (author)
Macías-Díaz, J. E.
2017-12-01
In this manuscript, we consider an initial-boundary-value problem governed by a (1 + 1)-dimensional hyperbolic partial differential equation with constant damping that generalizes many nonlinear wave equations from mathematical physics. The model considers the presence of a spatial Laplacian of fractional order which is defined in terms of Riesz fractional derivatives, as well as the inclusion of a generic continuously differentiable potential. It is known that the undamped regime has an associated positive energy functional, and we show here that it is preserved throughout time under suitable boundary conditions. To approximate the solutions of this model, we propose a finite-difference discretization based on fractional centered differences. Some discrete quantities are proposed in this work to estimate the energy functional, and we show that the numerical method is capable of conserving the discrete energy under the same boundary conditions for which the continuous model is conservative. Moreover, we establish suitable computational constraints under which the discrete energy of the system is positive. The method is consistent of second order, and is both stable and convergent. The numerical simulations shown here illustrate the most important features of our numerical methodology.
Asymptotic integration of some nonlinear differential equations with fractional time derivative
International Nuclear Information System (INIS)
Baleanu, Dumitru; Agarwal, Ravi P; Mustafa, Octavian G; Cosulschi, Mirel
2011-01-01
We establish that, under some simple integral conditions regarding the nonlinearity, the (1 + α)-order fractional differential equation 0 D α t (x') + f(t, x) = 0, t > 0, has a solution x element of C([0,+∞),R) intersection C 1 ((0,+∞),R), with lim t→0 [t 1-α x'(t)] element of R, which can be expanded asymptotically as a + bt α + O(t α-1 ) when t → +∞ for given real numbers a, b. Our arguments are based on fixed point theory. Here, 0 D α t designates the Riemann-Liouville derivative of order α in (0, 1).
On an Estimation Method for an Alternative Fractionally Cointegrated Model
DEFF Research Database (Denmark)
Carlini, Federico; Łasak, Katarzyna
In this paper we consider the Fractional Vector Error Correction model proposed in Avarucci (2007), which is characterized by a richer lag structure than models proposed in Granger (1986) and Johansen (2008, 2009). We discuss the identification issues of the model of Avarucci (2007), following th...
Yang, Yongge; Xu, Wei; Yang, Guidong; Jia, Wantao
2016-08-01
The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.
International Nuclear Information System (INIS)
Yang, Yongge; Xu, Wei; Yang, Guidong; Jia, Wantao
2016-01-01
The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.
Energy Technology Data Exchange (ETDEWEB)
Yang, Yongge; Xu, Wei, E-mail: weixu@nwpu.edu.cn; Yang, Guidong; Jia, Wantao [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2016-08-15
The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.
Abro, Kashif Ali; Memon, Anwar Ahmed; Uqaili, Muhammad Aslam
2018-03-01
This research article is analyzed for the comparative study of RL and RC electrical circuits by employing newly presented Atangana-Baleanu and Caputo-Fabrizio fractional derivatives. The governing ordinary differential equations of RL and RC electrical circuits have been fractionalized in terms of fractional operators in the range of 0 ≤ ξ ≤ 1 and 0 ≤ η ≤ 1. The analytic solutions of fractional differential equations for RL and RC electrical circuits have been solved by using the Laplace transform with its inversions. General solutions have been investigated for periodic and exponential sources by implementing the Atangana-Baleanu and Caputo-Fabrizio fractional operators separately. The investigated solutions have been expressed in terms of simple elementary functions with convolution product. On the basis of newly fractional derivatives with and without singular kernel, the voltage and current have interesting behavior with several similarities and differences for the periodic and exponential sources.
An in vitro lung model to assess true shunt fraction by multiple inert gas elimination.
Directory of Open Access Journals (Sweden)
Balamurugan Varadarajan
Full Text Available The Multiple Inert Gas Elimination Technique, based on Micropore Membrane Inlet Mass Spectrometry, (MMIMS-MIGET has been designed as a rapid and direct method to assess the full range of ventilation-to-perfusion (V/Q ratios. MMIMS-MIGET distributions have not been assessed in an experimental setup with predefined V/Q-distributions. We aimed (I to construct a novel in vitro lung model (IVLM for the simulation of predefined V/Q distributions with five gas exchange compartments and (II to correlate shunt fractions derived from MMIMS-MIGET with preset reference shunt values of the IVLM. Five hollow-fiber membrane oxygenators switched in parallel within a closed extracorporeal oxygenation circuit were ventilated with sweep gas (V and perfused with human red cell suspension or saline (Q. Inert gas solution was infused into the perfusion circuit of the gas exchange assembly. Sweep gas flow (V was kept constant and reference shunt fractions (IVLM-S were established by bypassing one or more oxygenators with perfusate flow (Q. The derived shunt fractions (MM-S were determined using MIGET by MMIMS from the retention data. Shunt derived by MMIMS-MIGET correlated well with preset reference shunt fractions. The in vitro lung model is a convenient system for the setup of predefined true shunt fractions in validation of MMIMS-MIGET.
International Nuclear Information System (INIS)
Sperotto, Fabiola Aiub; Segatto, Cynthia Feijo; Zabadal, Jorge
2002-01-01
In this work, we determine the dominant eigenvalue of the one-dimensional neutron transport equation in a slab constructing an integral form for the neutron transport equation which is the expressed in terms of fractional derivative of the angular flux. Equating the fractional derivative of the angular flux to the integrate equation, we determine the unknown order of the fractional derivative comparing the kernel of the integral equation with the one of Riemann-Liouville definition of fractional derivative. Once known the angular flux the dominant eigenvalue is calculated solving a transcendental equation resulting from the application of the boundary conditions. We report the methodology applied, for comparison with available results in literature. (author)
Kim, Myong-Ha; Ri, Guk-Chol; O, Hyong-Chol
2013-01-01
This paper provides the existence and representation of solution to an initial value problem for the general multi-term linear fractional differential equation with generalized Riemann-Liouville fractional derivatives and constant coefficients by using operational calculus of Mikusinski's type. We prove that the initial value problem has the solution of if and only if some initial values should be zero.
Li, Zhiyuan; Yamamoto, Masahiro
2014-01-01
This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace transform, we reduce the uniqueness for our inverse problems to the uniqueness of expansions of some special function and complete the proof.
Hansen, Christian T.; Meixner, Anette; Kasemann, Simone A.; Bach, Wolfgang
2017-11-01
Multiple batch experiments (100 °C, 200 °C; 40 MPa) were conducted, using Dickson-type reactors, to investigate Li and B partitioning and isotope fractionation between rock and water during serpentinization. We reacted fresh olivine (5 g; Fo90; [B] = anti-correlated with temperature, we argue for an overall attenuation of the isotopic effect through changes in B speciation in saline solutions (NaB(OH)4(aq) and B(OH)3Cl-) as well as variable B fixation and fractionation for different serpentinization product minerals (brucite, chrysotile). Breakdown of the Li-rich olivine and limited Li incorporation into product mineral phases resulted in an overall lower Li content of the final solid phase assemblage at 200 °C ([Li]final_200 °C = 0.77 μg/g; DS/FLi200 °C = 1.58). First order changes in Li isotopic compositions were defined by mixing of two isotopically distinct sources i.e. the fresh olivine and the fluid rather than by equilibrium isotope fraction. At 200 °C primary olivine is dissolved, releasing its Li budget into the fluid which shifts towards a lower δ7LiF of +38.62‰. Newly formed serpentine minerals (δ7LiS = +30.58‰) incorporate fluid derived Li with a minor preference of the 6Li isotope. At 100 °C Li enrichment of secondary phases exceeded Li release by olivine breakdown ([Li]final_100 °C = 2.10 μg/g; DS/FLi100 °C = 11.3) and it was accompanied by preferential incorporation of heavier 7Li isotope that might be due to incorporation of a 7Li enriched fluid fraction into chrysotile nanotubes.
Energy Technology Data Exchange (ETDEWEB)
Ali, Farhad, E-mail: farhadaliecomaths@yahoo.com [Department of Mathematics, City University of Science and Information Technology, Peshawar 25000 (Pakistan); Sheikh, Nadeem Ahmad [Department of Mathematics, City University of Science and Information Technology, Peshawar 25000 (Pakistan); Khan, Ilyas [Basic Engineering Sciences Department, College of Engineering Majmaah University, Majmaah 11952 (Saudi Arabia); Saqib, Muhammad [Department of Mathematics, City University of Science and Information Technology, Peshawar 25000 (Pakistan)
2017-02-01
The effects of magnetohydrodynamics on the blood flow when blood is represented as a Casson fluid, along with magnetic particles in a horizontal cylinder is studied. The flow is due to an oscillating pressure gradient. The Laplace and finite Hankel transforms are used to obtain the closed form solutions of the fractional partial differential equations. Effects of various parameters on the flow of both blood and magnetic particles are shown graphically. The analysis shows that, the model with fractional order derivatives bring a remarkable changes as compared to the ordinary model. The study highlights that applied magnetic field reduces the velocities of both the blood and magnetic particles.
International Nuclear Information System (INIS)
Ali, Farhad; Sheikh, Nadeem Ahmad; Khan, Ilyas; Saqib, Muhammad
2017-01-01
The effects of magnetohydrodynamics on the blood flow when blood is represented as a Casson fluid, along with magnetic particles in a horizontal cylinder is studied. The flow is due to an oscillating pressure gradient. The Laplace and finite Hankel transforms are used to obtain the closed form solutions of the fractional partial differential equations. Effects of various parameters on the flow of both blood and magnetic particles are shown graphically. The analysis shows that, the model with fractional order derivatives bring a remarkable changes as compared to the ordinary model. The study highlights that applied magnetic field reduces the velocities of both the blood and magnetic particles.
The role of initial values in nonstationary fractional time series models
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
We consider the nonstationary fractional model $\\Delta^{d}X_{t}=\\varepsilon _{t}$ with $\\varepsilon_{t}$ i.i.d.$(0,\\sigma^{2})$ and $d>1/2$. We derive an analytical expression for the main term of the asymptotic bias of the maximum likelihood estimator of $d$ conditional on initial values, and we...... discuss the role of the initial values for the bias. The results are partially extended to other fractional models, and three different applications of the theoretical results are given....
An approximate fractional Gaussian noise model with computational cost
Sø rbye, Sigrunn H.; Myrvoll-Nilsen, Eirik; Rue, Haavard
2017-01-01
Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood
Directory of Open Access Journals (Sweden)
Bashir Ahmad
2013-02-01
Full Text Available In this article, we discuss the existence of solutions for a boundary-value problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented.
Kumar, Dinesh; Rai, K N
2017-07-01
In this paper, we investigated the thermal behavior in living biological tissues using time fractional dual-phase-lag bioheat transfer (DPLBHT) model subjected to Dirichelt boundary condition in presence of metabolic and electromagnetic heat sources during thermal therapy. We solved this bioheat transfer model using finite element Legendre wavelet Galerkin method (FELWGM) with help of block pulse function in sense of Caputo fractional order derivative. We compared the obtained results from FELWGM and exact method in a specific case, and found a high accuracy. Results are interpreted in the form of standard and anomalous cases for taking different order of time fractional DPLBHT model. The time to achieve hyperthermia position is discussed in both cases as standard and time fractional order derivative. The success of thermal therapy in the treatment of metastatic cancerous cell depends on time fractional order derivative to precise prediction and control of temperature. The effect of variability of parameters such as time fractional derivative, lagging times, blood perfusion coefficient, metabolic heat source and transmitted power on dimensionless temperature distribution in skin tissue is discussed in detail. The physiological parameters has been estimated, corresponding to the value of fractional order derivative for hyperthermia treatment therapy. Copyright © 2017 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
M.B. Riaz
2016-12-01
Full Text Available The aim of this article was to analyze the rotational flow of an Oldroyd-B fluid with fractional derivatives, induced by an infinite circular cylinder that applies a constant couple to the fluid. Such kind of problem in the settings of fractional derivatives has not been found in the literature. The solutions are based on an important remark regarding the governing equation for the non-trivial shear stress. The solutions that have been obtained satisfy all imposed initial and boundary conditions and can easily be reduced to the similar solutions corresponding to ordinary Oldroyd-B, fractional/ordinary Maxwell, fractional/ordinary second-grade, and Newtonian fluids performing the same motion. The obtained results are expressed in terms of Newtonian and non-Newtonian contributions. Finally, the influence of fractional parameters on the velocity, shear stress and a comparison between generalized and ordinary fluids is graphically underlined.
Model for radial gas fraction profiles in vertical pipe flow
International Nuclear Information System (INIS)
Lucas, D.; Krepper, E.; Prasser, H.M.
2001-01-01
A one-dimensional model is presented, which predicts the radial volume fraction profiles from a given bubble size distribution. It bases on the assumption of an equilibrium of the forces acting on a bubble perpendicularly to the flow path (non drag forces). For the prediction of the flow pattern this model could be used within an procedure together with appropriate models for local bubble coalescence and break-up. (orig.)
Likelihood inference for a fractionally cointegrated vector autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Ørregård Nielsen, Morten
2012-01-01
such that the process X_{t} is fractional of order d and cofractional of order d-b; that is, there exist vectors ß for which ß'X_{t} is fractional of order d-b, and no other fractionality order is possible. We define the statistical model by 0inference when the true values satisfy b0¿1/2 and d0-b0......We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model with a restricted constant term, ¿, based on the Gaussian likelihood conditional on initial values. The model nests the I(d) VAR model. We give conditions on the parameters...... process in the parameters when errors are i.i.d. with suitable moment conditions and initial values are bounded. When the limit is deterministic this implies uniform convergence in probability of the conditional likelihood function. If the true value b0>1/2, we prove that the limit distribution of (ß...
Directory of Open Access Journals (Sweden)
Duan Jun-Sheng
2017-12-01
Full Text Available We conduct a detailed study and comparison for the one-degree-of-freedom steady-state vibrations under harmonic driving with a single fractional-order derivative and a distributed-order derivative. For each of the two vibration systems, we consider the stiffness contribution factor and damping contribution factor of the term of fractional derivatives, the amplitude and the phase difference for the response. The effects of driving frequency on these response quantities are discussed. Also the influences of the order α of the fractional derivative and the parameter γ parameterizing the weight function in the distributed-order derivative are analyzed. Two cases display similar response behaviors, but the stiffness contribution factor and damping contribution factor of the distributed-order derivative are almost monotonic change with the parameter γ, not exactly like the case of single fractional-order derivative for the order α. The case of the distributed-order derivative provides us more options for the weight function and parameters.
Fractional calculus phenomenology in two-dimensional plasma models
Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill
2006-10-01
Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).
Statistical properties of several models of fractional random point processes
Bendjaballah, C.
2011-08-01
Statistical properties of several models of fractional random point processes have been analyzed from the counting and time interval statistics points of view. Based on the criterion of the reduced variance, it is seen that such processes exhibit nonclassical properties. The conditions for these processes to be treated as conditional Poisson processes are examined. Numerical simulations illustrate part of the theoretical calculations.
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
S. Peiris (Shelton); M. Asai (Manabu); M.J. McAleer (Michael)
2016-01-01
textabstractIn recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility
López-Sánchez, Erick J.; Romero, Juan M.; Yépez-Martínez, Huitzilin
2017-09-01
Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.
Leaky-box approximation to the fractional diffusion model
International Nuclear Information System (INIS)
Uchaikin, V V; Sibatov, R T; Saenko, V V
2013-01-01
Two models based on fractional differential equations for galactic cosmic ray diffusion are applied to the leaky-box approximation. One of them (Lagutin-Uchaikin, 2000) assumes a finite mean free path of cosmic ray particles, another one (Lagutin-Tyumentsev, 2004) uses distribution with infinite mean distance between collision with magnetic clouds, when the trajectories have form close to ballistic. Calculations demonstrate that involving boundary conditions is incompatible with spatial distributions given by the second model.
Determination of bone mineral volume fraction using impedance analysis and Bruggeman model
Energy Technology Data Exchange (ETDEWEB)
Ciuchi, Ioana Veronica; Olariu, Cristina Stefania, E-mail: oocristina@yahoo.com; Mitoseriu, Liliana, E-mail: lmtsr@uaic.ro
2013-11-20
Highlights: • Mineral volume fraction of a bone sample was determined. • Dielectric properties for bone sample and for the collagen type I were determined by impedance spectroscopy. • Bruggeman effective medium approximation was applied in order to evaluate mineral volume fraction of the sample. • The computed values were compared with ones derived from a histogram test performed on SEM micrographs. -- Abstract: Measurements by impedance spectroscopy and Bruggeman effective medium approximation model were employed in order to determine the mineral volume fraction of dry bone. This approach assumes that two or more phases are present into the composite: the matrix (environment) and the other ones are inclusion phases. A fragment of femur diaphysis dense bone from a young pig was investigated in its dehydrated state. Measuring the dielectric properties of bone and its main components (hydroxyapatite and collagen) and using the Bruggeman approach, the mineral volume filling factor was determined. The computed volume fraction of the mineral volume fraction was confirmed by a histogram test analysis based on the SEM microstructures. In spite of its simplicity, the method provides a good approximation for the bone mineral volume fraction. The method which uses impedance spectroscopy and EMA modeling can be further developed by considering the conductive components of the bone tissue as a non-invasive in situ impedance technique for bone composition evaluation and monitoring.
Determination of bone mineral volume fraction using impedance analysis and Bruggeman model
International Nuclear Information System (INIS)
Ciuchi, Ioana Veronica; Olariu, Cristina Stefania; Mitoseriu, Liliana
2013-01-01
Highlights: • Mineral volume fraction of a bone sample was determined. • Dielectric properties for bone sample and for the collagen type I were determined by impedance spectroscopy. • Bruggeman effective medium approximation was applied in order to evaluate mineral volume fraction of the sample. • The computed values were compared with ones derived from a histogram test performed on SEM micrographs. -- Abstract: Measurements by impedance spectroscopy and Bruggeman effective medium approximation model were employed in order to determine the mineral volume fraction of dry bone. This approach assumes that two or more phases are present into the composite: the matrix (environment) and the other ones are inclusion phases. A fragment of femur diaphysis dense bone from a young pig was investigated in its dehydrated state. Measuring the dielectric properties of bone and its main components (hydroxyapatite and collagen) and using the Bruggeman approach, the mineral volume filling factor was determined. The computed volume fraction of the mineral volume fraction was confirmed by a histogram test analysis based on the SEM microstructures. In spite of its simplicity, the method provides a good approximation for the bone mineral volume fraction. The method which uses impedance spectroscopy and EMA modeling can be further developed by considering the conductive components of the bone tissue as a non-invasive in situ impedance technique for bone composition evaluation and monitoring
Fractional Poisson-Nernst-Planck Model for Ion Channels I: Basic Formulations and Algorithms.
Chen, Duan
2017-11-01
In this work, we propose a fractional Poisson-Nernst-Planck model to describe ion permeation in gated ion channels. Due to the intrinsic conformational changes, crowdedness in narrow channel pores, binding and trapping introduced by functioning units of channel proteins, ionic transport in the channel exhibits a power-law-like anomalous diffusion dynamics. We start from continuous-time random walk model for a single ion and use a long-tailed density distribution function for the particle jump waiting time, to derive the fractional Fokker-Planck equation. Then, it is generalized to the macroscopic fractional Poisson-Nernst-Planck model for ionic concentrations. Necessary computational algorithms are designed to implement numerical simulations for the proposed model, and the dynamics of gating current is investigated. Numerical simulations show that the fractional PNP model provides a more qualitatively reasonable match to the profile of gating currents from experimental observations. Meanwhile, the proposed model motivates new challenges in terms of mathematical modeling and computations.
Tesche, Christian; Vliegenthart, Rozemarijn; Duguay, Taylor M; De Cecco, Carlo N; Albrecht, Moritz H; De Santis, Domenico; Langenbach, Marcel C; Varga-Szemes, Akos; Jacobs, Brian E; Jochheim, David; Baquet, Moritz; Bayer, Richard R; Litwin, Sheldon E; Hoffmann, Ellen; Steinberg, Daniel H; Schoepf, U Joseph
2017-12-15
This study investigated the performance of coronary computed tomography angiography (cCTA) with cCTA-derived fractional flow reserve (CT-FFR) compared with invasive coronary angiography (ICA) with fractional flow reserve (FFR) for therapeutic decision making in patients with suspected coronary artery disease (CAD). Seventy-four patients (62 ± 11 years, 62% men) with at least 1 coronary stenosis of ≥50% on clinically indicated dual-source cCTA, who had subsequently undergone ICA with FFR measurement, were retrospectively evaluated. CT-FFR values were computed using an on-site machine-learning algorithm to assess the functional significance of CAD. The therapeutic strategy (optimal medical therapy alone vs revascularization) and the appropriate revascularization procedure (percutaneous coronary intervention vs coronary artery bypass grafting) were selected using cCTA-CT-FFR. Thirty-six patients (49%) had a functionally significant CAD based on ICA-FFR. cCTA-CT-FFR correctly identified a functionally significant CAD and the need of revascularization in 35 of 36 patients (97%). When revascularization was deemed indicated, the same revascularization procedure (32 percutaneous coronary interventions and 3 coronary artery bypass grafting) was chosen in 35 of 35 patients (100%). Overall, identical management strategies were selected in 73 of the 74 patients (99%). cCTA-CT-FFR shows excellent performance to identify patients with and without the need for revascularization and to select the appropriate revascularization strategy. cCTA-CT-FFR as a noninvasive "one-stop shop" has the potential to change diagnostic workflows and to directly inform therapeutic decision making in patients with suspected CAD. Copyright © 2017 Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
Ya-Juan Hao
2013-01-01
Full Text Available The main object of this paper is to investigate the Helmholtz and diffusion equations on the Cantor sets involving local fractional derivative operators. The Cantor-type cylindrical-coordinate method is applied to handle the corresponding local fractional differential equations. Two illustrative examples for the Helmholtz and diffusion equations on the Cantor sets are shown by making use of the Cantorian and Cantor-type cylindrical coordinates.
Analysis of two colliding fractionally damped spherical shells in modelling blunt human head impacts
Rossikhin, Yury A.; Shitikova, Marina V.
2013-06-01
The collision of two elastic or viscoelastic spherical shells is investigated as a model for the dynamic response of a human head impacted by another head or by some spherical object. Determination of the impact force that is actually being transmitted to bone will require the model for the shock interaction of the impactor and human head. This model is indended to be used in simulating crash scenarios in frontal impacts, and provide an effective tool to estimate the severity of effect on the human head and to estimate brain injury risks. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. It is assumed that the viscoelastic features of the shells are exhibited only in the contact domain, while the remaining parts retain their elastic properties. In this case, the contact spot is assumed to be a plane disk with constant radius, and the viscoelastic features of the shells are described by the fractional derivative standard linear solid model. In the case under consideration, the governing differential equations are solved analytically by the Laplace transform technique. It is shown that the fractional parameter of the fractional derivative model plays very important role, since its variation allows one to take into account the age-related changes in the mechanical properties of bone.
Liu, Zhengguang; Li, Xiaoli
2018-05-01
In this article, we present a new second-order finite difference discrete scheme for a fractal mobile/immobile transport model based on equivalent transformative Caputo formulation. The new transformative formulation takes the singular kernel away to make the integral calculation more efficient. Furthermore, this definition is also effective where α is a positive integer. Besides, the T-Caputo derivative also helps us to increase the convergence rate of the discretization of the α-order(0 < α < 1) Caputo derivative from O(τ2-α) to O(τ3-α), where τ is the time step. For numerical analysis, a Crank-Nicolson finite difference scheme to solve the fractal mobile/immobile transport model is introduced and analyzed. The unconditional stability and a priori estimates of the scheme are given rigorously. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.
Energy Technology Data Exchange (ETDEWEB)
Chvetsov, A; Schwartz, J; Mayr, N [University of Washington, Seattle, WA (United States); Yartsev, S [London Health Sciences Centre, London, Ontario (Canada)
2014-06-01
Purpose: To show that a distribution of cell surviving fractions S{sub 2} in a heterogeneous group of patients can be derived from tumor-volume variation curves during radiotherapy for non-small cell lung cancer. Methods: Our analysis was based on two data sets of tumor-volume variation curves for heterogeneous groups of 17 patients treated for nonsmall cell lung cancer with conventional dose fractionation. The data sets were obtained previously at two independent institutions by using megavoltage (MV) computed tomography (CT). Statistical distributions of cell surviving fractions S{sup 2} and cell clearance half-lives of lethally damaged cells T1/2 have been reconstructed in each patient group by using a version of the two-level cell population tumor response model and a simulated annealing algorithm. The reconstructed statistical distributions of the cell surviving fractions have been compared to the distributions measured using predictive assays in vitro. Results: Non-small cell lung cancer presents certain difficulties for modeling surviving fractions using tumor-volume variation curves because of relatively large fractional hypoxic volume, low gradient of tumor-volume response, and possible uncertainties due to breathing motion. Despite these difficulties, cell surviving fractions S{sub 2} for non-small cell lung cancer derived from tumor-volume variation measured at different institutions have similar probability density functions (PDFs) with mean values of 0.30 and 0.43 and standard deviations of 0.13 and 0.18, respectively. The PDFs for cell surviving fractions S{sup 2} reconstructed from tumor volume variation agree with the PDF measured in vitro. Comparison of the reconstructed cell surviving fractions with patient survival data shows that the patient survival time decreases as the cell surviving fraction increases. Conclusion: The data obtained in this work suggests that the cell surviving fractions S{sub 2} can be reconstructed from the tumor volume
International Nuclear Information System (INIS)
Shah, Nehad Ali; Khan, Ilyas
2016-01-01
This paper presents a Caputo-Fabrizio fractional derivatives approach to the thermal analysis of a second grade fluid over an infinite oscillating vertical flat plate. Together with an oscillating boundary motion, the heat transfer is caused by the buoyancy force induced by temperature differences between the plate and the fluid. Closed form solutions of the fluid velocity and temperature are obtained by means of the Laplace transform. The solutions of ordinary second grade and Newtonian fluids corresponding to time derivatives of integer and fractional orders are obtained as particular cases of the present solutions. Numerical computations and graphical illustrations are used in order to study the effects of the Caputo-Fabrizio time-fractional parameter α, the material parameter α 2 , and the Prandtl and Grashof numbers on the velocity field. A comparison for time derivative of integer order versus fractional order is shown graphically for both Newtonian and second grade fluids. It is found that fractional fluids (second grade and Newtonian) have highest velocities. This shows that the fractional parameter enhances the fluid flow. (orig.)
Mathematical modeling of fish burger baking using fractional calculus
Directory of Open Access Journals (Sweden)
Bainy Eduarda M.
2017-01-01
Full Text Available Tilapia (Oreochromis sp. is the most important and abundant fish species in Brazil due to its adaptability to different environments. The development of tilapia-based products could be an alternative in order to aggregate value and increase fish meat consumption. However, there is little information available on fishburger freezing and cooking in the literature. In this work, the mathematical modeling of the fish burger baking was studied. Previously to the baking process, the fishburgers were assembled in cylindrical shape of height equal to 8mm and diameter 100mm and then baked in an electrical oven with forced heat convection at 150ºC. A T-type thermocouple was inserted in the burger to obtain its temperature profile at the central position. In order to describe the temperature of the burger during the baking process, lumped-parameter models of integer and fractional order and also a nonlinear model due to heat capacity temperature dependence were considered. The burger physical properties were obtained from the literature. After proper parameter estimation tasks and statistical validation, the fractional order model could better describe the experimental temperature behavior, a value of 0.91±0.02 was obtained for the fractional order of the system with correlation coefficient of 0.99. Therefore, with the better temperature prediction, process control and economic optimization studies of the baking process can be conducted.
Mathematical modelling of the mass-spring-damper system - A fractional calculus approach
Directory of Open Access Journals (Sweden)
Jesus Bernal Alvarado
2012-08-01
Full Text Available In this paper the fractional differential equation for the mass-spring-damper system in terms of the fractional time derivatives of the Caputo type is considered. In order to be consistent with the physical equation, a new parameter is introduced. This parameter characterizes the existence of fractional components in the system. A relation between the fractional order time derivative and the new parameter is found. Different particular cases are analyzed
Black holes in multi-fractional and Lorentz-violating models
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [CSIC, Instituto de Estructura de la Materia, Madrid (Spain); Rodriguez Fernandez, David [Universidad de Oviedo, Department of Physics, Oviedo (Spain); Ronco, Michele [Universita di Roma ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); INFN, Rome (Italy)
2017-05-15
We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length l{sub *}. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to l{sub *}. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models. (orig.)
Black holes in multi-fractional and Lorentz-violating models
International Nuclear Information System (INIS)
Calcagni, Gianluca; Rodriguez Fernandez, David; Ronco, Michele
2017-01-01
We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length l_*. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to l_*. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models. (orig.)
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.
Lubrication pressure and fractional viscous damping effects on the spring-block model of earthquakes
Tanekou, G. B.; Fogang, C. F.; Kengne, R.; Pelap, F. B.
2018-04-01
We examine the dynamical behaviours of the "single mass-spring" model for earthquakes considering lubrication pressure effects on pre-existing faults and viscous fractional damping. The lubrication pressure supports a part of the load, thereby reducing the normal stress and the associated friction across the gap. During the co-seismic phase, all of the strain accumulated during the inter-seismic duration does not recover; a fraction of this strain remains as a result of viscous relaxation. Viscous damping friction makes it possible to study rocks at depth possessing visco-elastic behaviours. At increasing depths, rock deformation gradually transitions from brittle to ductile. The fractional derivative is based on the properties of rocks, including information about previous deformation events ( i.e., the so-called memory effect). Increasing the fractional derivative can extend or delay the transition from stick-slip oscillation to a stable equilibrium state and even suppress it. For the single block model, the interactions of the introduced lubrication pressure and viscous damping are found to give rise to oscillation death, which corresponds to aseismic fault behaviour. Our result shows that the earthquake occurrence increases with increases in both the damping coefficient and the lubrication pressure. We have also revealed that the accumulation of large stresses can be controlled via artificial lubrication.
Fractional-order mathematical model of an irrigation main canal pool
Directory of Open Access Journals (Sweden)
Shlomi N. Calderon-Valdez
2015-09-01
Full Text Available In this paper a fractional order model for an irrigation main canal is proposed. It is based on the experiments developed in a laboratory prototype of a hydraulic canal and the application of a direct system identification methodology. The hydraulic processes that take place in this canal are equivalent to those that occur in real main irrigation canals and the results obtained here can therefore be easily extended to real canals. The accuracy of the proposed fractional order model is compared by deriving two other integer-order models of the canal of a complexity similar to that proposed here. The parameters of these three mathematical models have been identified by minimizing the Integral Square Error (ISE performance index existing between the models and the real-time experimental data obtained from the canal prototype. A comparison of the performances of these three models shows that the fractional-order model has the lowest error and therefore the higher accuracy. Experiments showed that our model outperformed the accuracy of the integer-order models by about 25%, which is a significant improvement as regards to capturing the canal dynamics.
A 'simple' hybrid model for power derivatives
International Nuclear Information System (INIS)
Lyle, Matthew R.; Elliott, Robert J.
2009-01-01
This paper presents a method for valuing power derivatives using a supply-demand approach. Our method extends work in the field by incorporating randomness into the base load portion of the supply stack function and equating it with a noisy demand process. We obtain closed form solutions for European option prices written on average spot prices considering two different supply models: a mean-reverting model and a Markov chain model. The results are extensions of the classic Black-Scholes equation. The model provides a relatively simple approach to describe the complicated price behaviour observed in electricity spot markets and also allows for computationally efficient derivatives pricing. (author)
Fractional Modeling of the AC Large-Signal Frequency Response in Magnetoresistive Current Sensors
Directory of Open Access Journals (Sweden)
Sergio Iván Ravelo Arias
2013-12-01
Full Text Available Fractional calculus is considered when derivatives and integrals of non-integer order are applied over a specific function. In the electrical and electronic domain, the transfer function dependence of a fractional filter not only by the filter order n, but additionally, of the fractional order α is an example of a great number of systems where its input-output behavior could be more exactly modeled by a fractional behavior. Following this aim, the present work shows the experimental ac large-signal frequency response of a family of electrical current sensors based in different spintronic conduction mechanisms. Using an ac characterization set-up the sensor transimpedance function is obtained considering it as the relationship between sensor output voltage and input sensing current,[PLEASE CHECK FORMULA IN THE PDF]. The study has been extended to various magnetoresistance sensors based in different technologies like anisotropic magnetoresistance (AMR, giant magnetoresistance (GMR, spin-valve (GMR-SV and tunnel magnetoresistance (TMR. The resulting modeling shows two predominant behaviors, the low-pass and the inverse low-pass with fractional index different from the classical integer response. The TMR technology with internal magnetization offers the best dynamic and sensitivity properties opening the way to develop actual industrial applications.
A holographic model for the fractional quantum Hall effect
Energy Technology Data Exchange (ETDEWEB)
Lippert, Matthew [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, 1090GL Amsterdam (Netherlands); Meyer, René [Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo,Kashiwa, Chiba 277-8568 (Japan); Taliotis, Anastasios [Theoretische Natuurkunde, Vrije Universiteit Brussel andThe International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium)
2015-01-08
Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a Γ{sub 0}(2) modular symmetry group commuting with the renormalization group flow and hence mapping different phases of two-dimensional electron gases into each other. Based on this insight, we construct a phenomenological holographic model which captures many features of the fractional quantum Hall effect. Using an SL(2,ℤ)-invariant Einstein-Maxwell-axio-dilaton theory capturing the important modular transformation properties of quantum Hall physics, we find dyonic diatonic black hole solutions which are gapped and have a Hall conductivity equal to the filling fraction, as expected for quantum Hall states. We also provide several technical results on the general behavior of the gauge field fluctuations around these dyonic dilatonic black hole solutions: we specify a sufficient criterion for IR normalizability of the fluctuations, demonstrate the preservation of the gap under the SL(2,ℤ) action, and prove that the singularity of the fluctuation problem in the presence of a magnetic field is an accessory singularity. We finish with a preliminary investigation of the possible IR scaling solutions of our model and some speculations on how they could be important for the observed universality of quantum Hall transitions.
A holographic model for the fractional quantum Hall effect
Lippert, Matthew; Meyer, René; Taliotis, Anastasios
2015-01-01
Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a Γ0(2) modular symmetry group commuting with the renormalization group flow and hence mapping different phases of two-dimensional electron gases into each other. Based on this insight, we construct a phenomenological holographic model which captures many features of the fractional quantum Hall effect. Using an -invariant Einstein-Maxwell-axio-dilaton theory capturing the important modular transformation properties of quantum Hall physics, we find dyonic diatonic black hole solutions which are gapped and have a Hall conductivity equal to the filling fraction, as expected for quantum Hall states. We also provide several technical results on the general behavior of the gauge field fluctuations around these dyonic dilatonic black hole solutions: we specify a sufficient criterion for IR normalizability of the fluctuations, demonstrate the preservation of the gap under the action, and prove that the singularity of the fluctuation problem in the presence of a magnetic field is an accessory singularity. We finish with a preliminary investigation of the possible IR scaling solutions of our model and some speculations on how they could be important for the observed universality of quantum Hall transitions.
Transient heat conduction in a pebble fuel applying fractional model
International Nuclear Information System (INIS)
Gomez A, R.; Espinosa P, G.
2009-10-01
In this paper we presents the equation of thermal diffusion of temporary-fractional order in the one-dimensional space in spherical coordinates, with the objective to analyze the heat transference between the fuel and coolant in a fuel element of a Pebble Bed Modular Reactor. The pebble fuel is the heterogeneous system made by microsphere constitutes by U O, pyrolytic carbon and silicon carbide mixed with graphite. To describe the heat transfer phenomena in the pebble fuel we applied a constitutive law fractional (Non-Fourier) in order to analyze the behaviour transient of the temperature distribution in the pebble fuel with anomalous thermal diffusion effects a numerical model is developed. (Author)
Phase Diagram of a Simple Model for Fractional Topological Insulator
Chen, Hua; Yang, Kun
2012-02-01
We study a simple model of two species of (or spin-1/2) fermions with short-range intra-species repulsion in the presence of opposite (effetive) magnetic field, each at filling factor 1/3. In the absence of inter-species interaction, the ground state is simply two copies of the 1/3 Laughlin state, with opposite chirality. Due to the overall time-reversal symmetry, this is a fractional topological insulator. We show this phase is stable against moderate inter-species interactions. However strong enough inter-species repulsion leads to phase separation, while strong enough inter-species attraction drives the system into a superfluid phase. We obtain the phase diagram through exact diagonalization caluclations. Nature of the fractional topological insluator-superfluid phase transition is discussed using an appropriate Chern-Simons-Ginsburg-Landau effective field theory.
Deformed Calogero-Sutherland model and fractional quantum Hall effect
Atai, Farrokh; Langmann, Edwin
2017-01-01
The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases. We show that a known collective field description of the CS model, which is based on conformal field theory (CFT), is actually a collective field description of the deformed CS model. This provides a natural application of the deformed CS model in Wen's effective field theory of the fractional quantum Hall effect (FQHE), with the two kinds of particles corresponding to electrons and quasi-hole excitations. In particular, we use known mathematical results about super-Jack polynomials to obtain simple explicit formulas for the orthonormal CFT basis proposed by van Elburg and Schoutens in the context of the FQHE.
Energy Technology Data Exchange (ETDEWEB)
Xiao, Yanwen; Xu, Wei, E-mail: weixu@nwpu.edu.cn; Wang, Liang [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2016-03-15
This paper focuses on the study of the stochastic Van der Pol vibro-impact system with fractional derivative damping under Gaussian white noise excitation. The equations of the original system are simplified by non-smooth transformation. For the simplified equation, the stochastic averaging approach is applied to solve it. Then, the fractional derivative damping term is facilitated by a numerical scheme, therewith the fourth-order Runge-Kutta method is used to obtain the numerical results. And the numerical simulation results fit the analytical solutions. Therefore, the proposed analytical means to study this system are proved to be feasible. In this context, the effects on the response stationary probability density functions (PDFs) caused by noise excitation, restitution condition, and fractional derivative damping are considered, in addition the stochastic P-bifurcation is also explored in this paper through varying the value of the coefficient of fractional derivative damping and the restitution coefficient. These system parameters not only influence the response PDFs of this system but also can cause the stochastic P-bifurcation.
