Structural, electronic and magnetic properties of LaCr2Si2C: Ab initio calculation, mean field approximation and Monte-Carlo simulation

NASA Astrophysics Data System (ADS)

Endichi, A.; Zaari, H.; Benyoussef, A.; El Kenz, A.

2018-06-01

The magnetic behavior of LaCr2Si2C compound is investigated in this work, using first principle methods, Monte Carlo simulation (MCS) and mean field approximation (MFA). The structural, electronic and magnetic properties are described using ab initio method in the framework of the Generalized Gradient Approximation (GGA), and the Full Potential-Linearized Augmented Plane Wave (FP-LAPW) method implemented in the WIEN2K packages. We have also computed the coupling terms between magnetic atoms which are used in Hamiltonian model. A theoretical study realized by mean field approximation and Monte Carlo Simulation within the Ising model is used to more understand the magnetic properties of this compound. Thereby, our results showed a ferromagnetic ordering of the Cr magnetic moments below the Curie temperature of 30 K (Tc < 30 K) in LaCr2Si2C. Other parameters are also computed as: the magnetization, the energy, the specific heat and the susceptibility. This material shows the small sign of supra-conductivity; and future researches could be focused to enhance the transport and magnetic properties of this system.

Comparing methods for modelling spreading cell fronts.

PubMed

Markham, Deborah C; Simpson, Matthew J; Maini, Philip K; Gaffney, Eamonn A; Baker, Ruth E

2014-07-21

Spreading cell fronts play an essential role in many physiological processes. Classically, models of this process are based on the Fisher-Kolmogorov equation; however, such continuum representations are not always suitable as they do not explicitly represent behaviour at the level of individual cells. Additionally, many models examine only the large time asymptotic behaviour, where a travelling wave front with a constant speed has been established. Many experiments, such as a scratch assay, never display this asymptotic behaviour, and in these cases the transient behaviour must be taken into account. We examine the transient and the asymptotic behaviour of moving cell fronts using techniques that go beyond the continuum approximation via a volume-excluding birth-migration process on a regular one-dimensional lattice. We approximate the averaged discrete results using three methods: (i) mean-field, (ii) pair-wise, and (iii) one-hole approximations. We discuss the performance of these methods, in comparison to the averaged discrete results, for a range of parameter space, examining both the transient and asymptotic behaviours. The one-hole approximation, based on techniques from statistical physics, is not capable of predicting transient behaviour but provides excellent agreement with the asymptotic behaviour of the averaged discrete results, provided that cells are proliferating fast enough relative to their rate of migration. The mean-field and pair-wise approximations give indistinguishable asymptotic results, which agree with the averaged discrete results when cells are migrating much more rapidly than they are proliferating. The pair-wise approximation performs better in the transient region than does the mean-field, despite having the same asymptotic behaviour. Our results show that each approximation only works in specific situations, thus we must be careful to use a suitable approximation for a given system, otherwise inaccurate predictions could be made. Copyright © 2014 Elsevier Ltd. All rights reserved.

Thermodynamic States of the Mixed Spin 1/2 and Spin 1 Hexagonal Nanowire System Obtained from a Seven-Site Cluster Within an Improved Mean Field Approximation

NASA Astrophysics Data System (ADS)

Mendes, R. G. B.; Barreto, F. C. Sá; Santos, J. P.

2018-04-01

The mean field approximation results in the mixedspin 1/2 Ising model and spin 1 Blume-Capel model, in the hexagonal nanowire system, are obtained from the Bogoliubov inequality. The Gibbs free energy, magnetization, and critical frontiers are obtained. Besides the stable branches of the order parameters, we obtain the metastable and unstable parts of these curves and also find phase transitions of the metastable branches of the order parameters. The classification of the stable, metastable, and unstable states is made by comparing the free energy values of these states.

Mean-field approximation for spacing distribution functions in classical systems

NASA Astrophysics Data System (ADS)

González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.

2012-01-01

We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.

Modulated phases in a three-dimensional Maier-Saupe model with competing interactions

NASA Astrophysics Data System (ADS)

Bienzobaz, P. F.; Xu, Na; Sandvik, Anders W.

2017-07-01

This work is dedicated to the study of the discrete version of the Maier-Saupe model in the presence of competing interactions. The competition between interactions favoring different orientational ordering produces a rich phase diagram including modulated phases. Using a mean-field approach and Monte Carlo simulations, we show that the proposed model exhibits isotropic and nematic phases and also a series of modulated phases that meet at a multicritical point, a Lifshitz point. Though the Monte Carlo and mean-field phase diagrams show some quantitative disagreements, the Monte Carlo simulations corroborate the general behavior found within the mean-field approximation.

The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect

NASA Astrophysics Data System (ADS)

Archer, Andrew J.; Chacko, Blesson; Evans, Robert

2017-07-01

In classical density functional theory (DFT), the part of the Helmholtz free energy functional arising from attractive inter-particle interactions is often treated in a mean-field or van der Waals approximation. On the face of it, this is a somewhat crude treatment as the resulting functional generates the simple random phase approximation (RPA) for the bulk fluid pair direct correlation function. We explain why using standard mean-field DFT to describe inhomogeneous fluid structure and thermodynamics is more accurate than one might expect based on this observation. By considering the pair correlation function g(x) and structure factor S(k) of a one-dimensional model fluid, for which exact results are available, we show that the mean-field DFT, employed within the test-particle procedure, yields results much superior to those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that one should not judge the quality of a DFT based solely on the approximation it generates for the bulk pair direct correlation function.

Mean-field approximation for spacing distribution functions in classical systems.

PubMed

González, Diego Luis; Pimpinelli, Alberto; Einstein, T L

2012-01-01

We propose a mean-field method to calculate approximately the spacing distribution functions p((n))(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p((n))(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed. © 2012 American Physical Society

Accounting for crustal magnetization in models of the core magnetic field

NASA Technical Reports Server (NTRS)

Jackson, Andrew

1990-01-01

The problem of determining the magnetic field originating in the earth's core in the presence of remanent and induced magnetization is considered. The effect of remanent magnetization in the crust on satellite measurements of the core magnetic field is investigated. The crust as a zero-mean stationary Gaussian random process is modelled using an idea proposed by Parker (1988). It is shown that the matrix of second-order statistics is proportional to the Gram matrix, which depends only on the inner-products of the appropriate Green's functions, and that at a typical satellite altitude of 400 km the data are correlated out to an angular separation of approximately 15 deg. Accurate and efficient means of calculating the matrix elements are given. It is shown that the variance of measurements of the radial component of a magnetic field due to the crust is expected to be approximately twice that in horizontal components.

Simple Scaling of Mulit-Stream Jet Plumes for Aeroacoustic Modeling

NASA Technical Reports Server (NTRS)

Bridges, James

2016-01-01

When creating simplified, semi-empirical models for the noise of simple single-stream jets near surfaces it has proven useful to be able to generalize the geometry of the jet plume. Having a model that collapses the mean and turbulent velocity fields for a range of flows allows the problem to become one of relating the normalized jet field and the surface. However, most jet flows of practical interest involve jets of two or more coannular flows for which standard models for the plume geometry do not exist. The present paper describes one attempt to relate the mean and turbulent velocity fields of multi-stream jets to that of an equivalent single-stream jet. The normalization of single-stream jets is briefly reviewed, from the functional form of the flow model to the results of the modeling. Next, PIV data from a number of multi-stream jets is analyzed in a similar fashion. The results of several single-stream approximations of the multi-stream jet plume are demonstrated, with a best approximation determined and the shortcomings of the model highlighted.

Simple Scaling of Multi-Stream Jet Plumes for Aeroacoustic Modeling

NASA Technical Reports Server (NTRS)

Bridges, James

2015-01-01

When creating simplified, semi-empirical models for the noise of simple single-stream jets near surfaces it has proven useful to be able to generalize the geometry of the jet plume. Having a model that collapses the mean and turbulent velocity fields for a range of flows allows the problem to become one of relating the normalized jet field and the surface. However, most jet flows of practical interest involve jets of two or more co-annular flows for which standard models for the plume geometry do not exist. The present paper describes one attempt to relate the mean and turbulent velocity fields of multi-stream jets to that of an equivalent single-stream jet. The normalization of single-stream jets is briefly reviewed, from the functional form of the flow model to the results of the modeling. Next, PIV (Particle Image Velocimetry) data from a number of multi-stream jets is analyzed in a similar fashion. The results of several single-stream approximations of the multi-stream jet plume are demonstrated, with a 'best' approximation determined and the shortcomings of the model highlighted.

Metastates in Mean-Field Models with Random External Fields Generated by Markov Chains

NASA Astrophysics Data System (ADS)

Formentin, M.; Külske, C.; Reichenbachs, A.

2012-01-01

We extend the construction by Külske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are a sample of an external ergodic Markov chain in equilibrium. We show that for non-degenerate Markov chains, the structure of the theorems is analogous to the case of i.i.d. variables when the limiting weights in the metastate are expressed with the aid of a CLT for the occupation time measure of the chain. As a new phenomenon we also show in a Potts example that for a degenerate non-reversible chain this CLT approximation is not enough, and that the metastate can have less symmetry than the symmetry of the interaction and a Gaussian approximation of disorder fluctuations would suggest.

Simulations of sooting turbulent jet flames using a hybrid flamelet/stochastic Eulerian field method

NASA Astrophysics Data System (ADS)

Consalvi, Jean-Louis; Nmira, Fatiha; Burot, Daria

2016-03-01

The stochastic Eulerian field method is applied to simulate 12 turbulent C1-C3 hydrocarbon jet diffusion flames covering a wide range of Reynolds numbers and fuel sooting propensities. The joint scalar probability density function (PDF) is a function of the mixture fraction, enthalpy defect, scalar dissipation rate and representative soot properties. Soot production is modelled by a semi-empirical acetylene/benzene-based soot model. Spectral gas and soot radiation is modelled using a wide-band correlated-k model. Emission turbulent radiation interactions (TRIs) are taken into account by means of the PDF method, whereas absorption TRIs are modelled using the optically thin fluctuation approximation. Model predictions are found to be in reasonable agreement with experimental data in terms of flame structure, soot quantities and radiative loss. Mean soot volume fractions are predicted within a factor of two of the experiments whereas radiant fractions and peaks of wall radiative fluxes are within 20%. The study also aims to assess approximate radiative models, namely the optically thin approximation (OTA) and grey medium approximation. These approximations affect significantly the radiative loss and should be avoided if accurate predictions of the radiative flux are desired. At atmospheric pressure, the relative errors that they produced on the peaks of temperature and soot volume fraction are within both experimental and model uncertainties. However, these discrepancies are found to increase with pressure, suggesting that spectral models describing properly the self-absorption should be considered at over-atmospheric pressure.

Critical phenomena in active matter

NASA Astrophysics Data System (ADS)

Paoluzzi, M.; Maggi, C.; Marini Bettolo Marconi, U.; Gnan, N.

2016-11-01

We investigate the effect of self-propulsion on a mean-field order-disorder transition. Starting from a φ4 scalar field theory subject to an exponentially correlated noise, we exploit the unified colored-noise approximation to map the nonequilibrium active dynamics onto an effective equilibrium one. This allows us to follow the evolution of the second-order critical point as a function of the noise parameters: the correlation time τ and the noise strength D . Our results suggest that the universality class of the model remains unchanged. We also estimate the effect of Gaussian fluctuations on the mean-field approximation finding an Ornstein-Zernike-like expression for the static structure factor at long wavelengths. Finally, to assess the validity of our predictions, we compare the mean-field theoretical results with numerical simulations of active Lennard-Jones particles in two and three dimensions, finding good qualitative agreement at small τ values.

Three-dimensional vortex-bright solitons in a spin-orbit-coupled spin-1 condensate

NASA Astrophysics Data System (ADS)

Gautam, Sandeep; Adhikari, S. K.

2018-01-01

We demonstrate stable and metastable vortex-bright solitons in a three-dimensional spin-orbit-coupled three-component hyperfine spin-1 Bose-Einstein condensate (BEC) using numerical solution and variational approximation of a mean-field model. The spin-orbit coupling provides attraction to form vortex-bright solitons in both attractive and repulsive spinor BECs. The ground state of these vortex-bright solitons is axially symmetric for weak polar interaction. For a sufficiently strong ferromagnetic interaction, we observe the emergence of a fully asymmetric vortex-bright soliton as the ground state. We also numerically investigate moving solitons. The present mean-field model is not Galilean invariant, and we use a Galilean-transformed mean-field model for generating the moving solitons.

The timing and targeting of treatment in influenza pandemics influences the emergence of resistance in structured populations.

PubMed

Althouse, Benjamin M; Patterson-Lomba, Oscar; Goerg, Georg M; Hébert-Dufresne, Laurent

2013-01-01

Antiviral resistance in influenza is rampant and has the possibility of causing major morbidity and mortality. Previous models have identified treatment regimes to minimize total infections and keep resistance low. However, the bulk of these studies have ignored stochasticity and heterogeneous contact structures. Here we develop a network model of influenza transmission with treatment and resistance, and present both standard mean-field approximations as well as simulated dynamics. We find differences in the final epidemic sizes for identical transmission parameters (bistability) leading to different optimal treatment timing depending on the number initially infected. We also find, contrary to previous results, that treatment targeted by number of contacts per individual (node degree) gives rise to more resistance at lower levels of treatment than non-targeted treatment. Finally we highlight important differences between the two methods of analysis (mean-field versus stochastic simulations), and show where traditional mean-field approximations fail. Our results have important implications not only for the timing and distribution of influenza chemotherapy, but also for mathematical epidemiological modeling in general. Antiviral resistance in influenza may carry large consequences for pandemic mitigation efforts, and models ignoring contact heterogeneity and stochasticity may provide misleading policy recommendations.

Coalescing colony model: Mean-field, scaling, and geometry

NASA Astrophysics Data System (ADS)

Carra, Giulia; Mallick, Kirone; Barthelemy, Marc

2017-12-01

We analyze the coalescing model where a `primary' colony grows and randomly emits secondary colonies that spread and eventually coalesce with it. This model describes population proliferation in theoretical ecology, tumor growth, and is also of great interest for modeling urban sprawl. Assuming the primary colony to be always circular of radius r (t ) and the emission rate proportional to r (t) θ , where θ >0 , we derive the mean-field equations governing the dynamics of the primary colony, calculate the scaling exponents versus θ , and compare our results with numerical simulations. We then critically test the validity of the circular approximation for the colony shape and show that it is sound for a constant emission rate (θ =0 ). However, when the emission rate is proportional to the perimeter, the circular approximation breaks down and the roughness of the primary colony cannot be discarded, thus modifying the scaling exponents.

Class of cooperative stochastic models: Exact and approximate solutions, simulations, and experiments using ionic self-assembly of nanoparticles.

PubMed

Mazilu, I; Mazilu, D A; Melkerson, R E; Hall-Mejia, E; Beck, G J; Nshimyumukiza, S; da Fonseca, Carlos M

2016-03-01

We present exact and approximate results for a class of cooperative sequential adsorption models using matrix theory, mean-field theory, and computer simulations. We validate our models with two customized experiments using ionically self-assembled nanoparticles on glass slides. We also address the limitations of our models and their range of applicability. The exact results obtained using matrix theory can be applied to a variety of two-state systems with cooperative effects.

A model of geomagnetic secular variation for 1980-1983

USGS Publications Warehouse

Peddie, N.W.; Zunde, A.K.

1987-01-01

We developed an updated model of the secular variation of the main geomagnetic field during 1980 through 1983 based on annual mean values for that interval from 148 worldwide magnetic observatories. The model consists of a series of 80 spherical harmonics, up to and including those of degree and order 8. We used it to form a proposal for the 1985 revision of the International Geomagnetic Reference Field (IGRF). Comparison of the new model, whose mean epoch is approximately 1982.0, with the Provisional Geomagnetic Reference Field for 1975-1980 (PGRF 1975), indicates that the moment of the centered-dipole part of the geomagnetic field is now decreasing faster than it was 5 years ago. The rate (in field units) indicated by PGRF 1975 was about -25 nT a-1, while for the new model it is -28 nT a-1. ?? 1987.

Bifurcations in models of a society of reasonable contrarians and conformists

NASA Astrophysics Data System (ADS)

Bagnoli, Franco; Rechtman, Raúl

2015-10-01

We study models of a society composed of a mixture of conformist and reasonable contrarian agents that at any instant hold one of two opinions. Conformists tend to agree with the average opinion of their neighbors and reasonable contrarians tend to disagree, but revert to a conformist behavior in the presence of an overwhelming majority, in line with psychological experiments. The model is studied in the mean-field approximation and on small-world and scale-free networks. In the mean-field approximation, a large fraction of conformists triggers a polarization of the opinions, a pitchfork bifurcation, while a majority of reasonable contrarians leads to coherent oscillations, with an alternation of period-doubling and pitchfork bifurcations up to chaos. Similar scenarios are obtained by changing the fraction of long-range rewiring and the parameter of scale-free networks related to the average connectivity.

Bifurcations in models of a society of reasonable contrarians and conformists.

PubMed

Bagnoli, Franco; Rechtman, Raúl

2015-10-01

We study models of a society composed of a mixture of conformist and reasonable contrarian agents that at any instant hold one of two opinions. Conformists tend to agree with the average opinion of their neighbors and reasonable contrarians tend to disagree, but revert to a conformist behavior in the presence of an overwhelming majority, in line with psychological experiments. The model is studied in the mean-field approximation and on small-world and scale-free networks. In the mean-field approximation, a large fraction of conformists triggers a polarization of the opinions, a pitchfork bifurcation, while a majority of reasonable contrarians leads to coherent oscillations, with an alternation of period-doubling and pitchfork bifurcations up to chaos. Similar scenarios are obtained by changing the fraction of long-range rewiring and the parameter of scale-free networks related to the average connectivity.

Nonequilibrium phase transitions in isotropic Ashkin-Teller model

NASA Astrophysics Data System (ADS)

Akıncı, Ümit

2017-03-01

Dynamic behavior of an isotropic Ashkin-Teller model in the presence of a periodically oscillating magnetic field has been analyzed by means of the mean field approximation. The dynamic equation of motion has been constructed with the help of a Glauber type stochastic process and solved for a square lattice. After defining the possible dynamical phases of the system, phase diagrams have been given and the behavior of the hysteresis loops has been investigated in detail. The hysteresis loop for specific order parameter of isotropic Ashkin-Teller model has been defined and characteristics of this loop in different dynamical phases have been given.

Stochastic bifurcations in the nonlinear parallel Ising model.

PubMed

Bagnoli, Franco; Rechtman, Raúl

2016-11-01

We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to that seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a "bubbling" behavior, as also happens for dilution.

Theoretical approaches to the steady-state statistical physics of interacting dissipative units

NASA Astrophysics Data System (ADS)

Bertin, Eric

2017-02-01

The aim of this review is to provide a concise overview of some of the generic approaches that have been developed to deal with the statistical description of large systems of interacting dissipative ‘units’. The latter notion includes, e.g. inelastic grains, active or self-propelled particles, bubbles in a foam, low-dimensional dynamical systems like driven oscillators, or even spatially extended modes like Fourier modes of the velocity field in a fluid. We first review methods based on the statistical properties of a single unit, starting with elementary mean-field approximations, either static or dynamic, that describe a unit embedded in a ‘self-consistent’ environment. We then discuss how this basic mean-field approach can be extended to account for spatial dependences, in the form of space-dependent mean-field Fokker-Planck equations, for example. We also briefly review the use of kinetic theory in the framework of the Boltzmann equation, which is an appropriate description for dilute systems. We then turn to descriptions in terms of the full N-body distribution, starting from exact solutions of one-dimensional models, using a matrix-product ansatz method when correlations are present. Since exactly solvable models are scarce, we also present some approximation methods which can be used to determine the N-body distribution in a large system of dissipative units. These methods include the Edwards approach for dense granular matter and the approximate treatment of multiparticle Langevin equations with colored noise, which models systems of self-propelled particles. Throughout this review, emphasis is put on methodological aspects of the statistical modeling and on formal similarities between different physical problems, rather than on the specific behavior of a given system.

Deterministic Mean-Field Ensemble Kalman Filtering

DOE PAGES

Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul

2016-05-03

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d

Deterministic Mean-Field Ensemble Kalman Filtering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d

Finite temperature magnon spectra in yttrium iron garnet from a mean field approach in a tight-binding model

NASA Astrophysics Data System (ADS)

Shen, Ka

2018-04-01

We study magnon spectra at finite temperature in yttrium iron garnet using a tight-binding model with nearest-neighbor exchange interaction. The spin reduction due to thermal magnon excitation is taken into account via the mean field approximation to the local spin and is found to be different at two sets of iron atoms. The resulting temperature dependence of the spin wave gap shows good agreement with experiment. We find that only two magnon modes are relevant to the ferromagnetic resonance.

Epidemic spreading in weighted networks: an edge-based mean-field solution.

PubMed

Yang, Zimo; Zhou, Tao

2012-05-01

Weight distribution greatly impacts the epidemic spreading taking place on top of networks. This paper presents a study of a susceptible-infected-susceptible model on regular random networks with different kinds of weight distributions. Simulation results show that the more homogeneous weight distribution leads to higher epidemic prevalence, which, unfortunately, could not be captured by the traditional mean-field approximation. This paper gives an edge-based mean-field solution for general weight distribution, which can quantitatively reproduce the simulation results. This method could be applied to characterize the nonequilibrium steady states of dynamical processes on weighted networks.

Scattering models for some vegetation samples

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.; Antar, Y. M. M.

1987-01-01

The Helmholtz integral equation is presently derived for a scatterer of arbitrary shape, and reduced in order to obtain the far zone-scattered field in terms of the field within the scatterer. Attention is given to the effect of different approaches to field estimation within the scatterer on the backscattering cross section, as illustrated numerically by the cases of a circular disk, a needle, and a finite-length cylinder. A comparison is made of the results obtained by modeling a leaf by means of a circular disk within the Shifrin approximation, and a tree branch by means of a finite-length cylinder, with measurements from a single leaf and a single branch.

Self-consistent chaos in a mean-field Hamiltonian model of fluids and plasmas

NASA Astrophysics Data System (ADS)

del-Castillo-Negrete, D.; Firpo, Marie-Christine

2002-11-01

We present a mean-field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas. In plasmas, the model describes the self-consistent evolution of electron holes and clumps in phase space. In fluids, the model describes the dynamics of vortices with negative and positive circulation in shear flows. The mean-field nature of the system makes it a tractable model to study the dynamics of large degrees-of-freedom, coupled Hamiltonian systems. Here we focus in the role of self-consistent chaos in the formation and destruction of phase space coherent structures. Numerical simulations in the finite N and in the Narrow kinetic limit (where N is the number of particles) show the existence of coherent, rotating dipole states. We approximate the dipole as two macroparticles, and show that the N = 2 limit has a family of rotating integrable solutions described by a one degree-of-freedom nontwist Hamiltonian. The coherence of the dipole is explained in terms of a parametric resonance between the rotation frequency of the macroparticles and the oscillation frequency of the self-consistent mean field. For a class of initial conditions, the mean field exhibits a self-consistent, elliptic-hyperbolic bifurcation that leads to the destruction of the dipole and violent mixing of the phase space.

Electromagnetic backscattering from a random distribution of lossy dielectric scatterers

NASA Technical Reports Server (NTRS)

Lang, R. H.

1980-01-01

Electromagnetic backscattering from a sparse distribution of discrete lossy dielectric scatterers occupying a region 5 was studied. The scatterers are assumed to have random position and orientation. Scattered fields are calculated by first finding the mean field and then by using it to define an equivalent medium within the volume 5. The scatterers are then viewed as being embedded in the equivalent medium; the distorted Born approximation is then used to find the scattered fields. This technique represents an improvement over the standard Born approximation since it takes into account the attenuation of the incident and scattered waves in the equivalent medium. The method is used to model a leaf canopy when the leaves are modeled by lossy dielectric discs.

Geomagnetic modeling by optimal recursive filtering

NASA Technical Reports Server (NTRS)

Gibbs, B. P.; Estes, R. H.

1981-01-01

The results of a preliminary study to determine the feasibility of using Kalman filter techniques for geomagnetic field modeling are given. Specifically, five separate field models were computed using observatory annual means, satellite, survey and airborne data for the years 1950 to 1976. Each of the individual field models used approximately five years of data. These five models were combined using a recursive information filter (a Kalman filter written in terms of information matrices rather than covariance matrices.) The resulting estimate of the geomagnetic field and its secular variation was propogated four years past the data to the time of the MAGSAT data. The accuracy with which this field model matched the MAGSAT data was evaluated by comparisons with predictions from other pre-MAGSAT field models. The field estimate obtained by recursive estimation was found to be superior to all other models.

Mean field approximation for biased diffusion on Japanese inter-firm trading network.

PubMed

Watanabe, Hayafumi

2014-01-01

By analysing the financial data of firms across Japan, a nonlinear power law with an exponent of 1.3 was observed between the number of business partners (i.e. the degree of the inter-firm trading network) and sales. In a previous study using numerical simulations, we found that this scaling can be explained by both the money-transport model, where a firm (i.e. customer) distributes money to its out-edges (suppliers) in proportion to the in-degree of destinations, and by the correlations among the Japanese inter-firm trading network. However, in this previous study, we could not specifically identify what types of structure properties (or correlations) of the network determine the 1.3 exponent. In the present study, we more clearly elucidate the relationship between this nonlinear scaling and the network structure by applying mean-field approximation of the diffusion in a complex network to this money-transport model. Using theoretical analysis, we obtained the mean-field solution of the model and found that, in the case of the Japanese firms, the scaling exponent of 1.3 can be determined from the power law of the average degree of the nearest neighbours of the network with an exponent of -0.7.

Asymptotically inspired moment-closure approximation for adaptive networks

NASA Astrophysics Data System (ADS)

Shkarayev, Maxim S.; Shaw, Leah B.

2013-11-01

Adaptive social networks, in which nodes and network structure coevolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher-order topological structures. We propose a new approach to moment closure based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and adaptive epidemic model. We show a good agreement between the improved mean-field prediction and simulations of the full network system.

Anomalous Growth of Aging Populations

NASA Astrophysics Data System (ADS)

Grebenkov, Denis S.

2016-04-01

We consider a discrete-time population dynamics with age-dependent structure. At every time step, one of the alive individuals from the population is chosen randomly and removed with probability q_k depending on its age, whereas a new individual of age 1 is born with probability r. The model can also describe a single queue in which the service order is random while the service efficiency depends on a customer's "age" in the queue. We propose a mean field approximation to investigate the long-time asymptotic behavior of the mean population size. The age dependence is shown to lead to anomalous power-law growth of the population at the critical regime. The scaling exponent is determined by the asymptotic behavior of the probabilities q_k at large k. The mean field approximation is validated by Monte Carlo simulations.

Mean-field approximations of fixation time distributions of evolutionary game dynamics on graphs

NASA Astrophysics Data System (ADS)

Ying, Li-Min; Zhou, Jie; Tang, Ming; Guan, Shu-Guang; Zou, Yong

2018-02-01

The mean fixation time is often not accurate for describing the timescales of fixation probabilities of evolutionary games taking place on complex networks. We simulate the game dynamics on top of complex network topologies and approximate the fixation time distributions using a mean-field approach. We assume that there are two absorbing states. Numerically, we show that the mean fixation time is sufficient in characterizing the evolutionary timescales when network structures are close to the well-mixing condition. In contrast, the mean fixation time shows large inaccuracies when networks become sparse. The approximation accuracy is determined by the network structure, and hence by the suitability of the mean-field approach. The numerical results show good agreement with the theoretical predictions.

Microstructure from ferroelastic transitions using strain pseudospin clock models in two and three dimensions: A local mean-field analysis

NASA Astrophysics Data System (ADS)

Vasseur, Romain; Lookman, Turab; Shenoy, Subodh R.

2010-09-01

We show how microstructure can arise in first-order ferroelastic structural transitions, in two and three spatial dimensions, through a local mean-field approximation of their pseudospin Hamiltonians, that include anisotropic elastic interactions. Such transitions have symmetry-selected physical strains as their NOP -component order parameters, with Landau free energies that have a single zero-strain “austenite” minimum at high temperatures, and spontaneous-strain “martensite” minima of NV structural variants at low temperatures. The total free energy also has gradient terms, and power-law anisotropic effective interactions, induced by “no-dislocation” St Venant compatibility constraints. In a reduced description, the strains at Landau minima induce temperature dependent, clocklike ZNV+1 Hamiltonians, with NOP -component strain-pseudospin vectors S⃗ pointing to NV+1 discrete values (including zero). We study elastic texturing in five such first-order structural transitions through a local mean-field approximation of their pseudospin Hamiltonians, that include the power-law interactions. As a prototype, we consider the two-variant square/rectangle transition, with a one-component pseudospin taking NV+1=3 values of S=0,±1 , as in a generalized Blume-Capel model. We then consider transitions with two-component (NOP=2) pseudospins: the equilateral to centered rectangle (NV=3) ; the square to oblique polygon (NV=4) ; the triangle to oblique (NV=6) transitions; and finally the three-dimensional (3D) cubic to tetragonal transition (NV=3) . The local mean-field solutions in two-dimensional and 3D yield oriented domain-wall patterns as from continuous-variable strain dynamics, showing the discrete-variable models capture the essential ferroelastic texturings. Other related Hamiltonians illustrate that structural transitions in materials science can be the source of interesting spin models in statistical mechanics.

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth.

PubMed

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth

NASA Astrophysics Data System (ADS)

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

A compound reconstructed prediction model for nonstationary climate processes

NASA Astrophysics Data System (ADS)

Wang, Geli; Yang, Peicai

2005-07-01

Based on the idea of climate hierarchy and the theory of state space reconstruction, a local approximation prediction model with the compound structure is built for predicting some nonstationary climate process. By means of this model and the data sets consisting of north Indian Ocean sea-surface temperature, Asian zonal circulation index and monthly mean precipitation anomaly from 37 observation stations in the Inner Mongolia area of China (IMC), a regional prediction experiment for the winter precipitation of IMC is also carried out. When using the same sign ratio R between the prediction field and the actual field to measure the prediction accuracy, an averaged R of 63% given by 10 predictions samples is reached.

Variational and perturbative formulations of quantum mechanical/molecular mechanical free energy with mean-field embedding and its analytical gradients.

PubMed

Yamamoto, Takeshi

2008-12-28

Conventional quantum chemical solvation theories are based on the mean-field embedding approximation. That is, the electronic wavefunction is calculated in the presence of the mean field of the environment. In this paper a direct quantum mechanical/molecular mechanical (QM/MM) analog of such a mean-field theory is formulated based on variational and perturbative frameworks. In the variational framework, an appropriate QM/MM free energy functional is defined and is minimized in terms of the trial wavefunction that best approximates the true QM wavefunction in a statistically averaged sense. Analytical free energy gradient is obtained, which takes the form of the gradient of effective QM energy calculated in the averaged MM potential. In the perturbative framework, the above variational procedure is shown to be equivalent to the first-order expansion of the QM energy (in the exact free energy expression) about the self-consistent reference field. This helps understand the relation between the variational procedure and the exact QM/MM free energy as well as existing QM/MM theories. Based on this, several ways are discussed for evaluating non-mean-field effects (i.e., statistical fluctuations of the QM wavefunction) that are neglected in the mean-field calculation. As an illustration, the method is applied to an S(N)2 Menshutkin reaction in water, NH(3)+CH(3)Cl-->NH(3)CH(3) (+)+Cl(-), for which free energy profiles are obtained at the Hartree-Fock, MP2, B3LYP, and BHHLYP levels by integrating the free energy gradient. Non-mean-field effects are evaluated to be <0.5 kcal/mol using a Gaussian fluctuation model for the environment, which suggests that those effects are rather small for the present reaction in water.

