相关论文: Elementary slopes of plane-wide breakout

Recently it was experimentally demonstrated that sputtering under normal incidence leads to the formation of spatially ordered uniform nanoscale islands or holes. Here we show that these nanostructures have inherently nonlinear origin,…

This manuscript proposes a mathematical model for the game named Breakout. Its systematic study reveals unexpected complexity. After a survey of general properties of the model, we study in details a special case and exhibit combinatorial…

We consider a dynamical system given by an area-preserving map on a two-dimensional phase plane and consider a one-dimensional line of initial conditions within this plane. We record the number of iterates it takes a trajectory to escape…

In the present paper, we consider the family of all compact Alexandrov spaces with curvature bound below having a definite upper diameter bound of a fixed dimension. We introduce the notion of essential coverings by contractible metric…

We investigate the semiclassical energy spectrum of quantum elliptic billiard. The nearest neighbor spacing distribution, level number variance and spectral rigidity support the notion that the elliptic billiard is a generic integrable…

Neighborhood is an important concept in covering based rough sets. That under what condition neighborhoods form a partition is a meaningful issue induced by this concept. Many scholars have paid attention to this issue and presented some…

A simple model is presented for the formation of rolling grain ripples on a flat sand bed by the oscillatory flow generated by a surface wave. An equation of motion is derived for the individual ripples, seen as "particles", on the…

A solution concept on a class of transferable utility coalitional games is a multifunction satisfying given criteria of economic rationality. Every solution associates a set of payoff allocations with a coalitional game. This general…

We introduce a geometric dynamical system where iteration is defined as a cycling composition of different maps acting on a space composed of three or more lines in $\mathbb{R}^2$. This system is motivated by the dynamics of iterated…

We introduce CUT, the class of 2-player partition games. These are NIM type games, played on a finite number of heaps of beans. The rules are given by a set of positive integers, which specifies the number of allowed splits a player can…

We study the dynamics of a two-planet system, which evolves being in a $1/1$ mean motion resonance (co-orbital motion) with non-zero mutual inclination. In particular, we examine the existence of bifurcations of periodic orbits from the…

For a family of periodic SEIRS models with general incidence, we prove the existence of at least one endemic periodic orbit when R_0>1. Additionally, we prove the existence of a unique disease-free periodic orbit, that is globally…

Normally, in mathematics and physics, only point particle systems, which are either finite or countable, are studied. We introduce new formal mathematical object called regular continuum system of point particles (with continuum number of…

A set $A$ is said to split a finite set $B$ if exactly half the elements of $B$ (up to rounding) are contained in $A$. We study the dual notions: (1) splitting family, which is a collection of sets such that any subset of $\{1,\ldots,k\}$…

Classical results and recent developments on the theoretical description of elementary particles with "continuous" spin are reviewed. At free level, these fields are described by unitary irreducible representations of the isometry group…

We suggest a geometrical framework to discuss periodic layered structures in the unit disk. The band gaps appear when the point representing the system approaches the unit circle. We show that the trace of the matrix describing the basic…

The final "giant-impact" phase of terrestrial planet formation is believed to begin with a large number of planetary "embryos" on nearly circular, coplanar orbits. Mutual gravitational interactions gradually excite their eccentricities…

We study the relative Hilbert scheme of a family of nodal (or smooth) curves, over a base of arbitrary dimension, via its (birational) cycle map, going to the relative symmetric product. We show the cycle map is the blowing up of the…

Periodic orbits in chaotic systems form clusters, whose elements traverse approximately the same points of the phase space. The distribution of cluster sizes depends on the length n of orbits and the parameter p which controls closeness of…

The orbital evolution of particles released from the surface of a rubble-pile body by Earth's tides during flyby within the Roche limit is studied. Test particles initially placed on the surface leave the surface and escape the parent body.…