Xiao, Yanwen; Xu, Wei; Wang, Liang
2016-03-01
This paper focuses on the study of the stochastic Van der Pol vibro-impact system with fractional derivative damping under Gaussian white noise excitation. The equations of the original system are simplified by non-smooth transformation. For the simplified equation, the stochastic averaging approach is applied to solve it. Then, the fractional derivative damping term is facilitated by a numerical scheme, therewith the fourth-order Runge-Kutta method is used to obtain the numerical results. And the numerical simulation results fit the analytical solutions. Therefore, the proposed analytical means to study this system are proved to be feasible. In this context, the effects on the response stationary probability density functions (PDFs) caused by noise excitation, restitution condition, and fractional derivative damping are considered, in addition the stochastic P-bifurcation is also explored in this paper through varying the value of the coefficient of fractional derivative damping and the restitution coefficient. These system parameters not only influence the response PDFs of this system but also can cause the stochastic P-bifurcation.
Computing diffuse fraction of global horizontal solar radiation: A model comparison.
Dervishi, Sokol; Mahdavi, Ardeshir
2012-06-01
For simulation-based prediction of buildings' energy use or expected gains from building-integrated solar energy systems, information on both direct and diffuse component of solar radiation is necessary. Available measured data are, however, typically restricted to global horizontal irradiance. There have been thus many efforts in the past to develop algorithms for the derivation of the diffuse fraction of solar irradiance. In this context, the present paper compares eight models for estimating diffuse fraction of irradiance based on a database of measured irradiance from Vienna, Austria. These models generally involve mathematical formulations with multiple coefficients whose values are typically valid for a specific location. Subsequent to a first comparison of these eight models, three better performing models were selected for a more detailed analysis. Thereby, the coefficients of the models were modified to account for Vienna data. The results suggest that some models can provide relatively reliable estimations of the diffuse fractions of the global irradiance. The calibration procedure could only slightly improve the models' performance.
International Nuclear Information System (INIS)
Craiem, Damian; Magin, Richard L
2010-01-01
New lumped-element models of red blood cell mechanics can be constructed using fractional order generalizations of springs and dashpots. Such 'spring-pots' exhibit a fractional order viscoelastic behavior that captures a wide spectrum of experimental results through power-law expressions in both the time and frequency domains. The system dynamics is fully described by linear fractional order differential equations derived from first order stress–strain relationships using the tools of fractional calculus. Changes in the composition or structure of the membrane are conveniently expressed in the fractional order of the model system. This approach provides a concise way to describe and quantify the biomechanical behavior of membranes, cells and tissues. (perspective)
Craiem, Damian; Magin, Richard L
2010-01-20
New lumped-element models of red blood cell mechanics can be constructed using fractional order generalizations of springs and dashpots. Such 'spring-pots' exhibit a fractional order viscoelastic behavior that captures a wide spectrum of experimental results through power-law expressions in both the time and frequency domains. The system dynamics is fully described by linear fractional order differential equations derived from first order stress-strain relationships using the tools of fractional calculus. Changes in the composition or structure of the membrane are conveniently expressed in the fractional order of the model system. This approach provides a concise way to describe and quantify the biomechanical behavior of membranes, cells and tissues.
Kuldeep, B; Singh, V K; Kumar, A; Singh, G K
2015-01-01
In this article, a novel approach for 2-channel linear phase quadrature mirror filter (QMF) bank design based on a hybrid of gradient based optimization and optimization of fractional derivative constraints is introduced. For the purpose of this work, recently proposed nature inspired optimization techniques such as cuckoo search (CS), modified cuckoo search (MCS) and wind driven optimization (WDO) are explored for the design of QMF bank. 2-Channel QMF is also designed with particle swarm optimization (PSO) and artificial bee colony (ABC) nature inspired optimization techniques. The design problem is formulated in frequency domain as sum of L2 norm of error in passband, stopband and transition band at quadrature frequency. The contribution of this work is the novel hybrid combination of gradient based optimization (Lagrange multiplier method) and nature inspired optimization (CS, MCS, WDO, PSO and ABC) and its usage for optimizing the design problem. Performance of the proposed method is evaluated by passband error (ϕp), stopband error (ϕs), transition band error (ϕt), peak reconstruction error (PRE), stopband attenuation (As) and computational time. The design examples illustrate the ingenuity of the proposed method. Results are also compared with the other existing algorithms, and it was found that the proposed method gives best result in terms of peak reconstruction error and transition band error while it is comparable in terms of passband and stopband error. Results show that the proposed method is successful for both lower and higher order 2-channel QMF bank design. A comparative study of various nature inspired optimization techniques is also presented, and the study singles out CS as a best QMF optimization technique. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Gleyce Alves Machado
2013-05-01
Full Text Available The aim of the present study was to analyse Taenia solium metacestode antigens that were derived from the unbound fraction of jacalin affinity chromatography and subsequent tert-octylphenoxy poly (oxyethylene ethanol Triton X-114 (TX-114 partitioning in the diagnosis of human neurocysticercosis (NCC. Immunoassays were designed to detect T. solium-specific IgG antibodies by ELISA and immunoblot. Serum samples were collected from 132 individuals who were categorised as follows: 40 had NCC, 62 presented Taenia spp or other parasitic diseases and 30 were healthy individuals. The jacalin-unbound (J unbound fraction presented higher sensitivity and specificity rates than the jacalin-bound fraction and only this fraction was subjected to subsequent TX-114 partitioning, resulting in detergent (DJ unbound and aqueous (AJ unbound fractions. The ELISA sensitivity and specificity were 85% and 84.8% for J unbound , 92.5% and 93.5% for DJ unbound and 82.5% and 82.6% for AJ unbound . By immunoblot, the DJ unbound fraction showed 100% sensitivity and specificity and only serum samples from patients with NCC recognised the 50-70 kDa T. solium-specific components. We conclude that the DJ unbound fraction can serve as a useful tool for the differential immunodiagnosis of NCC by immunoblot.
Influence of the void fraction in the linear reactivity model
International Nuclear Information System (INIS)
Castillo, J.A.; Ramirez, J.R.; Alonso, G.
2003-01-01
The linear reactivity model allows the multicycle analysis in pressurized water reactors in a simple and quick way. In the case of the Boiling water reactors the void fraction it varies axially from 0% of voids in the inferior part of the fuel assemblies until approximately 70% of voids to the exit of the same ones. Due to this it is very important the determination of the average void fraction during different stages of the reactor operation to predict the burnt one appropriately of the same ones to inclination of the pattern of linear reactivity. In this work a pursuit is made of the profile of power for different steps of burnt of a typical operation cycle of a Boiling water reactor. Starting from these profiles it builds an algorithm that allows to determine the voids profile and this way to obtain the average value of the same one. The results are compared against those reported by the CM-PRESTO code that uses another method to carry out this calculation. Finally, the range in which is the average value of the void fraction during a typical cycle is determined and an estimate of the impact that it would have the use of this value in the prediction of the reactivity produced by the fuel assemblies is made. (Author)
Modeling discrete and continuous entities with fractions and decimals.
Rapp, Monica; Bassok, Miriam; DeWolf, Melissa; Holyoak, Keith J
2015-03-01
When people use mathematics to model real-life situations, their use of mathematical expressions is often mediated by semantic alignment (Bassok, Chase, & Martin, 1998): The entities in a problem situation evoke semantic relations (e.g., tulips and vases evoke the functionally asymmetric "contain" relation), which people align with analogous mathematical relations (e.g., the noncommutative division operation, tulips/vases). Here we investigate the possibility that semantic alignment is also involved in the comprehension and use of rational numbers (fractions and decimals). A textbook analysis and results from two experiments revealed that both mathematic educators and college students tend to align the discreteness versus continuity of the entities in word problems (e.g., marbles vs. distance) with distinct symbolic representations of rational numbers--fractions versus decimals, respectively. In addition, fractions and decimals tend to be used with nonmetric units and metric units, respectively. We discuss the importance of the ontological distinction between continuous and discrete entities to mathematical cognition, the role of symbolic notations, and possible implications of our findings for the teaching of rational numbers. PsycINFO Database Record (c) 2015 APA, all rights reserved.
Directory of Open Access Journals (Sweden)
Hossein Jafari
2016-04-01
Full Text Available The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.
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.
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.
Toward lattice fractional vector calculus
Tarasov, Vasily E.
2014-09-01
An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.
Directory of Open Access Journals (Sweden)
Fuqiang Zhao
2017-01-01
Full Text Available In the current study, a numerical technique for solving one-dimensional fractional nonsteady heat transfer model is presented. We construct the second kind Chebyshev wavelet and then derive the operational matrix of fractional-order integration. The operational matrix of fractional-order integration is utilized to reduce the original problem to a system of linear algebraic equations, and then the numerical solutions obtained by our method are compared with those obtained by CAS wavelet method. Lastly, illustrated examples are included to demonstrate the validity and applicability of the technique.
Analytical Solutions of a Space-Time Fractional Derivative of Groundwater Flow Equation
Directory of Open Access Journals (Sweden)
Abdon Atangana
2014-01-01
Full Text Available The classical Darcy law is generalized by regarding the water flow as a function of a noninteger order derivative of the piezometric head. This generalized law and the law of conservation of mass are then used to derive a new equation for groundwater flow. Two methods including Frobenius and Adomian decomposition method are used to obtain an asymptotic analytical solution to the generalized groundwater flow equation. The solution obtained via Frobenius method is valid in the vicinity of the borehole. This solution is in perfect agreement with the data observed from the pumping test performed by the institute for groundwater study on one of their boreholes settled on the test site of the University of the Free State. The test consisted of the pumping of the borehole at the constant discharge rate Q and monitoring the piezometric head for 350 minutes. Numerical solutions obtained via Adomian method are compared with the Barker generalized radial flow model for which a fractal dimension for the flow is assumed. Proposition for uncertainties in groundwater studies was given.
Murine Models of Heart Failure With Preserved Ejection Fraction
Directory of Open Access Journals (Sweden)
Maria Valero-Muñoz, PhD
2017-12-01
Full Text Available Heart failure with preserved ejection fraction (HFpEF is characterized by signs and symptoms of heart failure in the presence of a normal left ventricular ejection fraction. Despite accounting for up to 50% of all clinical presentations of heart failure, the mechanisms implicated in HFpEF are poorly understood, thus precluding effective therapy. The pathophysiological heterogeneity in the HFpEF phenotype also contributes to this disease and likely to the absence of evidence-based therapies. Limited access to human samples and imperfect animal models that completely recapitulate the human HFpEF phenotype have impeded our understanding of the mechanistic underpinnings that exist in this disease. Aging and comorbidities such as atrial fibrillation, hypertension, diabetes and obesity, pulmonary hypertension, and renal dysfunction are highly associated with HFpEF, yet the relationship and contribution between them remains ill-defined. This review discusses some of the distinctive clinical features of HFpEF in association with these comorbidities and highlights the advantages and disadvantage of commonly used murine models used to study the HFpEF phenotype.
Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad
2017-07-01
This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two numerical schemes namely an iterative scheme based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report numerical simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. Numerical experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative scheme.
Deriving simulators for hybrid Chi models
Beek, van D.A.; Man, K.L.; Reniers, M.A.; Rooda, J.E.; Schiffelers, R.R.H.
2006-01-01
The hybrid Chi language is formalism for modeling, simulation and verification of hybrid systems. The formal semantics of hybrid Chi allows the definition of provably correct implementations for simulation, verification and realtime control. This paper discusses the principles of deriving an
Particle Based Modeling of Electrical Field Flow Fractionation Systems
Directory of Open Access Journals (Sweden)
Tonguc O. Tasci
2015-10-01
Full Text Available Electrical Field Flow Fractionation (ElFFF is a sub method in the field flow fractionation (FFF family that relies on an applied voltage on the channel walls to effect a separation. ElFFF has fallen behind some of the other FFF methods because of the optimization complexity of its experimental parameters. To enable better optimization, a particle based model of the ElFFF systems has been developed and is presented in this work that allows the optimization of the main separation parameters, such as electric field magnitude, frequency, duty cycle, offset, flow rate and channel dimensions. The developed code allows visualization of individual particles inside the separation channel, generation of realistic fractograms, and observation of the effects of the various parameters on the behavior of the particle cloud. ElFFF fractograms have been generated via simulations and compared with experiments for both normal and cyclical ElFFF. The particle visualizations have been used to verify that high duty cycle voltages are essential to achieve long retention times and high resolution separations. Furthermore, by simulating the particle motions at the channel outlet, it has been demonstrated that the top channel wall should be selected as the accumulation wall for cyclical ElFFF to reduce band broadening and achieve high efficiency separations. While the generated particle based model is a powerful tool to estimate the outcomes of the ElFFF experiments and visualize particle motions, it can also be used to design systems with new geometries which may lead to the design of higher efficiency ElFFF systems. Furthermore, this model can be extended to other FFF techniques by replacing the electrical field component of the model with the fields used in the other FFF techniques.
Fractional Gaussian noise: Prior specification and model comparison
Sø rbye, Sigrunn Holbek; Rue, Haavard
2017-01-01
Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ(symbol) of a first-order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.
Fractional Gaussian noise: Prior specification and model comparison
Sørbye, Sigrunn Holbek
2017-07-07
Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ(symbol) of a first-order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.
International Nuclear Information System (INIS)
Lim, S C; Teo, L P
2009-01-01
Single-file diffusion behaves as normal diffusion at small time and as subdiffusion at large time. These properties can be described in terms of fractional Brownian motion with variable Hurst exponent or multifractional Brownian motion. We introduce a new stochastic process called Riemann–Liouville step fractional Brownian motion which can be regarded as a special case of multifractional Brownian motion with a step function type of Hurst exponent tailored for single-file diffusion. Such a step fractional Brownian motion can be obtained as a solution of the fractional Langevin equation with zero damping. Various kinds of fractional Langevin equations and their generalizations are then considered in order to decide whether their solutions provide the correct description of the long and short time behaviors of single-file diffusion. The cases where the dissipative memory kernel is a Dirac delta function, a power-law function and a combination of these functions are studied in detail. In addition to the case where the short time behavior of single-file diffusion behaves as normal diffusion, we also consider the possibility of a process that begins as ballistic motion
Distributed-order fractional diffusions on bounded domains
Meerschaert, Mark M.; Nane, Erkan; Vellaisamy, P.
2011-01-01
In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. The fractional derivative models time delays in a diffusion process. The order of the fractional derivative can be distributed over the unit interval, to model a mixture of delay sources. In this paper, we provide explicit strong solutions and stochastic analogues for distributed-order fractional Cauchy problems on bounded domains with Dirichlet boundary conditions. Stochastic solutio...
Fractional hydrodynamic equations for fractal media
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2005-01-01
We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the 'fractional' continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier-Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for fractional media are considered
An approximate fractional Gaussian noise model with computational cost
Sørbye, Sigrunn H.
2017-09-18
Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood-based approach is ${\\\\mathcal O}(n^{2})$, exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to ${\\\\mathcal O}(n^{3})$. This paper presents an approximate fGn model of ${\\\\mathcal O}(n)$ computational cost, both with direct or indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive processes, fitting the parameters of the approximation to match the autocorrelation function of the fGn model. The resulting approximation is stationary despite being Markov and gives a remarkably accurate fit using only four components. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.
Price models for oil derivates in Slovenia
International Nuclear Information System (INIS)
Nemac, F.; Saver, A.
1995-01-01
In Slovenia, a law is currently applied according to which any change in the price of oil derivatives is subject to the Governmental approval. Following the target of getting closer to the European Union, the necessity has arisen of finding ways for the introduction of liberalization or automated approach to price modifications depending on oscillations of oil derivative prices on the world market and the rate of exchange of the American dollar. It is for this reason that at the Agency for Energy Restructuring we made a study for the Ministry of Economic Affairs and Development regarding this issue. We analysed the possible models for the formation of oil derivative prices for Slovenia. Based on the assessment of experiences of primarily the west European countries, we proposed three models for the price formation for Slovenia. In future, it is expected that the Government of the Republic of Slovenia will make a selection of one of the proposed models to be followed by enforcement of price liberalization. The paper presents two representative models for price formation as used in Austria and Portugal. In the continuation the authors analyse the application of three models that they find suitable for the use in Slovenia. (author)
Energy Technology Data Exchange (ETDEWEB)
Liu, Shasha [College of Water Sciences, Beijing Normal University, Beijing 100875 (China); State Key Laboratory of Environment Criteria and Risk Assessment, Chinese Research Academy of Environmental Sciences, Beijing 100012 (China); Zhu, Yuanrong, E-mail: zhuyuanrong07@mails.ucas.ac.cn [State Key Laboratory of Environment Criteria and Risk Assessment, Chinese Research Academy of Environmental Sciences, Beijing 100012 (China); Wu, Fengchang, E-mail: wufengchang@vip.skleg.cn [State Key Laboratory of Environment Criteria and Risk Assessment, Chinese Research Academy of Environmental Sciences, Beijing 100012 (China); Meng, Wei [State Key Laboratory of Environment Criteria and Risk Assessment, Chinese Research Academy of Environmental Sciences, Beijing 100012 (China); He, Zhongqi [USDA-ARS Southern Regional Research Center, 1100 Robert E Lee Blvd, New Orleans, LA 70124 (United States); Giesy, John P. [State Key Laboratory of Environment Criteria and Risk Assessment, Chinese Research Academy of Environmental Sciences, Beijing 100012 (China); Department of Biomedical and Veterinary Biosciences and Toxicology Centre, University of Saskatchewan, Saskatoon, Saskatchewan (Canada)
2016-10-01
Although debris from aquatic macrophytes is one of the most important endogenous sources of organic matter (OM) and nutrients in lakes, its biogeochemical cycling and contribution to internal load of nutrients in eutrophic lakes are still poorly understood. In this study, sequential fractionation by H{sub 2}O, 0.1 M NaOH and 1.0 M HCl, combined with {sup 13}C and {sup 31}P NMR spectroscopy, was developed and used to characterize organic carbon (C) and phosphorus (P) in six aquatic plants collected from Tai Lake (Ch: Taihu), China. Organic matter, determined by total organic carbon (TOC), was unequally distributed in H{sub 2}O (21.2%), NaOH (29.9%), HCl (3.5%) and residual (45.3%) fractions. For P in debris of aquatic plants, 53.3% was extracted by H{sub 2}O, 31.9% by NaOH, and 11% by HCl, with 3.8% in residual fractions. Predominant OM components extracted by H{sub 2}O and NaOH were carbohydrates, proteins and aliphatic acids. Inorganic P (P{sub i}) was the primary form of P in H{sub 2}O fractions, whereas organic P (P{sub o}) was the primary form of P in NaOH fractions. The subsequent HCl fractions extracted fewer species of C and P. Some non-extractable carbohydrates, aromatics and metal phytate compounds remained in residual fractions. Based on sequential extraction and NMR analysis, it was proposed that those forms of C (54.7% of TOC) and P (96.2% of TP) in H{sub 2}O, NaOH and HCl fractions are potentially released to overlying water as labile components, while those in residues are stable and likely preserved in sediments of lakes. These results will be helpful in understanding internal loading of nutrients from debris of aquatic macrophytes and their recycling in lakes. - Highlights: • Sequential fractionation combined with NMR analysis was applied on aquatic plants. • Labile and stable C and P forms in aquatic plants were characterized. • 54.7% of OM and 96.2% of P in aquatic plants are potentially available. • 45.3% of OM and 3.8% of P in aquatic
Antioxidant Potential of the Extracts, Fractions and Oils Derived from Oilseeds
Directory of Open Access Journals (Sweden)
Shagufta Ishtiaque
2013-10-01
Full Text Available The polyphenolic extracts and oils were obtained from ajwain, mustard, fenugreek and poppy seeds. The extracts were partitioned into acidic and neutral polyphenolic fractions and following estimation of total phenolics in the crude extract, acidic and neutral fractions and oil, all were analyzed for their DPPH (2,2-diphenyl-1-picrylhydrazyl scavenging potential, ferric reducing ability and chelating power. The highest amount of polyphenols was found in ajwain (8330 ± 107, then in mustard seeds (2844 ± 56.00 and in fenugreek (1130 ± 29.00, and least in poppy seeds (937 ± 18.52. The higher amounts of polyphenols were estimated in neutral fraction compared to acidic (p fenugreek and least by poppy seed extracts (p < 0.05. The reducing power and the chelating effect of the oilseeds followed the same order as DPPH, but higher % chelation was shown by neutral than acidic fraction (p < 0.05. Though low in polyphenols, the oil fractions were as strong antioxidants as the acidic one. Though oilseeds are used in very small quantity in food, they are potential sources of natural antioxidants and may replace synthetic ones.
Directory of Open Access Journals (Sweden)
Ehab Malkawi
2014-01-01
Full Text Available The classical free Lagrangian admitting a constant of motion, in one- and two-dimensional space, is generalized using the Caputo derivative of fractional calculus. The corresponding metric is obtained and the fractional Christoffel symbols, Killing vectors, and Killing-Yano tensors are derived. Some exact solutions of these quantities are reported.
International Nuclear Information System (INIS)
Murillo Mejia, Mario Humberto
2006-01-01
The objective was to evaluate the data obtained by sensor MODIS onboard the EOS terra satellite land cover units. The study area is the republic of Colombia in South America. The methodology consisted of analyzing the multitemporal (vegetation, soil and shade-water) fraction images and vegetation indices (NDVI) apply the lineal spectral mixture model to products derived from derived images by sensor MODIS data obtained in years 2001 and 2003. The mosaics of the original and the transformed vegetation (soil and shade-water) bands were generated for the whole study area using SPRING 4. 0 software, developed by INPE then these mosaics were segmented, classified, mapped, and edited to obtain a moderate resolution land cover map. The results derived from MODIS analysis were compared with Landsat ETM+ data acquire for a single test site. The results of the project showed the usefulness of MODIS images for large-scale land cover mapping and monitoring studies
Tunable polymeric sorbent materials for fractionation of model naphthenates.
Mohamed, Mohamed H; Wilson, Lee D; Headley, John V
2013-04-04
The sorption properties are reported for several examples of single-component carboxylic acids representing naphthenic acids (NAs) with β-cyclodextrin (β-CD) based polyurethane sorbents. Seven single-component examples of NAs were chosen with variable z values, carbon number, and chemical structure as follows: 2-hexyldecanoic acid (z = 0 and C = 16; S1), n-caprylic acid (z = 0 and C = 8; S2), trans-4-pentylcyclohexanecarboxylic acid (z = -2 and C = 12; S3), 4-methylcyclohexanecarboxylic acid (z = -2 and C = 8; S4), dicyclohexylacetic acid (z = -4; C = 14; S5), 4-pentylbicyclo[2.2.2]octane-1-carboxylic acid (z = -4; C = 14; S6), and lithocholic acid (z = -6; C = 24; S7). The copolymer sorbents were synthesized at three relative β-CD:diisocyanate mole ratios (i.e., 1:1, 1:2, and 1:3) using 4,4'-dicyclohexylmethane diisocyanate (CDI) and 4,4'-diphenylmethane diisocyanate (MDI). The sorption properties of the copolymer sorbents were characterized using equilibrium sorption isotherms in aqueous solution at pH 9.00 with electrospray ionization mass spectrometry. The equilibrium fraction of the unbound carboxylate anions was monitored in the aqueous phase. The sorption properties of the copolymer sorbents (i.e., Qm) were obtained from the Sips isotherm model. The Qm values generally decrease as the number of accessible β-CD inclusion sites in the copolymer framework decreases. The chemical structure of the adsorbates played an important role in their relative uptake, as evidenced by the adsorbate lipophilic surface area (LSA) and the involvement of hydrophobic effects. The copolymers exhibit molecular selective sorption of the single-component carboxylates in mixtures which suggests their application as sorbents for fractionation of mixtures of NAs. By comparison, granular activated carbon (GAC) and chitosan sorbents did not exhibit any significant molecular selective sorption relative to the copolymer materials; however, evidence of variable sorption capacity was
A stochastic fractional dynamics model of space-time variability of rain
Kundu, Prasun K.; Travis, James E.
2013-09-01
varies in space and time in a highly irregular manner and is described naturally in terms of a stochastic process. A characteristic feature of rainfall statistics is that they depend strongly on the space-time scales over which rain data are averaged. A spectral model of precipitation has been developed based on a stochastic differential equation of fractional order for the point rain rate, which allows a concise description of the second moment statistics of rain at any prescribed space-time averaging scale. The model is thus capable of providing a unified description of the statistics of both radar and rain gauge data. The underlying dynamical equation can be expressed in terms of space-time derivatives of fractional orders that are adjusted together with other model parameters to fit the data. The form of the resulting spectrum gives the model adequate flexibility to capture the subtle interplay between the spatial and temporal scales of variability of rain but strongly constrains the predicted statistical behavior as a function of the averaging length and time scales. We test the model with radar and gauge data collected contemporaneously at the NASA TRMM ground validation sites located near Melbourne, Florida and on the Kwajalein Atoll, Marshall Islands in the tropical Pacific. We estimate the parameters by tuning them to fit the second moment statistics of radar data at the smaller spatiotemporal scales. The model predictions are then found to fit the second moment statistics of the gauge data reasonably well at these scales without any further adjustment.
Modelling in Primary School: Constructing Conceptual Models and Making Sense of Fractions
Shahbari, Juhaina Awawdeh; Peled, Irit
2017-01-01
This article describes sixth-grade students' engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students…
A fractional motion diffusion model for grading pediatric brain tumors.
Karaman, M Muge; Wang, He; Sui, Yi; Engelhard, Herbert H; Li, Yuhua; Zhou, Xiaohong Joe
2016-01-01
To demonstrate the feasibility of a novel fractional motion (FM) diffusion model for distinguishing low- versus high-grade pediatric brain tumors; and to investigate its possible advantage over apparent diffusion coefficient (ADC) and/or a previously reported continuous-time random-walk (CTRW) diffusion model. With approval from the institutional review board and written informed consents from the legal guardians of all participating patients, this study involved 70 children with histopathologically-proven brain tumors (30 low-grade and 40 high-grade). Multi- b -value diffusion images were acquired and analyzed using the FM, CTRW, and mono-exponential diffusion models. The FM parameters, D fm , φ , ψ (non-Gaussian diffusion statistical measures), and the CTRW parameters, D m , α , β (non-Gaussian temporal and spatial diffusion heterogeneity measures) were compared between the low- and high-grade tumor groups by using a Mann-Whitney-Wilcoxon U test. The performance of the FM model for differentiating between low- and high-grade tumors was evaluated and compared with that of the CTRW and the mono-exponential models using a receiver operating characteristic (ROC) analysis. The FM parameters were significantly lower ( p < 0.0001) in the high-grade ( D fm : 0.81 ± 0.26, φ : 1.40 ± 0.10, ψ : 0.42 ± 0.11) than in the low-grade ( D fm : 1.52 ± 0.52, φ : 1.64 ± 0.13, ψ : 0.67 ± 0.13) tumor groups. The ROC analysis showed that the FM parameters offered better specificity (88% versus 73%), sensitivity (90% versus 82%), accuracy (88% versus 78%), and area under the curve (AUC, 93% versus 80%) in discriminating tumor malignancy compared to the conventional ADC. The performance of the FM model was similar to that of the CTRW model. Similar to the CTRW model, the FM model can improve differentiation between low- and high-grade pediatric brain tumors over ADC.
Fractional calculus model of articular cartilage based on experimental stress-relaxation
Smyth, P. A.; Green, I.
2015-05-01
Articular cartilage is a unique substance that protects joints from damage and wear. Many decades of research have led to detailed biphasic and triphasic models for the intricate structure and behavior of cartilage. However, the models contain many assumptions on boundary conditions, permeability, viscosity, model size, loading, etc., that complicate the description of cartilage. For impact studies or biomimetic applications, cartilage can be studied phenomenologically to reduce modeling complexity. This work reports experimental results on the stress-relaxation of equine articular cartilage in unconfined loading. The response is described by a fractional calculus viscoelastic model, which gives storage and loss moduli as functions of frequency, rendering multiple advantages: (1) the fractional calculus model is robust, meaning that fewer constants are needed to accurately capture a wide spectrum of viscoelastic behavior compared to other viscoelastic models (e.g., Prony series), (2) in the special case where the fractional derivative is 1/2, it is shown that there is a straightforward time-domain representation, (3) the eigenvalue problem is simplified in subsequent dynamic studies, and (4) cartilage stress-relaxation can be described with as few as three constants, giving an advantage for large-scale dynamic studies that account for joint motion or impact. Moreover, the resulting storage and loss moduli can quantify healthy, damaged, or cultured cartilage, as well as artificial joints. The proposed characterization is suited for high-level analysis of multiphase materials, where the separate contribution of each phase is not desired. Potential uses of this analysis include biomimetic dampers and bearings, or artificial joints where the effective stiffness and damping are fundamental parameters.
Energy Technology Data Exchange (ETDEWEB)
Ludden, J.N.; Thompson, G.; Bryan, W.B.; Frey, F.A.
1980-08-10
Ferrobasalts from DSDP sites 214 and 216 on the Ninetyeast Ridge are characterized by high absolute iron (FeO>12.9 wt %), FeO/MgO>1.9, and TiO/sub 2/>2.0 wt %. Their trace element abundances indicate a tholeiitic affinity; however, they are distinct from midocean ridge incompatible element-depleted tholeiites owing to higher contents of Ba, Zr, and Sr and flat to slightly light-REE-enriched, chondrite-normalized REE patterns. Calculations using major and trace element abundances and phase compositions are generally consistent with a model relating most major elements and phase compositions in site 214 and 216 ferrobasalts by fractionation of clinopyroxene and plagio-class. However, some incompatible element abundances for site 216 basalts are not consistent with the fractional crystallization models. Baslats from site 214 can be related to andesitic rocks from the same site by fractionating clinopyroxene, plagioclase and titanomagnetite. Site 254 basalts, at the southern end of the Ninetyeast Ridge, and island tholeiites in the southern Indian Ocean (Amsterdam-St. Paul or Kerguelen-Heard volcanic provinces) possibly represent the most recent activity associated with a hot spot forming the Ninetyeast Ridge. These incompatible-element-enriched tholeiites have major element compositions consistent with those expected for a parental liquid for the site 214 and 216 ferrobasalts. However, differences in the trace element contents of the basalts from the Ninetyeast Ridge sites are not consistent with simple fractional crystallization derivation but require either a complex melting model or a heterogeneous mantle source.
Directory of Open Access Journals (Sweden)
Luciano Mescia
2017-11-01
Full Text Available Electromagnetic fields are involved in several therapeutic and diagnostic applications such as hyperthermia and electroporation. For these applications, pulsed electric fields (PEFs and transient phenomena are playing a key role for understanding the biological response due to the exposure to non-ionizing wideband pulses. To this end, the PEF propagation in the six-layered planar structure modeling the human head has been studied. The electromagnetic field and the specific absorption rate (SAR have been calculated through an accurate finite-difference time-domain (FDTD dispersive modeling based on the fractional derivative operator. The temperature rise inside the tissues due to the electromagnetic field exposure has been evaluated using both the non-thermoregulated and thermoregulated Gagge’s two-node models. Moreover, additional parametric studies have been carried out with the aim to investigate the thermal response by changing the amplitude and duration of the electric pulses.
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).
Energy Technology Data Exchange (ETDEWEB)
Tambone, Fulvia, E-mail: fulvia.tambone@unimi.it; Terruzzi, Laura; Scaglia, Barbara; Adani, Fabrizio
2015-01-15
Highlights: • Anaerobic digestion leads to the production of a biologically stable digestate. • Solid–liquid separation produces a solid fraction having high fertilizer value. • Composting process shows low biological activity due to high biological stability of digestate. • Solid digestate fraction can be composted in a short time or used directly as organic fertilizer. - Abstract: The aim of this paper was to assess the characteristics of the solid fractions (SF) obtained by mechanical separation of digestate, their compostability and compost quality. To do so, the SF of digestates obtained from anaerobic digestion of pig slurry, energy crops and agro-industrial residues were sampled in five plants located in Northern Italy. Results obtained indicated that anaerobic digestion by itself promoted the high biological stability of biomasses with a Potential Dynamic Respiration Index (PDRI) close to 1000 mgO{sub 2} kg V S{sup −1} h{sup −1}. Subsequent composting of digestates, with an added bulking agent, did not give remarkably different results, and led only to a slight modification of the characteristics of the initial non-composted mixtures; the composts obtained fully respected the legal limits for high quality compost. Chemical studies of organic matter composition of the biomasses by using CP MAS {sup 13}C NMR, indicated that the compost was composed of a high relative content of O-alkyl-C (71.47% of total C) (cellulose and hemicelluloses) and a low alkyl-C (12.42%) (i.e. volatile fatty acids, steroid-like molecules, aliphatic biopolymers and proteins)
International Nuclear Information System (INIS)
Tambone, Fulvia; Terruzzi, Laura; Scaglia, Barbara; Adani, Fabrizio
2015-01-01
Highlights: • Anaerobic digestion leads to the production of a biologically stable digestate. • Solid–liquid separation produces a solid fraction having high fertilizer value. • Composting process shows low biological activity due to high biological stability of digestate. • Solid digestate fraction can be composted in a short time or used directly as organic fertilizer. - Abstract: The aim of this paper was to assess the characteristics of the solid fractions (SF) obtained by mechanical separation of digestate, their compostability and compost quality. To do so, the SF of digestates obtained from anaerobic digestion of pig slurry, energy crops and agro-industrial residues were sampled in five plants located in Northern Italy. Results obtained indicated that anaerobic digestion by itself promoted the high biological stability of biomasses with a Potential Dynamic Respiration Index (PDRI) close to 1000 mgO 2 kg V S −1 h −1 . Subsequent composting of digestates, with an added bulking agent, did not give remarkably different results, and led only to a slight modification of the characteristics of the initial non-composted mixtures; the composts obtained fully respected the legal limits for high quality compost. Chemical studies of organic matter composition of the biomasses by using CP MAS 13 C NMR, indicated that the compost was composed of a high relative content of O-alkyl-C (71.47% of total C) (cellulose and hemicelluloses) and a low alkyl-C (12.42%) (i.e. volatile fatty acids, steroid-like molecules, aliphatic biopolymers and proteins)
International Nuclear Information System (INIS)
Yang, Xiao-Jun; Srivastava, H.M.; He, Ji-Huan; Baleanu, Dumitru
2013-01-01
In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.
Grazzini, Giuliano; Ceccarelli, Anna; Calteri, Deanna; Catalano, Liviana; Calizzani, Gabriele; Cicchetti, Americo
2013-09-01
In Italy, the financial reimbursement for labile blood components exchanged between Regions is regulated by national tariffs defined in 1991 and updated in 1993-2003. Over the last five years, the need for establishing standard costs of healthcare services has arisen critically. In this perspective, the present study is aimed at defining both the costs of production of blood components and the related prices, as well as the prices of plasma-derived medicinal products obtained by national plasma, to be used for interregional financial reimbursement. In order to analyse the costs of production of blood components, 12 out 318 blood establishments were selected in 8 Italian Regions. For each step of the production process, driving costs were identified and production costs were. To define the costs of plasma-derived medicinal products obtained by national plasma, industrial costs currently sustained by National Health Service for contract fractionation were taken into account. The production costs of plasma-derived medicinal products obtained from national plasma showed a huge variability among blood establishments, which was much lower after standardization. The new suggested plasma tariffs were quite similar to those currently in force. Comparing the overall costs theoretically sustained by the National Health Service for plasma-derived medicinal products obtained from national plasma to current commercial costs, demonstrates that the national blood system could gain a 10% cost saving if it were able to produce plasma for fractionation within the standard costs defined in this study. Achieving national self-sufficiency through the production of plasma-derived medicinal products from national plasma, is a strategic goal of the National Health Service which must comply not only with quality, safety and availability requirements but also with the increasingly pressing need for economic sustainability.
de Jesus Pereira, Nathália Cristina; Régis, Wiliam César Bento; Costa, Lourena Emanuele; de Oliveira, Jamil Silvano; da Silva, Alanna Gomes; Martins, Vivian Tamietti; Duarte, Mariana Costa; de Souza, José Roberto Rodrigues; Lage, Paula Sousa; Schneider, Mônica Santos; Melo, Maria Norma; Soto, Manuel; Soares, Sandra Aguiar; Tavares, Carlos Alberto Pereira; Chávez-Fumagalli, Miguel Angel; Coelho, Eduardo Antonio Ferraz
2015-06-01
The development of effective prophylactic strategies to prevent leishmaniasis has become a high priority. No less important than the choice of an antigen, the association of an appropriate adjuvant is necessary to achieve a successful vaccination, as the majority of the tested antigens contain limited immunogenic properties, and need to be supplemented with immune response adjuvants in order to boost their immunogenicity. However, few effective adjuvants that can be used against leishmaniasis exist on the market today; therefore, it is possible to speculate that the research aiming to identify new adjuvants could be considered relevant. Recently, Agaricus blazei extracts have proved to be useful in enhancing the immune response to DNA vaccines against some diseases. This was based on the Th1 adjuvant activity of the polysaccharide-rich fractions from this mushroom. In this context, the present study evaluated purified fractions derived from Agaricus blazei as Th1 adjuvants through in vitro assays of their immune stimulation of spleen cells derived from naive BALB/c mice. Two of the tested six fractions (namely F2 and F4) were characterized as polysaccharide-rich fractions, and were able to induce high levels of IFN-γ, and low levels of IL-4 and IL-10 in the spleen cells. The efficacy of adjuvant action against L. infantum was evaluated in BALB/c mice, with these fractions being administered together with a recombinant antigen, LiHyp1, which was previously evaluated as a vaccine candidate, associated with saponin, against visceral leishmaniasis (VL). The associations between LiHyp1/F2 and LiHyp1/F4 were able to induce an in vivo Th1 response, which was primed by high levels of IFN-γ, IL-12, and GM-CSF, by low levels of IL-4 and IL-10; as well as by a predominance of IgG2a antibodies in the vaccinated animals. After infection, the immune profile was maintained, and the vaccines proved to be effective against L. infantum. The immune stimulatory effects in the
Numerically pricing American options under the generalized mixed fractional Brownian motion model
Chen, Wenting; Yan, Bowen; Lian, Guanghua; Zhang, Ying
2016-06-01
In this paper, we introduce a robust numerical method, based on the upwind scheme, for the pricing of American puts under the generalized mixed fractional Brownian motion (GMFBM) model. By using portfolio analysis and applying the Wick-Itô formula, a partial differential equation (PDE) governing the prices of vanilla options under the GMFBM is successfully derived for the first time. Based on this, we formulate the pricing of American puts under the current model as a linear complementarity problem (LCP). Unlike the classical Black-Scholes (B-S) model or the generalized B-S model discussed in Cen and Le (2011), the newly obtained LCP under the GMFBM model is difficult to be solved accurately because of the numerical instability which results from the degeneration of the governing PDE as time approaches zero. To overcome this difficulty, a numerical approach based on the upwind scheme is adopted. It is shown that the coefficient matrix of the current method is an M-matrix, which ensures its stability in the maximum-norm sense. Remarkably, we have managed to provide a sharp theoretic error estimate for the current method, which is further verified numerically. The results of various numerical experiments also suggest that this new approach is quite accurate, and can be easily extended to price other types of financial derivatives with an American-style exercise feature under the GMFBM model.
