Related papers: Expansive periodic mechanisms
A wide variety of intricate dynamics may be created at border-collision bifurcations of piecewise-smooth maps, where a fixed point collides with a surface at which the map is nonsmooth. For the border-collision normal form in two…
The response of many materials to applied forces and boundary constraints depends upon internal geometric changes at multiple submacroscopic levels. Hierarchical structured deformations provide a mathematical setting for the description of…
The famous example of the double-Watt mechanism given by Connelly and Servatius raises some problems concerning the classical definitions of higher-order flexibility and rigidity, respectively. Recently, the author was able to give a proper…
We find a class of four dimensional deformed conformal field theories which appear extra dimensional when their gauge symmetries are spontaneously broken. The theories are supersymmetric moose models which flow to interacting conformal…
Three main statements are advocated in this talk: 1. Protons become more active at the periphery with increase of their collision energy as follows from comparison of ISR and LHC data. 2. The geometric scaling is violated even in the…
A recently developed linear algebraic method for the computation of perturbation expansion coefficients to large order is applied to the problem of a hydrogenic atom in a magnetic field. We take as the zeroth order approximation the $D…
In periodic, two-dimensional potentials a classical particle might be expected to escape from any finite region if it has enough energy to escape from a single cell. However, for a class of sinusoidal potentials in which the barriers…
In a recent work [Phys. Rev. E 109, L042102 (2024)], interesting dimensional crossovers [from two- to one-dimensional (2D to 1D) scaling] were found in the growth of Kardar-Parisi-Zhang (KPZ) interfaces on rectangular substrates, with…
We introduce a simple geometric model which describes the kinetics of fragmentation of d-dimensional objects. In one dimension our model coincides with the random scission model and show a simple scaling behavior in the long-time limit. For…
The theory of operads (May, cyclic, modular, PROPs, etc) is extended to include higher dimensional phenomena, i.e. operations between operations, mimicking the algebraic structure on varieties of arbitrary dimensions, having marked…
A recent "hidden symmetry" conjecture of B. Gin-ge Chen et al is resolved, concerning the dimension of the mechanical modes of a generic $2$-periodic triangulated surface $O$ in $R^3$ whose structure graph corresponds to a triangular tiling…
In this paper we give an algorithm to calculate the coefficients of the p-adic expansion of a rational numbers, and we give a method to decide whether this expansion is periodic or ultimately periodic.
A framework for understanding the geometry of continuous actions of Z^d was developed by Boyle and Lind using the notion of expansive behavior along lower-dimensional subspaces. For algebraic Z^d-actions of entropy rank one, the expansive…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
The paper gives a description of wave propagation in discrete-periodic one-dimensional media with block structure. For one-dimensional problems mathematical models are proposed that describe block structures in the form of a mass chain or…
We analyze intermittence and roughening of an elastic interface or domain wall pinned in a periodic potential, in the presence of random-bond disorder in (1+1) and (2+1) dimensions. Though the ensemble average behavior is smooth, the…
In this Letter, we clarify the physical origin of effective transport in periodic and tilted periodic systems. When Brownian dynamics is examined on the scale of a single period, the particle displacement admits a natural separation into a…
A variational framework is introduced to describe how a surface bends when it is subject to local constraints on its geometry. This framework is applied to describe the patterns of a folded sheet of paper. The unstretchability of paper…
We investigate dynamics of deformable self-propelled particles with a repulsive interaction whose magnitude depends on the relative direction of elongation of a pair of particles. A collective motion of the particles appears in two…
For dynamical systems that switch between different modes of operation, parameter variation can cause periodic solutions to lose or acquire new switching events. When this causes the eigenvalues (stability multipliers) associated with the…