Related papers: Deriving Pi from Colliding Blocks
The pi-pi interaction amplitudes have been calculated using a three coupled channel model both with and without constraints imposed by chiral models. Roy's equations have been used to compare the amplitudes and to study the role played by…
The paper considers the dynamics of the spreading liquid droplets after impact on a solid surface. The dynamics of a drop falling on a solid surface is shown using numerical simulation based on the solution of 2D and 3D Navier-Stokes…
An algorithm for computing /pi(N) is presented.It is shown that using a symmetry of natural numbers we can easily compute /pi(N).This method relies on the fact that counting the number of odd composites not exceeding N suffices to calculate…
Using classical differential geometry, the problem of elastic curves and surfaces in the presence of long-range interactions $\Phi$, is posed. Starting from a variational principle, the balance of elastic forces and the corresponding…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
In this paper, we give some recurrence formula and new and interesting identities for the poly-Bernoulli numbers and polynomials which are derived from umbral calculus.
The collision of water and elastic liquid drops with a thin cylinder (thread) is studied. The droplet flight trajectory and the cylinder axis are mutually perpendicular. Attention is focused on the difference between collisions of water…
In the open circular billiard particles are placed initially with a uniform distribution in their positions inside a planar circular vesicle. They all have velocities of the same magnitude, whose initial directions are also uniformly…
The static friction coefficient between two materials is considered to be a material constant. We present experiments demonstrating that the ratio of shear to normal force needed to move contacting blocks can, instead, vary systematically…
A new analytical criterion that captures the onset of separation of flow past elliptic cylinders is derived by considering the variation of the wall normal velocity in Reynolds number parameter space. It is shown that this criterion can be…
We joke about how to compute (promptly) the digits of $\pi$, in base 5, from a given place without computing preceding ones.
This paper is an elementary introduction to the theory of moduli spaces of curves and maps. As an application to enumerative geometry, we show how to count the number of bitangent lines to a projective plane curve of degree $d$ by doing…
The aim of this paper is to generalize the algorithm to compute jumping numbers on rational surfaces described in [AAD14] to varieties of dimension at least 3. Therefore, we introduce the notion of $\pi$-antieffective divisors, generalizing…
Numerical simulations are performed for the stick-slip motion in the Burridge-Knopoff model of one block. Calculated amplitude increases with the driving velocity. We argue that this effect can be a criterion to distinguish between the…
This is a note on calculating intersection numbers on moduli spaces of curves. A codimension 3 relation among tautological classes on the moduli space of genus 4 curves is given.
A theoretical analysis of binary collisions of quantum droplets under feasible experimental conditions is reported. Droplets formed from degenerate dilute Bose gases made up from binary mixtures of ultra cold atoms are considered. Reliable…
In this work, we develop a new iterative method for computing the digits of $\pi$ by argument reduction of the tangent function. This method combines a modified version of the iterative formula for $\pi$ with squared convergence that we…
We consider the effect of surface roughness on solid-solid contact in a Stokes flow. Various models for the roughness are considered, and a unified methodology is given to derive the corresponding asymptotics of the drag force. In this way,…
We determine the crossing number of polynomial size curve systems on standard surfaces, in terms of the genus, up to high precision.
A collision of viscoelastic bodies is analysed within a mathematically rigorous approach. We develop a perturbation scheme to solve continuum mechanics equation, which deals simultaneously with strain and strain rate in the bulk of the…