Testing approximate theories of first-order phase transitions on the two-dimensional Potts model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dasgupta, C.; Pandit, R.

The two-dimensional, q-state (q > 4) Potts model is used as a testing ground for approximate theories of first-order phase transitions. In particular, the predictions of a theory analogous to the Ramakrishnan-Yussouff theory of freezing are compared with those of ordinary mean-field (Curie-Wiess) theory. It is found that the Curie-Weiss theory is a better approximation than the Ramakrishnan-Yussouff theory, even though the former neglects all fluctuations. It is shown that the Ramakrishnan-Yussouff theory overestimates the effects of fluctuations in this system. The reasons behind the failure of the Ramakrishnan-Yussouff approximation and the suitability of using the two-dimensional Potts model asmore » a testing ground for these theories are discussed.« less

Aeroacoustic directivity via wave-packet analysis of mean or base flows

NASA Astrophysics Data System (ADS)

Edstrand, Adam; Schmid, Peter; Cattafesta, Louis

2017-11-01

Noise pollution is an ever-increasing problem in society, and knowledge of the directivity patterns of the sound radiation is required for prediction and control. Directivity is frequently determined through costly numerical simulations of the flow field combined with an acoustic analogy. We introduce a new computationally efficient method of finding directivity for a given mean or base flow field using wave-packet analysis (Trefethen, PRSA 2005). Wave-packet analysis approximates the eigenvalue spectrum with spectral accuracy by modeling the eigenfunctions as wave packets. With the wave packets determined, we then follow the method of Obrist (JFM, 2009), which uses Lighthill's acoustic analogy to determine the far-field sound radiation and directivity of wave-packet modes. We apply this method to a canonical jet flow (Gudmundsson and Colonius, JFM 2011) and determine the directivity of potentially unstable wave packets. Furthermore, we generalize the method to consider a three-dimensional flow field of a trailing vortex wake. In summary, we approximate the disturbances as wave packets and extract the directivity from the wave-packet approximation in a fraction of the time of standard aeroacoustic solvers. ONR Grant N00014-15-1-2403.

Tangent map intermittency as an approximate analysis of intermittency in a high dimensional fully stochastic dynamical system: The Tangled Nature model.

PubMed

Diaz-Ruelas, Alvaro; Jeldtoft Jensen, Henrik; Piovani, Duccio; Robledo, Alberto

2016-12-01

It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g., by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal candidate for such a study, a significant model as it is capable of reproducing a broad range of the phenomenology of macroevolution and ecosystems. The TaNa model exhibits strong intermittency reminiscent of punctuated equilibrium and, like the fossil record of mass extinction, the intermittency in the model is found to be non-stationary, a feature typical of many complex systems. We derive a mean-field version for the evolution of the likelihood function controlling the reproduction of species and find a local map close to tangency. This mean-field map, by our own local approximation, is able to describe qualitatively only one episode of the intermittent dynamics of the full TaNa model. To complement this result, we construct a complete nonlinear dynamical system model consisting of successive tangent bifurcations that generates time evolution patterns resembling those of the full TaNa model in macroscopic scales. The switch from one tangent bifurcation to the next in the sequences produced in this model is stochastic in nature, based on criteria obtained from the local mean-field approximation, and capable of imitating the changing set of types of species and total population in the TaNa model. The model combines full deterministic dynamics with instantaneous parameter random jumps at stochastically drawn times. In spite of the limitations of our approach, which entails a drastic collapse of degrees of freedom, the description of a high-dimensional model system in terms of a low-dimensional one appears to be illuminating.

Capturing nonlocal interaction effects in the Hubbard model: Optimal mappings and limits of applicability

NASA Astrophysics Data System (ADS)

van Loon, E. G. C. P.; Schüler, M.; Katsnelson, M. I.; Wehling, T. O.

2016-10-01

We investigate the Peierls-Feynman-Bogoliubov variational principle to map Hubbard models with nonlocal interactions to effective models with only local interactions. We study the renormalization of the local interaction induced by nearest-neighbor interaction and assess the quality of the effective Hubbard models in reproducing observables of the corresponding extended Hubbard models. We compare the renormalization of the local interactions as obtained from numerically exact determinant quantum Monte Carlo to approximate but more generally applicable calculations using dual boson, dynamical mean field theory, and the random phase approximation. These more approximate approaches are crucial for any application with real materials in mind. Furthermore, we use the dual boson method to calculate observables of the extended Hubbard models directly and benchmark these against determinant quantum Monte Carlo simulations of the effective Hubbard model.

Short-ranged interaction effects on Z2 topological phase transitions: The perturbative mean-field method

NASA Astrophysics Data System (ADS)

Lai, Hsin-Hua; Hung, Hsiang-Hsuan

2015-02-01

Time-reversal symmetric topological insulator (TI) is a novel state of matter that a bulk-insulating state carries dissipationless spin transport along the surfaces, embedded by the Z2 topological invariant. In the noninteracting limit, this exotic state has been intensively studied and explored with realistic systems, such as HgTe/(Hg, Cd)Te quantum wells. On the other hand, electronic correlation plays a significant role in many solid-state systems, which further influences topological properties and triggers topological phase transitions. Yet an interacting TI is still an elusive subject and most related analyses rely on the mean-field approximation and numerical simulations. Among the approaches, the mean-field approximation fails to predict the topological phase transition, in particular at intermediate interaction strength without spontaneously breaking symmetry. In this paper, we develop an analytical approach based on a combined perturbative and self-consistent mean-field treatment of interactions that is capable of capturing topological phase transitions beyond either method when used independently. As an illustration of the method, we study the effects of short-ranged interactions on the Z2 TI phase, also known as the quantum spin Hall (QSH) phase, in three generalized versions of the Kane-Mele (KM) model at half-filling on the honeycomb lattice. The results are in excellent agreement with quantum Monte Carlo (QMC) calculations on the same model and cannot be reproduced by either a perturbative treatment or a self-consistent mean-field treatment of the interactions. Our analytical approach helps to clarify how the symmetries of the one-body terms of the Hamiltonian determine whether interactions tend to stabilize or destabilize a topological phase. Moreover, our method should be applicable to a wide class of models where topological transitions due to interactions are in principle possible, but are not correctly predicted by either perturbative or self-consistent treatments.

Effect of nonlocal electron kinetics on the characteristics of a dielectric barrier discharge in xenon

DOE Office of Scientific and Technical Information (OSTI.GOV)

Avtaeva, S. V.; Skornyakov, A. V.

2009-07-15

The established dynamics of a dielectric barrier discharge in xenon at a pressure of 400 Torr is simulated in the framework of a one-dimensional fluid model in the local and nonlocal field approximations. It is shown that taking into account the nonlocal character of the electric field does not qualitatively change physical processes in a dielectric barrier discharge, but significantly affects its quantitative characteristics. In particular, the sheath thickness decreases, plasma ionization intensifies, the spatiotemporal distribution of the mean electron energy changes, and the discharge radiation efficiency increases. Electron kinetics in a dielectric barrier discharge in xenon is analyzed usingmore » the nonlocal field approximation.« less

Plasma Potential and Langmuir Probe Measurements in the Near-field Plume of the NASA-457Mv2 Hall Thruster

NASA Technical Reports Server (NTRS)

Shastry, Rohit; Huang, Wensheng; Herman, Daniel A.; Soulas, George C.; Kamhawi, Hani

2012-01-01

In order to further the design of future high-power Hall thrusters and provide experimental validation for ongoing modeling efforts, plasma potential and Langmuir probe measurements were performed on the 50-kW NASA-457Mv2. An electrostatic probe array comprised of a near-field Faraday probe, single Langmuir probe, and emissive probe was used to interrogate the near-field plume from approximately 0.1 - 2.0 mean thruster diameters downstream of the thruster exit plane at the following operating conditions: 300 V, 400 V and 500 V at 30 kW and 500 V at 50 kW. Results have shown that the acceleration zone is limited to within 0.4 mean thruster diameters of the exit plane while the high-temperature region is limited to 0.25 mean thruster diameters from the exit plane at all four operating conditions. Maximum plasma potentials in the near-field at 300 and 400 V were approximately 50 V with respect to cathode potential, while maximum electron temperatures varied from 24 - 32 eV, depending on operating condition. Isothermal lines at all operating conditions were found to strongly resemble the magnetic field topology in the high-temperature regions. This distribution was found to create regions of high temperature and low density near the magnetic poles, indicating strong, thick sheath formation along these surfaces. The data taken from this study are considered valuable for future design as well as modeling validation.

Bent dark soliton dynamics in two spatial dimensions beyond the mean field approximation

NASA Astrophysics Data System (ADS)

Mistakidis, Simeon; Katsimiga, Garyfallia; Koutentakis, Georgios; Kevrekidis, Panagiotis; Schmelcher, Peter; Theory Group of Fundamental Processes in Quantum Physics Team

2017-04-01

The dynamics of a bented dark soliton embedded in two spatial dimensions beyond the mean-field approximation is explored. We examine the case of a single bented dark soliton comparing the mean-field approximation to a correlated approach that involves multiple orbitals. Fragmentation is generally present and significantly affects the dynamics, especially in the case of stronger interparticle interactions and in that of lower atom numbers. It is shown that the presence of fragmentation allows for the appearance of solitonic and vortex structures in the higher-orbital dynamics. In particular, a variety of excitations including dark solitons in multiple orbitals and vortex-antidark complexes is observed to arise spontaneously within the beyond mean-field dynamics. Deutsche Forschungsgemeinschaft (DFG) in the framework of the SFB 925 ``Light induced dynamics and control of correlated quantum systems''.

Approximate probabilistic cellular automata for the dynamics of single-species populations under discrete logisticlike growth with and without weak Allee effects.

PubMed

Mendonça, J Ricardo G; Gevorgyan, Yeva

2017-05-01

We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with nonoverlapping generations. Beginning with a general six-parameter model, we find constraints on the transition probabilities of the PCA that guarantee that the ensuing approximations make sense in terms of population dynamics and classify the valid combinations thereof. Several possible models display a negative cubic term that can be interpreted as a weak Allee factor. We also investigate the conditions under which a one-parameter PCA derived from the more general six-parameter model can generate valid population growth dynamics. Numerical simulations illustrate the behavior of some of the PCA found.

EVOLUTION OF THE MAGNETIC FIELD LINE DIFFUSION COEFFICIENT AND NON-GAUSSIAN STATISTICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Snodin, A. P.; Ruffolo, D.; Matthaeus, W. H.

The magnetic field line random walk (FLRW) plays an important role in the transport of energy and particles in turbulent plasmas. For magnetic fluctuations that are transverse or almost transverse to a large-scale mean magnetic field, theories describing the FLRW usually predict asymptotic diffusion of magnetic field lines perpendicular to the mean field. Such theories often depend on the assumption that one can relate the Lagrangian and Eulerian statistics of the magnetic field via Corrsin’s hypothesis, and additionally take the distribution of magnetic field line displacements to be Gaussian. Here we take an ordinary differential equation (ODE) model with thesemore » underlying assumptions and test how well it describes the evolution of the magnetic field line diffusion coefficient in 2D+slab magnetic turbulence, by comparisons to computer simulations that do not involve such assumptions. In addition, we directly test the accuracy of the Corrsin approximation to the Lagrangian correlation. Over much of the studied parameter space we find that the ODE model is in fairly good agreement with computer simulations, in terms of both the evolution and asymptotic values of the diffusion coefficient. When there is poor agreement, we show that this can be largely attributed to the failure of Corrsin’s hypothesis rather than the assumption of Gaussian statistics of field line displacements. The degree of non-Gaussianity, which we measure in terms of the kurtosis, appears to be an indicator of how well Corrsin’s approximation works.« less

Quantitative kinetic theory of active matter

NASA Astrophysics Data System (ADS)

Ihle, Thomas; Chou, Yen-Liang

2014-03-01

Models of self-driven agents similar to the Vicsek model [Phys. Rev. Lett. 75 (1995) 1226] are studied by means of kinetic theory. In these models, particles try to align their travel directions with the average direction of their neighbours. At strong alignment a globally ordered state of collective motion forms. An Enskog-like kinetic theory is derived from the exact Chapman-Kolmogorov equation in phase space using Boltzmann's mean-field approximation of molecular chaos. The kinetic equation is solved numerically by a nonlocal Lattice-Boltzmann-like algorithm. Steep soliton-like waves are observed that lead to an abrupt jump of the global order parameter if the noise level is changed. The shape of the wave is shown to follow a novel scaling law and to quantitatively agree within 3 % with agent-based simulations at large particle speeds. This provides a mean-field mechanism to change the second-order character of the flocking transition to first order. Diagrammatic techniques are used to investigate small particle speeds, where the mean-field assumption of Molecular Chaos is invalid and where correlation effects need to be included.

Microscopic processes controlling the Herschel-Bulkley exponent

NASA Astrophysics Data System (ADS)

Lin, Jie; Wyart, Matthieu

2018-01-01

The flow curve of various yield stress materials is singular as the strain rate vanishes and can be characterized by the so-called Herschel-Bulkley exponent n =1 /β . A mean-field approximation due to Hebraud and Lequeux (HL) assumes mechanical noise to be Gaussian and leads to β =2 in rather good agreement with observations. Here we prove that the improved mean-field model where the mechanical noise has fat tails instead leads to β =1 with logarithmic correction. This result supports that HL is not a suitable explanation for the value of β , which is instead significantly affected by finite-dimensional effects. From considerations on elastoplastic models and on the limitation of speed at which avalanches of plasticity can propagate, we argue that β =1 +1 /(d -df) , where df is the fractal dimension of avalanches and d the spatial dimension. Measurements of df then supports that β ≈2.1 and β ≈1.7 in two and three dimensions, respectively. We discuss theoretical arguments leading to approximations of β in finite dimensions.

Model of chiral spin liquids with Abelian and non-Abelian topological phases

NASA Astrophysics Data System (ADS)

Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio; Tsvelik, A. M.

2017-12-01

We present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, the Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.

Forecasting transitions in systems with high-dimensional stochastic complex dynamics: a linear stability analysis of the tangled nature model.

PubMed

Cairoli, Andrea; Piovani, Duccio; Jensen, Henrik Jeldtoft

2014-12-31

We propose a new procedure to monitor and forecast the onset of transitions in high-dimensional complex systems. We describe our procedure by an application to the tangled nature model of evolutionary ecology. The quasistable configurations of the full stochastic dynamics are taken as input for a stability analysis by means of the deterministic mean-field equations. Numerical analysis of the high-dimensional stability matrix allows us to identify unstable directions associated with eigenvalues with a positive real part. The overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean-field approximation is found to be a good early warning of the transitions occurring intermittently.

Cosmological models constructed by van der Waals fluid approximation and volumetric expansion

NASA Astrophysics Data System (ADS)

Samanta, G. C.; Myrzakulov, R.

The universe modeled with van der Waals fluid approximation, where the van der Waals fluid equation of state contains a single parameter ωv. Analytical solutions to the Einstein’s field equations are obtained by assuming the mean scale factor of the metric follows volumetric exponential and power-law expansions. The model describes a rapid expansion where the acceleration grows in an exponential way and the van der Waals fluid behaves like an inflation for an initial epoch of the universe. Also, the model describes that when time goes away the acceleration is positive, but it decreases to zero and the van der Waals fluid approximation behaves like a present accelerated phase of the universe. Finally, it is observed that the model contains a type-III future singularity for volumetric power-law expansion.

Collective Behaviors in Spatially Extended Systems with Local Interactions and Synchronous Updating

NASA Astrophysics Data System (ADS)

ChatÉ, H.; Manneville, P.

1992-01-01

Assessing the extent to which dynamical systems with many degrees of freedom can be described within a thermodynamics formalism is a problem that currently attracts much attention. In this context, synchronously updated regular lattices of identical, chaotic elements with local interactions are promising models for which statistical mechanics may be hoped to provide some insights. This article presents a large class of cellular automata rules and coupled map lattices of the above type in space dimensions d = 2 to 6.Such simple models can be approached by a mean-field approximation which usually reduces the dynamics to that of a map governing the evolution of some extensive density. While this approximation is exact in the d = infty limit, where macroscopic variables must display the time-dependent behavior of the mean-field map, basic intuition from equilibrium statistical mechanics rules out any such behavior in a low-dimensional systems, since it would involve the collective motion of locally disordered elements.The models studied are chosen to be as close as possible to mean-field conditions, i.e., rather high space dimension, large connectivity, and equal-weight coupling between sites. While the mean-field evolution is never observed, a new type of non-trivial collective behavior is found, at odds with the predictions of equilibrium statistical mechanics. Both in the cellular automata models and in the coupled map lattices, macroscopic variables frequently display a non-transient, time-dependent, low-dimensional dynamics emerging out of local disorder. Striking examples are period 3 cycles in two-state cellular automata and a Hopf bifurcation for a d = 5 lattice of coupled logistic maps. An extensive account of the phenomenology is given, including a catalog of behaviors, classification tables for the celular automata rules, and bifurcation diagrams for the coupled map lattices.The observed underlying dynamics is accompanied by an intrinsic quasi-Gaussian noise (stemming from the local disorder) which disappears in the infinite-size limit. The collective behaviors constitute a robust phenomenon, resisting external noise, small changes in the local dynamics, and modifications of the initial and boundary conditions. Synchronous updating, high space dimension and the regularity of connections are shown to be crucial ingredients in the subtle build-up of correlations giving rise to the collective motion. The discussion stresses the need for a theoretical understanding that neither equilibrium statistical mechanics nor higher-order mean-field approximations are able to provide.

Learning and inference in a nonequilibrium Ising model with hidden nodes.

PubMed

Dunn, Benjamin; Roudi, Yasser

2013-02-01

We study inference and reconstruction of couplings in a partially observed kinetic Ising model. With hidden spins, calculating the likelihood of a sequence of observed spin configurations requires performing a trace over the configurations of the hidden ones. This, as we show, can be represented as a path integral. Using this representation, we demonstrate that systematic approximate inference and learning rules can be derived using dynamical mean-field theory. Although naive mean-field theory leads to an unstable learning rule, taking into account Gaussian corrections allows learning the couplings involving hidden nodes. It also improves learning of the couplings between the observed nodes compared to when hidden nodes are ignored.

Supersonic flow calculation using a Reynolds-stress and an eddy thermal diffusivity turbulence model

NASA Technical Reports Server (NTRS)

Sommer, T. P.; So, R. M. C.; Zhang, H. S.

1993-01-01

A second-order model for the velocity field and a two-equation model for the temperature field are used to calculate supersonic boundary layers assuming negligible real gas effects. The modeled equations are formulated on the basis of an incompressible assumption and then extended to supersonic flows by invoking Morkovin's hypothesis, which proposes that compressibility effects are completely accounted for by mean density variations alone. In order to calculate the near-wall flow accurately, correction functions are proposed to render the modeled equations asymptotically consistent with the behavior of the exact equations near a wall and, at the same time, display the proper dependence on the molecular Prandtl number. Thus formulated, the near-wall second order turbulence model for heat transfer is applicable to supersonic flows with different Prandtl numbers. The model is validated against flows with different Prandtl numbers and supersonic flows with free-stream Mach numbers as high as 10 and wall temperature ratios as low as 0.3. Among the flow cases considered, the momentum thickness Reynolds number varies from approximately 4,000 to approximately 21,000. Good correlation with measurements of mean velocity, temperature, and its variance is obtained. Discernible improvements in the law-of-the-wall are observed, especially in the range where the big-law applies.

Investigation of head group behaviour of lamellar liquid crystals

NASA Astrophysics Data System (ADS)

Delikatny, E. J.; Burnell, E. E.

A mean field equilibrium statistical mechanical model, based on the Samulski inertial frame model, was developed to simulate experimental dipolar and quadrupolar nmr couplings of isotopically substituted potassium palmitates. An isolated four spin system was synthesized (2,2,3,3,-H4-palmitic acid-d27) and in conjunction with data presented in a previous paper on perdeuterated and carbon 13 labelled soaps, the head group behaviour of the molecule was investigated. Two interactions were considered in the modelling procedure: a mean field steric interaction characterized by a constraining cylinder, and a head group interaction characterized by a mass on the end of a rod of variable length. The rod lies along the first C-C bond direction and accounts for the interaction between polar head group and water via its effect on the moment of inertia of the molecule. In potassium palmitate mean field steric repulsive forces remain constant over the entire temperature range studied. In contrast, electrostatic interactions between polar head group and water, approximately constant at higher temperatures, increase dramatically as the phase transition is approached. This evidence supports a previously proposed model of lipidwater interaction.

Coherent-Anomaly Method in Critical Phenomena. III. Mean-Field Transfer-Matrix Method in the 2D Ising Model

NASA Astrophysics Data System (ADS)

Hu, Xiao; Katori, Makoto; Suzuki, Masuo

1987-11-01

Two kinds of systematic mean-field transfer-matrix methods are formulated in the 2-dimensional Ising spin system, by introducing Weiss-like and Bethe-like approximations. All the critical exponents as well as the true critical point can be estimated in these methods following the CAM procedure. The numerical results of the above system are Tc*≃2.271 (J/kB), γ{=}γ'≃1.749, β≃0.131 and δ≃15.1. The specific heat is confirmd to be continuous and to have a logarithmic divergence at the true critical point, i.e., α{=}α'{=}0. Thus, the finite-degree-of-approximation scaling ansatz is shown to be correct and very powerful in practical estimations of the critical exponents as well as the true critical point.

Mean Field Variational Bayesian Data Assimilation

NASA Astrophysics Data System (ADS)

Vrettas, M.; Cornford, D.; Opper, M.

2012-04-01

Current data assimilation schemes propose a range of approximate solutions to the classical data assimilation problem, particularly state estimation. Broadly there are three main active research areas: ensemble Kalman filter methods which rely on statistical linearization of the model evolution equations, particle filters which provide a discrete point representation of the posterior filtering or smoothing distribution and 4DVAR methods which seek the most likely posterior smoothing solution. In this paper we present a recent extension to our variational Bayesian algorithm which seeks the most probably posterior distribution over the states, within the family of non-stationary Gaussian processes. Our original work on variational Bayesian approaches to data assimilation sought the best approximating time varying Gaussian process to the posterior smoothing distribution for stochastic dynamical systems. This approach was based on minimising the Kullback-Leibler divergence between the true posterior over paths, and our Gaussian process approximation. So long as the observation density was sufficiently high to bring the posterior smoothing density close to Gaussian the algorithm proved very effective, on lower dimensional systems. However for higher dimensional systems, the algorithm was computationally very demanding. We have been developing a mean field version of the algorithm which treats the state variables at a given time as being independent in the posterior approximation, but still accounts for their relationships between each other in the mean solution arising from the original dynamical system. In this work we present the new mean field variational Bayesian approach, illustrating its performance on a range of classical data assimilation problems. We discuss the potential and limitations of the new approach. We emphasise that the variational Bayesian approach we adopt, in contrast to other variational approaches, provides a bound on the marginal likelihood of the observations given parameters in the model which also allows inference of parameters such as observation errors, and parameters in the model and model error representation, particularly if this is written as a deterministic form with small additive noise. We stress that our approach can address very long time window and weak constraint settings. However like traditional variational approaches our Bayesian variational method has the benefit of being posed as an optimisation problem. We finish with a sketch of the future directions for our approach.

Perturbation Theory versus Thermodynamic Integration. Beyond a Mean-Field Treatment of Pair Correlations in a Nematic Model Liquid Crystal.

PubMed

Schoen, Martin; Haslam, Andrew J; Jackson, George

2017-10-24

The phase behavior and structure of a simple square-well bulk fluid with anisotropic interactions is described in detail. The orientation dependence of the intermolecular interactions allows for the formation of a nematic liquid-crystalline phase in addition to the more conventional isotropic gas and liquid phases. A version of classical density functional theory (DFT) is employed to determine the properties of the model, and comparisons are made with the corresponding data from Monte Carlo (MC) computer simulations in both the grand canonical and canonical ensembles, providing a benchmark to assess the adequacy of the DFT results. A novel element of the DFT approach is the assumption that the structure of the fluid is dominated by intermolecular interactions in the isotropic fluid. A so-called augmented modified mean-field (AMMF) approximation is employed accounting for the influence of anisotropic interactions. The AMMF approximation becomes exact in the limit of vanishing density. We discuss advantages and disadvantages of the AMMF approximation with respect to an accurate description of isotropic and nematic branches of the phase diagram, the degree of orientational order, and orientation-dependent pair correlations. The performance of the AMMF approximations is found to be good in comparison with the MC data; the AMMF approximation has clear advantages with respect to an accurate and more detailed description of the fluid structure. Possible strategies to improve the DFT are discussed.

Topological bifurcations in a model society of reasonable contrarians

NASA Astrophysics Data System (ADS)

Bagnoli, Franco; Rechtman, Raúl

2013-12-01

People are often divided into conformists and contrarians, the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority. In practice, however, the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion, which denotes a social norm. Such reasonable contrarian behavior is often considered a mark of independent thought and can be a useful strategy in financial markets. We present the opinion dynamics of a society of reasonable contrarian agents. The model is a cellular automaton of Ising type, with antiferromagnetic pair interactions modeling contrarianism and plaquette terms modeling social norms. We introduce the entropy of the collective variable as a way of comparing deterministic (mean-field) and probabilistic (simulations) bifurcation diagrams. In the mean-field approximation the model exhibits bifurcations and a chaotic phase, interpreted as coherent oscillations of the whole society. However, in a one-dimensional spatial arrangement one observes incoherent oscillations and a constant average. In simulations on Watts-Strogatz networks with a small-world effect the mean-field behavior is recovered, with a bifurcation diagram that resembles the mean-field one but where the rewiring probability is used as the control parameter. Similar bifurcation diagrams are found for scale-free networks, and we are able to compute an effective connectivity for such networks.

Topological bifurcations in a model society of reasonable contrarians.

PubMed

Bagnoli, Franco; Rechtman, Raúl

2013-12-01

People are often divided into conformists and contrarians, the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority. In practice, however, the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion, which denotes a social norm. Such reasonable contrarian behavior is often considered a mark of independent thought and can be a useful strategy in financial markets. We present the opinion dynamics of a society of reasonable contrarian agents. The model is a cellular automaton of Ising type, with antiferromagnetic pair interactions modeling contrarianism and plaquette terms modeling social norms. We introduce the entropy of the collective variable as a way of comparing deterministic (mean-field) and probabilistic (simulations) bifurcation diagrams. In the mean-field approximation the model exhibits bifurcations and a chaotic phase, interpreted as coherent oscillations of the whole society. However, in a one-dimensional spatial arrangement one observes incoherent oscillations and a constant average. In simulations on Watts-Strogatz networks with a small-world effect the mean-field behavior is recovered, with a bifurcation diagram that resembles the mean-field one but where the rewiring probability is used as the control parameter. Similar bifurcation diagrams are found for scale-free networks, and we are able to compute an effective connectivity for such networks.

Dark-Bright Soliton Dynamics Beyond the Mean-Field Approximation

NASA Astrophysics Data System (ADS)

Katsimiga, Garyfallia; Koutentakis, Georgios; Mistakidis, Simeon; Kevrekidis, Panagiotis; Schmelcher, Peter; Theory Group of Fundamental Processes in Quantum Physics Team

2017-04-01

The dynamics of dark bright solitons beyond the mean-field approximation is investigated. We first examine the case of a single dark-bright soliton and its oscillations within a parabolic trap. Subsequently, we move to the setting of collisions, comparing the mean-field approximation to that involving multiple orbitals in both the dark and the bright component. Fragmentation is present and significantly affects the dynamics, especially in the case of slower solitons and in that of lower atom numbers. It is shown that the presence of fragmentation allows for bipartite entanglement between the distinguishable species. Most importantly the interplay between fragmentation and entanglement leads to the decay of each of the initial mean-field dark-bright solitons into fast and slow fragmented dark-bright structures. A variety of excitations including dark-bright solitons in multiple (concurrently populated) orbitals is observed. Dark-antidark states and domain-wall-bright soliton complexes can also be observed to arise spontaneously in the beyond mean-field dynamics. Deutsche Forschungsgemeinschaft (DFG) in the framework of the SFB 925 ``Light induced dynamics and control of correlated quantum systems''.

Level-Set Variational Implicit-Solvent Modeling of Biomolecules with the Coulomb-Field Approximation

PubMed Central

2011-01-01

Central in the variational implicit-solvent model (VISM) [Dzubiella, Swanson, and McCammon Phys. Rev. Lett.2006, 96, 087802 and J. Chem. Phys.2006, 124, 084905] of molecular solvation is a mean-field free-energy functional of all possible solute–solvent interfaces or dielectric boundaries. Such a functional can be minimized numerically by a level-set method to determine stable equilibrium conformations and solvation free energies. Applications to nonpolar systems have shown that the level-set VISM is efficient and leads to qualitatively and often quantitatively correct results. In particular, it is capable of capturing capillary evaporation in hydrophobic confinement and corresponding multiple equilibrium states as found in molecular dynamics (MD) simulations. In this work, we introduce into the VISM the Coulomb-field approximation of the electrostatic free energy. Such an approximation is a volume integral over an arbitrary shaped solvent region, requiring no solutions to any partial differential equations. With this approximation, we obtain the effective boundary force and use it as the “normal velocity” in the level-set relaxation. We test the new approach by calculating solvation free energies and potentials of mean force for small and large molecules, including the two-domain protein BphC. Our results reveal the importance of coupling polar and nonpolar interactions in the underlying molecular systems. In particular, dehydration near the domain interface of BphC subunits is found to be highly sensitive to local electrostatic potentials as seen in previous MD simulations. This is a first step toward capturing the complex protein dehydration process by an implicit-solvent approach. PMID:22346739

Multiphase mean curvature flows with high mobility contrasts: A phase-field approach, with applications to nanowires

NASA Astrophysics Data System (ADS)

Bretin, Elie; Danescu, Alexandre; Penuelas, José; Masnou, Simon

2018-07-01

The structure of many multiphase systems is governed by an energy that penalizes the area of interfaces between phases weighted by surface tension coefficients. However, interface evolution laws depend also on interface mobility coefficients. Having in mind some applications where highly contrasted or even degenerate mobilities are involved, for which classical phase field models are inapplicable, we propose a new effective phase field approach to approximate multiphase mean curvature flows with mobilities. The key aspect of our model is to incorporate the mobilities not in the phase field energy (which is conventionally the case) but in the metric which determines the gradient flow. We show the consistency of such an approach by a formal analysis of the sharp interface limit. We also propose an efficient numerical scheme which allows us to illustrate the advantages of the model on various examples, as the wetting of droplets on solid surfaces or the simulation of nanowires growth generated by the so-called vapor-liquid-solid method.

