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

Learning a Unified Control Policy for Safe Falling

Being able to fall safely is a necessary motor skill for humanoids performing highly dynamic tasks, such as running and jumping. We propose a new method to learn a policy that minimizes the maximal impulse during the fall. The optimization solves for both a discrete contact planning problem and a continuous optimal control problem. Once trained, the policy can compute the optimal next contacting body part (e.g. left foot, right foot, or hands), contact location and timing, and the required joint actuation. We represent the policy as a mixture of actor-critic neural network, which consists of n control policies and the corresponding value functions. Each pair of actor-critic is associated with one of the n possible contacting body parts. During execution, the policy corresponding to the highest value function will be executed while the associated body part will be the next contact with the ground. With this mixture of actor-critic architecture, the discrete contact sequence planning is solved through the selection of the best critics while the continuous control problem is solved by the optimization of actors. We show that our policy can achieve comparable, sometimes even higher, rewards than a recursive search of the action space using dynamic programming, while enjoying 50 to 400 times of speed gain during online execution

Wavelet analysis of beam-soil structure response for fast moving train

This paper presents a wavelet based approach for the vibratory analysis of beam-soil structure related to a point load moving along a beam resting on the surface. The model is represented by the Euler-Bernoulli equation for the beam, elastodynamic equation of motion for the soil and appropriate boundary conditions. Two cases are analysed: the model with a half space under the beam and the model where the supporting medium has a finite thickness. Analytical solutions for the displacements are obtained and discussed in relation to the used boundary conditions and the type of considered loads: harmonic and constant. The analysis in time-frequency and velocity-frequency domains is carried out for realistic systems of parameters describing physical properties of the model. The approximate displacement values are determined by applying a wavelet method for a derivation of the inverse Fourier transform. A special form of the coiflet filter used in numerical calculations allows to carry out analysis without loss of accuracy related to singularities appearing in wavelet approximation formulas, when dealing with standard filters and complex dynamic systems. © 2009 IOP Publishing Ltd

Exact solution of DND_N type quantum Calogero model through a mapping to free harmonic oscillators

We solve the eigenvalue problem of the $D_N$ type of Calogero model by mapping it to a set of decoupled quantum harmonic oscillators through a similarity transformation. In particular, we construct the eigenfunctions of this Calogero model from those of bosonic harmonic oscillators having either all even parity or all odd parity. It turns out that the eigenfunctions of this model are orthogonal with respect to a nontrivial inner product, which can be derived from the quasi-Hermiticity property of the corresponding conserved quantities.Comment: 16 page

Social-aware Opportunistic Routing Protocol based on User's Interactions and Interests

Nowadays, routing proposals must deal with a panoply of heterogeneous devices, intermittent connectivity, and the users' constant need for communication, even in rather challenging networking scenarios. Thus, we propose a Social-aware Content-based Opportunistic Routing Protocol, SCORP, that considers the users' social interaction and their interests to improve data delivery in urban, dense scenarios. Through simulations, using synthetic mobility and human traces scenarios, we compare the performance of our solution against other two social-aware solutions, dLife and Bubble Rap, and the social-oblivious Spray and Wait, in order to show that the combination of social awareness and content knowledge can be beneficial when disseminating data in challenging networks