Linear-quadratic model underestimates sparing effect of small doses per fraction in rat spinal cord
International Nuclear Information System (INIS)
Shun Wong, C.; Toronto University; Minkin, S.; Hill, R.P.; Toronto University
1993-01-01
The application of the linear-quadratic (LQ) model to describe iso-effective fractionation schedules for dose fraction sizes less than 2 Gy has been controversial. Experiments are described in which the effect of daily fractionated irradiation given with a wide range of fraction sizes was assessed in rat cervical spine cord. The first group of rats was given doses in 1, 2, 4, 8 and 40 fractions/day. The second group received 3 initial 'top-up'doses of 9 Gy given once daily, representing 3/4 tolerance, followed by doses in 1, 2, 10, 20, 30 and 40 fractions/day. The fractionated portion of the irradiation schedule therefore constituted only the final quarter of the tolerance dose. The endpoint of the experiments was paralysis of forelimbs secondary to white matter necrosis. Direct analysis of data from experiments with full course fractionation up to 40 fractions/day (25.0-1.98 Gy/fraction) indicated consistency with the LQ model yielding an α/β value of 2.41 Gy. Analysis of data from experiments in which the 3 'top-up' doses were followed by up to 10 fractions (10.0-1.64 Gy/fraction) gave an α/β value of 3.41 Gy. However, data from 'top-up' experiments with 20, 30 and 40 fractions (1.60-0.55 Gy/fraction) were inconsistent with LQ model and gave a very small α/β of 0.48 Gy. It is concluded that LQ model based on data from large doses/fraction underestimates the sparing effect of small doses/fraction, provided sufficient time is allowed between each fraction for repair of sublethal damage. (author). 28 refs., 5 figs., 1 tab
Tcp and NTCP radiobiological models: conventional and hypo fractionated treatments in radiotherapy
Energy Technology Data Exchange (ETDEWEB)
Astudillo V, A.; Paredes G, L. [ININ, Carretera Mexico-Toluca s/n, Ocoyoacac 52750, Estado de Mexico (Mexico); Resendiz G, G.; Posadas V, A. [Hospital Angeles Lomas, Av. Vialidad de la Barranca s/n, Col. Valle de las Palmas, 52763 Huixquilucan de Degallado, Estado de Mexico (Mexico); Mitsoura, E. [Universidad Autonoma del Estado de Mexico, Facultad de Medicina, Paseo Tollocan, Esq. Jesus Carranza s/n, Col. Moderna de la Cruz, 50180 Toluca, Estado de Mexico (Mexico); Rodriguez L, A.; Flores C, J. M., E-mail: armando.astudillo@inin.gob.mx [Hospital Medica Sur, Puente de Piedra 150, Col. Toriello Guerra, 14050 Tlalpan, Mexico D. F. (Mexico)
2015-10-15
The hypo and conventional fractionated schedules performance were compared in terms of the tumor control and the normal tissue complications. From the records of ten patients, treated for adenocarcinoma and without mastectomy, the dose-volume histogram was used. Using radiobiological models the probabilities for tumor control and normal tissue complications were calculated. For both schedules the tumor control was approximately the same. However, the damage in the normal tissue was larger in conventional fractionated schedule. This is important because patients assistance time to their fractions (15 fractions/25 fractions) can be optimized. Thus, the hypo fractionated schedule has suitable characteristics to be implemented. (Author)
Tcp and NTCP radiobiological models: conventional and hypo fractionated treatments in radiotherapy
International Nuclear Information System (INIS)
Astudillo V, A.; Paredes G, L.; Resendiz G, G.; Posadas V, A.; Mitsoura, E.; Rodriguez L, A.; Flores C, J. M.
2015-10-01
The hypo and conventional fractionated schedules performance were compared in terms of the tumor control and the normal tissue complications. From the records of ten patients, treated for adenocarcinoma and without mastectomy, the dose-volume histogram was used. Using radiobiological models the probabilities for tumor control and normal tissue complications were calculated. For both schedules the tumor control was approximately the same. However, the damage in the normal tissue was larger in conventional fractionated schedule. This is important because patients assistance time to their fractions (15 fractions/25 fractions) can be optimized. Thus, the hypo fractionated schedule has suitable characteristics to be implemented. (Author)
A generic interference model for uplink OFDMA networks with fractional frequency reuse
Tabassum, Hina
2014-03-01
Fractional frequency reuse (FFR) has emerged as a viable solution to coordinate and mitigate cochannel interference (CCI) in orthogonal frequency-division multiple-access (OFDMA)-based wireless cellular networks. The incurred CCI in cellular networks with FFR is highly uncertain and varies as a function of various design parameters that include the user scheduling schemes, the transmit power distribution among multiple allocated subcarriers, the partitioning of the cellular region into cell-edge and cell-center zones, the allocation of spectrum within each zone, and the channel reuse factors. To this end, this paper derives a generic analytical model for uplink CCI in multicarrier OFDMA networks with FFR. The derived expressions capture several network design parameters and are applicable to any composite fading-channel models. The accuracy of the derivations is verified via Monte Carlo simulations. Moreover, their usefulness is demonstrated by obtaining closed-form expressions for the Rayleigh fading-channel model and by evaluating important network performance metrics such as ergodic capacity. Numerical results provide useful system design guidelines and highlight the trade-offs associated with the deployment of FFR schemes in OFDMA-based networks. © 2013 IEEE.
A generic interference model for uplink OFDMA networks with fractional frequency reuse
Tabassum, Hina; Dawy, Zaher; Alouini, Mohamed-Slim; Yilmaz, Ferkan
2014-01-01
Fractional frequency reuse (FFR) has emerged as a viable solution to coordinate and mitigate cochannel interference (CCI) in orthogonal frequency-division multiple-access (OFDMA)-based wireless cellular networks. The incurred CCI in cellular networks with FFR is highly uncertain and varies as a function of various design parameters that include the user scheduling schemes, the transmit power distribution among multiple allocated subcarriers, the partitioning of the cellular region into cell-edge and cell-center zones, the allocation of spectrum within each zone, and the channel reuse factors. To this end, this paper derives a generic analytical model for uplink CCI in multicarrier OFDMA networks with FFR. The derived expressions capture several network design parameters and are applicable to any composite fading-channel models. The accuracy of the derivations is verified via Monte Carlo simulations. Moreover, their usefulness is demonstrated by obtaining closed-form expressions for the Rayleigh fading-channel model and by evaluating important network performance metrics such as ergodic capacity. Numerical results provide useful system design guidelines and highlight the trade-offs associated with the deployment of FFR schemes in OFDMA-based networks. © 2013 IEEE.
Mutagenicity of basic fractions derived from lamb and beef cooked by common household methods.
Barrington, P J; Baker, R S; Truswell, A S; Bonin, A M; Ryan, A J; Paulin, A P
1990-03-01
Mutagen production was examined in lamb and beef in relation to certain common household cooking methods. Mutagenicity was assessed, after extraction of the basic fraction of cooked meat samples, using Salmonella typhimurium strain TA1538 with added rat-liver S-9 homogenate. Little or no mutagenicity was found in barbecued lamb chops, in microwave-cooked lamb chops, sirloin steak, leg of lamb, or rolled beef loaf, in roasted leg of lamb or rolled beef loaf, in stewed blade steak or in boiled chuck steak. However, the basic fraction from well-done, edible fried or grilled meat contained mutagenic activity equivalent to approximately 30,000 TA1538 revertants/100 g cooked meat. It was found tht the mutagenic activity of grilled lamb chops, sirloin and rump steaks was directly related to the average surface temperatures attained during cooking. Use of butter as a frying medium was particularly associated with higher mutagenicity in meat samples. Fried meats (rump and fillet steaks) generally yielded higher mutagenic activity than did grilled meats (rump steak, lamb chops) at comparable temperatures of the cooking medium. Using similar cooking procedures, lamb did not differ markedly from beef in mutagenic activity.
Best Approximation of the Fractional Semi-Derivative Operator by Exponential Series
Directory of Open Access Journals (Sweden)
Vladimir D. Zakharchenko
2018-01-01
Full Text Available A significant reduction in the time required to obtain an estimate of the mean frequency of the spectrum of Doppler signals when seeking to measure the instantaneous velocity of dangerous near-Earth cosmic objects (NEO is an important task being developed to counter the threat from asteroids. Spectral analysis methods have shown that the coordinate of the centroid of the Doppler signal spectrum can be found by using operations in the time domain without spectral processing. At the same time, an increase in the speed of resolving the algorithm for estimating the mean frequency of the spectrum is achieved by using fractional differentiation without spectral processing. Thus, an accurate estimate of location of the centroid for the spectrum of Doppler signals can be obtained in the time domain as the signal arrives. This paper considers the implementation of a fractional-differentiating filter of the order of ½ by a set of automation astatic transfer elements, which greatly simplifies practical implementation. Real technical devices have the ultimate time delay, albeit small in comparison with the duration of the signal. As a result, the real filter will process the signal with some error. In accordance with this, this paper introduces and uses the concept of a “pre-derivative” of ½ of magnitude. An optimal algorithm for realizing the structure of the filter is proposed based on the criterion of minimum mean square error. Relations are obtained for the quadrature coefficients that determine the structure of the filter.
Directory of Open Access Journals (Sweden)
Qiang Gao
2015-12-01
Full Text Available Aiming at balancing and positioning of a new electro-hydraulic servo system with iso-actuation configuration, an extended state observer–based fractional order proportional–integral–derivative controller is proposed in this study. To meet the lightweight requirements of heavy barrel weapons with large diameters, an electro-hydraulic servo system with a three-chamber hydraulic cylinder is especially designed. In the electro-hydraulic servo system, the balance chamber of the hydraulic cylinder is used to realize active balancing of the unbalanced forces, while the driving chambers consisting of the upper and lower chambers are adopted for barrel positioning and dynamic compensation of external disturbances. Compared with conventional proportional–integral–derivative controllers, the fractional order proportional–integral–derivative possesses another two adjustable parameters by expanding integer order to arbitrary order calculus, resulting in more flexibility and stronger robustness of the control system. To better compensate for strong external disturbances and system nonlinearities, the extended state observer strategy is further introduced to the fractional order proportional–integral–derivative control system. Numerical simulation and bench test indicate that the extended state observer–based fractional order proportional–integral–derivative significantly outperforms proportional–integral–derivative and fractional order proportional–integral–derivative control systems with better control accuracy and higher system robustness, well demonstrating the feasibility and effectiveness of the proposed extended state observer–based fractional order proportional–integral–derivative control strategy.
Oliveira, M.C.; Di Ceglie, I.; Arntz, O.J.; Berg, W.B. van den; Hoogen, F.H.J. van den; Ferreira, A.V.; Lent, P.L.E.M. van; Loo, F.A.J. van de
2017-01-01
The general consensus is that milk promotes bone growth and density because is a source of calcium and contains components that enhance intestinal calcium uptake or directly affect bone metabolism. In this study, we investigated the effect of bovine-derived milk 100,000 g pellet (P100), which
Slip effects on a generalized Burgers’ fluid flow between two side walls with fractional derivative
Directory of Open Access Journals (Sweden)
Shihao Han
2016-01-01
Full Text Available This paper presents a research for the 3D flow of a generalized Burgers’ fluid between two side walls generated by an exponential accelerating plate and a constant pressure gradient, where the no-slip assumption between the exponential accelerating plate and the Burgers’ fluid is no longer valid. The governing equations of the generalized Burgers’ fluid flow are established by using the fractional calculus approach. Exact analytic solutions for the 3D flow are established by employing the Laplace transform and the finite Fourier sine transform. Furthermore, some 3D and 2D figures for the fluid velocity and shear stress are plotted to analyze and discuss the effects of various parameters.
Wang, Zhen; Wang, Xiaohong; Li, Yuxia; Huang, Xia
2017-12-01
In this paper, the problems of stability and Hopf bifurcation in a class of fractional-order complex-valued single neuron model with time delay are addressed. With the help of the stability theory of fractional-order differential equations and Laplace transforms, several new sufficient conditions, which ensure the stability of the system are derived. Taking the time delay as the bifurcation parameter, Hopf bifurcation is investigated and the critical value of the time delay for the occurrence of Hopf bifurcation is determined. Finally, two representative numerical examples are given to show the effectiveness of the theoretical results.
The fractional diffusion limit of a kinetic model with biochemical pathway
Perthame, Benoît; Sun, Weiran; Tang, Min
2018-06-01
Kinetic-transport equations that take into account the intracellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathematical studies have shown their interest and their relations to more standard models. Macroscopic equations of Keller-Segel type have been derived using parabolic scaling. Due to the randomness of receptor methylation or intracellular chemical reactions, noise occurs in the signaling pathways and affects the tumbling rate. Then comes the question to understand the role of an internal noise on the behavior of the full population. In this paper we consider a kinetic model for chemotaxis which includes biochemical pathway with noises. We show that under proper scaling and conditions on the tumbling frequency as well as the form of noise, fractional diffusion can arise in the macroscopic limits of the kinetic equation. This gives a new mathematical theory about how long jumps can be due to the internal noise of the bacteria.
Fractional Response Models - A Replication Exercise of Papke and Wooldridge (1996
Directory of Open Access Journals (Sweden)
Harald Oberhofer
2012-09-01
Full Text Available This paper replicates the estimates of a fractional response model for share data reported in the seminal paper of Leslie E. Papke and Jeffrey M. Wooldridge published in the Journal of Applied Econometrics 11(6, 1996, pp.619-632. We have been able to replicate all of the reported estimation results concerning the determinants of employee participation rates in 401(k pension plans using the standard routines provided in Stata. As an alternative, we estimate a two-part model that is capable of coping with the excessive number of boundary values equalling one in the data. The estimated marginal effects are similar to those derived in the paper. A small-scale Monte Carlo simulation exercise suggests that the RESET tests proposed by Papke and Wooldridge in their robust form are useful for detecting neglected non-linearities in small samples.
International Nuclear Information System (INIS)
Jumarie, Guy
2006-01-01
The (complex-valued) Brownian motion of order n is defined as the limit of a random walk on the complex roots of the unity. Real-valued fractional noises are obtained as fractional derivatives of the Gaussian white noise (or order two). Here one combines these two approaches and one considers the new class of fractional noises obtained as fractional derivative of the complex-valued Brownian motion of order n. The key of the approach is the relation between differential and fractional differential provided by the fractional Taylor's series of analytic function f(z+h)=E α (h α D z α ).f(z), where E α is the Mittag-Leffler function on the one hand, and the generalized Maruyama's notation, on the other hand. Some questions are revisited such as the definition of fractional Brownian motion as integral w.r.t. (dt) α , and the exponential growth equation driven by fractional Brownian motion, to which a new solution is proposed. As a first illustrative example of application, in mathematical finance, one proposes a new approach to the optimal management of a stochastic portfolio of fractional order via the Lagrange variational technique applied to the state moment dynamical equations. In the second example, one deals with non-random Lagrangian mechanics of fractional order. The last example proposes a new approach to fractional stochastic mechanics, and the solution so obtained gives rise to the question as to whether physical systems would not have their own internal random times
Generalized relations among N-dimensional Coulomb Green's functions using fractional derivatives
International Nuclear Information System (INIS)
Blinder, S.M.; Pollock, E.L.
1989-01-01
Hostler [J. Math. Phys. 11, 2966 (1970)] has shown that Coulomb Green's functions of different dimensionality N are related by G (N+2) =OG (N) , where O is a first-order derivative operator in the variables x and y. Thus all the even-dimensional functions are connected, as are analogously the odd-dimensional functions. It is shown that the operations of functional differentiation and integration can further connect the even- to the odd-dimensional functions, so that Hostler's relation can be extended to give G (N+1) =O 1/2 G (N)
SU-E-T-429: Uncertainties of Cell Surviving Fractions Derived From Tumor-Volume Variation Curves
International Nuclear Information System (INIS)
Chvetsov, A
2014-01-01
Purpose: To evaluate uncertainties of cell surviving fraction reconstructed from tumor-volume variation curves during radiation therapy using sensitivity analysis based on linear perturbation theory. Methods: The time dependent tumor-volume functions V(t) have been calculated using a twolevel cell population model which is based on the separation of entire tumor cell population in two subpopulations: oxygenated viable and lethally damaged cells. The sensitivity function is defined as S(t)=[δV(t)/V(t)]/[δx/x] where δV(t)/V(t) is the time dependent relative variation of the volume V(t) and δx/x is the relative variation of the radiobiological parameter x. The sensitivity analysis was performed using direct perturbation method where the radiobiological parameter x was changed by a certain error and the tumor-volume was recalculated to evaluate the corresponding tumor-volume variation. Tumor volume variation curves and sensitivity functions have been computed for different values of cell surviving fractions from the practically important interval S 2 =0.1-0.7 using the two-level cell population model. Results: The sensitivity functions of tumor-volume to cell surviving fractions achieved a relatively large value of 2.7 for S 2 =0.7 and then approached zero as S 2 is approaching zero Assuming a systematic error of 3-4% we obtain that the relative error in S 2 is less that 20% in the range S2=0.4-0.7. This Resultis important because the large values of S 2 are associated with poor treatment outcome should be measured with relatively small uncertainties. For the very small values of S2<0.3, the relative error can be larger than 20%; however, the absolute error does not increase significantly. Conclusion: Tumor-volume curves measured during radiotherapy can be used for evaluation of cell surviving fractions usually observed in radiation therapy with conventional fractionation
Tambone, Fulvia; Terruzzi, Laura; Scaglia, Barbara; Adani, Fabrizio
2015-01-01
The aim of this paper was to assess the characteristics of the solid fractions (SF) obtained by mechanical separation of digestate, their compostability and compost quality. To do so, the SF of digestates obtained from anaerobic digestion of pig slurry, energy crops and agro-industrial residues were sampled in five plants located in Northern Italy. Results obtained indicated that anaerobic digestion by itself promoted the high biological stability of biomasses with a Potential Dynamic Respiration Index (PDRI) close to 1000 mgO2 kg V S(-1)h(-1). Subsequent composting of digestates, with an added bulking agent, did not give remarkably different results, and led only to a slight modification of the characteristics of the initial non-composted mixtures; the composts obtained fully respected the legal limits for high quality compost. Chemical studies of organic matter composition of the biomasses by using CP MAS (13)C NMR, indicated that the compost was composed of a high relative content of O-alkyl-C (71.47% of total C) (cellulose and hemicelluloses) and a low alkyl-C (12.42%) (i.e. volatile fatty acids, steroid-like molecules, aliphatic biopolymers and proteins). Copyright © 2014 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Niccolò Pampuro
2017-11-01
Full Text Available The phytotoxicity of four different composts obtained from pig slurry solid fraction composted by itself (SSFC and mixed with sawdust (SC, woodchips (WCC and wheat straw (WSC was tested with bioassay methods. For each compost type, the effect of water extracts of compost on seed germination and primary root growth of cress (Lepidium Sativum L. was investigated. Composts were also chemically analysed for total nitrogen, ammonium, electrical conductivity and heavy metal (Cu and Zn. The chemicals were correlated to phytotoxicity indices. The mean values of the germination index (GI obtained were 160.7, 187.9, 200.9 and 264.4 for WSC, WCC, SC and SSFC, respectively. Growth index (GrI ranged from the 229.4%, the highest value, for SSFC, followed by 201.9% for SC, and 193.1% for WCC, to the lowest value, 121.4%, for WSC. Electrical conductivity showed a significant and negative correlation with relative seed germination at the 50% and 75% concentrations. A strong positive correlation was found for water-extractable Cu with relative root growth and germination index at the 10% concentration. Water-extractable Zn showed a significant positive correlation with relative root growth and GI at the 10% concentration. These results highlighted that the four composts could be used for organic pellet production and subsequently distributed as a soil amendment with positive effects on seed germination and plant growth (GI > 80%.
International Nuclear Information System (INIS)
Hommer, E.
1981-01-01
An attempt has been made to develop formulas to determine cardiac pressures in an undisturbed flow in patients without valvular or shunt diseases. These are based entirely on the results of left ventricular ejection fraction rates, permitting pressure analysis of several compartments at the same tine. According to BORER et al. they also enable determination of left ventricular 'Functional Reserve' after bycycle exercise as well as left ventricular 'Relaxation Reserve'. They support the views of NYHA in determining the grades of cardiac insufficiency proving the system- and low-pressure participation. A single formula for pulmonary flow can determine the pulmonary arterial pressure. The left ventricular enddiastolic pressure can also be exclusively calculated by values of left ventricular functions, thus both formulas may be used in disorders of the mitral valves. The possibility to calculate pressures of all the compartments of the heart from left ventricular ejection rate shows, that in undisturbed flow global heart function depends on left ventricular function. Therefore the mutual dependence of these formulas presents an intercompartimental pressure regulation of the heart through pulmonary flow and pulmonary vascular pressure, which leaves an aspect of autonomous cardiac regulation open to discussion. (orig.) [de
Li, S; Tang, X; Peng, L; Luo, Y; Dong, R; Liu, J
2015-05-01
To review the literature on the diagnostic accuracy of CT-derived fractional flow reserve (FFRCT) for the evaluation of myocardial ischaemia in patients with suspected or known coronary artery disease, with invasive fractional flow reserve (FFR) as the reference standard. A PubMed, EMBASE, and Cochrane cross-search was performed. The pooled diagnostic accuracy of FFRCT, with FFR as the reference standard, was primarily analysed, and then compared with that of CT angiography (CTA). The thresholds to diagnose ischaemia were FFR ≤0.80 or CTA ≥50% stenosis. Data extraction, synthesis, and statistical analysis were performed by standard meta-analysis methods. Three multicentre studies (NXT Trial, DISCOVER-FLOW study and DeFACTO study) were included, examining 609 patients and 1050 vessels. The pooled sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), positive likelihood ratio (LR+), negative likelihood ratio (LR-), and diagnostic odds ratio (DOR) for FFRCT were 89% (85-93%), 71% (65-75%), 70% (65-75%), 90% (85-93%), 3.31 (1.79-6.14), 0.16 (0.11-0.23), and 21.21 (9.15-49.15) at the patient-level, and 83% (78-63%), 78% (75-81%), 61% (56-65%), 92% (89-90%), 4.02 (1.84-8.80), 0.22 (0.13-0.35), and 19.15 (5.73-63.93) at the vessel-level. At per-patient analysis, FFRCT has similar sensitivity but improved specificity, PPV, NPV, LR+, LR-, and DOR versus those of CTA. At per-vessel analysis, FFRCT had a slightly lower sensitivity, similar NPV, but improved specificity, PPV, LR+, LR-, and DOR compared with those of CTA. The area under the summary receiver operating characteristic curves for FFRCT was 0.8909 at patient-level and 0.8865 at vessel-level, versus 0.7402 for CTA at patient-level. FFRCT, which was associated with improved diagnostic accuracy versus CTA, is a viable alternative to FFR for detecting coronary ischaemic lesions. Copyright © 2015 The Royal College of Radiologists. Published by Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Li, S.; Tang, X.; Peng, L.; Luo, Y.; Dong, R.; Liu, J.
2015-01-01
Aim: To review the literature on the diagnostic accuracy of CT-derived fractional flow reserve (FFR CT ) for the evaluation of myocardial ischaemia in patients with suspected or known coronary artery disease, with invasive fractional flow reserve (FFR) as the reference standard. Materials and methods: A PubMed, EMBASE, and Cochrane cross-search was performed. The pooled diagnostic accuracy of FFR CT , with FFR as the reference standard, was primarily analysed, and then compared with that of CT angiography (CTA). The thresholds to diagnose ischaemia were FFR ≤0.80 or CTA ≥50% stenosis. Data extraction, synthesis, and statistical analysis were performed by standard meta-analysis methods. Results: Three multicentre studies (NXT Trial, DISCOVER-FLOW study and DeFACTO study) were included, examining 609 patients and 1050 vessels. The pooled sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), positive likelihood ratio (LR+), negative likelihood ratio (LR−), and diagnostic odds ratio (DOR) for FFR CT were 89% (85–93%), 71% (65–75%), 70% (65–75%), 90% (85–93%), 3.31 (1.79–6.14), 0.16 (0.11–0.23), and 21.21 (9.15–49.15) at the patient-level, and 83% (78–63%), 78% (75–81%), 61% (56–65%), 92% (89–90%), 4.02 (1.84–8.80), 0.22 (0.13–0.35), and 19.15 (5.73–63.93) at the vessel-level. At per-patient analysis, FFR CT has similar sensitivity but improved specificity, PPV, NPV, LR+, LR−, and DOR versus those of CTA. At per-vessel analysis, FFR CT had a slightly lower sensitivity, similar NPV, but improved specificity, PPV, LR+, LR−, and DOR compared with those of CTA. The area under the summary receiver operating characteristic curves for FFR CT was 0.8909 at patient-level and 0.8865 at vessel-level, versus 0.7402 for CTA at patient-level. Conclusions: FFR CT , which was associated with improved diagnostic accuracy versus CTA, is a viable alternative to FFR for detecting coronary ischaemic lesions
Energy Technology Data Exchange (ETDEWEB)
Fiorino, Claudio, E-mail: fiorino.claudio@hsr.it [Department of Medical Physics, San Raffaele Scientific Institute, Milan (Italy); Cozzarini, Cesare [Department of Radiotherapy, San Raffaele Scientific Institute, Milan (Italy); Rancati, Tiziana [Prostate Cancer Program, Fondazione Istituto di Ricovero e Cura a Carattere Scientifico Istituto Nazionale dei Tumori, Milan (Italy); Briganti, Alberto [Department of Urology, San Raffaele Scientific Institute, Milan (Italy); Cattaneo, Giovanni Mauro; Mangili, Paola [Department of Medical Physics, San Raffaele Scientific Institute, Milan (Italy); Di Muzio, Nadia Gisella [Department of Radiotherapy, San Raffaele Scientific Institute, Milan (Italy); Calandrino, Riccardo [Department of Medical Physics, San Raffaele Scientific Institute, Milan (Italy)
2014-12-01
Purpose: To fit urinary toxicity data of patients treated with postprostatectomy radiation therapy with the linear quadratic (LQ) model with/without introducing a time factor. Methods and Materials: Between 1993 and 2010, 1176 patients were treated with conventional fractionation (1.8 Gy per fraction, median 70.2 Gy, n=929) or hypofractionation (2.35-2.90 Gy per fraction, n=247). Data referred to 2004-2010 (when all schemes were in use, n=563; conventional fractionation: 316; hypofractionation: 247) were fitted as a logit function of biological equivalent dose (BED), according to the LQ model with/without including a time factor γ (fixing α/β = 5 Gy). The 3-year risks of severe urethral stenosis, incontinence, and hematuria were considered as endpoints. Best-fit parameters were derived, and the resulting BEDs were taken in multivariable backward logistic models, including relevant clinical variables, considering the whole population. Results: The 3-year incidences of severe stenosis, incontinence, and hematuria were, respectively, 6.6%, 4.8%, and 3.3% in the group treated in 2004-2010. The best-fitted α/β values were 0.81 Gy and 0.74 Gy for incontinence and hematuria, respectively, with the classic LQ formula. When fixing α/β = 5 Gy, best-fit values for γ were, respectively, 0.66 Gy/d and 0.85 Gy/d. Sensitivity analyses showed reasonable values for γ (0.6-1.0 Gy/d), with comparable goodness of fit for α/β values between 3.5 and 6.5 Gy. Likelihood ratio tests showed that the fits with/without including γ were equivalent. The resulting multivariable backward logistic models in the whole population included BED, pT4, and use of antihypertensives (area under the curve [AUC] = 0.72) for incontinence and BED, pT4, and year of surgery (AUC = 0.80) for hematuria. Stenosis data could not be fitted: a 4-variable model including only clinical factors (acute urinary toxicity, pT4, year of surgery, and use of antihypertensives) was suggested (AUC
International Nuclear Information System (INIS)
Fiorino, Claudio; Cozzarini, Cesare; Rancati, Tiziana; Briganti, Alberto; Cattaneo, Giovanni Mauro; Mangili, Paola; Di Muzio, Nadia Gisella; Calandrino, Riccardo
2014-01-01
Purpose: To fit urinary toxicity data of patients treated with postprostatectomy radiation therapy with the linear quadratic (LQ) model with/without introducing a time factor. Methods and Materials: Between 1993 and 2010, 1176 patients were treated with conventional fractionation (1.8 Gy per fraction, median 70.2 Gy, n=929) or hypofractionation (2.35-2.90 Gy per fraction, n=247). Data referred to 2004-2010 (when all schemes were in use, n=563; conventional fractionation: 316; hypofractionation: 247) were fitted as a logit function of biological equivalent dose (BED), according to the LQ model with/without including a time factor γ (fixing α/β = 5 Gy). The 3-year risks of severe urethral stenosis, incontinence, and hematuria were considered as endpoints. Best-fit parameters were derived, and the resulting BEDs were taken in multivariable backward logistic models, including relevant clinical variables, considering the whole population. Results: The 3-year incidences of severe stenosis, incontinence, and hematuria were, respectively, 6.6%, 4.8%, and 3.3% in the group treated in 2004-2010. The best-fitted α/β values were 0.81 Gy and 0.74 Gy for incontinence and hematuria, respectively, with the classic LQ formula. When fixing α/β = 5 Gy, best-fit values for γ were, respectively, 0.66 Gy/d and 0.85 Gy/d. Sensitivity analyses showed reasonable values for γ (0.6-1.0 Gy/d), with comparable goodness of fit for α/β values between 3.5 and 6.5 Gy. Likelihood ratio tests showed that the fits with/without including γ were equivalent. The resulting multivariable backward logistic models in the whole population included BED, pT4, and use of antihypertensives (area under the curve [AUC] = 0.72) for incontinence and BED, pT4, and year of surgery (AUC = 0.80) for hematuria. Stenosis data could not be fitted: a 4-variable model including only clinical factors (acute urinary toxicity, pT4, year of surgery, and use of antihypertensives) was suggested (AUC
Mittag-Leffler function for discrete fractional modelling
Directory of Open Access Journals (Sweden)
Guo-Cheng Wu
2016-01-01
Full Text Available From the difference equations on discrete time scales, this paper numerically investigates one discrete fractional difference equation in the Caputo delta’s sense which has an explicit solution in form of the discrete Mittag-Leffler function. The exact numerical values of the solutions are given in comparison with the truncated Mittag-Leffler function.
Beam shaping for conformal fractionated stereotactic radiotherapy: a modeling study
International Nuclear Information System (INIS)
Hacker, Fred L.; Kooy, Hanne M.; Bellerive, Marc R.; Killoran, Joseph H.; Leber, Zachary H.; Shrieve, Dennis C.; Tarbell, Nancy J.; Loeffler, Jay S.
1997-01-01
Purpose: The patient population treated with fractionated stereotactic radiotherapy (SRT) is significantly different than that treated with stereotactic radiosurgery (SRS). Generally, lesions treated with SRT are larger, less spherical, and located within critical regions of the central nervous system; hence, they offer new challenges to the treatment planner. Here a simple, cost effective, beam shaping system has been evaluated relative to both circular collimators and an ideal dynamically conforming system for effectiveness in providing conformal therapy for these lesions. Methods and Materials: We have modeled a simple system for conformal arc therapy using four independent jaws. The jaw positions and collimator angle are changed between arcs but held fixed for the duration of each arc. Eleven previously treated SRT cases have been replanned using this system. The rectangular jaw plans were then compared to the original treatment plans which used circular collimators. The plans were evaluated with respect to tissue sparing at 100%, 80%, 50%, and 20% of the prescription dose. A plan was also done for each tumor in which the beam aperture was continuously conformed to the beams eye view projection of the tumor. This was used as an ideal standard for conformal therapy in the absence of fluence modulation. Results: For tumors with a maximum extent of over 3.5 cm the rectangular jaw plans reduced the mean volume of healthy tissue involved at the prescription dose by 57% relative to the circular collimator plans. The ideal conformal plans offered no significant further improvement at the prescription dose. The relative advantage of the rectangular jaw plans decreased at lower isodoses so that at 20% of the prescription dose tissue involvement for the rectangular jaw plans was equivalent to that for the circular collimator plans. At these isodoses the ideal conformal plans gave substantially better tissue sparing. Conclusion: A simple and economical field shaping
LPV model for PV cell and fractional control of DC/DC converter for photovoltaic systems
Martínez González, Rubén; Bolea Monte, Yolanda; Grau Saldes, Antoni; Martínez García, Herminio
2011-01-01
This paper deals with the fractional modelling of a DC-DC converter, suitable in solar-powered electrical generation systems, and the design of a fractional controller for the aforementioned switching converter. A new model for PV cells is proposed in order to obtain a linear equation for V-I characteristic via scheduling dependence of temperature and irradiance. Due to the fractional nature of the ultracapacitors this kind of controller gives a suitable and good performance. Peer Reviewed
LPV model for PV cells and fractional control of DC/DC converter for photovoltaic systems
Martínez González, Rubén; Bolea Monte, Yolanda; Grau Saldes, Antoni; Martínez García, Herminio
2011-01-01
This paper deals with the fractional modelling of a DC-DC converter, suitable in solar-powered electrical generation systems, and the design of a fractional controller for the aforementioned switching converter. A new model for PV cells is proposed in order to obtain a linear equation for VI characteristic via scheduling dependence of temperature and irradiance. Due to the fractional nature of the ultracapacitors this kind of controller gives a suitable and good performance. Peer Rev...
A tracer diffusion model derived from microstructure
International Nuclear Information System (INIS)
Lehikoinen, Jarmo; Muurinen, Arto; Olin, Markus
2012-01-01
of reference, is shown to be given by the ratio of the effective diffusivity to the apparent diffusivity for an assumed non-interacting solute, such as tritiated water. Finally, the utility of the model and derivation of the model parameters are demonstrated with tracer diffusion data from the open literature for compacted bentonite. (authors)
Space-fractional model for the spreading of matter in heterogeneous porous media
International Nuclear Information System (INIS)
Krepysheva, N.; Neel, M.Ch.
2005-01-01
In very heterogeneous porous media (like the soil, or an aquifer, for instance), experimental results showed that mass transport sometimes does not obey Fourier's law. Continuous Time Random Walks in the form of L y Flights provide a small scale model for super diffusive spreading of a tracer plume, dissolved in a fluid, itself enclosed in a porous medium. In an infinite medium, the corresponding behavior of the concentration of solute is known to obey a variant of Fourier's law, with a Riesz-Feller operator in place of the Laplacian. Here we show that with some modifications the result extends to semi infinite media. A numerical method allowing for the simulation of fractional derivatives is adapted to semi infinite media, with special attention to convective terms, associated to a possibly non zero global trough flow. (authors)
Space-fractional model for the spreading of matter in heterogeneous porous media
Energy Technology Data Exchange (ETDEWEB)
Krepysheva, N. [Institut National de Recherches Agronomiques (INRA), UMRA Climat-Sol-Environnement, 84 - Avignon (France); Neel, M.Ch. [Universite d' Avignon, Faculte des Sciences, UMRA Climat-Sol-Environnement, 84 - Avignon (France)
2005-07-01
In very heterogeneous porous media (like the soil, or an aquifer, for instance), experimental results showed that mass transport sometimes does not obey Fourier's law. Continuous Time Random Walks in the form of L y Flights provide a small scale model for super diffusive spreading of a tracer plume, dissolved in a fluid, itself enclosed in a porous medium. In an infinite medium, the corresponding behavior of the concentration of solute is known to obey a variant of Fourier's law, with a Riesz-Feller operator in place of the Laplacian. Here we show that with some modifications the result extends to semi infinite media. A numerical method allowing for the simulation of fractional derivatives is adapted to semi infinite media, with special attention to convective terms, associated to a possibly non zero global trough flow. (authors)
Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru
2018-02-01
The mathematical model of breaking of non-linear dispersive water waves with memory effect is very important in mathematical physics. In the present article, we examine a novel fractional extension of the non-linear Fornberg-Whitham equation occurring in wave breaking. We consider the most recent theory of differentiation involving the non-singular kernel based on the extended Mittag-Leffler-type function to modify the Fornberg-Whitham equation. We examine the existence of the solution of the non-linear Fornberg-Whitham equation of fractional order. Further, we show the uniqueness of the solution. We obtain the numerical solution of the new arbitrary order model of the non-linear Fornberg-Whitham equation with the aid of the Laplace decomposition technique. The numerical outcomes are displayed in the form of graphs and tables. The results indicate that the Laplace decomposition algorithm is a very user-friendly and reliable scheme for handling such type of non-linear problems of fractional order.
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…
Saikia, Sangeeta; Mahanta, Charu Lata
2016-03-01
A comparative study was done on the health promoting and functional properties of the fibers obtained as by-products from six fruits viz., pomace of carambola (Averrhoa carambola L.) and pineapple (Ananas comosus L. Merr), peels of watermelon (Citrullus lanatus), Burmese grape (Baccurea sapida Muell. Arg) and Khasi mandarin orange (Citrus reticulata Blanco), and blossom of seeded banana (Musa balbisiana, ABB). Highest yield of fiber was obtained from Burmese grape peel (BGPL, 79.94 ± 0.41 g/100 g) and seeded banana blossom (BB 77.18 ± 0.20 g/100 g). The total dietary fiber content (TDF) was highest in fiber fraction derived from pineapple pomace (PNPM, 79.76 ± 0.42 g/100 g) and BGPL (67.27 ± 0.39 g/100 g). All the samples contained insoluble dietary fiber as the major fiber fraction. The fiber samples showed good water holding, oil holding and swelling capacities. The fiber samples exhibited antioxidant activity. All the samples showed good results for glucose adsorption, amylase activity inhibition, glucose diffusion rate and glucose diffusion reduction rate index.
