相关论文: Unification of visco-elastic wave equations
The dynamics of strongly interacting many-body quantum systems are notoriously complex and difficult to simulate. A new theory, generalized hydrodynamics (GHD), promises to efficiently accomplish such simulations for nearly-integrable…
We consider a space-time variational formulation of the second-order wave equation, where integration by parts is also applied with respect to the time variable. Conforming tensor-product finite element discretisations with piecewise…
Granular solid hydrodynamics (GSH) is a continuum-mechanical theory for granular media, the range of which is shown in this paper. Simple, frequently analytic solutions are related to classic observations at different shear rates,…
We point out that the Gaussian wave-packet formalism can serve as a concrete realization of the joint measurement of position and momentum, which is an essential element in understanding Heisenberg's original philosophy of the uncertainty…
Mathematical models and numerical simulations are widely used in the field of hemodynamics, representing a valuable resource to better understand physiological and pathological processes. The theory behind the phenomenon is closely related…
Semi-discrete and fully discrete mixed finite element methods are considered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid. This mixed finite element framework allows the use of a large class of existing…
We consider linear scalar wave equations with a hereditary integral term of the kind used to model viscoelastic solids. The kernel in this Volterra integral is a sum of decaying exponentials (The so-called Maxwell, or Zener model) and this…
A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the…
In acoustics, higher-order-in-time equations arise when taking into account a class of thermal relaxation laws in the modeling of sound wave propagation. In this work, we analyze initial boundary value problems for a family of such…
It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling…
The present contribution proves the asymptotic orbital stability of viscous regularizations of stable Riemann shocks of scalar balance laws, uniformly with respect to the viscosity/diffusion parameter $\epsilon$. The uniformity is…
In this paper, we propose a globally hyperbolic regularization to the general Grad's moment system in multi-dimensional spaces. Systems with moments up to an arbitrary order are studied. The characteristic speeds of the regularized moment…
We study the Cauchy-Dirichlet pbm for superquadratic viscous Hamilton-Jacobi eq. We give a complete classification, namely rates and space-time profiles, in 1d case when viscosity sol. undergo gradient blow-up (GBU) or recovery of boundary…
Three numerical algorithms are proposed to solve the time-dependent elastodynamic equations in elastic solids. All algorithms are based on approximating the solution of the equations, which can be written as a matrix exponential. By…
We address the problem of the response to a seismic wave of an urban site consisting of a large and infinite number ($N\_{b}$) of identical, equispaced blocks overlying a soft layer underlain by a hard substratum. The results of the…
We discuss a unified flow theory which in a single system of hyperbolic partial differential equations (PDEs) can describe the two main branches of continuum mechanics, fluid dynamics, and solid dynamics. The fundamental difference from the…
Earth introduces strong attenuation and dispersion to propagating waves. The time-fractional wave equation with very small fractional exponent, based on Kjartansson's constant-Q theory, is widely recognized in the field of geophysics as a…
This paper concerns the construction and analysis of a new family of exact general relativistic shock waves. The construction resolves the open problem of determining the expanding waves created behind a shock-wave explosion into a static…
In the one-dimensional isothermal case, we introduce a simple model of nonlinear viscoelasticity within the Rational Extended Thermodynamics (RET) framework. The differential system is determined by the universal principles of RET,…
We present a thermodynamically consistent theoretical framework for lyotropic liquid crystals (LCs) based on the GENERIC (General Equation for the Non-Equilibrium Reversible-Irreversible Coupling) formalism. This formalism ensures…