相关论文: Again anti-plane shear
A class of nonlinear problems on the plane, described by nonlinear inhomogeneous $\bar{\partial}$-equations, is considered. It is shown that the corresponding dynamics, generated by deformations of inhomogeneous terms (sources) is described…
The versal deformation of Stanley-Reisner schemes associated to equivelar triangulations of the torus is studied. The deformation space is defined by binomials and there is a toric smoothing component which I describe in terms of cones and…
This paper is a continuation of ``Operads, Grothendieck topologies and deformation theory'' (alg-geom/9502010). We show how to develop a cohomology theory that would control deformations of a sheaf of associative algebras over a scheme by…
We propose a new peridynamic formulation with shear deformation for linear elastic solid. The key idea lies in subtracting the rigid body rotation part from the total deformation. Based on the strain energy equivalence between classic local…
Affine deformations serve as basic examples in the continuum mechanics of deformable 3-dimensional bodies (referred as homogeneous deformations). They preserve parallelism and are often used as an approximation to general deformations.…
Designing reconfigurable materials based on deformable nanoparticles (NPs) hinges on an understanding of the energetically-favored shapes these NPs can adopt. Using simulations, we show that hollow, deformable patchy NPs tailored with…
We investigate the wrinkling dynamics of a thin elastic sheet that is indented or compressed while floating on a viscous liquid. We show that the deformation speed controls the dynamics, leading to a wrinkle wavelength significantly smaller…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
Topology is an important determinant of the behavior of a great number of condensed-matter systems, but until recently has played a minor role in elasticity. We develop a theory for the deformations of a class of twisted non-Euclidean…
Abstract. We present a framework for the kinematics of a material body undergoing anelastic deformation. For such processes, the material structure of the body, as reflected by the geometric structure given to the set of body points,…
Metric anomalies arising from a distribution of point defects (intrinsic interstitials, vacancies, point stacking faults), thermal deformation, biological growth, etc. are well known sources of material inhomogeneity and internal stress. By…
This paper is a continuation of our first paper [10] in which we showed how deformation theory of representation varieties can be used to study finite simple quotients of triangle groups. While in Part I, we mainly used deformations of the…
Through 2D granular Couette flow experiments, we probe failure and deformation of disordered solids under shear. Shear produces smooth affine deformations in such a solid and also irresversible so-called non-affine particle displacements.…
Inspired by the work of Fischer-Marsden [Duke Math. J. 42 (1975), 519-547], we study in this paper the deformation of the weighted scalar curvature. By studying the kernel of the formal $L_\phi^2$-adjoint for the linearization of the…
In this paper we review some recent results concerning inverse problems for thin elastic plates. The plate is assumed to be made by non-homogeneous linearly elastic material belonging to a general class of anisotropy. A first group of…
Many materials of contemporary interest, such as gels, biological tissues and elastomers, are easily deformed but essentially incompressible. Traditional linear theory of elasticity implements incompressibility only to first order and thus…
The proposed two-dimensional geometrically exact beam element extends our previous work by including the effects of shear distortion, and also of distributed forces and moments acting along the beam. The general flexibility-based…
We give a necessary and sufficient condition in order for a hyperplane arrangement to be of Torelli type, namely that it is recovered as the set of unstable hyperplanes of its Dolgachev sheaf of logarithmic differentials. Decompositions and…
We extend to non-orientable surfaces previous work on sewing constraints in Conformal Field Theory. A new constraint, related to the real projective plane, is described and is used to illustrate the correspondence with a previous…
Thin rigid sheets floating on a liquid substrate appear, for example, in coatings and surfactant monolayers. Upon uniaxial compression the sheet undergoes transitions from a compressed flat state to a periodic wrinkled pattern to a…