SOLVING FRACTIONAL-ORDER COMPETITIVE LOTKA-VOLTERRA MODEL BY NSFD SCHEMES
Directory of Open Access Journals (Sweden)
S.ZIBAEI
2016-12-01
Full Text Available In this paper, we introduce fractional-order into a model competitive Lotka- Volterra prey-predator system. We will discuss the stability analysis of this fractional system. The non-standard nite difference (NSFD scheme is implemented to study the dynamic behaviors in the fractional-order Lotka-Volterra system. Proposed non-standard numerical scheme is compared with the forward Euler and fourth order Runge-Kutta methods. Numerical results show that the NSFD approach is easy and accurate for implementing when applied to fractional-order Lotka-Volterra model.
Derivation of a well-posed and multidimensional drift-flux model for boiling flows
International Nuclear Information System (INIS)
Gregoire, O.; Martin, M.
2005-01-01
In this note, we derive a multidimensional drift-flux model for boiling flows. Within this framework, the distribution parameter is no longer a scalar but a tensor that might account for the medium anisotropy and the flow regime. A new model for the drift-velocity vector is also derived. It intrinsically takes into account the effect of the friction pressure loss on the buoyancy force. On the other hand, we show that most drift-flux models might exhibit a singularity for large void fraction. In order to avoid this singularity, a remedy based on a simplified three field approach is proposed. (authors)
Wilde, M. V.; Sergeeva, N. V.
2018-05-01
An explicit asymptotic model extracting the contribution of a surface wave to the dynamic response of a viscoelastic half-space is derived. Fractional exponential Rabotnov's integral operators are used for describing of material properties. The model is derived by extracting the principal part of the poles corresponding to the surface waves after applying Laplace and Fourier transforms. The simplified equations for the originals are written by using power series expansions. Padè approximation is constructed to unite short-time and long-time models. The form of this approximation allows to formulate the explicit model using a fractional exponential Rabotnov's integral operator with parameters depending on the properties of surface wave. The applicability of derived models is studied by comparing with the exact solutions of a model problem. It is revealed that the model based on Padè approximation is highly effective for all the possible time domains.
Liang, Yingjie; Ye, Allen Q.; Chen, Wen; Gatto, Rodolfo G.; Colon-Perez, Luis; Mareci, Thomas H.; Magin, Richard L.
2016-10-01
Non-Gaussian (anomalous) diffusion is wide spread in biological tissues where its effects modulate chemical reactions and membrane transport. When viewed using magnetic resonance imaging (MRI), anomalous diffusion is characterized by a persistent or 'long tail' behavior in the decay of the diffusion signal. Recent MRI studies have used the fractional derivative to describe diffusion dynamics in normal and post-mortem tissue by connecting the order of the derivative with changes in tissue composition, structure and complexity. In this study we consider an alternative approach by introducing fractal time and space derivatives into Fick's second law of diffusion. This provides a more natural way to link sub-voxel tissue composition with the observed MRI diffusion signal decay following the application of a diffusion-sensitive pulse sequence. Unlike previous studies using fractional order derivatives, here the fractal derivative order is directly connected to the Hausdorff fractal dimension of the diffusion trajectory. The result is a simpler, computationally faster, and more direct way to incorporate tissue complexity and microstructure into the diffusional dynamics. Furthermore, the results are readily expressed in terms of spectral entropy, which provides a quantitative measure of the overall complexity of the heterogeneous and multi-scale structure of biological tissues. As an example, we apply this new model for the characterization of diffusion in fixed samples of the mouse brain. These results are compared with those obtained using the mono-exponential, the stretched exponential, the fractional derivative, and the diffusion kurtosis models. Overall, we find that the order of the fractal time derivative, the diffusion coefficient, and the spectral entropy are potential biomarkers to differentiate between the microstructure of white and gray matter. In addition, we note that the fractal derivative model has practical advantages over the existing models from the
Druhan, J. L.; Giannetta, M.; Sanford, R. A.
2017-12-01
, resulting in model behavior which is, in effect, a microbial redox analog to the variable observed fractionation factor resulting from a transition state theory rate law as derived by DePaolo (2011).
Amato, Ernesto; Italiano, Antonio; Baldari, Sergio
2014-01-01
We developed a general model for the calculation of absorbed fractions in ellipsoidal volumes of soft tissue uniformly filled with alpha, beta and gamma emitting radionuclides. The approach exploited Monte Carlo simulations with the Geant4 code to determine absorbed fractions in ellipsoids characterized by a wide range of dimensions and ellipticities, for monoenergetic emissions of each radiation type. The so-obtained absorbed fractions were put in an analytical relationship with the 'general...
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.
Wang, Wei Z; Fang, Xin-Hua; Williams, Shelley J; Stephenson, Linda L; Baynosa, Richard C; Wong, Nancy; Khiabani, Kayvan T; Zamboni, William A
2013-01-01
Adipose-derived stem cells have become the most studied adult stem cells. The authors examined the apoptosis and necrosis rates for adipocyte, stromal vascular fraction, and adipose-derived stem cells in fresh human lipoaspirates. Human lipoaspirate (n = 8) was harvested using a standard liposuction technique. Stromal vascular fraction cells were separated from adipocytes and cultured to obtain purified adipose-derived stem cells. A panel of stem cell markers was used to identify the surface phenotypes of cultured adipose-derived stem cells. Three distinct stem cell subpopulations (CD90/CD45, CD105/CD45, and CD34/CD31) were selected from the stromal vascular fraction. Apoptosis and necrosis were determined by annexin V/propidium iodide assay and analyzed by flow cytometry. The cultured adipose-derived stem cells demonstrated long-term proliferation and differentiation evidenced by cell doubling time and positive staining with oil red O and alkaline phosphatase. Isolated from lipoaspirates, adipocytes exhibited 19.7 ± 3.7 percent apoptosis and 1.1 ± 0.3 percent necrosis; stromal vascular fraction cells revealed 22.0 ± 6.3 percent of apoptosis and 11.2 ± 1.9 percent of necrosis; stromal vascular fraction cells had a higher rate of necrosis than adipocytes (p vascular fraction cells, 51.1 ± 3.7 percent expressed CD90/CD45, 7.5 ± 1.0 percent expressed CD105/CD45, and 26.4 ± 3.8 percent expressed CD34/CD31. CD34/CD31 adipose-derived stem cells had lower rates of apoptosis and necrosis compared with CD105/CD45 adipose-derived stem cells (p necrosis than adipocytes. However, the extent of apoptosis and necrosis was significantly different among adipose-derived stem cell subpopulations.
Butt, A. R.; Abdullah, M.; Raza, N.; Imran, M. A.
2017-10-01
In this work, semi analytical solutions for the heat and mass transfer of a fractional MHD Jeffery fluid over an infinite oscillating vertical plate with exponentially heating and constant mass diffusion via the Caputo-Fabrizio fractional derivative are obtained. The governing equations are transformed into dimensionless form by introducing dimensionless variables. A modern definition of the Caputo-Fabrizio derivative has been used to develop the fractional model for a Jeffery fluid. The expressions for temperature, concentration and velocity fields are obtained in the Laplace transformed domain. We have used the Stehfest's and Tzou's algorithm for the inverse Laplace transform to obtain the semi analytical solutions for temperature, concentration and velocity fields. In the end, in order to check the physical impact of flow parameters on temperature, concentration and velocity fields, results are presented graphically and in tabular forms.
Linking the fractional derivative and the Lomnitz creep law to non-Newtonian time-varying viscosity
Pandey, Vikash; Holm, Sverre
2016-01-01
Many of the most interesting complex media are non-Newtonian and exhibit time-dependent behavior of thixotropy and rheopecty. They may also have temporal responses described by power laws. The material behavior is represented by the relaxation modulus and the creep compliance. On the one hand, it is shown that in the special case of a Maxwell model characterized by a linearly time-varying viscosity, the medium's relaxation modulus is a power law which is similar to that of a fractional deriva...
International Nuclear Information System (INIS)
Nilsson, P.; Joiner, M.C.
1990-01-01
A generalized equation for cell survival or tissue effects after fractionated low dose-rate irradiations, when there is incomplete repair between fractions and significant repair during fractions, is derived in terms of the h- and g-functions of the 'incomplete-repair' (IR) model. The model is critically dependent on α/β, repair half-time, treatment time and interfraction interval, and should therefore be regarded primarily as a tool for the analysis of fractionation and dose-rate effects in carefully designed radiobiological experiments, although it should also be useful in exploring, in a general way, the feasibility of clinical treatment protocols using fractionated low dose-rate treatments. (author)
Fractional Stochastic Field Theory
Honkonen, Juha
2018-02-01
Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.
Fractional statistics in 2+1 dimensions through the Gaussian model
International Nuclear Information System (INIS)
Murthy, G.
1986-01-01
The free massless field in 2+1 dimensions is written as an ''integral'' over free massless fields in 1+1 dimensions. Taking the operators with fractional dimension in the Gaussian model as a springboard we construct operators with fractional statistics in the former theory
On the identification of fractionally cointegrated VAR models with the F(d) condition
DEFF Research Database (Denmark)
Carlini, Federico; Santucci de Magistris, Paolo
with different fractional integration and cointegration parameters. The properties of these multiple non-identified sub-models are studied and a necessary and sufficient condition for the identification of the fractional parameters of the system is provided. The condition is named F(d). The assessment of the F(d...
A Fractional Supervision Game Model of Multiple Stakeholders and Numerical Simulation
Directory of Open Access Journals (Sweden)
Rongwu Lu
2017-01-01
Full Text Available Considering the popular use of a certain kind of supervision management problem in many fields, we firstly build an ordinary supervision game model of multiple stakeholders. Secondly, a fractional supervision game model is set up and solved based on the theory of fractional calculus and a predictor-corrector numerical approach. Thirdly, the methods of phase diagram and time series graph were applied to simulate and analyse the dynamic process of the fractional order game model. Results of numerical solutions are given to illustrate our conclusions and referred to the practice.
Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models
Directory of Open Access Journals (Sweden)
Shelton Peiris
2017-12-01
Full Text Available This paper considers a flexible class of time series models generated by Gegenbauer polynomials incorporating the long memory in stochastic volatility (SV components in order to develop the General Long Memory SV (GLMSV model. We examine the corresponding statistical properties of this model, discuss the spectral likelihood estimation and investigate the finite sample properties via Monte Carlo experiments. We provide empirical evidence by applying the GLMSV model to three exchange rate return series and conjecture that the results of out-of-sample forecasts adequately confirm the use of GLMSV model in certain financial applications.
DEFF Research Database (Denmark)
Cavaliere, Giuseppe; Nielsen, Morten Ørregaard; Taylor, Robert
We consider the problem of conducting estimation and inference on the parameters of univariate heteroskedastic fractionally integrated time series models. We first extend existing results in the literature, developed for conditional sum-of squares estimators in the context of parametric fractional...... time series models driven by conditionally homoskedastic shocks, to allow for conditional and unconditional heteroskedasticity both of a quite general and unknown form. Global consistency and asymptotic normality are shown to still obtain; however, the covariance matrix of the limiting distribution...... of the estimator now depends on nuisance parameters derived both from the weak dependence and heteroskedasticity present in the shocks. We then investigate classical methods of inference based on the Wald, likelihood ratio and Lagrange multiplier tests for linear hypotheses on either or both of the long and short...
Hydrogen solubility measurements of analyzed tall oil fractions and a solubility model
International Nuclear Information System (INIS)
Uusi-Kyyny, Petri; Pakkanen, Minna; Linnekoski, Juha; Alopaeus, Ville
2017-01-01
Highlights: • Hydrogen solubility was measured in four tall oil fractions between 373 and 597 K. • Continuous flow synthetic isothermal and isobaric method was used. • A Henry’s law model was developed for the distilled tall oil fractions. • The complex composition of the samples was analyzed and is presented. - Abstract: Knowledge of hydrogen solubility in tall oil fractions is important for designing hydrotreatment processes of these complex nonedible biobased materials. Unfortunately measurements of hydrogen solubility into these fractions are missing in the literature. This work reports hydrogen solubility measured in four tall oil fractions between 373 and 597 K and at pressures from 5 to 10 MPa. Three of the fractions were distilled tall oil fractions their resin acids contents are respectively 2, 20 and 23 in mass-%. Additionally one fraction was a crude tall oil (CTO) sample containing sterols as the main neutral fraction. Measurements were performed using a continuous flow synthetic isothermal and isobaric method based on the visual observation of the bubble point. Composition of the flow was changed step-wise for the bubble point composition determination. We assume that the tall oil fractions did not react during measurements, based on the composition analysis performed before and after the measurements. Additionally the densities of the fractions were measured at atmospheric pressure from 293.15 to 323.15 K. A Henry’s law model was developed for the distilled tall oil fractions describing the solubility with an absolute average deviation of 2.1%. Inputs of the solubility model are temperature, total pressure and the density of the oil at 323.15 K. The solubility of hydrogen in the CTO sample can be described with the developed model with an absolute average deviation of 3.4%. The solubility of hydrogen increases both with increasing pressure and/or increasing temperature. The more dense fractions of the tall oil exhibit lower hydrogen
Wasser, Leah; Day, Rick; Chasmer, Laura; Taylor, Alan
2013-01-01
Estimates of canopy height (H) and fractional canopy cover (FC) derived from lidar data collected during leaf-on and leaf-off conditions are compared with field measurements from 80 forested riparian buffer plots. The purpose is to determine if existing lidar data flown in leaf-off conditions for applications such as terrain mapping can effectively estimate forested riparian buffer H and FC within a range of riparian vegetation types. Results illustrate that: 1) leaf-off and leaf-on lidar percentile estimates are similar to measured heights in all plots except those dominated by deciduous compound-leaved trees where lidar underestimates H during leaf off periods; 2) canopy height models (CHMs) underestimate H by a larger margin compared to percentile methods and are influenced by vegetation type (conifer needle, deciduous simple leaf or deciduous compound leaf) and canopy height variability, 3) lidar estimates of FC are within 10% of plot measurements during leaf-on periods, but are underestimated during leaf-off periods except in mixed and conifer plots; and 4) depth of laser pulse penetration lower in the canopy is more variable compared to top of the canopy penetration which may influence within canopy vegetation structure estimates. This study demonstrates that leaf-off lidar data can be used to estimate forested riparian buffer canopy height within diverse vegetation conditions and fractional canopy cover within mixed and conifer forests when leaf-on lidar data are not available. PMID:23382966
Directory of Open Access Journals (Sweden)
S. L. Heck
2012-02-01
Full Text Available There is a widely recognized need to improve our understanding of biosphere-atmosphere carbon exchanges in areas of complex terrain including the United States Mountain West. CO2 fluxes over mountainous terrain are often difficult to measure due to unusual and complicated influences associated with atmospheric transport. Consequently, deriving regional fluxes in mountain regions with carbon cycle inversion of atmospheric CO2 mole fraction is sensitive to filtering of observations to those that can be represented at the transport model resolution. Using five years of CO2 mole fraction observations from the Regional Atmospheric Continuous CO2 Network in the Rocky Mountains (Rocky RACCOON, five statistical filters are used to investigate a range of approaches for identifying regionally representative CO2 mole fractions. Test results from three filters indicate that subsets based on short-term variance and local CO2 gradients across tower inlet heights retain nine-tenths of the total observations and are able to define representative diel variability and seasonal cycles even for difficult-to-model sites where the influence of local fluxes is much larger than regional mole fraction variations. Test results from two other filters that consider measurements from previous and following days using spline fitting or sliding windows are overly selective. Case study examples showed that these windowing-filters rejected measurements representing synoptic changes in CO2, which suggests that they are not well suited to filtering continental CO2 measurements. We present a novel CO2 lapse rate filter that uses CO2 differences between levels in the model atmosphere to select subsets of site measurements that are representative on model scales. Our new filtering techniques provide guidance for novel approaches to assimilating mountain-top CO2 mole fractions in carbon cycle inverse models.
Underprediction of human skin erythema at low doses per fraction by the linear quadratic model
International Nuclear Information System (INIS)
Hamilton, Christopher S.; Denham, James W.; O'Brien, Maree; Ostwald, Patricia; Kron, Tomas; Wright, Suzanne; Doerr, Wolfgang
1996-01-01
Background and purpose. The erythematous response of human skin to radiotherapy has proven useful for testing the predictions of the linear quadratic (LQ) model in terms of fractionation sensitivity and repair half time. No formal investigation of the response of human skin to doses less than 2 Gy per fraction has occurred. This study aims to test the validity of the LQ model for human skin at doses ranging from 0.4 to 5.2 Gy per fraction. Materials and methods. Complete erythema reaction profiles were obtained using reflectance spectrophotometry in two patient populations: 65 patients treated palliatively with 5, 10, 12 and 20 daily treatment fractions (varying thicknesses of bolus, various body sites) and 52 patients undergoing prostatic irradiation for localised carcinoma of the prostate (no bolus, 30-32 fractions). Results and conclusions. Gender, age, site and prior sun exposure influence pre- and post-treatment erythema values independently of dose administered. Out-of-field effects were also noted. The linear quadratic model significantly underpredicted peak erythema values at doses less than 1.5 Gy per fraction. This suggests that either the conventional linear quadratic model does not apply for low doses per fraction in human skin or that erythema is not exclusively initiated by radiation damage to the basal layer. The data are potentially explained by an induced repair model
Vulnerable Derivatives and Good Deal Bounds: A Structural Model
DEFF Research Database (Denmark)
Murgoci, Agatha
2013-01-01
We price vulnerable derivatives -- i.e. derivatives where the counterparty may default. These are basically the derivatives traded on the over-the-counter (OTC) markets. Default is modeled in a structural framework. The technique employed for pricing is good deal bounds (GDBs). The method imposes...
Modelling of diffuse solar fraction with multiple predictors
Energy Technology Data Exchange (ETDEWEB)
Ridley, Barbara; Boland, John [Centre for Industrial and Applied Mathematics, University of South Australia, Mawson Lakes Boulevard, Mawson Lakes, SA 5095 (Australia); Lauret, Philippe [Laboratoire de Physique du Batiment et des Systemes, University of La Reunion, Reunion (France)
2010-02-15
For some locations both global and diffuse solar radiation are measured. However, for many locations, only global radiation is measured, or inferred from satellite data. For modelling solar energy applications, the amount of radiation on a tilted surface is needed. Since only the direct component on a tilted surface can be calculated from direct on some other plane using trigonometry, we need to have diffuse radiation on the horizontal plane available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia. Boland et al. developed a validated model for Australian conditions. Boland et al. detailed our recent advances in developing the theoretical framework for the use of the logistic function instead of piecewise linear or simple nonlinear functions and was the first step in identifying the means for developing a generic model for estimating diffuse from global and other predictors. We have developed a multiple predictor model, which is much simpler than previous models, and uses hourly clearness index, daily clearness index, solar altitude, apparent solar time and a measure of persistence of global radiation level as predictors. This model performs marginally better than currently used models for locations in the Northern Hemisphere and substantially better for Southern Hemisphere locations. We suggest it can be used as a universal model. (author)
International Nuclear Information System (INIS)
Sasaki, Takehito; Kamata, Rikisaburo; Urahashi, Shingo; Yamaguchi, Tetsuji.
1993-01-01
One hundred and sixty-nine cervical lymph node-metastases from head and neck squamous cell carcinomas treated with either even fractionation or uneven fractionation regimens were analyzed in the present investigation. Logistic multivariate regression analysis indicated that: type of fractionation (even vs uneven), size of metastases, T value of primary tumors, and total dose are independent variables out of 18 variables that significantly influenced the rate of tumor clearance. The data, with statistical bias corrected by the regression equation, indicated that the uneven fractionation scheme significantly improved the rate of tumor clearance for the same size of metastases, total dose, and overall time compared to the even fractionation scheme. Further analysis by a linear-quadratic cell survival model indicated that the clinical improvement by uneven fractionation might not be explained entirely by a larger dose per fraction. It is suggested that tumor cells irradiated with an uneven fractionation regimen might repopulate more slowly, or they might be either less hypoxic or redistributed in a more radiosensitive phase in the cell cycle than those irradiated with even fractionation. This conclusion is clearly not definite, but it is suitable, pending the results of further investigation. (author)
Directory of Open Access Journals (Sweden)
Anupama Choudhary
2016-03-01
Full Text Available In this paper, a fractional model for the computation of temperature and heat flux distribution in a semi-infinite solid is discussed which is subjected to spatially decomposing, time-dependent laser source. The apt dimensionless parameters are identified and the reduced temperature and heat flux as a function of these parameters are presented in a numerical form. Some special cases of practical interest are also discussed. The solution is derived by the application of the Laplace transform, the Fourier sine transform and their derivatives. Also, we developed an alternative solution of it by using the Sumudu transform, the Fourier transform and their derivatives. These results are received in compact and graceful forms in terms of the generalized Mittag-Leffler function, which are suitable for numerical computation.
Chum, H.L.; Black, S.K.; Diebold, J.P.; Kreibich, R.E.
1993-08-10
A process for preparing phenol-formaldehyde resole resins by fractionating organic and aqueous condensates made by fast-pyrolysis of biomass materials while using a carrier gas to move feed into a reactor to produce phenolic-containing/neutrals in which portions of the phenol normally contained in said resins are replaced by a phenolic/neutral fractions extract obtained by fractionation.
Cusimano, N.; Gerardo-Giorda, L.
2018-06-01
Classical models of electrophysiology do not typically account for the effects of high structural heterogeneity in the spatio-temporal description of excitation waves propagation. We consider a modification of the Monodomain model obtained by replacing the diffusive term of the classical formulation with a fractional power of the operator, defined in the spectral sense. The resulting nonlocal model describes different levels of tissue heterogeneity as the fractional exponent is varied. The numerical method for the solution of the fractional Monodomain relies on an integral representation of the nonlocal operator combined with a finite element discretisation in space, allowing to handle in a natural way bounded domains in more than one spatial dimension. Numerical tests in two spatial dimensions illustrate the features of the model. Activation times, action potential duration and its dispersion throughout the domain are studied as a function of the fractional parameter: the expected peculiar behaviour driven by tissue heterogeneities is recovered.
Directory of Open Access Journals (Sweden)
Romain Gallet, MD
2016-01-01
Full Text Available The pathogenesis of heart failure with a preserved ejection fraction (HFpEF is unclear. Myocardial fibrosis, inflammation, and cardiac hypertrophy have been suggested to contribute to the pathogenesis of HFpEF. Cardiosphere-derived cells (CDCs are heart-derived cell products with antifibrotic and anti-inflammatory properties. This study tested whether rat CDCs were sufficient to decrease manifestations of HFpEF in hypertensive rats. Starting at 7 weeks of age, Dahl salt-sensitive rats were fed a high-salt diet for 6 to 7 weeks and randomized to receive intracoronary CDCs or placebo. Dahl rats fed normal chow served as controls. High-salt rats developed hypertension, left ventricular (LV hypertrophy, and diastolic dysfunction, without impairment of ejection fraction. Four weeks after treatment, diastolic dysfunction resolved in CDC-treated rats but not in placebo. The improved LV relaxation was associated with lower LV end-diastolic pressure, decreased lung congestion, and enhanced survival in CDC-treated rats. Histology and echocardiography revealed no decrease in cardiac hypertrophy after CDC treatment, consistent with the finding of sustained, equally-elevated blood pressure in CDC- and placebo-treated rats. Nevertheless, CDC treatment decreased LV fibrosis and inflammatory infiltrates. Serum inflammatory cytokines were likewise decreased after CDC treatment. Whole-transcriptome analysis revealed that CDCs reversed changes in numerous transcripts associated with HFpEF, including many involved in inflammation and/or fibrosis. These studies suggest that CDCs normalized LV relaxation and LV diastolic pressure while improving survival in a rat model of HFpEF. The benefits of CDCs occurred despite persistent hypertension and cardiac hypertrophy. By selectively reversing inflammation and fibrosis, CDCs may be beneficial in the treatment of HFpEF.
On the identification of fractionally cointegrated VAR models with the F(d) condition
DEFF Research Database (Denmark)
Carlini, Federico; Santucci de Magistris, Paolo
for any choice of the lag length, also when the true cointegration rank is known. The properties of these multiple non-identified models are studied and a necessary and sufficient condition for the identification of the fractional parameters of the system is provided. The condition is named F(d......) and it is a generalization to the fractional case of the I(1) condition in the VECM model. The assessment of the F(d) condition in the empirical analysis is relevant for the determination of the fractional parameters as well as the number of lags. The paper also illustrates the indeterminacy between the cointegration rank...
On the identification of fractionally cointegrated VAR models with the F(d) condition
DEFF Research Database (Denmark)
Santucci de Magistris, Paolo; Carlini, Federico
for any choice of the lag-length when the true cointegration rank is known. The properties of these multiple non-identified models are studied and a necessary and sufficient condition for the identification of the fractional parameters of the system is provided. The condition is named F(d......). This is a generalization of the well-known I(1) condition to the fractional case. Imposing a proper restriction on the fractional integration parameter, d, is sufficient to guarantee identification of all model parameters and the validity of the F(d) condition. The paper also illustrates the indeterminacy between...
Use of Angle Model to Understand Addition and Subtraction of Fractions
Directory of Open Access Journals (Sweden)
Muzwangowenyu Mukwambo
2018-02-01
Full Text Available Learners in lower primary and even some in upper primary grades grapple to perform mathematical operations which involve fractions. Failure to solve these mathematical operations creates a gap in the teaching and learning processes of mathematics. We opine that this is attributed to use of traditional mathematical approaches of teaching and learning (TMATL of operations of fraction. With the hope of engaging the reformed mathematical approach of teaching and learning (RMATL this study investigated the following: How can trainee teachers use the angle model in RMATL operations of fractions? What are the perceptions of trainee teachers in the use of the angle model which engages RMATL to teach the operations of fractions? With the goal to fill the mentioned gap in which learners struggle to perform operations involving fractions, we observed and analysed worksheets on operation with fractions students wrote. Observations and interviews with trainee teachers of lower primary revealed poor performance in problems related to operations with fractions. Observed patterns supported by cognitivism revealed that invented methods or strategies on which RMATL is anchored are suitable enough to engage learner–centred teaching and learning which can prevent the abstractness of the concept of operations with fractions.
International Nuclear Information System (INIS)
Ahmad, N.; Shinwari, Z.K.
2016-01-01
The extracts and its derived fractions from three medicinal plants species Nepeta leavigata, Nepeta kurramensis and Rhynchosia reniformis were tested for insecticidal activities and preliminary phytochemical evaluation with the intention of standardization and proper manage of bioactive principles in such heterogonous botanicals and to encourage drug finding work with plants. The crude extracts and fractions from Nepeta plants showed moderate to strong insecticidal activity. Among the fractions from Nepeta kurramensis the n-butanol fraction showed strongest insecticidal activity with 89% mortality rate against Tribolium castaneum followed by methanol extract with 88% mortality ratio and in case of Nepeta leavigata the potential activity was showed by methanol extracts with 93% mortality rate against the tested insect. Surprisingly none of the extract / fractions obtained from Rhynchosia reniformis plant exhibited any insecticidal activity. The phytochemicals screening results revealed that both species of Nepeta showed similar phytochemicals profile. The group of chemicals terpenes, flavonoids and glycosides were observed in all the extracts/fractions of Nepeta plants. While phenolic compounds, acidic compounds and alkaloids were found in methanolic extracts, chloroform fraction and ethyl acetate fraction. The Rhynchosia reniformis was observed to be a good source of phenolic compounds, flavonoids, terpenes, alkaloids and fats. (author)
International Nuclear Information System (INIS)
Wang, Yanan; Zeng, Xibai; Lu, Yahai; Su, Shiming; Bai, Lingyu; Li, Lianfang; Wu, Cuixia
2015-01-01
The effects of aging time and soil parent materials on the bioavailability and fractionations of arsenic (As) in five red soils were studied. The results indicated that As bioavailability in all soils decreased during aging, especially with a sharp decline occurring in the first 30 days. After aging for 360 days, the highest available As concentration, which accounted for 12.3% of the total, was observed in soils derived from purple sandy shale. While 2.67% was the lowest proportion of the available As in soils derived from quaternary red clay. Furthermore, the best fit of the available As changing with aging time was obtained using the pseudo-second-order model (R"2 = 0.939–0.998, P < 0.05). Notably, Al oxides played a more crucial role (R"2 = 0.89, P<0.05) than did Fe oxides in controlling the rate of As aging. The non-specially and specially absorbed As constituted the primary forms of available As. - Highlights: • The soil derived from purple sandy shale had a relatively higher risk of As toxicity for agricultural production. • The best fit of the variations of available As during the aging time was obtained using the pseudo-second-order model. • Al oxides played a more crucial role than did Fe oxides in controlling the rate of As aging. - Al oxides played a more crucial role than did Fe oxides in controlling the rate of As aging in these red soils.
Neutron fraction and neutrino mean free path predictions in relativistic mean field models
International Nuclear Information System (INIS)
Hutauruk, P.T.P.; Williams, C.K.; Sulaksono, A.; Mart, T.
2004-01-01
The equation of state (EOS) of dense matter and neutrino mean free path (NMFP) in a neutron star have been studied by using relativistic mean field models motivated by effective field theory. It is found that the models predict too large proton fractions, although one of the models (G2) predicts an acceptable EOS. This is caused by the isovector terms. Except G2, the other two models predict anomalous NMFP's. In order to minimize the anomaly, besides an acceptable EOS, a large M* is favorable. A model with large M* retains the regularity in the NMFP even for a small neutron fraction
Stochastic fractional differential equations: Modeling, method and analysis
International Nuclear Information System (INIS)
Pedjeu, Jean-C.; Ladde, Gangaram S.
2012-01-01
By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model described by a system of multi-time scale stochastic differential equations is formulated. The classical Picard–Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this leads to the problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations of Itô–Doob type. Finally, to illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are outlined.
Remarks on the microscopic derivation of the collective model
International Nuclear Information System (INIS)
Toyoda, T.; Wildermuth, K.
1984-01-01
The rotational part of the phenomenological collective model of Bohr and Mottelson and others is derived microscopically, starting with the Schrodinger equation written in projection form and introducing a new set of 'relative Euler angles'. In order to derive the local Schrodinger equation of the collective model, it is assumed that the intrinsic wave functions give strong peaking properties to the overlapping kernels
Model-order reduction of lumped parameter systems via fractional calculus
Hollkamp, John P.; Sen, Mihir; Semperlotti, Fabio
2018-04-01
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach to the simulation of non-homogeneous systems dictates the use of numerical solutions and often imposes stringent compromises between accuracy and computational performance. Fractional calculus provides an alternative approach where complex dynamical systems can be modeled with compact fractional equations that not only can still guarantee analytical solutions, but can also enable high levels of order reduction without compromising on accuracy. Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting fractional differential models have both a complex and frequency-dependent order of the differential operator. The implications of this type of approach for both model order reduction and model synthesis are discussed.
A set for relational reasoning: Facilitation of algebraic modeling by a fraction task.
DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J
2016-12-01
Recent work has identified correlations between early mastery of fractions and later math achievement, especially in algebra. However, causal connections between aspects of reasoning with fractions and improved algebra performance have yet to be established. The current study investigated whether relational reasoning with fractions facilitates subsequent algebraic reasoning using both pre-algebra students and adult college students. Participants were first given either a relational reasoning fractions task or a fraction algebra procedures control task. Then, all participants solved word problems and constructed algebraic equations in either multiplication or division format. The word problems and the equation construction tasks involved simple multiplicative comparison statements such as "There are 4 times as many students as teachers in a classroom." Performance on the algebraic equation construction task was enhanced for participants who had previously completed the relational fractions task compared with those who completed the fraction algebra procedures task. This finding suggests that relational reasoning with fractions can establish a relational set that promotes students' tendency to model relations using algebraic expressions. Copyright © 2016 Elsevier Inc. All rights reserved.
Local discrete symmetries from superstring derived models
International Nuclear Information System (INIS)
Faraggi, A.E.
1996-10-01
Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model the author illustrates how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non-Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations
No-arbitrage, leverage and completeness in a fractional volatility model
Vilela Mendes, R.; Oliveira, M. J.; Rodrigues, A. M.
2015-02-01
When the volatility process is driven by fractional noise one obtains a model which is consistent with the empirical market data. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions of the model are obtained with different leverage behaviors. Here, the no-arbitrage and completeness properties of the models are rigorously studied.
Aman, Sidra; Khan, Ilyas; Ismail, Zulkhibri; Salleh, Mohd Zuki; Tlili, I.
2018-06-01
In this article the idea of Caputo time fractional derivatives is applied to MHD mixed convection Poiseuille flow of nanofluids with graphene nanoparticles in a vertical channel. The applications of nanofluids in solar energy are argued for various solar thermal systems. It is argued in the article that using nanofluids is an alternate source to produce solar energy in thermal engineering and solar energy devices in industries. The problem is modelled in terms of PDE's with initial and boundary conditions and solved analytically via Laplace transform method. The obtained solutions for velocity, temperature and concentration are expressed in terms of Wright's function. These solutions are significantly controlled by the variations of parameters including thermal Grashof number, Solutal Grashof number and nanoparticles volume fraction. Expressions for skin-friction, Nusselt and Sherwood numbers are also determined on left and right walls of the vertical channel with important numerical results in tabular form. It is found that rate of heat transfer increases with increasing nanoparticles volume fraction and Caputo time fractional parameters.
DEFF Research Database (Denmark)
Ørregård Nielsen, Morten
This paper proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time series models. The model is parametric and quite general, and, in particular, encompasses...... the multivariate non-cointegrated fractional ARIMA model. The novelty of the consistency result, in particular, is that it applies to a multivariate model and to an arbitrarily large set of admissible parameter values, for which the objective function does not converge uniformly in probablity, thus making...
Fractional single-phase-lagging heat conduction model for describing anomalous diffusion
Directory of Open Access Journals (Sweden)
T.N. Mishra
2016-03-01
Full Text Available The fractional single-phase-lagging (FSPL heat conduction model is obtained by combining scalar time fractional conservation equation to the single-phase-lagging (SPL heat conduction model. Based on the FSPL heat conduction model, anomalous diffusion within a finite thin film is investigated. The effect of different parameters on solution has been observed and studied the asymptotic behavior of the FSPL model. The analytical solution is obtained using Laplace transform method. The whole analysis is presented in dimensionless form. Numerical examples of particular interest have been studied and discussed in details.
Rational Models for Inflation-Linked Derivatives
DEFF Research Database (Denmark)
Dam, Henrik; Macrina, Andrea; Skovmand, David
2018-01-01
in a multiplicative manner that allows for closed-form pricing of vanilla inflation products suchlike zero-coupon swaps, caps and floors, year-on-year swaps, caps and floors, and the exotic limited price index swap. The model retains the attractive features of a nominal multi-curve interest rate model such as closed...
Morales-Delgado, V. F.; Gómez-Aguilar, J. F.; Taneco-Hernandez, M. A.
2017-12-01
In this work we propose fractional differential equations for the motion of a charged particle in electric, magnetic and electromagnetic fields. Exact solutions are obtained for the fractional differential equations by employing the Laplace transform method. The temporal fractional differential equations are considered in the Caputo-Fabrizio-Caputo and Atangana-Baleanu-Caputo sense. Application examples consider constant, ramp and harmonic fields. In addition, we present numerical results for different values of the fractional order. In all cases, when α = 1, we recover the standard electrodynamics.
Directory of Open Access Journals (Sweden)
HASHEM SABERI NAJAFI
2016-07-01
Full Text Available Generalized differential transform method (GDTM is a powerful method to solve the fractional differential equations. In this paper, a new fractional model for systems with single degree of freedom (SDOF is presented, by using the GDTM. The advantage of this method compared with some other numerical methods has been shown. The analysis of new approximations, damping and acceleration of systems are also described. Finally, by reducing damping and analysis of the errors, in one of the fractional cases, we have shown that in addition to having a suitable solution for the displacement close to the exact one, the system enjoys acceleration once crossing the equilibrium point.
Energy Technology Data Exchange (ETDEWEB)
Kurata, Akira [Ehime University Graduate School of Medicine, Department of Radiology, Toon, Ehime (Japan); Erasmus University Medical Center, Department of Radiology, Rotterdam (Netherlands); Coenen, Adriaan; Lubbers, Marisa M.; Nieman, Koen [Erasmus University Medical Center, Department of Radiology, Rotterdam (Netherlands); Erasmus University Medical Center, Departmenet of Cardiology, Rotterdam (Netherlands); Kido, Teruhito; Mochizuki, Teruhito [Ehime University Graduate School of Medicine, Department of Radiology, Toon, Ehime (Japan); Kido, Tomoyuki [Matsuyama Saiseikai Hospital, Department of Radiology, Matsuyama, Ehime (Japan); Yamashita, Natsumi [Clinical Research Center, National Hospital Organization Shikoku Cancer Center, Division of Clinical Biostatistics, Section of Cancer Prevention and Epidemiology, Matsuyama, Ehime (Japan); Watanabe, Kouki [Matsuyama Saiseikai Hospital, Department of Cardiology, Matsuyama, Ehime (Japan); Krestin, Gabriel P. [Erasmus University Medical Center, Department of Radiology, Rotterdam (Netherlands)
2017-04-15
The aim of this study is to assess the effect of blood pressure (BP) on coronary computed tomography angiography (CTA) derived computational fractional flow reserve (CTA-FFR). Twenty-one patients who underwent coronary CTA and invasive FFR were retrospectively identified. Ischemia was defined as invasive FFR ≤0.80. Using a work-in-progress computational fluid dynamics algorithm, CTA-FFR was computed with BP measured before CTA, and simulated BPs of 60/50, 90/60, 110/70, 130/80, 150/90, and 180/100 mmHg respectively. Correlation between CTA-FFR and invasive FFR was assessed using Pearson test. The repeated measuring test was used for multiple comparisons of CTA-FFR values by simulated BP inputs. Twenty-nine vessels (14 with invasive FFR ≤0.80) were assessed. The average CTA-FFR for measured BP (134 ± 20/73 ± 12 mmHg) was 0.77 ± 0.12. Correlation between CTA-FFR by measured BP and invasive FFR was good (r = 0.735, P < 0.001). For simulated BPs of 60/50, 90/60, 110/70, 130/80, 150/90, and 180/100 mmHg, the CTA-FFR increased: 0.69 ± 0.13, 0.73 ± 0.12, 0.75 ± 0.12, 0.77 ± 0.11, 0.79 ± 0.11, and 0.81 ± 0.10 respectively (P < 0.05). Measurement of the BP just before CTA is preferred for accurate CTA-FFR simulation. BP variations in the common range slightly affect CTA-FFR. However, inaccurate BP assumptions differing from the patient-specific BP could cause misinterpretation of borderline significant lesions. (orig.)
