相关论文: Orbits closeness for slowly mixing dynamical syste…

Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…

Observations indicate that members of close stellar binaries often have mass ratios close to unity, while longer-period systems exhibit a more uniform mass-ratio distribution. This paper provides a theoretical explanation for this finding…

We display several examples of how fields with different limiting velocities (the "speed of light") at a high energy scale can nevertheless have a common limiting velocity at low energies due to the effects of interactions. We evaluate the…

We obtain a lower bound of the distance function (MOID) between two noncoplanar bounded Keplerian orbits (either circular or elliptic) with a common focus. This lower bound is positive and vanishes if and only if the orbits intersect. It is…

Motivated by the centering of biological objects in large cells, we study the generic properties of centering forces inside a ball (or a volume of spherical topology) in $n$ dimensions. We consider two scenarios : autonomous centering (in…

To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of $N$-body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that…

We consider the dynamics of the simplest chain of large number $N$ of particles. We find, in the double scaling limit, the partition of the parameter space onto two domains, where for one domain the supremum (over all time interval…

Let T_0=(A_0,..,A_d) be a d-simplex, G_0 its centroid, S its circumsphere, O the center of S. Let (B_i) be the points where S intersects the lines (G_0A_i), T_1 the d-simplex (B_1,..,B_d), and G_1 its centroid. By iterating this…

Dynamos operating in the interiors of rapidly rotating planets and low-mass stars might belong to a similar category where rotation plays a vital role. We quantify this similarity using scaling laws. We analyse direct numerical simulations…

We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…

Twisted permutation codes, introduced recently by the second and third authors, are frequency permutation arrays. They are similar to repetition permutation codes, in that they are obtained by a repetition construction applied to a smaller…

We consider an incompressible fluid with axial symmetry without swirl, assuming initial data such that the initial vorticity is very concentrated inside $N$ small disjoint rings of thickness $\varepsilon$, each one of vorticity mass and…

We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…

We study the phase-space behaviour of nearby trajectories in integrable potentials. We show that the separation of nearby orbits initially diverges very fast, mimicking a nearly exponential behaviour, while at late times it grows linearly.…

Recent research has shown that motile cells can adapt their mode of propulsion depending on the environment in which they find themselves. One mode is swimming by blebbing or other shape changes, and in this paper we analyze a class of…

The rhombus tilings of a simply connected domain of the Euclidean plane are known to form a flip-connected space (a flip is the elementary operation on rhombus tilings which rotates 180{\deg} a hexagon made of three rhombi). Motivated by…

Examples of dynamical systems proposed by Z. Artstein and C. M. Dafermos admit non-unique solutions that track a one parameter family of closed circular orbits contiguous at a single point. Switching between orbits at this single point…

We study distribution of orbits sampled at polynomial times for uniquely ergodic topological dynamical systems $(X, T)$. First, we prove that if there exists an increasing sequence $(q_n)$ for which the rigidity condition \[…

We study the orbital architecture of multi-planet systems detected by the Kepler transit mission using N-body simulations, focusing on the orbital spacing between adjacent planets in systems showing four or more transiting planets. We find…

We present an experimental study of a confined nanoflow, which is generated by a sphere oscillating in the proximity of a flat solid wall in a simple fluid. Varying the oscillation frequency, the confining length scale and the fluid mean…