Related papers: A unified multi-phase and multi-material formulati…
As a typical quantum many body problem, we consider the time evolution of density matrix elements in the Bose-Hubbard model. For an arbitrary initial state, these quantities can be obtained from an SDE or stochastic differential equation…
We develop a convergent reaction-drift-diffusion master equation (CRDDME) to facilitate the study of reaction processes in which spatial transport is influenced by drift due to one-body potential fields within general domain geometries. The…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…
This paper presents a modeling framework---mathematical model and computational framework---to study the response of a plastic material due to the presence and transport of a chemical species in the host material. Such a modeling framework…
We address a three-dimensional model capable of describing coupled damage and plastic effects in solids at finite strains. Formulated within the variational setting of {\it generalized standard materials}, the constitutive model results…
The mechanical behaviour of a poroelastic medium permeated by multiple interacting fluid networks can be described by a system of time-dependent partial differential equations known as the multiple-network poroelasticity (MPET) equations or…
We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing a statistically homogeneous set of multimodal spherical inclusions modeling the morphology of heterogeneous solid propellants (HSP).…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer…
An energy-based modeling framework for the nonlinear dynamics of spatial Cosserat rods undergoing large displacements and rotations is proposed. The mixed formulation features independent displacement, velocity and stress variables and is…
We investigate the expansion dynamics of a Bose-Einstein condensate that consists of two components and is initially confined in a quasi-one-dimensional trap. We classify the possible initial states of the two-component condensate by taking…
We present a hybrid mimetic finite-difference and virtual element formulation for coupled single-phase poromechanics on unstructured meshes. The key advantage of the scheme is that it is convergent on complex meshes containing highly…
Under compressive creep, visco-plastic solids experiencing internal mass transfer processes have been recently proposed to accommodate singular cnoidal wave solutions, as material instabilities at the stationary wave limit. These…
We develop a unified continuum modeling framework for viscous fluids and hyperelastic solids using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the…
Nonlinearities and instabilities in mechanical structures have shown great promise for embedding advanced functionalities. However, simulating structures subject to nonlinearities can be challenging due to the complexity of their behavior,…
We perform the linear stability analysis for a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes…
We introduce a coupled system of PDEs for the modeling of the fluid-fluid and fluid-solid interaction in a poroelastic material with a single static fracture. The fluid flow in the fracture is modeled by a lower-dimensional Darcy equation,…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…
Modeling nonlinear spatiotemporal dynamical systems has primarily relied on partial differential equations (PDEs). However, the explicit formulation of PDEs for many underexplored processes, such as climate systems, biochemical reaction and…
The development of accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions…