Oscillatory wave fronts in chains of coupled nonlinear oscillators

Wave front pinning and propagation in damped chains of coupled oscillators are studied. There are two important thresholds for an applied constant stress $F$: for $|F|<F_{cd}$ (dynamic Peierls stress), wave fronts fail to propagate, for $F_{cd} < |F| < F_{cs}$ stable static and moving wave fronts coexist, and for $|F| > F_{cs}$ (static Peierls stress) there are only stable moving wave fronts. For piecewise linear models, extending an exact method of Atkinson and Cabrera's to chains with damped dynamics corroborates this description. For smooth nonlinearities, an approximate analytical description is found by means of the active point theory. Generically for small or zero damping, stable wave front profiles are non-monotone and become wavy (oscillatory) in one of their tails.Comment: 18 pages, 21 figures, 2 column revtex. To appear in Phys. Rev.

Effects of disorder on the wave front depinning transition in spatially discrete systems

Pinning and depinning of wave fronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators with nearest-neighbor coupling and subject to random external forces. The presence of weak randomness shrinks the pinning interval and it changes the critical exponent of the wave front depinning transition from 1/2 to 3/2. This effect is derived by means of a recent asymptotic theory of the depinning transition, extended to discrete drift-diffusion models of transport in semiconductor superlattices and confirmed by numerical calculations.Comment: 4 pages, 3 figures, to appear as a Rapid Commun. in Phys. Rev.

Nonlinear stability of oscillatory wave fronts in chains of coupled oscillators

We present a stability theory for kink propagation in chains of coupled oscillators and a new algorithm for the numerical study of kink dynamics. The numerical solutions are computed using an equivalent integral equation instead of a system of differential equations. This avoids uncertainty about the impact of artificial boundary conditions and discretization in time. Stability results also follow from the integral version. Stable kinks have a monotone leading edge and move with a velocity larger than a critical value which depends on the damping strength.Comment: 11 figure

Biodiesel Mandate Laws in Argentina and Brazil: An Estimation of Soybean Oil Foregone Export Revenues

Replaced with revised version of paper 02/22/08.Research and Development/Tech Change/Emerging Technologies,

Bayesian approach to inverse scattering with topological priors

We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field representing the objects. To construct the prior distribution we use a topological sensitivity analysis. We demonstrate the approach on the Bayesian solution of 2D inverse problems in light and acoustic holography with synthetic data. Statistical information on objects such as their center location, diameter size, orientation, as well as material properties, are extracted by sampling the posterior distribution. Assuming the number of objects known, comparison of the results obtained by Markov Chain Monte Carlo sampling and by sampling a Gaussian distribution found by linearization about the maximum a posteriori estimate show reasonable agreement. The latter procedure has low computational cost, which makes it an interesting tool for uncertainty studies in 3D. However, MCMC sampling provides a more complete picture of the posterior distribution and yields multi-modal posterior distributions for problems with larger measurement noise. When the number of objects is unknown, we devise a stochastic model selection framework.FEDER/MICINN - AEI grant MTM2017-84446-C2-1-

Use of resistivity measurements to detect urban caves in Mexico City and to assess the related hazard

International audienceIn the XIX century when Mexico City was much smaller than at present, there was non-regulated mining of building materials in a region of tuffs northwest of the city in an inhabited countryside. With the growth of the city during the XX century, this region was increasingly populated and in the 1970's many two-level bricks houses were built, without regard for underground caves created by the earlier extractions. Some ground sinkings in adjacent areas alarmed the residents who now are worried about this permanent hazard. An association of residents contracted a private company for a geophysical study in order to know the distribution of the caves. Resistivity measurements were taken in the area to detect the caves in order to alert city authorities. Resistivity data along most of the streets were collected with the array pole-dipole that consisted of three grounded electrodes. We performed 2-D dimensional inversions to the data in order to get a 2-D resistivity image of every street. This is similar to a resistivity cross-section of the ground but obtained from the inversion of pole-dipole and Schlumberger resistivity data simultaneously. Using the information of previous drills we modified our programming code in order to perform constrained inversion and to get more accurate resistivity models in agreement with the drills. From the resistivity models obtained for every street it was possible to produce a map which shows the horizontal distribution of the resistive bodies at a depth of 12m. These resistive bodies show coherent alignments that seem to correspond with a distributions of interconnected caves or tunnels used for extracting the sandy-tuffs. From these kind of interpretation method it was intended to get a more accurate horizontal distribution of the excavated areas in order to better know the urbanized area affected and lead the authorities to remedy the area with refill material

Dynamics of Coherent States in Regular and Chaotic Regimes of the Non-integrable Dicke Model

The quantum dynamics of initial coherent states is studied in the Dicke model and correlated with the dynamics, regular or chaotic, of their classical limit. Analytical expressions for the survival probability, i.e. the probability of finding the system in its initial state at time $t$, are provided in the regular regions of the model. The results for regular regimes are compared with those of the chaotic ones. It is found that initial coherent states in regular regions have a much longer equilibration time than those located in chaotic regions. The properties of the distributions for the initial coherent states in the Hamiltonian eigenbasis are also studied. It is found that for regular states the components with no negligible contribution are organized in sequences of energy levels distributed according to Gaussian functions. In the case of chaotic coherent states, the energy components do not have a simple structure and the number of participating energy levels is larger than in the regular cases.Comment: Contribution to the proceedings of the Escuela Latinoamericana de F\'isica (ELAF) Marcos Moshinsky 2017. (9 pages, 4 figures