Large Space Scales Research Articles

On the Time Splitting Spectral Method for the Complex Ginzburg–Landau Equation in the Large Time and Space Scale Limit

We are interested in the numerical approximation of the complex Ginzburg-Landau equation in the large time and space limit. There are two interesting regimes in this problem, one being the large space time limit, and one being the nonlinear Schrodinger limit. These limits have been studied analytically in, for example, T. Colin and A. Soyeur, Asymptot. Anal., 13 (1996), pp. 361-372; F. H. Lin, Comm. Pure Appl. Math., 51 (1998), pp. 385-441; F. H. Lin and J. X. Xin, Comm. Math. Phys., 200 (1999), pp. 249-274. We study a time splitting spectral method for this problem. In particular, we are interested in whether such a scheme is asymptotic preserving (AP) with respect to these two limits. Our results show that the scheme is AP for the first limit but not the second one. For the large space time limit, our numerical experiments show that the scheme can capture the correct physical behavior without resolving the small scale dynamics, even for transitional problems, where small and large scales coexist.

Hydrological consistency using multi-sensor remote sensing data for water and energy cycle studies

A multi-sensor/multi-platform approach to water and energy cycle prediction is demonstrated in an effort to understand the variability and feedback of land surface and atmospheric processes over large space and time scales. Remote sensing-based variables including soil moisture (from AMSR-E), surface heat fluxes (from MODIS) and precipitation rates (from TRMM) are combined with North American Regional Reanalysis derived atmospheric components to examine the degree of hydrological consistency throughout these diverse and independent hydrologic data sets. The study focuses on the influence of the North American Monsoon System (NAMS) over the southwestern United States, and is timed to coincide with the SMEX04 North American Monsoon Experiment (NAME). The study is focused over the Arizona portion of the NAME domain to assist in better characterizing the hydrometeorological processes occurring across Arizona during the summer monsoon period. Results demonstrate that this multi-sensor approach, in combination with available atmospheric observations, can be used to obtain a comprehensive and hydrometeorologically consistent characterization of the land surface water cycle, leading to an improved understanding of water and energy cycles within the NAME region and providing a novel framework for future remote observation and analysis of the coupled land surface–atmosphere system.

Complexity in a cellular model of river avulsion

We propose a new model of river avulsion that emphasizes simplicity, self-organization, and unprogrammed behavior rather than detailed simulation. The model runs on a fixed cellular grid and tracks two elevations in each cell, a high elevation representing the channel (levee) top and a low one representing the channel bottom. The channel aggrades in place until a superelevation threshold for avulsion is met. After an avulsion is triggered a new flow path is selected by steepest descent based on the low values of elevation. Flow path depends sensitively on floodplain topography, particularly the presence of former abandoned channels. Several behavioral characteristics emerge consistently from this simple model: (1) a tendency of the active flow to switch among a small number of channel paths, which we term the active channel set, over extended periods, leading to clustering and formation of multistory sand bodies in the resulting deposits; (2) a tendency for avulsed channels to return to their previous paths, so that new channel length tends to be generated in relatively short segments; and (3) avulsion-related sediment storage and release, leading to pulsed sediment output even for constant input. Each of these behaviors is consistent with observations from depositional river systems. A single-valued threshold produces a wide variety of avulsion sizes and styles. Larger “nodal” avulsions are rarer because pre-existing floodplain topography acts to steer flow back to the active channel. Channel stacking pattern is very sensitive to floodplain deposition. This work highlights the need to develop models of floodplain evolution at large time and space scales to complement the improving models of river channel evolution.

Forcing a three‐dimensional, hydrostatic, primitive‐equation model for application in the surf zone: 1. Formulation

An Eulerian analysis for wave forcing of three‐dimensional (3D) wave‐averaged mean circulation in the surf zone is presented. The objective is to develop a dynamically consistent formulation for applications in a 3D primitive equation model. The analysis is carried out for the case of shallow‐water linear waves interacting with wave‐averaged depth‐independent horizontal currents that vary on larger space scales and timescales. Variations in wave properties are governed by a wave action equation that includes wave‐current interactions and dissipation representative of wave breaking. Wave forcing of the mean currents consists of a surface stress and a body force. The surface stress is proportional to the wave energy dissipation. The body force includes one term that is related to gradients of part of the radiation stress tensor and a second term that is related to the vortex force and is proportional to a product of the mean wave momentum and the vertical component of the mean vorticity vector. In addition, there is a nonzero normal velocity at the mean surface that arises from the divergence of the mean Eulerian wave mass flux. This velocity results in an additional momentum flux forcing of the mean flow. Applications of this formulation to the DUCK94 field experiment are presented in part 2.

Characterization of local calcium signals in tubular networks of endoplasmic reticulum

To explain the large time and space scales of elementary calcium events in Xenopus oocytes it is assumed that the Ca 2+ source is located on tubules of the endoplasmic reticulum, which provide local barriers for diffusion. The event duration, width and signal mass dependence on the total quantity of released Ca 2+ is determined at different orientations of the scan line and different ionic currents. Excellent agreement with published data is obtained with on- and off-rate constants of the fluorescent indicator of 15 μM −1 s −1 and 2.55 s −1, respectively. It is found that one signal mass unit, calculated with the classical method that assumes spherical symmetry of the cytosolic space surrounding the release site, corresponds to 0.189 fC of released Ca 2+ in the presence of a tubular network. It is estimated that release Ca 2+ currents and amounts are randomly distributed, with averages of 0.165 pA and 3.66 fC per event and average release duration of 22.2 ms. The total quantity of liberated Ca 2+ and the release current amplitude in the presence of endoplasmic reticulum tubules is predicted to be about one order of magnitude lower than estimated within the isotropic diffusion formalism. This could have implications in muscle cell Ca 2+ imaging as well.

Dispersal of Amazonian birds in continuous and fragmented forest

Many ecologists believe birds disappear from tropical forest fragments because they are poor dispersers. We test this idea using a spatially explicit capture data base from the Biological Dynamics of Forest Fragments Project near Manaus, Brazil. We measure bird movements directly, over relatively large scales of space and time, both before and after landscape fragmentation. We found that species which disappear from fragments move extensively between plots before isolation, but not after, and often disperse to longer distances in continuous forest than in fragmented forest. Such species also preferentially emigrate from smaller to larger fragments, showing no preference in continuous forest. In contrast, species that persist in fragments are generally less mobile, do not cross gaps as often, yet disperse further after fragmentation than before. 'Heavy tailed' probability models usually explain dispersal kernels better than exponential or Gaussian models, suggesting tropical forest birds may be better dispersers than assumed with some individuals moving very long distances.

LINEAR SUPERPOSITION IN NONLINEAR WAVE DYNAMICS

We study nonlinear dispersive wave systems described by hyperbolic PDE's in ℝdand difference equations on the lattice ℤd. The systems involve two small parameters: one is the ratio of the slow and the fast time scales, and another one is the ratio of the small and the large space scales. We show that a wide class of such systems, including nonlinear Schrodinger and Maxwell equations, Fermi–Pasta–Ulam model and many other not completely integrable systems, satisfy a superposition principle. The principle essentially states that if a nonlinear evolution of a wave starts initially as a sum of generic wavepackets (defined as almost monochromatic waves), then this wave with a high accuracy remains a sum of separate wavepacket waves undergoing independent nonlinear evolution. The time intervals for which the evolution is considered are long enough to observe fully-developed nonlinear phenomena for involved wavepackets. In particular, our approach provides a simple justification for numerically observed effect of almost non-interaction of solitons passing through each other without any recourse to the complete integrability. Our analysis does not rely on any ansatz or common asymptotic expansions with respect to the two small parameters but it uses rather explicit and constructive representation for solutions as functions of the initial data in the form of functional analytic series.

