相关论文: Arresting the collapse of a catenary arch
Understanding collective properties of driven particle systems is significant for naturally occurring aggregates and because the knowledge gained can be used as building blocks for the design of artificial ones. We model self propelling…
Elastic structures can be designed to exhibit precise, complex, and exotic functions. While recent work has focused on the quasistatic limit governed by force balance, the mechanics at a finite driving rate are governed by Newton's…
We establish sharp stability estimates of logarithmic type in determining an impedance obstacle in $\mathbb{R}^2$. The obstacle is of general polygonal shape and the impedance parameter can be variable. We establish the stability results by…
We consider nematic liquid crystals in a bounded, convex polyhedron described by a director field n(r) subject to tangent boundary conditions. We derive lower bounds for the one-constant elastic energy in terms of topological invariants.…
Purely rotational relative equilibria of an ellipsoidal underwater vehicle occur at nongeneric momentum where the symplectic reduced spaces change dimension. The stability these relative equilibria under momentum changing perturbations is…
Recent observations of hydrostatic structure and virial equilibrium in supersonically turbulent, self-gravitating molecular clouds imply a stability that contrasts with the transcience of turbulent structure. To investigate this…
We investigate the role of architected thin films in the interfacial failure properties of bi-layer composites. Our results show that, while graded structures can be used to prescribe failure at the interface, they do not offer significant…
Minimal surface problems arise naturally in many soft matter systems whose free energies are dominated by surface or interface energies. Of particular interest are the shapes, stability and mechanical stresses of minimal surfaces spanning…
Slow dynamic nonlinearity is widely observed in brittle materials with complex heterogeneous or cracked microstructures. It is seen in rocks, concrete and cracked glass blocks. Unconsolidated structures show the behavior as well: aggregates…
The study of elastic membranes carrying topological defects has a longstanding history, going back at least to the 1950s. When allowed to buckle in three-dimensional space, membranes with defects can totally relieve their in-plane strain,…
A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is…
The stability of a spherically symmetric self-gravitating magnetic monopole is examined in the thin wall approximation: modeling the interior false vacuum as a region of de Sitter space; the exterior as an asymptotically flat region of the…
We study positive definite kernels pulled back along a finite family of self-maps under a subinvariance inequality for the associated branching operator. Iteration produces an increasing kernel tower with defect kernels. Under diagonal…
Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider the case of a rectangular prism. For configurations with…
We consider the yielding behavior of amorphous solids under cyclic shear deformation and show that it can be mapped into a random walk in a confining potential with an absorbing boundary. The resulting dynamics is governed by the first…
Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple…
Contact-drop dispensing is central to many small-scale applications, such as direct-scanning probe lithography and micromachined fountain-pen techniques. Accurate and controllable dispensing required for nanometer-resolved surface…
Buckling strength estimation of architected materials has mainly been restricted to load cases oriented along symmetry axes. However, realistic load scenarios normally exhibit more general stress distributions. In this paper we propose a…
A geometric formulation for stabilization of systems with one degree of underactuation which fully solves the energy shaping problem for these system is given. The results show that any linearly controllable simple mechanical system with…
Structural excitations of model Lennard-Jones glass systems are investigated using the Activation-Relaxation-Technique (ART), which explores the potential energy landscape of a local minimum energy configuration by converging to a nearby…