☆ 4.1 Article

A Generalized Diffusion Equation: Solutions and Anomalous Diffusion

FLUIDS (2023)

Related references

Note: Only part of the references are listed.

Article Engineering, Multidisciplinary

Chebyshev spectral method for solving a class of local and nonlocal elliptic boundary value problems

Harendra Singh

Summary: This paper focuses on Bratu's type, Troesch's, and nonlocal elliptic boundary value problems, which are difficult to solve due to their strong nonlinearity and the presence of parameter delta. The Chebyshev spectral collocation method is used to tackle these important equations, and the convergence of the method is demonstrated. The method's effectiveness is confirmed through illustrative examples, showing negligible error and high accuracy compared to other known methods.

INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION (2023)

Add to Collection

Article Physics, Multidisciplinary

Transient anomalous diffusion in heterogeneous media with stochastic resetting

M. K. Lenzi et al.

Summary: In this study, we investigated a diffusion process in heterogeneous media with stochastic resetting to initial positions at a constant rate. Exact solutions for the probability distribution and mean square displacement of particles' positions were obtained using the Green function approach, which were compared with numerical simulations. The system exhibited non-Gaussian distributions, transient anomalous diffusion, and stationary states depending on media heterogeneity and resetting rate, with media heterogeneity affecting the mean first-passage time and yielding an optimal resetting rate with a minimum value for this quantity.

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS (2022)

Add to Collection

Article Thermodynamics

Solving a class of local and nonlocal elliptic boundary value problems arising in heat transfer

Harendra Singh

Summary: This paper investigates a class of elliptic boundary value problems related to heat transfer, successfully solved using the Jacobi spectral collocation method. Numerical and theoretical results demonstrate the convergence and accuracy of the proposed scheme, with negligible error compared to other methods.

HEAT TRANSFER (2022)

Add to Collection

Article Mathematics, Interdisciplinary Applications

Fractional Schrodinger equation for heterogeneous media and Levy like distributions

E. K. Lenzi et al.

Summary: We investigate an extension of the Schrodinger equation by introducing a fractional differential operator for the spatial variable, taking into account the heterogeneity of the media and the Levy-like distributions. Using the Green's function method, we obtain solutions for the free particle case and when the particle is subjected to a delta potential. We also explore the influence of a non-local contribution added to the delta potential on the wave function. The solutions exhibit a rich class of spreading behaviors, which differ significantly from the usual wave function and may be related to power-laws and stretched exponential distributions.

CHAOS SOLITONS & FRACTALS (2022)

Add to Collection

Article Chemistry, Analytical

Time-fractional approach to the electrochemical impedance: The Displacement current

G. Barbero et al.

Summary: In this study, we discuss the conditions for the time-fractional approach formulation of the Poisson-Nernst-Planck model to ensure that the total current across the sample is solenoidal, as required by the Maxwell equations. We also show that in the case of anomalous diffusion, the model predicts a constant phase element behavior for the electric impedance of the cell.

JOURNAL OF ELECTROANALYTICAL CHEMISTRY (2022)

Add to Collection

Article Chemistry, Physical

Frequency-Dependent Dielectric Permittivity in Poisson-Nernst-Planck Model

M. P. Rosseto et al.

Summary: The research aims to investigate the interaction between free and bound charge densities and their influence on permittivity and impedance profiles by modifying the Poisson-Nernst-Planck model.

JOURNAL OF PHYSICAL CHEMISTRY B (2022)

Add to Collection

Article Materials Science, Composites

Multiscale heat conduction and fractal oxidation behaviors of needle-punched carbon/carbon composites

Meng Han et al.

Summary: This study investigated the longitudinal and transverse heat conduction in carbon/carbon composites and predicted their oxidation behavior using a fractional Brownian motion strategy. The results showed that the punching structures of the composites slowed down the process of heat conduction, and the heat transfer interface of the fiber bundle exhibited a peak-like morphology.

SCIENCE AND ENGINEERING OF COMPOSITE MATERIALS (2022)

Add to Collection

Article Engineering, Multidisciplinary

An inverse problem to simulate the transport of chloride in concrete by time-space fractional diffusion model

Chenqing Feng et al.

Summary: The proposed fractional diffusion model in this paper simulates the movement of chloride in concrete, considering the complex porous structure and the influence of the surrounding environment on the bound and free chlorides. Experiments show heavy-tailed phenomena in diffusion process, which are explained by the introduced time and spatial fractional derivatives. The numerical research demonstrates that the model fits the experimental data well and the diffusion of chloride in concrete is both time-dependent and space-dependent.

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING (2021)

Add to Collection

Article Mathematics, Applied

Classes of operators in fractional calculus: A case study

Arran Fernandez et al.

Summary: The article introduces a method of classifying operators into general categories, and uses this to understand operators defined by Prabhakar with Mittag-Leffler kernels. This approach allows for a better understanding of the fundamental nature of operators and different special cases, as well as the characterization of singular and nonsingular operators within the class. Additionally, a catalogue of subclasses with different properties is obtained by considering cases where these operators can be written as finite or infinite sums of Riemann-Liouville differintegrals.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2021)

Add to Collection

Article Physics, Mathematical

Space-time fractional diffusion equations in d-dimensions

E. K. Lenzi et al.

Summary: This study analyzes a new space-time fractional diffusion equation to tackle anomalous diffusion in heterogeneous media, incorporating power-law distributions. By utilizing the Green function method, a formal solution can be proposed to model anomalous diffusion and relaxation problems effectively in such media.

