Related papers: On the correspondence between 2D force networks, t…
We study the elastic response of bilayer membranes with fixed projected area to both stretching and shape deformations. A surface tension is associated to each of these deformations. By using model amphiphilic membranes and computer…
Two-dimensional turbulence in a rectangular domain self-organises into large-scale unidirectional jets. While several results are present to characterize the mean jets velocity profile, much less is known about the fluctuations. We study…
This is a survey article on the infinitesimal rigidity of frameworks in Euclidean, hyperbolic, and spherical geometry. We discuss the equivalence of the static and kinematic formulations of the infinitesimal rigidity, the projective…
We propose two families of mixed finite elements for solving the classical Hellinger-Reissner mixed problem of the linear elasticity equations in three dimensions. First, a family of conforming mixed triangular prism elements is constructed…
We study linear programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT), referred to as RLT relaxations. We investigate the relations between the polyhedral properties of the feasible…
Due to the limit of mesh density, the improvement of the spatial precision of numerical computation always leads to a decrease in computing efficiency. Aiming at this inability of numerical computation, we propose a novel method for…
Neural-network models have been employed to predict the instantaneous flow close to the wall in a viscoelastic turbulent channel flow. Numerical simulation data at the wall is utilized to predict the instantaneous velocity-fluctuations and…
Modern micromanipulation techniques typically involve trapping using electromagnetic, acoustic or flow fields that produce stresses on the trapped particles thereby precluding stress-free manipulations. Here, we show that by employing…
We employ a mathematical model to analyze stress chains in thermoplastic elastomers (TPEs) with a microphase-separated spherical structure composed of triblock copolymers. The model represents stress chains during uniaxial and biaxial…
In this paper we study newly developed methods for linear elasticity on polyhedral meshes. Our emphasis is on applications of the methods to geological models. Models of subsurface, and in particular sedimentary rocks, naturally lead to…
A family of mixed finite elements is proposed for solving the first order system of linear elasticity equations in any space dimension, where the stress field is approximated by symmetric finite element tensors. This family of elements has…
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…
In this paper, we study the construction of low-degree robust finite element schemes for planar linear elasticity on general triangulations. Firstly, we present a low-degree nonconforming Helling-Reissner finite element scheme. For the…
Nonlinear tranlational symmetric equilibria with up to quartic flux terms in the free functions, reversed magnetic shear and sheared flow are constructed in two ways: i) quasianalytically by an ansatz which reduces the pertinent generalized…
We discuss the problem of regularizing correlators in conformal field theories. The only way to do it in coordinate space is to interpret them as distributions. Unfortunately except for the simplest cases we do not have tabulated…
Strongly correlated layered 2D systems are of central importance in condensed matter physics, but their numerical study is very challenging. Motivated by the enormous successes of tensor networks for 1D and 2D systems, we develop an…
Townsend (1961) introduced the concept of active and inactive motions for wall-bounded turbulent flows, where the active motions are solely responsible for producing the Reynolds shear stress, the key momentum transport term in these flows.…
For a given external loading on a structure we consider the optimal stresses. Ignoring the material properties the structure may have, we look for the distribution of internal forces or stresses that is in equilibrium with the external…
In this paper, we consider the problem of improving 2D triangle meshes tessellating planar regions. We propose a new variational principle for improving 2D triangle meshes where the energy functional is a convex function over the angle…
We present a complete analytical solution for the stress field inside a homogeneous, inside a homogeneous, linearly elastic solid sphere subjected to a concentrated normal load applied on its surface. Starting from the three-dimensional…