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In this paper, we study the Cauchy problem of the Poiseuille flow of full Ericksen-Leslie model for nematic liquid crystals. The model is a coupled system of a parabolic equation for the velocity and a quasilinear wave equation for the…
Tidal disruption events involve numerous physical processes (fluid dynamics, magnetohydrodynamics, radiation transport, self-gravity, general relativistic dynamics) in highly nonlinear ways, and, because TDEs are transients by definition,…
In the field of nonlinear mechanics, many challenging problems (e.g. plasticity, contact, masonry structures, nonlinear membranes) turn out to be expressible as conic programs. In general, such problems are non-smooth in nature (plasticity…
Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at…
We study regularity and decay properties for the solutions of the Cauchy problem for time-fractional partial differential equations, with tempered initial data, belonging to suitable (weighted) Sobolev spaces, associated with a differential…
We consider the Cauchy problem for the nonlinear dynamical Lam\'e system with double wave speeds in a $d$-dimensional $(d=2,3)$ periodic domain. Moreover, the equations can be transformed into a linearly degenerate hyperbolic system. We…
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The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a…
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Inability of low-resolution ocean models to simulate many important aspects of the large-scale general circulation is a common problem. In the view of physics, the main reason for this failure are the missed dynamical effects of the…
The theory of the effect of external fluctuation force on the stability and spatial distribution of mutually interacting and slowly evaporating charged drops, levitated in an electrodynamic balance, is presented using classical…
I describe a new algorithm for solving nonlinear wave equations. In this approach, evolution takes place on characteristic hypersurfaces. The algorithm is directly applicable to electromagnetic, Yang-Mills and gravitational fields and other…
We introduce a finite volume scheme to solve a special case of isotropic 3-wave kinetic equations. We test our numerical solution against theoretical results concerning the long time behavior of the energy and observe that our solutions…
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We prove that the smooth solutions to the Cauchy problem for the compressible general three-dimensional Ericksen--Leslie system modeling nematic liquid crystal flow with conserved mass, linear momentum, and dissipating total energy,…
This work aims to describe a mathematical model and a numerical method to simulate a thin anisotropic composite membrane moving and deforming in 3D space under a dynamic load of an arbitrary time and space profile. The model and the method…
We present an efficient and flexible method for solving the non-linear lasing equations of the steady-state ab initio laser theory. Our strategy is to solve the underlying system of partial differential equations directly, without the need…