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

Global Newtonian limit for the Relativistic Boltzmann Equation near Vacuum

We study the Cauchy Problem for the relativistic Boltzmann equation with near Vacuum initial data. Unique global in time "mild" solutions are obtained uniformly in the speed of light parameter $c \ge 1$. We furthermore prove that solutions to the relativistic Boltzmann equation converge to solutions of the Newtonian Boltzmann equation in the limit as $c\to\infty$ on arbitrary time intervals $[0,T]$, with convergence rate $1/c^{2-\epsilon}$ for any $\epsilon \in(0,2)$. This may be the first proof of unique global in time validity of the Newtonian limit for a Kinetic equation.Comment: 35 page

On graphs with a large chromatic number containing no small odd cycles

In this paper, we present the lower bounds for the number of vertices in a graph with a large chromatic number containing no small odd cycles

Antonio Gramsci’s impact on critical pedagogy

This paper provides an account of Antonio Gramsci’s impact on the area of critical pedagogy. It indicates the Gramscian influence on the thinking of major exponents of the field. It foregrounds Gramsci's ideas and then indicates how they have been taken up by a selection of critical pedagogy exponents who were chosen on the strength of their identification and engagement with Gramsci's ideas, some of them even having written entire essays on Gramsci. The essay concludes with a discussion concerning an aspect of Gramsci's concerns, the question of powerful knowledge, which, in the present author's view, provides a formidable challenge to critical pedagogues.peer-reviewe

Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids

Using the Calogero model as an example, we show that the transport in interacting non-dissipative electronic systems is essentially non-linear. Non-linear effects are due to the curvature of the electronic spectrum near the Fermi energy. As is typical for non-linear systems, propagating wave packets are unstable. At finite time shock wave singularities develop, the wave packet collapses, and oscillatory features arise. They evolve into regularly structured localized pulses carrying a fractionally quantized charge - {\it soliton trains}. We briefly discuss perspectives of observation of Quantum Shock Waves in edge states of Fractional Quantum Hall Effect and a direct measurement of the fractional charge

Exact ground state of finite Bose-Einstein condensates on a ring

The exact ground state of the many-body Schr\"odinger equation for $N$ bosons on a one-dimensional ring interacting via pairwise $\delta$-function interaction is presented for up to fifty particles. The solutions are obtained by solving Lieb and Liniger's system of coupled transcendental equations for finite $N$. The ground state energies for repulsive and attractive interaction are shown to be smoothly connected at the point of zero interaction strength, implying that the \emph{Bethe-ansatz} can be used also for attractive interaction for all cases studied. For repulsive interaction the exact energies are compared to (i) Lieb and Liniger's thermodynamic limit solution and (ii) the Tonks-Girardeau gas limit. It is found that the energy of the thermodynamic limit solution can differ substantially from that of the exact solution for finite $N$ when the interaction is weak or when $N$ is small. A simple relation between the Tonks-Girardeau gas limit and the solution for finite interaction strength is revealed. For attractive interaction we find that the true ground state energy is given to a good approximation by the energy of the system of $N$ attractive bosons on an infinite line, provided the interaction is stronger than the critical interaction strength of mean-field theory.Comment: 28 pages, 11 figure

Separability problem for multipartite states of rank at most four

One of the most important problems in quantum information is the separability problem, which asks whether a given quantum state is separable. We investigate multipartite states of rank at most four which are PPT (i.e., all their partial transposes are positive semidefinite). We show that any PPT state of rank two or three is separable and has length at most four. For separable states of rank four, we show that they have length at most six. It is six only for some qubit-qutrit or multiqubit states. It turns out that any PPT entangled state of rank four is necessarily supported on a 3x3 or a 2x2x2 subsystem. We obtain a very simple criterion for the separability problem of the PPT states of rank at most four: such a state is entangled if and only if its range contains no product vectors. This criterion can be easily applied since a four-dimensional subspace in the 3x3 or 2x2x2 system contains a product vector if and only if its Pluecker coordinates satisfy a homogeneous polynomial equation (the Chow form of the corresponding Segre variety). We have computed an explicit determinantal expression for the Chow form in the former case, while such expression was already known in the latter case.Comment: 19 page

Slow-light and evanescent modes at interfaces in photonic crystal waveguides: optimal extraction from experimental near-field measurements

We develop a systematic approach for simultaneous extraction of the dispersion relations and profiles of multiple modes in periodic waveguides though a special global optimization procedure applied to near-field electric field measurements in the waveguide plane. We apply this method to perform in-depth analysis of experimental data on wave propagation close to an interface between waveguide sections with different dispersion characteristics, and we successfully identify several modes contributing to the experimentally measured fields. We find clear evidence that when the group velocity is reduced across the interface, evanescent modes that facilitate the excitation of propagating slow-light waves appear, confirming previous theoretical predictions. (C) 2011 Optical Society of AmericaPublisher PDFPeer reviewe