Shock fluctuations in asymmetric simple exclusion

Summary The one dimensional nearest neighbors asymmetric simple exclusion process in used as a microscopic approximation to the Burgers equation. We study the process with rates of jumpsp>q to the right and left, respectively, and with initial product measure with densities < to the left and right of the origin, respectively (with shock initial conditions). We prove that a second class particle added to the system at the origin at time zero identifies microscopically the shock for all later times. If this particle is added at another site, then it describes the behavior of a characteristic of the Burgers equation. For vanishing left density (=0) we prove, in the scale t^1/2, that the position of the shock at timet depends only on the initial configuration in a region depending ont. The proofs are based on laws of large numbers for the second class particle.     

Delayed feedback control of phase synchronisation in a neuronal network model

The human cerebral cortex can be separated into cortical areas forming a clustered network structure. We build two different clustered networks, where one network is based on a healthy brain and the other according to a brain affected by a neurodegenerative process. Each cortical area has a subnetwork with small-world properties. We verify that both networks exhibit rich-club organisation and phase synchronisation. Due to the fact that neuronal synchronisation can be related to brain diseases, we consider the delayed feedback control as a method to suppress synchronous behaviours. In this work, it is presented that depending on the feedback parameters, intensity and time delay, phase synchronisation in both networks can be suppressed. Therefore, one of our main results is to show that delayed feedback control can be used to suppress undesired synchronous behaviours not only in the healthy brain, but also in the brain marked by neurodegenerative processes.     

Thermal conductivity of isolated and interacting carbon nanotubes: comparing results from molecular dynamics and the boltzmann transport equation

We investigate the thermal conductivity of single-wall carbon nanotubes (SWCNT) either isolated or in contact with external media by using equilibrium molecular dynamics and the Boltzmann transport equation. We show that, contrary to existing controversies, both methods yield a finite value of the thermal conductivity for infinitely long tubes, as opposed to the case of 1D, momentum-conserving systems. Acoustic and flexure modes with mean free paths of the order of a few microns are identified as major contributors to the high value of SWCNT conductivity. We also find that the interaction with an external medium may substantially decrease the lifetime of the low-frequency vibrations, reducing the thermal conductivity by up to 2 orders of magnitude.     

Edge linking and image segmentation by combining optical and digital methods

We present a hybrid method for segmentation of intensity images, which combines an optical contouring technique and digital algorithms for linking edge points or image segmentation. In a first stage, the digital image to be processed is displayed in a twisted-nematic liquid-crystal display (LCD), which is placed between a polarizer–analyzer pair at 45 deg (instead of 90 deg as occurs in standard LCDs). It is not difficult to demonstrate that the proposed setup produces a resultant image with very pronounced dark contours at middle intensity. After the optical preprocessing, two different digital algorithms are applied: an edge linking algorithm (modified chain code) and a simple thresholding technique for image segmentation. The proposed procedure works well with monochromatic and color images. The method could be useful as a robust technique for segmentation of large images in real-time, which presents potential applications in medical and biological imaging.     

Freezing of a Lennard-Jones fluid: from nucleation to spinodal regime

Using molecular dynamics, we investigate the crystal nucleation in a Lennard-Jones fluid as a function of the degree of supercooling. At moderate supercooling, a nucleation picture applies, while for deeper quenches, the phenomenon progressively acquires a spinodal character. We show that in the nucleation regime, the freezing is a two-step process. The formation of the critical nucleus is indeed preceded by the abrupt formation of a precritical crystallite from a density fluctuation in the fluid. In contrast, as the degree of supercooling is increased, crystallization proceeds in a more continuous and collective fashion and becomes more spatially diffuse, indicating that the liquid is unstable and crystallizes by a spinodal mechanism.     

Tricritical point in heterogeneous k-core percolation

k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understanding the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with heterogeneous k-cores, where each vertex is assigned a local threshold k(i). In this Letter we identify a binary mixture of heterogeneous k-cores which exhibits a tricritical point. We investigate the new scaling scenario and calculate the relevant critical exponents, by analytical and computational methods, for Erd?s-Rényi networks and 2D square lattices.     

Static cylindrically symmetric solution of the Kaluza-Klein equations

In this paper we investigate the (static) solution of the Kaluza-Klein equations for a cylindrically symmetric current distribution. Specifically, we are interested in the fields generated by a long, cylindrical solenoid. We shall examine in some detail the concept of effective mass of a charged test particle. We shall show that, for a certain charge-to(rest)mass ratio of the test particle, the effective mass becomes imaginary at a certain distance from the axis of our solenoid.     

Phase modulation by polarization recording in bacteriorhodopsin: application to phase-shifting interferometry

A novel phase-control method with application to phase-shifting interferometry is presented. The linear polarization state of an external (green) light beam is recorded on a bacteriorhodopsin film, and this polarization state is read by a circular polarized (red) laser beam. By reading the bacteriorhodopsin film, the original (red) wave reverses its circularity and becomes phase shifted by an amount that is dependent on the polarization of the external (green) beam. This method of phase control can be applied in a two-beam interferometer in which the test and reference waves are orthogonally polarized, which allows one to obtain phase modulation without moving parts inside the interferometer.