JOURNAL OF MATHEMATICAL PHYSICS (2021)

Add to Collection

Article Mathematics

Slices of the Anomalous Phase Cube Depict Regions of Sub- and Super-Diffusion in the Fractional Diffusion Equation

Richard L. Magin et al.

Summary: Fractional-order time and space derivatives enhance classical diffusion equations to explain non-Gaussian processes. Phase diagrams display different diffusion propagators (Gaussian, Cauchy), specific stochastic models (Levy process, subordinated Brownian motion), and regions of super- and sub-diffusion. Anomalous diffusion phase cubes classify models of anomalous diffusion using lines of super-diffusion, sub-diffusion, and quasi-Gaussian behavior.

MATHEMATICS (2021)

Add to Collection

Review Physics, Multidisciplinary

Stochastic resetting and applications

Martin R. Evans et al.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2020)

Add to Collection

Review Computer Science, Interdisciplinary Applications

Modelling of fluid flow through porous media using memory A review

Mahamudul Hashan et al.

MATHEMATICS AND COMPUTERS IN SIMULATION (2020)

Add to Collection

Article Physics, Multidisciplinary

Numerical Investigation of the Fractional-Order Lienard and Duffing Equations Arising in Oscillating Circuit Theory

Harendra Singh et al.

FRONTIERS IN PHYSICS (2020)

Add to Collection

Article Mathematics, Interdisciplinary Applications

Fractal-fractional modelling of partially penetrating wells

Kambiz Razminia et al.

CHAOS SOLITONS & FRACTALS (2019)

Add to Collection

Article Mathematics, Applied

Macroscale modeling the methanol anomalous transport in the porous pellet using the time-fractional diffusion and fractional Brownian motion: A model comparison

Alexey Zhokh et al.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2019)

Add to Collection

Article Energy & Fuels

The Theis solution for subdiffusive flow in rocks

Rajagopal Raghavan et al.

OIL & GAS SCIENCE AND TECHNOLOGY-REVUE D IFP ENERGIES NOUVELLES (2019)

Add to Collection

Article Acoustics

The fractal derivative wave equation: Application to clinical amplitude/velocity reconstruction imaging

Wei Cai et al.

JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA (2018)

Add to Collection

Article Materials Science, Multidisciplinary

Fractal calculus and its geometrical explanation

Ji-Huan He

RESULTS IN PHYSICS (2018)

Add to Collection

Article Physics, Multidisciplinary

Fractional Hunter-Saxton equation involving partial operators with bi-order in Riemann-Liouville and Liouville-Caputo sense

J. F. Gomez-Aguilar et al.

EUROPEAN PHYSICAL JOURNAL PLUS (2017)

Add to Collection

Article Physics, Multidisciplinary

The Role of Fractional Time-Derivative Operators on Anomalous Diffusion

Angel A. Tateishi et al.

FRONTIERS IN PHYSICS (2017)

Add to Collection

Article Mathematics, Interdisciplinary Applications

New methodologies in fractional and fractal derivatives modeling

Wen Chen et al.

CHAOS SOLITONS & FRACTALS (2017)

Add to Collection

Article Thermodynamics

NEW FRACTIONAL DERIVATIVES WITH NON-LOCAL AND NON-SINGULAR KERNEL Theory and Application to Heat Transfer Model

Abdon Atangana et al.

THERMAL SCIENCE (2016)

Add to Collection

Article Physics, Multidisciplinary

Anomalous diffusion and power-law relaxation of the time averaged mean squared displacement in worm-like micellar solutions

Jae-Hyung Jeon et al.

NEW JOURNAL OF PHYSICS (2013)

Add to Collection

Article Physics, Multidisciplinary

Diffusion with Stochastic Resetting

Martin R. Evans et al.

PHYSICAL REVIEW LETTERS (2011)

Add to Collection

Article Physics, Multidisciplinary

The time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems

Xiaoyun Jiang et al.

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS (2010)

Add to Collection

Article Physics, Multidisciplinary

Solutions for a non-Markovian diffusion equation

E. K. Lenzi et al.

PHYSICS LETTERS A (2010)

Add to Collection

Article Engineering, Multidisciplinary

Similarity solutions for solute transport in fractal porous media using a time- and scale-dependent dispersivity

NH Su et al.

APPLIED MATHEMATICAL MODELLING (2005)

Add to Collection

Article Physics, Multidisciplinary

Relative dispersion in fully developed turbulence: The Richardson's law and intermittency corrections

G Boffetta et al.

PHYSICAL REVIEW LETTERS (2002)

Add to Collection

Article Physics, Applied

Experimental evidence and theoretical analysis of anomalous diffusion during water infiltration in porous building materials

M Küntz et al.

JOURNAL OF PHYSICS D-APPLIED PHYSICS (2001)

Add to Collection

Review Physics, Multidisciplinary

The random walk's guide to anomalous diffusion: a fractional dynamics approach

R Metzler et al.

PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS (2000)

Add to Collection

© Peeref 2019-2024. All rights reserved.