How to excite the internal modes of sine-Gordon solitons

We investigate the dynamics of the sine-Gordon solitons perturbed by spatiotemporal external forces. We prove the existence of internal (shape) modes of sine-Gordon solitons when they are in the presence of inhomogeneous space-dependent external forces, provided some conditions (for these forces) hold. Additional periodic time-dependent forces can sustain oscillations of the soliton width. We show that, in some cases, the internal mode even can become unstable, causing the soliton to decay in an antisoliton and two solitons. In general, in the presence of spatiotemporal forces the soliton behaves as a deformable (non-rigid) object. A soliton moving in an array of inhomogeneities can also present sustained oscillations of its width. There are very important phenomena (like the soliton-antisoliton collisions) where the existence of internal modes plays a crucial role. We show that, under some conditions, the dynamics of the soliton shape modes can be chaotic. A short report of some of our results has been published in [J. A. Gonzalez et al., Phys. Rev. E, 65 (2002) 065601(R)].Comment: 14 .eps figures.To appear in Chaos, Solitons and Fractal

Spatiotemporal chaotic dynamics of solitons with internal structure in the presence of finite-width inhomogeneities

We present an analytical and numerical study of the Klein-Gordon kink-soliton dynamics in inhomogeneous media. In particular, we study an external field that is almost constant for the whole system but that changes its sign at the center of coordinates and a localized impurity with finite-width. The soliton solution of the Klein-Gordon-like equations is usually treated as a structureless point-like particle. A richer dynamics is unveiled when the extended character of the soliton is taken into account. We show that interesting spatiotemporal phenomena appear when the structure of the soliton interacts with finite-width inhomogeneities. We solve an inverse problem in order to have external perturbations which are generic and topologically equivalent to well-known bifurcation models and such that the stability problem can be solved exactly. We also show the different quasiperiodic and chaotic motions the soliton undergoes as a time-dependent force pumps energy into the traslational mode of the kink and relate these dynamics with the excitation of the shape modes of the soliton.Comment: 10 pages Revtex style article, 22 gziped postscript figures and 5 jpg figure

Numerical test of the Cardy-Jacobsen conjecture in the site-diluted Potts model in three dimensions

We present a microcanonical Monte Carlo simulation of the site-diluted Potts model in three dimensions with eight internal states, partly carried out in the citizen supercomputer Ibercivis. Upon dilution, the pure model's first-order transition becomes of the second-order at a tricritical point. We compute accurately the critical exponents at the tricritical point. As expected from the Cardy-Jacobsen conjecture, they are compatible with their Random Field Ising Model counterpart. The conclusion is further reinforced by comparison with older data for the Potts model with four states.Comment: Final version. 9 pages, 9 figure

Three-dimensional numerical simulations of free convection in a layered porous enclosure

Three-dimensional numerical simulations are carried out for the study of free convection in a layered porous enclosure heated from below and cooled from the top. The system is defined as a cubic porous enclosure comprising three layers, of which the external ones share constant physical properties and the internal layer is allowed to vary in both permeability and thermal conductivity. The model is based on Darcy's law and the Boussinesq approximation. A parametric study to evaluate the sensitivity of the Nusselt number to a decrease in the permeability of the internal layer shows that strong permeability contrasts are required to observe an appreciable drop in the Nusselt number. If additionally the thickness of the internal layer is increased, a further decrease in the Nusselt number is observed as long as the convective modes remain the same, if the convective modes change the Nusselt number may increase. Decreasing the thermal conductivity of the middle layer causes first an increment in the Nusselt number and then a drop. On the other hand, the Nusselt number decreases in an approximately linear trend when the thermal conductivity of the layer is increased

Geothermal systems simulation: A case study

Geothermal reservoir simulation is a key step for developing sustainable and efficient strategies for the exploitation of geothermal resources. It is applied in the assessment of several areas of reservoir engineering, such as reservoir performance and re-injection programs, pressure decline in depletion, phase transition conditions, and natural evolution of hydrothermal convection systems. Fluid flow and heat transfer in rock masses, fluid-rock chemical interaction and rock mass deformation are some of the processes addressed in reservoir modelling. The case study of the Las Tres Virgenes (LTV) geothermal field (10 MWe), Baja California Sur, Mexico is presented. Three dimensional (3D) natural state simulations were carried out from emplacement and cooling of two spherical magma chambers using a conductive approach. A conceptual model of the volcanic system was developed on a lithostratigraphic and geochronological basis. Magma chamber volumes were established from eruptive volumes estimations. The thermophysical properties of the medium were assumed to correspond to the dominant rock in each lithological unit as an initial value, and further calibration was made considering histograms of experimentally obtained thermophysical properties of rocks. As the boundaries of the model lie far from the thermal anomaly, we assumed specified temperature boundaries. A Finite Volume (FV) numerical scheme was implemented in a Fortran 90 code to solve the heat equation. Static formation temperatures from well logs were used for validation of the numerical results. Good agreement was observed in those geothermal wells dominated by conductive heat transfer. For other wells, however, it is clear that conduction alone cannot explain observed behaviour, three-dimensional convective models are being implemented for future multiphysics simulations

Rings and arcs around evolved stars. II. The Carbon Star AFGL 3068 and the Planetary Nebulae NGC 6543, NGC 7009 and NGC 7027

We present a detailed comparative study of the arcs and fragmented ring-like features in the haloes of the planetary nebulae (PNe) NGC 6543, NGC 7009, and NGC 7027 and the spiral pattern around the carbon star AFGL 3068 using high-quality multi-epoch HST images. This comparison allows us to investigate the connection and possible evolution between the regular patterns surrounding AGB stars and the irregular concentric patterns around PNe. The radial proper motion of these features, ~15 km/s, are found to be consistent with the AGB wind and their linear sizes and inter-lapse times (500-1900 yr) also agree with those found around AGB stars, suggesting a common origin. We find evidence using radiative-hydrodynamic simulations that regular patterns produced at the end of the AGB phase become highly distorted by their interactions with the expanding PN and the anisotropic illumination and ionization patterns caused by shadow instabilities. These processes will disrupt the regular (mostly spiral) patterns around AGB stars, plausibly becoming the arcs and fragmented rings observed in the haloes of PNe.Comment: 13 pages, 9 figures, accepted for publication in MNRA