相关论文: Nonlinear weakly curved rod by Gamma convergence

We introduce two kurt-spectra to probe fourth-order statistics of weak lensing convergence maps. Using state-of-the-art numerical simulations, we study the shapes of these kurt-spectra as a function of source redshifts and smoothing angular…

We investigate non-linear elastic deformations in the phase field crystal model and derived amplitude equations formulations. Two sources of non-linearity are found, one of them based on geometric non-linearity expressed through a finite…

We study the $\Gamma$-convergence of a class of elastica-type energies defined on immersed planar curves and depending on a small positive parameter $\epsilon$. As $\epsilon\to 0^+$, sequences with equibounded energy develop concentration…

We investigate a quasicontinuum method by means of analytical tools. More precisely, we compare a discrete-to-continuum analysis of an atomistic one-dimensional model problem with a corresponding quasicontinuum model. We consider next and…

In the study of weakly turbulent wave systems possessing incomplete self-similarity it is possible to use dimensional arguments to derive the scaling exponents of the Kolmogorov-Zakharov spectra, provided the order of the resonant wave…

In the first part of this paper, we apply a well known discrete-to-continuum approach to a Frenkel-Kontorova-type model of an infinitely long one-dimensional chain of atoms weakly interacting with a line of fixed atoms. The rescaled model…

Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…

The nonlinear dynamics of a warped accretion disc is investigated in the important case of a thin Keplerian disc with negligible viscosity and self-gravity. A one-dimensional evolutionary equation is formally derived that describes the…

Weak turbulence is commonly modeled using the log-normal distribution. Our experimental results show that this distribution fails to capture irradiance fluctuations in this regime. The Gamma-Gamma model is shown to be more accurate.

We derive a strain-gradient theory for plasticity as the $\Gamma$-limit of discrete dislocation fractional energies, without the introduction of a core-radius. By using the finite horizon fractional gradient introduced by Bellido, Cueto,…

We analyze the Saffman-Taylor viscous fingering problem in rectangular geometry. We investigate the onset of nonlinear effects and the basic symmetries of the mode coupling equations, highlighting the link between interface asymmetry and…

We consider a class of models motivated by previous numerical studies of wrinkling in highly stretched, thin rectangular elastomer sheets. The model used is characterized by a finite-strain hyperelastic membrane energy perturbed by small…

A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane…

We consider quasi-static poroelastic systems with incompressible constituents. The nonlinear permeability is taken to be dependent on solid dilation, and physical types of boundary conditions (Dirichlet, Neumann, and mixed) for the fluid…

We deduce a 1D model of elastic planar rods starting from the F\"{o}ppl--von K\'{a}rm\'{a}n model of thin shells. Such model is enhanced by additional kinematical descriptors that keep explicit track of the compatibility condition requested…

A note on the property of weak contraction, which implies that all bounded solutions of a nonlinear system converge to a (possibly non-unique) equilibrium. We provide some simple results about interconnections of such systems, and a brief…

In this paper, the modelling strategy of a Cosserat rod element (CRE) is addressed systematically for 3-dimensional dynamical analysis of slender structures. We employ the exact nonlinear kinematic relationships in the sense of Cosserat…

We propose a novel variationally consistent membrane wrinkling model for analyzing the mechanical responses of wrinkled thin membranes. The elastic strain energy density is split into tensile and compressive terms via a spectral…

We have studied the weakly non-linear quantum transport properties of a two-dimensional quantum wire which can be solved exactly. The non-linear transport coefficients have been calculated and interesting physical properties revealed. In…

We consider the dynamical evolution of a thin rod described by an appropriately scaled wave equation of nonlinear elasticity. Under the assumption of well-prepared initial data and external forces, we prove that a solution exists for…