相关论文: Analytical solution of the cylindrical torsion pro…

We study the existence of solutions arising from the modelling of elastic materials using generalized theories of continua. In view of some evidence from physics of meta-materials we focus our effort on two recent nonstandard relaxed…

We describe wave decay rates associated to embedded resonances and spectral thresholds for waveguides and manifolds with infinite cylindrical ends. We show that if the cut-off resolvent is polynomially bounded at high energies, as is the…

We study the stable configurations of a thin three-dimensional weakly prestrained rod subject to a terminal load as the thickness of the section vanishes. By $\Gamma$-convergence we derive a one-dimensional limit theory and show that…

Complex fluids containing low concentrations of slender colloidal rods can display a high viscosity, while little flow is needed to thin the fluid. This feature makes slender rods essential constituents in industrial applications and…

The precise description of the motion of anisotropic particles in a flow rests on the understanding of the force and torque acting on them. Here, we study experimentally small, very elongated particles settling in a fluid at small Reynolds…

A submerged finite cylinder moving under its own weight along a soft incline lifts off and slides at a steady velocity while also spinning. Here, we experimentally quantify the steady spinning of the cylinder and show theoretically that it…

We prove existence of global in time strong solutions to the truncated thermo- visco-plasticity with an inelastic constitutive function of Norton-Hoff type. This result is a starting point to obtain renoramlised solutions for the considered…

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…

An account of the transversality conditions of variational problems gives rise to essential results in the analysis of different physical phenomena. This powerful and elegant approach has proven to be fruitful in a diversity of variational…

We establish the stability of solutions to the entropically regularized optimal transport problem with respect to the marginals and the cost function. The result is based on the geometric notion of cyclical invariance and inspired by the…

Tangent stabilised large strain isotropic elasticity was recently proposed by Poya et al. [1] wherein by working directly with principal stretches the entire eigenstructure of constitutive and geometric/initial stiffness terms were found in…

In this paper we study analytically the viscous `sabra' shell model of energy turbulent cascade. We prove the global regularity of solutions and show that the shell model has finitely many asymptotic degrees of freedom, specifically: a…

In this work, we prove existence and uniqueness of a bounded viscosity solution for the Cauchy problem of degenerate parabolic equations with variable exponent coefficients. We construct the solution directly using the stochastic…

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…

The present article studies variational principles for the formulation of static and dynamic problems involving Kirchhoff rods in a fully nonlinear setting. These results, some of them new, others scattered in the literature, are presented…

In this paper, we consider the isotropic relaxed micromorphic model in polar coordinates and use this representation to solve explicitly an elastostatic axisymmetric extension problem involving a linear system of ordinary differential…

Numerical simulations show that microscopic rod-like bodies suspended in a turbulent flow tend to align with the vorticity vector, rather than with the dominant eignevector of the strain-rate tensor. This paper investigates an analytically…

We study well-posedness for the relaxed linear elastic micromorphic continuum model with symmetric Cauchy force-stresses and curvature contribution depending only on the micro-dislocation tensor. In contrast to classical micromorphic models…

In this paper, we formulate a continuum theory of solidification within the context of finite-strain coupled thermoelasticity. We aim to fill a gap in the existing literature, as the existing studies on solidification typically decouple the…

We prove that, in the limit of vanishing thickness, equilibrium configurations of inhomogeneous, three-dimensional non-linearly elastic rods converge to equilibrium configurations of the variational limit theory. More precisely, we show…