Exact solution and asymptotic behaviour of the asymmetric simple exclusion process on a ring

In this paper, we study an exact solution of the asymmetric simple exclusion process on a periodic lattice of finite sites with two typical updates, i.e., random and parallel. Then, we find that the explicit formulas for the partition function and the average velocity are expressed by the Gauss hypergeometric function. In order to obtain these results, we effectively exploit the recursion formula for the partition function for the zero-range process. The zero-range process corresponds to the asymmetric simple exclusion process if one chooses the relevant hop rates of particles, and the recursion gives the partition function, in principle, for any finite system size. Moreover, we reveal the asymptotic behaviour of the average velocity in the thermodynamic limit, expanding the formula as a series in system size.Comment: 10 page

Calibration of the Particle Density in Cellular-Automaton Models for Traffic Flow

We introduce density dependence of the cell size in cellular-automaton models for traffic flow, which allows a more precise correspondence between real-world phenomena and what observed in simulation. Also, we give an explicit calibration of the particle density particularly for the asymmetric simple exclusion process with some update rules. We thus find that the present method is valid in that it reproduces a realistic flow-density diagram.Comment: 2 pages, 2 figure

Level-of-Detail Triangle Strips for Deforming Meshes

Applications such as video games or movies often contain deforming meshes. The most-commonly used representation of these types of meshes consists in dense polygonal models. Such a large amount of geometry can be efficiently managed by applying level-of-detail techniques and specific solutions have been developed in this field. However, these solutions do not offer a high performance in real-time applications. We thus introduce a multiresolution scheme for deforming meshes. It enables us to obtain different approximations over all the frames of an animation. Moreover, we provide an efficient connectivity coding by means of triangle strips as well as a flexible framework adapted to the GPU pipeline. Our approach enables real-time performance and, at the same time, provides accurate approximations

Temperature dependence of the Kondo resonance and its satellites in CeCu_2Si_2

We present high-resolution photoemission spectroscopy studies on the Kondo resonance of the strongly-correlated Ce system CeCu$_2$Si$_2$. Exploiting the thermal broadening of the Fermi edge we analyze position, spectral weight, and temperature dependence of the low-energy 4f spectral features, whose major weight lies above the Fermi level $E_F$. We also present theoretical predictions based on the single-impurity Anderson model using an extended non-crossing approximation (NCA), including all spin-orbit and crystal field splittings of the 4f states. The excellent agreement between theory and experiment provides strong evidence that the spectral properties of CeCu$_2$Si$_2$ can be described by single-impurity Kondo physics down to $T \approx 5$ K.Comment: 4 pages, 3 figure

A new mechanism for electron spin echo envelope modulation

Electron spin echo envelope modulation (ESEEM) has been observed for the first time from a coupled hetero-spin pair of electron and nucleus in liquid solution. Previously, modulation effects in spin echo experiments have only been described in liquid solutions for a coupled pair of homonuclear spins in NMR or a pair of resonant electron spins in EPR. We observe low-frequency ESEEM (26 and 52 kHz) due to a new mechanism present for any electron spin with S>1/2 that is hyperfine coupled to a nuclear spin. In our case these are electron spin (S=3/2) and nuclear spin (I=1) in the endohedral fullerene N@C60. The modulation is shown to arise from second order effects in the isotropic hyperfine coupling of an electron and 14N nucleus.Comment: 15 pages, 4 figure

Brain activity dynamics in human parietal regions during spontaneous switches in bistable perception.

The neural mechanisms underlying conscious visual perception have been extensively investigated using bistable perception paradigms. Previous functional magnetic resonance imaging (fMRI) and transcranial magnetic stimulation (TMS) studies suggest that the right anterior superior parietal (r-aSPL) and the right posterior superior parietal lobule (r-pSPL) have opposite roles in triggering perceptual reversals. It has been proposed that these two areas are part of a hierarchical network whose dynamics determine perceptual switches. However, how these two parietal regions interact with each other and with the rest of the brain during bistable perception is not known. Here, we investigated such a model by recording brain activity using fMRI while participants viewed a bistable structure-from-motion stimulus. Using dynamic causal modeling (DCM), we found that resolving such perceptual ambiguity was specifically associated with reciprocal interactions between these parietal regions and V5/MT. Strikingly, the strength of bottom-up coupling between V5/MT to r-pSPL and from r-pSPL to r-aSPL predicted individual mean dominance duration. Our findings are consistent with a hierarchical predictive coding model of parietal involvement in bistable perception and suggest that visual information processing underlying spontaneous perceptual switches can be described as changes in connectivity strength between parietal and visual cortical regions

Inverting Time-Dependent Harmonic Oscillator Potential by a Unitary Transformation and a New Class of Exactly Solvable Oscillators

A time-dependent unitary (canonical) transformation is found which maps the Hamiltonian for a harmonic oscillator with time-dependent real mass and real frequency to that of a generalized harmonic oscillator with time-dependent real mass and imaginary frequency. The latter may be reduced to an ordinary harmonic oscillator by means of another unitary (canonical) transformation. A simple analysis of the resulting system leads to the identification of a previously unknown class of exactly solvable time-dependent oscillators. Furthermore, it is shown how one can apply these results to establish a canonical equivalence between some real and imaginary frequency oscillators. In particular it is shown that a harmonic oscillator whose frequency is constant and whose mass grows linearly in time is canonically equivalent with an oscillator whose frequency changes from being real to imaginary and vice versa repeatedly.Comment: 7 pages, 1 figure include

Velocity quantization approach of the one-dimensional dissipative harmonic oscillator

Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the constant of motion instead of the Hamiltonian.Comment: 10 pages, 2 figure