Related papers: Throwing $\pi$ at a wall
Let $(\{1,2,\ldots,n\},d)$ be a metric space. We analyze the expected value and the variance of $\sum_{i=1}^{\lfloor n/2\rfloor}\,d({\boldsymbol{\pi}}(2i-1),{\boldsymbol{\pi}}(2i))$ for a uniformly random permutation ${\boldsymbol{\pi}}$ of…
We present an analytical calculation of the hydrodynamic interaction between two spherical particles near an elastic interface such as a cell membrane. The theory predicts the frequency dependent self- and pair-mobilities accounting for the…
The problem of $\gamma \pi \to \pi \pi$ is studied using the axial anomaly, elastic unitarity, analyticity and crossing symmetry. The solution of the integral equation for this amplitude is given by an iteration procedure.The final solution…
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…
We study an interacting particle system of a finite number of labelled particles on the integer lattice, in which particles have intrinsic masses and left/right jump rates. If a particle is the minimal-label particle at its site when it…
In this note we consider $2$-dimensional lattice random walks killed at leaving a wedge with opening $\alpha\in(0,\pi]$. Assuming that the walk cannot jump over the boundary of the wedge we prove that there exists a harmonic polynomial if…
In this work, we consider the properties of the two-term Machin-like formula and develop an algorithm for computing digits of $\pi$ by using its rational approximation. In this approximation, both terms are constructed by using a…
Through an inversion approach, we suggest a possible estimation for the absolute value of Mertens function $\vert M(x) \vert$ that $ \left\vert M(x) \right\vert \sim \left[\frac{1}{\pi \sqrt{\varepsilon}(x+\varepsilon)}\right]\sqrt{x}$…
The one-dimensional scattering of a two body interacting system by an infinite wall is studied in a quantum-mechanical framework. This problem contains some of the dynamical features present in the collision of atomic, molecular and nuclear…
We present a model calculation to reproduce the differential mass distribution for the $D^*\pi$ system in the reactions $B^- \to D^{*+} \pi^- \pi^-$ and $B^{+}\to D_s^+D^{*-}\pi^{+}$ analyzed by the LHCb Collaboration, which shows a…
We compute the wall velocity in the MSSM with W, tops and stops contributing to the friction. In a wide range of parameters including those which fulfil the requirements of baryogenesis we find a wall velocity of order v_w=O(0.01) much…
In this article we provide a motivation for studying integrals $\displaystyle \int_0^{\frac{\pi}{2}}x\cos^mx~dx$, $m\in \mathbb{N}$. We demonstrate several properties of this class of integrals and show that it is closely related to the…
We study the behavior of the pulse waves of water into a flexible tube for application to blood flow simulations. In pulse waves both fluid friction and wall viscosity are damping factors, and difficult to evaluate separately. In this…
A non-slip constraint between a particle and a wall is applied at the microscopic level of collision dynamics using the rough sphere model. We analyse the consequences of the translation-rotation coupling of the rough sphere confined…
We introduce a new method of calculating intersections on \bar{M}_{g,n}, using localization of equivariant cohomology. As an application, we give a proof of Mirzakhani's recursion relation for calculating intersections of mixed psi and…
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…
We propose to use the coincidence method of Ma to measure an entropy of the system created in heavy ion collisions. Moreover we estimate, in a simple model, the values of parameters for which the thermodynamical behaviour sets in.
A previously proposed geometric definition of mass in terms of energy, in a geometrical unified theory, is used to obtain a numerical expression for a ratio of masses of geometrical excitations. The resultant geometric ratio is…
We study the time dependency of the (average) interfacial separation between an elastic solid with a flat surface and a rigid solid with a randomly rough surface, squeezed together in a fluid. We use an analytical theory describing the…
It has recently been suggested that many contact mechanics problems between solids can be accurately studied by mapping the problem on an effective one dimensional (1D) elastic foundation model. Using this 1D mapping we calculate the…