Related papers: Second-order prestress stability and third-order r…
We study the constraints imposed by conformal symmetry on the equations of fluid dynamics at second order in gradients of the hydrodynamic variables. At zeroth order conformal symmetry implies a constraint on the equation of state, E=2/3 P,…
The presence of prestrain can have a tremendous effect on the mechanical behavior of slender structures. Prestrained elastic plates show spontaneous bending in equilibrium -- a property that makes such objects relevant for the fabrication…
We consider the constrained stabilization problem of second-order systems evolving on the n-sphere. We propose a control strategy with a constraint proximity-based dynamic damping mechanism that ensures safe and almost global asymptotic…
Accurately predicting friction in sliding interfaces that contain third body wear particles is critical for engineering applications such as sliding movement in pistons, bearings, or metal forming. We present a hierarchical multiscale…
Consider a surface, enclosing a fixed volume, described by a free-energy depending only on the local geometry; for example, the Canham-Helfrich energy quadratic in the mean curvature describes a fluid membrane. The stress at any point on…
We propose bending energies for isotropic elastic plates and shells. For a plate, we define and employ a surface tensor that symmetrically couples stretch and curvature such that any elastic energy density constructed from its invariants is…
This work focuses on the bearing rigidity theory, namely the branch of knowledge investigating the structural properties necessary for multi-element systems to preserve the inter-units bearings when exposed to deformations. The original…
The second gradient model of poromechanics, introduced in Part I, is here linearized in the neighborhood of a prestressed reference configuration to be applied to the one-dimensional consolidation problem originally considered by Terzaghi…
We apply the convection stability criterion to a fluid in global thermodynamic equilibrium with a rigid rotation or with a constant acceleration along the streamlines. Different equations of state describing strongly interacting matter are…
We extend the mathematical theory of rigidity of frameworks (graphs embedded in $d$-dimensional space) to consider nonlocal rigidity and flexibility properties. We provide conditions on a framework under which (I) as the framework flexes…
In this paper, we give a summary of stability criteria that have been derived for hierarchical triple systems over the past few decades. We give a brief description and we discuss the criteria that are based on the generalisation of the…
Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e.,…
In this work, a higher-order irrotational strain gradient plasticity theory is studied in the small strain regime. A detailed numerical study is based on the problem of simple shear of a non-homogeneous block comprising an elastic-plastic…
New criteria for energy stability of multi-step, multi-stage, and mixed schemes are introduced in the context of evolution equations that arise as gradient flow with respect to a metric. These criteria are used to exhibit second and third…
This paper investigates a well-posedness property of parametric constraint systems named here Robinson stability. Based on advanced tools of variational analysis and generalized differentiation, we derive first-order and second-order…
First-order energy dissipative schemes in time are available in literature for the Poisson-Nernst-Planck (PNP) equations, but second-order ones are still in lack. This work proposes novel second-order discretization in time and finite…
The notion of the n-th order local energy, generated by the n-th power of the Hamiltonian, has been introduced. The n-th order two-particle coalescence conditions have been derived from the requirements that the n-th order local energy at…
We formulate and discuss the relationship between polyhedral stress functions and internally self-equilibrated frameworks in 2D, and a two-mesh technique for the prediction of the stress field associated with such systems. We generalize…
The theory of disordered elastic systems is one of the most powerful frameworks to assess the physics of multiple systems that span from ferromagnets to migrating biological cells. In this formalism, one assumes that the system can be…
We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area…