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We give a necessary and sufficient condition, of geometric type, for the uniform decay of energy of solutions of the linear system of magnetoelasticity in a bounded domain with smooth boundary. A Dirichlet-type boundary condition is…

Analysis of PDEs · Mathematics 2007-05-23 Thomas Duyckaerts

In order to clarify common assumptions on the form of energy and momentum in elasticity, a generalized conservation format is proposed for finite elasticity, in which total energy and momentum are not specified a priori. Velocity, stress,…

Mathematical Physics · Physics 2007-05-23 P. Podio-Guidugli , S. Sellers , G. Vergara Caffarelli

Optimality principles in nonequilibrium transport networks are linked to a thermodynamic formalism based on generalized transport potentials endowed with Legendre duality and related contact structure. This allows quantifying the distance…

Statistical Mechanics · Physics 2025-06-23 Amilcare Porporato , Shashank Kumar Anand , Salvatore Calabrese , Luca Ridolfi , Lamberto Rondoni

In this article we focus our attention on the principle of energy conservation within the context of systems of fluid dynamics. We give an overview of results concerning the resolution of the famous Onsager conjecture - which states…

Analysis of PDEs · Mathematics 2017-08-01 Tomasz Dębiec , Piotr Gwiazda , Agnieszka Świerczewska-Gwiazda

The problem of discontinuous functions and their representations in the form of Legendre polynomial series in quantum nuclear scattering theory is presented briefly. The problem is quite old yet not adequately explained in numerous Quantum…

Nuclear Theory · Physics 2016-02-10 Henryk Wojciechowski

We study the anomalous elasticity of nematic elastomers by employing the powers of renormalized field theory. Using general arguments of symmetry and relevance, we introduce a minimal Landau-Ginzburg-Wilson elastic energy for nematic…

Soft Condensed Matter · Physics 2009-11-07 Olaf Stenull , T. C. Lubensky

We adopt the continuum limit of a linear, isotropic, homogeneous, transparent, dispersion-negligible dielectric of refractive index $n$ and examine the consequences of the effective speed of light in a stationary dielectric, $c/n$, for…

Classical Physics · Physics 2014-04-23 Michael E. Crenshaw

We use the Landau-de Gennes energy to describe a particle immersed into nematic liquid crystals with a constant applied magnetic field. We derive a limit energy in a regime where both line and point defects are present, showing…

Analysis of PDEs · Mathematics 2024-04-03 François Alouges , Antonin Chambolle , Dominik Stantejsky

Clapeyron's Theorem in classical linear elasticity provides a way to explicitly express the energy stored in an equilibrium configuration in terms of the work of the forces applied on the boundary. We derive several new integral relations…

Mathematical Physics · Physics 2025-08-19 Yury Grabovsky , Lev Truskinovsky

An introduction to the minimal supersymmetric Standard Model (MSSM) is given. The motivation for ``low-energy'' supersymmetry is reviewed, and the structure of the MSSM is outlined. In its most general form, the MSSM can be viewed as a…

High Energy Physics - Phenomenology · Physics 2008-02-03 Howard E. Haber

We investigate minimizers defined on a bounded domain in $\mathbb{R}^2$ for the Maier--Saupe Q--tensor energy used to characterize nematic liquid crystal configurations. The energy density is singular, as in Ball and Mujamdar's modification…

Analysis of PDEs · Mathematics 2015-11-04 Patricia Bauman , Daniel Phillips

This paper introduces a comprehensive finite element approximation framework for three-dimensional Landau-de Gennes $Q$-tensor energies for nematic liquid crystals, with a particular focus on the anisotropy of the elastic energy and the…

Numerical Analysis · Mathematics 2025-06-06 Heiko Gimperlein , Ruma R. Maity

The polyconvexity of a strain-energy function is nowadays increasingly presented as the ultimate material stability condition for an idealized elastic response. While the mathematical merits of polyconvexity are clearly understood, its…

Mathematical Physics · Physics 2026-02-09 Maximilian P. Wollner , Gerhard A. Holzapfel , Patrizio Neff

We present a sufficient condition under which a weak solution of the Euler-Lagrange equations in nonlinear elasticity is already a global minimizer of the corresponding elastic energy functional. This criterion is applicable to energies…

Analysis of PDEs · Mathematics 2015-08-25 David Yang Gao , Patrizio Neff , Ionel Roventa , Christian Thiel

Modelling MEMS involves a variety of software tools that deal with the analysis of complex geometrical structures and the assessment of various interactions among different energy domains and components. Moreover, the MEMS market is growing…

Other Computer Science · Computer Science 2008-12-18 Mustafa Calis , Omar Laghrouche , Marc Desmulliez

In this note we formulate a sufficient condition for the quasiconvexity at $x \mapsto \lambda x$ of certain functionals $I(u)$ which model the stored-energy of elastic materials subject to a deformation $u$. The materials we consider may…

Classical Analysis and ODEs · Mathematics 2015-07-10 Jonathan J. Bevan , Caterina Ida Zeppieri

Close to equilibrium, the kinetic coefficients of a thermodynamic system must satisfy a set of symmetry conditions, which follow from the Onsager-Casimir principle. Here, we show that, if a system of hydrodynamic equations is analysed from…

Nuclear Theory · Physics 2023-03-22 Lorenzo Gavassino

We are concerned with the following constrained minimization problem: $$e(a_{1},a_{2},\beta) := \inf\left\{E_{a_{1},a_{2},\beta}(u_{1},u_{2}): \|u_{1}\|_{L^{2}(\mathbb{R}^{3})} = \|u_{2}\|_{L^{2}(\mathbb{R}^{3})} = 1\right\},$$ where…

Analysis of PDEs · Mathematics 2022-03-11 Wenqing Wang , Xiaoyu Zeng , Huan-Song Zhou

In this paper, we consider the problem of minimizing quantum free energies under the constraint that the density of particles is fixed at each point of Rd, for any d $\ge$ 1. We are more particularly interested in the characterization of…

Mathematical Physics · Physics 2019-04-02 Romain Duboscq , Olivier Pinaud

The paper proposes a new fragmentation mechanism of dendrite arms. The theoretical basis of this mechanism is a shift in the thermodynamical equilibrium at the solid-liquid interface due to the presence of elastic energy. This effect is…

Materials Science · Physics 2008-10-14 S. Ananiev , P. Nikrityuk , K. Eckert