International Nuclear Information System (INIS)
Kurata, Akira; Coenen, Adriaan; Lubbers, Marisa M.; Nieman, Koen; Kido, Teruhito; Mochizuki, Teruhito; Kido, Tomoyuki; Yamashita, Natsumi; Watanabe, Kouki; Krestin, Gabriel P.
2017-01-01
The aim of this study is to assess the effect of blood pressure (BP) on coronary computed tomography angiography (CTA) derived computational fractional flow reserve (CTA-FFR). Twenty-one patients who underwent coronary CTA and invasive FFR were retrospectively identified. Ischemia was defined as invasive FFR ≤0.80. Using a work-in-progress computational fluid dynamics algorithm, CTA-FFR was computed with BP measured before CTA, and simulated BPs of 60/50, 90/60, 110/70, 130/80, 150/90, and 180/100 mmHg respectively. Correlation between CTA-FFR and invasive FFR was assessed using Pearson test. The repeated measuring test was used for multiple comparisons of CTA-FFR values by simulated BP inputs. Twenty-nine vessels (14 with invasive FFR ≤0.80) were assessed. The average CTA-FFR for measured BP (134 ± 20/73 ± 12 mmHg) was 0.77 ± 0.12. Correlation between CTA-FFR by measured BP and invasive FFR was good (r = 0.735, P < 0.001). For simulated BPs of 60/50, 90/60, 110/70, 130/80, 150/90, and 180/100 mmHg, the CTA-FFR increased: 0.69 ± 0.13, 0.73 ± 0.12, 0.75 ± 0.12, 0.77 ± 0.11, 0.79 ± 0.11, and 0.81 ± 0.10 respectively (P < 0.05). Measurement of the BP just before CTA is preferred for accurate CTA-FFR simulation. BP variations in the common range slightly affect CTA-FFR. However, inaccurate BP assumptions differing from the patient-specific BP could cause misinterpretation of borderline significant lesions. (orig.)
A model to accumulate fractionated dose in a deforming organ
International Nuclear Information System (INIS)
Yan Di; Jaffray, D.A.; Wong, J.W.
1999-01-01
Purpose: Measurements of internal organ motion have demonstrated that daily organ deformation exists throughout the course of radiation treatment. However, a method of constructing the resultant dose delivered to the organ volume remains a difficult challenge. In this study, a model to quantify internal organ motion and a method to construct a cumulative dose in a deforming organ are introduced. Methods and Materials: A biomechanical model of an elastic body is used to quantify patient organ motion in the process of radiation therapy. Intertreatment displacements of volume elements in an organ of interest is calculated by applying an finite element method with boundary conditions, obtained from multiple daily computed tomography (CT) measurements. Therefore, by incorporating also the measurements of daily setup error, daily dose delivered to a deforming organ can be accumulated by tracking the position of volume elements in the organ. Furthermore, distribution of patient-specific organ motion is also predicted during the early phase of treatment delivery using the daily measurements, and the cumulative dose distribution in the organ can then be estimated. This dose distribution will be updated whenever a new measurement becomes available, and used to reoptimize the ongoing treatment. Results: An integrated process to accumulate dosage in a daily deforming organ was implemented. In this process, intertreatment organ motion and setup error were systematically quantified, and incorporated in the calculation of the cumulative dose. An example of the rectal wall motion in a prostate treatment was applied to test the model. The displacements of volume elements in the rectal wall, as well as the resultant doses, were calculated. Conclusion: This study is intended to provide a systematic framework to incorporate daily patient-specific organ motion and setup error in the reconstruction of the cumulative dose distribution in an organ of interest. The realistic dose
Weather Derivatives and Stochastic Modelling of Temperature
Directory of Open Access Journals (Sweden)
Fred Espen Benth
2011-01-01
Full Text Available We propose a continuous-time autoregressive model for the temperature dynamics with volatility being the product of a seasonal function and a stochastic process. We use the Barndorff-Nielsen and Shephard model for the stochastic volatility. The proposed temperature dynamics is flexible enough to model temperature data accurately, and at the same time being analytically tractable. Futures prices for commonly traded contracts at the Chicago Mercantile Exchange on indices like cooling- and heating-degree days and cumulative average temperatures are computed, as well as option prices on them.
The infinitesimal model: Definition, derivation, and implications.
Barton, N H; Etheridge, A M; Véber, A
2017-12-01
Our focus here is on the infinitesimal model. In this model, one or several quantitative traits are described as the sum of a genetic and a non-genetic component, the first being distributed within families as a normal random variable centred at the average of the parental genetic components, and with a variance independent of the parental traits. Thus, the variance that segregates within families is not perturbed by selection, and can be predicted from the variance components. This does not necessarily imply that the trait distribution across the whole population should be Gaussian, and indeed selection or population structure may have a substantial effect on the overall trait distribution. One of our main aims is to identify some general conditions on the allelic effects for the infinitesimal model to be accurate. We first review the long history of the infinitesimal model in quantitative genetics. Then we formulate the model at the phenotypic level in terms of individual trait values and relationships between individuals, but including different evolutionary processes: genetic drift, recombination, selection, mutation, population structure, …. We give a range of examples of its application to evolutionary questions related to stabilising selection, assortative mating, effective population size and response to selection, habitat preference and speciation. We provide a mathematical justification of the model as the limit as the number M of underlying loci tends to infinity of a model with Mendelian inheritance, mutation and environmental noise, when the genetic component of the trait is purely additive. We also show how the model generalises to include epistatic effects. We prove in particular that, within each family, the genetic components of the individual trait values in the current generation are indeed normally distributed with a variance independent of ancestral traits, up to an error of order 1∕M. Simulations suggest that in some cases the convergence
Toward lattice fractional vector calculus
International Nuclear Information System (INIS)
Tarasov, Vasily E
2014-01-01
An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity. (papers)
Algorithms for testing of fractional dynamics: a practical guide to ARFIMA modelling
International Nuclear Information System (INIS)
Burnecki, Krzysztof; Weron, Aleksander
2014-01-01
In this survey paper we present a systematic methodology which demonstrates how to identify the origins of fractional dynamics. We consider three mechanisms which lead to it, namely fractional Brownian motion, fractional Lévy stable motion and an autoregressive fractionally integrated moving average (ARFIMA) process but we concentrate on the ARFIMA modelling. The methodology is based on statistical tools for identification and validation of the fractional dynamics, in particular on an ARFIMA parameter estimator, an ergodicity test, a self-similarity index estimator based on sample p-variation and a memory parameter estimator based on sample mean-squared displacement. A complete list of algorithms needed for this is provided in appendices A–F. Finally, we illustrate the methodology on various empirical data and show that ARFIMA can be considered as a universal model for fractional dynamics. Thus, we provide a practical guide for experimentalists on how to efficiently use ARFIMA modelling for a large class of anomalous diffusion data. (paper)
Stochastic Fractional Programming Approach to a Mean and Variance Model of a Transportation Problem
Directory of Open Access Journals (Sweden)
V. Charles
2011-01-01
Full Text Available In this paper, we propose a stochastic programming model, which considers a ratio of two nonlinear functions and probabilistic constraints. In the former, only expected model has been proposed without caring variability in the model. On the other hand, in the variance model, the variability played a vital role without concerning its counterpart, namely, the expected model. Further, the expected model optimizes the ratio of two linear cost functions where as variance model optimize the ratio of two non-linear functions, that is, the stochastic nature in the denominator and numerator and considering expectation and variability as well leads to a non-linear fractional program. In this paper, a transportation model with stochastic fractional programming (SFP problem approach is proposed, which strikes the balance between previous models available in the literature.
Silicon Carbide Derived Carbons: Experiments and Modeling
Energy Technology Data Exchange (ETDEWEB)
Kertesz, Miklos [Georgetown University, Washington DC 20057
2011-02-28
The main results of the computational modeling was: 1. Development of a new genealogical algorithm to generate vacancy clusters in diamond starting from monovacancies combined with energy criteria based on TBDFT energetics. The method revealed that for smaller vacancy clusters the energetically optimal shapes are compact but for larger sizes they tend to show graphitized regions. In fact smaller clusters of the size as small as 12 already show signatures of this graphitization. The modeling gives firm basis for the slit-pore modeling of porous carbon materials and explains some of their properties. 2. We discovered small vacancy clusters and their physical characteristics that can be used to spectroscopically identify them. 3. We found low barrier pathways for vacancy migration in diamond-like materials by obtaining for the first time optimized reaction pathways.
Directory of Open Access Journals (Sweden)
Bin Wang
2016-01-01
Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.
Wind gust models derived from field data
Gawronski, W.
1995-01-01
Wind data measured during a field experiment were used to verify the analytical model of wind gusts. Good coincidence was observed; the only discrepancy occurred for the azimuth error in the front and back winds, where the simulated errors were smaller than the measured ones. This happened because of the assumption of the spatial coherence of the wind gust model, which generated a symmetric antenna load and, in consequence, a low azimuth servo error. This result indicates a need for upgrading the wind gust model to a spatially incoherent one that will reflect the real gusts in a more accurate manner. In order to design a controller with wind disturbance rejection properties, the wind disturbance should be known at the input to the antenna rate loop model. The second task, therefore, consists of developing a digital filter that simulates the wind gusts at the antenna rate input. This filter matches the spectrum of the measured servo errors. In this scenario, the wind gusts are generated by introducing white noise to the filter input.
A spatial structural derivative model for ultraslow diffusion
Directory of Open Access Journals (Sweden)
Xu Wei
2017-01-01
Full Text Available This study investigates the ultraslow diffusion by a spatial structural derivative, in which the exponential function ex is selected as the structural function to construct the local structural derivative diffusion equation model. The analytical solution of the diffusion equation is a form of Biexponential distribution. Its corresponding mean squared displacement is numerically calculated, and increases more slowly than the logarithmic function of time. The local structural derivative diffusion equation with the structural function ex in space is an alternative physical and mathematical modeling model to characterize a kind of ultraslow diffusion.
Fractional vector calculus for fractional advection dispersion
Meerschaert, Mark M.; Mortensen, Jeff; Wheatcraft, Stephen W.
2006-07-01
We develop the basic tools of fractional vector calculus including a fractional derivative version of the gradient, divergence, and curl, and a fractional divergence theorem and Stokes theorem. These basic tools are then applied to provide a physical explanation for the fractional advection-dispersion equation for flow in heterogeneous porous media.
International Nuclear Information System (INIS)
Dong, Jianping
2011-01-01
The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas-Fermi model, obtain the quantum pressure of the free electron gas. We also show the validity of the Hohenberg-Kohn theorems in the space fractional quantum mechanics and generalize the density functional theory to the fractional quantum mechanics. -- Highlights: → Thomas-Fermi model under the framework of fractional quantum mechanics is studied. → We show the validity of the HK theorems in the space fractional quantum mechanics. → The density functional theory is generalized to the fractional quantum mechanics.
International Nuclear Information System (INIS)
Gerweck, Leo E.; Dubois, Willum; Baumann, Michael; Suit, Herman D.
1995-01-01
, the rank-order correlation coefficient between the single dose hypoxic versus fractionated dose TCD50s under hypoxic or aerobic conditions was 1.0. For all 5 tumors examined, a trend for rank correlation was observed between the single dose and the fractionated dose TCD50s performed under normal or clamp hypoxic conditions (r=0.7, p=0.16 in both cases). The linear correlation coefficients were 0.83, p=0.08 and 0.72, p=0.17, respectively. Failure to attain a rank correlation of 1.0 was due to one tumor exhibiting an insignificant fractionation effect. The rank correlation between the TCD50s for fractionated treatments under normal versus the extrapolated TCD50s under clamp hypoxic conditions was 1.00; the linear correlation coefficient was 0.97 (p=0.01). Conclusions: In the tumor models examined, factors controlling the single fraction tumor control dose, also impact the response to fractionated treatments. These results suggest that laboratory estimates of intrinsic radiosensitivity and tumor clonogen number at the onset of treatment, will be of use in predicting radiocurability for fractionated treatments, as has been observed for single dose treatments
DEFF Research Database (Denmark)
Ørregård Nielsen, Morten
2015-01-01
the multivariate non-cointegrated fractional autoregressive integrated moving average (ARIMA) model. The novelty of the consistency result, in particular, is that it applies to a multivariate model and to an arbitrarily large set of admissible parameter values, for which the objective function does not converge...
Fractional order creep model for dam concrete considering degree of hydration
Huang, Yaoying; Xiao, Lei; Bao, Tengfei; Liu, Yu
2018-05-01
Concrete is a material that is an intermediate between an ideal solid and an ideal fluid. The creep of concrete is related not only to the loading age and duration, but also to its temperature and temperature history. Fractional order calculus is a powerful tool for solving physical mechanics modeling problems. Using a software element based on the generalized Kelvin model, a fractional order creep model of concrete considering the loading age and duration is established. Then, the hydration rate of cement is considered in terms of the degree of hydration, and the fractional order creep model of concrete considering the degree of hydration is established. Moreover, uniaxial tensile creep tests of dam concrete under different curing temperatures were conducted, and the results were combined with the creep test data and complex optimization method to optimize the parameters of a new creep model. The results show that the fractional tensile creep model based on hydration degree can better describe the tensile creep properties of concrete, and this model involves fewer parameters than the 8-parameter model.
Forecasting daily political opinion polls using the fractionally cointegrated VAR model
DEFF Research Database (Denmark)
Nielsen, Morten Ørregaard; Shibaev, Sergei S.
We examine forecasting performance of the recent fractionally cointegrated vector autoregressive (FCVAR) model. We use daily polling data of political support in the United Kingdom for 2010-2015 and compare with popular competing models at several forecast horizons. Our findings show that the four...... trend from the model follows the vote share of the UKIP very closely, and we thus interpret it as a measure of Euro-skepticism in public opinion rather than an indicator of the more traditional left-right political spectrum. In terms of prediction of vote shares in the election, forecasts generated...... variants of the FCVAR model considered are generally ranked as the top four models in terms of forecast accuracy, and the FCVAR model significantly outperforms both univariate fractional models and the standard cointegrated VAR (CVAR) model at all forecast horizons. The relative forecast improvement...
Energy Technology Data Exchange (ETDEWEB)
Mavroidis, Panayiotis, E-mail: mavroidis@uthscsa.edu [Department of Radiation Oncology, University of Texas Health Sciences Center, San Antonio, Texas (United States); Department of Medical Radiation Physics, Karolinska Institutet and Stockholm University, Stockholm (Sweden); Milickovic, Natasa [Department of Medical Physics and Engineering, Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Cruz, Wilbert F. [Department of Radiation Oncology, University of Texas Health Sciences Center, San Antonio, Texas (United States); Tselis, Nikolaos [Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Karabis, Andreas [Pi-Medical Ltd., Athens (Greece); Stathakis, Sotirios; Papanikolaou, Nikos [Department of Radiation Oncology, University of Texas Health Sciences Center, San Antonio, Texas (United States); Zamboglou, Nikolaos [Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Baltas, Dimos [Department of Medical Physics and Engineering, Strahlenklinik, Klinikum Offenbach GmbH, Offenbach (Germany); Nuclear and Particle Physics Section, Physics Department, University of Athens, Athens (Greece)
2014-01-01
Purpose: The aim of the present study was the investigation of different fractionation schemes to estimate their clinical impact. For this purpose, widely applied radiobiological models and dosimetric measures were used to associate their results with clinical findings. Methods and Materials: The dose distributions of 12 clinical high-dose-rate brachytherapy implants for prostate were evaluated in relation to different fractionation schemes. The fractionation schemes compared were: (1) 1 fraction of 20 Gy; (2) 2 fractions of 14 Gy; (3) 3 fractions of 11 Gy; and (4) 4 fractions of 9.5 Gy. The clinical effectiveness of the different fractionation schemes was estimated through the complication-free tumor control probability (P{sub +}), the biologically effective uniform dose, and the generalized equivalent uniform dose index. Results: For the different fractionation schemes, the tumor control probabilities were 98.5% in 1 × 20 Gy, 98.6% in 2 × 14 Gy, 97.5% in 3 × 11 Gy, and 97.8% in 4 × 9.5 Gy. The corresponding P{sub +} values were 88.8% in 1 × 20 Gy, 83.9% in 2 × 14 Gy, 86.0% in 3 × 11 Gy, and 82.3% in 4 × 9.5 Gy. With use of the fractionation scheme 4 × 9.5 Gy as reference, the isoeffective schemes regarding tumor control for 1, 2, and 3 fractions were 1 × 19.68 Gy, 2 × 13.75 Gy, and 3 × 11.05 Gy. The optimum fractionation schemes for 1, 2, 3, and 4 fractions were 1 × 19.16 Gy with a P{sub +} of 91.8%, 2 × 13.2 Gy with a P{sub +} of 89.6%, 3 × 10.6 Gy with a P{sub +} of 88.4%, and 4 × 9.02 Gy with a P{sub +} of 86.9%. Conclusions: Among the fractionation schemes 1 × 20 Gy, 2 × 14 Gy, 3 × 11 Gy, and 4 × 9.5 Gy, the first scheme was more effective in terms of P{sub +}. After performance of a radiobiological optimization, it was shown that a single fraction of 19.2 to 19.7 Gy (average 19.5 Gy) should produce at least the same benefit as that given by the 4 × 9.5 Gy scheme, and it should reduce the expected total complication probability by
Fractionations of rare earth elements in plants and their conceptive model.
Ding, ShiMing; Liang, Tao; Yan, JunCai; Zhang, ZiLi; Huang, ZeChun; Xie, YaNing
2007-02-01
Fractionations of rare earth elements (REEs) and their mechanisms in soybean were studied through application of exogenous mixed REEs under hydroponic conditions. Significant enrichment of middle REEs (MREEs) and heavy REEs (HREEs) was observed in plant roots and leaves respectively, with slight fractionation between light REEs (LREEs) and HREEs in stems. Moreover, the tetrad effect was observed in these organs. Investigations into REE speciation in roots and in the xylem sap using X-ray absorption spectroscopy (XAS) and nanometer-sized TiO2 adsorption techniques, associated with other controlled experiments, demonstrated that REE fractionations should be dominated by fixation mechanism in roots caused by cell wall absorption and phosphate precipitation, and by the combined effects of fixation mechanism and transport mechanism in aboveground parts caused by solution complexation by intrinsic organic ligands. A conceptive model was established for REE fractionations in plants based on the above studies.
Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate
Directory of Open Access Journals (Sweden)
Adnane Boukhouima
2017-01-01
Full Text Available We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV infection. In the model, the infection transmission process is modeled by a specific functional response. First, we show that the model is mathematically and biologically well posed. Second, the local and global stabilities of the equilibria are investigated. Finally, some numerical simulations are presented in order to illustrate our theoretical results.
Directory of Open Access Journals (Sweden)
Salman IJAZ
2018-05-01
Full Text Available In this paper, a methodology has been developed to address the issue of force fighting and to achieve precise position tracking of control surface driven by two dissimilar actuators. The nonlinear dynamics of both actuators are first approximated as fractional order models. Based on the identified models, three fractional order controllers are proposed for the whole system. Two Fractional Order PID (FOPID controllers are dedicated to improving transient response and are designed in a position feedback configuration. In order to synchronize the actuator dynamics, a third fractional order PI controller is designed, which feeds the force compensation signal in position feedback loop of both actuators. Nelder-Mead (N-M optimization technique is employed in order to optimally tune controller parameters based on the proposed performance criteria. To test the proposed controllers according to real flight condition, an external disturbance of higher amplitude that acts as airload is applied directly on the control surface. In addition, a disturbance signal function of system states is applied to check the robustness of proposed controller. Simulation results on nonlinear system model validated the performance of the proposed scheme as compared to optimal PID and high gain PID controllers. Keywords: Aerospace, Fractional order control, Model identification, Nelder-Mead optimization, Robustness
Modelling size-fractionated primary production in the Atlantic Ocean from remote sensing
Brewin, Robert J. W.; Tilstone, Gavin H.; Jackson, Thomas; Cain, Terry; Miller, Peter I.; Lange, Priscila K.; Misra, Ankita; Airs, Ruth L.
2017-11-01
Marine primary production influences the transfer of carbon dioxide between the ocean and atmosphere, and the availability of energy for the pelagic food web. Both the rate and the fate of organic carbon from primary production are dependent on phytoplankton size. A key aim of the Atlantic Meridional Transect (AMT) programme has been to quantify biological carbon cycling in the Atlantic Ocean and measurements of total primary production have been routinely made on AMT cruises, as well as additional measurements of size-fractionated primary production on some cruises. Measurements of total primary production collected on the AMT have been used to evaluate remote-sensing techniques capable of producing basin-scale estimates of primary production. Though models exist to estimate size-fractionated primary production from satellite data, these have not been well validated in the Atlantic Ocean, and have been parameterised using measurements of phytoplankton pigments rather than direct measurements of phytoplankton size structure. Here, we re-tune a remote-sensing primary production model to estimate production in three size fractions of phytoplankton (10 μm) in the Atlantic Ocean, using measurements of size-fractionated chlorophyll and size-fractionated photosynthesis-irradiance experiments conducted on AMT 22 and 23 using sequential filtration-based methods. The performance of the remote-sensing technique was evaluated using: (i) independent estimates of size-fractionated primary production collected on a number of AMT cruises using 14C on-deck incubation experiments and (ii) Monte Carlo simulations. Considering uncertainty in the satellite inputs and model parameters, we estimate an average model error of between 0.27 and 0.63 for log10-transformed size-fractionated production, with lower errors for the small size class (10 μm), and errors generally higher in oligotrophic waters. Application to satellite data in 2007 suggests the contribution of cells 2 μm to total
Directory of Open Access Journals (Sweden)
José Francisco Gómez Aguilar
2012-07-01
Full Text Available Using the fractional calculus approach, we present the Laplace analysis of an equivalent electrical circuit for a multilayered system, which includes distributed elements of the Cole model type. The Bode graphs are obtained from the numerical simulation of the corresponding transfer functions using arbitrary electrical parameters in order to illustrate the methodology. A numerical Laplace transform is used with respect to the simulation of the fractional differential equations. From the results shown in the analysis, we obtain the formula for the equivalent electrical circuit of a simple spectrum, such as that generated by a real sample of blood tissue, and the corresponding Nyquist diagrams. In addition to maintaining consistency in adjusted electrical parameters, the advantage of using fractional differential equations in the study of the impedance spectra is made clear in the analysis used to determine a compact formula for the equivalent electrical circuit, which includes the Cole model and a simple RC model as special cases.
International Nuclear Information System (INIS)
Baumann, Stefan; Wang, Rui; Schoepf, U.J.; Steinberg, Daniel H.; Spearman, James V.; Bayer, Richard R.; Hamm, Christian W.; Renker, Matthias
2015-01-01
The present study aimed to determine the feasibility of a novel fractional flow reserve (FFR) algorithm based on coronary CT angiography (cCTA) that permits point-of-care assessment, without data transfer to core laboratories, for the evaluation of potentially ischemia-causing stenoses. To obtain CT-based FFR, anatomical coronary information and ventricular mass extracted from cCTA datasets were integrated with haemodynamic parameters. CT-based FFR was assessed for 36 coronary artery stenoses in 28 patients in a blinded fashion and compared to catheter-based FFR. Haemodynamically relevant stenoses were defined by an invasive FFR ≤0.80. Time was measured for the processing of each cCTA dataset and CT-based FFR computation. Assessment of cCTA image quality was performed using a 5-point scale. Mean total time for CT-based FFR determination was 51.9 ± 9.0 min. Per-vessel analysis for the identification of lesion-specific myocardial ischemia demonstrated good correlation (Pearson's product-moment r = 0.74, p < 0.0001) between the prototype CT-based FFR algorithm and invasive FFR. Subjective image quality analysis resulted in a median score of 4 (interquartile ranges, 3-4). Our initial data suggest that the CT-based FFR method for the detection of haemodynamically significant stenoses evaluated in the selected population correlates well with invasive FFR and renders time-efficient point-of-care assessment possible. (orig.)
Alvarez-Zaldívar, Pablo; Imfeld, Gwenaël; Maier, Uli; Centler, Florian; Thullner, Martin
2013-04-01
In recent years, the use of (constructed) wetlands has gained significant attention for the in situ remediation of groundwater contaminated with (chlorinated) organic hydrocarbons. Although many sophisticated experimental methods exist for the assessment of contaminant removal in such wetlands the understanding how changes in wetland hydrochemistry affect the removal processes is still limited. This knowledge gap might be reduced by the use of biogeochemical reactive transport models. This study presents the reactive transport simulation of a small-scale constructed wetland treated with groundwater containing cis-1,2-dichloroethene (cDCE). Simulated processes consider different cDCE biodegradation pathways and the associated carbon isotope fractionation, a set of further (bio)geochemical processes as well as the activity of the plant roots. Spatio-temporal hydrochemical and isotope data from a long-term constructed wetland experiment [1] are used to constrain the model. Simulation results for the initial oxic phase of the wetland experiment indicate carbon isotope enrichment factors typical for cometabolic DCE oxidation, which suggests that aerobic treatment of cDCE is not an optimal remediation strategy. For the later anoxic phase of the experiment model derived enrichment factors indicate reductive dechlorination pathways. This degradation is promoted at all wetland depths by a sufficient availability of electron donor and carbon sources from root exudates, which makes the anoxic treatment of groundwater in such wetlands an effective remediation strategy. In combination with the previous experimental data results from this study suggest that constructed wetlands are viable remediation means for the treatment of cDCE contaminated groundwater. Reactive transport models can improve the understanding of the factors controlling chlorinated ethenes removal, and the used model approach would also allow for an optimization of the wetland operation needed for a complete
A mathematical model of the nine-month pregnant woman for calculating specific absorbed fractions
International Nuclear Information System (INIS)
Watson, E.E.; Stabin, M.G.
1987-01-01
Existing models which allow calculation of internal doses from radionuclide intakes by both men and women are based on a mathematical model of Reference Man. No attempt has been made to allow for the changing geometric relationships that occur during pregnancy which would affect the doses to the mother's organs and to the fetus. As pregnancy progresses, many of the mother's abdominal organs are repositioned, and their shapes may be somewhat changed. Estimation of specific absorbed fractions requires that existing mathematical models be modified to accommodate these changes. Specific absorbed fractions for Reference Woman at three, six and nine months of pregnancy should be sufficient for estimating the doses to the pregnant woman and the fetus. This report describes a model for the pregnant woman at nine months. An enlarged uterus was incorporated into a model for Reference Woman. Several abdominal organs as well as the exterior of the trunk were modified to accommodate the new uterus. This model will allow calculation of specific absorbed fractions for the fetus from photon emitters in maternal organs. Specific absorbed fractions for the repositioned maternal organs from other organs can also be calculated. 14 refs.; 2 figs
A mathematical model of the nine-month pregnant woman for calculating specific absorbed fractions
International Nuclear Information System (INIS)
Watson, E.E.; Stabin, M.G.
1986-01-01
Existing models that allow calculation of internal doses from radionuclide intakes by both men and women are based on a mathematical model of Reference Man. No attempt has been made to allow for the changing geometric relationships that occur during pregnancy which would affect the doses to the mother's organs and to the fetus. As pregnancy progresses, many of the mother's abdominal organs are repositioned, and their shapes may be somewhat changed. Estimation of specific absorbed fractions requires that existing mathematical models be modified to accommodate these changes. Specific absorbed fractions for Reference Woman at three, six, and nine months of pregnancy should be sufficient for estimating the doses to the pregnant woman and the fetus. This report describes a model for the pregnant woman at nine months. An enlarged uterus was incorporated into a model for Reference Woman. Several abdominal organs as well as the exterior of the trunk were modified to accommodate the new uterus. This model will allow calculation of specific absorbed fractions for the fetus from photon emitters in maternal organs. Specific absorbed fractions for the repositioned maternal organs from other organs can also be calculated. 14 refs., 2 figs
Directory of Open Access Journals (Sweden)
Anette Hauge
2017-11-01
Full Text Available Abstract Background Abnormalities in the tumor microenvironment are associated with resistance to treatment, aggressive growth, and poor clinical outcome in patients with advanced cervical cancer. The potential of dynamic contrast-enhanced (DCE MRI to assess the microvascular density (MVD, interstitial fluid pressure (IFP, and hypoxic fraction of patient-derived cervical cancer xenografts was investigated in the present study. Methods Four patient-derived xenograft (PDX models of squamous cell carcinoma of the uterine cervix (BK-12, ED-15, HL-16, and LA-19 were subjected to Gd-DOTA-based DCE-MRI using a 7.05 T preclinical scanner. Parametric images of the volume transfer constant (K trans and the fractional distribution volume (v e of the contrast agent were produced by pharmacokinetic analyses utilizing the standard Tofts model. Whole tumor median values of the DCE-MRI parameters were compared with MVD and the fraction of hypoxic tumor tissue, as determined histologically, and IFP, as measured with a Millar catheter. Results Both on the PDX model level and the single tumor level, a significant inverse correlation was found between K trans and hypoxic fraction. The extent of hypoxia was also associated with the fraction of voxels with unphysiological v e values (v e > 1.0. None of the DCE-MRI parameters were related to MVD or IFP. Conclusions DCE-MRI may provide valuable information on the hypoxic fraction of squamous cell carcinoma of the uterine cervix, and thereby facilitate individualized patient management.
Two-Part Models for Fractional Responses Defined as Ratios of Integers
Directory of Open Access Journals (Sweden)
Harald Oberhofer
2014-09-01
Full Text Available This paper discusses two alternative two-part models for fractional response variables that are defined as ratios of integers. The first two-part model assumes a Binomial distribution and known group size. It nests the one-part fractional response model proposed by Papke and Wooldridge (1996 and, thus, allows one to apply Wald, LM and/or LR tests in order to discriminate between the two models. The second model extends the first one by allowing for overdispersion in the data. We demonstrate the usefulness of the proposed two-part models for data on the 401(k pension plan participation rates used in Papke and Wooldridge (1996.
Simultaneous inference for model averaging of derived parameters
DEFF Research Database (Denmark)
Jensen, Signe Marie; Ritz, Christian
2015-01-01
Model averaging is a useful approach for capturing uncertainty due to model selection. Currently, this uncertainty is often quantified by means of approximations that do not easily extend to simultaneous inference. Moreover, in practice there is a need for both model averaging and simultaneous...... inference for derived parameters calculated in an after-fitting step. We propose a method for obtaining asymptotically correct standard errors for one or several model-averaged estimates of derived parameters and for obtaining simultaneous confidence intervals that asymptotically control the family...
Inflationary models with non-minimally derivative coupling
International Nuclear Information System (INIS)
Yang, Nan; Fei, Qin; Gong, Yungui; Gao, Qing
2016-01-01
We derive the general formulae for the scalar and tensor spectral tilts to the second order for the inflationary models with non-minimally derivative coupling without taking the high friction limit. The non-minimally kinetic coupling to Einstein tensor brings the energy scale in the inflationary models down to be sub-Planckian. In the high friction limit, the Lyth bound is modified with an extra suppression factor, so that the field excursion of the inflaton is sub-Planckian. The inflationary models with non-minimally derivative coupling are more consistent with observations in the high friction limit. In particular, with the help of the non-minimally derivative coupling, the quartic power law potential is consistent with the observational constraint at 95% CL. (paper)
Model for the isotopic fractionation of water in the Amazon basin
International Nuclear Information System (INIS)
Dall'Olio, A.; Azevedo, C.T. de
1979-01-01
Two models on the isotopic fractionation of water are presented. In the first model. It is assumed that the only source of water vapour for the Amazon region is the Atlantic Ocean, introduced by the predominant easterly winds. The second model contains the assumption that the forest also serves as a source of water vapour contributing an equal volume of water to the regional rains as the vapour of oceanic origin. (Author) [pt
Nascimento, Paulo Cicero; Gobo, Luciana Assis; Bohrer, Denise; Carvalho, Leandro Machado; Cravo, Margareth Coutinho; Leite, Leni Figueiredo Mathias
2015-12-01
Liquid chromatography coupled to mass spectrometry with atmospheric pressure chemical ionization was used for the determination of polycyclic aromatic hydrocarbon derivatives, the oxygenated polycyclic aromatic hydrocarbons and nitrated polycyclic aromatic hydrocarbons, formed in asphalt fractions. Two different methods have been developed for the determination of five oxygenated and seven nitrated polycyclic aromatic hydrocarbons that are characterized by having two or more condensed aromatic rings and present mutagenic and carcinogenic properties. The parameters of the atmospheric pressure chemical ionization interface were optimized to obtain the highest possible sensitivity for all compounds. The detection limits of the methods ranged from 0.1 to 57.3 μg/L for nitrated and from 0.1 to 6.6 μg/L for oxygenated derivatives. The limits of quantification were in the range of 4.6-191 μg/L for nitrated and 0.3-8.9 μg/L for oxygenated derivatives. The methods were validated against a diesel particulate extract standard reference material (National Institute of Standards and Technology SRM 1975), and the obtained concentrations (two nitrated derivatives) agreed with the certified values. The methods were applied in the analysis of asphalt samples after their fractionation into asphaltenes and maltenes, according to American Society for Testing and Material D4124, where the maltenic fraction was further separated into its basic, acidic, and neutral parts following the method of Green. Only two nitrated derivatives were found in the asphalt sample, quinoline and 2-nitrofluorene, with concentrations of 9.26 and 2146 mg/kg, respectively, whereas no oxygenated derivatives were detected. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Xin, X.; Li, F.; Peng, Z.; Qinhuo, L.
2017-12-01
Land surface heterogeneities significantly affect the reliability and accuracy of remotely sensed evapotranspiration (ET), and it gets worse for lower resolution data. At the same time, temporal scale extrapolation of the instantaneous latent heat flux (LE) at satellite overpass time to daily ET are crucial for applications of such remote sensing product. The purpose of this paper is to propose a simple but efficient model for estimating daytime evapotranspiration considering heterogeneity of mixed pixels. In order to do so, an equation to calculate evapotranspiration fraction (EF) of mixed pixels was derived based on two key assumptions. Assumption 1: the available energy (AE) of each sub-pixel equals approximately to that of any other sub-pixels in the same mixed pixel within acceptable margin of bias, and as same as the AE of the mixed pixel. It's only for a simpification of the equation, and its uncertainties and resulted errors in estimated ET are very small. Assumption 2: EF of each sub-pixel equals to the EF of the nearest pure pixel(s) of same land cover type. This equation is supposed to be capable of correcting the spatial scale error of the mixed pixels EF and can be used to calculated daily ET with daily AE data.The model was applied to an artificial oasis in the midstream of Heihe River. HJ-1B satellite data were used to estimate the lumped fluxes at the scale of 300 m after resampling the 30-m resolution datasets to 300 m resolution, which was used to carry on the key step of the model. The results before and after correction were compare to each other and validated using site data of eddy-correlation systems. Results indicated that the new model is capable of improving accuracy of daily ET estimation relative to the lumped method. Validations at 12 sites of eddy-correlation systems for 9 days of HJ-1B overpass showed that the R² increased to 0.82 from 0.62; the RMSE decreased to 1.60 MJ/m² from 2.47MJ/m²; the MBE decreased from 1.92 MJ/m² to 1
Popović, Jovan K.; Spasić, Dragan T.; Tošić, Jela; Kolarović, Jovanka L.; Malti, Rachid; Mitić, Igor M.; Pilipović, Stevan; Atanacković, Teodor M.
2015-05-01
The aim of this study is to promote a model based on the fractional differential calculus related to the pharmacokinetic individualization of high dose methotrexate treatment in children with acute lymphoblastic leukaemia, especially in high risk patients. We applied two-compartment fractional model on 8 selected cases with the largest number (4-19) of measured concentrations, among 43 pediatric patients received 24-h methotrexate 2-5 g/m2 infusions. The plasma concentrations were determined by fluorescence polarization immunoassay. Our mathematical procedure, designed by combining Post's and Newton's method, was coded in Mathematica 8.0 and performed on Fujicu Celsius M470-2 PC. Experimental data show that most of the measured values of methotrexate were in decreasing order. However, in certain treatments local maximums were detected. On the other hand, integer order compartmental models do not give values which fit well with the observed data. By the use of our model, we obtained better results, since it gives more accurate behavior of the transmission, as well as the local maximums which were recognized in methotrexate monitoring. It follows from our method that an additional test with a small methotrexate dose can be suggested for the fractional system parameter identification and the prediction of a possible pattern with a full dose in the case of high risk patients. A special feature of the fractional model is that it can also recognize and better fit an observed non-monotonic behavior. A new parameter determination procedure can be successfully used.
Flow of magnetic particles in blood with isothermal heating: A fractional model for two-phase flow
Ali, Farhad; Imtiaz, Anees; Khan, Ilyas; Sheikh, Nadeem Ahmad
2018-06-01
In the sixteenth century, medical specialists were of the conclusion that magnet can be utilized for the treatment or wipe out the illnesses from the body. On this basis, the research on magnet advances day by day for the treatment of different types of diseases in mankind. This study aims to investigate the effect of magnetic field and their applications in human body specifically in blood. Blood is a non-Newtonian fluid because its viscosity depends strongly on the fraction of volume occupied by red cells also called the hematocrit. Therefore, in this paper blood is considered as an example of non-Newtonian Casson fluid. The blood flow is considered in a vertical cylinder together with heat transfer due to mixed conviction caused by buoyancy force and the external pressure gradient. Effect of magnetic field on the velocities of blood and magnetic particles is also considered. The problem is modelled using the Caputo-Fabrizio derivative approach. The governing fractional partial differential equations are solved using Laplace and Hankel transformation techniques and exact solutions are obtained. Effects of different parameters such as Grashof number, Prandtl number, Casson fluid parameter and fractional parameters, and magnetic field are shown graphically. Both velocity profiles increase with the increase of Grashoff number and Casson fluid parameter and reduce with the increase of magnetic field.
