Related papers: Throwing $\pi$ at a wall
Numerical simulations of the dynamics of an elastic collision between a rigid sphere and an elastic half-space are carried out. We assume an Amontons-Coulomb frictional force with a fixed coefficient of friction between the contacting…
We study the average separation between an elastic solid and a hard solid with a nominal flat but randomly rough surface, as a function of the squeezing pressure. We present experimental results for a silicon rubber (PDMS) block with a flat…
There is presented an algorithm for computing the topological degree for a large class of polynomial mappings. As an application there is given an effective algebraic formula for the intersection number of a polynomial immersion M --> R^2m,…
We estimate the cross section for quasi-elastic double pion exchange in high energy proton-proton collisions. Total and elastic $\pi\pi$ cross sections are calculated in an equivalent pion approximation, with pion-baryon vertices taken from…
We compare two high order finite-difference methods that solve the elastic wave equation in two dimensional domains with curved boundaries and material discontinuities. Two numerical experiments are designed with focus on wave boundary…
We study the adhesive contact between elastic solids with randomly rough, self affine fractal surfaces. We present molecular dynamics (MD) simulation results for the interfacial stress distribution and the wall-wall separation. We compare…
Using a simple and generic molecular dynamics model, we study the damage in a disc of interacting particles as the disc fragments upon impact with a wall. The damage, defined as the ratio of the number of bonds broken by the impact to the…
The impact of a two-dimensional elastic disk with a wall is numerically studied. It is clarified that the coefficient of restitution (COR) decreases with the impact velocity. The result is not consistent with the recent quasi-static theory…
The ratio of the circumference, C, of a circle to its diameter, D, is a constant number denoted by $\pi$ and is independent of the size of the circle. It is known that $\pi$ is an irrational number and therefore cannot be expressed as a…
For a single membrane of stiffness kappa fluctuating between two planar walls of distance d, we calculate analytically the proportionality constant in the pressure law p proportional to T^2/kappa^2 d^3, in very good agreement with results…
We study the molecular dynamics of two discs undergoing Newtonian ("inertial") dynamics, with elastic collisions in a rectangular box. Using a mapping to a billiard model and a key result from ergodic theory, we obtain exact, analytical…
We study the distribution of interfacial separations P(u) at the contact region between two elastic solids with randomly rough surfaces. An analytical expression is derived for P(u) using Persson's theory of contact mechanics, and is…
We present a method of computing Casimir forces for arbitrary geometries, with any desired accuracy, that can directly exploit the efficiency of standard numerical-electromagnetism techniques. Using the simplest possible finite-difference…
The ratio of productions of pi+pi- atoms to free pi+pi- pairs is calculated with account of the strong interaction in final states. It is shown that this ratio is expressed via a squared ratio of the well-known Coulomb wave functions and…
We prove by example that the number of elastic collisions of $n$ balls of equal mass and equal size in $d$-dimensional space can be greater than $n^3/27$ for $n\geq 3$ and $d\geq 2$. The previously known lower bound was of order $n^2$.
We give a new and elementary proof that the number of elastic collisions of a finite number of balls in the Euclidean space is finite. We show that if there are $n$ balls of equal masses and radii 1, and at the time of a collision between…
We present a model of solids made from polygonal cells connected via beams. We calculate the macroscopic elastic moduli from the beam and cell parameters. This modellisation is particularly suited for the simulation of fragmentation…
There are two popular ways to speed up simulations of planet formation via increasing the collision probability: ({\it i}) confine motion to 2D, ({\it ii}) artificially enhance the physical radii of the bodies by an expansion factor. In…
We present an improved version of the analytic method for calculating $\pi(x)$, the number of prime numbers not exceeding $x$. We implemented this method in cooperation with J. Franke, T. Kleinjung and A. Jost and calculated the value…
We study one-dimensional elastic collisions of three point masses on a line under vacuum, with no triple collisions. We express momentum conservation in matrix form and analyze the composite map $D=D_{BC}D_{AB}$ and its powers $D^k$, which…