Interpreting the Coulomb-field approximation for generalized-Born electrostatics using boundary-integral equation theory.

PubMed

Bardhan, Jaydeep P

2008-10-14

The importance of molecular electrostatic interactions in aqueous solution has motivated extensive research into physical models and numerical methods for their estimation. The computational costs associated with simulations that include many explicit water molecules have driven the development of implicit-solvent models, with generalized-Born (GB) models among the most popular of these. In this paper, we analyze a boundary-integral equation interpretation for the Coulomb-field approximation (CFA), which plays a central role in most GB models. This interpretation offers new insights into the nature of the CFA, which traditionally has been assessed using only a single point charge in the solute. The boundary-integral interpretation of the CFA allows the use of multiple point charges, or even continuous charge distributions, leading naturally to methods that eliminate the interpolation inaccuracies associated with the Still equation. This approach, which we call boundary-integral-based electrostatic estimation by the CFA (BIBEE/CFA), is most accurate when the molecular charge distribution generates a smooth normal displacement field at the solute-solvent boundary, and CFA-based GB methods perform similarly. Conversely, both methods are least accurate for charge distributions that give rise to rapidly varying or highly localized normal displacement fields. Supporting this analysis are comparisons of the reaction-potential matrices calculated using GB methods and boundary-element-method (BEM) simulations. An approximation similar to BIBEE/CFA exhibits complementary behavior, with superior accuracy for charge distributions that generate rapidly varying normal fields and poorer accuracy for distributions that produce smooth fields. This approximation, BIBEE by preconditioning (BIBEE/P), essentially generates initial guesses for preconditioned Krylov-subspace iterative BEMs. Thus, iterative refinement of the BIBEE/P results recovers the BEM solution; excellent agreement is obtained in only a few iterations. The boundary-integral-equation framework may also provide a means to derive rigorous results explaining how the empirical correction terms in many modern GB models significantly improve accuracy despite their simple analytical forms.

Static quadrupolar susceptibility for a Blume-Emery-Griffiths model based on the mean-field approximation

NASA Astrophysics Data System (ADS)

Pawlak, A.; Gülpınar, G.; Erdem, R.; Ağartıoğlu, M.

2015-12-01

The expressions for the dipolar and quadrupolar susceptibilities are obtained within the mean-field approximation in the Blume-Emery-Griffiths model. Temperature as well as crystal field dependences of the susceptibilities are investigated for two different phase diagram topologies which take place for K/J=3 and K/J=5.0.Their behavior near the second and first order transition points as well as multi-critical points such as tricritical, triple and critical endpoint is presented. It is found that in addition to the jumps connected with the phase transitions there are broad peaks in the quadrupolar susceptibility. It is indicated that these broad peaks lie on a prolongation of the first-order line from a triple point to a critical point ending the line of first-order transitions between two distinct paramagnetic phases. It is argued that the broad peaks are a reminiscence of very strong quadrupolar fluctuations at the critical point. The results reveal the fact that near ferromagnetic-paramagnetic phase transitions the quadrupolar susceptibility generally shows a jump whereas near the phase transition between two distinct paramagnetic phases it is an edge-like.

Dynamics and Self-consistent Chaos in a Mean Field Hamiltonian Model

NASA Astrophysics Data System (ADS)

del-Castillo-Negrete, Diego

We study a mean field Hamiltonian model that describes the collective dynamics of marginally stable fluids and plasmas in the finite N and N-> infty kinetic limit (where N is the number of particles). The linear stability of equilibria in the kinetic model is studied as well as the initial value problem including Landau damping . Numerical simulations show the existence of coherent, rotating dipole states. We approximate the dipole as two macroparticles and show that the N=2 limit has a family of rotating integrable solutions that provide an accurate description of the dynamics. We discuss the role of self-consistent Hamiltonian chaos in the formation of coherent structures, and discuss a mechanism of "violent" mixing caused by a self-consistent elliptic-hyperbolic bifurcation in phase space.

Testing validity of the Kirkwood approximation using an extended Sznajd model

NASA Astrophysics Data System (ADS)

Timpanaro, André M.; Galam, Serge

2015-12-01

We revisit the deduction of the exit probability of the one-dimensional Sznajd model through the Kirkwood approximation [F. Slanina et al., Europhys. Lett. 82, 18006 (2008), 10.1209/0295-5075/82/18006]. This approximation is peculiar in that, in spite of the agreement with simulation results [F. Slanina et al., Europhys. Lett. 82, 18006 (2008), 10.1209/0295-5075/82/18006; R. Lambiotte and S. Redner, Europhys. Lett. 82, 18007 (2008), 10.1209/0295-5075/82/18007; A. M. Timpanaro and C. P. C. Prado, Phys. Rev. E 89, 052808 (2014), 10.1103/PhysRevE.89.052808], the hypothesis about the correlation lengths behind it are inconsistent and fixing these inconsistencies leads to the same results as a simple mean field. We use an extended version of the Sznajd model to test the Kirkwood approximation in a wider context. This model includes the voter, Sznajd, and "United we stand, divided we fall" models [R. A. Holley and T. M. Liggett, Ann. Prob. 3, 643 (1975), 10.1214/aop/1176996306; K. Sznajd-Weron and J. Sznajd, Int. J. Mod. Phys. C 11, 1157 (2000), 10.1142/S0129183100000936] as different parameter combinations, meaning that some analytical results from these models can be used to evaluate the performance of the Kirkwood approximation. We also compare the predicted exit probability with simulation results for networks with 103 sites. The results show clearly the regions in parameter space where the approximation gives accurate predictions, as well as where it starts failing, leading to a better understanding of its reliability.

Critical study of the dispersive n- 90Zr mean field by means of a new variational method

NASA Astrophysics Data System (ADS)

Mahaux, C.; Sartor, R.

1994-02-01

A new variational method is developed for the construction of the dispersive nucleon-nucleus mean field at negative and positive energies. Like the variational moment approach that we had previously proposed, the new method only uses phenomenological optical-model potentials as input. It is simpler and more flexible than the previous approach. It is applied to a critical investigation of the n- 90Zr mean field between -25 and +25 MeV. This system is of particular interest because conflicting results had recently been obtained by two different groups. While the imaginary parts of the phenomenological optical-model potentials provided by these two groups are similar, their real parts are quite different. Nevertheless, we demonstrate that these two sets of phenomenological optical-model potentials are both compatible with the dispersion relation which connects the real and imaginary parts of the mean field. Previous hints to the contrary, by one of the two other groups, are shown to be due to unjustified approximations. A striking outcome of the present study is that it is important to explicitly introduce volume absorption in the dispersion relation, although volume absorption is negligible in the energy domain investigated here. Because of the existence of two sets of phenomenological optical-model potentials, our variational method yields two dispersive mean fields whose real parts are quite different at small or negative energies. No preference for one of the two dispersive mean fields can be expressed on purely empirical grounds since they both yield fair agreement with the experimental cross sections as well as with the observed energies of the bound single-particle states. However, we argue that one of these two mean fields is physically more meaningful, because the radial shape of its Hartree-Fock type component is independent of energy, as expected on theoretical grounds. This preferred mean field is very close to the one which had been obtained by the Ohio University group by means of fits to experimental cross sections. It is also in good agreement with a recent determination of the p- 90Zr average potential.

Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stottmeister, Alexander, E-mail: alexander.stottmeister@gravity.fau.de; Thiemann, Thomas, E-mail: thomas.thiemann@gravity.fau.de

2016-06-15

This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems,more » which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).« less

Neutron Stars with Delta-Resonances in the Walecka and Zimanyi-Moszkowski Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fong, C. T.; Oliveira, J. C. T.; Rodrigues, H.

2010-11-12

In the present work we have obtained the equation of state of the highly asymmetric dense stellar matter focusing on the delta resonance formation. We extended the nonlinear Walecka (NLW) and Zimanyi-Moszkowski (ZM) models to accommodate in the context of the relativistic mean field approximation the Rarita-Schwinger field for the spin 3/2 resonances. With the constructed stellar matter equations of state we solve numerically the TOV equation (Tolman-Oppenheimer-Volkoff) in order to determine the internal structure of neutron stars, and discuss the obtained masses versus radii diagram.

Model many-body Stoner Hamiltonian for binary FeCr alloys

NASA Astrophysics Data System (ADS)

Nguyen-Manh, D.; Dudarev, S. L.

2009-09-01

We derive a model tight-binding many-body d -electron Stoner Hamiltonian for FeCr binary alloys and investigate the sensitivity of its mean-field solutions to the choice of hopping integrals and the Stoner exchange parameters. By applying the local charge-neutrality condition within a self-consistent treatment we show that the negative enthalpy-of-mixing anomaly characterizing the alloy in the low chromium concentration limit is due entirely to the presence of the on-site exchange Stoner terms and that the occurrence of this anomaly is not specifically related to the choice of hopping integrals describing conventional chemical bonding between atoms in the alloy. The Bain transformation pathway computed, using the proposed model Hamiltonian, for the Fe15Cr alloy configuration is in excellent agreement with ab initio total-energy calculations. Our investigation also shows how the parameters of a tight-binding many-body model Hamiltonian for a magnetic alloy can be derived from the comparison of its mean-field solutions with other, more accurate, mean-field approximations (e.g., density-functional calculations), hence stimulating the development of large-scale computational algorithms for modeling radiation damage effects in magnetic alloys and steels.

Phases and approximations of baryonic popcorn in a low-dimensional analogue of holographic QCD

NASA Astrophysics Data System (ADS)

Elliot-Ripley, Matthew

2015-07-01

The Sakai-Sugimoto model is the most pre-eminent model of holographic QCD, in which baryons correspond to topological solitons in a five-dimensional bulk spacetime. Recently it has been shown that a single soliton in this model can be well approximated by a flat-space self-dual Yang-Mills instanton with a small size, although studies of multi-solitons and solitons at finite density are currently beyond numerical computations. A lower-dimensional analogue of the model has also been studied in which the Sakai-Sugimoto soliton is replaced by a baby Skyrmion in three spacetime dimensions with a warped metric. The lower dimensionality of this model means that full numerical field calculations are possible, and static multi-solitons and solitons at finite density were both investigated, in particular the baryonic popcorn phase transitions at high densities. Here we present and investigate an alternative lower-dimensional analogue of the Sakai-Sugimoto model in which the Sakai-Sugimoto soliton is replaced by an O(3)-sigma model instanton in a warped three-dimensional spacetime stabilized by a massive vector meson. A more detailed range of baryonic popcorn phase transitions are found, and the low-dimensional model is used as a testing ground to check the validity of common approximations made in the full five-dimensional model, namely approximating fields using their flat-space equations of motion, and performing a leading order expansion in the metric.

Near Identifiability of Dynamical Systems

NASA Technical Reports Server (NTRS)

Hadaegh, F. Y.; Bekey, G. A.

1987-01-01

Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.

Effects of anisotropies in turbulent magnetic diffusion in mean-field solar dynamo models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pipin, V. V.; Kosovichev, A. G.

2014-04-10

We study how anisotropies of turbulent diffusion affect the evolution of large-scale magnetic fields and the dynamo process on the Sun. The effect of anisotropy is calculated in a mean-field magnetohydrodynamics framework assuming that triple correlations provide relaxation to the turbulent electromotive force (so-called the 'minimal τ-approximation'). We examine two types of mean-field dynamo models: the well-known benchmark flux-transport model and a distributed-dynamo model with a subsurface rotational shear layer. For both models, we investigate effects of the double- and triple-cell meridional circulation, recently suggested by helioseismology and numerical simulations. To characterize the anisotropy effects, we introduce a parameter ofmore » anisotropy as a ratio of the radial and horizontal intensities of turbulent mixing. It is found that the anisotropy affects the distribution of magnetic fields inside the convection zone. The concentration of the magnetic flux near the bottom and top boundaries of the convection zone is greater when the anisotropy is stronger. It is shown that the critical dynamo number and the dynamo period approach to constant values for large values of the anisotropy parameter. The anisotropy reduces the overlap of toroidal magnetic fields generated in subsequent dynamo cycles, in the time-latitude 'butterfly' diagram. If we assume that sunspots are formed in the vicinity of the subsurface shear layer, then the distributed dynamo model with the anisotropic diffusivity satisfies the observational constraints from helioseismology and is consistent with the value of effective turbulent diffusion estimated from the dynamics of surface magnetic fields.« less

Finite-temperature Gutzwiller approximation from the time-dependent variational principle

NASA Astrophysics Data System (ADS)

Lanatà, Nicola; Deng, Xiaoyu; Kotliar, Gabriel

2015-08-01

We develop an extension of the Gutzwiller approximation to finite temperatures based on the Dirac-Frenkel variational principle. Our method does not rely on any entropy inequality, and is substantially more accurate than the approaches proposed in previous works. We apply our theory to the single-band Hubbard model at different fillings, and show that our results compare quantitatively well with dynamical mean field theory in the metallic phase. We discuss potential applications of our technique within the framework of first-principle calculations.

Field theoretic approach to roughness corrections

NASA Astrophysics Data System (ADS)

Wu, Hua Yao; Schaden, Martin

2012-02-01

We develop a systematic field theoretic description of roughness corrections to the Casimir free energy of a massless scalar field in the presence of parallel plates with mean separation a. Roughness is modeled by specifying a generating functional for correlation functions of the height profile. The two-point correlation function being characterized by its variance, σ2, and correlation length, ℓ. We obtain the partition function of a massless scalar quantum field interacting with the height profile of the surface via a δ-function potential. The partition function is given by a holographic reduction of this model to three coupled scalar fields on a two-dimensional plane. The original three-dimensional space with a flat parallel plate at a distance a from the rough plate is encoded in the nonlocal propagators of the surface fields on its boundary. Feynman rules for this equivalent 2+1-dimensional model are derived and its counterterms constructed. The two-loop contribution to the free energy of this model gives the leading roughness correction. The effective separation, aeff, to a rough plate is measured to a plane that is displaced a distance ρ∝σ2/ℓ from the mean of its profile. This definition of the separation eliminates corrections to the free energy of order 1/a4 and results in unitary scattering matrices. We obtain an effective low-energy model in the limit ℓ≪a. It determines the scattering matrix and equivalent planar scattering surface of a very rough plate in terms of the single length scale ρ. The Casimir force on a rough plate is found to always weaken with decreasing correlation length ℓ. The two-loop approximation to the free energy interpolates between the free energy of the effective low-energy model and that of the proximity force approximation - the force on a very rough plate with σ≳0.5ℓ being weaker than on a planar Dirichlet surface at any separation.

Polynomial Chaos decomposition applied to stochastic dosimetry: study of the influence of the magnetic field orientation on the pregnant woman exposure at 50 Hz.

PubMed

Liorni, I; Parazzini, M; Fiocchi, S; Guadagnin, V; Ravazzani, P

2014-01-01

Polynomial Chaos (PC) is a decomposition method used to build a meta-model, which approximates the unknown response of a model. In this paper the PC method is applied to the stochastic dosimetry to assess the variability of human exposure due to the change of the orientation of the B-field vector respect to the human body. In detail, the analysis of the pregnant woman exposure at 7 months of gestational age is carried out, to build-up a statistical meta-model of the induced electric field for each fetal tissue and in the fetal whole-body by means of the PC expansion as a function of the B-field orientation, considering a uniform exposure at 50 Hz.

Modeling tracer transport in randomly heterogeneous porous media by nonlocal moment equations: Anomalous transport

NASA Astrophysics Data System (ADS)

Morales-Casique, E.; Lezama-Campos, J. L.; Guadagnini, A.; Neuman, S. P.

2013-05-01

Modeling tracer transport in geologic porous media suffers from the corrupt characterization of the spatial distribution of hydrogeologic properties of the system and the incomplete knowledge of processes governing transport at multiple scales. Representations of transport dynamics based on a Fickian model of the kind considered in the advection-dispersion equation (ADE) fail to capture (a) the temporal variation associated with the rate of spreading of a tracer, and (b) the distribution of early and late arrival times which are often observed in field and/or laboratory scenarios and are considered as the signature of anomalous transport. Elsewhere we have presented exact stochastic moment equations to model tracer transport in randomly heterogeneous aquifers. We have also developed a closure scheme which enables one to provide numerical solutions of such moment equations at different orders of approximations. The resulting (ensemble) average and variance of concentration fields were found to display a good agreement against Monte Carlo - based simulation results for mildly heterogeneous (or well-conditioned strongly heterogeneous) media. Here we explore the ability of the moment equations approach to describe the distribution of early arrival times and late time tailing effects which can be observed in Monte-Carlo based breakthrough curves (BTCs) of the (ensemble) mean concentration. We show that BTCs of mean resident concentration calculated at a fixed space location through higher-order approximations of moment equations display long tailing features of the kind which is typically associated with anomalous transport behavior and are not represented by an ADE model with constant dispersive parameter, such as the zero-order approximation.

Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model

NASA Astrophysics Data System (ADS)

Guerra, Francesco

By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend this argument in order to compare the limiting free energy with the expression given by the Parisi Ansatz, and including full spontaneous replica symmetry breaking. Our main result is that the quenched average of the free energy is bounded from below by the value given in the Parisi Ansatz, uniformly in the size of the system. Moreover, the difference between the two expressions is given in the form of a sum rule, extending our previous work on the comparison between the true free energy and its replica symmetric Sherrington-Kirkpatrick approximation. We give also a variational bound for the infinite volume limit of the ground state energy per site.

Quasielastic charged-current neutrino scattering in the scaling model with relativistic effective mass

NASA Astrophysics Data System (ADS)

Ruiz Simo, I.; Martinez-Consentino, V. L.; Amaro, J. E.; Ruiz Arriola, E.

2018-06-01

We use a recent scaling analysis of the quasielastic electron scattering data from C 12 to predict the quasielastic charge-changing neutrino scattering cross sections within an uncertainty band. We use a scaling function extracted from a selection of the (e ,e') cross section data, and an effective nucleon mass inspired by the relativistic mean-field model of nuclear matter. The corresponding superscaling analysis with relativistic effective mass (SuSAM*) describes a large amount of the electron data lying inside a phenomenological quasielastic band. The effective mass incorporates the enhancement of the transverse current produced by the relativistic mean field. The scaling function incorporates nuclear effects beyond the impulse approximation, in particular meson-exchange currents and short-range correlations producing tails in the scaling function. Besides its simplicity, this model describes the neutrino data as reasonably well as other more sophisticated nuclear models.

Risk perception in epidemic modeling

NASA Astrophysics Data System (ADS)

Bagnoli, Franco; Liò, Pietro; Sguanci, Luca

2007-12-01

We investigate the effects of risk perception in a simple model of epidemic spreading. We assume that the perception of the risk of being infected depends on the fraction of neighbors that are ill. The effect of this factor is to decrease the infectivity, that therefore becomes a dynamical component of the model. We study the problem in the mean-field approximation and by numerical simulations for regular, random, and scale-free networks. We show that for homogeneous and random networks, there is always a value of perception that stops the epidemics. In the “worst-case” scenario of a scale-free network with diverging input connectivity, a linear perception cannot stop the epidemics; however, we show that a nonlinear increase of the perception risk may lead to the extinction of the disease. This transition is discontinuous, and is not predicted by the mean-field analysis.

Model of chiral spin liquids with Abelian and non-Abelian topological phases

DOE PAGES

Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio; ...

2017-12-15

In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, themore » Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.« less

Model of chiral spin liquids with Abelian and non-Abelian topological phases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio

In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, themore » Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.« less

Susceptible-infected-susceptible epidemics on networks with general infection and cure times.

PubMed

Cator, E; van de Bovenkamp, R; Van Mieghem, P

2013-06-01

The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS) model, is believed to have a much larger applicability to real-world epidemics (such as information spread in online social networks, real diseases, malware spread in computer networks, etc.) that likely do not feature exponential times. While the exact governing equations for the GSIS model are difficult to deduce due to their non-Markovian nature, accurate mean-field equations are derived that resemble our previous N-intertwined mean-field approximation (NIMFA) and so allow us to transfer the whole analytic machinery of the NIMFA to the GSIS model. In particular, we establish the criterion to compute the epidemic threshold in the GSIS model. Moreover, we show that the average number of infection attempts during a recovery time is the more natural key parameter, instead of the effective infection rate in the classical, continuous-time SIS Markov model. The relative simplicity of our mean-field results enables us to treat more general types of SIS epidemics, while offering an easier key parameter to measure the average activity of those general viral agents.

Susceptible-infected-susceptible epidemics on networks with general infection and cure times

NASA Astrophysics Data System (ADS)

Cator, E.; van de Bovenkamp, R.; Van Mieghem, P.

2013-06-01

The classical, continuous-time susceptible-infected-susceptible (SIS) Markov epidemic model on an arbitrary network is extended to incorporate infection and curing or recovery times each characterized by a general distribution (rather than an exponential distribution as in Markov processes). This extension, called the generalized SIS (GSIS) model, is believed to have a much larger applicability to real-world epidemics (such as information spread in online social networks, real diseases, malware spread in computer networks, etc.) that likely do not feature exponential times. While the exact governing equations for the GSIS model are difficult to deduce due to their non-Markovian nature, accurate mean-field equations are derived that resemble our previous N-intertwined mean-field approximation (NIMFA) and so allow us to transfer the whole analytic machinery of the NIMFA to the GSIS model. In particular, we establish the criterion to compute the epidemic threshold in the GSIS model. Moreover, we show that the average number of infection attempts during a recovery time is the more natural key parameter, instead of the effective infection rate in the classical, continuous-time SIS Markov model. The relative simplicity of our mean-field results enables us to treat more general types of SIS epidemics, while offering an easier key parameter to measure the average activity of those general viral agents.

Approximate Joint Diagonalization and Geometric Mean of Symmetric Positive Definite Matrices

PubMed Central

Congedo, Marco; Afsari, Bijan; Barachant, Alexandre; Moakher, Maher

2015-01-01

We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint diagonalization (AJD). Today there is a considerable interest in estimating the geometric mean of a SPD matrix set in the manifold of SPD matrices endowed with the Fisher information metric. The resulting mean has several important invariance properties and has proven very useful in diverse engineering applications such as biomedical and image data processing. While for two SPD matrices the mean has an algebraic closed form solution, for a set of more than two SPD matrices it can only be estimated by iterative algorithms. However, none of the existing iterative algorithms feature at the same time fast convergence, low computational complexity per iteration and guarantee of convergence. For this reason, recently other definitions of geometric mean based on symmetric divergence measures, such as the Bhattacharyya divergence, have been considered. The resulting means, although possibly useful in practice, do not satisfy all desirable invariance properties. In this paper we consider geometric means of covariance matrices estimated on high-dimensional time-series, assuming that the data is generated according to an instantaneous mixing model, which is very common in signal processing. We show that in these circumstances we can approximate the Fisher information geometric mean by employing an efficient AJD algorithm. Our approximation is in general much closer to the Fisher information geometric mean as compared to its competitors and verifies many invariance properties. Furthermore, convergence is guaranteed, the computational complexity is low and the convergence rate is quadratic. The accuracy of this new geometric mean approximation is demonstrated by means of simulations. PMID:25919667

Magnetic probing of the solar interior

NASA Technical Reports Server (NTRS)

Benton, E. R.; Estes, R. H.

1985-01-01

The magnetic field patterns in the region beneath the solar photosphere is determined. An approximate method for downward extrapolation of line of sight magnetic field measurements taken at the solar photosphere was developed. It utilizes the mean field theory of electromagnetism in a form thought to be appropriate for the solar convection zone. A way to test that theory is proposed. The straightforward application of the lowest order theory with the complete model fit to these data does not indicate the existence of any reasonable depth at which flux conservation is achieved.

Antiferromagnetism and DX2-Y2-WAVE Pairing in the Colored Hubbard Model

NASA Astrophysics Data System (ADS)

Baier, Tobias; Bick, Eike

2001-08-01

We introduce a new formulation of the 2d Hubbard model on a square lattice (the "colored" Hubbard model). In this formulation interesting physical nonlocal properties as antiferromagnetic or dx2-y2-wave superconducting behavior are included in an explicit way. Analyzing the phase diagram in a mean field approximation numerically, we show that our approach yields results which are in qualitative agreement with experiment.

Semiclassical theory of the self-consistent vibration-rotation fields and its application to the bending-rotation interaction in the H{sub 2}O molecule

DOE Office of Scientific and Technical Information (OSTI.GOV)

Skalozub, A.S.; Tsaune, A.Ya.

1994-12-01

A new approach for analyzing the highly excited vibration-rotation (VR) states of nonrigid molecules is suggested. It is based on the separation of the vibrational and rotational terms in the molecular VR Hamiltonian by introducing periodic auxiliary fields. These fields transfer different interactions within a molecule and are treated in terms of the mean-field approximation. As a result, the solution of the stationary Schroedinger equation with the VR Hamiltonian amounts to a quantization of the Berry phase in a problem of the molecular angular-momentum motion in a certain periodic VR field (rotational problem). The quantization procedure takes into account themore » motion of the collective vibrational variables in the appropriate VR potentials (vibrational problem). The quantization rules, the mean-field configurations of auxiliary interactions, and the solutions to the Schrodinger equations for the vibrational and rotational problems are self-consistently connected with one another. The potentialities of the theory are demonstrated by the bending-rotation interaction modeled by the Bunker-Landsberg potential function in the H{sub 2} molecule. The calculations are compared with both the results of the exact computations and those of other approximate methods. 32 refs., 4 tabs.« less

Dynamics of anisotropies close to a cosmological bounce in quantum gravity

NASA Astrophysics Data System (ADS)

de Cesare, Marco; Oriti, Daniele; Pithis, Andreas G. A.; Sakellariadou, Mairi

2018-01-01

We study the dynamics of perturbations representing deviations from perfect isotropy in the context of the emergent cosmology obtained from the group field theory formalism for quantum gravity. Working in the mean field approximation of the group field theory formulation of the Lorentzian EPRL model, we derive the equations of motion for such perturbations to first order. We then study these equations around a specific simple isotropic background, characterised by the fundamental representation of SU(2) , and in the regime of the effective cosmological dynamics corresponding to the bouncing region replacing the classical singularity, well approximated by the free GFT dynamics. In this particular example, we identify a region in the parameter space of the model such that perturbations can be large at the bounce but become negligible away from it, i.e. when the background enters the non-linear regime. We also study the departures from perfect isotropy by introducing specific quantities, such as the surface-area-to-volume ratio and the effective volume per quantum, which make them quantitative.

Effect of deformation on structure and reaction of Al isotopes using relativistic mean field densities in Glauber model

NASA Astrophysics Data System (ADS)

Panda, R. N.; Sharma, Mahesh K.; Panigrahi, M.; Patra, S. K.

2018-02-01

We have examined the ground state properties of Al isotopes towards the proton rich side from A = 22 to 28 using the well known relativistic mean field (RMF) formalism with NLSH parameter set. The calculated results are compared with the predictions of finite range droplet model and experimental data. The calculation is extended to estimate the reaction cross section for ^{22-28} Al as projectiles with ^{12} C as target. The incident energy of the projectiles are taken as 950 MeV/nucleon, for both spherical and deformed RMF densities as inputs in the Glauber model approximation. Further investigation of enhanced values of total reaction cross section for ^{23} Al and ^{24} Al in comparison to rest of the isotopes indicates the proton skin structure of these isotopes. Specifically, the large value of root mean square radius and total reaction cross section of ^{23} Al could not be ruled out the formation of proton halo.

Effect of deformation on structure and reaction of Al isotopes using relativistic mean field densities in Glauber model

NASA Astrophysics Data System (ADS)

Panda, R. N.; Sharma, Mahesh K.; Panigrahi, M.; Patra, S. K.

2018-06-01

We have examined the ground state properties of Al isotopes towards the proton rich side from A = 22 to 28 using the well known relativistic mean field (RMF) formalism with NLSH parameter set. The calculated results are compared with the predictions of finite range droplet model and experimental data. The calculation is extended to estimate the reaction cross section for ^{22-28}Al as projectiles with ^{12}C as target. The incident energy of the projectiles are taken as 950 MeV/nucleon, for both spherical and deformed RMF densities as inputs in the Glauber model approximation. Further investigation of enhanced values of total reaction cross section for ^{23}Al and ^{24}Al in comparison to rest of the isotopes indicates the proton skin structure of these isotopes. Specifically, the large value of root mean square radius and total reaction cross section of ^{23}Al could not be ruled out the formation of proton halo.

Technical Note: Approximate Bayesian parameterization of a complex tropical forest model

NASA Astrophysics Data System (ADS)

Hartig, F.; Dislich, C.; Wiegand, T.; Huth, A.

2013-08-01

Inverse parameter estimation of process-based models is a long-standing problem in ecology and evolution. A key problem of inverse parameter estimation is to define a metric that quantifies how well model predictions fit to the data. Such a metric can be expressed by general cost or objective functions, but statistical inversion approaches are based on a particular metric, the probability of observing the data given the model, known as the likelihood. Deriving likelihoods for dynamic models requires making assumptions about the probability for observations to deviate from mean model predictions. For technical reasons, these assumptions are usually derived without explicit consideration of the processes in the simulation. Only in recent years have new methods become available that allow generating likelihoods directly from stochastic simulations. Previous applications of these approximate Bayesian methods have concentrated on relatively simple models. Here, we report on the application of a simulation-based likelihood approximation for FORMIND, a parameter-rich individual-based model of tropical forest dynamics. We show that approximate Bayesian inference, based on a parametric likelihood approximation placed in a conventional MCMC, performs well in retrieving known parameter values from virtual field data generated by the forest model. We analyze the results of the parameter estimation, examine the sensitivity towards the choice and aggregation of model outputs and observed data (summary statistics), and show results from using this method to fit the FORMIND model to field data from an Ecuadorian tropical forest. Finally, we discuss differences of this approach to Approximate Bayesian Computing (ABC), another commonly used method to generate simulation-based likelihood approximations. Our results demonstrate that simulation-based inference, which offers considerable conceptual advantages over more traditional methods for inverse parameter estimation, can successfully be applied to process-based models of high complexity. The methodology is particularly suited to heterogeneous and complex data structures and can easily be adjusted to other model types, including most stochastic population and individual-based models. Our study therefore provides a blueprint for a fairly general approach to parameter estimation of stochastic process-based models in ecology and evolution.

The effect of horizontal resolution on simulation quality in the Community Atmospheric Model, CAM5.1

DOE PAGES

Wehner, Michael F.; Reed, Kevin A.; Li, Fuyu; ...

2014-10-13

We present an analysis of version 5.1 of the Community Atmospheric Model (CAM5.1) at a high horizontal resolution. Intercomparison of this global model at approximately 0.25°, 1°, and 2° is presented for extreme daily precipitation as well as for a suite of seasonal mean fields. In general, extreme precipitation amounts are larger in high resolution than in lower-resolution configurations. In many but not all locations and/or seasons, extreme daily precipitation rates in the high-resolution configuration are higher and more realistic. The high-resolution configuration produces tropical cyclones up to category 5 on the Saffir-Simpson scale and a comparison to observations revealsmore » both realistic and unrealistic model behavior. In the absence of extensive model tuning at high resolution, simulation of many of the mean fields analyzed in this study is degraded compared to the tuned lower-resolution public released version of the model.« less

Nonthermal steady states after an interaction quench in the Falicov-Kimball model.