Hamiltonian derivation of a gyrofluid model for collisionless magnetic reconnection
International Nuclear Information System (INIS)
Tassi, E
2014-01-01
We consider a simple electromagnetic gyrokinetic model for collisionless plasmas and show that it possesses a Hamiltonian structure. Subsequently, from this model we derive a two-moment gyrofluid model by means of a procedure which guarantees that the resulting gyrofluid model is also Hamiltonian. The first step in the derivation consists of imposing a generic fluid closure in the Poisson bracket of the gyrokinetic model, after expressing such bracket in terms of the gyrofluid moments. The constraint of the Jacobi identity, which every Poisson bracket has to satisfy, selects then what closures can lead to a Hamiltonian gyrofluid system. For the case at hand, it turns out that the only closures (not involving integro/differential operators or an explicit dependence on the spatial coordinates) that lead to a valid Poisson bracket are those for which the second order parallel moment, independently for each species, is proportional to the zero order moment. In particular, if one chooses an isothermal closure based on the equilibrium temperatures and derives accordingly the Hamiltonian of the system from the Hamiltonian of the parent gyrokinetic model, one recovers a known Hamiltonian gyrofluid model for collisionless reconnection. The proposed procedure, in addition to yield a gyrofluid model which automatically conserves the total energy, provides also, through the resulting Poisson bracket, a way to derive further conservation laws of the gyrofluid model, associated with the so called Casimir invariants. We show that a relation exists between Casimir invariants of the gyrofluid model and those of the gyrokinetic parent model. The application of such Hamiltonian derivation procedure to this two-moment gyrofluid model is a first step toward its application to more realistic, higher-order fluid or gyrofluid models for tokamaks. It also extends to the electromagnetic gyrokinetic case, recent applications of the same procedure to Vlasov and drift- kinetic systems
Monbouquette, H G
1987-06-01
Intrinsic models, which take into account biomass volume fraction, must be formulated for adequate simulation of high-biomass-density fermentations with cell recycle. Through comparison of corresponding intrinsic and non-intrinsic models in dimensionless form, constraints for non-intrinsic model usage in terms of biokinetic and fermenter operating parameters can be identified a priori. Analysis of a simple product-inhibition model indicates that the non-intrinsic approach is suitable only when the attainable biomass volume fraction in the fermentation broth is less than about 0.10. Inappropriate application of a non-intrinsic model can lead to gross errors in calculated substrate and product concentrations, substrate conversion, and volumetric productivity.
Models for high cell density bioreactors must consider biomass volume fraction: cell recycle example
Energy Technology Data Exchange (ETDEWEB)
Monbouquette, H.G.
1987-06-01
Intrinsic models, which take into account biomass volume fraction, must be formulated for adequate simulation of high-biomass-density fermentations with cell recycle. Through comparison of corresponding intrinsic and non-intrinsic models in dimensionless form, constraints for non-intrinsic model usage in terms of biokinetic and fermenter operating parameters can be identified a priori. Analysis of a simple product-inhibition model indicates that the non-intrinsic approach is suitable only when the attainable biomass volume fraction in the fermentation broth is less than about 0.10. Inappropriate application of a non-intrinsic model can lead to gross errors in calculated substrate and product concentrations, substrate conversion, and volumetric productivity. (Refs. 14).
Directory of Open Access Journals (Sweden)
Rafał Stanisławski
2016-01-01
Full Text Available This paper presents new results on modeling and analysis of dynamics of fractional-order discrete-time linear time-invariant single-input single-output (LTI SISO systems by means of new, two-layer, “fractional-order discrete-time Laguerre filters.” It is interesting that the fractionality of the filters at the upper system dynamics layer is directly projected from the lower Laguerre-based approximation layer for the Grünwald-Letnikov difference. A new stability criterion for discrete-time fractional-order Laguerre-based LTI SISO systems is introduced and supplemented with a stability preservation analysis. Both the stability criterion and the stability preservation analysis bring up rather surprising results, which is illustrated with simulation examples.
Directory of Open Access Journals (Sweden)
Kai Liu
2017-05-01
Full Text Available Quantifying vegetation fractional cover (VFC and assessing its role in heat fluxes modeling using medium resolution remotely sensed data has received less attention than it deserves in heterogeneous urban regions. This study examined two approaches (Normalized Difference Vegetation Index (NDVI-derived and Multiple Endmember Spectral Mixture Analysis (MESMA-derived methods that are commonly used to map VFC based on Landsat imagery, in modeling surface heat fluxes in urban landscape. For this purpose, two different heat flux models, Two-source energy balance (TSEB model and Pixel Component Arranging and Comparing Algorithm (PCACA model, were adopted for model evaluation and analysis. A comparative analysis of the NDVI-derived and MESMA-derived VFCs showed that the latter achieved more accurate estimates in complex urban regions. When the two sources of VFCs were used as inputs to both TSEB and PCACA models, MESMA-derived urban VFC produced more accurate urban heat fluxes (Bowen ratio and latent heat flux relative to NDVI-derived urban VFC. Moreover, our study demonstrated that Landsat imagery-retrieved VFC exhibited greater uncertainty in obtaining urban heat fluxes for the TSEB model than for the PCACA model.
Fractional poisson--a simple dose-response model for human norovirus.
Messner, Michael J; Berger, Philip; Nappier, Sharon P
2014-10-01
This study utilizes old and new Norovirus (NoV) human challenge data to model the dose-response relationship for human NoV infection. The combined data set is used to update estimates from a previously published beta-Poisson dose-response model that includes parameters for virus aggregation and for a beta-distribution that describes variable susceptibility among hosts. The quality of the beta-Poisson model is examined and a simpler model is proposed. The new model (fractional Poisson) characterizes hosts as either perfectly susceptible or perfectly immune, requiring a single parameter (the fraction of perfectly susceptible hosts) in place of the two-parameter beta-distribution. A second parameter is included to account for virus aggregation in the same fashion as it is added to the beta-Poisson model. Infection probability is simply the product of the probability of nonzero exposure (at least one virus or aggregate is ingested) and the fraction of susceptible hosts. The model is computationally simple and appears to be well suited to the data from the NoV human challenge studies. The model's deviance is similar to that of the beta-Poisson, but with one parameter, rather than two. As a result, the Akaike information criterion favors the fractional Poisson over the beta-Poisson model. At low, environmentally relevant exposure levels (Poisson model; however, caution is advised because no subjects were challenged at such a low dose. New low-dose data would be of great value to further clarify the NoV dose-response relationship and to support improved risk assessment for environmentally relevant exposures. © 2014 Society for Risk Analysis Published 2014. This article is a U.S. Government work and is in the public domain for the U.S.A.
DEFF Research Database (Denmark)
Nielsen, Kræn Vodder; Blanke, Mogens; Eriksson, Lars
2016-01-01
the behavior of the scavenge oxygen fraction well over the entire envelope of load and blower speed range that are relevant for EGR. The simplicity of the new model makes it suitable for observer and control design, which are essential steps to meet the emission requirements for marine diesel engines that take...
Wang, Xiao-Tian; Wu, Min; Zhou, Ze-Min; Jing, Wei-Shu
2012-02-01
This paper deals with the problem of discrete time option pricing using the fractional long memory stochastic volatility model with transaction costs. Through the 'anchoring and adjustment' argument in a discrete time setting, a European call option pricing formula is obtained.
Using Semiotic Resources to Build Images When Teaching the Part-Whole Model of Fractions
Mildenhall, Paula
2013-01-01
This paper reports an exploration into the use of a combination of semiotic resources when teaching the part-whole model of fractions. The study involved a single case study of one class teacher and six students in an Australian primary classroom. Using video as the predominate research tool it was possible to describe how gesture and language…
Hopf bifurcations in a fractional reaction–diffusion model for the ...
African Journals Online (AJOL)
The phenomenon of hopf bifurcation has been well-studied and applied to many physical situations to explain behaviour of solutions resulting from differential and partial differential equations. This phenomenon is applied to a fractional reaction diffusion model for tumor invasion and development. The result suggests that ...
Modelling of stable isotope fractionation by methane oxidation and diffusion in landfill cover soils
International Nuclear Information System (INIS)
Mahieu, Koenraad; De Visscher, Alex; Vanrolleghem, Peter A.; Van Cleemput, Oswald
2008-01-01
A technique to measure biological methane oxidation in landfill cover soils that is gaining increased interest is the measurement of stable isotope fractionation in the methane. Usually to quantify methane oxidation, only fractionation by oxidation is taken into account. Recently it was shown that neglecting the isotope fractionation by diffusion results in underestimation of the methane oxidation. In this study a simulation model was developed that describes gas transport and methane oxidation in landfill cover soils. The model distinguishes between 12 CH 4 , 13 CH 4 , and 12 CH 3 D explicitly, and includes isotope fractionation by diffusion and oxidation. To evaluate the model, the simulations were compared with column experiments from previous studies. The predicted concentration profiles and isotopic profiles match the measured ones very well, with a root mean square deviation (RMSD) of 1.7 vol% in the concentration and a RMSD of 0.8 per mille in the δ 13 C value, with δ 13 C the relative 13 C abundance as compared to an international standard. Overall, the comparison shows that a model-based isotope approach for the determination of methane oxidation efficiencies is feasible and superior to existing isotope methods
Sharp, Emily; Shih Dennis, Minyi
2017-01-01
This study used a multiple probe across participants design to examine the effects of a model drawing strategy (MDS) intervention package on fraction comparing and ordering word problem-solving performance of three Grade 4 students. MDS is a form of cognitive strategy instruction for teaching word problem solving that includes explicit instruction…
Analytical modeling for fractional multi-dimensional diffusion equations by using Laplace transform
Directory of Open Access Journals (Sweden)
Devendra Kumar
2015-01-01
Full Text Available In this paper, we propose a simple numerical algorithm for solving multi-dimensional diffusion equations of fractional order which describes density dynamics in a material undergoing diffusion by using homotopy analysis transform method. The fractional derivative is described in the Caputo sense. This homotopy analysis transform method is an innovative adjustment in Laplace transform method and makes the calculation much simpler. The technique is not limited to the small parameter, such as in the classical perturbation method. The scheme gives an analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive.
Modeling neurodegenerative diseases with patient-derived induced pluripotent cells
DEFF Research Database (Denmark)
Poon, Anna; Zhang, Yu; Chandrasekaran, Abinaya
2017-01-01
patient-specific induced pluripotent stem cells (iPSCs) and isogenic controls generated using CRISPR-Cas9 mediated genome editing. The iPSCs are self-renewable and capable of being differentiated into the cell types affected by the diseases. These in vitro models based on patient-derived iPSCs provide...... the possibilities of generating three-dimensional (3D) models using the iPSCs-derived cells and compare their advantages and disadvantages to conventional two-dimensional (2D) models....
Fractional dosing of yellow fever vaccine to extend supply: a modelling study.
Wu, Joseph T; Peak, Corey M; Leung, Gabriel M; Lipsitch, Marc
2016-12-10
The ongoing yellow fever epidemic in Angola strains the global vaccine supply, prompting WHO to adopt dose sparing for its vaccination campaign in Kinshasa, Democratic Republic of the Congo, in July-August, 2016. Although a 5-fold fractional-dose vaccine is similar to standard-dose vaccine in safety and immunogenicity, efficacy is untested. There is an urgent need to ensure the robustness of fractional-dose vaccination by elucidation of the conditions under which dose fractionation would reduce transmission. We estimate the effective reproductive number for yellow fever in Angola using disease natural history and case report data. With simple mathematical models of yellow fever transmission, we calculate the infection attack rate (the proportion of population infected over the course of an epidemic) with various levels of transmissibility and 5-fold fractional-dose vaccine efficacy for two vaccination scenarios, ie, random vaccination in a hypothetical population that is completely susceptible, and the Kinshasa vaccination campaign in July-August, 2016, with different age cutoff for fractional-dose vaccines. We estimate the effective reproductive number early in the Angola outbreak was between 5·2 and 7·1. If vaccine action is all-or-nothing (ie, a proportion of vaccine recipients receive complete protection [VE] and the remainder receive no protection), n-fold fractionation can greatly reduce infection attack rate as long as VE exceeds 1/n. This benefit threshold becomes more stringent if vaccine action is leaky (ie, the susceptibility of each vaccine recipient is reduced by a factor that is equal to the vaccine efficacy). The age cutoff for fractional-dose vaccines chosen by WHO for the Kinshasa vaccination campaign (2 years) provides the largest reduction in infection attack rate if the efficacy of 5-fold fractional-dose vaccines exceeds 20%. Dose fractionation is an effective strategy for reduction of the infection attack rate that would be robust with a
Fractional Dosing of Yellow Fever Vaccine to Extend Supply: A Modeling Study
Peak, Corey M.; Leung, Gabriel M.
2016-01-01
Background The ongoing yellow fever (YF) epidemic in Angola strains the global vaccine supply, prompting WHO to adopt dose sparing for its vaccination campaign in Kinshasa in July–August 2016. Although a 5-fold fractional-dose vaccine is similar to standard-dose vaccine in safety and immunogenicity, efficacy is untested. There is an urgent need to ensure the robustness of fractional-dose vaccination by elucidating the conditions under which dose fractionation would reduce transmission. Methods We estimate the effective reproductive number for YF in Angola using disease natural history and case report data. With simple mathematical models of YF transmission, we calculate the infection attack rate (IAR, the proportion of population infected over the course of an epidemic) under varying levels of transmissibility and five-fold fractional-dose vaccine efficacy for two vaccination scenarios: (i) random vaccination in a hypothetical population that is completely susceptible; (ii) the Kinshasa vaccination campaign in July–August 2016 with different age cutoff for fractional-dose vaccines. Findings We estimate the effective reproductive number early in the Angola outbreak was between 5·2 and 7·1. If vaccine action is all-or-nothing (i.e. a proportion VE of vaccinees receives complete and the remainder receive no protection), n-fold fractionation can dramatically reduce IAR as long as efficacy VE exceeds 1/n. This benefit threshold becomes more stringent if vaccine action is leaky (i.e. the susceptibility of each vaccinee is reduced by a factor that is equal to the vaccine efficacy VE). The age cutoff for fractional-dose vaccines chosen by the WHO for the Kinshasa vaccination campaign (namely, 2 years) provides the largest reduction in IAR if the efficacy of five-fold fractional-dose vaccines exceeds 20%. Interpretation Dose fractionation is a very effective strategy for reducing infection attack rate that would be robust with a large margin for error in case
Directory of Open Access Journals (Sweden)
Petráš Ivo
2011-01-01
Full Text Available This paper deals with the fractional-order linear and nonlinear models used in bioengineering applications and an effective method for their numerical solution. The proposed method is based on the power series expansion of a generating function. Numerical solution is in the form of the difference equation, which can be simply applied in the Matlab/Simulink to simulate the dynamics of system. Several illustrative examples are presented, which can be widely used in bioengineering as well as in the other disciplines, where the fractional calculus is often used.
Deriving the Dividend Discount Model in the Intermediate Microeconomics Class
Norman, Stephen; Schlaudraff, Jonathan; White, Karianne; Wills, Douglas
2013-01-01
In this article, the authors show that the dividend discount model can be derived using the basic intertemporal consumption model that is introduced in a typical intermediate microeconomics course. This result will be of use to instructors who teach microeconomics to finance students in that it demonstrates the value of utility maximization in…
On a derivation of the Salam-Weinberg model
International Nuclear Information System (INIS)
Squires, E.J.
1979-01-01
It is shown how the graded Lie-algebra structure of a recent derivation of the Salam-Weinberg model might arise from the form of allowed transformations on the lepton lagrangian in a 6-dimensional space. The possibility that the model might allow two identically coupled leptonic sectors, and others in which the chiralites are reversed, are discussed. (Auth.)
Some remarks on the small-distance derivative model
International Nuclear Information System (INIS)
Jannussis, A.
1985-01-01
In the present work the new expressions of the derivatives for small distance are investigated according to Gonzales-Diaz model. This model is noncanonical, is a particular case of the Lie-admissible formulation and has applications for distance and time scales comparable with the Planck dimensions
Modelling the spread of Ebola virus with Atangana-Baleanu fractional operators
Koca, Ilknur
2018-03-01
The model of Ebola spread within a targeted population is extended to the concept of fractional differentiation and integration with non-local and non-singular fading memory introduced by Atangana and Baleanu. It is expected that the proposed model will show better approximation than the models established before. The existence and uniqueness of solutions for the spread of Ebola disease model is given via the Picard-Lindelof method. Finally, numerical solutions for the model are given by using different parameter values.
Magin, Richard L.; Li, Weiguo; Velasco, M. Pilar; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.
2011-01-01
We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena (T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter (α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for microstructural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues. PMID:21498095
Stochastic modeling for neural spiking events based on fractional superstatistical Poisson process
Directory of Open Access Journals (Sweden)
Hidetoshi Konno
2018-01-01
Full Text Available In neural spike counting experiments, it is known that there are two main features: (i the counting number has a fractional power-law growth with time and (ii the waiting time (i.e., the inter-spike-interval distribution has a heavy tail. The method of superstatistical Poisson processes (SSPPs is examined whether these main features are properly modeled. Although various mixed/compound Poisson processes are generated with selecting a suitable distribution of the birth-rate of spiking neurons, only the second feature (ii can be modeled by the method of SSPPs. Namely, the first one (i associated with the effect of long-memory cannot be modeled properly. Then, it is shown that the two main features can be modeled successfully by a class of fractional SSPP (FSSPP.
Stochastic modeling for neural spiking events based on fractional superstatistical Poisson process
Konno, Hidetoshi; Tamura, Yoshiyasu
2018-01-01
In neural spike counting experiments, it is known that there are two main features: (i) the counting number has a fractional power-law growth with time and (ii) the waiting time (i.e., the inter-spike-interval) distribution has a heavy tail. The method of superstatistical Poisson processes (SSPPs) is examined whether these main features are properly modeled. Although various mixed/compound Poisson processes are generated with selecting a suitable distribution of the birth-rate of spiking neurons, only the second feature (ii) can be modeled by the method of SSPPs. Namely, the first one (i) associated with the effect of long-memory cannot be modeled properly. Then, it is shown that the two main features can be modeled successfully by a class of fractional SSPP (FSSPP).
Eluru, Naveen; Chakour, Vincent; Chamberlain, Morgan; Miranda-Moreno, Luis F
2013-10-01
Vehicle operating speed measured on roadways is a critical component for a host of analysis in the transportation field including transportation safety, traffic flow modeling, roadway geometric design, vehicle emissions modeling, and road user route decisions. The current research effort contributes to the literature on examining vehicle speed on urban roads methodologically and substantively. In terms of methodology, we formulate a new econometric model framework for examining speed profiles. The proposed model is an ordered response formulation of a fractional split model. The ordered nature of the speed variable allows us to propose an ordered variant of the fractional split model in the literature. The proposed formulation allows us to model the proportion of vehicles traveling in each speed interval for the entire segment of roadway. We extend the model to allow the influence of exogenous variables to vary across the population. Further, we develop a panel mixed version of the fractional split model to account for the influence of site-specific unobserved effects. The paper contributes substantively by estimating the proposed model using a unique dataset from Montreal consisting of weekly speed data (collected in hourly intervals) for about 50 local roads and 70 arterial roads. We estimate separate models for local roads and arterial roads. The model estimation exercise considers a whole host of variables including geometric design attributes, roadway attributes, traffic characteristics and environmental factors. The model results highlight the role of various street characteristics including number of lanes, presence of parking, presence of sidewalks, vertical grade, and bicycle route on vehicle speed proportions. The results also highlight the presence of site-specific unobserved effects influencing the speed distribution. The parameters from the modeling exercise are validated using a hold-out sample not considered for model estimation. The results indicate
Gao, Feng-Yin; Kang, Yan-Mei; Chen, Xi; Chen, Guanrong
2018-05-01
This paper reveals the effect of fractional Gaussian noise with Hurst exponent H ∈(1 /2 ,1 ) on the information capacity of a general nonlinear neuron model with binary signal input. The fGn and its corresponding fractional Brownian motion exhibit long-range, strong-dependent increments. It extends standard Brownian motion to many types of fractional processes found in nature, such as the synaptic noise. In the paper, for the subthreshold binary signal, sufficient conditions are given based on the "forbidden interval" theorem to guarantee the occurrence of stochastic resonance, while for the suprathreshold binary signal, the simulated results show that additive fGn with Hurst exponent H ∈(1 /2 ,1 ) could increase the mutual information or bits count. The investigation indicated that the synaptic noise with the characters of long-range dependence and self-similarity might be the driving factor for the efficient encoding and decoding of the nervous system.
Rigorous theoretical derivation of lumped models to transmission line systems
International Nuclear Information System (INIS)
Zhao Jixiang
2012-01-01
By virtue of the negative electric parameter concept, i.e. negative lumped resistance, inductance, conductance and capacitance (N-RLGC), the lumped equivalent models of transmission line systems, including the circuit model, two-port π-network and T-network, are given. We start from the N-segment-ladder-like equivalent networks composed distributed parameters, and achieve the input impedance in the form of a continued fraction. Utilizing the continued fraction theory, the expressions of input impedance are obtained under three kinds of extreme cases, i.e. the load impedances are equal to zero, infinity and characteristic impedance, respectively. When the number of segment N is limited to infinity, they are transformed to lumped elements. Comparison between the distributed model and lumped model of transmission lines, the expression of tanh γd, which is the key term in the transmission line equations, are obtained by RLGC, furthermore, according to input admittance, admittance matrix and ABCD matrix of transmission lines, the lumped equivalent circuit models, π-networks and T-networks have been given. The models are verified in the frequency and time domain, respectively, showing that the models are accurate and efficient. (semiconductor integrated circuits)
Yoshioka, M; Konno, S
1970-05-01
The endotoxin-altering activity of fractions isolated from normal horse serum was examined by incubation of Salmonella typhosa strain 0-901 endotoxin (Boivin) in a solution of the fraction, and subsequent quantitation of any diminution in the capacity of endotoxin to be precipitated by specific anti-endotoxin antiserum. The horse serum fraction isolated by precipitation with ammonium sulfate at a concentration between 1.6 and 2.7 m was incubated with Pronase PA and then with trypsin. When this partly digested fraction was passed twice through a Sephadex G-200 column and eluted with 0.2 m tris(hydroxymethyl)aminomethane buffer, most of the endotoxinaltering activity was found in the first protein peak designated F-1a. F-1a was found to be homogeneous and corresponded to an alpha(2)-macroglobulin by the techniques of electrophoresis, immunodiffusion, and ultracentrifugation. Approximately 100-fold more F-1a than endotoxin was needed to reduce the antigenicity of the endotoxin by one-half. Alteration was increased when F-1a was incubated with the endotoxin at acid pH or at 45 C rather than at 37 C and was lost after heating F-1a at 56 C for 30 min. N-ethylmaleimide increased the endotoxin-altering activity of horse serum, F-1a, and human plasma fraction III(0), whereas p-chloromercuribenzoate did not. On the other hand, diazonium-1-H-tetrazole, iodoacetic acid, and benzylchloride suppressed the activity of F-1a. When the interaction of endotoxin and F-1a was examined by immunodiffusion techniques, depolymerization of the endotoxin molecule was indicated. The endotoxin-altering factor of horse serum is discussed in relation to the mechanisms of other known reagents, such as deoxycholate and sodium lauryl sulfate.
Yoshioka, Morimasa; Konno, Seishi
1970-01-01
The endotoxin-altering activity of fractions isolated from normal horse serum was examined by incubation of Salmonella typhosa strain 0-901 endotoxin (Boivin) in a solution of the fraction, and subsequent quantitation of any diminution in the capacity of endotoxin to be precipitated by specific anti-endotoxin antiserum. The horse serum fraction isolated by precipitation with ammonium sulfate at a concentration between 1.6 and 2.7 m was incubated with Pronase PA and then with trypsin. When this partly digested fraction was passed twice through a Sephadex G-200 column and eluted with 0.2 m tris(hydroxymethyl)aminomethane buffer, most of the endotoxinaltering activity was found in the first protein peak designated F-1a. F-1a was found to be homogeneous and corresponded to an α2-macroglobulin by the techniques of electrophoresis, immunodiffusion, and ultracentrifugation. Approximately 100-fold more F-1a than endotoxin was needed to reduce the antigenicity of the endotoxin by one-half. Alteration was increased when F-1a was incubated with the endotoxin at acid pH or at 45 C rather than at 37 C and was lost after heating F-1a at 56 C for 30 min. N-ethylmaleimide increased the endotoxin-altering activity of horse serum, F-1a, and human plasma fraction III0, whereas p-chloromercuribenzoate did not. On the other hand, diazonium-1-H-tetrazole, iodoacetic acid, and benzylchloride suppressed the activity of F-1a. When the interaction of endotoxin and F-1a was examined by immunodiffusion techniques, depolymerization of the endotoxin molecule was indicated. The endotoxin-altering factor of horse serum is discussed in relation to the mechanisms of other known reagents, such as deoxycholate and sodium lauryl sulfate. Images PMID:16557754
International Nuclear Information System (INIS)
Ojima, Koichi; Uezumi, Akiyoshi; Miyoshi, Hiroyuki; Masuda, Satoru; Morita, Yohei; Fukase, Akiko; Hattori, Akihito; Nakauchi, Hiromitsu; Miyagoe-Suzuki, Yuko; Takeda, Shin'ichi
2004-01-01
Recent studies have shown that bone marrow (BM) cells, including the BM side population (BM-SP) cells that enrich hematopoietic stem cells (HSCs), are incorporated into skeletal muscle during regeneration, but it is not clear how and what kinds of BM cells contribute to muscle fiber regeneration. We found that a large number of SP cells migrated from BM to muscles following injury in BM-transplanted mice. These BM-derived SP cells in regenerating muscles expressed different surface markers from those of HSCs and could not reconstitute the mouse blood system. BM-derived SP/Mac-1 low cells increased in number in regenerating muscles following injury. Importantly, our co-culture studies with activated satellite cells revealed that this fraction carried significant potential for myogenic differentiation. By contrast, mature inflammatory (Mac-1 high ) cells showed negligible myogenic activities. Further, these BM-derived SP/Mac-1 low cells gave rise to mononucleate myocytes, indicating that their myogenesis was not caused by stochastic fusion with host myogenic cells, although they required cell-to-cell contact with myogenic cells for muscle differentiation. Taken together, our data suggest that neither HSCs nor mature inflammatory cells, but Mac-1 low early myeloid cells in the BM-derived SP fraction, play an important role in regenerating skeletal muscles
International Nuclear Information System (INIS)
Reis, Arlene A. dos; Cardoso, Joaquim C.S.; Lourenco, Maria Cristina
2005-01-01
The Publication 66 of International Commission of Radiological Protection (ICRP, 1994) presented the Human Respiratory tract Model that simulates the deposition and translocation of radioactive material in the air that penetrates in the body by inhalation. The main objective of this study is to evaluate the variation in fractional activity absorbed into blood when physiological and morphological parameters from Brazilian population are applied in the deposition model. The clearance model was implemented in the software Excel (version 2000) using a system of differential equations to solve simultaneous process of translocation and absorption of material deposited. After implementation were applied in the model fractional deposition calculated by deposition model using physiological and morphological parameters from Brazilian population. The results show that the variation in the clearance model depends on the material dissolution. For materials of rapid absorption, the variations calculated are not significant. Materials of moderate and slow absorption, presented variation greater than 20% in fractional activity absorbed into blood, depending on levels of exercise. (author)
Long-range transport and global fractionation of POPs: insights from multimedia modeling studies
International Nuclear Information System (INIS)
Scheringer, M.; Salzmann, M.; Stroebe, M.; Wegmann, F.; Fenner, K.; Hungerbuehler, K.
2004-01-01
The long-range transport of persistent organic pollutants (POPs) is investigated with two multimedia box models of the global system. ChemRange is a purely evaluative, one-dimensional steady-state (level III) model; CliMoChem is a two-dimensional model with different temperatures, land/water ratios and vegetation types in different latitudinal zones. Model results are presented for three case studies: (i) the effect of atmospheric aerosol particles on the long-range transport of POPs, (ii) the effect of oceanic deposition on the long-range transport of different PCB congeners, (iii) the global fractionation of different PCB congeners. The model results for these case studies show: (i) the low atmospheric half-lives estimated for several organochlorine pesticides are likely to be inconsistent with the observed long-range transport of these compounds; (ii) export to the deep sea reduces the potential for long-range transport of highly hydrophobic compounds (but does not remove these chemicals from the biosphere); (iii) there are different meanings of the term global fractionation that refer to different aspects of the fractionation process and need to be distinguished. The case-study results further indicate that the influences of varying environmental conditions on the physicochemical properties and the degradation rate constants of POPs need to be determined. - Multimedia box models are applied to case studies of the behavior of POPs
Ping, Bonnie Tay Yen; Aziz, Haliza Abdul; Idris, Zainab
2018-01-01
High-Performance Liquid Chromatography (HPLC) methods via evaporative light scattering (ELS) and refractive index (RI) detectors are used by the local palm oil industry to monitor the TAG profiles of palm oil and its fractions. The quantitation method used is based on area normalization of the TAG components and expressed as percentage area. Although not frequently used, peak-area ratios based on TAG profiles are a possible qualitative method for characterizing the TAG of palm oil and its fractions. This paper aims to compare these two detectors in terms of peak-area ratio, percentage peak area composition, and TAG elution profiles. The triacylglycerol (TAG) composition for palm oil and its fractions were analysed under similar HPLC conditions i.e. mobile phase and column. However, different sample concentrations were used for the detectors while remaining within the linearity limits of the detectors. These concentrations also gave a good baseline resolved separation for all the TAGs components. The results of the ELSD method's percentage area composition for the TAGs of palm oil and its fractions differed from those of RID. This indicates an unequal response of TAGs for palm oil and its fractions using the ELSD, also affecting the peak area ratios. They were found not to be equivalent to those obtained using the HPLC-RID. The ELSD method showed a better baseline separation for the TAGs components, with a more stable baseline as compared with the corresponding HPLC-RID. In conclusion, the percentage area compositions and peak-area ratios for palm oil and its fractions as derived from HPLC-ELSD and RID were not equivalent due to different responses of TAG components to the ELSD detector. The HPLC-RID has a better accuracy for percentage area composition and peak-area ratio because the TAG components response equally to the detector.
Longhi, J.
1977-01-01
A description is presented of an empirical model of fractional crystallization which predicts that slightly modified versions of certain of the proposed whole moon compositions can reproduce the major-element chemistry and mineralogy of most of the primitive highland rocks through equilibrium and fractional crystallization processes combined with accumulation of crystals and trapping of residual liquids. These compositions contain sufficient Al to form a plagioclase-rich crust 60 km thick on top of a magma ocean that was initially no deeper than about 300 km. Implicit in the model are the assumptions that all cooling and crystallization take place at low pressure and that there are no compositional or thermal gradients in the liquid. Discussions of the cooling and crystallization of the proposed magma ocean show these assumptions to be disturbingly naive when applied to the ocean as a whole. However, the model need not be applied to the whole ocean, but only to layers of cooling liquid near the surface.
Frequency dependence of complex moduli of brain tissue using a fractional Zener model
International Nuclear Information System (INIS)
Kohandel, M; Sivaloganathan, S; Tenti, G; Darvish, K
2005-01-01
Brain tissue exhibits viscoelastic behaviour. If loading times are substantially short, static tests are not sufficient to determine the complete viscoelastic behaviour of the material, and dynamic test methods are more appropriate. The concept of complex modulus of elasticity is a powerful tool for characterizing the frequency domain behaviour of viscoelastic materials. On the other hand, it is well known that classical viscoelastic models can be generalized by means of fractional calculus to describe more complex viscoelastic behaviour of materials. In this paper, the fractional Zener model is investigated in order to describe the dynamic behaviour of brain tissue. The model is fitted to experimental data of oscillatory shear tests of bovine brain tissue to verify its behaviour and to obtain the material parameters
Energy Technology Data Exchange (ETDEWEB)
Canat, S.
2005-07-15
Induction machine is most widespread in industry. Its traditional modeling does not take into account the eddy current in the rotor bars which however induce strong variations as well of the resistance as of the resistance of the rotor. This diffusive phenomenon, called 'skin effect' could be modeled by a compact transfer function using fractional derivative (non integer order). This report theoretically analyzes the electromagnetic phenomenon on a single rotor bar before approaching the rotor as a whole. This analysis is confirmed by the results of finite elements calculations of the magnetic field, exploited to identify a fractional order model of the induction machine (identification method of Levenberg-Marquardt). Then, the model is confronted with an identification of experimental results. Finally, an automatic method is carried out to approximate the dynamic model by integer order transfer function on a frequency band. (author)
Doubly 15N-substituted diazenylium: THz laboratory spectra and fractionation models
Dore, L.; Bizzocchi, L.; Wirström, E. S.; Degli Esposti, C.; Tamassia, F.; Charnley, S. B.
2017-07-01
Context. Isotopic fractionation in dense molecular cores has been suggested as a possible origin of large 14N/15N ratio variations in solar system materials. While chemical models can explain some observed variations with different fractionation patterns for molecules with -NH or -CN functional groups, they fail to reproduce the observed ratios in diazenylium (N2H+). Aims: Observations of doubly 15N-substituted species could provide important constraints and insights for theoretical chemical models of isotopic fractionation. However, spectroscopic data are very scarce. Methods: The rotational spectra of the fully 15N-substituted isopologues of the diazenylium ion, 15N2H+ and 15N2D+, have been investigated in the laboratory well into the THz region by using a source-modulation microwave spectrometer equipped with a negative glow discharge cell. An extended chemical reaction network has been used to estimate what ranges of 15N fractionation in doubly 15N-substituted species could be expected in the interstellar medium (ISM). Results: For each isotopologue of the H- and D-containing pair, nine rotational transitions were accurately measured in the frequency region 88 GHz-1.2 THz. The analysis of the spectrum provided very precise rest frequencies at millimeter and sub-millimeter wavelengths, useful for the radioastronomical identification of the rotational lines of 15N2H+ and 15N2D+ in the ISM.
Dipierro, Serena; Valdinoci, Enrico
2018-07-01
Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of hyperbolic equations, which typically exhibit shocks and discontinuities. In this paper, we show how a simple toy-model of a highly ramified structure, somehow inspired by that of the Purkinje cells, may produce a fractional diffusion via the superposition of travelling waves that solve a hyperbolic equation. This could suggest that the high ramification of the Purkinje cells might have provided an evolutionary advantage of "smoothing" the transmission of signals and avoiding shock propagations (at the price of slowing a bit such transmission). Although an experimental confirmation of the possibility of such evolutionary advantage goes well beyond the goals of this paper, we think that it is intriguing, as a mathematical counterpart, to consider the time fractional diffusion as arising from the superposition of delayed travelling waves in highly ramified transmission media. The case of a travelling concave parabola with sufficiently small curvature is explicitly computed. The new link that we propose between time fractional diffusion and hyperbolic equation also provides a novelty with respect to the usual paradigm relating time fractional diffusion with parabolic equations in the limit. This paper is written in such a way as to be of interest to both biologists and mathematician alike. In order to accomplish this aim, both complete explanations of the objects considered and detailed lists of references are provided.
Cheong, Chin Wen
2008-02-01
This article investigated the influences of structural breaks on the fractionally integrated time-varying volatility model in the Malaysian stock markets which included the Kuala Lumpur composite index and four major sectoral indices. A fractionally integrated time-varying volatility model combined with sudden changes is developed to study the possibility of structural change in the empirical data sets. Our empirical results showed substantial reduction in fractional differencing parameters after the inclusion of structural change during the Asian financial and currency crises. Moreover, the fractionally integrated model with sudden change in volatility performed better in the estimation and specification evaluations.
Diffusion with space memory modelled with distributed order space fractional differential equations
Directory of Open Access Journals (Sweden)
M. Caputo
2003-06-01
Full Text Available Distributed order fractional differential equations (Caputo, 1995, 2001; Bagley and Torvik, 2000a,b were fi rst used in the time domain; they are here considered in the space domain and introduced in the constitutive equation of diffusion. The solution of the classic problems are obtained, with closed form formulae. In general, the Green functions act as low pass fi lters in the frequency domain. The major difference with the case when a single space fractional derivative is present in the constitutive equations of diffusion (Caputo and Plastino, 2002 is that the solutions found here are potentially more fl exible to represent more complex media (Caputo, 2001a. The difference between the space memory medium and that with the time memory is that the former is more fl exible to represent local phenomena while the latter is more fl exible to represent variations in space. Concerning the boundary value problem, the difference with the solution of the classic diffusion medium, in the case when a constant boundary pressure is assigned and in the medium the pressure is initially nil, is that one also needs to assign the fi rst order space derivative at the boundary.
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.
Tan, Xiao Wei; Zheng, Qishi; Shi, Luming; Gao, Fei; Allen, John Carson; Coenen, Adriaan; Baumann, Stefan; Schoepf, U Joseph; Kassab, Ghassan S; Lim, Soo Teik; Wong, Aaron Sung Lung; Tan, Jack Wei Chieh; Yeo, Khung Keong; Chin, Chee Tang; Ho, Kay Woon; Tan, Swee Yaw; Chua, Terrance Siang Jin; Chan, Edwin Shih Yen; Tan, Ru San; Zhong, Liang
2017-06-01
To evaluate the combined diagnostic accuracy of coronary computed tomography angiography (CCTA) and computed tomography derived fractional flow reserve (FFRct) in patients with suspected or known coronary artery disease (CAD). PubMed, The Cochrane library, Embase and OpenGray were searched to identify studies comparing diagnostic accuracy of CCTA and FFRct. Diagnostic test measurements of FFRct were either extracted directly from the published papers or calculated from provided information. Bivariate models were conducted to synthesize the diagnostic performance of combined CCTA and FFRct at both "per-vessel" and "per-patient" levels. 7 articles were included for analysis. The combined diagnostic outcomes from "both positive" strategy, i.e. a subject was considered as "positive" only when both CCTA and FFRct were "positive", demonstrated relative high specificity (per-vessel: 0.91; per-patient: 0.81), high positive likelihood ratio (LR+, per-vessel: 7.93; per-patient: 4.26), high negative likelihood ratio (LR-, per-vessel: 0.30; per patient: 0.24) and high accuracy (per-vessel: 0.91; per-patient: 0.81) while "either positive" strategy, i.e. a subject was considered as "positive" when either CCTA or FFRct was "positive", demonstrated relative high sensitivity (per-vessel: 0.97; per-patient: 0.98), low LR+ (per-vessel: 1.50; per-patient: 1.17), low LR- (per-vessel: 0.07; per-patient: 0.09) and low accuracy (per-vessel: 0.57; per-patient: 0.54). "Both positive" strategy showed better diagnostic performance to rule in patients with non-significant stenosis compared to "either positive" strategy, as it efficiently reduces the proportion of testing false positive subjects. Copyright © 2017 Elsevier B.V. All rights reserved.
