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This work presents a new conforming stabilized virtual element method for the generalized Boussinesq equation with temperature-dependent viscosity and thermal conductivity. A gradient-based local projection stabilization method is…

Numerical Analysis · Mathematics 2025-12-29 Sudheer Mishra , Sundararajan Natarajan , Natarajan E

In this paper we consider and compare special classes of static theories of gradient elasticity, nonlocal elasticity, gradient micropolar elasticity and nonlocal micropolar elasticity with only one gradient coefficient. Equilibrium…

Materials Science · Physics 2009-11-11 M. Lazar , G. A. Maugin , E. C. Aifantis

We derive a semi-geostrophic variational balance model for the three-dimensional Euler--Boussinesq equations on the non-traditional $f$-plane under the rigid lid approximation. The model is obtained by a small Rossby number expansion in the…

Analysis of PDEs · Mathematics 2021-07-28 Gözde Özden , Marcel Oliver

In this work we establish the well-posedness for infinitesimal dislocation based gradient viscoplasticity with isotropic hardening for general gradient monotone plastic flows. We assume an additive split of the displacement gradient into…

Analysis of PDEs · Mathematics 2014-11-06 Nataliya Kraynyukova , Patrizio Neff , Sergiy Nesenenko , Krzysztof Chełmiński

We consider the evolution of two incompressible fluids with homogeneous densities $\rho_-<\rho_+$ subject to gravity described by the inviscid Boussinesq equations and provide the explicit relaxation of the associated differential…

Analysis of PDEs · Mathematics 2022-01-24 Björn Gebhard , József J. Kolumbán

This study presents a physically consistent displacement-driven reformulation of the concept of action-at-a-distance, which is at the foundation of nonlocal elasticity. In contrast to existing approaches that adopts an integral…

Numerical Analysis · Mathematics 2021-11-03 Sansit Patnaik , Sai Sidhardh , Fabio Semperlotti

Fundamental solutions for two- and three-dimensional linear isotropic size-dependent couple stress elasticity are derived, based upon the decomposition of displacement fields into dilatational and solenoidal components. While several…

Mathematical Physics · Physics 2011-07-15 Ali R. Hadjesfandiari , Gary F. Dargush

In this paper, we are concerned with the tridimensional anisotropic Boussinesq equations which can be described by {equation*} {{array}{ll} (\partial_{t}+u\cdot\nabla)u-\kappa\Delta_{h} u+\nabla \Pi=\rho…

Analysis of PDEs · Mathematics 2014-05-30 Changxing Miao , Xiaoxin Zheng

The linear wave and geostrophic (vortex) solutions are shown to be a complete basis for physical variables $(u,v,w,\rho)$ in a rotating non-hydrostatic Boussinesq model with arbitrary stratification. As a consequence, the fluid can be…

Fluid Dynamics · Physics 2021-02-16 Jeffrey J. Early , M. Pascale Lelong , Miles A. Sundermeyer

We introduce models for viscoelastic materials, both solids and fluids, based on logarithmic stresses to capture the elastic contribution to the material response. The matrix logarithm allows to link the measures of strain, that naturally…

Analysis of PDEs · Mathematics 2024-10-10 Gennaro Ciampa , Giulio G. Giusteri , Alessio G. Soggiu

In this paper, we consider the viscous, incompressible, nonlinear Boussinesq system in two and three spatial dimension. We study the existence and regularity of solutions to the Boussinesq system with nonhomogeneous boundary conditions for…

Analysis of PDEs · Mathematics 2023-06-21 Arnab Roy

The isothermal quasistatic (i.e.\ acceleration neglected) hardening-free plasticity at large strains is considered, based on the standard multiplicative decomposition of the total strain and the isochoric plastic distortion. The Eulerian…

Analysis of PDEs · Mathematics 2022-06-01 Tomáš Roubíček

This paper deals with stability and the large-time decay to any given global smooth solutions of the 3D density-dependent incompressible Boussinesq system. The decay rate for solutions of the corresponding Cauchy problem is obtained in this…

Analysis of PDEs · Mathematics 2021-09-07 Xiaopan Liu , Qingshan Zhang

Weakly non-linear stability of regimes of free hydromagnetic thermal convection in a rotating horizontal layer with free electrically conducting boundaries is considered in the Boussinesq approximation. Perturbations are supposed to involve…

Chaotic Dynamics · Physics 2015-05-13 V. Zheligovsky

Recent experimental results on the static or quasistatic response of granular materials have been interpreted to suggest the inapplicability of the traditional engineering approaches, which are based on elasto-plastic models (which are…

Soft Condensed Matter · Physics 2007-05-23 Chay Goldenberg , Isaac Goldhirsch

This paper presents a comprehensive computational framework for investigating thermo-elastic fracture in transversely isotropic materials, where classical linear elasticity fails to predict physically realistic behavior near stress…

Numerical Analysis · Mathematics 2025-10-08 Saugata Ghosh , Dambaru Bhatta , S. M. Mallikarjunaiah

We consider a family of linear viscoelastic shells with thickness $2\varepsilon$ ( $\varepsilon$ , small parameter), clamped along a portion of their lateral face, all having the same middle surface $S$. We formulate the three-dimensional…

Analysis of PDEs · Mathematics 2017-02-16 G. Castiñeira , Á. Rodríguez-Arós

A theoretical and computational investigation is carried out of a dissipative model of rate-independent strain-gradient plasticity and its regularization. It is shown that the flow relation, when expressed in terms of the Cauchy stress, is…

Materials Science · Physics 2017-04-12 C Carstensen , F Ebobisse , AT McBride , BD Reddy , P Steinmann

We devise variants of classical nonconforming methods for symmetric elliptic problems. These variants differ from the original ones only by transforming discrete test functions into conforming functions before applying the load functional.…

Numerical Analysis · Mathematics 2017-10-11 Andreas Veeser , Pietro Zanotti

In this paper we revisit the derivations of model equations describing long nonlinear longitudinal bulk strain waves in elastic rods within the scope of the Murnaghan model in order to derive a Boussinesq-type model, and extend these…

Pattern Formation and Solitons · Physics 2020-03-17 F. E. Garbuzov , K. R. Khusnutdinova , I. V. Semenova