Identification of a stratigraphic model with seismic constraints

Stratigraphic models are used in oil exploration in order to determine the geometry of sedimentary layers and to characterize the geological properties of the sediments. They simulate the infill of a sedimentary basin at large scales of space and time, governed by the interaction of accommodation change, sediment supply and sediment transport. One of the main difficulties in the use of such models is that all their input parameters have to be identified to fit well-log and seismic data. A basic issue is to compute the rate of accommodation change in order to fit the sediment thicknesses measured between each successive seismic marker. This leads to the solution to an inverse problem for which existence is proved in the single lithology case. Numerical algorithms are proposed and studied based on the construction of a reduced model and Newton–Krylov methods.

A phase-field simulation of austenite to ferrite transformation kinetics in low carbon steels

A new phase field model has been developed which can simulate the austenite to ferrite (γ → α) transformation in low carbon steels at large space and time scales and involving multiple ferrite grain growth. The two-dimensional phase-field simulation shows that interface composition does not obey the local equilibrium assumption, while grain growth obeys a parabolic law for most of the transformation. The kinetics of continuous cooling transformation are successfully modelled. Results suggest that nucleation occurs both along austenite grain boundaries and within grains for high cooling rate transformations. Grain coarsening behind the transformation front is predicted. Two interesting phenomena, namely, interface acceleration, and solute enrichment behind the impingement fronts, are disclosed via this phase-field simulation.

A robust unstructured grid discretization for 3-dimensional hydrostatic flows in spherical geometry: A new numerical structure for ocean general circulation modeling

Current models of the general circulation of the global oceans employ a spatial discretization of the relevant hydrodynamic fields on Cartesian rectilinear grids. For many applications, significant benefit would be expected to accrue from the versatility offered by unstructured grids. However, until very recently, available numerical methods for performing integrations on unstructured grids could not conserve discrete dynamical invariants, a numerical model characteristic that is important for robust ocean simulations over large space and time scales (as needed, for instance, in climate modeling applications). Our purpose in this paper is to describe such a conservative discretization scheme for rotating hydrostatic Boussinesq fluid dynamics on general triangular tessellations of the sphere, and to demonstrate its properties in a number of simulations that incorporate realistic ocean basin geometry. Several different implicit time discretizations are possible, each of which exhibits a form of exact numerical energy conservation in the absence of dissipation. The properties of this new numerical methodology are validated through analysis of a sequence of unforced nonlinear dynamical problems, which clearly demonstrate the capacity of the model to resolve the geostrophic adjustment process and the onset of baroclinic instability in collapsing density fronts. As a final test, a number of ocean modeling experiments with realistic climatological and wind-stress forcing are performed in order to investigate the manner in which different mesh structures and resolutions influence the simulated phenomenology. As the theoretical properties of the numerical methodology suggest, it is thereby shown to be both robust and stable. The further work that will be required to implement this structure in a state-of-the-art oceanic general circulation model, as well as other potential applications of the techniques, are discussed in the concluding section of the paper.

Numerical Simulation of Tripolar Vortex in Dusty Plasma with Sheared Flow and Sheared Magnetic Field

This article presents a study we have made of one class of coherent structures of the tripolar vortex. Considering the sheared flow and sheared magnetic field which are common in the thermonuclear plasma and space plasma, we have simulated the dynamics of the tripolar vortex. The results show that the tripolar vortex is largely stable in most cases, but a strongly sheared magnetic field will make the structure less stable, and lead it to decays into single vortices with the large space scale. These results are consistent with findings from former research about the dipolar vortex.

Special Section on Multiscale Modeling in Materials and Life Sciences

This special section of Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, on multiscale modeling in life and materials sciences, is based on a summer program with the same theme, held August 4--30, 2003, at the Universita della Svizzera Italiana in Lugano, Switzerland, and organized by the ETH Zurich Computational Laboratory (CoLab). This workshop emphasized that multiscale modeling and simulation can serve as a commonscientific language enabling cross-fertilization across disciplines and the definition of new scientific frontiers. Materials science was one of the first disciplines that emphasized the need for novel multiscaling approaches bridging continuum and atomistic models. In life sciences, the rapid growth of the role played by computational methods has led to the early realization that a multiscaling approach is necessary to tackle inherently complex phenomena involving cells, organisms, and ecosystems. This summer program provided the opportunity to scientists from these different scientific fields to exchange ideas and to pursue research in an interdisciplinary fashion using multiscale computational methods as a common language. These interactions demonstrated that research in multiscaling is a fertile breeding ground for the development of novel powerful computational tools for domains where computing is established as a tool for scientific inquiry and for the dissemination of this know-how to disciplines for which computation is an emerging form of scientific investigation. This special section of MMS is a representative sample of theoretical and computational approaches to multiscale modeling and simulation in materials and life sciences. The papers discuss multiscale coupling of physical models and time/space multiresolution techniques. The problem of coupling models across space and time scales is a fundamental issue in multiscale modeling and simulation. Multiscale approaches often require the rigorous integration of diverse physical models, such as the case of blood flow in the circulatory system (Fernandez, Milisic}, and Quarteroni). The multiscale integration of diverse physical models in nanoscale magnetic systems involves the proper coupling of quantum effects in classical descriptions (Wessel, Trebst, and Troyer). Multiscale simulations of materials with heterogeneous properties are tackled using asymptotic expansions for the case of conducting inclusions embedded in a homogeneous matrix phase (Ben Hassen and Bonnetier). A broad class of multiscale problems involves the description of macroscale systems using only the information available by suitable microscopic models. This technique is demonstrated in simulating the evolution of parabolic homogenization problems with nonlinear reactions, using as a microscopic model a partial differential equation with rapidly oscillating coefficients (Samaey, Roose, and Kevrekidis). A related work extends this concept to problems with a wide separation in time scales. Using as an application a model of bacterial chemotaxis it is shown that projective time integration of coarse variables can be carried out in time scales that are long compared to those of the microscopic dynamics (Setayeshgar, Gear, Othmer, and Kevrekidis). In problems with time-dependent, large space scale variations a new class of multiresolution particle methods enhances their inherent adaptivity and presents an alternative to grid-based methods (Bergdorf, Cottet, and Koumoutsakos). Future research in multiscale modeling would continue to rely on synergies across disciplines for the development of novel computational methods, the integration of physical models, and the formulation of new challenges. This principle will continue to guide future workshops in multiscale modeling and simulations at the CoLab and, we believe, an ever-increasing number of scientific institutions. The editors in charge would like to credit, for their hard work and dedication, those editors who helped handle the peer-review process for papers submitted to this special section. Thanks to Emily Carter, Wolfgang Hackbusch, Robert Kohn, Hans Christian Ottinger, Olivier Pironneau, and John Willis. We also wish to thank SIAM Publications Manager Mitch Chernoff for his invaluable advice and help in preparing this section.

The study on density change of carbon dioxide seawater solution at high pressure and low temperature

It has been widely considered that the global warming, induced by the increasing concentration of carbon dioxide and other greenhouse gases in the atmosphere, is an environmental task affecting the world economic development. In order to mitigate the concentration of CO 2 in the atmosphere, the sequestration of carbon dioxide into the ocean had been investigated theoretically and experimentally over the last 10 years. In addition to ocean dynamics, ocean geological, and biological information on large space and long time scales, the physical-chemistry properties of seawater–carbon dioxide system at high pressure ( P>5.0 MPa) and lower temperature (274.15 K< T<280.15 K) (the deep ocean environment) is very important for both fundamental and engineering investigations. The density of carbon dioxide seawater solution is one of the key physical properties, which is an indispensable property for numerically estimating the dynamic evolution of carbon dioxide enriched seawater plume. In this study, the density of carbon dioxide seawater solution was measured by applying Mach-Zehnder Interferometry to a visible high-pressure vessel experimental system. The preliminary experimental results reveal that (1) the density of carbon dioxide seawater solution increases with the increase of mass fraction of carbon dioxide in its seawater solution at a pressure ranging from 4.0 to 12.0 MPa and temperatures of 276.15 and 283.15 K; (2) the density deference between carbon dioxide seawater solution and pure seawater is linearly proportional to the mass fraction of carbon dioxide and independent on pressure, temperature, and salinity; (3) the slope of this linear function of density deference with respect to carbon dioxide mass fraction is 0.273 g/cm 3, which is approximately same with that of carbon dioxide freshwater solution, the slope of which is 0.275 g/cm 3.