A New Model of the Fractional Order Dynamics of the Planetary Gears
Directory of Open Access Journals (Sweden)
Vera Nikolic-Stanojevic
2013-01-01
Full Text Available A theoretical model of planetary gears dynamics is presented. Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. In the paper, it has been indicated that even the small disturbance in design realizations of this gear cause nonlinear properties of dynamics which are the source of vibrations and noise in the gear transmission. Dynamic model of the planetary gears with four degrees of freedom is used. Applying the basic principles of analytical mechanics and taking the initial and boundary conditions into consideration, it is possible to obtain the system of equations representing physical meshing process between the two or more gears. This investigation was focused to a new model of the fractional order dynamics of the planetary gear. For this model analytical expressions for the corresponding fractional order modes like one frequency eigen vibrational modes are obtained. For one planetary gear, eigen fractional modes are obtained, and a visualization is presented. By using MathCAD the solution is obtained.
Modeling and Forecasting Average Temperature for Weather Derivative Pricing
Directory of Open Access Journals (Sweden)
Zhiliang Wang
2015-01-01
Full Text Available The main purpose of this paper is to present a feasible model for the daily average temperature on the area of Zhengzhou and apply it to weather derivatives pricing. We start by exploring the background of weather derivatives market and then use the 62 years of daily historical data to apply the mean-reverting Ornstein-Uhlenbeck process to describe the evolution of the temperature. Finally, Monte Carlo simulations are used to price heating degree day (HDD call option for this city, and the slow convergence of the price of the HDD call can be found through taking 100,000 simulations. The methods of the research will provide a frame work for modeling temperature and pricing weather derivatives in other similar places in China.
Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems
N'Doye, Ibrahima; Laleg-Kirati, Taous-Meriem
2015-01-01
This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.
Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems
N'Doye, Ibrahima
2015-07-01
This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.
DEFF Research Database (Denmark)
Stegmann, Mikkel Bille; Pedersen, Dorthe
2005-01-01
in four-dimensional MRI. The theoretical foundation of our work is the generative two-dimensional Active Appearance Models by Cootes et al., here extended to bi-temporal, three-dimensional models. Further issues treated include correction of respiratory induced slice displacements, systole detection......, and a texture model pruning strategy. Cross-validation carried out on clinical-quality scans of twelve volunteers indicates that ejection fraction and cardiac blood pool volumes can be estimated automatically and rapidly with accuracy on par with typical inter-observer variability....
On the continuing relevance of Mandelbrot's non-ergodic fractional renewal models of 1963 to 1967
Watkins, Nicholas W.
2017-12-01
The problem of "1/f" noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot's fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal models, and their links to the CTRW, I present preliminary results of my research into the history of Mandelbrot's very little known work in that area from 1963 to 1967. I speculate about how the lack of awareness of this work in the physics and statistics communities may have affected the development of complexity science, and I discuss the differences between the Hurst effect, "1/f" noise and LRD, concepts which are often treated as equivalent. Contribution to the "Topical Issue: Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Aspects of the derivative coupling model in four dimensions
International Nuclear Information System (INIS)
Aste, Andreas
2014-01-01
A concise discussion of a 3 + 1-dimensional derivative coupling model, in which a massive Dirac field couples to the four-gradient of a massless scalar field, is given in order to elucidate the role of different concepts in quantum field theory like the regularization of quantum fields as operator-valued distributions, correlation distributions, locality, causality, and field operator gauge transformations. (orig.)
Aspects of the derivative coupling model in four dimensions
Energy Technology Data Exchange (ETDEWEB)
Aste, Andreas [University of Basel, Department of Physics, Basel (Switzerland); Paul Scherrer Institute, Villigen (Switzerland)
2014-01-15
A concise discussion of a 3 + 1-dimensional derivative coupling model, in which a massive Dirac field couples to the four-gradient of a massless scalar field, is given in order to elucidate the role of different concepts in quantum field theory like the regularization of quantum fields as operator-valued distributions, correlation distributions, locality, causality, and field operator gauge transformations. (orig.)
Microscopic Derivation of the Ginzburg-Landau Model
DEFF Research Database (Denmark)
Frank, Rupert; Hainzl, Christian; Seiringer, Robert
2014-01-01
We present a summary of our recent rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit...
Modelling the fine and coarse fraction of Pb, Cd, As and Ni air concentration in Spain
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, M. A.; Vivanco, M. G.
2015-07-01
Lead, cadmium, arsenic and nickel are present in the air due to natural and anthropogenic emissions, normally joined to particles. Human health and ecosystems can be damaged by high atmospheric levels of these metals, since they can be introduced in organisms via inhalation or ingestion. Small particles are inhaled and embebed in lungs and alveolus more easily than coarse particles. The CHIMERE model is a eulerian air quality model extensively used in air quality modelling. Metals have been recently included in this model in a special version developed in the CIEMAT modelling group (Madrid, Spain). Vivanco et al. (2011) and Gonzalez et al. (2012) showed an evaluation of the model performance for some metals in Spain and Europe. In these studies, metals were considered as fine particles. Nevertheless there is some observational evidence of the presence of some metals also in the coarse fraction. For this reason, a new attempt of modelling metals considering a fine (<2.5 μm) and coarse (2.5-10 μm) fraction has been done. Measurements of metal concentration in PM10, PM2.5 and PM1 recorded in Spain were used to obtain the new metal particle distribution size. On the other hand, natural emissions, not considered in the above mentioned studies, were implemented in the model, by considering metal emissions associated to dust resuspensiont. An evaluation of the new version is presented and discussed for two domains in Spain, centered on Barcelona and Huelva respectively. (Author)
Modelling the fine and coarse fraction of Pb, Cd, As and Ni air concentration in Spain
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, M.A.; Vivanco, M.
2015-07-01
Lead, cadmium, arsenic and nickel are present in the air due to natural and anthropogenic emissions, normally joined to particles. Human health and ecosystems can be damaged by high atmospheric levels of these metals, since they can be introduced in organisms via inhalation or ingestion. Small particles are inhaled and embebed in lungs and alveolus more easily than coarse particles. The CHIMERE model is a eulerian air quality model extensively used in air quality modelling. Metals have been recently included in this model in a special version developed in the CIEMAT modelling group (Madrid, Spain). Vivanco et al. (2011) and González et al. (2012) showed an evaluation of the model performance for some metals in Spain and Europe. In these studies, metals were considered as fine particles. Nevertheless there is some observational evidence of the presence of some metals also in the coarse fraction. For this reason, a new attempt of modelling metals considering a fine (<2.5 μm) and coarse (2.5-10 μm) fraction has been done. Measurements of metal concentration in PM10, PM2.5 and PM1 recorded in Spain were used to obtain the new metal particle distribution size. On the other hand, natural emissions, not considered in the above mentioned studies, were implemented in the model, by considering metal emissions associated to dust resuspensiont. An evaluation of the new version is presented and discussed for two domains in Spain, centered on Barcelona and Huelva respectively. (Author)
Modelling the fine and coarse fraction of Pb, Cd, As and Ni air concentration in Spain
International Nuclear Information System (INIS)
Gonzalez, M. A.; Vivanco, M. G.
2015-01-01
Lead, cadmium, arsenic and nickel are present in the air due to natural and anthropogenic emissions, normally joined to particles. Human health and ecosystems can be damaged by high atmospheric levels of these metals, since they can be introduced in organisms via inhalation or ingestion. Small particles are inhaled and embebed in lungs and alveolus more easily than coarse particles. The CHIMERE model is a eulerian air quality model extensively used in air quality modelling. Metals have been recently included in this model in a special version developed in the CIEMAT modelling group (Madrid, Spain). Vivanco et al. (2011) and Gonzalez et al. (2012) showed an evaluation of the model performance for some metals in Spain and Europe. In these studies, metals were considered as fine particles. Nevertheless there is some observational evidence of the presence of some metals also in the coarse fraction. For this reason, a new attempt of modelling metals considering a fine (<2.5 μm) and coarse (2.5-10 μm) fraction has been done. Measurements of metal concentration in PM10, PM2.5 and PM1 recorded in Spain were used to obtain the new metal particle distribution size. On the other hand, natural emissions, not considered in the above mentioned studies, were implemented in the model, by considering metal emissions associated to dust resuspensiont. An evaluation of the new version is presented and discussed for two domains in Spain, centered on Barcelona and Huelva respectively. (Author)
Modelling ocean-colour-derived chlorophyll a
Directory of Open Access Journals (Sweden)
S. Dutkiewicz
2018-01-01
Full Text Available This article provides a proof of concept for using a biogeochemical/ecosystem/optical model with a radiative transfer component as a laboratory to explore aspects of ocean colour. We focus here on the satellite ocean colour chlorophyll a (Chl a product provided by the often-used blue/green reflectance ratio algorithm. The model produces output that can be compared directly to the real-world ocean colour remotely sensed reflectance. This model output can then be used to produce an ocean colour satellite-like Chl a product using an algorithm linking the blue versus green reflectance similar to that used for the real world. Given that the model includes complete knowledge of the (model water constituents, optics and reflectance, we can explore uncertainties and their causes in this proxy for Chl a (called derived Chl a in this paper. We compare the derived Chl a to the actual model Chl a field. In the model we find that the mean absolute bias due to the algorithm is 22 % between derived and actual Chl a. The real-world algorithm is found using concurrent in situ measurement of Chl a and radiometry. We ask whether increased in situ measurements to train the algorithm would improve the algorithm, and find a mixed result. There is a global overall improvement, but at the expense of some regions, especially in lower latitudes where the biases increase. Not surprisingly, we find that region-specific algorithms provide a significant improvement, at least in the annual mean. However, in the model, we find that no matter how the algorithm coefficients are found there can be a temporal mismatch between the derived Chl a and the actual Chl a. These mismatches stem from temporal decoupling between Chl a and other optically important water constituents (such as coloured dissolved organic matter and detrital matter. The degree of decoupling differs regionally and over time. For example, in many highly seasonal regions, the timing of initiation
The Initial Conditions of Fractional Calculus
International Nuclear Information System (INIS)
Trigeassou, J. C.; Maamri, N.
2011-01-01
During the past fifty years , Fractional Calculus has become an original and renowned mathematical tool for the modelling of diffusion Partial Differential Equations and the design of robust control algorithms. However, in spite of these celebrated results, some theoretical problems have not yet received a satisfying solution. The mastery of initial conditions, either for Fractional Differential Equations (FDEs) or for the Caputo and Riemann-Liouville fractional derivatives, remains an open research domain. The solution of this fundamental problem, also related to the long range memory property, is certainly the necessary prerequisite for a satisfying approach to modelling and control applications. The fractional integrator and its continuously frequency distributed differential model is a valuable tool for the simulation of fractional systems and the solution of initial condition problems. Indeed, the infinite dimensional state vector of fractional integrators allows the direct generalization to fractional calculus of the theoretical results of integer order systems. After a reminder of definitions and properties related to fractional derivatives and systems, this presentation is intended to show, based on the results of two recent publications [1,2], how the fractional integrator provides the solution of the initial condition problem of FDEs and of Caputo and Riemann-Liouville fractional derivatives. Numerical simulation examples illustrate and validate these new theoretical concepts.
Directory of Open Access Journals (Sweden)
Ernesto Amato
2014-03-01
Full Text Available We developed a general model for the calculation of absorbed fractions in ellipsoidal volumes of soft tissue uniformly filled with alpha, beta and gamma emitting radionuclides. The approach exploited Monte Carlo simulations with the Geant4 code to determine absorbed fractions in ellipsoids characterized by a wide range of dimensions and ellipticities, for monoenergetic emissions of each radiation type. The so-obtained absorbed fractions were put in an analytical relationship with the 'generalized radius', calculated as 3V/S, where V is the ellipsoid volume and S its surface. Radiation-specific parametric functions were obtained in order to calculate the absorbed fraction of a given radiation in a generic ellipsoidal volume. The dose from a generic radionuclide can be calculated through a process of summation and integration over the whole radionuclide emission spectrum, profitably implemented in an electronic spreadsheet. We compared the results of our analytical calculation approach with those obtained from the OLINDA/EXM computer software, finding a good agreement in a wide range of sphere radii, for the high-energy pure beta emitter 90Y, the commonly employed beta-gamma emitter 131I, and the pure alpha emitter 213Po. The generality of our approach makes it useful an easy to implement in clinical dosimetry calculations as well as in radiation safety estimations when doses from internal radionuclide uptake are to be taken into account.
Wildschut, J.; Arentz, J.; Rasrendra, C. B.; Venderbosch, R. H.; Heeres, H. J.
2009-01-01
Fast pyrolysis oil can be upgraded by a catalytic hydrotreatment (250-400 degrees C, 100-200 bar) using heterogeneous catalysts such as Ru/C to hydrocarbon-like products that can serve as liquid transportation fuels. Insight into the complex reaction pathways of the various component fractions during hydrotreatment is desirable to reduce the formation of by-products such as char and gaseous components. This paper deals with the catalytic hydrotreatment of representative model components for t...
Directory of Open Access Journals (Sweden)
Eric Pei Ping Pang
2018-01-01
Full Text Available Background and purpose: During radiotherapy, prostate motion changes over time. Quantifying and accounting for this motion is essential. This study aimed to assess intra-fraction prostate motion and derive duration-dependent planning margins for two treatment techniques. Material and methods: A four-dimension (4D transperineal ultrasound Clarity® system was used to track prostate motion. We analysed 1913 fractions from 60 patients undergoing volumetric-modulated arc therapy (VMAT to the prostate. The mean VMAT treatment duration was 3.4 min. Extended monitoring was conducted weekly to simulate motion during intensity-modulated radiation therapy (IMRT treatment (an additional seven minutes. A motion-time trend analysis was conducted and the mean intra-fraction motion between VMAT and IMRT treatments compared. Duration-dependent margins were calculated and anisotropic margins for VMAT and IMRT treatments were derived. Results: There were statistically significant differences in the mean intra-fraction motion between VMAT and the simulated IMRT duration in the inferior (0.1 mm versus 0.3 mm and posterior (−0.2 versus −0.4 mm directions respectively (p ≪ 0.01. An intra-fraction motion trend inferiorly and posteriorly was observed. The recommended minimum anisotropic margins are 1.7 mm/2.7 mm (superior/inferior; 0.8 mm (left/right, 1.7 mm/2.9 mm (anterior/posterior for VMAT treatments and 2.9 mm/4.3 mm (superior/inferior, 1.5 mm (left/right, 2.8 mm/4.8 mm (anterior/posterior for IMRT treatments. Smaller anisotropic margins were required for VMAT compared to IMRT (differences ranging from 1.2 to 1.6 mm superiorly/inferiorly, 0.7 mm laterally and 1.1–1.9 mm anteriorly/posteriorly. Conclusions: VMAT treatment is preferred over IMRT as prostate motion increases with time. Larger margins should be employed in the inferior and posterior directions for both treatment durations. Duration-dependent margins should
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
Operational derivation of Boltzmann distribution with Maxwell's demon model.
Hosoya, Akio; Maruyama, Koji; Shikano, Yutaka
2015-11-24
The resolution of the Maxwell's demon paradox linked thermodynamics with information theory through information erasure principle. By considering a demon endowed with a Turing-machine consisting of a memory tape and a processor, we attempt to explore the link towards the foundations of statistical mechanics and to derive results therein in an operational manner. Here, we present a derivation of the Boltzmann distribution in equilibrium as an example, without hypothesizing the principle of maximum entropy. Further, since the model can be applied to non-equilibrium processes, in principle, we demonstrate the dissipation-fluctuation relation to show the possibility in this direction.
Development of a three dimensional circulation model based on fractional step method
Directory of Open Access Journals (Sweden)
Mazen Abualtayef
2010-03-01
Full Text Available A numerical model was developed for simulating a three-dimensional multilayer hydrodynamic and thermodynamic model in domains with irregular bottom topography. The model was designed for examining the interactions between flow and topography. The model was based on the three-dimensional Navier-Stokes equations and was solved using the fractional step method, which combines the finite difference method in the horizontal plane and the finite element method in the vertical plane. The numerical techniques were described and the model test and application were presented. For the model application to the northern part of Ariake Sea, the hydrodynamic and thermodynamic results were predicted. The numerically predicted amplitudes and phase angles were well consistent with the field observations.
Directory of Open Access Journals (Sweden)
J.-P. Lhomme
1999-01-01
Full Text Available In many experimental conditions, the evaporative fraction, defined as the ratio between evaporation and available energy, has been found stable during daylight hours. This constancy is investigated over fully covering vegetation by means of a land surface scheme coupled with a mixed-layer model, which accounts for entrainment of overlying air. The evaporation rate follows the Penman-Monteith equation and the surface resistance is given by a Jarvis type parameterization involving solar radiation, saturation deficit and leaf water potential. The diurnal course of the evaporative fraction is examined, together with the influence of environmental factors (soil water availability, solar radiation input, wind velocity, saturation deficit above the well-mixed layer. In conditions of fair weather, the curves representing the diurnal course of the evaporative fraction have a typical concave-up shape. Around midday (solar time these curves appear as relatively constant, but always lower that the daytime mean value. Evaporative fraction decreases when soil water decreases or when solar energy increases. An increment of saturation deficit above the mixed-layer provokes only a slight increase of evaporative fraction, and wind velocity has almost no effect. The possibility of estimation daytime evaporation from daytime available energy multiplied by the evaporative fraction at a single time of the day is also investigated. It appears that it is possible to obtain fairly good estimates of daytime evaporation by choosing adequately the time of the measurement of the evaporative fraction. The central hours of the day, and preferably about 3 hr before or after noon, are the most appropriate to provide good estimates. The estimation appears also to be much better when soil water availability (or evaporation is high than when it is low.
A stochastic post-processing method for solar irradiance forecasts derived from NWPs models
Lara-Fanego, V.; Pozo-Vazquez, D.; Ruiz-Arias, J. A.; Santos-Alamillos, F. J.; Tovar-Pescador, J.
2010-09-01
Solar irradiance forecast is an important area of research for the future of the solar-based renewable energy systems. Numerical Weather Prediction models (NWPs) have proved to be a valuable tool for solar irradiance forecasting with lead time up to a few days. Nevertheless, these models show low skill in forecasting the solar irradiance under cloudy conditions. Additionally, climatic (averaged over seasons) aerosol loading are usually considered in these models, leading to considerable errors for the Direct Normal Irradiance (DNI) forecasts during high aerosols load conditions. In this work we propose a post-processing method for the Global Irradiance (GHI) and DNI forecasts derived from NWPs. Particularly, the methods is based on the use of Autoregressive Moving Average with External Explanatory Variables (ARMAX) stochastic models. These models are applied to the residuals of the NWPs forecasts and uses as external variables the measured cloud fraction and aerosol loading of the day previous to the forecast. The method is evaluated for a set one-moth length three-days-ahead forecast of the GHI and DNI, obtained based on the WRF mesoscale atmospheric model, for several locations in Andalusia (Southern Spain). The Cloud fraction is derived from MSG satellite estimates and the aerosol loading from the MODIS platform estimates. Both sources of information are readily available at the time of the forecast. Results showed a considerable improvement of the forecasting skill of the WRF model using the proposed post-processing method. Particularly, relative improvement (in terms of the RMSE) for the DNI during summer is about 20%. A similar value is obtained for the GHI during the winter.
Liang, Yingjie; Chen, Wen
2018-03-01
Ultraslow diffusion has been observed in numerous complicated systems. Its mean squared displacement (MSD) is not a power law function of time, but instead a logarithmic function, and in some cases grows even more slowly than the logarithmic rate. The distributed-order fractional diffusion equation model simply does not work for the general ultraslow diffusion. Recent study has used the local structural derivative to describe ultraslow diffusion dynamics by using the inverse Mittag-Leffler function as the structural function, in which the MSD is a function of inverse Mittag-Leffler function. In this study, a new stretched logarithmic diffusion law and its underlying non-local structural derivative diffusion model are proposed to characterize the ultraslow diffusion in aging dense colloidal glass at both the short and long waiting times. It is observed that the aging dynamics of dense colloids is a class of the stretched logarithmic ultraslow diffusion processes. Compared with the power, the logarithmic, and the inverse Mittag-Leffler diffusion laws, the stretched logarithmic diffusion law has better precision in fitting the MSD of the colloidal particles at high densities. The corresponding non-local structural derivative diffusion equation manifests clear physical mechanism, and its structural function is equivalent to the first-order derivative of the MSD.
Fractional Generalizations of Maxwell and Kelvin-Voigt Models for Biopolymer Characterization.
Directory of Open Access Journals (Sweden)
Bertrand Jóźwiak
Full Text Available The paper proposes a fractional generalization of the Maxwell and Kelvin-Voigt rheological models for a description of dynamic behavior of biopolymer materials. It was found that the rheological models of Maxwell-type do not work in the case of modeling of viscoelastic solids, and the model which significantly better describes the nature of changes in rheological properties of such media is the modified fractional Kelvin-Voigt model with two built-in springpots (MFKVM2. The proposed model was used to describe the experimental data from the oscillatory and creep tests of 3% (w/v kuzu starch pastes, and to determine the values of their rheological parameters as a function of pasting time. These parameters provide a lot of additional information about structure and viscoelastic properties of the medium in comparison to the classical analysis of dynamic curves G' and G" and shear creep compliance J(t. It allowed for a comprehensive description of a wide range of properties of kuzu starch pastes, depending on the conditions of pasting process.
International Nuclear Information System (INIS)
Pors Nielsen, S.; Baerenholdt, O.; Munck, O.
1975-01-01
By application of a power function model, fractional intestinal calcium absorption was investigated with a new technique involving whole-body counting after successive oral and intravenous administration of standard doses of 47 Ca. The fractional calcium retention 7 days after the oral load of 47 Ca was also measured. Fractional calcium retention averaged 30.3% in normal subjects and 11.5% in 11 patients with intestinal malabsorption. In the same groups fractional calcium absorption averaged 46.6% and 16.4%, respectively. Fractional calcium retention and intestinal calcium absorption were significantly correlated to body surface area, and there was a well-defined relation between fractional retention and absorption of calcium. These studies demonstrate that measurements of fractional retention and fractional intestinal absorption of calcium can be combined by the use of a whole-body counter, that fractional retention and intestinal absorption are proportional to total body surface area and therefore probably also to the total bone mass, and that fractional retention and absorption are so closely interrelated that frational absorption can be estimated from fractional retention with reasonable accuracy in normal subjects. (auth.)
International Nuclear Information System (INIS)
Noergaard, B.L.; Jensen, J.M.; Leipsic, J.
2015-01-01
Fractional flow reserve (FFR) measured during invasive coronary angiography is the gold standard for lesion-specific decisions on coronary revascularization in patients with stable coronary artery disease (CAD). Current guidelines recommend non-invasive functional or anatomic testing as a gatekeeper to the catheterization laboratory. However, the ''holy grail'' in non-invasive testing of CAD is to establish a single test that quantifies both coronary lesion severity and the associated ischemia. Most evidence to date of such a test is based on the addition of computational analysis of FFR to the anatomic information obtained from standard-acquired coronary CTA data sets at rest (FFR CT ). This review summarizes the clinical evidence for the use of FFR CT in stable CAD in context to the diagnostic performance of other non-invasive testing modalities. (orig.)
Yu, Min; He, Shudong; Tang, Mingming; Zhang, Zuoyong; Zhu, Yongsheng; Sun, Hanju
2018-03-15
Four peptide fractions PF1 (>5;kDa), PF2 (3-5;kDa), PF3 (1-3;kDa), PF4 (Maillard reaction products (MRPF1, MRPF2, MRPF3 and MRPF4) were evaluated, respectively. Peptides with low molecular weight showed higher contribution to the changes of pH, colour and browning intensity during Maillard reaction. The DPPH radical-scavenging activity of PF4 was significantly improved after Maillard reaction. Aroma volatiles and PLSR analysis suggested MRPF3 had the best sensory characteristics with higher contents of umami amino acids and lower of bitter amino acids, therefore it could be deduced that the umami and meaty characteristics were correlated with the peptides of 1-3;kDa. Copyright © 2017 Elsevier Ltd. All rights reserved.
Gauge coupling unification in superstring derived standard-like models
International Nuclear Information System (INIS)
Faraggi, A.E.
1992-11-01
I discuss gauge coupling unification in a class of superstring standard-like models, which are derived in the free fermionic formulation. Recent calculations indicate that the superstring unification scale is at O(10 18 GeV) while the minimal supersymmetric standard model is consistent with LEP data if the unification scale is at O(10 16 )GeV. A generic feature of the superstring standard-like models is the appearance of extra color triplets (D,D), and electroweak doublets (l,l), in vector-like representations, beyond the supersymmetric standard model. I show that the gauge coupling unification at O(10 18 GeV) in the superstring standard-like models can be consistent with LEP data. I present an explicit standard-like model that can realize superstring gauge coupling unification. (author)
Fitting the Fractional Polynomial Model to Non-Gaussian Longitudinal Data
Directory of Open Access Journals (Sweden)
Ji Hoon Ryoo
2017-08-01
Full Text Available As in cross sectional studies, longitudinal studies involve non-Gaussian data such as binomial, Poisson, gamma, and inverse-Gaussian distributions, and multivariate exponential families. A number of statistical tools have thus been developed to deal with non-Gaussian longitudinal data, including analytic techniques to estimate parameters in both fixed and random effects models. However, as yet growth modeling with non-Gaussian data is somewhat limited when considering the transformed expectation of the response via a linear predictor as a functional form of explanatory variables. In this study, we introduce a fractional polynomial model (FPM that can be applied to model non-linear growth with non-Gaussian longitudinal data and demonstrate its use by fitting two empirical binary and count data models. The results clearly show the efficiency and flexibility of the FPM for such applications.
Directory of Open Access Journals (Sweden)
Abigail O. Ojo
2018-04-01
Full Text Available Phosphorus inputs to the soil are primarily from the application of fertilizer P and organic resources. A ten week incubation study was carried out to determine the effects of organic and inorganic P sources on phosphorus fractions in three derived savanna soils. Poultry manure was applied at 0, 0.75g, 1.5g, 2.25g and 3g per 300g weight of soil while single superphosphate was applied at 0.0023g, 0.0046g, 0.0069g and 0.0092g per 300g of soil. Sampling was done at two weeks interval. At 0 week of the incubation study, Ekiti series had the largest amount of P fractions i.e. Fe-P, Al-P, residual P, reductant soluble P, occluded P, organic P and occluded P while Ca-P was high in Apomu series. However, increases in Fe-P, Al-P, Ca-P and organic P were observed in the three soil series evaluated and poultry manure was notably effective in reducing P occlusion. In conclusion, it was observed that irrespective of the soil series at different stages of the incubation studies, poultry manure and the combined application of poultry manure and Single superphosphate was highly effective in increasing P fractions.
Krieter, Detlef H; Lange, Florian; Lemke, Horst-Dieter; Bonn, Florian; Wanner, Christoph
2018-04-01
Technical problems during clinical lipid apheresis interfere with fractionator performance. Therefore, a large animal model was established to characterize a new plasma fractionation membrane. Four sheep were randomized, controlled, and crossover subjected to double ofiltration lipoprotein apheresis with three specimens of FractioPES R having slightly different HDL sieving coefficients (S K ) (FPESa, 0.30, FPESb, 0.26, and FPESc, 0.22) versus a control fractionator (EVAL). S K and reduction ratios were determined for LDL, HDL, fibrinogen, IgG, and albumin. Compared to EVAL (0.42 ± 0.04 to 0.74 ± 0.08) and FPESa (0.36 ± 0.06 to 0.64 ± 0.04), S K for HDL were lower (P < 0.05) with FPESc (0.30 ± 0.04 to 0.49 ± 0.10). Fibrinogen S K were higher (P < 0.05) with EVAL (0.02 ± 0.01 to 0.40 ± 0.08) compared to FPESb (0.05 ± 0.02 to 0.26 ± 0.34) and FPESc (0.01 ± 0.01 to 0.21 ± 0.16). No further differences were determined. The animal model distinguished between minor differences in fractionation membrane permeability, demonstrating equivalent sieving of FPESa and EVAL and slightly inferior permeability of FPESb and FPESc. © 2018 International Society for Apheresis, Japanese Society for Apheresis, and Japanese Society for Dialysis Therapy.
Hamiltonian derivation of the nonhydrostatic pressure-coordinate model
Salmon, Rick; Smith, Leslie M.
1994-07-01
In 1989, the Miller-Pearce (MP) model for nonhydrostatic fluid motion governed by equations written in pressure coordinates was extended by removing the prescribed reference temperature, T(sub s)(p), while retaining the conservation laws and other desirable properties. It was speculated that this extension of the MP model had a Hamiltonian structure and that a slick derivation of the Ertel property could be constructed if the relevant Hamiltonian were known. In this note, the extended equations are derived using Hamilton's principle. The potential vorticity law arises from the usual particle-relabeling symmetry of the Lagrangian, and even the absence of sound waves is anticipated from the fact that the pressure inside the free energy G(p, theta) in the derived equation is hydrostatic and thus G is insensitive to local pressure fluctuations. The model extension is analogous to the semigeostrophic equations for nearly geostrophic flow, which do not incorporate a prescribed reference state, while the earlier MP model is analogous to the quasigeostrophic equations, which become highly inaccurate when the flow wanders from a prescribed state with nearly flat isothermal surfaces.
Evaluation of bias associated with capture maps derived from nonlinear groundwater flow models
Nadler, Cara; Allander, Kip K.; Pohll, Greg; Morway, Eric D.; Naranjo, Ramon C.; Huntington, Justin
2018-01-01
The impact of groundwater withdrawal on surface water is a concern of water users and water managers, particularly in the arid western United States. Capture maps are useful tools to spatially assess the impact of groundwater pumping on water sources (e.g., streamflow depletion) and are being used more frequently for conjunctive management of surface water and groundwater. Capture maps have been derived using linear groundwater flow models and rely on the principle of superposition to demonstrate the effects of pumping in various locations on resources of interest. However, nonlinear models are often necessary to simulate head-dependent boundary conditions and unconfined aquifers. Capture maps developed using nonlinear models with the principle of superposition may over- or underestimate capture magnitude and spatial extent. This paper presents new methods for generating capture difference maps, which assess spatial effects of model nonlinearity on capture fraction sensitivity to pumping rate, and for calculating the bias associated with capture maps. The sensitivity of capture map bias to selected parameters related to model design and conceptualization for the arid western United States is explored. This study finds that the simulation of stream continuity, pumping rates, stream incision, well proximity to capture sources, aquifer hydraulic conductivity, and groundwater evapotranspiration extinction depth substantially affect capture map bias. Capture difference maps demonstrate that regions with large capture fraction differences are indicative of greater potential capture map bias. Understanding both spatial and temporal bias in capture maps derived from nonlinear groundwater flow models improves their utility and defensibility as conjunctive-use management tools.
Generalised and Fractional Langevin Equations-Implications for Energy Balance Models
Watkins, N. W.; Chapman, S. C.; Chechkin, A.; Ford, I.; Klages, R.; Stainforth, D. A.
2017-12-01
Energy Balance Models (EBMs) have a long heritage in climate science, including their use in modelling anomalies in global mean temperature. Many types of EBM have now been studied, and this presentation concerns the stochastic EBMs, which allow direct treatment of climate fluctuations and noise. Some recent stochastic EBMs (e.g. [1]) map on to Langevin's original form of his equation, with temperature anomaly replacing velocity, and other corresponding replacements being made. Considerable sophistication has now been reached in the application of multivariate stochastic Langevin modelling in many areas of climate. Our work is complementary in intent and investigates the Mori-Kubo "Generalised Langevin Equation" (GLE) which incorporates non-Markovian noise and response in a univariate framework, as a tool for modelling GMT [2]. We show how, if it is present, long memory simplifies the GLE to a fractional Langevin equation (FLE). Evidence for long range memory in global temperature, and the success of fractional Gaussian noise in its prediction [5] has already motivated investigation of a power law response model [3,4,5]. We go beyond this work to ask whether an EBM of FLE-type exists, and what its solutions would be. [l] Padilla et al, J. Climate (2011); [2] Watkins, GRL (2013); [3] Rypdal, JGR (2012); [4] Rypdal and Rypdal, J. Climate (2014); [5] Lovejoy et al, ESDD (2015).
International Nuclear Information System (INIS)
Wu, Yuhu; Kumar, Madan; Shen, Tielong
2016-01-01
Highlights: • An in-cylinder pressure based measuring method for the RGF is derived. • A stochastic logical dynamical model is proposed to represent the transient behavior of the RGF. • The receding horizon controller is designed to reduce the variance of the RGF. • The effectiveness of the proposed model and control approach is validated by the experimental evidence. - Abstract: In four stroke internal combustion engines, residual gas from the previous cycle is an important factor influencing the combustion quality of the current cycle, and the residual gas fraction (RGF) is a popular index to monitor the influence of residual gas. This paper investigates the cycle-to-cycle transient behavior of the RGF in the view of systems theory and proposes a multi-valued logic-based control strategy for attenuation of RGF fluctuation. First, an in-cylinder pressure sensor-based method for measuring the RGF is provided by following the physics of the in-cylinder transient state of four-stroke internal combustion engines. Then, the stochastic property of the RGF is examined based on statistical data obtained by conducting experiments on a full-scale gasoline engine test bench. Based on the observation of the examination, a stochastic logical transient model is proposed to represent the cycle-to-cycle transient behavior of the RGF, and with the model an optimal feedback control law, which targets on rejection of the RGF fluctuation, is derived in the framework of stochastic logical system theory. Finally, experimental results are demonstrated to show the effectiveness of the proposed model and the control strategy.
Leite, Maria Bernadete Neiva Lemos; de Araújo, Milena Maria Sampaio; Nascimento, Iracema Andrade; da Cruz, Andrea Cristina Santos; Pereira, Solange Andrade; do Nascimento, Núbia Costa
2011-04-01
Concerns over the sustained availability of fossil fuels and their impact on global warming and pollution have led to the search for fuels from renewable sources to address worldwide rising energy demands. Biodiesel is emerging as one of the possible solutions for the transport sector. It shows comparable engine performance to that of conventional diesel fuel, while reducing greenhouse gas emissions. However, the toxicity of products and effluents from the biodiesel industry has not yet been sufficiently investigated. Brazil has a very high potential as a biodiesel producer, in view of its climatic conditions and vast areas for cropland, with consequent environmental risks because of possible accidental biodiesel spillages into water bodies and runoff to coastal areas. This research determined the toxicity to two marine organisms of the water-soluble fractions (WSF) of three different biodiesel fuels obtained by methanol transesterification of castor oil (CO), palm oil (PO), and waste cooking oil (WCO). Microalgae and sea urchins were used as the test organisms, respectively, for culture-growth-inhibition and early-life-stage-toxicity tests. The toxicity levels of the analyzed biodiesel WSF showed the highest toxicity for the CO, followed by WCO and the PO. Methanol was the most prominent contaminant; concentrations increased over time in WSF samples stored up to 120 d. Copyright © 2010 SETAC.
Novel Thiazole Derivatives of Medicinal Potential: Synthesis and Modeling
Directory of Open Access Journals (Sweden)
Nour E. A. Abdel-Sattar
2017-01-01
Full Text Available This paper reports on the synthesis of new thiazole derivatives that could be profitably exploited in medical treatment of tumors. Molecular electronic structures have been modeled within density function theory (DFT framework. Reactivity indices obtained from the frontier orbital energies as well as electrostatic potential energy maps are discussed and correlated with the molecular structure. X-ray crystallographic data of one of the new compounds is measured and used to support and verify the theoretical results.
Directory of Open Access Journals (Sweden)
A. Devasthale
2012-02-01
Full Text Available The Advanced Very High Resolution Radiometer (AVHRR instruments onboard the series of National Oceanic and Atmospheric Administration (NOAA satellites offer the longest available meteorological data records from space. These satellites have drifted in orbit resulting in shifts in the local time sampling during the life span of the sensors onboard. Depending upon the amplitude of the diurnal cycle of the geophysical parameters derived, orbital drift may cause spurious trends in their time series. We investigate tropical deep convective clouds, which show pronounced diurnal cycle amplitude, to estimate an upper bound of the impact of orbital drift on their time series. We carry out a rotated empirical orthogonal function analysis (REOF and show that the REOFs are useful in delineating orbital drift signal and, more importantly, in subtracting this signal in the time series of convective cloud amount. These results will help facilitate the derivation of homogenized data series of cloud amount from NOAA satellite sensors and ultimately analyzing trends from them. However, we suggest detailed comparison of various methods and rigorous testing thereof applying final orbital drift corrections.
Derivative Geometric Modeling of Basic Rotational Solids on CATIA
Institute of Scientific and Technical Information of China (English)
MENG Xiang-bao; PAN Zi-jian; ZHU Yu-xiang; LI Jun
2011-01-01
Hybrid models derived from rotational solids like cylinders, cones and spheres were implemented on CATIA software. Firstly, make the isosceles triangular prism, cuboid, cylinder, cone, sphere, and the prism with tangent conic and curved triangle ends, the cuboid with tangent cylindrical and curved rectangle ends, the cylinder with tangent spherical and curved circular ends as the basic Boolean deference units to the primary cylinders, cones and spheres on symmetrical and some critical geometric conditions, forming a series of variant solid models. Secondly, make the deference units above as the basic union units to the main cylinders, cones, and spheres accordingly, forming another set of solid models. Thirdly, make the tangent ends of union units into oblique conic, cylindrical, or with revolved triangular pyramid, quarterly cylinder and annulus ends on sketch based features to the main cylinders, cones, and spheres repeatedly, thus forming still another set of solid models. It is expected that these derivative models be beneficial both in the structure design, hybrid modeling, and finite element analysis of engineering components and in comprehensive training of spatial configuration of engineering graphics.
