Liesegang patterns : Studies on the width law

The so-called "width law" for Liesegang patterns, which states that the positions x_n and widths w_n of bands verify the relation x_n \sim w_n^{\alpha} for some \alpha>0, is investigated both experimentally and theoretically. We provide experimental data exhibiting good evidence for values of \alpha close to 1. The value \alpha=1 is supported by theoretical arguments based on a generic model of reaction-diffusion.Comment: 7 pages, RevTeX, two columns, 5 figure

Derivation of the Matalon-Packter law for Liesegang patterns

Theoretical models of the Liesegang phenomena are studied and simple expressions for the spacing coefficients characterizing the patterns are derived. The emphasis is on displaying the explicit dependences on the concentrations of the inner- and the outer-electrolytes. Competing theories (ion-product supersaturation, nucleation and droplet growth, induced sol- coagulation) are treated with the aim of finding the distinguishing features of the theories. The predictions are compared with experiments and the results suggest that the induced sol-coagulation theory is the best candidate for describing the experimental observations embodied in the Matalon-Packter law.Comment: 9 pages, 7 figures, RevTe

Simultaneous segmentation of the left and right heart ventricles in 3D cine MR images of small animals

New high resolution image techniques allow to capture the anatomy and movement of the heart of small animals. The availability of these in vivo images can be very useful for medical research, however the amount of generated data for large animal studies makes manual analysis a very tedious task. To cope with the problem of automatic analysis of these images, we propose the use of the Deformable Elastic Template method to perform automatic segmentation of the ventricles. To adapt the method to the specificities of high-resolution MRI, several improvements are presented, including an image-context dependent scheme for more robust segmentation. Qualitative results show that our method is able to correctly retrieve the heart’s contours in 3D. 1

Commissioning of the Control System for the LHC Beam Dump Kicker System

The beam dumping system of the Large Hadron Collider (LHC) provides a loss-free fast extraction of the circulating beams. It consists per ring of 15 extraction kickers, followed by 15 septum magnets, 10 dilution kickers and an external absorber. A dump request can occur at any moment during the operation of the collider, from injection energy up to collision energy. All kickers must fire synchronously with the beam abort gap to properly extract the whole beam in one single turn into the extraction channel. Incorrect operation of the extraction kickers can lead to beam losses and severe damage to the machine. The control system of the LHC beam dump kickers is based on a modular architecture composed of 4 different sub-systems, each with a specific function, in order to detect internal failures, to ensure a correct extraction trajectory over the whole LHC operational range, to synchronise and distribute dumps requests, and to analyse the transient signals recorded during the beam dumping process. The control architecture is presented and the different steps performed for its validation, from the individual sub-systems tests to the final commissioning with beam, are describe

Bargmann-Michel-Telegdi equation and one-particle relativistic approach

A reexamination of the semiclassical approach of the relativistic electron indicates a possible variation of its helicity for electric and magnetic static fields applied along its global motion due to zitterbewegung effects, proportional to the anomalous part of the magnetic moment.Comment: 10 pages, LATEX2E, uses amsb

Results from the LHC Beam Dump Reliability Run

The LHC Beam Dumping System is one of the vital elements of the LHC Machine Protection System and has to operate reliably every time a beam dump request is made. Detailed dependability calculations have been made, resulting in expected rates for the different system failure modes. A 'reliability run' of the whole system, installed in its final configuration in the LHC, has been made to discover infant mortality problems and to compare the occurrence of the measured failure modes with their calculations

Formation of Liesegang patterns: A spinodal decomposition scenario

Spinodal decomposition in the presence of a moving particle source is proposed as a mechanism for the formation of Liesegang bands. This mechanism yields a sequence of band positions x_n that obeys the spacing law x_n~Q(1+p)^n. The dependence of the parameters p and Q on the initial concentration of the reagents is determined and we find that the functional form of p is in agreement with the experimentally observed Matalon-Packter law.Comment: RevTex, 4 pages, 4 eps figure

Asymptotic expansion for reversible A + B <-> C reaction-diffusion process

We study long-time properties of reversible reaction-diffusion systems of type A + B C by means of perturbation expansion in powers of 1/t (inverse of time). For the case of equal diffusion coefficients we present exact formulas for the asymptotic forms of reactant concentrations and a complete, recursive expression for an arbitrary term of the expansions. Taking an appropriate limit we show that by studying reversible reactions one can obtain "singular" solutions typical of irreversible reactions.Comment: 6 pages, no figures, to appear in PR

Localization-delocalization transition of a reaction-diffusion front near a semipermeable wall

The A+B --> C reaction-diffusion process is studied in a system where the reagents are separated by a semipermeable wall. We use reaction-diffusion equations to describe the process and to derive a scaling description for the long-time behavior of the reaction front. Furthermore, we show that a critical localization-delocalization transition takes place as a control parameter which depends on the initial densities and on the diffusion constants is varied. The transition is between a reaction front of finite width that is localized at the wall and a front which is detached and moves away from the wall. At the critical point, the reaction front remains at the wall but its width diverges with time [as t^(1/6) in mean-field approximation].Comment: 7 pages, PS fil