Quantitative comparison of simulations of seismic wave propagation in heterogeneous poro-elastic media involving fluid-solid interfaces and in equivalent visco-elastic solids

There is increasing evidence to suggest that the presence of mesoscopic heterogeneities constitutes the predominant attenuation mechanism at seismic frequencies. As a consequence, centimeter-scale perturbations of the subsurface physical properties should be taken into account for seismic modeling whenever detailed and accurate responses of the target structures are desired. This is, however, computationally prohibitive since extremely small grid spacings would be necessary. A convenient way to circumvent this problem is to use an upscaling procedure to replace the heterogeneous porous media by equivalent visco-elastic solids. In this work, we solve Biot's equations of motion to perform numerical simulations of seismic wave propagation through porous media containing mesoscopic heterogeneities. We then use an upscaling procedure to replace the heterogeneous poro-elastic regions by homogeneous equivalent visco-elastic solids and repeat the simulations using visco-elastic equations of motion. We find that, despite the equivalent attenuation behavior of the heterogeneous poro-elastic medium and the equivalent visco-elastic solid, the seismograms may differ due to diverging boundary conditions at fluid-solid interfaces, where there exist additional options for the poro-elastic case. In particular, we observe that the seismograms agree for closed-pore boundary conditions, but differ significantly for open-pore boundary conditions. This is an interesting result, which has potentially important implications for wave-equation-based algorithms in exploration geophysics involving fluid-solid interfaces, such as, for example, wave field decomposition.

Hydrologic Simulations of the Maquoketa River Watershed Using SWAT Working Paper 09-WP 49,June 2009

This paper describes the application of the Soil and Water Assessment Tool (SWAT) model to the Maquoketa River watershed, located in northeast Iowa. The inputs to the model were obtained from the Environmental Protection Agency’s geographic information/database system called Better Assessment Science Integrating Point and Nonpoint Sources (BASINS). Climatic data from six weather stations located in and around the watershed, and measured streamflow data from a U.S. Geological Survey gage station at the watershed outlet were used in the sensitivity analysis of SWAT model parameters as well as its calibration and validation for watershed hydrology and streamflow. A sensitivity analysis was performed using an influence coefficient method to evaluate surface runoff and base flow variations in response to changes in model input hydrologic parameters. The curve number, evaporation compensation factor, and soil available water capacity were found to be the most sensitive parameters among eight selected parameters when applying SWAT to the Maquoketa River watershed. Model calibration, facilitated by the sensitivity analysis, was performed for the period 1988 through 1993, and validation was performed for 1982 through 1987. The model performance was evaluated by well-established statistical methods and was found to explain at least 86% and 69% of the variability in the measured stream flow data for the calibration and validation periods, respectively. This initial hydrologic modeling analysis will facilitate future applications of SWAT to the Maquoketa River watershed for various watershed analysis, including water quality.

Simulations of action of DNA topoisomerases to investigate boundaries and shapes of spaces of knots.

The configuration space available to randomly cyclized polymers is divided into subspaces accessible to individual knot types. A phantom chain utilized in numerical simulations of polymers can explore all subspaces, whereas a real closed chain forming a figure-of-eight knot, for example, is confined to a subspace corresponding to this knot type only. One can conceptually compare the assembly of configuration spaces of various knot types to a complex foam where individual cells delimit the configuration space available to a given knot type. Neighboring cells in the foam harbor knots that can be converted into each other by just one intersegmental passage. Such a segment-segment passage occurring at the level of knotted configurations corresponds to a passage through the interface between neighboring cells in the foamy knot space. Using a DNA topoisomerase-inspired simulation approach we characterize here the effective interface area between neighboring knot spaces as well as the surface-to-volume ratio of individual knot spaces. These results provide a reference system required for better understanding mechanisms of action of various DNA topoisomerases.

Simulations in evolution. II. Relative fitness and the propagation of mutants.

In Neo-Darwinism, variation and natural selection are the two evolutionary mechanisms which propel biological evolution. Our previous article presented a histogram model [1] consisting in populations of individuals whose number changed under the influence of variation and/or fitness, the total population remaining constant. Individuals are classified into bins, and the content of each bin is calculated generation after generation by an Excel spreadsheet. Here, we apply the histogram model to a stable population with fitness F(1)=1.00 in which one or two fitter mutants emerge. In a first scenario, a single mutant emerged in the population whose fitness was greater than 1.00. The simulations ended when the original population was reduced to a single individual. The histogram model was validated by excellent agreement between its predictions and those of a classical continuous function (Eqn. 1) which predicts the number of generations needed for a favorable mutation to spread throughout a population. But in contrast to Eqn. 1, our histogram model is adaptable to more complex scenarios, as demonstrated here. In the second and third scenarios, the original population was present at time zero together with two mutants which differed from the original population by two higher and distinct fitness values. In the fourth scenario, the large original population was present at time zero together with one fitter mutant. After a number of generations, when the mutant offspring had multiplied, a second mutant was introduced whose fitness was even greater. The histogram model also allows Shannon entropy (SE) to be monitored continuously as the information content of the total population decreases or increases. The results of these simulations illustrate, in a graphically didactic manner, the influence of natural selection, operating through relative fitness, in the emergence and dominance of a fitter mutant.

Comparison between molecular dynamics abd Monte Carlo simulations of an ordering process in a binary alloy

Ordering in a binary alloy is studied by means of a molecular-dynamics (MD) algorithm which allows to reach the domain growth regime. Results are compared with Monte Carlo simulations using a realistic vacancy-atom (MC-VA) mechanism. At low temperatures fast growth with a dynamical exponent x>1/2 is found for MD and MC-VA. The study of a nonequilibrium ordering process with the two methods shows the importance of the nonhomogeneity of the excitations in the system for determining its macroscopic kinetics.

Decay of unstable states in the presence of colored noise and random initial conditions. II. Analog experiments and digital simulations

The decay of an unstable state under the influence of external colored noise has been studied by means of analog experiments and digital simulations. For both fixed and random initial conditions, the time evolution of the second moment ¿x2(t)¿ of the system variable was determined and then used to evaluate the nonlinear relaxation time. The results obtained are found to be in excellent agreement with the theoretical predictions of the immediately preceding paper [Casademunt, Jiménez-Aquino, and Sancho, Phys. Rev. A 40, 5905 (1989)].

Simulations of electrophoretic collisions of DNA knots with gel obstacles

Gel electrophoresis can be used to separate nicked circular DNA molecules of equal length but forming different knot types. At low electric fields, complex knots drift faster than simpler knots. However, at high electric field the opposite is the case and simpler knots migrate faster than more complex knots. Using Monte Carlo simulations we investigate the reasons of this reversal of relative order of electrophoretic mobility of DNA molecules forming different knot types. We observe that at high electric fields the simulated knotted molecules tend to hang over the gel fibres and require passing over a substantial energy barrier to slip over the impeding gel fibre. At low electric field the interactions of drifting molecules with the gel fibres are weak and there are no significant energy barriers that oppose the detachment of knotted molecules from transverse gel fibres.

Magnetic structure of Li2CuO2: From ab initio calculations to macroscopic simulations

The magnetic structure of the edge-sharing cuprate compound Li2CuO2 has been investigated with highly correlated ab initio electronic structure calculations. The first- and second-neighbor in-chain magnetic interactions are calculated to be 142 and -22 K, respectively. The ratio between the two parameters is smaller than suggested previously in the literature. The interchain interactions are antiferromagnetic in nature and of the order of a few K only. Monte Carlo simulations using the ab initio parameters to define the spin model Hamiltonian result in a Nel temperature in good agreement with experiment. Spin population analysis situates the magnetic moment on the copper and oxygen ions between the completely localized picture derived from experiment and the more delocalized picture based on local-density calculations.

Understanding and modulating the competitive surface-adsorption of proteins through coarse-grained molecular dynamics simulations

It is now well accepted that cellular responses to materials in a biological medium reflect greatly the adsorbed biomolecular layer, rather than the material itself. Here, we study by molecular dynamics simulations the competitive protein adsorption on a surface (Vroman effect), i.e. the non-monotonic behavior of the amount of protein adsorbed on a surface in contact with plasma as functions of contact time and plasma concentration. We find a complex behavior, with regimes during which small and large proteins are not necessarily competing between them, but are both competing with others in solution ("cooperative" adsorption). We show how the Vroman effect can be understood, controlled and inverted.

Simulations in Evolution. III. Randomness as a Generator of Opportunities.

In Neo-Darwinism, variation and natural selection are the two evolutionary mechanisms which propel biological evolution. Our previous reports presented a histogram model to simulate the evolution of populations of individuals classified into bins according to an unspecified, quantifiable phenotypic character, and whose number in each bin changed generation after generation under the influence of fitness, while the total population was maintained constant. The histogram model also allowed Shannon entropy (SE) to be monitored continuously as the information content of the total population decreased or increased. Here, a simple Perl (Practical Extraction and Reporting Language) application was developed to carry out these computations, with the critical feature of an added random factor in the percent of individuals whose offspring moved to a vicinal bin. The results of the simulations demonstrate that the random factor mimicking variation increased considerably the range of values covered by Shannon entropy, especially when the percentage of changed offspring was high. This increase in information content is interpreted as facilitated adaptability of the population.

Magnetic structure of Li2CuO2: From ab initio calculations to macroscopic simulations

The magnetic structure of the edge-sharing cuprate compound Li2CuO2 has been investigated with highly correlated ab initio electronic structure calculations. The first- and second-neighbor in-chain magnetic interactions are calculated to be 142 and -22 K, respectively. The ratio between the two parameters is smaller than suggested previously in the literature. The interchain interactions are antiferromagnetic in nature and of the order of a few K only. Monte Carlo simulations using the ab initio parameters to define the spin model Hamiltonian result in a Nel temperature in good agreement with experiment. Spin population analysis situates the magnetic moment on the copper and oxygen ions between the completely localized picture derived from experiment and the more delocalized picture based on local-density calculations.