Behavior dominated by slow particles in a disordered asymmetric exclusion process

We study the large space and time scale behavior of a totally asymmetric, nearest-neighbor exclusion process in one dimension with random jump rates attached to the particles. When slow particles are sufficiently rare, the system has a phase transition. At low densities there are no equilibrium distributions, and on the hydrodynamic scale the initial profile is transported rigidly. We elaborate this situation further by finding the correct order of the correction from the hydrodynamic limit, together with distributional bounds averaged over the disorder. We consider two settings, a macroscopically constant low density profile and the outflow from a large jam.

Phytoplankton absorption, photosynthetic parameters, and primary production off Baja California: summer and autumn 1998

To estimate ocean primary production at large space and time scales, it is necessary to use models combined with ocean-color satellite data. Detailed estimates of primary production are typically done at only a few representative stations. To get survey-scale estimates of primary production, one must introduce routinely measured Chlorophyll-a (Chl-a) into models. For best precision, models should be based on accurate parameterizations developed from optical and photosynthesis data collected in the region of interest. To develop regional model parameterizations 14 Cbicarbonate was used to estimate in situ primary production and photosynthetic parameters ða � ; P �, and Ek) derived from photosynthesis–irradiance (P–E) experiments from IMECOCAL cruises to the southern California Current during July and October 1998. The P–E experiments were done for samples collected from the 50% surface light depth for which we also determined particle and phytoplankton absorption coefficients (ap, af, and a �Þ. *

Interpretation of environmental tracers in groundwater systems with stagnant water zones

Lumped-parameter models are commonly applied for determining the age of water from time records of transient environmental tracers. The simplest models (e.g. piston flow or exponential) are also applicable for dating based on the decay or accumulation of tracers in groundwater systems. The models are based on the assumption that the transit time distribution function (exit age distribution function) of the tracer particles in the investigated system adequately represents the distribution of flow lines and is described by a simple function. A chosen or fitted function (called the response function) describes the transit time distribution of a tracer which would be observed at the output (discharge area, spring, stream, or pumping wells) in the case of an instantaneous injection at the entrance (recharge area). Due to large space and time scales, response functions are not measurable in groundwater systems, therefore, functions known from other fields of science, mainly from chemical engineering, are usually used. The type of response function and the values of its parameters define the lumped-parameter model of a system. The main parameter is the mean transit time of tracer through the system, which under favourable conditions may represent the mean age of mobile water. The parameters of the model are found by fitting calculated concentrations to the experimental records of concentrations measured at the outlet. The mean transit time of tracer (often called the tracer age), whether equal to the mean age of water or not, serves in adequate combinations with other data for determining other useful parameters, e.g. the recharge rate or the content of water in the system. The transit time distribution and its mean value serve for confirmation or determination of the conceptual model of the system and/or estimation of its potential vulnerability to anthropogenic pollution. In the interpretation of environmental tracer data with the aid of the lumped-parameter models, the influence of diffusion exchange between mobile water and stagnant or quasi-stagnant water is seldom considered, though it leads to large differences between tracer and water ages. Therefore, the article is focused on the transit time distribution functions of the most common lumped-parameter models, particularly those applicable for the interpretation of environmental tracer data in double-porosity aquifers, or aquifers in which aquitard diffusion may play an important role. A case study is recalled for a confined aquifer in which the diffusion exchange with aquitard most probably strongly influenced the transport of environmental tracers. Another case study presented is related to the interpretation of environmental tracer data obtained from lysimeters installed in the unsaturated zone with a fraction of stagnant water.

Phase-field model of island growth in epitaxy.

Nucleation and growth of islands in epitaxy is simulated using a continuum phase-field model. In addition to local density of adatoms, a local phase-field variable, varying in the real space, is introduced to describe the epitaxial islands. Evolution of this phase field is determined by a time-dependent Ginzburg-Landau-like equation coupled to a diffusive transport equation of adatoms. When applied to nucleation and growth of islands in the submonolayer regime, this model reproduces both the scaling laws of island density and experimental size and spatial distributions of islands. For island growth in the multilayer regime, this phase-field model reproduces mound structures consistent with experimental images concerned. Accurate coarsening and roughening exponents of the mounds are obtained in this model. Compared with atomic models and mean-field models, this model can provide a fine visualized morphology of islands at large space and time scales of practical engineering interests.

The relationship between summer aggregation of fin whales and satellite-derived environmental conditions in the northwestern Mediterranean Sea

Few studies have tried to explain the summer distribution pattern of fin whales ( Balaenoptera physalus) in the northwestern Mediterranean Sea, an area characterized with heterogeneous and transient hydrobiological features. Satellite imagery was used to gain knowledge on primary biomass over large time and space scales and to process environmental variables of significance to the problem of fin whale distribution. Fin whale distribution was obtained from survey data and expressed into sightings per unit of effort. Net primary production (g C/m 2/day), NPP, can be estimated with a model by processing remote-sensed measurements of chlorophyll concentration, provided by SeaWIFS DAAC. NPP was integrated over different temporal scales, related to primary production cycles in the area. Additional variables were derived from sea surface temperature (AVHRR/NOAA sensors). Multiple cross-correlation coefficients were calculated between these environmental parameters and the fin whale summer distribution from 1998 to 2002. A predictive model, the potential grouping index, was developed from this statistical approach. This study improves our understanding of the variability of fin whale distribution in summer. While food availability at a particular time and place is a function of environmental conditions in the previous months, this study provides evidence that whales adapt their movements and group size directly to food availability rather than to instantaneous environmental conditions.

Bio[statistics]philia

Bio[statistics]philia

An introduction to the Farm‐Scale Evaluations of genetically modified herbicide‐tolerant crops

1. Several genetically modified herbicide-tolerant (GMHT) crops have cleared most of the regulatory hurdles required for commercial growing in the United Kingdom. However, concerns have been expressed that their management will have negative impacts on farmland biodiversity as a result of improved control given by the new herbicide regimes of the arable plants that support farmland birds and other species of conservation value. 2. The Farm-Scale Evaluations (FSE) project is testing the null hypothesis that there is no difference between the management of GMHT varieties of beet, oilseed rape and maize and that of comparable conventional varieties in their effect on the abundance and diversity of arable plants and invertebrates. The FSE also aims to estimate the magnitude and consider the implications of any differences that are found. 3. The experimental design of the FSE is a randomized block, with two treatments allocated at random to half-fields. The target sample is around 60-75 fields for each crop, selected to represent variation of geography and intensity of management across Britain. The experimental crops are managed by commercial farmers as if under commercial conditions. 4. Biodiversity indicators have been selected from plants and terrestrial invertebrates to identify differences between crop management regimes that may result in important ecological changes over larger scales of space and time. Field sampling is at fixed points, mainly along transects from the field boundary, starting before the crop is sown and continuing into following crops. 5. Synthesis and applications. The FSE is best considered as an investigation into the effects of contrasting crop management regimes on farmland biodiversity, rather than a study of the effects of genetic modification. It could become a model for future studies of ecological effects of the way we use and manage agricultural land.