PubMed

Eckstein, Martin; Kollar, Marcus

2008-03-28

We present the exact solution of the Falicov-Kimball model after a sudden change of its interaction parameter using nonequilibrium dynamical mean-field theory. For different interaction quenches between the homogeneous metallic and insulating phases the system relaxes to a nonthermal steady state on time scales on the order of variant Planck's over 2pi/bandwidth, showing collapse and revival with an approximate period of h/interaction if the interaction is large. We discuss the reasons for this behavior and provide a statistical description of the final steady state by means of generalized Gibbs ensembles.

Stormtime transport of ring current and radiation belt ions

NASA Technical Reports Server (NTRS)

Chen, Margaret W.; Schulz, Michael; Lyons, L. R.; Gorney, David J.

1993-01-01

This is an investigation of stormtime particle transport that leads to formation of the ring current. Our method is to trace the guiding-center motion of representative ions (having selected first adiabatic invariants mu) in response to model substorm-associated impulses in the convection electric field. We compare our simulation results qualitatively with existing analytically tractable idealizations of particle transport (direct convective access and radial diffusion) in order to assess the limits of validity of these approximations. For mu approximately less than 10 MeV/G (E approximately less than 10 keV at L equivalent to 3) the ion drift period on the final (ring-current) drift shell of interest (L equivalent to 3) exceeds the duration of the main phase of our model storm, and we find that the transport of ions to this drift shell is appropriately idealized as direct convective access, typically from open drift paths. Ion transport to a final closed drift path from an open (plasma-sheet) drift trajectory is possible for those portions of that drift path that lie outside the mean stormtime separatrix between closed and open drift trajectories, For mu approximately 10-25 MeV/G (110 keV approximately less than E approximately less than 280 keV at L equivalent to 3) the drift period at L equivalent to 3 is comparable to the postulated 3-hr duration of the storm, and the mode of transport is transitional between direct convective access and transport that resembles radial diffusion. (This particle population is transitional between the ring current and radiation belt). For mu approximately greater than 25 MeV/G (radiation-belt ions having E approximately greater than 280 keV at L equivalent to 3) the ion drift period is considerably shorter than the main phase of a typical storm, and ions gain access to the ring-current region essentially via radial diffusion. By computing the mean and mean-square cumulative changes in 1/L among (in this case) 12 representative ions equally spaced in drift time around the steady-state drift shell of interest (L equivalent to 3), we have estimated (from both our forward and our time-reversed simulations) the time-integrated radial-diffusion coefficients D(sup sim)(sub LL) for particles having selected values of mu approximately greater than 15 MeV/G. The results agree surprisingly well with the predictions (D(sup ql)(sub LL)) of quasilinear radial diffusion theory, despite the rather brief duration (approximately 3 hrs) of our model storm and despite the extreme variability (with frequency) of the spectral-density function that characterizes the applied electric field during our model storm. As expected, the values of D(sup sim)(sub LL) deduced (respectively) from our forward and time-reversed simulations agree even better with each other and with D(sup sim)(sub LL) when the impulse amplitudes which characterize the individual substorms of our model storm are systematically reduced.

Warm ''pasta'' phase in the Thomas-Fermi approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Avancini, Sidney S.; Menezes, Debora P.; Chiacchiera, Silvia

In the present article, the 'pasta' phase is studied at finite temperatures within a Thomas-Fermi (TF) approach. Relativistic mean-field models, both with constant and density-dependent couplings, are used to describe this frustrated system. We compare the present results with previous ones obtained within a phase-coexistence description and conclude that the TF approximation gives rise to a richer inner ''pasta'' phase structure and the homogeneous matter appears at higher densities. Finally, the transition density calculated within TF is compared with the results for this quantity obtained with other methods.

Ground-state phase diagram in the Kugel-Khomskii model with finite spin-orbit interactions

NASA Astrophysics Data System (ADS)

Koga, Akihisa; Nakauchi, Shiryu; Nasu, Joji

2018-05-01

We study ground-state properties in the Kugel-Khomskii model on the two-dimensional honeycomb lattice. Using the cluster mean-field approximations, we deal with the exchange and spin-orbit couplings on an equal footing. We then discuss the stability of the ferromagnetically ordered states against the nonmagnetic state, which is adiabatically connected to the quantum spin liquid state realized in a strong spin-orbit coupling limit.

Critical behavior of the contact process on small-world networks

NASA Astrophysics Data System (ADS)

Ferreira, Ronan S.; Ferreira, Silvio C.

2013-11-01

We investigate the role of clustering on the critical behavior of the contact process (CP) on small-world networks using the Watts-Strogatz (WS) network model with an edge rewiring probability p. The critical point is well predicted by a homogeneous cluster-approximation for the limit of vanishing clustering ( p → 1). The critical exponents and dimensionless moment ratios of the CP are in agreement with those predicted by the mean-field theory for any p > 0. This independence on the network clustering shows that the small-world property is a sufficient condition for the mean-field theory to correctly predict the universality of the model. Moreover, we compare the CP dynamics on WS networks with rewiring probability p = 1 and random regular networks and show that the weak heterogeneity of the WS network slightly changes the critical point but does not alter other critical quantities of the model.

Spatial correlations in driven-dissipative photonic lattices

NASA Astrophysics Data System (ADS)

Biondi, Matteo; Lienhard, Saskia; Blatter, Gianni; Türeci, Hakan E.; Schmidt, Sebastian

2017-12-01

We study the nonequilibrium steady-state of interacting photons in cavity arrays as described by the driven-dissipative Bose–Hubbard and spin-1/2 XY model. For this purpose, we develop a self-consistent expansion in the inverse coordination number of the array (∼ 1/z) to solve the Lindblad master equation of these systems beyond the mean-field approximation. Our formalism is compared and benchmarked with exact numerical methods for small systems based on an exact diagonalization of the Liouvillian and a recently developed corner-space renormalization technique. We then apply this method to obtain insights beyond mean-field in two particular settings: (i) we show that the gas–liquid transition in the driven-dissipative Bose–Hubbard model is characterized by large density fluctuations and bunched photon statistics. (ii) We study the antibunching–bunching transition of the nearest-neighbor correlator in the driven-dissipative spin-1/2 XY model and provide a simple explanation of this phenomenon.

Multifrequency observations of the radio continuum emission from NGC 253. 1: Magnetic fields and rotation measures in the bar and halo

NASA Astrophysics Data System (ADS)

Beck, R.; Carilli, C. L.; Holdaway, M. A.; Klein, U.

1994-12-01

Radio continuum observations of the spiral galaxy NGC 253 with the Effelsberg and Very Large Array (VLA) telescopes reveal polarized emission from the bar and halo regions. Within the bar Faraday depolarization is strong at 1.5 and 5 GHz, due to ionized gas with ne approximately equal 0.1 - 3/cu cm which is mixed with turbulent magnetic fields of approximately equal 17 microG estimated strength. Even at 10 GHz the degree of polarization in the bar is low (only approximately equal 5% east and approximately equal 2% west of the nucleus) due to beam depolarization by unresolved tangled fields. In contrast, the magnetic fields in the halo are highly uniform, as indicated by fractional polarizations up to 40% at 10 GHz. Faraday depolarization in the halo at 1.5 GHz calls for a warm, clumpy gas component with ne approximately equal 0.02/cu cm and approximately equal 6 microG turbulent fields. We detected Faraday rotation in the bar, with rotation measures absolute value of RM approximately equal 100 rad/sq m (between 10 and 5 GHz) having different signs east and west of the nucleus. Below 5 GHz Faraday rotation is strongly reduced by the limited transparency for polarized emission in the bar. Faraday rotation in the halo in two regions at approximately 5 kpc above and below the plane with RM approximately equal -7 rad/sq m between 10 and 1.5 GHz can be ascribed to hot gas with mean value of ne approximately equal 0.002/cu cm and uniform fields along the line of sight of mean value of Bu parallel approximately equal -2 microG. The magnetic field structure in the bar and halo of NGC 253 is best described by the quadrupole-type dynamo mode SO, with a ring-like field in the bar and a field mainly parallel to the plane in a co-rotating halo. A major perturbation occurs in the east where the field is perpendicular to the plane and follows a 'spur'. The galactic wind is suppressed by the dominating plane-parallel field, except along the spur.

Coherent-Anomaly Method in Critical Phenomena. IV. Study of the Wave-Number-Dependent Susceptibility in the 2D Ising Model

NASA Astrophysics Data System (ADS)

Hu, Xiao; Suzuki, Masuo

1988-03-01

The systematic Weiss-like and Bethe-like approximations based on the mean-field transfer-matrix method are used to investigate the asymptotic behavior of the induced magnetization on a semi-infinite square lattice, and to investigate the wave-number dependence of the susceptibility in a nonuniform external field. The critical exponents ν, ν', ηi and η are estimated following the general CAM prescription. A new scaling relation ν{\\cdot}ηi{=}β is obtained in the framework of the finite-degree-of-approximation scaling. Together with previous papers, all the static critical exponents have been estimated by the CAM, and are shown to satisfy the well-known scaling relations.

Development of a towing tank PIV system and a wake survey of a marine current turbine under steady conditions

NASA Astrophysics Data System (ADS)

Lust, Ethan; Luznik, Luksa; Flack, Karen

2015-11-01

A submersible particle image velocimetry (PIV) system was designed and built at the U.S. Naval Academy. The system was used to study the wake of a scale-independent horizontal axis marine current turbine. The turbine is a 1/25th scale model of the U.S. National Renewable Energy Laboratory's Reference Model 1 (RM1) tidal turbine. It is a two-bladed turbine measuring 0.8 m in diameter and featuring a NACA 63-618 airfoil cross-section. The wake survey was conducted over an area extending 0.25D forward of the turbine tip path to 2.0D aft to a depth of 1.0D beneath the turbine output shaft in the streamwise plane. Each field of view was approximately 30 cm by 30 cm, and each overlapped the adjacent fields of view by 5 cm. The entire flow field was then reconstructed by registering the resultant vector fields together into a single field of investigation. Results include the field of investigation from a representative case, for the mean velocity field averaged over approximately 1,000 realizations, and turbulent statistics including turbulence intensities, Reynolds shear stresses, and turbulent kinetic energy. This research was funded by the Office of Naval Research.

Numerical simulation of photocurrent generation in bilayer organic solar cells: Comparison of master equation and kinetic Monte Carlo approaches

NASA Astrophysics Data System (ADS)

Casalegno, Mosè; Bernardi, Andrea; Raos, Guido

2013-07-01

Numerical approaches can provide useful information about the microscopic processes underlying photocurrent generation in organic solar cells (OSCs). Among them, the Kinetic Monte Carlo (KMC) method is conceptually the simplest, but computationally the most intensive. A less demanding alternative is potentially represented by so-called Master Equation (ME) approaches, where the equations describing particle dynamics rely on the mean-field approximation and their solution is attained numerically, rather than stochastically. The description of charge separation dynamics, the treatment of electrostatic interactions and numerical stability are some of the key issues which have prevented the application of these methods to OSC modelling, despite of their successes in the study of charge transport in disordered system. Here we describe a three-dimensional ME approach to photocurrent generation in OSCs which attempts to deal with these issues. The reliability of the proposed method is tested against reference KMC simulations on bilayer heterojunction solar cells. Comparison of the current-voltage curves shows that the model well approximates the exact result for most devices. The largest deviations in current densities are mainly due to the adoption of the mean-field approximation for electrostatic interactions. The presence of deep traps, in devices characterized by strong energy disorder, may also affect result quality. Comparison of the simulation times reveals that the ME algorithm runs, on the average, one order of magnitude faster than KMC.

Discrete and Continuum Approximations for Collective Cell Migration in a Scratch Assay with Cell Size Dynamics.

PubMed

Matsiaka, Oleksii M; Penington, Catherine J; Baker, Ruth E; Simpson, Matthew J

2018-04-01

Scratch assays are routinely used to study the collective spreading of cell populations. In general, the rate at which a population of cells spreads is driven by the combined effects of cell migration and proliferation. To examine the effects of cell migration separately from the effects of cell proliferation, scratch assays are often performed after treating the cells with a drug that inhibits proliferation. Mitomycin-C is a drug that is commonly used to suppress cell proliferation in this context. However, in addition to suppressing cell proliferation, mitomycin-C also causes cells to change size during the experiment, as each cell in the population approximately doubles in size as a result of treatment. Therefore, to describe a scratch assay that incorporates the effects of cell-to-cell crowding, cell-to-cell adhesion, and dynamic changes in cell size, we present a new stochastic model that incorporates these mechanisms. Our agent-based stochastic model takes the form of a system of Langevin equations that is the system of stochastic differential equations governing the evolution of the population of agents. We incorporate a time-dependent interaction force that is used to mimic the dynamic increase in size of the agents. To provide a mathematical description of the average behaviour of the stochastic model we present continuum limit descriptions using both a standard mean-field approximation and a more sophisticated moment dynamics approximation that accounts for the density of agents and density of pairs of agents in the stochastic model. Comparing the accuracy of the two continuum descriptions for a typical scratch assay geometry shows that the incorporation of agent growth in the system is associated with a decrease in accuracy of the standard mean-field description. In contrast, the moment dynamics description provides a more accurate prediction of the evolution of the scratch assay when the increase in size of individual agents is included in the model.

Photolysis rates in correlated overlapping cloud fields: Cloud-J 7.3

DOE PAGES

Prather, M. J.

2015-05-27

A new approach for modeling photolysis rates ( J values) in atmospheres with fractional cloud cover has been developed and implemented as Cloud-J – a multi-scattering eight-stream radiative transfer model for solar radiation based on Fast-J. Using observed statistics for the vertical correlation of cloud layers, Cloud-J 7.3 provides a practical and accurate method for modeling atmospheric chemistry. The combination of the new maximum-correlated cloud groups with the integration over all cloud combinations represented by four quadrature atmospheres produces mean J values in an atmospheric column with root-mean-square errors of 4% or less compared with 10–20% errors using simpler approximations.more » Cloud-J is practical for chemistry-climate models, requiring only an average of 2.8 Fast-J calls per atmosphere, vs. hundreds of calls with the correlated cloud groups, or 1 call with the simplest cloud approximations. Another improvement in modeling J values, the treatment of volatile organic compounds with pressure-dependent cross sections is also incorporated into Cloud-J.« less

Photolysis rates in correlated overlapping cloud fields: Cloud-J 7.3c

DOE PAGES

Prather, M. J.

2015-08-14

A new approach for modeling photolysis rates ( J values) in atmospheres with fractional cloud cover has been developed and is implemented as Cloud-J – a multi-scattering eight-stream radiative transfer model for solar radiation based on Fast-J. Using observations of the vertical correlation of cloud layers, Cloud-J 7.3c provides a practical and accurate method for modeling atmospheric chemistry. The combination of the new maximum-correlated cloud groups with the integration over all cloud combinations by four quadrature atmospheres produces mean J values in an atmospheric column with root mean square (rms) errors of 4 % or less compared with 10–20 %more » errors using simpler approximations. Cloud-J is practical for chemistry–climate models, requiring only an average of 2.8 Fast-J calls per atmosphere vs. hundreds of calls with the correlated cloud groups, or 1 call with the simplest cloud approximations. Another improvement in modeling J values, the treatment of volatile organic compounds with pressure-dependent cross sections, is also incorporated into Cloud-J.« less

Mean-field dynamo in a turbulence with shear and kinetic helicity fluctuations.

PubMed

Kleeorin, Nathan; Rogachevskii, Igor

2008-03-01

We study the effects of kinetic helicity fluctuations in a turbulence with large-scale shear using two different approaches: the spectral tau approximation and the second-order correlation approximation (or first-order smoothing approximation). These two approaches demonstrate that homogeneous kinetic helicity fluctuations alone with zero mean value in a sheared homogeneous turbulence cannot cause a large-scale dynamo. A mean-field dynamo is possible when the kinetic helicity fluctuations are inhomogeneous, which causes a nonzero mean alpha effect in a sheared turbulence. On the other hand, the shear-current effect can generate a large-scale magnetic field even in a homogeneous nonhelical turbulence with large-scale shear. This effect was investigated previously for large hydrodynamic and magnetic Reynolds numbers. In this study we examine the threshold required for the shear-current dynamo versus Reynolds number. We demonstrate that there is no need for a developed inertial range in order to maintain the shear-current dynamo (e.g., the threshold in the Reynolds number is of the order of 1).

The noisy voter model on complex networks.

PubMed

Carro, Adrián; Toral, Raúl; San Miguel, Maxi

2016-04-20

We propose a new analytical method to study stochastic, binary-state models on complex networks. Moving beyond the usual mean-field theories, this alternative approach is based on the introduction of an annealed approximation for uncorrelated networks, allowing to deal with the network structure as parametric heterogeneity. As an illustration, we study the noisy voter model, a modification of the original voter model including random changes of state. The proposed method is able to unfold the dependence of the model not only on the mean degree (the mean-field prediction) but also on more complex averages over the degree distribution. In particular, we find that the degree heterogeneity--variance of the underlying degree distribution--has a strong influence on the location of the critical point of a noise-induced, finite-size transition occurring in the model, on the local ordering of the system, and on the functional form of its temporal correlations. Finally, we show how this latter point opens the possibility of inferring the degree heterogeneity of the underlying network by observing only the aggregate behavior of the system as a whole, an issue of interest for systems where only macroscopic, population level variables can be measured.

Burst of virus infection and a possibly largest epidemic threshold of non-Markovian susceptible-infected-susceptible processes on networks

NASA Astrophysics Data System (ADS)

Liu, Qiang; Van Mieghem, Piet

2018-02-01

Since a real epidemic process is not necessarily Markovian, the epidemic threshold obtained under the Markovian assumption may be not realistic. To understand general non-Markovian epidemic processes on networks, we study the Weibullian susceptible-infected-susceptible (SIS) process in which the infection process is a renewal process with a Weibull time distribution. We find that, if the infection rate exceeds 1 /ln(λ1+1 ) , where λ1 is the largest eigenvalue of the network's adjacency matrix, then the infection will persist on the network under the mean-field approximation. Thus, 1 /ln(λ1+1 ) is possibly the largest epidemic threshold for a general non-Markovian SIS process with a Poisson curing process under the mean-field approximation. Furthermore, non-Markovian SIS processes may result in a multimodal prevalence. As a byproduct, we show that a limiting Weibullian SIS process has the potential to model bursts of a synchronized infection.

Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation

NASA Astrophysics Data System (ADS)

Joo, Jaewook; Lebowitz, Joel L.

2004-06-01

We investigate saturation effects in susceptible-infected-susceptible models of the spread of epidemics in heterogeneous populations. The structure of interactions in the population is represented by networks with connectivity distribution P(k) , including scale-free (SF) networks with power law distributions P(k)˜ k-γ . Considering cases where the transmission of infection between nodes depends on their connectivity, we introduce a saturation function C(k) which reduces the infection transmission rate λ across an edge going from a node with high connectivity k . A mean-field approximation with the neglect of degree-degree correlation then leads to a finite threshold λc >0 for SF networks with 2<γ⩽3 . We also find, in this approximation, the fraction of infected individuals among those with degree k for λ close to λc . We investigate via computer simulation the contact process on a heterogeneous regular lattice and compare the results with those obtained from mean-field theory with and without neglect of degree-degree correlations.

Neural networks with excitatory and inhibitory components: Direct and inverse problems by a mean-field approach

NASA Astrophysics Data System (ADS)

di Volo, Matteo; Burioni, Raffaella; Casartelli, Mario; Livi, Roberto; Vezzani, Alessandro

2016-01-01

We study the dynamics of networks with inhibitory and excitatory leak-integrate-and-fire neurons with short-term synaptic plasticity in the presence of depressive and facilitating mechanisms. The dynamics is analyzed by a heterogeneous mean-field approximation, which allows us to keep track of the effects of structural disorder in the network. We describe the complex behavior of different classes of excitatory and inhibitory components, which give rise to a rich dynamical phase diagram as a function of the fraction of inhibitory neurons. Using the same mean-field approach, we study and solve a global inverse problem: reconstructing the degree probability distributions of the inhibitory and excitatory components and the fraction of inhibitory neurons from the knowledge of the average synaptic activity field. This approach unveils new perspectives on the numerical study of neural network dynamics and the possibility of using these models as a test bed for the analysis of experimental data.

Landau ghost pole problem in quantum field theory: From 50th of last century to the present day

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jafarov, Rauf G., E-mail: rauf-jafarov@hotmail.com; Mutallimov, Mutallim M.

2016-03-25

In this paper we present our results of the investigation of asymptotical behavior of amplitude at short distances in four-dimensional scalar field theory with ϕ{sup 4} interaction. To formulate of our calculating model – two-particle approximation of the mean-field expansion we have used an Rochev’s iteration scheme of solution of the Schwinger-Dyson equations with the fermion bilocal source. We have considered the nonlinear integral equations in deep-inelastic region of momenta. As result we have a non-trivial behavior of amplitude at large momenta.

A new effective correlation mean-field theory for the ferromagnetic spin-1 Blume-Capel model in a transverse crystal field

NASA Astrophysics Data System (ADS)

Roberto Viana, J.; Rodriguez Salmon, Octavio D.; Neto, Minos A.; Carvalho, Diego C.

2018-02-01

A new approximation technique is developed so as to study the quantum ferromagnetic spin-1 Blume-Capel model in the presence of a transverse crystal field in the square lattice. Our proposal consists of approaching the spin system by considering islands of finite clusters whose frontiers are surrounded by noninteracting spins that are treated by the effective-field theory. The resulting phase diagram is qualitatively correct, in contrast to most effective-field treatments, in which the first-order line exhibits spurious behavior by not being perpendicular to the anisotropy axis at low-temperatures. The effect of the transverse anisotropy is also verified by the presence of quantum phase transitions. The possibility of using larger sizes constitutes an advantage to other approaches where the implementation of larger sizes is computationally costly.

Lumping of degree-based mean-field and pair-approximation equations for multistate contact processes

NASA Astrophysics Data System (ADS)

Kyriakopoulos, Charalampos; Grossmann, Gerrit; Wolf, Verena; Bortolussi, Luca

2018-01-01

Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information-spreading networks. While devising stochastic models of such processes is relatively easy, analyzing them is very challenging from a computational point of view, particularly for large networks appearing in real applications. One strategy to reduce the complexity of their analysis is to rely on approximations, often in terms of a set of differential equations capturing the evolution of a random node, distinguishing nodes with different topological contexts (i.e., different degrees of different neighborhoods), such as degree-based mean-field (DBMF), approximate-master-equation (AME), or pair-approximation (PA) approaches. The number of differential equations so obtained is typically proportional to the maximum degree kmax of the network, which is much smaller than the size of the master equation of the underlying stochastic model, yet numerically solving these equations can still be problematic for large kmax. In this paper, we consider AME and PA, extended to cope with multiple local states, and we provide an aggregation procedure that clusters together nodes having similar degrees, treating those in the same cluster as indistinguishable, thus reducing the number of equations while preserving an accurate description of global observables of interest. We also provide an automatic way to build such equations and to identify a small number of degree clusters that give accurate results. The method is tested on several case studies, where it shows a high level of compression and a reduction of computational time of several orders of magnitude for large networks, with minimal loss in accuracy.

Hierarchical mean-field approach to the J1-J2 Heisenberg model on a square lattice

NASA Astrophysics Data System (ADS)

Isaev, L.; Ortiz, G.; Dukelsky, J.

2009-01-01

We study the quantum phase diagram and excitation spectrum of the frustrated J1-J2 spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying relevant degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry-preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers, and other degrees of freedom, and show that only the symmetric plaquette covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) plaquette crystal, connected with the neighboring Néel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the Néel and columnar phases. Our results suggest that the quantum phase transition between Néel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.

Hierarchical mean-field approach to the J1-J2 Heisenberg model on a square lattice

NASA Astrophysics Data System (ADS)

Isaev, Leonid; Ortiz, Gerardo; Dukelsky, Jorge

2009-03-01

We study the quantum phase diagram and excitation spectrum of the frustrated J1-J2 spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying relevant degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers and other degrees of freedom, and show that only the symmetric plaquette covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) plaquette crystal, connected with the neighbouring N'eel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the N'eel and columnar phases. Our results suggest that the quantum phase transition between N'eel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.

Comparative study of the requantization of the time-dependent mean field for the dynamics of nuclear pairing

NASA Astrophysics Data System (ADS)

Ni, Fang; Nakatsukasa, Takashi

2018-04-01

To describe quantal collective phenomena, it is useful to requantize the time-dependent mean-field dynamics. We study the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory for the two-level pairing Hamiltonian, and compare results of different quantization methods. The one constructing microscopic wave functions, using the TDHFB trajectories fulfilling the Einstein-Brillouin-Keller quantization condition, turns out to be the most accurate. The method is based on the stationary-phase approximation to the path integral. We also examine the performance of the collective model which assumes that the pairing gap parameter is the collective coordinate. The applicability of the collective model is limited for the nuclear pairing with a small number of single-particle levels, because the pairing gap parameter represents only a half of the pairing collective space.

Loop expansion around the Bethe approximation through the M-layer construction

NASA Astrophysics Data System (ADS)

Altieri, Ada; Chiara Angelini, Maria; Lucibello, Carlo; Parisi, Giorgio; Ricci-Tersenghi, Federico; Rizzo, Tommaso

2017-11-01

For every physical model defined on a generic graph or factor graph, the Bethe M-layer construction allows building a different model for which the Bethe approximation is exact in the large M limit, and coincides with the original model for M=1 . The 1/M perturbative series is then expressed by a diagrammatic loop expansion in terms of so-called fat diagrams. Our motivation is to study some important second-order phase transitions that do exist on the Bethe lattice, but are either qualitatively different or absent in the corresponding fully connected case. In this case, the standard approach based on a perturbative expansion around the naive mean field theory (essentially a fully connected model) fails. On physical grounds, we expect that when the construction is applied to a lattice in finite dimension there is a small region of the external parameters, close to the Bethe critical point, where strong deviations from mean-field behavior will be observed. In this region, the 1/M expansion for the corrections diverges, and can be the starting point for determining the correct non-mean-field critical exponents using renormalization group arguments. In the end, we will show that the critical series for the generic observable can be expressed as a sum of Feynman diagrams with the same numerical prefactors of field theories. However, the contribution of a given diagram is not evaluated by associating Gaussian propagators to its lines, as in field theories: one has to consider the graph as a portion of the original lattice, replacing the internal lines with appropriate one-dimensional chains, and attaching to the internal points the appropriate number of infinite-size Bethe trees to restore the correct local connectivity of the original model. The actual contribution of each (fat) diagram is the so-called line-connected observable, which also includes contributions from sub-diagrams with appropriate prefactors. In order to compute the corrections near to the critical point, Feynman diagrams (with their symmetry factors) can be read directly from the appropriate field-theoretical literature; the computation of momentum integrals is also quite similar; the extra work consists of computing the line-connected observable of the associated fat diagram in the limit of all lines becoming infinitely long.

Assimilation of Altimeter Data into a Quasigeostrophic Model of the Gulf Stream System. Part 2; Assimilation Results

NASA Technical Reports Server (NTRS)

Capotondi, Antonietta; Holland, William R.; Malanotte-Rizzoli, Paola

1995-01-01

The improvement in the climatological behavior of a numerical model as a consequence of the assimilation of surface data is investigated. The model used for this study is a quasigeostrophic (QG) model of the Gulf Stream region. The data that have been assimilated are maps of sea surface height that have been obtained as the superposition of sea surface height variability deduced from the Geosat altimeter measurements and a mean field constructed from historical hydrographic data. The method used for assimilating the data is the nudging technique. Nudging has been implemented in such a way as to achieve a high degree of convergence of the surface model fields toward the observations. Comparisons of the assimilation results with available in situ observations show a significant improvement in the degree of realism of the climatological model behavior, with respect to the model in which no data are assimilated. The remaining discrepancies in the model mean circulation seem to be mainly associated with deficiencies in the mean component of the surface data that are assimilated. On the other hand, the possibility of building into the model more realistic eddy characteristics through the assimilation of the surface eddy field proves very successful in driving components of the mean model circulation that are in relatively good agreement with the available observations. Comparisons with current meter time series during a time period partially overlapping the Geosat mission show that the model is able to 'correctly' extrapolate the instantaneous surface eddy signals to depths of approximately 1500 m. The correlation coefficient between current meter and model time series varies from values close to 0.7 in the top 1500 m to values as low as 0.1-0.2 in the deep ocean.

Metal-insulator transition in a doubly orbitally degenerate model with correlated hopping

NASA Astrophysics Data System (ADS)

Didukh, L.; Skorenkyy, Yu.; Dovhopyaty, Yu.; Hankevych, V.

2000-03-01

In the present paper, we propose a doubly orbitally degenerate narrow-band model with correlated hopping. The peculiarity of the model is taking into account the matrix element of electron-electron interaction, which describes intersite hoppings of electrons. In particular, this leads to the concentration dependence of the effective hopping integral. The cases of the strong and weak Hund's coupling are considered. By means of a generalized mean-field approximation the single-particle Green function and quasiparticle energy spectrum are calculated. Metal-insulator transition is studied in the model at different integer values of the electron concentration. With the help of the obtained energy spectrum, we find energy gap width and criteria of metal-insulator transition.

Random Interchange of Magnetic Connectivity

NASA Astrophysics Data System (ADS)

Matthaeus, W. H.; Ruffolo, D. J.; Servidio, S.; Wan, M.; Rappazzo, A. F.

2015-12-01

Magnetic connectivity, the connection between two points along a magnetic field line, has a stochastic character associated with field lines random walking in space due to magnetic fluctuations, but connectivity can also change in time due to dynamical activity [1]. For fluctuations transverse to a strong mean field, this connectivity change be caused by stochastic interchange due to component reconnection. The process may be understood approximately by formulating a diffusion-like Fokker-Planck coefficient [2] that is asymptotically related to standard field line random walk. Quantitative estimates are provided, for transverse magnetic field models and anisotropic models such as reduced magnetohydrodynamics. In heliospheric applications, these estimates may be useful for understanding mixing between open and close field line regions near coronal hole boundaries, and large latitude excursions of connectivity associated with turbulence. [1] A. F. Rappazzo, W. H. Matthaeus, D. Ruffolo, S. Servidio & M. Velli, ApJL, 758, L14 (2012) [2] D. Ruffolo & W. Matthaeus, ApJ, 806, 233 (2015)

Modeling Sound Propagation Through Non-Axisymmetric Jets

NASA Technical Reports Server (NTRS)

Leib, Stewart J.

2014-01-01

A method for computing the far-field adjoint Green's function of the generalized acoustic analogy equations under a locally parallel mean flow approximation is presented. The method is based on expanding the mean-flow-dependent coefficients in the governing equation and the scalar Green's function in truncated Fourier series in the azimuthal direction and a finite difference approximation in the radial direction in circular cylindrical coordinates. The combined spectral/finite difference method yields a highly banded system of algebraic equations that can be efficiently solved using a standard sparse system solver. The method is applied to test cases, with mean flow specified by analytical functions, corresponding to two noise reduction concepts of current interest: the offset jet and the fluid shield. Sample results for the Green's function are given for these two test cases and recommendations made as to the use of the method as part of a RANS-based jet noise prediction code.

Diffusion of test particles in stochastic magnetic fields for small Kubo numbers.

PubMed

Neuer, Marcus; Spatschek, Karl H

2006-02-01

Motion of charged particles in a collisional plasma with stochastic magnetic field lines is investigated on the basis of the so-called A-Langevin equation. Compared to the previously used A-Langevin model, here finite Larmor radius effects are taken into account. The A-Langevin equation is solved under the assumption that the Lagrangian correlation function for the magnetic field fluctuations is related to the Eulerian correlation function (in Gaussian form) via the Corrsin approximation. The latter is justified for small Kubo numbers. The velocity correlation function, being averaged with respect to the stochastic variables including collisions, leads to an implicit differential equation for the mean square displacement. From the latter, different transport regimes, including the well-known Rechester-Rosenbluth diffusion coefficient, are derived. Finite Larmor radius contributions show a decrease of the diffusion coefficient compared to the guiding center limit. The case of small (or vanishing) mean fields is also discussed.

Soft computing methods for geoidal height transformation

NASA Astrophysics Data System (ADS)

Akyilmaz, O.; Özlüdemir, M. T.; Ayan, T.; Çelik, R. N.

2009-07-01

Soft computing techniques, such as fuzzy logic and artificial neural network (ANN) approaches, have enabled researchers to create precise models for use in many scientific and engineering applications. Applications that can be employed in geodetic studies include the estimation of earth rotation parameters and the determination of mean sea level changes. Another important field of geodesy in which these computing techniques can be applied is geoidal height transformation. We report here our use of a conventional polynomial model, the Adaptive Network-based Fuzzy (or in some publications, Adaptive Neuro-Fuzzy) Inference System (ANFIS), an ANN and a modified ANN approach to approximate geoid heights. These approximation models have been tested on a number of test points. The results obtained through the transformation processes from ellipsoidal heights into local levelling heights have also been compared.

Grain-size dynamics beneath mid-ocean ridges: Implications for permeability and melt extraction.

PubMed

Turner, Andrew J; Katz, Richard F; Behn, Mark D

2015-03-01

Grain size is an important control on mantle viscosity and permeability, but is difficult or impossible to measure in situ. We construct a two-dimensional, single phase model for the steady state mean grain size beneath a mid-ocean ridge. The mantle rheology is modeled as a composite of diffusion creep, dislocation creep, dislocation accommodated grain boundary sliding, and a plastic stress limiter. The mean grain size is calculated by the paleowattmeter relationship of Austin and Evans (2007). We investigate the sensitivity of our model to global variations in grain growth exponent, potential temperature, spreading-rate, and mantle hydration. We interpret the mean grain-size field in terms of its permeability to melt transport. The permeability structure due to mean grain size may be approximated as a high permeability region beneath a low permeability region. The transition between high and low permeability regions occurs across a boundary that is steeply inclined toward the ridge axis. We hypothesize that such a permeability structure generated from the variability of the mean grain size may focus melt toward the ridge axis, analogous to Sparks and Parmentier (1991)-type focusing. This focusing may, in turn, constrain the region where significant melt fractions are observed by seismic or magnetotelluric surveys. This interpretation of melt focusing via the grain-size permeability structure is consistent with MT observation of the asthenosphere beneath the East Pacific Rise. The grain-size field beneath MORs can vary over orders of magnitude The grain-size field affects the rheology and permeability of the asthenosphere The grain-size field may focus melt toward the ridge axis.

Polymer-induced forces at interfaces

NASA Astrophysics Data System (ADS)

Rangarajan, Murali

This dissertation concerns studies of forces generated by confined and physisorbed flexible polymers using lattice mean-field theories, and those generated by confined and clamped semiflexible polymers modeled as slender elastic rods. Lattice mean-field theories have been used in understanding and predicting the behavior of polymeric interfacial systems. In order to efficiently tailor such systems for various applications of interest, one has to understand the forces generated in the interface due to the polymer molecules. The present work examines the abilities and limitations of lattice mean-field theories in predicting the structure of physisorbed polymer layers and the resultant forces. Within the lattice mean-field theory, a definition of normal force of compression as the negative derivative of the partition-function-based excess free energy with surface separation gives misleading results because the theory does not explicitly account for the normal stresses involved in the system. Correct expressions for normal and tangential forces are obtained from a continuum-mechanics-based formulation. Preliminary comparisons with lattice Monte Carlo simulations show that mean-field theories fail to predict significant attractive forces when the surfaces are undersaturated, as one would expect. The corrections to the excluded volume (non-reversal chains) and the mean-field (anisotropic field) approximations improve the predictions of layer structure, but not the forces. Bending of semiflexible polymer chains (elastic rods) is considered for two boundary conditions---where the chain is hinged on both ends and where the chain is clamped on one end and hinged on the other. For the former case, the compressive forces and chain shapes obtained are consistent with the inflexional elastica published by Love. For the latter, multiple and higher-order solutions are observed for the hinged-end position for a given force. Preliminary studies are conducted on actin-based motility of Listeria monocytogenes by treating actin filaments as elastic rods, using the actoclampin model. The results show qualitative agreement with calculations where the filaments are modeled as Hookean springs. The feasibility of the actoclampin model to address long length-scale rotation of Listeria during actin-based motility is addressed.

Dispersive stresses in wind farms

NASA Astrophysics Data System (ADS)

Segalini, Antonio; Braunbehrens, Robert; Hyvarinen, Ann

2017-11-01

One of the most famous models of wind farms is provided by the assumption that the farm can be approximated as a horizontally-homogeneous forest canopy with vertically-varying force intensity. By means of this approximation, the flow-motion equations become drastically simpler, as many of the three-dimensional effects are gone. However, the application of the horizontal average operator to the RANS equations leads to the appearance of new transport terms (called dispersive stresses) originating from the horizontal (small-scale) variation of the mean velocity field. Since these terms are related to the individual turbine signature, they are expected to vanish outside the roughness sublayer, providing a definition for the latter. In the present work, an assessment of the dispersive stresses is performed by means of a wake-model approach and through the linearised code ORFEUS developed at KTH. Both approaches are very fast and enable the characterization of a large number of wind-farm layouts. The dispersive stress tensor and its effect on the turbulence closure models are investigated, providing guidelines for those simulations where it is impossible to resolve the farm at a turbine scale due to grid requirements (as, for instance, mesoscale simulations).

Investigation of flow fields within large scale hypersonic inlet models

NASA Technical Reports Server (NTRS)

Gnos, A. V.; Watson, E. C.; Seebaugh, W. R.; Sanator, R. J.; Decarlo, J. P.

1973-01-01

Analytical and experimental investigations were conducted to determine the internal flow characteristics in model passages representative of hypersonic inlets for use at Mach numbers to about 12. The passages were large enough to permit measurements to be made in both the core flow and boundary layers. The analytical techniques for designing the internal contours and predicting the internal flow-field development accounted for coupling between the boundary layers and inviscid flow fields by means of a displacement-thickness correction. Three large-scale inlet models, each having a different internal compression ratio, were designed to provide high internal performance with an approximately uniform static-pressure distribution at the throat station. The models were tested in the Ames 3.5-Foot Hypersonic Wind Tunnel at a nominal free-stream Mach number of 7.4 and a unit free-stream Reynolds number of 8.86 X one million per meter.

Structure of neutron star crusts from new Skyrme effective interactions constrained by chiral effective field theory

NASA Astrophysics Data System (ADS)

Lim, Yeunhwan; Holt, Jeremy W.

2017-06-01

We investigate the structure of neutron star crusts, including the crust-core boundary, based on new Skyrme mean field models constrained by the bulk-matter equation of state from chiral effective field theory and the ground-state energies of doubly-magic nuclei. Nuclear pasta phases are studied using both the liquid drop model as well as the Thomas-Fermi approximation. We compare the energy per nucleon for each geometry (spherical nuclei, cylindrical nuclei, nuclear slabs, cylindrical holes, and spherical holes) to obtain the ground state phase as a function of density. We find that the size of the Wigner-Seitz cell depends strongly on the model parameters, especially the coefficients of the density gradient interaction terms. We employ also the thermodynamic instability method to check the validity of the numerical solutions based on energy comparisons.

Nonequilibrium Fluctuations and Enhanced Diffusion of a Driven Particle in a Dense Environment

NASA Astrophysics Data System (ADS)

Illien, Pierre; Bénichou, Olivier; Oshanin, Gleb; Sarracino, Alessandro; Voituriez, Raphaël

2018-05-01

We study the diffusion of a tracer particle driven out of equilibrium by an external force and traveling in a dense environment of arbitrary density. The system evolves on a discrete lattice and its stochastic dynamics is described by a master equation. Relying on a decoupling approximation that goes beyond the naive mean-field treatment of the problem, we calculate the fluctuations of the position of the tracer around its mean value on a lattice of arbitrary dimension, and with different boundary conditions. We reveal intrinsically nonequilibrium effects, such as enhanced diffusivity of the tracer induced by both the crowding interactions and the external driving. We finally consider the high-density and low-density limits of the model and show that our approximation scheme becomes exact in these limits.

Langevin equation versus kinetic equation: Subdiffusive behavior of charged particles in a stochastic magnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balescu, R.; Wang, H.; Misguich, J.H.

1994-12-01

The running diffusion coefficient [ital D]([ital t]) is evaluated for a system of charged particles undergoing the effect of a fluctuating magnetic field and of their mutual collisions. The latter coefficient can be expressed either in terms of the mean square displacement (MSD) of a test particle, or in terms of a correlation between a fluctuating distribution function and the magnetic field fluctuation. In the first case a stochastic differential equation of Langevin type for the position of a test particle must be solved; the second problem requires the determination of the distribution function from a kinetic equation. Using suitablemore » simplifications, both problems are amenable to exact analytic solution. The conclusion is that the equivalence of the two approaches is by no means automatically guaranteed. A new type of object, the hybrid kinetic equation'' is constructed: it automatically ensures the equivalence with the Langevin results. The same conclusion holds for the generalized Fokker--Planck equation. The (Bhatnagar--Gross--Krook) (BGK) model for the collisions yields a completely wrong result. A linear approximation to the hybrid kinetic equation yields an inexact behavior, but represents an acceptable approximation in the strongly collisional limit.« less

Towards a universal master curve in magnetorheology

NASA Astrophysics Data System (ADS)

Ruiz-López, José Antonio; Hidalgo-Alvarez, Roque; de Vicente, Juan

2017-05-01

We demonstrate that inverse ferrofluids behave as model magnetorheological fluids. A universal master curve is proposed, using a reduced Mason number, under the frame of a structural viscosity model where the magnetic field strength dependence is solely contained in the Mason number and the particle concentration is solely contained in the critical Mason number (i.e. the yield stress). A linear dependence of the critical Mason number with the particle concentration is observed that is in good agreement with a mean (average) magnetization approximation, particle level dynamic simulations and micromechanical models available in the literature.

An Exact Model-Based Method for Near-Field Sources Localization with Bistatic MIMO System.

PubMed

Singh, Parth Raj; Wang, Yide; Chargé, Pascal

2017-03-30

In this paper, we propose an exact model-based method for near-field sources localization with a bistatic multiple input, multiple output (MIMO) radar system, and compare it with an approximated model-based method. The aim of this paper is to propose an efficient way to use the exact model of the received signals of near-field sources in order to eliminate the systematic error introduced by the use of approximated model in most existing near-field sources localization techniques. The proposed method uses parallel factor (PARAFAC) decomposition to deal with the exact model. Thanks to the exact model, the proposed method has better precision and resolution than the compared approximated model-based method. The simulation results show the performance of the proposed method.

Evaluation of Hydration Free Energy by Level-Set Variational Implicit-Solvent Model with Coulomb-Field Approximation.

PubMed

Guo, Zuojun; Li, Bo; Dzubiella, Joachim; Cheng, Li-Tien; McCammon, J Andrew; Che, Jianwei

2013-03-12

In this article, we systematically apply a novel implicit-solvent model, the variational implicit-solvent model (VISM) together with the Coulomb-Field Approximation (CFA), to calculate the hydration free energy of a large set of small organic molecules. Because these molecules have been studied in detail by molecular dynamics simulations and other implicit-solvent models, they provide a good benchmark for evaluating the performance of VISM-CFA. With all-atom Amber force field parameters, VISM-CFA is able to reproduce well not only the experimental and MD simulated total hydration free energy but also the polar and nonpolar contributions individually. The correlation between VISM-CFA and experiments is R 2 = 0.763 for the total hydration free energy, with a root-mean-square deviation (RMSD) of 1.83 kcal/mol, and the correlation to results from TIP3P explicit water MD simulations is R 2 = 0.839 with a RMSD = 1.36 kcal/mol. In addition, we demonstrate that VISM captures dewetting phenomena in the p53/MDM2 complex and hydrophobic characteristics in the system. This work demonstrates that the level-set VISM-CFA can be used to study the energetic behavior of realistic molecular systems with complicated geometries in solvation, protein-ligand binding, protein-protein association, and protein folding processes.

Stimulus Sensitivity of a Spiking Neural Network Model

NASA Astrophysics Data System (ADS)

Chevallier, Julien

2018-02-01

Some recent papers relate the criticality of complex systems to their maximal capacity of information processing. In the present paper, we consider high dimensional point processes, known as age-dependent Hawkes processes, which have been used to model spiking neural networks. Using mean-field approximation, the response of the network to a stimulus is computed and we provide a notion of stimulus sensitivity. It appears that the maximal sensitivity is achieved in the sub-critical regime, yet almost critical for a range of biologically relevant parameters.

First- and second-order metal-insulator phase transitions and topological aspects of a Hubbard-Rashba system

NASA Astrophysics Data System (ADS)

Marcelino, Edgar

2017-05-01

This paper considers a model consisting of a kinetic term, Rashba spin-orbit coupling and short-range Coulomb interaction at zero temperature. The Coulomb interaction is decoupled by a mean-field approximation in the spin channel using field theory methods. The results feature a first-order phase transition for any finite value of the chemical potential and quantum criticality for vanishing chemical potential. The Hall conductivity is also computed using the Kubo formula in a mean-field effective Hamiltonian. In the limit of infinite mass the kinetic term vanishes and all the phase transitions are of second order; in this case the spontaneous symmetry-breaking mechanism adds a ferromagnetic metallic phase to the system and features a zero-temperature quantization of the Hall conductivity in the insulating one.

The physics of evolution and biodiversity: Old answers to new questions, and more...

NASA Astrophysics Data System (ADS)

Bar-Yam, Yaneer

2013-03-01

In recent years there has been a contentious battle among prominent biologists about the validity of Kin versus Group Selection as models of evolutionary biology. I will show that the controversy is widely misunderstood and is rooted in the mean field basis of RA Fisher's statistical treatment of population biology, which is the origin of the ``gene centered view''-kin selection and inclusive fitness-but is also often used in analysis of group selection. As in statistical physics, symmetry breaking and pattern formation, and their spatial realizations, result in breakdown of the mean field approximation and the widely believed mathematical 'proofs' of the universality of the gene centered view. Our simulation and analysis (http://necsi.edu/research/evoeco/) of the role of this breakdown in spatial ecology, biodiversity, speciation and altruism, suggest there is an entire field of new opportunities to explore in the implications for evolutionary theory. The difference between biodiversity of wildtype populations and narrowly homogeneous laboratory types manifest the self-consistency of theoretical assumptions and laboratory experiments performed under conditions in which the mean field approximation applies. In contrast, the highly diverse natural populations manifest the role of boundaries between types (hybrid zones), speciation by spontaneous clustering, and spatio-temporal dynamics in predator prey systems. Altruism arises in evolving populations due to the spontaneous dynamic group formation and the heritability of environmental conditions created by parents and experienced by offspring (niche construction with symmetry breaking), so that altruists are better able to survive over the long term than selfish variants. Many versions of the mean field approximation that are traditionally used eliminate these spatio-temporal processes, leading to false analytic conclusions about their impossibility. The traditional view of altruism influenced views also of individuals in their relationship to society. In addition to the basic reframing of the origin of altruism, the role of space in evolution has important implications for understanding global dangers today, including pandemics driven by evolution of virulent pathogens that escape death through long-range transportation, and economic or environmental overexploitation when globalization enables exploiters to escape the consequences of their actions.

Geometric factor and influence of sensors in the establishment of a resistivity-moisture relation in soil samples

NASA Astrophysics Data System (ADS)

López-Sánchez, M.; Mansilla-Plaza, L.; Sánchez-de-laOrden, M.

2017-10-01

Prior to field scale research, soil samples are analysed on a laboratory scale for electrical resistivity calibrations. Currently, there are a variety of field instruments to estimate the water content in soils using different physical phenomena. These instruments can be used to develop moisture-resistivity relationships on the same soil samples. This assures that measurements are performed on the same material and under the same conditions (e.g., humidity and temperature). A geometric factor is applied to the location of electrodes, in order to calculate the apparent electrical resistivity of the laboratory test cells. This geometric factor can be determined in three different ways: by means of the use of an analytical approximation, laboratory trials (experimental approximation), or by the analysis of a numerical model. The first case, the analytical approximation, is not appropriate for complex cells or arrays. And both, the experimental and numerical approximation can lead to inaccurate results. Therefore, we propose a novel approach to obtain a compromise solution between both techniques, providing a more precise determination of the geometrical factor.

Mott physics beyond the Brinkman-Rice scenario

NASA Astrophysics Data System (ADS)

Wysokiński, Marcin M.; Fabrizio, Michele

2017-04-01

The main flaw of the well-known Brinkman-Rice description, obtained through the Gutzwiller approximation, of the paramagnetic Mott transition in the Hubbard model is in neglecting high-energy virtual processes that generate, for instance, the antiferromagnetic exchange J ˜t2/U . Here, we propose a way to capture those processes by combining the Brinkman-Rice approach with a variational Schrieffer-Wolff transformation, and apply this method to study the single-band metal-to-insulator transition in a Bethe lattice with infinite coordination number, where the Gutzwiller approximation becomes exact. We indeed find for the Mott transition a description very close to the real one provided by the dynamical mean-field theory, an encouraging result in view of possible applications to more involved models.

A multimodal detection model of dolphins to estimate abundance validated by field experiments.

PubMed

Akamatsu, Tomonari; Ura, Tamaki; Sugimatsu, Harumi; Bahl, Rajendar; Behera, Sandeep; Panda, Sudarsan; Khan, Muntaz; Kar, S K; Kar, C S; Kimura, Satoko; Sasaki-Yamamoto, Yukiko

2013-09-01

Abundance estimation of marine mammals requires matching of detection of an animal or a group of animal by two independent means. A multimodal detection model using visual and acoustic cues (surfacing and phonation) that enables abundance estimation of dolphins is proposed. The method does not require a specific time window to match the cues of both means for applying mark-recapture method. The proposed model was evaluated using data obtained in field observations of Ganges River dolphins and Irrawaddy dolphins, as examples of dispersed and condensed distributions of animals, respectively. The acoustic detection probability was approximately 80%, 20% higher than that of visual detection for both species, regardless of the distribution of the animals in present study sites. The abundance estimates of Ganges River dolphins and Irrawaddy dolphins fairly agreed with the numbers reported in previous monitoring studies. The single animal detection probability was smaller than that of larger cluster size, as predicted by the model and confirmed by field data. However, dense groups of Irrawaddy dolphins showed difference in cluster sizes observed by visual and acoustic methods. Lower detection probability of single clusters of this species seemed to be caused by the clumped distribution of this species.

Field-dependent critical state of high-Tc superconducting strip simultaneously exposed to transport current and perpendicular magnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xue, Cun; He, An; Yong, Huadong

We present an exact analytical approach for arbitrary field-dependent critical state of high-T{sub c} superconducting strip with transport current. The sheet current and flux-density profiles are derived by solving the integral equations, which agree with experiments quite well. For small transport current, the approximate explicit expressions of sheet current, flux-density and penetration depth for the Kim model are derived based on the mean value theorem for integration. We also extend the results to the field-dependent critical state of superconducting strip in the simultaneous presence of applied field and transport current. The sheet current distributions calculated by the Kim model agreemore » with experiments better than that by the Bean model. Moreover, the lines in the I{sub a}-B{sub a} plane for the Kim model are not monotonic, which is quite different from that the Bean model. The results reveal that the maximum transport current in thin superconducting strip will decrease with increasing applied field which vanishes for the Bean model. The results of this paper are useful to calculate ac susceptibility and ac loss.« less

An Avoidance Model for Short-Range Order Induced by Soft Repulsions in Systems of Rigid Rods

NASA Astrophysics Data System (ADS)

Han, Jining; Herzfeld, Judith

1996-03-01

The effects of soft repulsions on hard particle systems are calculated using an avoidance model which improves upon the simple mean field approximation. Avoidance reduces, but does not eliminate, the energy due to soft repulsions. On the other hand, it also reduces the configurational entropy. Under suitable conditions, this simple trade-off yields a free energy that is lower than the mean field value. In these cases, the variationally determined avoidance gives an estimate for the short-range positional order induced by soft repulsions. The results indicate little short-range order for isotropically oriented rods. However, for parallel rods, short-range order increases to significant levels as the particle axial ratio increases. The implications for long- range positional ordering are also discussed. In particular, avoidance may explain the smectic ordering of tobacco mosaic virus at volume fractions lower than those necessary for smectic ordering of hard particles.

Mean-field theory on mixed ferro-ferrimagnetic compounds with (A aB bC c) yD

NASA Astrophysics Data System (ADS)

Wei, Guo-Zhu; Xin, Zihua; Liang, Yaqiu; Zhang, Qi

2004-01-01

The magnetic properties of the mixed ferro-ferrimagnetic compounds with (A aB bC c) yD, in which A, B, C and D are four different magnetic ions and form four different sublattices, are studied by using the Ising model. And the Ising model was dealt with standard mean-field approximation. The regions of concentration in which two compensation points or one compensation point exit are given in c- a, b- c and a- b planes. The phase diagrams of the transition temperature Tc and compensation temperature Tcomp are obtained. The temperature dependences of the magnetization are also investigated. Some of the result can be used to explain the experimental work of the molecule-based ferro-ferrimagnet (Ni IIaMn IIbFe IIc) 1.5[Cr III(CN) 6]· zH 2O.

Mott-Hubbard transition and Anderson localization: A generalized dynamical mean-field theory approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuchinskii, E. Z.; Nekrasov, I. A.; Sadovskii, M. V.

The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + {sigma} approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamicmore » conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition.« less

Mean-field theory for multipole ordering in f-electron systems on the basis of a j-j coupling scheme

NASA Astrophysics Data System (ADS)

Yamamura, Ryosuke; Hotta, Takashi

2018-05-01

We develop a microscopic theory for multipole ordering, applicable to the system with plural numbers of f electrons per ion, from an itinerant picture on the basis of a j-j coupling scheme. For the purpose, by introducing the Γ8 Hubbard Hamiltonian as the minimum model to discuss the multipole ordering in f-electron systems, we describe the mean-field approximation in terms of the multipole operators. For the case of n = 2 , where n denotes the average f-electron number per ion, we analyze the model on a simple cubic lattice to obtain the multipole phase diagram. In particular, we find the order of non-Kramers Γ3 quadrupoles, O20 and O22 , with different ordering vectors. We attempt to explain the phase diagram from the discussion on the interaction energy.

Disordered λ φ4+ρ φ6 Landau-Ginzburg model

NASA Astrophysics Data System (ADS)

Diaz, R. Acosta; Svaiter, N. F.; Krein, G.; Zarro, C. A. D.

2018-03-01

We discuss a disordered λ φ4+ρ φ6 Landau-Ginzburg model defined in a d -dimensional space. First we adopt the standard procedure of averaging the disorder-dependent free energy of the model. The dominant contribution to this quantity is represented by a series of the replica partition functions of the system. Next, using the replica-symmetry ansatz in the saddle-point equations, we prove that the average free energy represents a system with multiple ground states with different order parameters. For low temperatures we show the presence of metastable equilibrium states for some replica fields for a range of values of the physical parameters. Finally, going beyond the mean-field approximation, the one-loop renormalization of this model is performed, in the leading-order replica partition function.

Dynamics of polymers: A mean-field theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fredrickson, Glenn H.; Materials Research Laboratory, University of California, Santa Barbara, California 93106; Department of Materials, University of California, Santa Barbara, California 93106

2014-02-28

We derive a general mean-field theory of inhomogeneous polymer dynamics; a theory whose form has been speculated and widely applied, but not heretofore derived. Our approach involves a functional integral representation of a Martin-Siggia-Rose (MSR) type description of the exact many-chain dynamics. A saddle point approximation to the generating functional, involving conditions where the MSR action is stationary with respect to a collective density field ρ and a conjugate MSR response field ϕ, produces the desired dynamical mean-field theory. Besides clarifying the proper structure of mean-field theory out of equilibrium, our results have implications for numerical studies of polymer dynamicsmore » involving hybrid particle-field simulation techniques such as the single-chain in mean-field method.« less

Modeling of phonon scattering in n-type nanowire transistors using one-shot analytic continuation technique

NASA Astrophysics Data System (ADS)

Bescond, Marc; Li, Changsheng; Mera, Hector; Cavassilas, Nicolas; Lannoo, Michel

2013-10-01

We present a one-shot current-conserving approach to model the influence of electron-phonon scattering in nano-transistors using the non-equilibrium Green's function formalism. The approach is based on the lowest order approximation (LOA) to the current and its simplest analytic continuation (LOA+AC). By means of a scaling argument, we show how both LOA and LOA+AC can be easily obtained from the first iteration of the usual self-consistent Born approximation (SCBA) algorithm. Both LOA and LOA+AC are then applied to model n-type silicon nanowire field-effect-transistors and are compared to SCBA current characteristics. In this system, the LOA fails to describe electron-phonon scattering, mainly because of the interactions with acoustic phonons at the band edges. In contrast, the LOA+AC still well approximates the SCBA current characteristics, thus demonstrating the power of analytic continuation techniques. The limits of validity of LOA+AC are also discussed, and more sophisticated and general analytic continuation techniques are suggested for more demanding cases.

Spin-diffusions and diffusive molecular dynamics

NASA Astrophysics Data System (ADS)

Farmer, Brittan; Luskin, Mitchell; Plecháč, Petr; Simpson, Gideon

2017-12-01

Metastable configurations in condensed matter typically fluctuate about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of classical molecular dynamics (MD) methods and has spurned the development of a host of approximate algorithms. One recently proposed method is diffusive MD which aims at integrating a system of ordinary differential equations describing the likelihood of occupancy by one of two species, in the case of a binary alloy, while quasistatically evolving the locations of the atoms. While diffusive MD has shown itself to be efficient and provide agreement with observations, it is fundamentally a model, with unclear connections to classical MD. In this work, we formulate a spin-diffusion stochastic process and show how it can be connected to diffusive MD. The spin-diffusion model couples a classical overdamped Langevin equation to a kinetic Monte Carlo model for exchange amongst the species of a binary alloy. Under suitable assumptions and approximations, spin-diffusion can be shown to lead to diffusive MD type models. The key assumptions and approximations include a well-defined time scale separation, a choice of spin-exchange rates, a low temperature approximation, and a mean field type approximation. We derive several models from different assumptions and show their relationship to diffusive MD. Differences and similarities amongst the models are explored in a simple test problem.

Poiseuille flow of a Quincke suspension

NASA Astrophysics Data System (ADS)

CÄ`bers, A.

2014-09-01

The controversy of models of dielectric particle suspensions with antisymmetric stress, which predict a nonphysical cusp of the velocity profile in plane Poiseuille flow under the action of the electrical field, is resolved. In the mean-field approximation, the nonlinear kinetic equation is derived for coupled due to the flow translational and rotational motion of the particles. By its numerical solution, it is shown that the velocity profile is smeared due to the translational diffusion of the particles with opposite directions of rotation. The obtained results for the velocity profiles and flow rates as a function of the electric field strength are in qualitative agreement with the existing experimental results.

Poiseuille flow of a Quincke suspension.

PubMed

Cēbers, A

2014-09-01

The controversy of models of dielectric particle suspensions with antisymmetric stress, which predict a nonphysical cusp of the velocity profile in plane Poiseuille flow under the action of the electrical field, is resolved. In the mean-field approximation, the nonlinear kinetic equation is derived for coupled due to the flow translational and rotational motion of the particles. By its numerical solution, it is shown that the velocity profile is smeared due to the translational diffusion of the particles with opposite directions of rotation. The obtained results for the velocity profiles and flow rates as a function of the electric field strength are in qualitative agreement with the existing experimental results.

A surface spherical harmonic expansion of gravity anomalies on the ellipsoid

NASA Astrophysics Data System (ADS)

Claessens, S. J.; Hirt, C.

2015-10-01

A surface spherical harmonic expansion of gravity anomalies with respect to a geodetic reference ellipsoid can be used to model the global gravity field and reveal its spectral properties. In this paper, a direct and rigorous transformation between solid spherical harmonic coefficients of the Earth's disturbing potential and surface spherical harmonic coefficients of gravity anomalies in ellipsoidal approximation with respect to a reference ellipsoid is derived. This transformation cannot rigorously be achieved by the Hotine-Jekeli transformation between spherical and ellipsoidal harmonic coefficients. The method derived here is used to create a surface spherical harmonic model of gravity anomalies with respect to the GRS80 ellipsoid from the EGM2008 global gravity model. Internal validation of the model shows a global RMS precision of 1 nGal. This is significantly more precise than previous solutions based on spherical approximation or approximations to order or , which are shown to be insufficient for the generation of surface spherical harmonic coefficients with respect to a geodetic reference ellipsoid. Numerical results of two applications of the new method (the computation of ellipsoidal corrections to gravimetric geoid computation, and area means of gravity anomalies in ellipsoidal approximation) are provided.

CONSISTENT SCALING LAWS IN ANELASTIC SPHERICAL SHELL DYNAMOS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yadav, Rakesh K.; Gastine, Thomas; Christensen, Ulrich R.

2013-09-01

Numerical dynamo models always employ parameter values that differ by orders of magnitude from the values expected in natural objects. However, such models have been successful in qualitatively reproducing properties of planetary and stellar dynamos. This qualitative agreement fuels the idea that both numerical models and astrophysical objects may operate in the same asymptotic regime of dynamics. This can be tested by exploring the scaling behavior of the models. For convection-driven incompressible spherical shell dynamos with constant material properties, scaling laws had been established previously that relate flow velocity and magnetic field strength to the available power. Here we analyzemore » 273 direct numerical simulations using the anelastic approximation, involving also cases with radius-dependent magnetic, thermal, and viscous diffusivities. These better represent conditions in gas giant planets and low-mass stars compared to Boussinesq models. Our study provides strong support for the hypothesis that both mean velocity and mean magnetic field strength scale as a function of the power generated by buoyancy forces in the same way for a wide range of conditions.« less

The physics of chromatin silencing: Bi-stability and front propagation

NASA Astrophysics Data System (ADS)

Sedighi, Mohammad

A mean-field dynamical model of chromatin silencing in budding yeast is provided and the conditions giving rise to two states: one silenced and another un-silenced, is studied. Based on these conditions, the space of control parameters is divided into two distinct regions of mono-stable and bi-stable solutions (the bifurcation diagram). Then, considering both the discrete and continuous versions of the model, the formation of a stable boundary between the silenced and un-silenced areas on DNA is investigated. As a result, a richer phase diagram is provided. The dynamics of the boundary is also studied under different conditions. Consequently, assuming negative feedback due to possible depletion of silencing proteins, the model explains a paradoxical epigenetic behavior of yeast that happens under some mutation. A stochastic treatment of the model is also considered to verify the results of the mean-field approximation and also to understand the role of intrinsic noise at single cell level. This model could be used as a general guide to discuss chromatin silencing in many organisms.

