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After reviewing the variational approach to splitting mean flow and fluctuation kinetics in the standard Vlasov theory, the same method is applied to the drift-kinetic equation from Littlejohn's theory of guiding-center motion. This process…
This article revisits an analysis on inaccuracies of time series averaging under dynamic time warping conducted by \cite{Niennattrakul2007}. The authors presented a correctness-criterion and introduced drift-outs of averages from clusters.…
Large-scale cosmological simulations are an indispensable tool for modern cosmology. To enable model-space exploration, fast and accurate predictions are critical. In this paper, we show that the performance of such simulations can be…
An iterative scheme is presented to solve analytically the relativistic fluid dynamics equations. The scheme is applied to longitudinal expansion, transversal symmetric and transversal asymmetric (triaxial) expansion as well. Within this…
We employ an effective kinetic description to study the space-time dynamics and development of transverse flow of small and large collision systems. By combining analytical insights in the few interactions limit with numerical simulations…
Physics-informed deep learning has been developed as a novel paradigm for learning physical dynamics recently. While general physics-informed deep learning methods have shown early promise in learning fluid dynamics, they are difficult to…
Three different topics in phase-field modelling of solidification are discussed, with particular emphasis on the limitations of the currently available modelling approaches. First, thin-interface limits of two-sided phase-field models are…
A continuum theory of partially fluidized granular flows is developed. The theory is based on a combination of the equations for the flow velocity and shear stresses coupled with the order parameter equation which describes the transition…
In self-gravitating stars, two dimensional or geophysical flows and in plasmas, long range interactions imply a lack of additivity for the energy; as a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with…
Plasmas with varying collisionalities occur in many applications, such as tokamak edge regions, where the flows are characterized by significant variations in density and temperature. While a kinetic model is necessary for…
The distinction between the plasma dynamics dominated by collisional transport versus collective processes has never been rigorously addressed until recently. A recent paper [Yoon et al., Phys. Rev. E 93, 033203 (2016)] formulates for the…
In response to the comment by Zhu and Berakdar (arXiv:1207.3457) that the physical system considered by them in their previous work [Ding et al., PRB 84, 115433 (2011)] is conceptually different from ours in the appendix of our latest paper…
We provide the proof of convergence of the directional diffusion splitting scheme for two-dimensional parabolic and elliptic advection-diffusion-reaction problems with certain restrictions on problem data
Our goal is to develop a flux limiter of the Flux-Corrected Transport method for a nonconservative convection-diffusion equation. For this, we consider a hybrid difference scheme that is a linear combination of a monotone scheme and a…
Many multiscale problems have a high contrast, which is expressed as a very large ratio between the media properties. The contrast is known to introduce many challenges in the design of multiscale methods and domain decomposition…
A recent paper (Phys. Rev A. 75, 022513 (2007), arXiv:cond-mat/0602020) challenges exact time-dependent density functional theory (TDDFT) on several grounds. We explain why these criticisms are either irrelevant or incorrect, and that TDDFT…
Irradiation of a solid with intense plasma ion beams produced by Rod Plasma Injector is a strongly nonequilibrium process, which enables achieving a number of effects which are impossible to be achieved with other method. In the paper, the…
Sub-diffusion equations are used in a large range of applications including fluids, plasma physics and biology. Their mathematical analysis is advanced even if a much larger literature addresses super-diffusions. The goal of this paper is…
A time-stepping L1 scheme for subdiffusion equation with a Riemann--Liouville time-fractional derivative is developed and analyzed. This is the first paper to show that the L1 scheme for the model problem under consideration is second-order…
We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate…