Simulation of surface waves in porous media

We present a novel numerical algorithm for the simulation of seismic wave propagation in porous media, which is particularly suitable for the accurate modelling of surface wave-type phenomena. The differential equations of motion are based on Biot's theory of poro-elasticity and solved with a pseudospectral approach using Fourier and Chebyshev methods to compute the spatial derivatives along the horizontal and vertical directions, respectively. The time solver is a splitting algorithm that accounts for the stiffness of the differential equations. Due to the Chebyshev operator the grid spacing in the vertical direction is non-uniform and characterized by a denser spatial sampling in the vicinity of interfaces, which allows for a numerically stable and accurate evaluation of higher order surface wave modes. We stretch the grid in the vertical direction to increase the minimum grid spacing and reduce the computational cost. The free-surface boundary conditions are implemented with a characteristics approach, where the characteristic variables are evaluated at zero viscosity. The same procedure is used to model seismic wave propagation at the interface between a fluid and porous medium. In this case, each medium is represented by a different grid and the two grids are combined through a domain-decomposition method. This wavefield decomposition method accounts for the discontinuity of variables and is crucial for an accurate interface treatment. We simulate seismic wave propagation with open-pore and sealed-pore boundary conditions and verify the validity and accuracy of the algorithm by comparing the numerical simulations to analytical solutions based on zero viscosity obtained with the Cagniard-de Hoop method. Finally, we illustrate the suitability of our algorithm for more complex models of porous media involving viscous pore fluids and strongly heterogeneous distributions of the elastic and hydraulic material properties.

Interaction of Spiral Waves in the Complex Ginzburg-Landau Equation

Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered, and laws of motion for the centers are derived. The direction of the motion changes from along the line of centers to perpendicular to the line of centers as the separation increases, with the strength of the interaction algebraic at small separations and exponentially small at large separations. The corresponding asymptotic wave number and frequency are also determined, which evolve slowly as the spirals move

Wave-height hazard analysis in Eastern Coast of Spain : Bayesian approach using generalized Pareto distribution

Standard practice of wave-height hazard analysis often pays little attention to the uncertainty of assessed return periods and occurrence probabilities. This fact favors the opinion that, when large events happen, the hazard assessment should change accordingly. However, uncertainty of the hazard estimates is normally able to hide the effect of those large events. This is illustrated using data from the Mediterranean coast of Spain, where the last years have been extremely disastrous. Thus, it is possible to compare the hazard assessment based on data previous to those years with the analysis including them. With our approach, no significant change is detected when the statistical uncertainty is taken into account. The hazard analysis is carried out with a standard model. Time-occurrence of events is assumed Poisson distributed. The wave-height of each event is modelled as a random variable which upper tail follows a Generalized Pareto Distribution (GPD). Moreover, wave-heights are assumed independent from event to event and also independent of their occurrence in time. A threshold for excesses is assessed empirically. The other three parameters (Poisson rate, shape and scale parameters of GPD) are jointly estimated using Bayes' theorem. Prior distribution accounts for physical features of ocean waves in the Mediterranean sea and experience with these phenomena. Posterior distribution of the parameters allows to obtain posterior distributions of other derived parameters like occurrence probabilities and return periods. Predictives are also available. Computations are carried out using the program BGPE v2.0

Integro-difference equations for interacting species and the Neolithic transition

We introduce a set of sequential integro-difference equations to analyze the dynamics of two interacting species. Firstly, we derive the speed of the fronts when a species invades a space previously occupied by a second species, and check its validity by means of numerical random-walk simulations. As an example, we consider the Neolithic transition: the predictions of the model are consistent with the archaeological data for the front speed, provided that the interaction parameter is low enough. Secondly, an equation for the coexistence time between the invasive and the invaded populations is obtained for the first time. It agrees well with the simulations, is consistent with observations of the Neolithic transition, and makes it possible to estimate the value of the interaction parameter between the incoming and the indigenous populations

Fronts from integrodifference equations and persistence effects on the Neolithic transition

We extend a previous model of the Neolithic transition in Europe [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)] by taking two effects into account: (i) we do not use the diffusion approximation (which corresponds to second-order Taylor expansions), and (ii) we take proper care of the fact that parents do not migrate away from their children (we refer to this as a time-order effect, in the sense that it implies that children grow up with their parents, before they become adults and can survive and migrate). We also derive a time-ordered, second-order equation, which we call the sequential reaction-diffusion equation, and use it to show that effect (ii) is the most important one, and that both of them should in general be taken into account to derive accurate results. As an example, we consider the Neolithic transition: the model predictions agree with the observed front speed, and the corrections relative to previous models are important (up to 70%)

Biomass equations for European trees : addendum

Abstract

Seismic Wave Velocity as a Means of In-Place Density Measurement, Part 1, HR-114

Velocity-density tests conducted in the laboratory involved small 4-inch diameter by 4.58-inch-long compacted soil cylinders made up of 3 differing soil types and for varying degrees of density and moisture content, the latter being varied well beyond optimum moisture values. Seventeen specimens were tested, 9 with velocity determinations made along two elements of the cylinder, 180 degrees apart, and 8 along three elements, 120 degrees apart. Seismic energy was developed by blows of a small tack hammer on a 5/8-inch diameter steel ball placed at the center of the top of the cylinder, with the detector placed successively at four points spaced 1/2-inch apart on the side of the specimen involving wave travel paths varying from 3.36 inches to 4.66 inches in length. Time intervals were measured using a model 217 micro-seismic timer in both laboratory and field measurements. Forty blows of the hammer were required for each velocity determination, which amounted to 80 blows on 9 laboratory specimens and 120 blows on the remaining 8 cylinders. Thirty-five field tests were made over the three selected soil types, all fine-grained, using a 2-foot seismic line with hammer-impact points at 6-inch intervals. The small tack hammer and 5/8-inch steel ball was, again, used to develop seismic wave energy. Generally, the densities obtained from the velocity measurements were lower than those measured in the conventional field testing. Conclusions were reached that: (1) the method does not appear to be usable for measurement of density of essentially fine-grained soils when the moisture content greatly exceeds the optimum for compaction, and (2) due to a gradual reduction in velocity upon aging, apparently because of gradual absorption of pore water into the expandable interlayer region of the clay, the seismic test should be conducted immediately after soil compaction to obtain a meaningful velocity value.

P-wave velocities of samples from the Penninic of the western Alps along NFP20-west seismic-reflection profiles

Using the transit pulse method, we have determined compressional wave velocities of rocks from various geological units belonging to the Penninic zone along the NFP20-West profiles of the Swiss western Alps. The velocities have been measured at confining pressures up to 400 MPa, along three orthogonal axes defined by the macrostructure of the rocks. The samples analysed show a degree of metamorphism ranging from greenschist to eclogite facies. This collection includes schists, dolomites, gneisses and ophiolitic rocks. The mean velocities range from 5.9 km/s for a quartzitic calcschist to 7.9 km/s for an eclogitic metagabbro. The velocity anisotropy is as high as 20 %. The range of acoustic impedance is wide, from 15 to 27 10(6) kg/m2s. From these measurements, normal incident reflection coefficients for likely rock assemblages within and between geological units were estimated in order to interpret zone of the strong reflections recorded along the seismic profiles. Reflection coefficients as high as 0.17 could be determined.

General electromagnetic simulation tool to predict the microwave nonlinear response of planar, arbitrarily-shaped HTS structures

This work describes a simulation tool being developed at UPC to predict the microwave nonlinear behavior of planar superconducting structures with very few restrictions on the geometry of the planar layout. The software is intended to be applicable to most structures used in planar HTS circuits, including line, patch, and quasi-lumped microstrip resonators. The tool combines Method of Moments (MoM) algorithms for general electromagnetic simulation with Harmonic Balance algorithms to take into account the nonlinearities in the HTS material. The Method of Moments code is based on discretization of the Electric Field Integral Equation in Rao, Wilton and Glisson Basis Functions. The multilayer dyadic Green's function is used with Sommerfeld integral formulation. The Harmonic Balance algorithm has been adapted to this application where the nonlinearity is distributed and where compatibility with the MoM algorithm is required. Tests of the algorithm in TM010 disk resonators agree with closed-form equations for both the fundamental and third-order intermodulation currents. Simulations of hairpin resonators show good qualitative agreement with previously published results, but it is found that a finer meshing would be necessary to get correct quantitative results. Possible improvements are suggested.

Optical evidence for the proximity to a spin-density-wave metallic state in Na0.7CoO2

We present the optical properties of Na0.7CoO2 single crystals, measured over a broad spectral range as a function of temperature (T). The capability to cover the energy range from the far-infrared up to the ultraviolet allows us to perform reliable Kramers-Kronig transformation, in order to obtain the absorption spectrum (i.e., the complex optical conductivity). To the complex optical conductivity we apply the generalized Drude model, extracting the frequency dependence of the scattering rate (Gamma) and effective mass (m*) of the itinerant charge carriers. We find that Gamma(omega) at low temperatures and for similar to omega. This suggests that Na0.7CoO2 is at the verge of a spin-density-wave metallic phase.

T-wave alternans predicts mortality in a population undergoing a clinically indicated exercise test.

Eur Heart J. 2007 Oct;28(19):2332-7. Epub 2007 Jul 25.

Dynamical sectors of a relativistic two particle model

We reconsider a model of two relativistic particles interacting via a multiplicative potential, as an example of a simple dynamical system with sectors, or branches, with different dynamics and degrees of freedom. The presence or absence of sectors depends on the values of rest masses. Some aspects of the canonical quantization are described. The model could be interpreted as a bigravity model in one dimension.

Calculation of Activity Coefficients of Uni-Univalent Electrolytes by Equations Containing No Adjustable Parameters in Aqueous Solutions at 298.15 K

Normally either the Güntelberg or Davies equation is used to predict activity coefficients of electrolytes in dilute solutions when no better equation is available. The validity of these equations and, additionally, of the parameter-free equations used in the Bates-Guggenheim convention and in the Pitzerformalism for activity coefficients were tested with experimentally determined activity coefficients of HCl, HBr, HI, LiCl, NaCl, KCl, RbCl, CsCl, NH4Cl, LiBr,NaBr and KBr in aqueous solutions at 298.15 K. The experimental activity coefficients of these electrolytes can be usually reproduced within experimental errorby means of a two-parameter equation of the Hückel type. The best Hückel equations were also determined for all electrolytes considered. The data used in the calculations of this study cover almost all reliable galvanic cell results available in the literature for the electrolytes considered. The results of the calculations reveal that the parameter-free activity coefficient equations can only beused for very dilute electrolyte solutions in thermodynamic studies.