Examples of exponentially many collisions in a hard ball system

Consider the system of n identical hard balls in ${\mathbb {R}}^3$ moving freely and colliding elastically. We show that there exist initial conditions such that the number of collisions is exponential in n.

INFINITE SYSTEM OF BROWNIAN BALLS: EQUILIBRIUM MEASURES ARE CANONICAL GIBBS

We consider a system of infinitely many hard balls in ℝd undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with a local time term. We prove that the set of all equilibrium measures, solution of a detailed balance equation, coincides with the set of canonical Gibbs measures associated to the hard core potential added to the smooth interaction potential.

A Biological Sensor for Detecting Foreign Bodies Using a Balloon Probe

For effective medical treatment, sensors that can find foreign bodies such as tumors in early stage are required. This paper describes a new sensor for foreign body detection utilizing the fact that the property hardness of foreign bodies differs from that of normal tissues. It consists of a balloon probe, which is constructed with a thin rubber membrane inflated with compressed air, and an optical deformation analyzing system. Experiments are carried out using samples in which single hard balls are embedded to model single tumor in soft tissue. It was confirmed that this sensor can detect the existence of the hard ball and can also distinguish the inequality of size and hardness of the ball. Furthermore, experimental results detecting multi-objects showed that this sensor has the ability to detect the existence of multi objects and their relative positions simultaneously. By measuring the consistence of the arm and the abdomen of human body, it is proved that the sensor is also suitable for consistence measurement of human anatomy.

Ergodicity of hard spheres in a box

We prove that the system of two hard balls in a $\nu$-dimensional ($\nu\ge 2$) rectangular box is ergodic and, therefore, actually it is a Bernoulli flow.

Nonuniformly hyperbolic K-systems are Bernoulli

We prove that those non-uniformly hyperbolic maps and flows (with singularities) that enjoy the K-property are also Bernoulli. In particular, many billiard systems, including those systems of hard balls and stadia that have the K-property, and hyperbolic billiards, such as the Lorentz gas in any dimension, are Bernoulli. We obtain the Bernoulli property for both the billiard flows and the associated maps on the boundary of the phase space.