Related papers: Deriving Pi from Colliding Blocks
A notion of heaps of modules as an affine version of modules over a ring or, more generally, over a truss, is introduced and studied. Basic properties of heaps of modules are derived. Examples arising from geometry (connections, affine…
The statistical methods used in deriving physics results in the BaBar collaboration are reviewed, with especial emphasis on areas where practice is not uniform in particle physics.
Consider a random geometric graph over a random point process in $\mathbb{R}^d$. Two points are connected by an edge if and only if their distance is bounded by a prescribed distance parameter. We show that projecting the graph onto a two…
We investigate hydrodynamic interaction effects between colloidal particles in the vicinity of a wall in the low Reynolds-number limit. Hydrodynamically interacting pairs of beads being dragged by a force parallel to a wall, as for instance…
Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods, six old and fourteen new. It allows easy assessment of…
We study the static structure of piles made of polydisperse disks in the rigid limit with and without friction using molecular dynamic simulations for various elasticities of the disks and pile preparation procedures. The coordination…
This paper is devoted to presenting a new approach to determine the intersection of two quadrics based on the detailed analysis of its projection in the plane (the so called cutcurve) allowing to perform the corresponding lifting correctly.…
In this paper we give a survey of methods used to calculate values of resistance distance (also known as effective resistance) in graphs. Resistance distance has played a prominent role not only in circuit theory and chemistry, but also in…
I present a variant of the Buffon Needle method for determination of the value of the mathematical constant, pi. The original method is based on the random casting of a needle of length l onto a planked floor of plank width L. The described…
Suppose an interval is put on a horizontal line with random roughness. With probability one it is supported at two points, one from the left, and another from the right from its center. We compute probability distribution of support points…
A rough collision law describes the limiting contact dynamics of a pair of rough rigid bodies, as the scale of the rough features (asperities) on the surface of each body goes to zero. The class of rough collision laws is quite large and…
The oblique collision between an elastic disk and an elastic wall is numerically studied. We investigate the dependency of the tangential coefficient of restitution on the incident angle of impact. From the results of simulation, our model…
There are two methods for counting the number of occurrences of a string in another large string. One is to count the number of places where the string is found. The other is to determine how many pieces of string can be extracted without…
The blocking number of a manifold is the minimal number of points needed to block out lights between any two given points in the manifold. It has been conjectured that if the blocking number of a manifold is finite, then the manifold must…
The coefficient of static friction between solids generally depends on the time they have remained in static contact before the measurement. Such frictional aging is at the origin of the difference between static and dynamic friction…
We prove that there is an algorithm to compute the class of the intersection of the divisor of schemes incident to a fixed line with any other class of a basis of the Chow ring $A^*(\mathbb{P}^{2[N]})$ due to Mallavibarrena and Sols. This…
The present work is essentially concerned with the development of statistical theory for the low temperature dislocation glide in concentrated solid solutions where atom-sized obstacles impede plastic flow. In connection with such a…
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…
Line intersection with convex and un-convex polygons or polyhedron algorithms are well known as line clipping algorithms and very often used in computer graphics. Rendering of geometrical problems often leads to ray tracing techniques, when…
We investigate some aspects of bounding, splitting, and almost disjointness. In particular, we investigate the relationship between the bounding number, the closed almost disjointness number, splitting number, and the existence of certain…