Probability tilting of compensated fragmentations

Fragmentation processes are part of a broad class of models describing the evolution of a system of particles which split apart at random. These models are widely used in biology, materials science and nuclear physics, and their asymptotic behaviour at large times is interesting both mathematically and practically. The spine decomposition is a key tool in its study. In this work, we consider the class of compensated fragmentations, or homogeneous growth-fragmentations, recently defined by Bertoin. We give a complete spine decomposition of these processes in terms of a L\'evy process with immigration, and apply our result to study the asymptotic properties of the derivative martingale.Comment: 41 pages, 1 figure. This revised version improves the conditions in Theorem 6.

Convergent-divergent nozzle flows

Uniform two-zone perfect gas expansions in convergent-divergent nozzle

Rigorous Proof of Pseudospin Ferromagnetism in Two-Component Bosonic Systems with Component-Independent Interactions

For a two-component bosonic system, the components can be mapped onto a pseudo-spin degree of freedom with spin quantum number S=1/2. We provide a rigorous proof that for a wide-range of real Hamiltonians with component independent mass and interaction, the ground state is a ferromagnetic state with pseudospin fully polarized. The spin-wave excitations are studied and found to have quadratic dispersion relations at long wave length.Comment: 4 pages, no figur

Axisymmetric reacting gas nonequilibrium performance program

Computer program calculates the inviscid one-dimensional equilibrium, frozen, and nonequilibrium nozzle expansion of propellant exhaust mixtures containing these six elements - carbon, hydrogen, oxygen, nitrogen, fluorine, and chlorine plus either aluminum, beryllium, boron or lithium. This program will perform calculations for contoured and conical nozzles

Numerical and Monte Carlo Bethe ansatz method: 1D Heisenberg model

In this paper we present two new numerical methods for studying thermodynamic quantities of integrable models. As an example of the effectiveness of these two approaches, results from numerical solutions of all sets of Bethe ansatz equations, for small Heisenberg chains, and Monte Carlo simulations in quasi-momentum space, for a relatively larger chains, are presented. Our results agree with those obtained by thermodynamics Bethe ansatz (TBA) and Quantum Transfer Matrix (QTM).Comment: 8 pages, 6 figure

The role of inter-well tunneling strength on coherence dynamics of two-species Bose-Einstein condensates

Coherence dynamics of two-species Bose-Einstein condensates in double wells is investigated in mean field approximation. We show that the system can exhibit decoherence phenomena even without the condensate-environment coupling and the variation tendency of the degree of coherence depends on not only the parameters of the system but also the initial states. We also investigate the time evolution of the degree of coherence for a Rosen-Zener form of tunneling strength, and propose a method to get a condensate system with certain degree of coherence through a time-dependent tunneling strength

Space shuttle: Supersonic aerodynamic characteristics of the MSC 040A orbiter (M equals 2.0 to 4.0)

A wind tunnel test of the space shuttle orbiter configuration 040A was run in a 20 in. supersonic wind tunnel. Basic aerodynamic data for this vehicle were determined at Mach 2.0, 2.4, 3.0 and 4.0

A mechanism to pin skyrmions in chiral magnets

We propose a mechanism to pin skyrmions in chiral magnets by introducing local maximum of magnetic exchange strength, which can be realized in chiral magnetic thin films by engineering the local density of itinerate electrons. Thus we find a way to artificially control the position of a single skyrmion in chiral magnetic thin films. The stationary properties and the dynamical pinning and depinning processes of an isolated skyrmion around a pinning center are studied. We do a series of simulations to show that the critical current to depin a skyrmion has linearly dependence on the pinning strength. We also estimate the critical current to have order of magnitude 10^{7}\sim10^{8}A/m^{2}

A Reduction of the Elastic Net to Support Vector Machines with an Application to GPU Computing

The past years have witnessed many dedicated open-source projects that built and maintain implementations of Support Vector Machines (SVM), parallelized for GPU, multi-core CPUs and distributed systems. Up to this point, no comparable effort has been made to parallelize the Elastic Net, despite its popularity in many high impact applications, including genetics, neuroscience and systems biology. The first contribution in this paper is of theoretical nature. We establish a tight link between two seemingly different algorithms and prove that Elastic Net regression can be reduced to SVM with squared hinge loss classification. Our second contribution is to derive a practical algorithm based on this reduction. The reduction enables us to utilize prior efforts in speeding up and parallelizing SVMs to obtain a highly optimized and parallel solver for the Elastic Net and Lasso. With a simple wrapper, consisting of only 11 lines of MATLAB code, we obtain an Elastic Net implementation that naturally utilizes GPU and multi-core CPUs. We demonstrate on twelve real world data sets, that our algorithm yields identical results as the popular (and highly optimized) glmnet implementation but is one or several orders of magnitude faster.Comment: 10 page