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Modified implicit fractional difference scheme for 2D modified anomalous fractional sub-diffusion equation

Umair Ali, Farah Aini Abdullah, Syed Tauseef Mohyud-Din
2017 Advances in Difference Equations  
In this paper, we solve two-dimensional modified anomalous fractional sub-diffusion equation using modified implicit finite difference approximation.  ...  The stability and convergence of the proposed scheme are analyzed by the Fourier series method.  ...  Cao et al. [] studied the implicit midpoint method and constructed a new numerical scheme for modified fractional sub-diffusion equation with nonlinear source term.  ... 
doi:10.1186/s13662-017-1192-4 fatcat:htw6iakbw5anpg2x7trzs6fdga

Numerical Solutions of Space-Fractional Advection–Diffusion–Reaction Equations

Valentina Anna Lia Salomoni, Nico De Marchi
2021 Fractal and Fractional  
Methods: a nonlinear-coupled 3D fractional hydro-mechanical model accounting for anomalous diffusion (FD) and advection–dispersion (FAD) for solute flux is described, accounting for a Riesz derivative  ...  solute transport in highly heterogeneous media and even neutron diffusion in nuclear environments are among the numerous applications of fractional differential equations (FDEs), being demonstrated by  ...  Hence, the advection step was solved via an explicit secondorder midpoint method, together with the β-method for the fractional diffusion-dispersion step and the trapezoidal rule for the fluid excess step  ... 
doi:10.3390/fractalfract6010021 fatcat:ovptv6g42nhfnei4emyu37wncu

Finite difference scheme for solving general 3D convection–diffusion equation

N. McTaggart, R. Zagórski, X. Bonnin, A. Runov, R. Schneider
2004 Computer Physics Communications  
We are solving a transport equation simultaneously at every point in a mesh (implicit method) and the resulting system of simultaneous equations is a matrix equation of the form Ax = b where A is the matrix  ...  The time derivative is approximated with the help of the first-order Euler scheme and the source term is split into two parts representing the explicit and implicit contribution.  ... 
doi:10.1016/j.cpc.2004.06.043 fatcat:xrpkrtcoo5boxgkux5pmtlkezm

Estimating Dissipation Rates Associated with Double Diffusion

L. Middleton, E. C. Fine, J. A. MacKinnon, M. H. Alford, J.R. Taylor
2021 Geophysical Research Letters  
For example, a doubling of the Beaufort Gyre halocline heat content has influenced sea-ice extent (Shimada et al., 2006; Timmermans et al., 2018) .  ...  However, common shear and strain based parameterisations for internal wave breaking do not apply well to areas of double-diffusive convection (Gregg, 1989) .  ...  Acknowledgments The authors thank Barry Ruddick and an anonymous reviewer for their valuable input on the development of this manuscript.  ... 
doi:10.1029/2021gl092779 fatcat:syqcer5hpfattbic32a7hq445e

Numerical Stabilization of the Melt Front for Laser Beam Cutting [chapter]

Torsten Adolph, Willi Schönauer, Markus Niessen, Wolfgang Schulz
2010 Numerical Mathematics and Advanced Applications 2009  
Numerical experiments will be done for simple linear problems, the Burger's equation, and for the Euler equations with high Mach numbers. 24 This contribution deals with the modeling of soft biological  ...  The model is based on Navier-Stokes equations for viscous incompressible flow and convection-diffusion equation describing pollution transport.  ...  DG method for nonstationary convection-diffusion problems Finite element methods with symmetric stabilization for the transient convection-diffusion--reaction equation We consider implicit and semi-implicit  ... 
doi:10.1007/978-3-642-11795-4_6 fatcat:nx4nvuxaxfbcdjknopny53ck5e

A local stabilized approach for approximating the modified time-fractional diffusion problem arising in heat and mass transfer

O. Nikan, Z. Avazzadeh, J.A. Tenreiro Machado
2021 Journal of Advanced Research  
The modified time-fractional diffusion equation provides a deeper understanding of several dynamic phenomena.  ...  This paper adopts a local hybrid kernel meshless approach to solve the modified time-fractional diffusion problem.  ...  Acknowledgements The authors would like to thank the editors and three anonymous reviewers for their insightful comments and suggestions that greatly improved the quality of this paper.  ... 
doi:10.1016/j.jare.2021.03.002 pmid:34484825 pmcid:PMC8408339 fatcat:jnhncypwqbawjmxkd2ekcmuyzq

Superdiffusion in spin chains [article]

Vir B. Bulchandani, Sarang Gopalakrishnan, Enej Ilievski
2021 arXiv   pre-print
Numerical advances, based on tensor-network methods, have shown that transport in many canonical integrable spin chains -- most famously the Heisenberg model -- is anomalous.  ...  We present what is currently understood about these mechanisms, and discuss how they resemble (and differ from) the mechanisms for anomalous transport in other contexts.  ...  The latter can be thought of as a source of nonlinearity which ultimately renders time-evolution non-trivial.  ... 
arXiv:2103.01976v1 fatcat:lmdxo34idbexnpkllhrda4rtdy

