相关论文: New principles for auxetic periodic design

New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…

We show that classical U(infinity) gauge theories can be obtained from the dimensional reduction of a certain class of higher-derivative theories. In general, the exact symmetry is attained in the limit of degenerate metric; otherwise, the…

We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…

Combinatorial mechanical metamaterials are made of anisotropic, flexible blocks, such that multiple metamaterials may be constructed using a single block type, and the system's response depends on the frustration (or its absence) due to the…

In his Ph.D. thesis, Michal Szabados conjectured that for a not fully periodic configuration with a minimal periodic decomposition the nonexpansive lines are exactly the lines that contain a period for some periodic configuration in such…

For materials science, diamond crystals are almost unrivaled for hardness and a range of other properties. Yet, when simply abstracting the carbon bonding structure as a geometric bar-and-joint periodic framework, it is far from rigid. We…

Differential-geometric structures on the space of orbits of a finite Coxeter group, determined by Groth\'endieck residues, are calculated. This gives a construction of a 2D topological field theory for an arbitrary Coxeter group.

This paper considers the optimal control problem of connecting two periodic trajectories with maximal persistence. A maximally persistent trajectory is close to the periodic type in the sense that the norm of the image of this trajectory…

We obtain structural results on translational tilings of periodic functions in $\mathbb{Z}^d$ by finite tiles. In particular, we show that any level one tiling of a periodic set in $\mathbb{Z}^2$ must be weakly periodic (the disjoint union…

In this paper, we study the possible bifurcations of periodic orbits by reducing them to graphs. The aforementioned allows to study the genericity of routes to chaos, as well as to analyze their possible complexity. In particular, our…

Motivated by recent theoretical and experimental interest in metamaterials comprising non-local coupling terms, we present an analytic framework to realise materials with arbitrary complex dispersion relations. Building on the inverse…

This paper concerns the existence of multiple rotating periodic solutions for $2n$ dimensional convex Hamiltonian systems. For the symplectic orthogonal matrix $Q$, the rotating periodic solution has the form of $z(t+T)=Qz(t)$, which might…

We describe the generalization of spherical field theory to other modal expansion methods. The main approach remains the same, to reduce a d-dimensional field theory into a set of coupled one-dimensional systems. The method we discuss here…

The concept of synthetic dimensions has emerged as a powerful framework in photonics and atomic physics, enabling the exploration of high-dimensional physics beyond conventional spatial constraints. Originally developed for quantum…

In this paper we give an explicit construction of bounded remainder sets of all possible volumes, for any irrational rotation on the adelic torus $\mathbb A/\mathbb Q$. Our construction involves ideas from dynamical systems and harmonic…

We study Hamiltonian diffeomorphisms on symplectic Euclidean spaces that are equal to non-degenerate linear maps at infinity. Under the assumption that there exists an isolated homologically nontrivial fixed point satisfying the twist…

We investigate the existence of periodic solutions for a class of nonlocal continuity equations, which include mean-field equations derived from systems of coupled oscillators. While periodic solutions at the particle level have been…

We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…

By a result of Blokh from 1984, every transitive map of a tree has the relative specification property, and so it has finite decomposition ideal, positive entropy and dense periodic points. In this paper we construct a transitive dendrite…

We investigate global continuation of periodic orbits of a differential equation depending on a parameter, assuming that a closed 1-form satisfying certain properties exists. We begin by extending the global continuation theory of…