Relativistic nuclear matter with alternative derivative coupling models
International Nuclear Information System (INIS)
Delfino, A.; Coelho, C.T.; Malheiro, M.
1994-01-01
Effective Lagrangians involving nucleons coupled to scalar and vector fields are investigated within the framework of relativistic mean-field theory. The study presents the traditional Walecka model and different kinds of scalar derivative coupling suggested by Zimanyi and Moszkowski. The incompressibility (presented in an analytical form), scalar potential, and vector potential at the saturation point of nuclear matter are compared for these models. The real optical potential for the models are calculated and one of the models fits well the experimental curve from-50 to 400 MeV while also gives a soft equation of state. By varying the coupling constants and keeping the saturation point of nuclear matter approximately fixed, only the Walecka model presents a first order phase transition of finite temperature at zero density. (author)
Rahimi, Zaher; Sumelka, Wojciech; Yang, Xiao-Jun
2017-11-01
The application of fractional calculus in fractional models (FMs) makes them more flexible than integer models inasmuch they can conclude all of integer and non-integer operators. In other words FMs let us use more potential of mathematics to modeling physical phenomena due to the use of both integer and fractional operators to present a better modeling of problems, which makes them more flexible and powerful. In the present work, a new fractional nonlocal model has been proposed, which has a simple form and can be used in different problems due to the simple form of numerical solutions. Then the model has been used to govern equations of the motion of the Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT). Next, free vibration of the Timoshenko and Euler-Bernoulli simply-supported (S-S) beam has been investigated. The Galerkin weighted residual method has been used to solve the non-linear governing equations.
Physics of the Kitaev Model: Fractionalization, Dynamic Correlations, and Material Connections
Hermanns, M.; Kimchi, I.; Knolle, J.
2018-03-01
Quantum spin liquids have fascinated condensed matter physicists for decades because of their unusual properties such as spin fractionalization and long-range entanglement. Unlike conventional symmetry breaking, the topological order underlying quantum spin liquids is hard to detect experimentally. Even theoretical models are scarce for which the ground state is established to be a quantum spin liquid. The Kitaev honeycomb model and its generalizations to other tricoordinated lattices are chief counterexamples - they are exactly solvable, harbor a variety of quantum spin liquid phases, and are also relevant for certain transition metal compounds including the polymorphs of (Na,Li)2IrO3 iridates and RuCl3. In this review, we give an overview of the rich physics of the Kitaev model, including two-dimensional and three-dimensional fractionalization as well as dynamic correlations and behavior at finite temperatures. We discuss the different materials and argue how the Kitaev model physics can be relevant even though most materials show magnetic ordering at low temperatures.
A predictor-corrector algorithm to estimate the fractional flow in oil-water models
International Nuclear Information System (INIS)
Savioli, Gabriela B; Berdaguer, Elena M Fernandez
2008-01-01
We introduce a predictor-corrector algorithm to estimate parameters in a nonlinear hyperbolic problem. It can be used to estimate the oil-fractional flow function from the Buckley-Leverett equation. The forward model is non-linear: the sought- for parameter is a function of the solution of the equation. Traditionally, the estimation of functions requires the selection of a fitting parametric model. The algorithm that we develop does not require a predetermined parameter model. Therefore, the estimation problem is carried out over a set of parameters which are functions. The algorithm is based on the linearization of the parameter-to-output mapping. This technique is new in the field of nonlinear estimation. It has the advantage of laying aside parametric models. The algorithm is iterative and is of predictor-corrector type. We present theoretical results on the inverse problem. We use synthetic data to test the new algorithm.
International Nuclear Information System (INIS)
Fakir, Hatim; Hlatky, Lynn; Li, Huamin; Sachs, Rainer
2013-01-01
Purpose: Optimal treatment planning for fractionated external beam radiation therapy requires inputs from radiobiology based on recent thinking about the “five Rs” (repopulation, radiosensitivity, reoxygenation, redistribution, and repair). The need is especially acute for the newer, often individualized, protocols made feasible by progress in image guided radiation therapy and dose conformity. Current stochastic tumor control probability (TCP) models incorporating tumor repopulation effects consider “stem-like cancer cells” (SLCC) to be independent, but the authors here propose that SLCC-SLCC interactions may be significant. The authors present a new stochastic TCP model for repopulating SLCC interacting within microenvironmental niches. Our approach is meant mainly for comparing similar protocols. It aims at practical generalizations of previous mathematical models. Methods: The authors consider protocols with complete sublethal damage repair between fractions. The authors use customized open-source software and recent mathematical approaches from stochastic process theory for calculating the time-dependent SLCC number and thereby estimating SLCC eradication probabilities. As specific numerical examples, the authors consider predicted TCP results for a 2 Gy per fraction, 60 Gy protocol compared to 64 Gy protocols involving early or late boosts in a limited volume to some fractions. Results: In sample calculations with linear quadratic parameters α = 0.3 per Gy, α/β = 10 Gy, boosting is predicted to raise TCP from a dismal 14.5% observed in some older protocols for advanced NSCLC to above 70%. This prediction is robust as regards: (a) the assumed values of parameters other than α and (b) the choice of models for intraniche SLCC-SLCC interactions. However, α = 0.03 per Gy leads to a prediction of almost no improvement when boosting. Conclusions: The predicted efficacy of moderate boosts depends sensitively on α. Presumably, the larger values of α are
Fakir, Hatim; Hlatky, Lynn; Li, Huamin; Sachs, Rainer
2013-12-01
Optimal treatment planning for fractionated external beam radiation therapy requires inputs from radiobiology based on recent thinking about the "five Rs" (repopulation, radiosensitivity, reoxygenation, redistribution, and repair). The need is especially acute for the newer, often individualized, protocols made feasible by progress in image guided radiation therapy and dose conformity. Current stochastic tumor control probability (TCP) models incorporating tumor repopulation effects consider "stem-like cancer cells" (SLCC) to be independent, but the authors here propose that SLCC-SLCC interactions may be significant. The authors present a new stochastic TCP model for repopulating SLCC interacting within microenvironmental niches. Our approach is meant mainly for comparing similar protocols. It aims at practical generalizations of previous mathematical models. The authors consider protocols with complete sublethal damage repair between fractions. The authors use customized open-source software and recent mathematical approaches from stochastic process theory for calculating the time-dependent SLCC number and thereby estimating SLCC eradication probabilities. As specific numerical examples, the authors consider predicted TCP results for a 2 Gy per fraction, 60 Gy protocol compared to 64 Gy protocols involving early or late boosts in a limited volume to some fractions. In sample calculations with linear quadratic parameters α = 0.3 per Gy, α∕β = 10 Gy, boosting is predicted to raise TCP from a dismal 14.5% observed in some older protocols for advanced NSCLC to above 70%. This prediction is robust as regards: (a) the assumed values of parameters other than α and (b) the choice of models for intraniche SLCC-SLCC interactions. However, α = 0.03 per Gy leads to a prediction of almost no improvement when boosting. The predicted efficacy of moderate boosts depends sensitively on α. Presumably, the larger values of α are the ones appropriate for individualized
Anticonvulsant activity of DNS II fraction in the acute seizure models.
Raza, Muhammad Liaquat; Zeeshan, Mohammad; Ahmad, Manzoor; Shaheen, Farzana; Simjee, Shabana U
2010-04-21
Delphinium nordhagenii belongs to family Ranunculaceae, it is widely found in tropical areas of Pakistan. Other species of Delphinium are reported as anticonvulsant and are traditionally used in the treatment of epilepsy. Delphinium nordhagenii is used by local healer in Pakistan but never used for scientific investigation as anticonvulsant. Thus, Delphinium nordhagenii was subjected to bioassay-guided fractionation and the most active fraction, i.e. DNS II acetone was chosen for further testing in the acute seizure models of epilepsy to study the antiepileptic potential in male mice. Different doses (60, 65 and 70mg/kg, i.p.) of DNS II acetone fraction of Delphinium nordhagenii was administered 30min prior the chemoconvulsant's injection in the male mice. Convulsive doses of chemoconvulsants (pentylenetetrazole 90mg/kg, s.c. and picrotoxin 3.15mg/kg, s.c.) were used. The mice were observed 45-90min for the presence of seizures. Moreover, four different doses of DNS II (60, 65, 70 and 100mg/kg, i.p.) were tested in the MES test. The DNS II acetone fraction of Delphinium nordhagenii has exhibited the anticonvulsant actions by preventing the seizures against PTZ- and picrotoxin-induced seizure as well as 100% seizure protection in MES test. The results are comparable with standard AEDs (diazepam 7.5mg/kg, i.p. and phenytoin 20mg/kg, i.p.). These findings suggest that the Delphinium nordhagenii possesses the anticonvulsant activity. Further analysis is needed to confirm the structure and target the extended activity profile. Copyright 2010 Elsevier Ireland Ltd. All rights reserved.
Ab initio derivation of model energy density functionals
International Nuclear Information System (INIS)
Dobaczewski, Jacek
2016-01-01
I propose a simple and manageable method that allows for deriving coupling constants of model energy density functionals (EDFs) directly from ab initio calculations performed for finite fermion systems. A proof-of-principle application allows for linking properties of finite nuclei, determined by using the nuclear nonlocal Gogny functional, to the coupling constants of the quasilocal Skyrme functional. The method does not rely on properties of infinite fermion systems but on the ab initio calculations in finite systems. It also allows for quantifying merits of different model EDFs in describing the ab initio results. (letter)
A Consistent Pricing Model for Index Options and Volatility Derivatives
DEFF Research Database (Denmark)
Kokholm, Thomas
to be priced consistently, while allowing for jumps in volatility and returns. An affine specification using Lévy processes as building blocks leads to analytically tractable pricing formulas for volatility derivatives, such as VIX options, as well as efficient numerical methods for pricing of European options...... on the underlying asset. The model has the convenient feature of decoupling the vanilla skews from spot/volatility correlations and allowing for different conditional correlations in large and small spot/volatility moves. We show that our model can simultaneously fit prices of European options on S&P 500 across...
A Consistent Pricing Model for Index Options and Volatility Derivatives
DEFF Research Database (Denmark)
Cont, Rama; Kokholm, Thomas
2013-01-01
to be priced consistently, while allowing for jumps in volatility and returns. An affine specification using Lévy processes as building blocks leads to analytically tractable pricing formulas for volatility derivatives, such as VIX options, as well as efficient numerical methods for pricing of European options...... on the underlying asset. The model has the convenient feature of decoupling the vanilla skews from spot/volatility correlations and allowing for different conditional correlations in large and small spot/volatility moves. We show that our model can simultaneously fit prices of European options on S&P 500 across...
International Nuclear Information System (INIS)
Pitkaenen, Maunu.
1986-04-01
X-ray induced changes in rat and human bone and bone marrow vasculature and in rat brain vasculature were measured as a function of time after irradiation and absorbed dose. The absorbed dose in the organ varied from 5 to 25 Gy for single dose irradiations and from 19 to 58 Gy for fractionated irradiations.The number of fractions varied from 3 to 10 for the rats and from 12 to 25 for the human. Blood flow changes were measured using an ''1''2''5I antipyrine or ''8''6RbCl extraction technique. The red blood cell (RBC) volume was examined by ''5''1Cr labelled red cells. Different fractionation models have been compared. Radiation induced reduction of bone and bone marrow blood flow were both time and dose dependent. Reduced blood flow 3 months after irradiation would seem to be an important factor in the subsequent atrophy of bones. With a single dose of 10 Gy the bone marrow blood flow returned to the control level by 7 months after irradiation. In the irradiated bone the RBC volume was about same as that in the control side but in bone marrow the reduction was from 32 to 59%. The dose levels predicted by the nominal standard dose (NSD) formula produced about the same damage to the rat femur seven months after irradiation when the extraction of ''8''6Rb chloride and the dry weight were concerned as the end points. However, the results suggest that the NSB formula underestimates the late radiation damage in bone marrow when a small number of large fractions are used. In the irradiated brains of the rats the blood flow was on average 20.4% higher compared to that in the control group. There was no significant difference in brain blood flow between different fractionation schemes. The value of 0.42 for the exponent of N corresponds to the average value for central nervous system tolerance in the literature. The model used may be sufficiently accurate for clinical work provided the treatment schemes used do not depart too radically from standard practice
Qin, Shanlin; Liu, Fawang; Turner, Ian W.
2018-03-01
The consideration of diffusion processes in magnetic resonance imaging (MRI) signal attenuation is classically described by the Bloch-Torrey equation. However, many recent works highlight the distinct deviation in MRI signal decay due to anomalous diffusion, which motivates the fractional order generalization of the Bloch-Torrey equation. In this work, we study the two-dimensional multi-term time and space fractional diffusion equation generalized from the time and space fractional Bloch-Torrey equation. By using the Galerkin finite element method with a structured mesh consisting of rectangular elements to discretize in space and the L1 approximation of the Caputo fractional derivative in time, a fully discrete numerical scheme is derived. A rigorous analysis of stability and error estimation is provided. Numerical experiments in the square and L-shaped domains are performed to give an insight into the efficiency and reliability of our method. Then the scheme is applied to solve the multi-term time and space fractional Bloch-Torrey equation, which shows that the extra time derivative terms impact the relaxation process.
Vo, Tam D. L.; Chung, Duy T. M.; Doan, Kien T.; Le, Duy T.; Trinh, Hung V.
2017-09-01
In this study, the antioxidant capacity of peptide fractions isolated from the Tra Catfish (Pangasius hypophthalmus) by-product-derived proteolysate using ultrafiltration centrifugal devices with 5 distinct molecular-weight cutoffs (MWCOs) of 1 kDa, 3 kDa, 5 kDa, 10 kDa, and 30 kDa was investigated. Firstly, the chemical composition of the Tra Catfish by-products was analyzed. The result showed that the Tra Catfish by-products contained 58.5% moisture, 33.9% crude protein, 50.1% crude lipid and 15.8% ash (on dry weight basis). Secondly, the effects of hydrolysis time, enzyme content on the antioxidant potential of the proteolysate were studied using DPPH• (2,2-diphenyl-1-picrylhydrazyl) radical scavenging method (DPPH• SM) and FRAP (Ferric Reducing Antioxidant Potential) method. Alcalase® 2.4 L FG was used for hydrolysis. The result of antioxidant activity of the hydrolysate showed that the 50% DPPH• inhibition concentration (IC50) of the hydrolysate reached about 6775 µg/mL which was 1645-fold higher than that of vitamin C and 17-fold higher than that of BHT (ButylatedHydroxytoluene) with the degree of hydrolysis (DH) of the hydrolysate of 14.6% when hydrolysis time was 5 hours, enzyme/substrate (E/S) ratio was 30 U/g protein, hydrolysis temperature was 55°C, and pH was 7.5. The antioxidant potential of hydrolysate using FRAP method reached about 52.12 µM Trolox equivalent which was 53-fold and 18-fold lower than those of vitamin C and BHT, respectively, when the hydrolysis time was 5 h, enzyme/substrate ratio was 30 U/g protein, temperature was 500C, and pH level was 8. Next, the proteolysate was further fractionated using MWCOs of 1 kDa, 3 kDa, 5 kDa, 10 kDa, and 30 kDa and the peptide fractions were investigated for their antioxidant activity. The result showed that the <1 kDa fraction showed strongest antioxidant activity with the IC50 of 1313.31 ± 50.65 µg/mL and FRAP value of 906.90 ± 44.32 µM Trolox equivalent. The second strongest fraction
Financial analysis of technology acquisition using fractionated lasers as a model.
Jutkowitz, Eric; Carniol, Paul J; Carniol, Alan R
2010-08-01
Ablative fractional lasers are among the most advanced and costly devices on the market. Yet, there is a dearth of published literature on the cost and potential return on investment (ROI) of such devices. The objective of this study was to provide a methodological framework for physicians to evaluate ROI. To facilitate this analysis, we conducted a case study on the potential ROI of eight ablative fractional lasers. In the base case analysis, a 5-year lease and a 3-year lease were assumed as the purchase option with a $0 down payment and 3-month payment deferral. In addition to lease payments, service contracts, labor cost, and disposables were included in the total cost estimate. Revenue was estimated as price per procedure multiplied by total number of procedures in a year. Sensitivity analyses were performed to account for variability in model assumptions. Based on the assumptions of the model, all lasers had higher ROI under the 5-year lease agreement compared with that for the 3-year lease agreement. When comparing results between lasers, those with lower operating and purchase cost delivered a higher ROI. Sensitivity analysis indicates the model is most sensitive to purchase method. If physicians opt to purchase the device rather than lease, they can significantly enhance ROI. ROI analysis is an important tool for physicians who are considering making an expensive device acquisition. However, physicians should not rely solely on ROI and must also consider the clinical benefits of a laser. (c) Thieme Medical Publishers.
Directory of Open Access Journals (Sweden)
Škugor Stanko
2010-01-01
Full Text Available Abstract Background Excessive fat deposition is one of the largest problems faced by salmon aquaculture industries, leading to production losses due to high volume of adipose tissue offal. In addition, increased lipid accumulation may impose considerable stress on adipocytes leading to adipocyte activation and production and secretion of inflammatory mediators, as observed in mammals. Results Microarray and qPCR analyses were performed to follow transcriptome changes during adipogenesis in the primary culture of adipose stromo-vascular fraction (aSVF of Atlantic salmon. Cellular heterogeneity decreased by confluence as evidenced by the down-regulation of markers of osteo/chondrogenic, myogenic, immune and vasculature lineages. Transgelin (TAGLN, a marker of the multipotent pericyte, was prominently expressed around confluence while adipogenic PPARγ was up-regulated already in subconfluent cells. Proliferative activity and subsequent cell cycle arrest were reflected in the fluctuations of pro- and anti-mitotic regulators. Marked regulation of genes involved in lipid and glucose metabolism and pathways producing NADPH and glycerol-3-phosphate (G3P was seen during the terminal differentiation, also characterised by diverse stress responses. Activation of the glutathione and thioredoxin antioxidant systems and changes in the iron metabolism suggested the need for protection against oxidative stress. Signs of endoplasmic reticulum (ER stress and unfolded protein response (UPR occured in parallel with the increased lipid droplet (LD formation and production of secretory proteins (adipsin, visfatin. The UPR markers XBP1 and ATF6 were induced together with genes involved in ubiquitin-proteasome and lysosomal proteolysis. Concurrently, translation was suppressed as evidenced by the down-regulation of genes encoding elongation factors and components of the ribosomal machinery. Notably, expression changes of a panel of genes that belong to different
Directory of Open Access Journals (Sweden)
Ana Paula Delowski Ciniello
Full Text Available Abstract The present paper aims at presenting a methodology for characterizing viscoelastic materials in time domain, taking into account the fractional Zener constitutive model and the influence of temperature through Williams, Landel, and Ferry’s model. To that effect, a set of points obtained experimentally through uniaxial tensile tests with different constant strain rates is considered. The approach is based on the minimization of the quadratic relative distance between the experimental stress-strain curves and the corresponding ones given by the theoretical model. In order to avoid the local minima in the process of optimization, a hybrid technique based on genetic algorithms and non-linear programming techniques is used. The methodology is applied in the characterization of two different commercial viscoelastic materials. The results indicate that the proposed methodology is effective in identifying thermorheologically simple viscoelastic materials.
Model of chromosomal loci dynamics in bacteria as fractional diffusion with intermittent transport
Gherardi, Marco; Calabrese, Ludovico; Tamm, Mikhail; Cosentino Lagomarsino, Marco
2017-10-01
The short-time dynamics of bacterial chromosomal loci is a mixture of subdiffusive and active motion, in the form of rapid relocations with near-ballistic dynamics. While previous work has shown that such rapid motions are ubiquitous, we still have little grasp on their physical nature, and no positive model is available that describes them. Here, we propose a minimal theoretical model for loci movements as a fractional Brownian motion subject to a constant but intermittent driving force, and compare simulations and analytical calculations to data from high-resolution dynamic tracking in E. coli. This analysis yields the characteristic time scales for intermittency. Finally, we discuss the possible shortcomings of this model, and show that an increase in the effective local noise felt by the chromosome associates to the active relocations.
Directory of Open Access Journals (Sweden)
Olaniyi Samuel Iyiola
2014-09-01
Full Text Available In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation using q-Homotopy Analysis Method (q-HAM. Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.
Muserere, Simon Takawira; Hoko, Zvikomborero; Nhapi, Innocent
Varying conditions are required for different species of microorganisms for the complex biological processes taking place within the activated sludge treatment system. It is against the requirement to manage this complex dynamic system that computer simulators were developed to aid in optimising activated sludge treatment processes. These computer simulators require calibration with quality data input that include wastewater fractionation among others. Thus, this research fractionated raw sewage, at Firle Sewage Treatment Works (STW), for calibration of the BioWin simulation model. Firle STW is a 3-stage activated sludge system. Wastewater characteristics of importance for activated sludge process design can be grouped into carbonaceous, nitrogenous and phosphorus compounds. Division of the substrates and compounds into their constituent fractions is called fractionation and is a valuable tool for process assessment. Fractionation can be carried out using bioassay methods or much simpler physico-chemical methods. The bioassay methods require considerable experience with experimental activated sludge systems and associated measurement techniques while the physico-chemical methods are straight forward. Plant raw wastewater fractionation was carried out through two 14-day campaign periods, the first being from 3 to 16 July 2013 and the second was from 1 to 14 October 2013. According to the Zimbabwean Environmental Management Act, and based on the sensitivity of its catchment, Firle STW effluent discharge regulatory standards in mg/L are COD (<60), TN (<10), ammonia (<0.2), and TP (<1). On the other hand Firle STW Unit 4 effluent quality results based on City of Harare records in mg/L during the period of study were COD (90 ± 35), TN (9.0 ± 3.0), ammonia (0.2 ± 0.4) and TP (3.0 ± 1.0). The raw sewage parameter concentrations measured during the study in mg/L and fractions for raw sewage respectively were as follows total COD (680 ± 37), slowly biodegradable COD
Directory of Open Access Journals (Sweden)
Zachau Anne C
2012-09-01
Full Text Available Abstract Introduction Amyotrophic lateral sclerosis is a progressive neurodegenerative disorder characterized by degeneration of motoneuron cells in anterior spinal horns. There is a need for early and accurate diagnosis with this condition. In this case report we used two complementary methods: scanning electron microscopy and fluorescence-activated cell sorting. This is the first report to our knowledge of microparticles in the cerebrospinal fluid of a patient with amyotrophic lateral sclerosis. Case presentation An 80-year-old Swedish man of Caucasian ethnicity presented to our facility with symptoms of amyotrophic lateral sclerosis starting a year before his first hospital examination, such as muscle weakness and twitching in his right hand progressing to arms, body and leg muscles. Electromyography showed classical neurophysiological findings of amyotrophic lateral sclerosis. Routine blood sample results were normal. A lumbar puncture was performed as a routine investigation and his cerebrospinal fluid was normal with regard to cell count and protein levels, and there were no signs of inflammation. However, scanning electron microscopy and fluorescence-activated cell sorting showed pronounced abnormalities compared to healthy controls. Flow cytometry analysis of two fractions of cerebrospinal fluid from our patient with amyotrophic lateral sclerosis was used to measure the specific binding of antibodies to CD42a, CD144 and CD45, and of phosphatidylserine to lactadherin. Our patient displayed over 100 times more phosphatidylserine-positive microparticles and over 400 times more cell-derived microparticles of leukocyte origin in his cerebrospinal fluid compared to healthy control subjects. The first cerebrospinal fluid fraction contained about 50% more microparticles than the second fraction. The scanning electron microscopy filters used with cerebrospinal fluid from our patient were filled with compact aggregates of spherical particles of
Modelling the fine and coarse fraction of heavy metals in Spain
García Vivanco, Marta; González, M. Angeles
2014-05-01
Heavy metals, such as cadmium, lead, nickel, arsenic, copper, chrome, zinc and selenium, are present in the air due to natural and anthropogenic emissions, normally joined to particles. These metals can affect life organisms via inhalation or ingestion, causing damages in human health and ecosystems. Small particles are inhaled and embebed in lungs and alveolus more easily than coarse particles. The CHIMERE model is a eulerian air quality model extensively used in air quality modelling. Metals have been recently included in this model in a special version developed in the CIEMAT (Madrid, Spain) modelling group. Vivanco et al. (2011) and González et al. (2012) showed the model performance for some metals in Spain and Europe. However, in these studies, metals were considered as fine particles. Some studies based on observed heavy metals air concentration indicate the presence of metals also in the coarse fraction, in special for Cu and Zn. For this reason, a new attempt of modelling metals considering a fine (Arsenic, Lead, Cadmium and Nickel Ambient Air Concentrations in Spain, 2011. Proceedings of the 11 th International Conference on Computational Science and Its Applications (ICCSA 11) 243-246 - González, Ma Vivanco, Marta; Palomino, Inmaculada; Garrido, Juan; Santiago, Manuel; Bessagnet, Bertrand Modelling Some Heavy Metals Air Concentration in Europe. // Water, Air & Soil Pollution;Sep2012, Vol. 223 Issue 8, p5227
M. M. Clark; T. H. Fletcher; R. R. Linn
2010-01-01
The chemical processes of gas phase combustion in wildland fires are complex and occur at length-scales that are not resolved in computational fluid dynamics (CFD) models of landscape-scale wildland fire. A new approach for modelling fire chemistry in HIGRAD/FIRETEC (a landscape-scale CFD wildfire model) applies a mixtureâ fraction model relying on thermodynamic...
Energy Technology Data Exchange (ETDEWEB)
Choi, A. S.; Flach, G. P.; Martino, C. J.; Zamecnik, J. R.; Harris, M. K.; Wilmarth, W. R.; Calloway, T. B.
2005-03-23
In order to accelerate waste treatment and disposal of Hanford tank waste by 2028, the Department of Energy (DOE) and CH2M Hill Hanford Group (CHG), Inc. are evaluating alternative technologies which will be used in conjunction with the Waste Treatment Plant (WTP) to safely pretreat and immobilize the tank waste. Several technologies (Bulk Vitrification and Steam Reforming) are currently being evaluated for immobilizing the pretreated waste. Since the WTP does not have sufficient capacity to pretreat all the waste going to supplemental treatment by the 2028 milestone, two technologies (Selective Dissolution and Fractional Crystallization) are being considered for pretreatment of salt waste. The scope of this task was to: (1) evaluate the recent Savannah River Site (SRS) Tank 41 dissolution campaign and other literature to provide a more complete understanding of selective dissolution, (2) provide an update on the progress of salt dissolution and modeling activities at SRS, (3) investigate SRS experience and outside literature sources on industrial equipment and experimental results of previous fractional crystallization processes, and (4) evaluate recent Hanford AP104 boildown experiments and modeling results and recommend enhancements to the Environmental Simulation Program (ESP) to improve its predictive capabilities. This report provides a summary of this work and suggested recommendations.
Skovbølling Haak, Christina; Illes, Monica; Paasch, Uwe; Hædersdal, Merete
2011-07-01
Ablative fractional resurfacing (AFR) represents a new treatment potential for various skin conditions and new laser devices are being introduced. It is important to gain information about the impact of laser settings on the dimensions of the created laser channels for obtaining a safe and efficient treatment outcome. The aim of this study was to establish a standard model to document the histological tissue damage profiles after AFR and to test a new laser device at diverse settings. Ex vivo abdominal pig skin was treated with a MedArt 620, prototype fractional carbon dioxide (CO(2)) laser (Medart, Hvidovre, Denmark) delivering single microbeams (MB) with a spot size of 165 μm. By using a constant pulse duration of 2 ms, intensities of 1-18 W, single and 2-4 stacked pulses, energies were delivered in a range from 2-144 mJ/MB. Histological evaluations included 3-4 high-quality histological measurements for each laser setting (n = 28). AFR created cone-shaped laser channels. Ablation depths varied from reaching the superficial dermis (2 mJ, median 41 μm) to approaching the subcutaneous fat (144 mJ, median 1,943 μm) and correlated to the applied energy levels in an approximate linear relation (r(2) = 0.84, p skin model to characterize AFR laser channels histologically.
Directory of Open Access Journals (Sweden)
Lazarević Mihailo P.
2013-01-01
Full Text Available In this paper, the applications of biologically inspired modeling and control of (biomechanical (nonredundant mechanisms are presented, as well as newly obtained results of author in mechanics which are based on using fractional calculus. First, it is proposed to use biological analog-synergy due to existence of invariant features in the execution of functional motion. Second, the model of (biomechanical system may be obtained using another biological concept called distributed positioning (DP, which is based on the inertial properties and actuation of joints of considered mechanical system. In addition, it is proposed to use other biological principles such as: principle of minimum interaction, which takes a main role in hierarchical structure of control and self-adjusting principle (introduce local positive/negative feedback on control with great amplifying, which allows efficiently realization of control based on iterative natural learning. Also, new, recently obtained results of the author in the fields of stability, electroviscoelasticity, and control theory are presented which are based on using fractional calculus (FC. [Projekat Ministarstva nauke Republike Srbije, br. 35006
Energy Technology Data Exchange (ETDEWEB)
Morais, A. P. [Biomedical Engineering Program, COPPE, Rio de Janeiro (Brazil); Salgado de Oliveira University, Marechal Deodoro Street, 217 – Centro, Niterói, Rio de Janeiro (Brazil); Pino, A. V. [Biomedical Engineering Program, COPPE, Rio de Janeiro (Brazil); Souza, M. N. [Biomedical Engineering Program, COPPE, Rio de Janeiro (Brazil); Electronics Department at Polytechnic School, Federal University of Rio de Janeiro, Centro de Tecnologia Bloco H sala 217, Ilha do Fundão, Rio de Janeiro (Brazil)
2016-08-15
This in vitro study evaluated the diagnostic performance of an alternative electric bioimpedance spectroscopy technique (BIS-STEP) detect questionable occlusal carious lesions. Six specialists carried out the visual (V), radiography (R), and combined (VR) exams of 57 sound or non-cavitated occlusal carious lesion teeth classifying the occlusal surfaces in sound surface (H), enamel caries (EC), and dentinal caries (DC). Measurements were based on the current response to a step voltage excitation (BIS-STEP). A fractional electrical model was used to predict the current response in the time domain and to estimate the model parameters: Rs and Rp (resistive parameters), and C and α (fractional parameters). Histological analysis showed caries prevalence of 33.3% being 15.8% hidden caries. Combined examination obtained the best traditional diagnostic results with specificity = 59.0%, sensitivity = 70.9%, and accuracy = 60.8%. There were statistically significant differences in bioimpedance parameters between the H and EC groups (p = 0.016) and between the H and DC groups (Rs, p = 0.006; Rp, p = 0.022, and α, p = 0.041). Using a suitable threshold for the Rs, we obtained specificity = 60.7%, sensitivity = 77.9%, accuracy = 73.2%, and 100% of detection for deep lesions. It can be concluded that BIS-STEP method could be an important tool to improve the detection and management of occlusal non-cavitated primary caries and pigmented sites.
International Nuclear Information System (INIS)
Morais, A. P.; Pino, A. V.; Souza, M. N.
2016-01-01
This in vitro study evaluated the diagnostic performance of an alternative electric bioimpedance spectroscopy technique (BIS-STEP) detect questionable occlusal carious lesions. Six specialists carried out the visual (V), radiography (R), and combined (VR) exams of 57 sound or non-cavitated occlusal carious lesion teeth classifying the occlusal surfaces in sound surface (H), enamel caries (EC), and dentinal caries (DC). Measurements were based on the current response to a step voltage excitation (BIS-STEP). A fractional electrical model was used to predict the current response in the time domain and to estimate the model parameters: Rs and Rp (resistive parameters), and C and α (fractional parameters). Histological analysis showed caries prevalence of 33.3% being 15.8% hidden caries. Combined examination obtained the best traditional diagnostic results with specificity = 59.0%, sensitivity = 70.9%, and accuracy = 60.8%. There were statistically significant differences in bioimpedance parameters between the H and EC groups (p = 0.016) and between the H and DC groups (Rs, p = 0.006; Rp, p = 0.022, and α, p = 0.041). Using a suitable threshold for the Rs, we obtained specificity = 60.7%, sensitivity = 77.9%, accuracy = 73.2%, and 100% of detection for deep lesions. It can be concluded that BIS-STEP method could be an important tool to improve the detection and management of occlusal non-cavitated primary caries and pigmented sites.
Yukawa couplings in Superstring derived Standard-like models
International Nuclear Information System (INIS)
Faraggi, A.E.
1991-01-01
I discuss Yukawa couplings in Standard-like models which are derived from Superstring in the free fermionic formulation. I introduce new notation for the construction of these models. I show how choice of boundary conditions selects a trilevel Yukawa coupling either for +2/3 charged quark or for -1/3 charged quark. I prove this selection rule. I make the conjecture that in this class of standard-like models a possible connection may exist between the requirements of F and D flatness at the string level and the heaviness of the top quark relative to lighter quarks and leptons. I discuss how the choice of boundary conditions determines the non vanishing mass terms for quartic order terms. I discuss the implication on the mass of the top quark. (author)
Multi-factor energy price models and exotic derivatives pricing
Hikspoors, Samuel
The high pace at which many of the world's energy markets have gradually been opened to competition have generated a significant amount of new financial activity. Both academicians and practitioners alike recently started to develop the tools of energy derivatives pricing/hedging as a quantitative topic of its own. The energy contract structures as well as their underlying asset properties set the energy risk management industry apart from its more standard equity and fixed income counterparts. This thesis naturally contributes to these broad market developments in participating to the advances of the mathematical tools aiming at a better theory of energy contingent claim pricing/hedging. We propose many realistic two-factor and three-factor models for spot and forward price processes that generalize some well known and standard modeling assumptions. We develop the associated pricing methodologies and propose stable calibration algorithms that motivate the application of the relevant modeling schemes.
International Nuclear Information System (INIS)
Yanagisawa, Hidefumi; Chikamori, Taishiro; Tanaka, Nobuhiro
2002-01-01
Although a relationship between the coronary pressure-derived fractional flow reserve (FFR) and the presence of myocardial ischemia as demonstrated by radionuclide imaging has been reported in a select group of patients, it remains to be established whether this relation also holds true in actual clinical settings with a heterogeneous group of patients. Accordingly, 194 coronary vessels and their supply territories were evaluated in 165 consecutive patients with suspected or known coronary artery disease. An FFR 201 Tl (p 201 Tl reversibility score (r=-0.62; p<0.0001). These results suggest that the FFR has a significant relationship with scintigraphic evidence of myocardial ischemia and can be regarded as a marker of its presence or absence in patients in actual clinical settings. (author)
Impact of Scattering Model on Disdrometer Derived Attenuation Scaling
Zemba, Michael; Luini, Lorenzo; Nessel, James; Riva, Carlo (Compiler)
2016-01-01
NASA Glenn Research Center (GRC), the Air Force Research Laboratory (AFRL), and the Politecnico di Milano (POLIMI) are currently entering the third year of a joint propagation study in Milan, Italy utilizing the 20 and 40 GHz beacons of the Alphasat TDP5 Aldo Paraboni scientific payload. The Ka- and Q-band beacon receivers were installed at the POLIMI campus in June of 2014 and provide direct measurements of signal attenuation at each frequency. Collocated weather instrumentation provides concurrent measurement of atmospheric conditions at the receiver; included among these weather instruments is a Thies Clima Laser Precipitation Monitor (optical disdrometer) which records droplet size distributions (DSD) and droplet velocity distributions (DVD) during precipitation events. This information can be used to derive the specific attenuation at frequencies of interest and thereby scale measured attenuation data from one frequency to another. Given the ability to both predict the 40 GHz attenuation from the disdrometer and the 20 GHz timeseries as well as to directly measure the 40 GHz attenuation with the beacon receiver, the Milan terminal is uniquely able to assess these scaling techniques and refine the methods used to infer attenuation from disdrometer data.In order to derive specific attenuation from the DSD, the forward scattering coefficient must be computed. In previous work, this has been done using the Mie scattering model, however, this assumes a spherical droplet shape. The primary goal of this analysis is to assess the impact of the scattering model and droplet shape on disdrometer derived attenuation predictions by comparing the use of the Mie scattering model to the use of the T-matrix method, which does not assume a spherical droplet. In particular, this paper will investigate the impact of these two scattering approaches on the error of the resulting predictions as well as on the relationship between prediction error and rain rate.
Evidence of a fractional quantum Hall nematic phase in a microscopic model
Regnault, N.; Maciejko, J.; Kivelson, S. A.; Sondhi, S. L.
2017-07-01
At small momenta, the Girvin-MacDonald-Platzman (GMP) mode in the fractional quantum Hall (FQH) effect can be identified with gapped nematic fluctuations in the isotropic FQH liquid. This correspondence would be exact as the GMP mode softens upon approach to the putative point of a quantum phase transition to a FQH nematic. Motivated by these considerations as well as by suggestive evidence of an FQH nematic in tilted field experiments, we have sought evidence of such a nematic FQHE in a microscopic model of interacting electrons in the lowest Landau level at filling factor 1/3. Using a family of anisotropic Laughlin states as trial wave functions, we find a continuous quantum phase transition between the isotropic Laughlin liquid and the FQH nematic. Results of numerical exact diagonalization also suggest that rotational symmetry is spontaneously broken, and that the phase diagram of the model contains both a nematic and a stripe phase.
Directory of Open Access Journals (Sweden)
Jagdev Singh
2017-07-01
Full Text Available In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM, to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotopy analysis method and homotopy polynomials that makes the calculation very easy. To compare the results obtained by using q-HASTM, we solve the same nonlinear problem by Adomian’s decomposition method (ADM. The convergence of the q-HASTM series solution for the model is adapted and controlled by auxiliary parameter ℏ and asymptotic parameter n. The numerical results are demonstrated graphically and in tabular form. The result obtained by employing the proposed scheme reveals that the approach is very accurate, effective, flexible, simple to apply and computationally very nice.