Related papers: On Exponents of Thickness in Geometry Rigidity Ine…
We use well resolved numerical simulations with the Lattice Boltzmann Method to study Rayleigh-B\'enard convection in cells with a fractal boundary in two dimensions for $Pr = 1$ and $Ra \in \left[10^7, 10^{10}\right]$. The fractal…
In the current paper, first we give the correct version of the formula for mean Berwald curvature of a spherically symmetric Finsler metric given in paper \cite{YCheWSon2015}. Further, we establish differential equations characterizing…
In this note, we address several issues, including some raised in recent works and commentary, related to bending measures and energies for plates and shells, and certain of their invariance properties. We discuss overlaps and distinctions…
We used numerical simulations based on the finite element method (FEM) to calculate both the amplitude and phase information of the scattered electric field from random rough surfaces, which can be directly compared to ellipsometric…
We study the fracture surface of three dimensional samples through a model for quasi-static fractures known as Born Model. We find for the roughness exponent a value of 0.5 expected for ``small length scales'' in microfracturing…
The anomalous exponents governing the long wavelength behavior of the flat phase of physical crystalline membranes are calculated within a self-consistent screening approximation (SCSA) applied to second order expansion in 1/d_C (d_C is the…
The aim of this paper is to prove two results concerning the rigidity of complete, immersed, orientable, stable minimal hypersurfaces: we show that they are hyperplane in $\mathbb{R}^4$, while they do not exist in positively curved closed…
This is a continuation of our previous work [13]. Let $(\Sigma,g)$ be a closed Riemann surface, where the metric $g$ has conical singularities at finite points. Suppose $\mathbf{G}$ is a group whose elements are isometries acting on…
We give rigidity results for the discrete Bonnet-Myers diameter bound and the Lichnerowicz eigenvalue estimate. Both inequalities are sharp if and only if the underlying graph is a hypercube. The proofs use well-known semigroup methods as…
The set $GU_f$ of possible effective elastic tensors of composites built from two materials with positive definite elasticity tensors $\BC_1$ and $\BC_2=\Gd\BC_0$ comprising the set $U=\{\BC_1,\Gd\BC_0\}$ and mixed in proportions $f$ and…
Understanding the interfacial electrical properties between metallic electrodes and low dimensional semiconductors is essential for both fundamental science and practical applications. Here we report the observation of thickness reduction…
We present a systematic analysis of scale-dependent properties of filamentary structures in seven nearby molecular clouds $-$ Taurus, Ophiuchus, Perseus, Orion A, California, IC 5146, Vela C $-$ using the multiscale extraction method…
The squeezing of soft solids, the constrained growth of biological tissues, and the swelling of soft elastic solids such as gels can generate large compressive stresses at their surfaces. This causes the otherwise smooth surface of such a…
This study examines the stability of a flexible material interface between two fluids of the same viscosity in interaction with a free surface. When the layers are motionless, we provide evidence for the onset of a novel instability by…
For every connected graph $G$ and surface $S$, we consider the well-known string of inequalities $\delta_S(G) \leq \mu_S(G) \leq \nu_S(G)$, where $\mu$ and $\nu$ denote skewness and crossing number and $\delta$ is the Euler-formula lower…
Understanding asymptotics of gradient components in relation to the symmetrized gradient is im- portant for the analysis of buckling of slender structures. For circular cylindrical shells we obtain the exact scaling exponent of the Korn…
In this paper, the numerical approximation of isometric deformations of thin elastic shells is discussed. To this end, for a thin shell represented by a parametrized surface, it is shown how to transform the stored elastic energy for an…
We analyze the buckling of a rigid thin membrane floating on a dense fluid substrate. The interplay of curvature and substrate energy is known to create wrinkling at a characteristic wavelength $\lambda$, which localizes into a fold at…
We compute properties of the interface of the 3-dimensional Ising model for a wide range of temperatures, covering the whole region from the low temperature domain through the roughening transition to the bulk critical point. The interface…
We compare the roughness of minimal energy(ME) surfaces and scalar ``quasi-static'' fracture surfaces(SQF). Two dimensional ME and SQF surfaces have the same roughness scaling, w sim L^zeta (L is system size) with zeta = 2/3. The 3-d ME and…