Diffusion in a continuum model of self-propelled particles with alignment interaction

In this paper, we provide the $O(\epsilon)$ corrections to the hydrodynamic model derived by Degond and Motsch from a kinetic version of the model by Vicsek & coauthors describing flocking biological agents. The parameter $\epsilon$ stands for the ratio of the microscopic to the macroscopic scales. The $O(\epsilon)$ corrected model involves diffusion terms in both the mass and velocity equations as well as terms which are quadratic functions of the first order derivatives of the density and velocity. The derivation method is based on the standard Chapman-Enskog theory, but is significantly more complex than usual due to both the non-isotropy of the fluid and the lack of momentum conservation

Entanglement witnesses arising from Choi type positive linear maps

We construct optimal PPTES witnesses to detect $3\otimes 3$ PPT entangled edge states of type $(6,8)$ constructed recently \cite{kye_osaka}. To do this, we consider positive linear maps which are variants of the Choi type map involving complex numbers, and examine several notions related to optimality for those entanglement witnesses. Through the discussion, we suggest a method to check the optimality of entanglement witnesses without the spanning property.Comment: 18 pages, 4 figures, 1 tabl

Low-energy structures embedded with smart dampers

© 2018 Elsevier B.V. Building structures, subject to dynamic loadings or external disturbances, may undergo destructive vibrations and encounter different degrees of deformation. Modeling and control techniques can be applied to effectively damp out these vibrations and maintain structural health with a low energy cost. Smart structures embedded with semi-active control devices, offer a promising solution to the problem. The smart damping concept has been proven to be an effective approach for input energy shaping and suppressing unwanted vibrations in structural control for buildings embedded with magnetorheological fluid dampers (MRDs). In this paper, the dissipation energy in MRD is studied by using results from induced hysteretic effect of structural vibrations while the fluid is placed under a controlled magnetic field. Then, a frequency-shaped second-order sliding mode controller (FS2SMC) is designed along with a low-pass filter to implement the desired dynamic sliding surface, wherein the frequency responses of the hysteretic MRD is represented by its magnitude and phase describing functions. The proposed controller can thus shape the frequency characteristics of the equivalent dynamics for the MRD-embedded structure against induced vibrations, and hence, dissipate the energy flow within the smart devices to prevent structural damage. Simulation results for a 10-floor building model equipped with current-controlled MRDs, subject to horizontal seismic excitations validate the proposed technique for low-energy structures with smart devices. The closed-loop performance and comparison in terms of energy signals indicate that the proposed method allows not only to reduce induced vibrations and input energy, but also its spectrum can be adjusted to prevent natural modes of the structure under external excitations

Combinatorial interpretation of Haldane-Wu fractional exclusion statistics

Assuming that the maximal allowed number of identical particles in state is an integer parameter, q, we derive the statistical weight and analyze the associated equation which defines the statistical distribution. The derived distribution covers Fermi-Dirac and Bose-Einstein ones in the particular cases q = 1 and q -> infinity (n_i/q -> 1), respectively. We show that the derived statistical weight provides a natural combinatorial interpretation of Haldane-Wu fractional exclusion statistics, and present exact solutions of the distribution equation.Comment: 8 pages, 2 eps-figure

Spin-Charge Separation at Finite Temperature in the Supersymmetric t-J Model with Long-Range Interactions

Thermodynamics is derived rigorously for the 1D supersymmetric {\it t-J} model and its SU($K,1$) generalization with inverse-square exchange. The system at low temperature is described in terms of spinons, antispinons, holons and antiholons obeying fractional statistics. They are all free and make the spin susceptibility independent of electron density, and the charge susceptibility independent of magnetization. Thermal spin excitations responsible for the entropy of the SU($K,1$) model are ascribed to free para-fermions of order $K-1$.Comment: 10 pages, REVTE

Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with integrable angular cross section

This paper focuses on the study of existence and uniqueness of distributional and classical solutions to the Cauchy Boltzmann problem for the soft potential case assuming $S^{n-1}$ integrability of the angular part of the collision kernel (Grad cut-off assumption). For this purpose we revisit the Kaniel--Shinbrot iteration technique to present an elementary proof of existence and uniqueness results that includes large data near a local Maxwellian regime with possibly infinite initial mass. We study the propagation of regularity using a recent estimate for the positive collision operator given in [3], by E. Carneiro and the authors, that permits to study such propagation without additional conditions on the collision kernel. Finally, an $L^{p}$-stability result (with $1\leq p\leq\infty$) is presented assuming the aforementioned condition.Comment: 19 page

Performance of a prototype active veto system using liquid scintillator for a dark matter search experiment

We report the performance of an active veto system using a liquid scintillator with NaI(Tl) crystals for use in a dark matter search experiment. When a NaI(Tl) crystal is immersed in the prototype detector, the detector tags 48% of the internal K-40 background in the 0-10 keV energy region. We also determined the tagging efficiency for events at 6-20 keV as 26.5 +/- 1.7% of the total events, which corresponds to 0.76 +/- 0.04 events/keV/kg/day. According to a simulation, approximately 60% of the background events from U, Th, and K radioisotopes in photomultiplier tubes are tagged at energies of 0-10 keV. Full shielding with a 40-cm-thick liquid scintillator can increase the tagging efficiency for both the internal K-40 and external background to approximately 80%.Comment: Submitted to Nuclear Instruments and Methods in Physics Research Section