Quantum fluctuations on domain walls, strings, and vacuum bubbles

We develop a covariant quantum theory of fluctuations on vacuum domain walls and strings. The fluctuations are described by a scalar field defined on the classical world sheet of the defects. We consider the following cases: straight strings and planar walls in flat space, true vacuum bubbles nucleating in false vacuum, and strings and walls nucleating during inflation. The quantum state for the perturbations is constructed so that it respects the original symmetries of the classical solution. In particular, for the case of vacuum bubbles and nucleating strings and walls, the geometry of the world sheet is that of a lower-dimensional de Sitter space, and the problem reduces to the quantization of a scalar field of tachyonic mass in de Sitter space. In all cases, the root-mean-squared fluctuation is evaluated in detail, and the physical implications are briefly discussed.

Quantum tunneling of domain walls in ferromagnets

We present a theoretical study of the quantum depinning of domain walls. Our approach extends earlier work by Stamp and confirms his suggestion that quantum tunneling of domain walls in ferromagnets may reveal itself at a macroscopic level in a manner similar to the Josephson effect in superconductors. The rate of tunneling of a domain wall through a barrier formed by a planar defect is calculated in terms of macroscopic parameters of the ferromagnet. A universal behavior of the WKB exponent in the limit of small barriers is demonstrated. The effect of dissipation on the tunneling rate is studied. It is argued that quantum diffusion of domain walls apparently explains a nonthermal magnetic relaxation observed in some materials at low temperatures.

Wave competition in excitable modulated media.

The propagation of an initially planar front is studied within the framework of the photosensitive Belousov-Zhabotinsky reaction modulated by a smooth spatial variation of the local front velocity in the direction perpendicular to front propagation. Under this modulation, the wave front develops several fingers corresponding to the local maxima of the modulation function. After a transient, the wave front achieves a stationary shape that does not necessarily coincide with the one externally imposed by the modulation. Theoretical predictions for the selection criteria of fingers and steady-state velocity are experimentally validated.

Growth and melting of the nematic phase: sample thickness dependence of the Mullins-Sekerka instability

In this article we report our systematic studies of the dependence on the sample thickness of the onset parameters of the instability of the nematic-isotropic interface during directional growth and melting, in homeotropic or planar anchoring.

Backflow-induced asymmetric collapse of disclination lines in liquid crystals

We present experiments where opposed pairs of planar parallel disclination lines of topological strength s=±1 move due to their mutual attraction. Our measurements show that their motion is clearly asymmetric, with +1 defects moving up to twice as fast as -1 ones. This is a clear indication of backflow, given the intrinsic isotropic elasticity of our system. A phenomenological model is able to account for the experimental observations by renormalizing the orientational diffusivity estimated from the velocity of each defect.

The Hercynian structure of the Catalonian Coastal Ranges (NE Spain)

In the Catalonian Coastal Ranges, Paleozoic sedimentary and meta-sedimentary rocks crop out in severa1 areas, intruded by late tectonic Hercynian granitoids and separated by Mesozoic and Tertiary cover sediments. Large structures are often difficult to recognize, although a general east-west trend can be observed on the geological map. Deformation was accompanied by the development of cleavages and regional metamorphism. Green-schist facies rocks are prominent throughout the Ranges, while amphibolite facies are restricted to small areas. In low-grade areas, the main deformation phase generated south-facing folds with an axial plane cleavage (slaty cleavage in metapelitic rocks). The intersection lineation (Ss/Sl) and the axes of minor folds trend cast-west, as do all mapable structures. Late deformations generated coarse crenulations, small chevrons and kink-bands, all intersecting the slaty cleavage at high angles. In medium- to high-grade areas no major folds have been observed. In these areas, the main foliation is a schistosity and is often folded, giving centimetric to decimetric, nearly isoclinal intrafolial folds. In schists, these folds aremuchmore common than inother lithologies, and can be associated with a crenulation cleavage. All these planar structures in high-grade rocks are roughly parallel. The late Hercynian deformational events, which gave rise to the crenulations and small chevrons, also produced large (often kilometric) open folds which fold the slaty cleavage and schistosity. As aconsequence, alternating belts with opposite dip (north and south) of the main foliation were formed. With respect to the Hercynian orogenic belt, the Paleozoic outcrops of the Catalonian Coastal Ranges are located within the northern branch of the Ibero-Armorican arc, and have a relatively frontal position within the belt. The Carboniferous of the Priorat-Prades area, together with other outcrops in the Castellón Province, the Montalbán massif (Iberian Chain) and the Cantabrian zone (specially the Pisuerga-Carrión Province) probably form part of a wide area of foreland Carboniferous deposition placed at the core of the arc.

Formation of disclinations line near a free nematic interface

We have studied the nucleation and the physical properties of a -1/2 wedge disclination line near the free surface of a confined nematic liquid crystal. The position of the disclination line has been related to the material parameters (elastic constants, anchoring energy, and favored anchoring angle of the molecules at the free surface). The use of a planar model for the structure of the director field (whose predictions have been contrasted to those of a fully three-dimensional model) has allowed us to relate the experimentally observed position of the disclination line to the relevant properties of the liquid crystals. In particular, we have been able to observe the collapse of the disclination line due to a temperature-induced anchoring-angle transition, which has allowed us to rule out the presence of a real disclination line near the nematic/isotropic front in directional growth experiments.