Networks with fourfold connectivity in two dimensions.

PubMed

Tessier, Frédéric; Boal, David H; Discher, Dennis E

2003-01-01

The elastic properties of planar, C4-symmetric networks under stress and at nonzero temperature are determined by simulation and mean field approximations. Attached at fourfold coordinated junction vertices, the networks are self-avoiding in that their elements (or bonds) may not intersect each other. Two different models are considered for the potential energy of the elements: either Hooke's law springs or flexible tethers (square well potential). For certain ranges of stress and temperature, the properties of the networks are captured by one of several models: at large tensions, the networks behave like a uniform system of square plaquettes, while at large compressions or high temperatures, they display many characteristics of an ideal gas. Under less severe conditions, mean field models with more general shapes (parallelograms) reproduce many essential features of both networks. Lastly, the spring network expands without limit at a two-dimensional tension equal to the force constant of the spring; however, it does not appear to collapse under compression, except at zero temperature.

Beyond mean-field description of Gamow-Teller resonances and β-decay

NASA Astrophysics Data System (ADS)

Niu, Yifei; Colò, Gianluca; Vigezzi, Enrico; Bai, Chunlin; Niu, Zhongming; Sagawa, Hiroyuki

2018-02-01

β-decay half-lives set the time scale of the rapid neutron capture process, and are therefore essential for understanding the origin of heavy elements in the universe. The random-phase approximation (RPA) based on Skyrme energy density functionals is widely used to calculate the properties of Gamow-Teller (GT) transitions, which play a dominant role in β-decay half-lives. However, the RPA model has its limitations in reproducing the resonance width and often overestimates β-decay half-lives. To overcome these problems, effects beyond mean-field can be included on top of the RPA model. In particular, this can be obtained by taking into account the particle-vibration coupling (PVC). Within the RPA+PVC model, we successfully reproduce the experimental GT resonance width and β-decay half-lives in magic nuclei. We then extend the formalism to superfluid nuclei and apply it to the GT resonance in 120Sn, obtaining a good reproduction of the experimental strength distribution. The effect of isoscalar pairing is also discussed.

2D/3D image charge for modeling field emission

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jensen, Kevin L.; Shiffler, Donald A.; Harris, John R.

Analytic image charge approximations exist for planar and spherical metal surfaces but approximations for more complex geometries, such as the conical and wirelike structures characteristic of field emitters, are lacking. Such models are the basis for the evaluation of Schottky lowering factors in equations for current density. The development of a multidimensional image charge approximation, useful for a general thermal-field emission equation used in space charge studies, is given and based on an analytical model using a prolate spheroidal geometry. A description of how the model may be adapted to be used with a line charge model appropriate for carbonmore » nanotube and carbon fiber field emitters is discussed. [http://dx.doi.org/10.1116/1.4968007]« less

2D/3D image charge for modeling field emission

DOE PAGES

Jensen, Kevin L.; Shiffler, Donald A.; Harris, John R.; ...

2017-03-01

Analytic image charge approximations exist for planar and spherical metal surfaces but approximations for more complex geometries, such as the conical and wirelike structures characteristic of field emitters, are lacking. Such models are the basis for the evaluation of Schottky lowering factors in equations for current density. The development of a multidimensional image charge approximation, useful for a general thermal-field emission equation used in space charge studies, is given and based on an analytical model using a prolate spheroidal geometry. A description of how the model may be adapted to be used with a line charge model appropriate for carbonmore » nanotube and carbon fiber field emitters is discussed. [http://dx.doi.org/10.1116/1.4968007]« less

Lumping of degree-based mean-field and pair-approximation equations for multistate contact processes.

PubMed

Kyriakopoulos, Charalampos; Grossmann, Gerrit; Wolf, Verena; Bortolussi, Luca

2018-01-01

Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information-spreading networks. While devising stochastic models of such processes is relatively easy, analyzing them is very challenging from a computational point of view, particularly for large networks appearing in real applications. One strategy to reduce the complexity of their analysis is to rely on approximations, often in terms of a set of differential equations capturing the evolution of a random node, distinguishing nodes with different topological contexts (i.e., different degrees of different neighborhoods), such as degree-based mean-field (DBMF), approximate-master-equation (AME), or pair-approximation (PA) approaches. The number of differential equations so obtained is typically proportional to the maximum degree k_{max} of the network, which is much smaller than the size of the master equation of the underlying stochastic model, yet numerically solving these equations can still be problematic for large k_{max}. In this paper, we consider AME and PA, extended to cope with multiple local states, and we provide an aggregation procedure that clusters together nodes having similar degrees, treating those in the same cluster as indistinguishable, thus reducing the number of equations while preserving an accurate description of global observables of interest. We also provide an automatic way to build such equations and to identify a small number of degree clusters that give accurate results. The method is tested on several case studies, where it shows a high level of compression and a reduction of computational time of several orders of magnitude for large networks, with minimal loss in accuracy.

Auxiliary-fermion approach to critical fluctuations in the two-dimensional quantum antiferromagnetic Heisenberg model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brinckmann, Jan; Woelfle, Peter

2004-11-01

The nearest-neighbor quantum antiferromagnetic (AF) Heisenberg model for spin-1/2 on a two-dimensional square lattice is studied in the auxiliary-fermion representation. Expressing spin operators by canonical fermionic particles requires a constraint on the fermion charge Q{sub i}=1 on each lattice site i, which is imposed approximately through the thermal average. The resulting interacting fermion system is first treated in mean-field theory (MFT), which yields an AF ordered ground state and spin waves in quantitative agreement with conventional spin-wave theory. At finite temperature a self-consistent approximation beyond mean field is required in order to fulfill the Mermin-Wagner theorem. We first discuss amore » fully self-consistent approximation, where fermions are renormalized due to fluctuations of their spin density, in close analogy to FLEX. While static properties like the correlation length, {xi}(T){proportional_to}exp(aJ/T), come out correctly, the dynamical response lacks the magnon-like peaks which would reflect the appearance of short-range order at low T. This drawback, which is caused by overdamping, is overcome in a 'minimal self-consistent approximation' (MSCA), which we derive from the equations of motion. The MSCA features dynamical scaling at small energy and temperature and is qualitatively correct both in the regime of order-parameter relaxation at long wavelengths {lambda}>{xi} and in the short-range-order regime at {lambda}<{xi}. We also discuss the impact of vertex corrections and the problem of pseudo-gap formation in the single-particle density of states due to long-range fluctuations. Finally we show that the (short-range) magnetic order in MFT and MSCA helps to fulfill the constraint on the local fermion occupancy.« less

Bose-Einstein condensation in atomic alkali gases

NASA Astrophysics Data System (ADS)

Dodd, Robert J.

1998-05-01

I present a review of the time-independent Gross-Pitaevskii (GP), Bogoliubov, and finite-temperature Hartree-Fock-Bogoliubov (HFB) mean-field theories used to study trapped, Bose-Einstein condensed alkali gases. Numerical solutions of the (zero-temperature) GP equation are presented for attractive (negative scattering length) and repulsive (positive scattering length) interactions. Comparison is made with the Thomas-Fermi and (variational) trial wavefunction appr oximations that are used in the literature to study condensed gases. Numerical calculations of the (zero-temperature) Bogoliubov quasi-particle excitation frequencies are found to be in excellent agreement with the experimental results. The finite-temperature properties of condensed gases are examined using the Popov approximation (of the HFB theory) and a simple two-gas model. Specific, quantitative comparisons are made with experimental results for finite-temperature excitation frequencies. Qualitative comparisons are made between the results of the Popov approximation, two-gas model, and other published models for condensate fraction and thermal density distribution. The time-independent mean-field theories are found to be in excellent agreement with experimental results at relatively low temperatures (high condensate fractions). However, at higher temperatures (and condensate fractions of less than 50%) there are significant discrepancies between experimental data and theoretical calculations. This work was undertaken at the University of Maryland at College Park and was supported in part by the National Science Foundation (PHY-9601261) and the U.S. Office of Naval Research.

Comparisons of characteristic timescales and approximate models for Brownian magnetic nanoparticle rotations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reeves, Daniel B., E-mail: dbr@Dartmouth.edu; Weaver, John B.

2015-06-21

Magnetic nanoparticles are promising tools for a host of therapeutic and diagnostic medical applications. The dynamics of rotating magnetic nanoparticles in applied magnetic fields depend strongly on the type and strength of the field applied. There are two possible rotation mechanisms and the decision for the dominant mechanism is often made by comparing the equilibrium relaxation times. This is a problem when particles are driven with high-amplitude fields because they are not necessarily at equilibrium at all. Instead, it is more appropriate to consider the “characteristic timescales” that arise in various applied fields. Approximate forms for the characteristic time ofmore » Brownian particle rotations do exist and we show agreement between several analytical and phenomenological-fit models to simulated data from a stochastic Langevin equation approach. We also compare several approximate models with solutions of the Fokker-Planck equation to determine their range of validity for general fields and relaxation times. The effective field model is an excellent approximation, while the linear response solution is only useful for very low fields and frequencies for realistic Brownian particle rotations.« less

Relativistic equation of state at subnuclear densities in the Thomas-Fermi approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Z. W.; Shen, H., E-mail: shennankai@gmail.com

We study the non-uniform nuclear matter using the self-consistent Thomas-Fermi approximation with a relativistic mean-field model. The non-uniform matter is assumed to be composed of a lattice of heavy nuclei surrounded by dripped nucleons. At each temperature T, proton fraction Y{sub p} , and baryon mass density ρ {sub B}, we determine the thermodynamically favored state by minimizing the free energy with respect to the radius of the Wigner-Seitz cell, while the nucleon distribution in the cell can be determined self-consistently in the Thomas-Fermi approximation. A detailed comparison is made between the present results and previous calculations in the Thomas-Fermimore » approximation with a parameterized nucleon distribution that has been adopted in the widely used Shen equation of state.« less

On the Approximation of Generalized Lipschitz Function by Euler Means of Conjugate Series of Fourier Series

PubMed Central

Kushwaha, Jitendra Kumar

2013-01-01

Approximation theory is a very important field which has various applications in pure and applied mathematics. The present study deals with a new theorem on the approximation of functions of Lipschitz class by using Euler's mean of conjugate series of Fourier series. In this paper, the degree of approximation by using Euler's means of conjugate of functions belonging to Lip (ξ(t), p) class has been obtained. Lipα and Lip (α, p) classes are the particular cases of Lip (ξ(t), p) class. The main result of this paper generalizes some well-known results in this direction. PMID:24379744

Mean Field Approach to the Giant Wormhole Problem

NASA Astrophysics Data System (ADS)

Gamba, A.; Kolokolov, I.; Martellini, M.

We introduce a gaussian probability density for the space-time distribution of worm-holes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic “large” universe.

Extinction threshold for spatial forest dynamics with height structure.

PubMed

Garcia-Domingo, Josep L; Saldaña, Joan

2011-05-07

We present a pair-approximation model for spatial forest dynamics defined on a regular lattice. The model assumes three possible states for a lattice site: empty (gap site), occupied by an immature tree, and occupied by a mature tree, and considers three nonlinearities in the dynamics associated to the processes of light interference, gap expansion, and recruitment. We obtain an expression of the basic reproduction number R(0) which, in contrast to the one obtained under the mean-field approach, uses information about the spatial arrangement of individuals close to extinction. Moreover, we analyze the corresponding survival-extinction transition of the forest and the spatial correlations among gaps, immature and mature trees close to this critical point. Predictions of the pair-approximation model are compared with those of a cellular automaton. Copyright © 2011 Elsevier Ltd. All rights reserved.

Ferromagnetic transition in a simple variant of the Ising model on multiplex networks

NASA Astrophysics Data System (ADS)

Krawiecki, A.

2018-02-01

Multiplex networks consist of a fixed set of nodes connected by several sets of edges which are generated separately and correspond to different networks ("layers"). Here, a simple variant of the Ising model on multiplex networks with two layers is considered, with spins located in the nodes and edges corresponding to ferromagnetic interactions between them. Critical temperatures for the ferromagnetic transition are evaluated for the layers in the form of random Erdös-Rényi graphs or heterogeneous scale-free networks using the mean-field approximation and the replica method, from the replica symmetric solution. Both methods require the use of different "partial" magnetizations, associated with different layers of the multiplex network, and yield qualitatively similar results. If the layers are strongly heterogeneous the critical temperature differs noticeably from that for the Ising model on a network being a superposition of the two layers, evaluated in the mean-field approximation neglecting the effect of the underlying multiplex structure on the correlations between the degrees of nodes. The critical temperature evaluated from the replica symmetric solution depends sensitively on the correlations between the degrees of nodes in different layers and shows satisfactory quantitative agreement with that obtained from Monte Carlo simulations. The critical behavior of the magnetization for the model with strongly heterogeneous layers can depend on the distributions of the degrees of nodes and is then determined by the properties of the most heterogeneous layer.

Quantum noise of a Bose-Einstein condensate in an optical cavity, correlations, and entanglement

NASA Astrophysics Data System (ADS)

Szirmai, G.; Nagy, D.; Domokos, P.

2010-04-01

A Bose-Einstein condensate of ultracold atoms inside the field of a laser-driven optical cavity exhibits dispersive optical bistability. We describe this system by using mean-field approximation and by analyzing the correlation functions of the linearized quantum fluctuations around the mean-field solution. The entanglement and the statistics of the atom-field quadratures are given in the stationary state. It is shown that the mean-field solution, that is, the Bose-Einstein condensate, is robust against entanglement generation for most of the phase diagram.

Correlations and analytical approaches to co-evolving voter models

NASA Astrophysics Data System (ADS)

Ji, M.; Xu, C.; Choi, C. W.; Hui, P. M.

2013-11-01

The difficulty in formulating analytical treatments in co-evolving networks is studied in light of the Vazquez-Eguíluz-San Miguel voter model (VM) and a modified VM (MVM) that introduces a random mutation of the opinion as a noise in the VM. The density of active links, which are links that connect the nodes of opposite opinions, is shown to be highly sensitive to both the degree k of a node and the active links n among the neighbors of a node. We test the validity in the formalism of analytical approaches and show explicitly that the assumptions behind the commonly used homogeneous pair approximation scheme in formulating a mean-field theory are the source of the theory's failure due to the strong correlations between k, n and n2. An improved approach that incorporates spatial correlation to the nearest-neighbors explicitly and a random approximation for the next-nearest neighbors is formulated for the VM and the MVM, and it gives better agreement with the simulation results. We introduce an empirical approach that quantifies the correlations more accurately and gives results in good agreement with the simulation results. The work clarifies why simply mean-field theory fails and sheds light on how to analyze the correlations in the dynamic equations that are often generated in co-evolving processes.

Multiple zonal jets and convective heat transport barriers in a quasi-geostrophic model of planetary cores

NASA Astrophysics Data System (ADS)

Guervilly, C.; Cardin, P.

2017-10-01

We study rapidly rotating Boussinesq convection driven by internal heating in a full sphere. We use a numerical model based on the quasi-geostrophic approximation for the velocity field, whereas the temperature field is 3-D. This approximation allows us to perform simulations for Ekman numbers down to 10-8, Prandtl numbers relevant for liquid metals (˜10-1) and Reynolds numbers up to 3 × 104. Persistent zonal flows composed of multiple jets form as a result of the mixing of potential vorticity. For the largest Rayleigh numbers computed, the zonal velocity is larger than the convective velocity despite the presence of boundary friction. The convective structures and the zonal jets widen when the thermal forcing increases. Prograde and retrograde zonal jets are dynamically different: in the prograde jets (which correspond to weak potential vorticity gradients) the convection transports heat efficiently and the mean temperature tends to be homogenized; by contrast, in the cores of the retrograde jets (which correspond to steep gradients of potential vorticity) the dynamics is dominated by the propagation of Rossby waves, resulting in the formation of steep mean temperature gradients and the dominance of conduction in the heat transfer process. Consequently, in quasi-geostrophic systems, the width of the retrograde zonal jets controls the efficiency of the heat transfer.

Quasi-analytical treatment of spatially averaged radiation transfer in complex terrain

NASA Astrophysics Data System (ADS)

Löwe, H.; Helbig, N.

2012-04-01

We provide a new quasi-analytical method to compute the topographic influence on the effective albedo of complex topography as required for meteorological, land-surface or climate models. We investigate radiative transfer in complex terrain via the radiosity equation on isotropic Gaussian random fields. Under controlled approximations we derive expressions for domain averages of direct, diffuse and terrain radiation and the sky view factor. Domain averaged quantities are related to a type of level-crossing probability of the random field which is approximated by longstanding results developed for acoustic scattering at ocean boundaries. This allows us to express all non-local horizon effects in terms of a local terrain parameter, namely the mean squared slope. Emerging integrals are computed numerically and fit formulas are given for practical purposes. As an implication of our approach we provide an expression for the effective albedo of complex terrain in terms of the sun elevation angle, mean squared slope, the area averaged surface albedo, and the direct-to-diffuse ratio of solar radiation. As an application, we compute the effective albedo for the Swiss Alps and discuss possible generalizations of the method.

Multi-orbital non-crossing approximation from maximally localized Wannier functions: the Kondo signature of copper phthalocyanine on Ag(100).

PubMed

Korytár, Richard; Lorente, Nicolás

2011-09-07

We have developed a multi-orbital approach to compute the electronic structure of a quantum impurity using the non-crossing approximation. The calculation starts with a mean-field evaluation of the system's electronic structure using a standard quantum chemistry code; here we use density functional theory (DFT). We transformed the one-electron structure into an impurity Hamiltonian by using maximally localized Wannier functions. Hence, we have developed a method to study the Kondo effect in systems based on an initial one-electron calculation. We have applied our methodology to a copper phthalocyanine molecule chemisorbed on Ag(100), and we have described its spectral function for three different cases where the molecule presents a single spin or two spins with ferro- and anti-ferromagnetic exchange couplings. We find that the use of broken-symmetry mean-field theories such as Kohn-Sham DFT cannot deal with the complexity of the spin of open-shell molecules on metal surfaces and extra modeling is needed. © 2011 IOP Publishing Ltd

Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory: Convergence analysis of the dual fermion technique

NASA Astrophysics Data System (ADS)

Gukelberger, Jan; Kozik, Evgeny; Hafermann, Hartmut

2017-07-01

The dual fermion approach provides a formally exact prescription for calculating properties of a correlated electron system in terms of a diagrammatic expansion around dynamical mean-field theory (DMFT). Most practical implementations, however, neglect higher-order interaction vertices beyond two-particle scattering in the dual effective action and further truncate the diagrammatic expansion in the two-particle scattering vertex to a leading-order or ladder-type approximation. In this work, we compute the dual fermion expansion for the two-dimensional Hubbard model including all diagram topologies with two-particle interactions to high orders by means of a stochastic diagrammatic Monte Carlo algorithm. We benchmark the obtained self-energy against numerically exact diagrammatic determinant Monte Carlo simulations to systematically assess convergence of the dual fermion series and the validity of these approximations. We observe that, from high temperatures down to the vicinity of the DMFT Néel transition, the dual fermion series converges very quickly to the exact solution in the whole range of Hubbard interactions considered (4 ≤U /t ≤12 ), implying that contributions from higher-order vertices are small. As the temperature is lowered further, we observe slower series convergence, convergence to incorrect solutions, and ultimately divergence. This happens in a regime where magnetic correlations become significant. We find, however, that the self-consistent particle-hole ladder approximation yields reasonable and often even highly accurate results in this regime.

The Cold Land Processes Experiment (CLPX-1): Analysis and Modelling of LSOS Data (IOP3 Period)

NASA Technical Reports Server (NTRS)

Tedesco, Marco; Kim, Edward J.; Cline, Don; Graf, Tobias; Koike, Toshio; Hardy, Janet; Armstrong, Richard; Brodzik, Mary

2004-01-01

Microwave brightness temperatures at 18.7,36.5, and 89 GHz collected at the Local-Scale Observation Site (LSOS) of the NASA Cold-Land Processes Field Experiment in February, 2003 (third Intensive Observation Period) were simulated using a Dense Media Radiative Transfer model (DMRT), based on the Quasi Crystalline Approximation with Coherent Potential (QCA-CP). Inputs to the model were averaged from LSOS snow pit measurements, although different averages were used for the lower frequencies vs. the highest one, due to the different penetration depths and to the stratigraphy of the snowpack. Mean snow particle radius was computed as a best-fit parameter. Results show that the model was able to reproduce satisfactorily brightness temperatures measured by the University of Tokyo s Ground Based Microwave Radiometer system (CBMR-7). The values of the best-fit snow particle radii were found to fall within the range of values obtained by averaging the field-measured mean particle sizes for the three classes of Small, Medium and Large grain sizes measured at the LSOS site.

Qualitative methods in quantum theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Migdal, A.B.

The author feels that the solution of most problems in theoretical physics begins with the application of qualitative methods - dimensional estimates and estimates made from simple models, the investigation of limiting cases, the use of the analytic properties of physical quantities, etc. This book proceeds in this spirit, rather than in a formal, mathematical way with no traces of the sweat involved in the original work left to show. The chapters are entitled Dimensional and model approximations, Various types of perturbation theory, The quasi-classical approximation, Analytic properties of physical quantities, Methods in the many-body problem, and Qualitative methods inmore » quantum field theory. Each chapter begins with a detailed introduction, in which the physical meaning of the results obtained in that chapter is explained in a simple way. 61 figures. (RWR)« less

Quintessence from virtual dark matter

NASA Astrophysics Data System (ADS)

Damdinsuren, Battsetseg; Sim, Jonghyun; Lee, Tae Hoon

2017-09-01

Considering a theory of Brans-Dicke gravity with general couplings of Higgs-like bosons including a non-renormalizable term, we derive the low-energy effective theory action in the Universe of a temperature much lower than the Higgs-like boson mass. Necessary equations containing gravitational field equations and an effective potential of the Brans-Dicke scalar field are obtained, which are induced through virtual interactions of the Higgs-like heavy field in the late-time Universe. We find a de Sitter cosmological solution with the inverse power law effective potential of the scalar field and discuss the possibility that the late-time acceleration of our Universe can be naturally explained by means of the solution. We also investigate stability properties of the quintessence model by using a linear approximation.

Effects of renormalizing the chiral SU(2) quark-meson model

NASA Astrophysics Data System (ADS)

Zacchi, Andreas; Schaffner-Bielich, Jürgen

2018-04-01

We investigate the restoration of chiral symmetry at finite temperature in the SU(2) quark-meson model, where the mean field approximation is compared to the renormalized version for quarks and mesons. In a combined approach at finite temperature, all the renormalized versions show a crossover transition. The inclusion of different renormalization scales leave the order parameter and the mass spectra nearly untouched but strongly influence the thermodynamics at low temperatures and around the phase transition. We find unphysical results for the renormalized version of mesons and the combined one.

Implementation of a finite-amplitude method in a relativistic meson-exchange model

NASA Astrophysics Data System (ADS)

Sun, Xuwei; Lu, Dinghui

2017-08-01

The finite-amplitude method is a feasible numerical approach to large scale random phase approximation calculations. It avoids the storage and calculation of residual interaction elements as well as the diagonalization of the RPA matrix, which will be prohibitive when the configuration space is huge. In this work we finished the implementation of a finite-amplitude method in a relativistic meson exchange mean field model with axial symmetry. The direct variation approach makes our FAM scheme capable of being extended to the multipole excitation case.

Correlation effects in fcc-Fe(x)Ni(1-x) alloys investigated by means of the KKR-CPA.

PubMed

Minár, J; Mankovsky, S; Šipr, O; Benea, D; Ebert, H

2014-07-09

The electronic structure and magnetic properties of the disordered alloy system fcc-FexNi1-x (fcc: face centered cubic) have been investigated by means of the KKR-CPA (Korringa-Kohn-Rostoker coherent potential approximation) band structure method. To investigate the impact of correlation effects, the calculations have been performed on the basis of the LSDA (local spin density approximation), the LSDA + U as well as the LSDA + DMFT (dynamical mean field theory). It turned out that the inclusion of correlation effects hardly changed the spin magnetic moments and the related hyperfine fields. The spin-orbit induced orbital magnetic moments and hyperfine fields, on the other hand, show a pronounced and element-specific enhancement. These findings are in full accordance with the results of a recent experimental study.

A neighborhood statistics model for predicting stream pathogen indicator levels.

PubMed

Pandey, Pramod K; Pasternack, Gregory B; Majumder, Mahbubul; Soupir, Michelle L; Kaiser, Mark S

2015-03-01

Because elevated levels of water-borne Escherichia coli in streams are a leading cause of water quality impairments in the U.S., water-quality managers need tools for predicting aqueous E. coli levels. Presently, E. coli levels may be predicted using complex mechanistic models that have a high degree of unchecked uncertainty or simpler statistical models. To assess spatio-temporal patterns of instream E. coli levels, herein we measured E. coli, a pathogen indicator, at 16 sites (at four different times) within the Squaw Creek watershed, Iowa, and subsequently, the Markov Random Field model was exploited to develop a neighborhood statistics model for predicting instream E. coli levels. Two observed covariates, local water temperature (degrees Celsius) and mean cross-sectional depth (meters), were used as inputs to the model. Predictions of E. coli levels in the water column were compared with independent observational data collected from 16 in-stream locations. The results revealed that spatio-temporal averages of predicted and observed E. coli levels were extremely close. Approximately 66 % of individual predicted E. coli concentrations were within a factor of 2 of the observed values. In only one event, the difference between prediction and observation was beyond one order of magnitude. The mean of all predicted values at 16 locations was approximately 1 % higher than the mean of the observed values. The approach presented here will be useful while assessing instream contaminations such as pathogen/pathogen indicator levels at the watershed scale.

Addendum to "Colored-noise-induced discontinuous transitions in symbiotic ecosystems".

PubMed

Sauga, Ako; Mankin, Romi

2005-06-01

A symbiotic ecosystem with Gompertz self-regulation and with adaptive competition between populations is studied by means of a N-species Lotka-Volterra stochastic model. The influence of fluctuating environment on the carrying capacity of a population is modeled as a dichotomous noise. The study is a follow up of previous investigations of symbiotic ecosystems subjected to the generalized Verhulst self-regulation [Phys. Rev. E 69, 061106 (2004); 65, 051108 (2002)]. In the framework of mean-field approximation the behavior of the solutions of the self-consistency equation for a stationary system is examined analytically in the full phase space of system parameters. Depending on the mutual interplay of symbiosis and competition of species, variation of noise parameters (amplitude, correlation time) can induce doubly unidirectional discontinuous transitions as well as single unidirectional discontinuous transitions of the mean population size.

Addendum to ``Colored-noise-induced discontinuous transitions in symbiotic ecosystems''

NASA Astrophysics Data System (ADS)

Sauga, Ako; Mankin, Romi

2005-06-01

A symbiotic ecosystem with Gompertz self-regulation and with adaptive competition between populations is studied by means of a N -species Lotka-Volterra stochastic model. The influence of fluctuating environment on the carrying capacity of a population is modeled as a dichotomous noise. The study is a follow up of previous investigations of symbiotic ecosystems subjected to the generalized Verhulst self-regulation [Phys. Rev. E 69, 061106 (2004); 65, 051108 (2002)]. In the framework of mean-field approximation the behavior of the solutions of the self-consistency equation for a stationary system is examined analytically in the full phase space of system parameters. Depending on the mutual interplay of symbiosis and competition of species, variation of noise parameters (amplitude, correlation time) can induce doubly unidirectional discontinuous transitions as well as single unidirectional discontinuous transitions of the mean population size.

On the role of fluctuations in the modeling of complex systems.

NASA Astrophysics Data System (ADS)

Droz, Michel; Pekalski, Andrzej

2016-09-01

The study of models is ubiquitous in sciences like physics, chemistry, ecology, biology or sociology. Models are used to explain experimental facts or to make new predictions. For any system, one can distinguish several levels of description. In the simplest mean-field like description the dynamics is described in terms of spatially averaged quantities while in a microscopic approach local properties are taken into account and local fluctuations for the relevant variables are present. The properties predicted by these two different approaches may be drastically different. In a large body of research literature concerning complex systems this problem is often overlooked and simple mean-field like approximation are used without asking the question of the robustness of the corresponding predictions. The goal of this paper is twofold, first to illustrate the importance of the fluctuations in a self-contained and pedagogical way, by revisiting two different classes of problems where thorough investigations have been conducted (equilibrium and non-equilibrium statistical physics). Second, we present our original research on the dynamics of population of annual plants which are competing among themselves for just one resource (water) through a stochastic dynamics. Depending on the observable considered, the mean-field like and microscopic approaches agree or totally disagree. There is not a general criterion allowing to decide a priori when the two approaches will agree.

A Unified Treatment of the Acoustic and Elastic Scattered Waves from Fluid-Elastic Media

NASA Astrophysics Data System (ADS)

Denis, Max Fernand

In this thesis, contributions are made to the numerical modeling of the scattering fields from fluid-filled poroelastic materials. Of particular interest are highly porous materials that demonstrate strong contrast to the saturating fluid. A Biot's analysis of porous medium serves as the starting point of the elastic-solid and pore-fluid governing equations of motion. The longitudinal scattering waves of the elastic-solid mode and the pore-fluid mode are modeled by the Kirchhoff-Helmholtz integral equation. The integral equation is evaluated using a series approximation, describing the successive perturbation of the material contrasts. To extended the series' validity into larger domains, rational fraction extrapolation methods are employed. The local Pade□ approximant procedure is a technique that allows one to extrapolate from a scattered field of small contrast into larger values, using Pade□ approximants. To ensure the accuracy of the numerical model, comparisons are made with the exact solution of scattering from a fluid sphere. Mean absolute error analyses, yield convergent and accurate results. In addition, the numerical model correctly predicts the Bragg peaks for a periodic lattice of fluid spheres. In the case of trabecular bones, the far-field scattering pressure attenuation is a superposition of the elastic-solid mode and the pore-fluid mode generated waves from the surrounding fluid and poroelastic boundaries. The attenuation is linearly dependent with frequency between 0.2 and 0.6MHz. The slope of the attenuation is nonlinear with porosity, and does not reflect the mechanical properties of the trabecular bone. The attenuation shows the anisotropic effects of the trabeculae structure. Thus, ultrasound can possibly be employed to non-invasively predict the principal structural orientation of trabecular bones.

Aspects of metallic low-temperature transport in Mott-insulator/band-insulator superlattices: Optical conductivity and thermoelectricity

NASA Astrophysics Data System (ADS)

Rüegg, Andreas; Pilgram, Sebastian; Sigrist, Manfred

2008-06-01

We investigate the low-temperature electrical and thermal transport properties in atomically precise metallic heterostructures involving strongly correlated electron systems. The model of the Mott-insulator/band-insulator superlattice was discussed in the framework of the slave-boson mean-field approximation and transport quantities were derived by use of the Boltzmann transport equation in the relaxation-time approximation. The results for the optical conductivity are in good agreement with recently published experimental data on (LaTiO3)N/(SrTiO3)M superlattices and allow us to estimate the values of key parameters of the model. Furthermore, predictions for the thermoelectric response were made and the dependence of the Seebeck coefficient on model parameters was studied in detail. The width of the Mott-insulating material was identified as the most relevant parameter, in particular, this parameter provides a way to optimize the thermoelectric power factor at low temperatures.

First-Principles Study on the Ferromagnetism and Curie Temperature of Mn-Doped AlX and InX (X=N, P, As, and Sb)

NASA Astrophysics Data System (ADS)

Sato, Kazunori; Dederichs, Peter H.; Katayama-Yoshida, Hiroshi

2007-02-01

We investigate the electronic structure and magnetic properties of AlN-, AlP-, AlAs-, AlSb-, InN-, InP-, InAs-, and InSb-based dilute magnetic semiconductors (DMS) with Mn impurities from first-principles. The electronic structure of DMS is calculated by using the Korringa-Kohn-Rostoker coherent potential approximation (KKR-CPA) method in connection with the local density approximation (LDA) and the LDA+U method. Describing the magnetic properties by a classical Heisenberg model, effective exchange interactions are calculated by applying magnetic force theorem for two impurities embedded in the CPA medium. With the calculated exchange interactions, TC is estimated by using the mean field approximation, the random phase approximation and the Monte Carlo simulation. It is found that the p-d exchange model [Dietl et al.: Science 287 (2000) 1019] is adequate for a limited class of DMS and insufficient to describe the ferromagnetism in wide gap semiconductor based DMS such as (Ga,Mn)N and the presently investigated (Al,Mn)N and (In,Mn)N.

Statistical thermodynamics of protein folding: Comparison of a mean-field theory with Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Hao, Ming-Hong; Scheraga, Harold A.

1995-01-01

A comparative study of protein folding with an analytical theory and computer simulations, respectively, is reported. The theory is based on an improved mean-field formalism which, in addition to the usual mean-field approximations, takes into account the distributions of energies in the subsets of conformational states. Sequence-specific properties of proteins are parametrized in the theory by two sets of variables, one for the energetics of mean-field interactions and one for the distribution of energies. Simulations are carried out on model polypeptides with different sequences, with different chain lengths, and with different interaction potentials, ranging from strong biases towards certain local chain states (bond angles and torsional angles) to complete absence of local conformational preferences. Theoretical analysis of the simulation results for the model polypeptides reveals three different types of behavior in the folding transition from the statistical coiled state to the compact globular state; these include a cooperative two-state transition, a continuous folding, and a glasslike transition. It is found that, with the fitted theoretical parameters which are specific for each polypeptide under a different potential, the mean-field theory can describe the thermodynamic properties and folding behavior of the different polypeptides accurately. By comparing the theoretical descriptions with simulation results, we verify the basic assumptions of the theory and, thereby, obtain new insights about the folding transitions of proteins. It is found that the cooperativity of the first-order folding transition of the model polypeptides is determined mainly by long-range interactions, in particular the dipolar orientation; the local interactions (e.g., bond-angle and torsion-angle potentials) have only marginal effect on the cooperative characteristic of the folding, but have a large impact on the difference in energy between the folded lowest-energy structure and the unfolded conformations of a protein.

A Markov model for blind image separation by a mean-field EM algorithm.

PubMed

Tonazzini, Anna; Bedini, Luigi; Salerno, Emanuele

2006-02-01

This paper deals with blind separation of images from noisy linear mixtures with unknown coefficients, formulated as a Bayesian estimation problem. This is a flexible framework, where any kind of prior knowledge about the source images and the mixing matrix can be accounted for. In particular, we describe local correlation within the individual images through the use of Markov random field (MRF) image models. These are naturally suited to express the joint pdf of the sources in a factorized form, so that the statistical independence requirements of most independent component analysis approaches to blind source separation are retained. Our model also includes edge variables to preserve intensity discontinuities. MRF models have been proved to be very efficient in many visual reconstruction problems, such as blind image restoration, and allow separation and edge detection to be performed simultaneously. We propose an expectation-maximization algorithm with the mean field approximation to derive a procedure for estimating the mixing matrix, the sources, and their edge maps. We tested this procedure on both synthetic and real images, in the fully blind case (i.e., no prior information on mixing is exploited) and found that a source model accounting for local autocorrelation is able to increase robustness against noise, even space variant. Furthermore, when the model closely fits the source characteristics, independence is no longer a strict requirement, and cross-correlated sources can be separated, as well.

Modelling dynamic changes in blood flow and volume in the cerebral vasculature.

PubMed

Payne, S J; El-Bouri, W K

2018-08-01

The cerebral microvasculature plays a key role in the transport of blood and the delivery of nutrients to the cells that perform brain function. Although recent advances in experimental imaging techniques mean that its structure and function can be interrogated to very small length scales, allowing individual vessels to be mapped to a fraction of 1 μm, these techniques currently remain confined to animal models. In-vivo human data can only be obtained at a much coarser length scale, of order 1 mm, meaning that mathematical models of the microvasculature play a key role in interpreting flow and metabolism data. However, there are close to 10,000 vessels even within a single voxel of size 1 mm 3 . Given the number of vessels present within a typical voxel and the complexity of the governing equations for flow and volume changes, it is computationally challenging to solve these in full, particularly when considering dynamic changes, such as those found in response to neural activation. We thus consider here the governing equations and some of the simplifications that have been proposed in order more rigorously to justify in what generations of blood vessels these approximations are valid. We show that two approximations (neglecting the advection term and assuming a quasi-steady state solution for blood volume) can be applied throughout the cerebral vasculature and that two further approximations (a simple first order differential relationship between inlet and outlet flows and inlet and outlet pressures, and matching of static pressure at nodes) can be applied in vessels smaller than approximately 1 mm in diameter. We then show how these results can be applied in solving flow fields within cerebral vascular networks providing a simplified yet rigorous approach to solving dynamic flow fields and compare the results to those obtained with alternative approaches. We thus provide a framework to model cerebral blood flow and volume within the cerebral vasculature that can be used, particularly at sub human imaging length scales, to provide greater insight into the behaviour of blood flow and volume in the cerebral vasculature. Copyright © 2018 Elsevier Inc. All rights reserved.

The ambivalent effect of lattice structure on a spatial game

NASA Astrophysics Data System (ADS)

Zhang, Hui; Gao, Meng; Li, Zizhen; Maa, Zhihui; Wang, Hailong

2011-06-01

The evolution of cooperation is studied in lattice-structured populations, in which each individual who adopts one of the following strategies ‘always defect' (ALLD), ‘tit-for-tat' (TFT), and ‘always cooperate' (ALLC) plays the repeated Prisoner's Dilemma game with its neighbors according to an asynchronous update rule. Computer simulations are applied to analyse the dynamics depending on major parameters. Mathematical analyses based on invasion probability analysis, mean-field approximation, as well as pair approximation are also used. We find that the lattice structure promotes the evolution of cooperation compared with a non-spatial population, this is also confirmed by invasion probability analysis in one dimension. Meanwhile, it also inhibits the evolution of cooperation due to the advantage of being spiteful, which indicates the key role of specific life-history assumptions. Mean-field approximation fails to predict the outcome of computer simulations. Pair approximation is accurate in two dimensions but fails in one dimension.

Vector solution for the mean electromagnetic fields in a layer of random particles

NASA Technical Reports Server (NTRS)

Lang, R. H.; Seker, S. S.; Levine, D. M.

1986-01-01

The mean electromagnetic fields are found in a layer of randomly oriented particles lying over a half space. A matrix-dyadic formulation of Maxwell's equations is employed in conjunction with the Foldy-Lax approximation to obtain equations for the mean fields. A two variable perturbation procedure, valid in the limit of small fractional volume, is then used to derive uncoupled equations for the slowly varying amplitudes of the mean wave. These equations are solved to obtain explicit expressions for the mean electromagnetic fields in the slab region in the general case of arbitrarily oriented particles and arbitrary polarization of the incident radiation. Numerical examples are given for the application to remote sensing of vegetation.

Mean Field Games for Stochastic Growth with Relative Utility

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Minyi, E-mail: mhuang@math.carleton.ca; Nguyen, Son Luu, E-mail: sonluu.nguyen@upr.edu

This paper considers continuous time stochastic growth-consumption optimization in a mean field game setting. The individual capital stock evolution is determined by a Cobb–Douglas production function, consumption and stochastic depreciation. The individual utility functional combines an own utility and a relative utility with respect to the population. The use of the relative utility reflects human psychology, leading to a natural pattern of mean field interaction. The fixed point equation of the mean field game is derived with the aid of some ordinary differential equations. Due to the relative utility interaction, our performance analysis depends on some ratio based approximation errormore » estimate.« less

The transition between immune and disease states in a cellular automaton model of clonal immune response

NASA Astrophysics Data System (ADS)

Bezzi, Michele; Celada, Franco; Ruffo, Stefano; Seiden, Philip E.

1997-02-01

In this paper we extend the Celada-Seiden (CS) model of the humoral immune response to include infections virus and killer T cells (cellular response). The model represents molecules and cells with bitstrings. The response of the system to virus involves a competition between the ability of the virus to kill the host cells and the host's ability to eliminate the virus. We find two basins of attraction in the dynamics of this system, one is identified with disease and the other with the immune state. There is also an oscillating state that exists on the border of these two stable states. Fluctuations in the population of virus or antibody can end the oscillation and drive the system into one of the stable states. The introduction of mechanisms of cross-regulation between the two responses can bias the system towards one of them. We also study a mean field model, based on coupled maps, to investigate virus-like infections. This simple model reproduces the attractors for average populations observed in the cellular automaton. All the dynamical behavior connected to spatial extension is lost, as is the oscillating feature. Thus the mean field approximation introduced with coupled maps destroys oscillations.

Scattering of magnetized electrons at the boundary of low temperature plasmas

NASA Astrophysics Data System (ADS)

Krüger, Dennis; Trieschmann, Jan; Brinkmann, Ralf Peter

2018-02-01

Magnetized technological plasmas with magnetic fields of 10-200 mT, plasma densities of 1017-1019 m-3, gas pressures of less than 1 Pa, and electron energies from a few to (at most) a few hundred electron volts are characterized by electron Larmor radii r L, that are small compared to all other length scales of the system, including the spatial scale L of the magnetic field and the collisional mean free path λ. In this regime, the classical drift approximation applies. In the boundary sheath of these discharges, however, that approximation breaks down: The sheath penetration depth of electrons (a few to some ten Debye length λ D; depending on the kinetic energy; typically much smaller than the sheath thickness of tens/hundreds of λ D) is even smaller than r L. For a model description of the electron dynamics, an appropriate boundary condition for the plasma/sheath interface is required. To develop such, the interaction of magnetized electrons with the boundary sheath is investigated using a 3D kinetic single electron model that sets the larger scales L and λ to infinity, i.e. neglects magnetic field gradients, the electric field in the bulk, and collisions. A detailed comparison of the interaction for a Bohm sheath (which assumes a finite Debye length) and a hard wall model (representing the limit {λ }{{D}}\\to 0; also called the specular reflection model) is conducted. Both models are found to be in remarkable agreement with respect to the sheath-induced drift. It is concluded that the assumption of specular reflection can be used as a valid boundary condition for more realistic kinetic models of magnetized technological plasmas.

Effect of electron Monte Carlo collisions on a hybrid simulation of a low-pressure capacitively coupled plasma

NASA Astrophysics Data System (ADS)

Hwang, Seok Won; Lee, Ho-Jun; Lee, Hae June

2014-12-01

Fluid models have been widely used and conducted successfully in high pressure plasma simulations where the drift-diffusion and the local-field approximation are valid. However, fluid models are not able to demonstrate non-local effects related to large electron energy relaxation mean free path in low pressure plasmas. To overcome this weakness, a hybrid model coupling electron Monte Carlo collision (EMCC) method with the fluid model is introduced to obtain precise electron energy distribution functions using pseudo-particles. Steady state simulation results by a one-dimensional hybrid model which includes EMCC method for the collisional reactions but uses drift-diffusion approximation for electron transport in a fluid model are compared with those of a conventional particle-in-cell (PIC) and a fluid model for low pressure capacitively coupled plasmas. At a wide range of pressure, the hybrid model agrees well with the PIC simulation with a reduced calculation time while the fluid model shows discrepancy in the results of the plasma density and the electron temperature.

Self-consistent field model for strong electrostatic correlations and inhomogeneous dielectric media.

PubMed

Ma, Manman; Xu, Zhenli

2014-12-28

Electrostatic correlations and variable permittivity of electrolytes are essential for exploring many chemical and physical properties of interfaces in aqueous solutions. We propose a continuum electrostatic model for the treatment of these effects in the framework of the self-consistent field theory. The model incorporates a space- or field-dependent dielectric permittivity and an excluded ion-size effect for the correlation energy. This results in a self-energy modified Poisson-Nernst-Planck or Poisson-Boltzmann equation together with state equations for the self energy and the dielectric function. We show that the ionic size is of significant importance in predicting a finite self energy for an ion in an inhomogeneous medium. Asymptotic approximation is proposed for the solution of a generalized Debye-Hückel equation, which has been shown to capture the ionic correlation and dielectric self energy. Through simulating ionic distribution surrounding a macroion, the modified self-consistent field model is shown to agree with particle-based Monte Carlo simulations. Numerical results for symmetric and asymmetric electrolytes demonstrate that the model is able to predict the charge inversion at high correlation regime in the presence of multivalent interfacial ions which is beyond the mean-field theory and also show strong effect to double layer structure due to the space- or field-dependent dielectric permittivity.

On Geomagnetism and Paleomagnetism I

NASA Technical Reports Server (NTRS)

Voorhies, Coerte V.

2000-01-01

A partial description of Earth's broad scale, core-source magnetic field has been developed and tested three ways. The description features an expected, or mean, spatial magnetic power spectrum that is approximately inversely proportional to horizontal wavenumber atop Earth's core. This multipole spectrum describes a magnetic energy range; it is not steep enough for Gubbins' magnetic dissipation range. Temporal variations of core multipole powers about mean values are to be expected and are described statistically, via trial probability distribution functions, instead of deterministically, via trial solution of closed transport equations. The distributions considered here are closed and neither require nor prohibit magnetic isotropy. The description is therefore applicable to, and tested against, both dipole and low degree non-dipole fields. In Part 1, a physical basis for an expectation spectrum is developed and checked. The description is then combined with main field models of twentieth century satellite and surface geomagnetic field measurements to make testable predictions of the radius of Earth's core. The predicted core radius is 0.7% above the 3480 km seismological value. Partial descriptions of other planetary dipole fields are noted.

Energy Dependence of Synchrotron X-Ray Rims in Tycho's Supernova Remnant

NASA Technical Reports Server (NTRS)

Tran, Aaron; Williams, Brian J.; Petre, Robert; Ressler, Sean M.; Reynolds, Stephen P.

2015-01-01

Several young supernova remnants exhibit thin X-ray bright rims of synchrotron radiation at their forward shocks. Thin rims require strong magnetic field amplification beyond simple shock compression if rim widths are only limited by electron energy losses. But, magnetic field damping behind the shock could produce similarly thin rims with less extreme field amplification. Variation of rim width with energy may thus discriminate between competing influences on rim widths. We measured rim widths around Tycho's supernova remnant in 5 energy bands using an archival 750 ks Chandra observation. Rims narrow with increasing energy and are well described by either loss-limited or damped scenarios, so X-ray rim width-energy dependence does not uniquely specify a model. But, radio counterparts to thin rims are not loss-limited and better reflect magnetic field structure. Joint radio and X-ray modeling favors magnetic damping in Tycho's SNR with damping lengths approximately 1-5% of remnant radius and magnetic field strengths approximately 50-400 micron G assuming Bohm diffusion. X-ray rim widths are approximately 1% of remnant radius, somewhat smaller than inferred damping lengths. Electron energy losses are important in all models of X-ray rims, suggesting that the distinction between loss-limited and damped models is blurred in soft X-rays. All loss-limited and damping models require magnetic fields approximately greater than 20 micron G, arming the necessity of magnetic field amplification beyond simple compression.

Spin-orbit splitted excited states using explicitly-correlated equation-of-motion coupled-cluster singles and doubles eigenvectors

NASA Astrophysics Data System (ADS)

Bokhan, Denis; Trubnikov, Dmitrii N.; Perera, Ajith; Bartlett, Rodney J.

2018-04-01

An explicitly-correlated method of calculation of excited states with spin-orbit couplings, has been formulated and implemented. Developed approach utilizes left and right eigenvectors of equation-of-motion coupled-cluster model, which is based on the linearly approximated explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] method. The spin-orbit interactions are introduced by using the spin-orbit mean field (SOMF) approximation of the Breit-Pauli Hamiltonian. Numerical tests for several atoms and molecules show good agreement between explicitly-correlated results and the corresponding values, calculated in complete basis set limit (CBS); the highly-accurate excitation energies can be obtained already at triple- ζ level.

Validity of the local approximation in iron pnictides and chalcogenides

DOE PAGES

Sémon, Patrick; Haule, Kristjan; Kotliar, Gabriel

2017-05-08

We introduce a methodology to treat different degrees of freedom at different levels of approximation. We use cluster DMFT (dynamical mean field theory) for the t 2g electrons and single site DMFT for the e g electrons to study the normal state of the iron pnictides and chalcogenides. Furthermore, in the regime of moderate mass renormalizations, the self-energy is very local, justifying the success of single site DMFT for these materials and for other Hunds metals. Here we solve the corresponding impurity model with CTQMC (continuous time quantum Monte Carlo) and find that the minus sign problem is not severemore » in regimes of moderate mass renormalization.« less

Dynamic Kerr effect in a strong uniform AC electric field for interacting polar and polarizable molecules in the mean field approximation

NASA Astrophysics Data System (ADS)

Deshmukh, Snehal D.; Déjardin, Pierre-Michel; Kalmykov, Yuri P.

2017-09-01

Analytical formulas for the electric birefringence response of interacting polar and anisotropically polarizable molecules due to a uniform alternating electric field are derived using Berne's forced rotational diffusion model [B. J. Berne, J. Chem. Phys. 62, 1154 (1975)] in the nonlinear version described by Warchol and Vaughan [J. Chem. Phys. 71, 502 (1979)]. It is found for noninteracting molecules that the signal consists of a frequency-dependent DC component superimposed on an oscillatory part with a frequency twice that of the AC driving field. However, unlike noninteracting molecules, the AC part strongly deviates from its dilute counterpart. This suggests a possible way of motivating new experimental studies of intermolecular interactions involving electro-optical methods and complementary nonlinear dielectric relaxation experiments.

Comment on "the one dimensional acoustic field with arbitrary mean axial temperature gradient and mean flow" (J.Li and A.S.Morgans, Journal of Sound and Vibration 400 (2017) 248-269)

NASA Astrophysics Data System (ADS)

Dokumaci, Erkan

2017-12-01

In a recent study, Li and Morgans [1] present an ingenious WKB approximation for the acoustic plane wave field in a straight uniform duct with mean temperature gradient and mean flow. The authors state that the previous solutions are limited to small linear mean temperature gradients and low mean flow Mach numbers and claim that their solution applies for arbitrary mean temperature profiles and moderate-to-large mean flow velocity Mach numbers at both low and high frequencies.

Dynamics analysis of SIR epidemic model with correlation coefficients and clustering coefficient in networks.

PubMed

Zhang, Juping; Yang, Chan; Jin, Zhen; Li, Jia

2018-07-14

In this paper, the correlation coefficients between nodes in states are used as dynamic variables, and we construct SIR epidemic dynamic models with correlation coefficients by using the pair approximation method in static networks and dynamic networks, respectively. Considering the clustering coefficient of the network, we analytically investigate the existence and the local asymptotic stability of each equilibrium of these models and derive threshold values for the prevalence of diseases. Additionally, we obtain two equivalent epidemic thresholds in dynamic networks, which are compared with the results of the mean field equations. Copyright © 2018 Elsevier Ltd. All rights reserved.

Efficient Mean Field Variational Algorithm for Data Assimilation (Invited)

NASA Astrophysics Data System (ADS)

Vrettas, M. D.; Cornford, D.; Opper, M.

2013-12-01

Data assimilation algorithms combine available observations of physical systems with the assumed model dynamics in a systematic manner, to produce better estimates of initial conditions for prediction. Broadly they can be categorized in three main approaches: (a) sequential algorithms, (b) sampling methods and (c) variational algorithms which transform the density estimation problem to an optimization problem. However, given finite computational resources, only a handful of ensemble Kalman filters and 4DVar algorithms have been applied operationally to very high dimensional geophysical applications, such as weather forecasting. In this paper we present a recent extension to our variational Bayesian algorithm which seeks the ';optimal' posterior distribution over the continuous time states, within a family of non-stationary Gaussian processes. Our initial work on variational Bayesian approaches to data assimilation, unlike the well-known 4DVar method which seeks only the most probable solution, computes the best time varying Gaussian process approximation to the posterior smoothing distribution for dynamical systems that can be represented by stochastic differential equations. This approach was based on minimising the Kullback-Leibler divergence, over paths, between the true posterior and our Gaussian process approximation. Whilst the observations were informative enough to keep the posterior smoothing density close to Gaussian the algorithm proved very effective on low dimensional systems (e.g. O(10)D). However for higher dimensional systems, the high computational demands make the algorithm prohibitively expensive. To overcome the difficulties presented in the original framework and make our approach more efficient in higher dimensional systems we have been developing a new mean field version of the algorithm which treats the state variables at any given time as being independent in the posterior approximation, while still accounting for their relationships in the mean solution arising from the original system dynamics. Here we present this new mean field approach, illustrating its performance on a range of benchmark data assimilation problems whose dimensionality varies from O(10) to O(10^3)D. We emphasise that the variational Bayesian approach we adopt, unlike other variational approaches, provides a natural bound on the marginal likelihood of the observations given the model parameters which also allows for inference of (hyper-) parameters such as observational errors, parameters in the dynamical model and model error representation. We also stress that since our approach is intrinsically parallel it can be implemented very efficiently to address very long data assimilation time windows. Moreover, like most traditional variational approaches our Bayesian variational method has the benefit of being posed as an optimisation problem therefore its complexity can be tuned to the available computational resources. We finish with a sketch of possible future directions.

Low temperature mobility in hafnium-oxide gated germanium p-channel metal-oxide-semiconductor field-effect transistors

NASA Astrophysics Data System (ADS)

Beer, Chris; Whall, Terry; Parker, Evan; Leadley, David; De Jaeger, Brice; Nicholas, Gareth; Zimmerman, Paul; Meuris, Marc; Szostak, Slawomir; Gluszko, Grzegorz; Lukasiak, Lidia

2007-12-01

Effective mobility measurements have been made at 4.2K on high performance high-k gated germanium p-type metal-oxide-semiconductor field effect transistors with a range of Ge/gate dielectric interface state densities. The mobility is successfully modelled by assuming surface roughness and interface charge scattering at the SiO2 interlayer/Ge interface. The deduced interface charge density is approximately equal to the values obtained from the threshold voltage and subthreshold slope measurements on each device. A hydrogen anneal reduces both the interface state density and the surface root mean square roughness by 20%.

Nonequilibrium itinerant-electron magnetism: A time-dependent mean-field theory

NASA Astrophysics Data System (ADS)

Secchi, A.; Lichtenstein, A. I.; Katsnelson, M. I.

2016-08-01

We study the dynamical magnetic susceptibility of a strongly correlated electronic system in the presence of a time-dependent hopping field, deriving a generalized Bethe-Salpeter equation that is valid also out of equilibrium. Focusing on the single-orbital Hubbard model within the time-dependent Hartree-Fock approximation, we solve the equation in the nonequilibrium adiabatic regime, obtaining a closed expression for the transverse magnetic susceptibility. From this, we provide a rigorous definition of nonequilibrium (time-dependent) magnon frequencies and exchange parameters, expressed in terms of nonequilibrium single-electron Green's functions and self-energies. In the particular case of equilibrium, we recover previously known results.

The Relationship between Root Mean Square Error of Approximation and Model Misspecification in Confirmatory Factor Analysis Models

ERIC Educational Resources Information Center

Savalei, Victoria

2012-01-01

The fit index root mean square error of approximation (RMSEA) is extremely popular in structural equation modeling. However, its behavior under different scenarios remains poorly understood. The present study generates continuous curves where possible to capture the full relationship between RMSEA and various "incidental parameters," such as…

On the Effect of Dipole-Dipole Interactions on the Quantum Statistics of Surface Plasmons in Multiparticle Spaser Systems

NASA Astrophysics Data System (ADS)

Shesterikov, A. V.; Gubin, M. Yu.; Karpov, S. N.; Prokhorov, A. V.

2018-04-01

The problem of controlling the quantum dynamics of localized plasmons has been considered in the model of a four-particle spaser composed of metallic nanoparticles and semiconductor quantum dots. Conditions for the observation of stable steady-state regimes of the formation of surface plasmons in this model have been determined in the mean-field approximation. It has been shown that the presence of strong dipole-dipole interactions between metallic nanoparticles of the spaser system leads to a considerable change in the quantum statistics of plasmons generated on the nanoparticles.

Can we scan the supernova model space for collective oscillations?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pehlivan, Y., E-mail: yamac.pehlivan@msgsu.edu.tr; National Astronomical Observatory of Japan 2-21-1 Osawa, Mitaka, Tokyo, 181-8588; Subaşı, A. L.

Collective neutrino oscillations in a core collapse supernova is a many-body phenomenon which can transform the neutrino energy spectra through emergent effects. One example of this behavior is the neutrino spectral swaps in which neutrinos of different flavors partially or completely exchange their spectra. In this talk, we address the question of how model dependent this behavior is. In particular, we demonstrate that these swaps may be independent of the mean field approximation that is typically employed in numerical treatments by showing an example of a spectral swap in the exact many-body picture.

Time-dependent Perpendicular Transport of Energetic Particles for Different Turbulence Configurations and Parallel Transport Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lasuik, J.; Shalchi, A., E-mail: andreasm4@yahoo.com

Recently, a new theory for the transport of energetic particles across a mean magnetic field was presented. Compared to other nonlinear theories the new approach has the advantage that it provides a full time-dependent description of the transport. Furthermore, a diffusion approximation is no longer part of that theory. The purpose of this paper is to combine this new approach with a time-dependent model for parallel transport and different turbulence configurations in order to explore the parameter regimes for which we get ballistic transport, compound subdiffusion, and normal Markovian diffusion.

The tight binding model study of the role of band filling on the charge gap in graphene-on-substrate in paramagnetic state

NASA Astrophysics Data System (ADS)

Panda, Rudrashish; Sahu, Sivabrata; Rout, G. C.

2017-05-01

We communicate here a tight binding theoretical model study of the band filling effect on the charge gap in graphene-on-substrate. The Hamiltonian consists of nearest neighbor electron hopping and substrate induced gap. Besides this the Coulomb interaction is considered here within mean-field approximation in the paramagnetic limit. The electron occupancies at two sublattices are calculated by Green's function technique and are solved self consistently. Finally the charge gap i.e. Δ ¯=U [ < na > -< nb > ] is calculated and computed numerically. The results are reported.

The Kubo-Greenwood formula as a result of the random phase approximation for the electrons of the metal

NASA Astrophysics Data System (ADS)

Ivliev, S. V.

2017-12-01

For calculation of short laser pulse absorption in metal the imaginary part of permittivity, which is simply related to the conductivity, is required. Currently to find the static and dynamic conductivity the Kubo-Greenwood formula is most commonly used. It describes the electromagnetic energy absorption in the one-electron approach. In the present study, this formula is derived directly from the expression for the permittivity expression in the random phase approximation, which in fact is equivalent to the method of the mean field. The detailed analysis of the role of electron-electron interaction in the calculation of the matrix elements of the velocity operator is given. It is shown that in the one-electron random phase approximation the single-particle conductive electron wave functions in the field of fixed ions should be used. The possibility of considering the exchange and correlation effects by means of an amendment to a local function field is discussed.

A DOUBLE-RING ALGORITHM FOR MODELING SOLAR ACTIVE REGIONS: UNIFYING KINEMATIC DYNAMO MODELS AND SURFACE FLUX-TRANSPORT SIMULATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Munoz-Jaramillo, Andres; Martens, Petrus C. H.; Nandy, Dibyendu

The emergence of tilted bipolar active regions (ARs) and the dispersal of their flux, mediated via processes such as diffusion, differential rotation, and meridional circulation, is believed to be responsible for the reversal of the Sun's polar field. This process (commonly known as the Babcock-Leighton mechanism) is usually modeled as a near-surface, spatially distributed {alpha}-effect in kinematic mean-field dynamo models. However, this formulation leads to a relationship between polar field strength and meridional flow speed which is opposite to that suggested by physical insight and predicted by surface flux-transport simulations. With this in mind, we present an improved double-ring algorithmmore » for modeling the Babcock-Leighton mechanism based on AR eruption, within the framework of an axisymmetric dynamo model. Using surface flux-transport simulations, we first show that an axisymmetric formulation-which is usually invoked in kinematic dynamo models-can reasonably approximate the surface flux dynamics. Finally, we demonstrate that our treatment of the Babcock-Leighton mechanism through double-ring eruption leads to an inverse relationship between polar field strength and meridional flow speed as expected, reconciling the discrepancy between surface flux-transport simulations and kinematic dynamo models.« less

Field-Scale Soil Moisture Observations in Irrigated Agriculture Fields Using the Cosmic-ray Neutron Rover

NASA Astrophysics Data System (ADS)

Franz, T. E.; Avery, W. A.; Finkenbiner, C. E.; Wang, T.; Brocca, L.

2014-12-01

Approximately 40% of global food production comes from irrigated agriculture. With the increasing demand for food even greater pressures will be placed on water resources within these systems. In this work we aimed to characterize the spatial and temporal patterns of soil moisture at the field-scale (~500 m) using the newly developed cosmic-ray neutron rover near Waco, NE. Here we mapped soil moisture of 144 quarter section fields (a mix of maize, soybean, and natural areas) each week during the 2014 growing season (May to September). The 11 x11 km study domain also contained 3 stationary cosmic-ray neutron probes for independent validation of the rover surveys. Basic statistical analysis of the domain indicated a strong inverted parabolic relationship between the mean and variance of soil moisture. The relationship between the mean and higher order moments were not as strong. Geostatistical analysis indicated the range of the soil moisture semi-variogram was significantly shorter during periods of heavy irrigation as compared to non-irrigated periods. Scaling analysis indicated strong power law behavior between the variance of soil moisture and averaging area with minimal dependence of mean soil moisture on the slope of the power law function. Statistical relationships derived from the rover dataset offer a novel set of observations that will be useful in: 1) calibrating and validating land surface models, 2) calibrating and validating crop models, 3) soil moisture covariance estimates for statistical downscaling of remote sensing products such as SMOS and SMAP, and 4) provide center-pivot scale mean soil moisture data for optimal irrigation timing and volume amounts.

