Related papers: Deriving Pi from Colliding Blocks
An earlier four-loop calculation of the fluctuation pressure of a fluid membrane between two infinite walls is extended to five loops. Variational perturbation theory is used to extract the hard-wall limit from perturbative results obtained…
It is known that the flip distance between two triangulations of a convex polygon is related to the minimum number of tetrahedra in the triangulation of some polyhedron. It is interesting to know whether these two numbers are the same. In…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
An investigation of the comparative efficiency of the different methods in which {\pi} is cal- culated. This thesis will compare and contrast five different methods in calculating {\pi} by first deriving the various proofs to each method…
This article is about Pi Formulas, infinite series of fractions which sum to multiples of Pi. Each such one can be associated with a unique set $S_k$ of rough numbers, where $k$ is a prime number. Given $S_k$ for any prime $k$, the set…
For wall turbulence, moments of velocity fluctuations are known to be logarithmic functions of the height from the wall. This logarithmic scaling is due to the existence of a characteristic velocity and to the nonexistence of any…
Subject of this letter is the dynamics of a chain obtained performing the continuous limit of a system of links and beads. In particular, the probability distribution of the relative position between two points of the chain averaged over a…
The mathematical constant pi has recently been computed up to 22,459,157,718,361 decimal and 18,651,926,753,033 hexadecimal digits. As a simple check for the normality of pi, the frequencies of all sequences with length one, two and three…
An algorithm has been devised to compute the inner and outer product between two arbitrary multi-dimensional arrays A and B in a single piece of code. It was derived using A Mathematics of Arrays (MoA) and the $\psi$-calculus. Extensive…
We present {\it block analysis}, an efficient method to perform finite-size scaling for obtaining the length scale of dynamic heterogeneity and the point-to-set length scale for generic glass-forming liquids. This method involves…
In this paper, the dynamic case of a system made up of two blocks connected by a string over a smooth pulley is revisited. One mass lies on a horizontal surface without friction, and the other mass has a vertical displacement. The motion…
An analytical expression of the coefficient of restitution for viscoelastic materials is derived for the viscous-dominant case, such as collisions of polymeric melt. The recently proposed normal impact force model between two colliding…
In two previous papers we have presented partition formulae for the Fibonacci numbers motivated by the appearance of the Fibonacci numbers in the representation theory of the 3-Kronecker quiver and its universal cover, the 3-regular tree.…
The correlations between the segments of a semidilute polymer solution are found to induce correlations in the positions of small particles added to the solution. Small means a diameter much less than the polymer's correlation length. In…
We derive the short distance interaction of star polymers in a colloidal solution. We calculate the corresponding force between two stars with arbitrary numbers of legs f_1 and f_2. We show that a simple scaling theory originally derived…
The aim of this paper is to derive explicit formulas for two distinct values. The first is the total number of symmetric peaks in a set partition of $[n]$ with exactly $k$ blocks, and the second one is the total number of non-symmetric…
After defining convex near-polygons, a formula enumerating the number of triangulations of such configurations is derived in terms of edge-polynomials. The paper describes also a transfer-matrix approach for computing quantities related to…
A method for computing the thermopower in interacting systems is proposed. This approach, which relies on Monte Carlo simulations, is illustrated first for a diatomic chain of hard-point elastically colliding particles and then in the case…
An important concept in digital geometry for computer imagery is that of tunnel. In this paper we obtain a formula for the number of tunnels as a function of the number of the object vertices, pixels, holes, connected components, and 2x2…
We derive a formula for the expected number of blocks of a given size from a non-crossing partition chosen uniformly at random. Moreover, we refine this result subject to the restriction of having a number of blocks given. Furthermore, we…