Related papers: A Global Method for Relaxation for Multi-levelled …
Limbless organisms of all sizes use undulating patterns of self-deformation to locomote. Geometric mechanics, which maps deformations to motions, provides a powerful framework to formalize and investigate the theoretical properties and…
We study the general solution of the Yang-Baxter equation with deformed $sl(2)$ symmetry. The universal R operator acting on tensor products of arbitrary representations is obtained in spectral decomposition and in integral forms. The…
This article deals with universal deformations of dihedral representations with a particular focus on the question when the universal deformation is dihedral. Results are obtained in three settings: (1) representation theory, (2) algebraic…
In this work, we study the relaxation of a degenerate functional with linear growth, depending on a weight $w$ that does not exhibit doubling or Muckenhoupt-type conditions. In order to obtain an explicit representation of the relaxed…
We propose a novel framework for model-order reduction of hyperbolic differential equations. The approach combines a relaxation formulation of the hyperbolic equations with a discretization using shifted base functions. Model-order…
This paper presents an angle-based approach for distributed formation shape stabilization of multi-agent systems in the plane. We develop an angle rigidity theory to study whether a planar framework can be determined by angles between…
We prove a general representation stability result for polynomial coefficient systems which lets us prove representation stability and secondary homological stability for many families of groups with polynomial coefficients. This gives two…
We consider the global optimization of nonconvex quadratic programs and mixed-integer quadratic programs. We present a family of convex quadratic relaxations which are derived by convexifying nonconvex quadratic functions through…
In this study, we approach the analysis of a degenerate nonlinear functional in one dimension, accommodating a degenerate weight $w$. Our investigation focuses on establishing an explicit relaxation formula for a functional exhibiting…
We introduce a systematic method to solve a type of Cartan's realization problem. Our method builds upon a new theory of Lie algebroids and Lie groupoids with structure group and connection. This approach allows to find local as well as…
In the framework of bidifferential graded algebras, we present universal solution generating techniques for a wide class of integrable systems.
We discuss here geometric structures of condensed matters by means of a fundamental topological method. Any geometric pattern can be universally represented by a decomposition space of a topological space consisting of the infinite product…
This work introduces ``generalized meshes", a type of meshes suited for the discretization of partial differential equations in non-regular geometries. Generalized meshes extend regular simplicial meshes by allowing for overlapping elements…
We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…
We present a class of nonconforming virtual element methods for general fourth order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element…
This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints.…
We develop the equations of motion for full body models that describe the dynamics of rigid bodies, acting under their mutual gravity. The equations are derived using a variational approach where variations are defined on the Lie group of…
Nowadays the sector decomposition technique, which can isolate divergences from parametric representations of integrals, becomes a quite useful tool for numerical evaluations of the Feynman loop integrals. It is used to verify the…
This paper proposes a novel way to solve transient linear, and non-linear solid dynamics for compressible, nearly incompressible, and incompressible material in the updated Lagrangian framework for tetrahedral unstructured finite elements.…
Geometric frustration appears in a broad range of systems, generally emerging as disordered ground configurations, thereby impeding understanding of the phenomenon's underlying mechanics. We report on a continuum system featuring locally…