Silicon quantum dots embedded in a SiO2 matrix: From structural study to carrier transport properties

We study the details of electronic transport related to the atomistic structure of silicon quantum dots embedded in a silicon dioxide matrix using ab initio calculations of the density of states. Several structural and composition features of quantum dots (QDs), such as diameter and amorphization level, are studied and correlated with transport under transfer Hamiltonian formalism. The current is strongly dependent on the QD density of states and on the conduction gap, both dependent on the dot diameter. In particular, as size increases, the available states inside the QD increase, while the QD band gap decreases due to relaxation of quantum confinement. Both effects contribute to increasing the current with the dot size. Besides, valence band offset between the band edges of the QD and the silica, and conduction band offset in a minor grade, increases with the QD diameter up to the theoretical value corresponding to planar heterostructures, thus decreasing the tunneling transmission probability and hence the total current. We discuss the influence of these parameters on electron and hole transport, evidencing a correlation between the electron (hole) barrier value and the electron (hole) current, and obtaining a general enhancement of the electron (hole) transport for larger (smaller) QD. Finally, we show that crystalline and amorphous structures exhibit enhanced probability of hole and electron current, respectively.

Self-organization mechanisms for the formation on nearshore crescentic and transverse sand bars

The formation and development of transverse and crescentic sand bars in the coastal marine environment has been investigated by means of a nonlinear numerical model based on the shallow-water equations and on a simpli ed sediment transport parameterization. By assuming normally approaching waves and a saturated surf zone, rhythmic patterns develop from a planar slope where random perturbations of small amplitude have been superimposed. Two types of bedforms appear: one is a crescentic bar pattern centred around the breakpoint and the other, herein modelled for the rst time, is a transverse bar pattern. The feedback mechanism related to the formation and development of the patterns can be explained by coupling the water and sediment conservation equations. Basically, the waves stir up the sediment and keep it in suspension with a certain cross-shore distribution of depth-averaged concentration. Then, a current flowing with (against) the gradient of sediment concentration produces erosion (deposition). It is shown that inside the surf zone, these currents may occur due to the wave refraction and to the redistribution of wave breaking produced by the growing bedforms. Numerical simulations have been performed in order to understand the sensitivity of the pattern formation to the parameterization and to relate the hydro-morphodynamic input conditions to which of the patterns develops. It is suggested that crescentic bar growth would be favoured by high-energy conditions and ne sediment while transverse bars would grow for milder waves and coarser sediment. In intermediate conditions mixed patterns may occur.

On an asymptotic formula for the maximum voltage drop in a on-chip power distribution network

We present a new asymptotic formula for the maximum static voltage in a simplified model for on-chip power distribution networks of array bonded integrated circuits. In this model the voltage is the solution of a Poisson equation in an infinite planar domain whose boundary is an array of circular pads of radius ", and we deal with the singular limit Ɛ → 0 case. In comparison with approximations that appear in the electronic engineering literature, our formula is more complete since we have obtained terms up to order Ɛ15. A procedure will be presented to compute all the successive terms, which can be interpreted as using multipole solutions of equations involving spatial derivatives of functions. To deduce the formula we use the method of matched asymptotic expansions. Our results are completely analytical and we make an extensive use of special functions and of the Gauss constant G

Bacterial membrane injuries induced by lactacin F and nisin

The combined action of nisin and lactacin F, two bacteriocins produced by lactic acid bacteria, is additive. In this report, the basis of this effect is examined. Channels formed by lactacin F were studied by experiments using planar lipid bilayers, and bactericidal effects were analyzed by flow cytometry. Lactacin F produced pores with a conductance of 1 ns in black lipid bilayers in 1 mM KClat 10 mV at 20°C. Pore formation was strongly dependent on voltage. Although lactacin F formed pores at very low potential (10 mV), the dependence was exponentialabov e 40 mV. The injuries induced by nisin and lactacin F in the membranes of Lactobacillus helveticus produced different flow cytometric profiles. Probably, when both bacteriocins are present, each acts separately; their cooperation may be due to an increase in the number of single membrane injuries

Weierstrass integrability of differential equations

The integrability problem consists in finding the class of functions a first integral of a given planar polynomial differential system must belong to. We recall the characterization of systems which admit an elementary or Liouvillian first integral. We define {\it Weierstrass integrability} and we determine which Weierstrass integrable systems are Liouvillian integrable. Inside this new class of integrable systems there are non--Liouvillian integrable systems.

Cyclicity versus center problem

We prove that there are one-parameter families of planar differential equations for which the center problem has a trivial solution and on the other hand the cyclicity of the weak focus is arbitrarily high. We illustrate this phenomenon in several examples for which this cyclicity is computed.

A survey on the inverse integrating factor

The relation between limit cycles of planar differential systems and the inverse integrating factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From that moment on, many research articles are devoted to the study of the properties of the inverse integrating factor and its relationwith limit cycles and their bifurcations. This paper is a summary of all the results about this topic. We include a list of references together with the corresponding related results aiming at being as much exhaustive as possible. The paper is, nonetheless, self-contained in such a way that all the main results on the inverse integrating factor are stated and a complete overview of the subject is given. Each section contains a different issue to which the inverse integrating factor plays a role: the integrability problem, relation with Lie symmetries, the center problem, vanishing set of an inverse integrating factor, bifurcation of limit cycles from either a period annulus or from a monodromic ω-limit set and some generalizations.

From Full stopping to transparency in a holographic model of heavy ion collisions

We numerically simulate planar shock wave collisions in anti-de Sitter space as a model for heavy ion collisions of large nuclei. We uncover a crossover between two different dynamical regimes as a function of the collision energy. At low energies the shocks first stop and then explode in a manner approximately described by hydrodynamics, in close similarity with the Landau model. At high energies the receding fragments move outwards at the speed of light, with a region of negative energy density and negative longitudinal pressure trailing behind them. The rapidity distribution of the energy density at late times around midrapidity is not approximately boost invariant but Gaussian, albeit with a width that increases with the collision energy.