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We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart…

Probability · Mathematics 2016-09-21 Nathan E. Glatt-Holtz , Jonathan C. Mattingly , Geordie Richards

We consider the asymptotic solutions of an interface problem corresponding to an elliptic partial differential equation with Dirich- let boundary condition and transmission condition, subject to the small geometric perturbation and the high…

Analysis of PDEs · Mathematics 2017-08-16 Jingrun Chen , Ling Lin , Zhiwen Zhang , Xiang Zhou

We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are…

Pattern Formation and Solitons · Physics 2009-11-11 J. P. Sharpe , P. L. Ramazza , N. Sungar , Karl Saunders

The discrete modeling of a large class of mechanical structures can be based on a stick-and-spring concept. We here present a stick-and-spring theory with potential application to the statics and the dynamics of such nanostructures as…

Materials Science · Physics 2013-07-16 Antonino Favata , Andrea Micheletti , Paolo Podio-Guidugli

Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the…

Soft Condensed Matter · Physics 2009-11-13 Efi Efrati , Eran Sharon , Raz Kupferman

We define an abstract nonlinear elliptic system, admitting a variational structure, and including the vortex equations for some Maxwell-Chern-Simons gauge theories as special cases. We analyze the asymptotic behavior of its solutions, and…

Analysis of PDEs · Mathematics 2007-05-23 Tonia Ricciardi

We discuss whether homogeneous Cauchy stress implies homogeneous strain in isotropic nonlinear elasticity. While for linear elasticity the positive answer is clear, we exhibit, through detailed calculations, an example with inhomogeneous…

Classical Physics · Physics 2019-04-04 L. Angela Mihai , Patrizio Neff

Two series of uniaxial tensile tests are performed on isotactic polypropylene with the strain rates ranging from 5 to 200 mm/min. In the first series, injection-molded specimens are used without thermal pre-treatment, whereas in the other…

Materials Science · Physics 2007-05-23 A. D. Drozdov , J. deC. Christiansen

We introduce the notion of asymptotic integrability into the theory of nonlinear wave equations. It means that the Hamiltonian structure of equations describing propagation of high-frequency wave packets is preserved by hydrodynamic…

Exactly Solvable and Integrable Systems · Physics 2024-07-08 A. M. Kamchatnov

Experiments have shown that elasticity of disordered filamentous networks with compliant crosslinks is very different from networks with rigid crosslinks. Here, we model and analyze filamentous networks as a collection of randomly oriented…

Biological Physics · Physics 2015-06-17 A. Sharma , M. Sheinman , K. M. Heidemann , F. C. MacKintosh

The mechanical, structural and functional properties of crystals are determined by their defects and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect…

Materials Science · Physics 2016-09-02 Neil Y. C. Lin , Matthew Bierbaum , Peter Schall , James P. Sethna , Itai Cohen

A general approach is presented to describing nonlinear classical Maxwell electrodynamics with conformal symmetry. We introduce generalized nonlinear constitutive equations, expressed in terms of constitutive tensors dependent on…

High Energy Physics - Theory · Physics 2020-01-29 Steven Duplij , Gerald A. Goldin , Vladimir M. Shtelen

A finite element framework is presented for analyzing crack-tip phenomena in transversely isotropic, strain-limiting elastic materials. Mechanical response is characterized by an algebraically nonlinear constitutive model, relating stress…

Numerical Analysis · Mathematics 2025-07-03 Saugata Ghosh , Dambaru Bhatta , S. M. Mallikarjunaiah

We experimentally characterize the impact response of concentrated suspensions consisting of cornstarch and water. We observe that the suspensions support a large normal stress -- on the order of MPa -- with a delay after the impactor hits…

Soft Condensed Matter · Physics 2018-05-09 Rijan Maharjan , Shomeek Mukhopadhyay , Benjamin Allen , Tobias Storz , Eric Brown

A recently proposed connection between closed string field and an open Wilson line defined on an arbitrary contour is further explored here. We suggest that reparametrization invariance of a Wilson line is the principle which determines the…

High Energy Physics - Theory · Physics 2010-05-28 Avinash Dhar , Yoshihisa Kitazawa

A general approach is presented for understanding the stress response function in anisotropic granular layers in two dimensions. The formalism accommodates both classical anisotropic elasticity theory and linear theories of anisotropic…

Statistical Mechanics · Physics 2009-11-07 M. Otto , J. -P. Bouchaud , P. Claudin , J. E. S. Socolar

The classical continuous mixed formulation of linear elasticity with pointwise symmetric stresses allows for a conforming finite element discretization with piecewise polynomials of degree at least three. Symmetric stress approximations of…

Numerical Analysis · Mathematics 2025-03-17 Carsten Carstensen , Norbert Heuer

A (bar-and-joint) framework is a set of points in a normed space with a set of fixed distance constraints between them. Determining whether a framework is locally rigid - i.e. whether every other suitably close framework with the same…

Metric Geometry · Mathematics 2024-01-18 Sean Dewar

We investigate the structure and mechanical behavior of assemblies of frictionless, nearly rigid equal-sized beads, in the quasistatic limit, by numerical simulation. Three different loading paths are explored: triaxial compression,…

Materials Science · Physics 2008-10-24 Pierre-Emmanuel Peyneau , Jean-Noël Roux

We find the strain energy function for isotropic incompressible solids exhibiting a linear relationship between shear stress and amount of shear, and between torque and amount of twist, when subject to large simple shear or torsion…

Soft Condensed Matter · Physics 2020-09-10 Robert Mangan , Michel Destrade , Giuseppe Saccomandi