Multi-scale simulations of particle acceleration in astrophysical systems

Alexandre Marcowith, Gilles Ferrand, Mickael Grech, Zakaria Meliani, Illya Plotnikov, Rolf Walder
2020 Living Reviews in Computational Astrophysics  
and the SMILEI dev-team for various discussions on the PIC method.  ...  RW thanks Mickaël Melzani who contributed a lot to his knowledge of magnetic reconnection and Doris Folini for profound discussions and proof-reading.  ...  The diffusive method reduces the numerical error of ∇ · B by adding a source term in the induction equation and the energy equation.  ... 
doi:10.1007/s41115-020-0007-6 fatcat:vl7sss2lejcwrbcmb3huovzkvy

State of the Art and Future Research Needs for Multiscale Analysis of Li-Ion Cells

K. Shah, N. Balsara, S. Banerjee, M. Chintapalli, A. P. Cocco, W. K. S. Chiu, I. Lahiri, S. Martha, A. Mistry, P. P. Mukherjee, V. Ramadesigan, C. S. Sharma (+3 others)
2017 Journal of Electrochemical Energy Conversion and Storage  
It is expected that this summary will help understand the complex nature of Li-ion batteries and help highlight the critical directions for future research.  ...  This paper provides a summary of the state of the art in a variety of research fields related to Li-ion battery materials, processes, and systems.  ...  For implicit methods, order conditions are easy to satisfy. Note that implicit midpoint method (IMP) is also the Gauss Runge-Kutta method of order 2 (single stage).  ... 
doi:10.1115/1.4036456 fatcat:xsclpai3y5efzeb7udpgich4x4

Multi-scale simulations of particle acceleration in astrophysical systems [article]

A. Marcowith, G. Ferrand, M. Grech, Z. Meliani, I. Plotnikov, R. Walder
2020 arXiv   pre-print
We analyze with some details the particle-in-cell (PIC) approach used to describe particle kinetics.  ...  We review the main results obtained with PIC simulations in the recent years concerning particle acceleration at shocks and in reconnection events.  ...  the SMILEI dev-team for various discussions on the PIC method.  ... 
arXiv:2002.09411v2 fatcat:bsyoqzwnibgqldkvlb33ujrjw4

Statistical mechanics of combat with human factors

Lester Ingber, David D. Sworder
1991 Mathematical and computer modelling  
Theoretically, these equations are nested within a larger set of nonlinear stochastic operator-equations which include C 3 human factors, e.g., supervisory decisions.  ...  Our approach is to "subordinate" the SMC nonlinear stochastic equations, fitted to NTC scenarios, to establish the zeroth order description of that combat.  ...  These methods are not conveniently used for other sources of noise, e.g., Poisson processes or Bernoulli processes.  ... 
doi:10.1016/0895-7177(91)90108-j fatcat:x2ix4ysw2vaszkqj2g7rgnfkh4

Multi-time correlations in the positive-P, Q, and doubled phase-space representations

Piotr Deuar
2021 Quantum  
In addition, a robust but simple algorithm for integration of stochastic equations for phase-space samples is provided.  ...  A number of physically intuitive results for the calculation of multi-time correlations in phase-space representations of quantum mechanics are obtained.  ...  The bulk of the method is based on the semi-implicit midstep algorithm described in [51, 140] , adding some modified propagators as per [44] which allow for more efficient treatment of exponential and  ... 
doi:10.22331/q-2021-05-10-455 fatcat:dm3ybb7b3rdubpuxzkmlbeyreq

Implicit large eddy simulations of anisotropic weakly compressible turbulence with application to core-collapse supernovae

David Radice, Sean M Couch, Christian D Ott
2015 Computational Astrophysics and Cosmology  
We discuss the consequences for CCSN simulations.  ...  Recent 3D simulations suggest that turbulence might play a crucial role in core-collapse supernova explosions, however the fidelity with which turbulence is simulated in these studies is unclear.  ...  Acknowledgements We acknowledge helpful discussions with E Abdikamalov, WD Arnett, A Burrows, R Fisher, C Meakin, P Mösta, J Murphy, M Norman, and L Roberts.  ... 
doi:10.1186/s40668-015-0011-0 fatcat:axma7sls5rgglf6r2v2wnpn53y

Approach and separation of quantised vortices with balanced cores

C. Rorai, J. Skipper, R. M. Kerr, K. R. Sreenivasan
2016 Journal of Fluid Mechanics  
for a quantum fluid.  ...  The scaling laws for the reconnection of isolated pairs of quantised vortices are characterised by numerically integrating the three-dimensional Gross–Pitaevskii equations, the simplest mean-field equations  ...  RMK acknowledges support from the EU COST Action program MP0806 Particles in Turbulence. Discussions with C. Barenghi and M.E. Fisher have been appreciated. Support with graphics from R.  ... 
doi:10.1017/jfm.2016.638 fatcat:gslxh5ppnvhxbpr2r75sipoh2a

Approach and separation of quantum vortices with balanced cores [article]

Cecilia Rorai, Jack Skipper, Robert M. Kerr, Katepalli R. Sreenivasan
2016 arXiv   pre-print
Gross-Pitaevskii equations, the simplest mean-field non-linear Schrödinger equation for a quantum fluid.  ...  For the anti-parallel case, the scaling laws just before and after reconnection obey the dimensional δ∼|t_r-t|^1/2 prediction with temporal symmetry about the reconnection time t_r and physical space symmetry  ...  RMK acknowledges support from the EU COST Action program MP0806 Particles in Turbulence. Discussions with C. Barenghi and M.E. Fisher have been appreciated. Support with graphics from R.  ... 
arXiv:1410.1259v2 fatcat:gq6rwgjbirb6xiea52ze2xjwty
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