Exact and approximate many-body dynamics with stochastic one-body density matrix evolution

NASA Astrophysics Data System (ADS)

Lacroix, Denis

2005-06-01

We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, Dab=|Φa><Φb|, where each state evolves according to the stochastic Schrödinger equation given by O. Juillet and Ph. Chomaz [Phys. Rev. Lett. 88, 142503 (2002)]. A stochastic Liouville-von Neumann equation is derived as well as the associated. Bogolyubov-Born-Green-Kirwood-Yvon hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean-field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean-field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended time-dependent Hartree-Fock scheme. In this stochastic mean-field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.

Mean-field description of topological charge 4e superconductors

NASA Astrophysics Data System (ADS)

Gabriele, Victoria; Luo, Jing; Teo, Jeffrey C. Y.

BCS superconductors can be understood by a mean-field approximation of two-body interacting Hamiltonians, whose ground states break charge conservation spontaneously by allowing non-vanishing expectation values of charge 2e Cooper pairs. Topological superconductors, such as one-dimensional p-wave wires, have non-trivial ground states that support robust gapless boundary excitations. We construct a four-body Hamiltonian in one dimension and perform a mean-field analysis. The mean-field Hamiltonian is now quartic in fermions but is still exactly solvable. The ground state exhibits 4-fermion expectation values instead of Cooper pair ones. There also exists a topological phase, where the charge 4e superconductor carries exotic zero energy boundary excitations.

Diffraction Analysis of Antennas With Mesh Surfaces

NASA Technical Reports Server (NTRS)

Rahmat-Samii, Yahya

1987-01-01

Strip-aperture model replaces wire-grid model. Far-field radiation pattern of antenna with mesh reflector calculated more accurately with new strip-aperture model than with wire-grid model of reflector surface. More adaptable than wire-grid model to variety of practical configurations and decidedly superior for reflectors in which mesh-cell width exceeds mesh thickness. Satisfies reciprocity theorem. Applied where mesh cells are no larger than tenth of wavelength. Small cell size permits use of simplifying approximation that reflector-surface current induced by electromagnetic field is present even in apertures. Approximation useful in calculating far field.

Impulsion of nanoparticles as a drug carrier for the theoretical investigation of stenosed arteries with induced magnetic effects

NASA Astrophysics Data System (ADS)

Nadeem, S.; Ijaz, S.

2016-07-01

In this paper hemodynamics of stenosis are discussed to predict effect of atherosclerosis by means of mathematical models in the presence of uniform transverse magnetic field. The analysis is carried out using silver and copper nanoparticles as a drug carrier. Exact solution for the fluid temperature, velocity, axial induced magnetic field and current density distribution are obtained under mild stenosis approximation. The results indicate that with an increase in the concentration of nanoparticle hemodynamics effects of stenosis reduces throughout the inclined composite stenosed arteries. The considered analysis also summarizes that the drug silver nanoparticles is more efficient to reduce hemodynamics of stenosis when compare to the drug copper nanoparticle. In future this model could be helpful to predict important properties in some biomedical applications.

Recalculation of regional and detailed gravity database from Slovak Republic and qualitative interpretation of new generation Bouguer anomaly map

NASA Astrophysics Data System (ADS)

Pasteka, Roman; Zahorec, Pavol; Mikuska, Jan; Szalaiova, Viktoria; Papco, Juraj; Krajnak, Martin; Kusnirak, David; Panisova, Jaroslava; Vajda, Peter; Bielik, Miroslav

2014-05-01

In this contribution results of the running project "Bouguer anomalies of new generation and the gravimetrical model of Western Carpathians (APVV-0194-10)" are presented. The existing homogenized regional database (212478 points) was enlarged by approximately 107 500 archive detailed gravity measurements. These added gravity values were measured since the year 1976 to the present, therefore they need to be unified and reprocessed. The improved positions of more than 8500 measured points were acquired by digitizing of archive maps (we recognized some local errors within particular data sets). Besides the local errors (due to the wrong positions, heights or gravity of measured points) we have found some areas of systematic errors probably due to the gravity measurement or processing errors. Some of them were confirmed and consequently corrected by field measurements within the frame of current project. Special attention is paid to the recalculation of the terrain corrections - we have used a new developed software as well as the latest version of digital terrain model of Slovakia DMR-3. Main improvement of the new terrain corrections evaluation algorithm is the possibility to calculate it in the real gravimeter position and involving of 3D polyhedral bodies approximation (accepting the spherical approximation of Earth's curvature). We have realized several tests by means of the introduction of non-standard distant relief effects introduction. A new complete Bouguer anomalies map was constructed and transformed by means of higher derivatives operators (tilt derivatives, TDX, theta-derivatives and the new TDXAS transformation), using the regularization approach. A new interesting regional lineament of probably neotectonic character was recognized in the new map of complete Bouguer anomalies and it was confirmed also by realized in-situ field measurements.

Multivariate Markov chain modeling for stock markets

NASA Astrophysics Data System (ADS)

Maskawa, Jun-ichi

2003-06-01

We study a multivariate Markov chain model as a stochastic model of the price changes of portfolios in the framework of the mean field approximation. The time series of price changes are coded into the sequences of up and down spins according to their signs. We start with the discussion for small portfolios consisting of two stock issues. The generalization of our model to arbitrary size of portfolio is constructed by a recurrence relation. The resultant form of the joint probability of the stationary state coincides with Gibbs measure assigned to each configuration of spin glass model. Through the analysis of actual portfolios, it has been shown that the synchronization of the direction of the price changes is well described by the model.

Upscaling of dilution and mixing using a trajectory based Spatial Markov random walk model in a periodic flow domain

NASA Astrophysics Data System (ADS)

Sund, Nicole L.; Porta, Giovanni M.; Bolster, Diogo

2017-05-01

The Spatial Markov Model (SMM) is an upscaled model that has been used successfully to predict effective mean transport across a broad range of hydrologic settings. Here we propose a novel variant of the SMM, applicable to spatially periodic systems. This SMM is built using particle trajectories, rather than travel times. By applying the proposed SMM to a simple benchmark problem we demonstrate that it can predict mean effective transport, when compared to data from fully resolved direct numerical simulations. Next we propose a methodology for using this SMM framework to predict measures of mixing and dilution, that do not just depend on mean concentrations, but are strongly impacted by pore-scale concentration fluctuations. We use information from trajectories of particles to downscale and reconstruct pore-scale approximate concentration fields from which mixing and dilution measures are then calculated. The comparison between measurements from fully resolved simulations and predictions with the SMM agree very favorably.

Large-Scale Flows and Magnetic Fields Produced by Rotating Convection in a Quasi-Geostrophic Model of Planetary Cores

NASA Astrophysics Data System (ADS)

Guervilly, C.; Cardin, P.

2017-12-01

Convection is the main heat transport process in the liquid cores of planets. The convective flows are thought to be turbulent and constrained by rotation (corresponding to high Reynolds numbers Re and low Rossby numbers Ro). Under these conditions, and in the absence of magnetic fields, the convective flows can produce coherent Reynolds stresses that drive persistent large-scale zonal flows. The formation of large-scale flows has crucial implications for the thermal evolution of planets and the generation of large-scale magnetic fields. In this work, we explore this problem with numerical simulations using a quasi-geostrophic approximation to model convective and zonal flows at Re 104 and Ro 10-4 for Prandtl numbers relevant for liquid metals (Pr 0.1). The formation of intense multiple zonal jets strongly affects the convective heat transport, leading to the formation of a mean temperature staircase. We also study the generation of magnetic fields by the quasi-geostrophic flows at low magnetic Prandtl numbers.

Existence of ground state of an electron in the BDF approximation

NASA Astrophysics Data System (ADS)

Sok, Jérémy

2014-05-01

The Bogoliubov-Dirac-Fock (BDF) model allows us to describe relativistic electrons interacting with the Dirac sea. It can be seen as a mean-field approximation of Quantum Electrodynamics (QED) where photons are neglected. This paper treats the case of an electron together with the Dirac sea in the absence of any external field. Such a system is described by its one-body density matrix, an infinite rank, self-adjoint operator. The parameters of the model are the coupling constant α > 0 and the ultraviolet cut-off Λ > 0: we consider the subspace of squared integrable functions made of the functions whose Fourier transform vanishes outside the ball B(0, Λ). We prove the existence of minimizers of the BDF energy under the charge constraint of one electron and no external field provided that α, Λ-1 and α log(Λ) are sufficiently small. The interpretation is the following: in this regime the electron creates a polarization in the Dirac vacuum which allows it to bind. We then study the non-relativistic limit of such a system in which the speed of light tends to infinity (or equivalently α tends to zero) with αlog(Λ) fixed: after rescaling and translation the electronic solution tends to a Choquard-Pekar ground state.

Critical behavior of the anisotropic Heisenberg model by effective-field renormalization group

NASA Astrophysics Data System (ADS)

de Sousa, J. Ricardo; Fittipaldi, I. P.

1994-05-01

A real-space effective-field renormalization-group method (ERFG) recently derived for computing critical properties of Ising spins is extended to treat the quantum spin-1/2 anisotropic Heisenberg model. The formalism is based on a generalized but approximate Callen-Suzuki spin relation and utilizes a convenient differential operator expansion technique. The method is illustrated in several lattice structures by employing its simplest approximation version in which clusters with one (N'=1) and two (N=2) spins are used. The results are compared with those obtained from the standard mean-field (MFRG) and Migdal-Kadanoff (MKRG) renormalization-group treatments and it is shown that this technique leads to rather accurate results. It is shown that, in contrast with the MFRG and MKRG predictions, the EFRG, besides correctly distinguishing the geometries of different lattice structures, also provides a vanishing critical temperature for all two-dimensional lattices in the isotropic Heisenberg limit. For the simple cubic lattice, the dependence of the transition temperature Tc with the exchange anisotropy parameter Δ [i.e., Tc(Δ)], and the resulting value for the critical thermal crossover exponent φ [i.e., Tc≂Tc(0)+AΔ1/φ ] are in quite good agreement with results available in the literature in which more sophisticated treatments are used.

Modeling and calculation of turbulent lifted diffusion flames

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanders, J.P.H.; Lamers, A.P.G.G.

1994-01-01

Liftoff heights of turbulent diffusion flames have been modeled using the laminar diffusion flamelet concept of Peters and Williams. The strain rate of the smallest eddies is used as the stretch describing parameter, instead of the more common scalar dissipation rate. The h(U) curve, which is the mean liftoff height as a function of fuel exit velocity can be accurately predicted, while this was impossible with the scalar dissipation rate. Liftoff calculations performed in the flames as well as in the equivalent isothermal jets, using a standard k-[epsilon] turbulence model yield approximately the same correct slope for the h(U) curvemore » while the offset has to be reproduced by choosing an appropriate coefficient in the strain rate model. For the flame calculations a model for the pdf of the fluctuating flame base is proposed. The results are insensitive to its width. The temperature field is qualitatively different from the field calculated by Bradley et al. who used a premixed flamelet model for diffusion flames.« less

High-resolution Monte Carlo simulation of flow and conservative transport in heterogeneous porous media: 1. Methodology and flow results

USGS Publications Warehouse

Naff, R.L.; Haley, D.F.; Sudicky, E.A.

1998-01-01

In this, the first of two papers concerned with the use of numerical simulation to examine flow and transport parameters in heterogeneous porous media via Monte Carlo methods, various aspects of the modelling effort are examined. In particular, the need to save on core memory causes one to use only specific realizations that have certain initial characteristics; in effect, these transport simulations are conditioned by these characteristics. Also, the need to independently estimate length scales for the generated fields is discussed. The statistical uniformity of the flow field is investigated by plotting the variance of the seepage velocity for vector components in the x, y, and z directions. Finally, specific features of the velocity field itself are illuminated in this first paper. In particular, these data give one the opportunity to investigate the effective hydraulic conductivity in a flow field which is approximately statistically uniform; comparisons are made with first- and second-order perturbation analyses. The mean cloud velocity is examined to ascertain whether it is identical to the mean seepage velocity of the model. Finally, the variance in the cloud centroid velocity is examined for the effect of source size and differing strengths of local transverse dispersion.

Dilution and Mixing in transient velocity fields: a first-order analysis

NASA Astrophysics Data System (ADS)

Di Dato, Mariaines; de Barros, Felipe, P. J.; Fiori, Aldo; Bellin, Alberto

2017-04-01

An appealing remediation technique is in situ oxidation, which effectiveness is hampered by difficulties in obtaining good mixing of the injected oxidant with the contaminant, particularly when the contaminant plume is contained and therefore its deformation is physically constrained. Under such conditions (i.e. containment), mixing may be augmented by inducing temporal fluctuations of the velocity field. The temporal variability of the flow field may increase the deformation of the plume such that diffusive mass flux becomes more effective. A transient periodic velocity field can be obtained by an engineered sequence of injections and extractions from wells, which may serve also as a hydraulic barrier to confine the plume. Assessing the effectiveness of periodic flows to maximize solute mixing is a difficult task given the need to use a 3D setup and the large number of possible flow configurations that should be analyzed in order to identify the optimal one. This is the typical situation in which analytical solutions, though approximated, may assist modelers in screening possible alternative flow configurations such that solute dilution is maximized. To quantify dilution (i.e. a precondition that enables reactive mixing) we utilize the concept of the dilution index [1]. In this presentation, the periodic flow takes place in an aquifer with spatially variable hydraulic conductivity field which is modeled as a Stationary Spatial Random Function. We developed a novel first-order analytical solution of the dilution index under the hypothesis that the flow can be approximated as a sequence of steady state configurations with the mean velocity changing with time in intensity and direction. This is equivalent to assume that the characteristic time of the transient behavior is small compared to the period characterizing the change in time of the mean velocity. A few closed paths have been analyzed quantifying their effectiveness in enhancing dilution and thereby mixing between the resident contaminant and an oxidant. In particular, we considered three different flow configurations: (1) a "circular" pattern, in which the vector of the mean velocity rotates at a constant celerity; (2) a "shake" pattern, in which the velocity has a constant magnitude and changes direction alternatively leading to a "back and forth" type of movement and finally (3) a more general "shake and rotate" pattern, which combines the previous two configurations. The new analytical solution shows that dilution is affected by the configuration of the periodic mean flow. Results show that the dilution index increases when the rotation-shake configuration is adopted. In addition, the dilution index is augmented with the oscillation amplitude of the shake component. This analysis is useful to identify optimal flow configurations that may be approximately reproduced in the field and which efficiency may be checked more accurately by numerical simulations, thereby alleviating the computational burden by efficiently screening among alternative configurations. References [1] Kitanidis, P. K. (1994), The concept of the Dilution Index, Water Resour. Res., 30(7), 2011-2026, doi:10.1029/94WR00762.

Electrical percolation in the presence of attractive interactions: An effective medium lattice approach applied to microemulsion systems

NASA Astrophysics Data System (ADS)

Hattori, Y.; Ushiki, H.; Engl, W.; Courbin, L.; Panizza, P.

2005-08-01

Within the framework of an effective medium approach and a mean-field approximation, we present a simple lattice model to treat electrical percolation in the presence of attractive interactions. We show that the percolation line depends on the magnitude of interactions. In 2 dimensions, the percolation line meets the binodal line at the critical point. A good qualitative agreement is observed with experimental results on a ternary AOT-based water-in-oil microemulsion system.

Properties of a large-scale interplanetary loop structure as deduced from low-energy proton anisotropy and magnetic field measurements

NASA Technical Reports Server (NTRS)

Tranquille, C.; Sanderson, T. R.; Marsden, R. G.; Wenzel, K.-P.; Smith, E. J.

1987-01-01

Correlated particle and magnetic field measurements by the ISEE 3 spacecraft are presented for the loop structure behind the interplanetary traveling shock event of Nov. 12, 1978. Following the passage of the turbulent shock region, strong bidirectional streaming of low-energy protons is observed for approximately 6 hours, corresponding to a loop thickness of about 0.07 AU. This region is also characterized by a low relative variance of the magnetic field, a depressed proton intensity, and a reduction in the magnetic power spectral density. Using quasi-linear theory applied to a slab model, a value of 3 AU is derived for the mean free path during the passage of the closed loop. It is inferred from this observation that the proton regime associated with the loop structure is experiencing scatter-free transport and that either the length of the loop is approximately 3 AU between the sun and the earth or else the protons are being reflected at both ends of a smaller loop.

A new spherical model for computing the radiation field available for photolysis and heating at twilight

NASA Technical Reports Server (NTRS)

Dahlback, Arne; Stamnes, Knut

1991-01-01

Accurate computation of atmospheric photodissociation and heating rates is needed in photochemical models. These quantities are proportional to the mean intensity of the solar radiation penetrating to various levels in the atmosphere. For large solar zenith angles a solution of the radiative transfer equation valid for a spherical atmosphere is required in order to obtain accurate values of the mean intensity. Such a solution based on a perturbation technique combined with the discrete ordinate method is presented. Mean intensity calculations are carried out for various solar zenith angles. These results are compared with calculations from a plane parallel radiative transfer model in order to assess the importance of using correct geometry around sunrise and sunset. This comparison shows, in agreement with previous investigations, that for solar zenith angles less than 90 deg adequate solutions are obtained for plane parallel geometry as long as spherical geometry is used to compute the direct beam attenuation; but for solar zenith angles greater than 90 deg this pseudospherical plane parallel approximation overstimates the mean intensity.

Direct computation of stochastic flow in reservoirs with uncertain parameters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dainton, M.P.; Nichols, N.K.; Goldwater, M.H.

1997-01-15

A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the time-dependent, one phase, two- or three-dimensional equations of flow through a porous medium. The uncertainty in the solution is modelled as a probability distribution function and is computed from given statistical data for input parameters such as permeability. The method generates an expansion for the mean of the pressure about a deterministic solution to the system equations using a perturbation to the mean of the input parameters. Hierarchical equations that define approximations to the mean solution at each point andmore » to the field convariance of the pressure are developed and solved numerically. The procedure is then used to find the statistics of the flow and the risked value of the field, defined by the NPV, for a given development scenario. This method involves only one (albeit complicated) solution of the equations and contrasts with the more usual Monte-Carlo approach where many such solutions are required. The procedure is applied easily to other physical systems modelled by linear or nonlinear partial differential equations with uncertain data. 14 refs., 14 figs., 3 tabs.« less

Atomic density functional and diagram of structures in the phase field crystal model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ankudinov, V. E., E-mail: vladimir@ankudinov.org; Galenko, P. K.; Kropotin, N. V.

2016-02-15

The phase field crystal model provides a continual description of the atomic density over the diffusion time of reactions. We consider a homogeneous structure (liquid) and a perfect periodic crystal, which are constructed from the one-mode approximation of the phase field crystal model. A diagram of 2D structures is constructed from the analytic solutions of the model using atomic density functionals. The diagram predicts equilibrium atomic configurations for transitions from the metastable state and includes the domains of existence of homogeneous, triangular, and striped structures corresponding to a liquid, a body-centered cubic crystal, and a longitudinal cross section of cylindricalmore » tubes. The method developed here is employed for constructing the diagram for the homogeneous liquid phase and the body-centered iron lattice. The expression for the free energy is derived analytically from density functional theory. The specific features of approximating the phase field crystal model are compared with the approximations and conclusions of the weak crystallization and 2D melting theories.« less

Adiabatic particle motion in a nearly drift-free magnetic field: Application to the geomagnetic tail

NASA Technical Reports Server (NTRS)

Stern, D. P.

1977-01-01

The guiding center motion of particles in a nearly drift free magnetic field is analyzed in order to investigate the dependence of mean drift velocity on equatorial pitch angle, the variation of local drift velocity along the trajectory, and other properties. The mean drift for adiabatic particles is expressed by means of elliptic integrals. Approximations to the twice-averaged Hamiltonian W near z = O are derived, permitting simple representation of drift paths if an electric potential also exists. In addition, the use of W or of expressions for the longitudinal invariant allows the derivation of the twice averaged Liouville equation and of the corresponding Vlasov equation. Bounce times are calculated (using the drift-free approximation), as are instantaneous guiding center drift velocities, which are then used to provide a numerical check on the formulas for the mean drift.

Twisted-Light-Ion Interaction: The Role of Longitudinal Fields

NASA Astrophysics Data System (ADS)

Quinteiro, G. F.; Schmidt-Kaler, Ferdinand; Schmiegelow, Christian T.

2017-12-01

The propagation of light beams is well described using the paraxial approximation, where field components along the propagation direction are usually neglected. For strongly inhomogeneous or shaped light fields, however, this approximation may fail, leading to intriguing variations of the light-matter interaction. This is the case of twisted light having opposite orbital and spin angular momenta. We compare experimental data for the excitation of a quadrupole transition in a single trapped 40Ca+ ion from Schmiegelow et al. [Nat. Commun. 7, 12998 (2016), 10.1038/ncomms12998] with a complete model where longitudinal components of the electric field are taken into account. Our model matches the experimental data and excludes by 11 standard deviations the approximation of a complete transverse field. This demonstrates the relevance of all field components for the interaction of twisted light with matter.

Decadal variability in core surface flows deduced from geomagnetic observatory monthly means

NASA Astrophysics Data System (ADS)

Whaler, K. A.; Olsen, N.; Finlay, C. C.

2016-10-01

Monthly means of the magnetic field measurements at ground observatories are a key data source for studying temporal changes of the core magnetic field. However, when they are calculated in the usual way, contributions of external (magnetospheric and ionospheric) origin may remain, which make them less favourable for studying the field generated by dynamo action in the core. We remove external field predictions, including a new way of characterizing the magnetospheric ring current, from the data and then calculate revised monthly means using robust methods. The geomagnetic secular variation (SV) is calculated as the first annual differences of these monthly means, which also removes the static crustal field. SV time-series based on revised monthly means are much less scattered than those calculated from ordinary monthly means, and their variances and correlations between components are smaller. On the annual to decadal timescale, the SV is generated primarily by advection in the fluid outer core. We demonstrate the utility of the revised monthly means by calculating models of the core surface advective flow between 1997 and 2013 directly from the SV data. One set of models assumes flow that is constant over three months; such models exhibit large and rapid temporal variations. For models of this type, less complex flows achieve the same fit to the SV derived from revised monthly means than those from ordinary monthly means. However, those obtained from ordinary monthly means are able to follow excursions in SV that are likely to be external field contamination rather than core signals. Having established that we can find models that fit the data adequately, we then assess how much temporal variability is required. Previous studies have suggested that the flow is consistent with torsional oscillations (TO), solid body-like oscillations of fluid on concentric cylinders with axes aligned along the Earth's rotation axis. TO have been proposed to explain decadal timescale changes in the length-of-day. We invert for flow models where the only temporal changes are consistent with TO, but such models have an unacceptably large data misfit. However, if we relax the TO constraint to allow a little more temporal variability, we can fit the data as well as with flows assumed constant over three months, demonstrating that rapid SV changes can be reproduced by rather small flow changes. Although the flow itself changes slowly, its time derivative can be locally (temporally and spatially) large, in particular when and where core surface secular acceleration peaks. Spherical harmonic expansion coefficients of the flows are not well resolved, and many of them are strongly correlated. Averaging functions, a measure of our ability to determine the flow at a given location from the data distribution available, are poor approximations to the ideal, even when centred on points of the core surface below areas of high observatory density. Both resolution and averaging functions are noticeably worse for the toroidal flow component, which dominates the flow, than the poloidal flow component, except around the magnetic equator where averaging functions for both components are poor.

Effective potentials in nonlinear polycrystals and quadrature formulae

NASA Astrophysics Data System (ADS)

Michel, Jean-Claude; Suquet, Pierre

2017-08-01

This study presents a family of estimates for effective potentials in nonlinear polycrystals. Noting that these potentials are given as averages, several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields. Two of these quadrature formulae reduce to known schemes, including a recent proposition (Ponte Castañeda 2015 Proc. R. Soc. A 471, 20150665 (doi:10.1098/rspa.2015.0665)) obtained by completely different means. Other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments. These quadrature formulae are applied to the estimation of effective potentials in polycrystals governed by two potentials, by means of a reduced-order model proposed by the authors (non-uniform transformation field analysis). It is shown how the quadrature formulae improve on the tangent second-order approximation in porous crystals at high stress triaxiality. It is found that, in order to retrieve a satisfactory accuracy for highly nonlinear porous crystals under high stress triaxiality, a quadrature formula of higher order is required.

Effective potentials in nonlinear polycrystals and quadrature formulae.

PubMed

Michel, Jean-Claude; Suquet, Pierre

2017-08-01

This study presents a family of estimates for effective potentials in nonlinear polycrystals. Noting that these potentials are given as averages, several quadrature formulae are investigated to express these integrals of nonlinear functions of local fields in terms of the moments of these fields. Two of these quadrature formulae reduce to known schemes, including a recent proposition (Ponte Castañeda 2015 Proc. R. Soc. A 471 , 20150665 (doi:10.1098/rspa.2015.0665)) obtained by completely different means. Other formulae are also reviewed that make use of statistical information on the fields beyond their first and second moments. These quadrature formulae are applied to the estimation of effective potentials in polycrystals governed by two potentials, by means of a reduced-order model proposed by the authors (non-uniform transformation field analysis). It is shown how the quadrature formulae improve on the tangent second-order approximation in porous crystals at high stress triaxiality. It is found that, in order to retrieve a satisfactory accuracy for highly nonlinear porous crystals under high stress triaxiality, a quadrature formula of higher order is required.

Entropy production in a Glauber–Ising irreversible model with dynamical competition

NASA Astrophysics Data System (ADS)

Barbosa, Oscar A.; Tomé, Tânia

2018-06-01

An out of equilibrium Glauber–Ising model, evolving in accordance with an irreversible and stochastic Markovian dynamics, is analyzed in order to improve our comprehension concerning critical behavior and phase transitions in nonequilibrium systems. Therefore, a lattice model ruled by the competition between two Glauber dynamics acting on interlaced square lattices is proposed. Previous results have shown how the entropy production provides information about irreversibility and criticality. Mean-field approximations and Monte Carlo simulations were used in the analysis. The results obtained here show a continuous phase transition, reflected in the entropy production as a logarithmic divergence of its derivative, which suggests a shared universality class with the irreversible models invariant under the symmetry operations of the Ising model.

The converse magnetoelectric coupling in asymmetric granule/matrix composite film with Ni/PZT component

NASA Astrophysics Data System (ADS)

Chen, Bo; Su, Ning-Ning; Cui, Wen-Li; Yan, Shi-Nong

2018-04-01

In this work, a type of asymmetric granule/matrix composite film is designed, where the Ni granule is dispersed in PZT matrix, meanwhile the top and bottom electrode is constituted by Au and SRO respectively. Predicted through the electrostatic screening model and mean field approximation, considerable electrostatic charge is induced on Ni granule surface by ferroelectric PZT polarization. Predicted through the spin splitting model and spherical shell approximation, both the magnetization and magnetic anisotropy of Ni granule are modulated by ferroelectric PZT polarization. As the volume fraction of Ni granule is increased, the electric modulation of magnetization and magnetic anisotropy is reduced and enhanced respectively. As the dimension of granule/matrix composite is varied, such modulation is retained. Due to the large area-volume ratio of nano-granule, this work benefits to realize the converse magnetoelectric coupling in nanoscale.

Effect of lost charged particles on the breakdown characteristics of the gaseous electrical discharge in non-uniform axial electric field

NASA Astrophysics Data System (ADS)

Noori, H.; Ranjbar, A. H.

2017-10-01

The secondary emission coefficient is a valuable parameter for numerical modeling of the discharge process in gaseous insulation. A theoretical model has been developed to consider the effects of the radial electric field, non-uniformity of the axial electric field, and radial diffusion of charged particles on the secondary emission coefficient. In the model, a modified breakdown criterion is employed to determine the effective secondary electron emission, γeff. Using the geometry factor gi which is introduced based on the effect of radial diffusion of charged particles on the fraction of ions which arrive at the cathode, the geometry-independent term of γeff (Δi) was obtained as a function of the energy of the incident ions on the cathode. The results show that Δi is approximately a unique function of the ion energy for the ratios of d/R = 39, 50, 77, 115, and 200. It means that the considered mechanisms in the model are responsible for the deviation from Paschen's law.

Renormalized charge in a two-dimensional model of colloidal suspension from hypernetted chain approach.

PubMed

Camargo, Manuel; Téllez, Gabriel

2008-04-07

The renormalized charge of a simple two-dimensional model of colloidal suspension was determined by solving the hypernetted chain approximation and Ornstein-Zernike equations. At the infinite dilution limit, the asymptotic behavior of the correlation functions is used to define the effective interactions between the components of the system and these effective interactions were compared to those derived from the Poisson-Boltzmann theory. The results we obtained show that, in contrast to the mean-field theory, the renormalized charge does not saturate, but exhibits a maximum value and then decays monotonically as the bare charge increases. The results also suggest that beyond the counterion layer near to the macroion surface, the ionic cloud is not a diffuse layer which can be handled by means of the linearized theory, as the two-state model claims, but a more complex structure is settled by the correlations between microions.

The effects of transverse magnetic field and local electronic interaction on thermoelectric properties of monolayer graphene

NASA Astrophysics Data System (ADS)

Rezania, Hamed; Azizi, Farshad

2018-02-01

We study the effects of a transverse magnetic field and electron doping on the thermoelectric properties of monolayer graphene in the context of Hubbard model at the antiferromagnetic sector. In particular, the temperature dependence of thermal conductivity and Seebeck coefficient has been investigated. Mean field approximation has been employed in order to obtain the electronic spectrum of the system in the presence of local electron-electron interaction. Our results show the peak in thermal conductivity moves to higher temperatures with increase of both chemical potential and Hubbard parameter. Moreover the increase of magnetic field leads to shift of peak in temperature dependence of thermal conductivity to higher temperatures. Finally the behavior of Seebeck coefficient in terms of temperature has been studied and the effects of magnetic field and Hubbard parameter on this coefficient have been investigated in details.

Modular synchronization in complex networks.

PubMed

Oh, E; Rho, K; Hong, H; Kahng, B

2005-10-01

We study the synchronization transition (ST) of a modified Kuramoto model on two different types of modular complex networks. It is found that the ST depends on the type of intermodular connections. For the network with decentralized (centralized) intermodular connections, the ST occurs at finite coupling constant (behaves abnormally). Such distinct features are found in the yeast protein interaction network and the Internet, respectively. Moreover, by applying the finite-size scaling analysis to an artificial network with decentralized intermodular connections, we obtain the exponent associated with the order parameter of the ST to be beta approximately 1 different from beta(MF) approximately 1/2 obtained from the scale-free network with the same degree distribution but the absence of modular structure, corresponding to the mean field value.

Virtual-source diffusion approximation for enhanced near-field modeling of photon-migration in low-albedo medium.

PubMed

Jia, Mengyu; Chen, Xueying; Zhao, Huijuan; Cui, Shanshan; Liu, Ming; Liu, Lingling; Gao, Feng

2015-01-26

Most analytical methods for describing light propagation in turbid medium exhibit low effectiveness in the near-field of a collimated source. Motivated by the Charge Simulation Method in electromagnetic theory as well as the established discrete source based modeling, we herein report on an improved explicit model for a semi-infinite geometry, referred to as "Virtual Source" (VS) diffuse approximation (DA), to fit for low-albedo medium and short source-detector separation. In this model, the collimated light in the standard DA is analogously approximated as multiple isotropic point sources (VS) distributed along the incident direction. For performance enhancement, a fitting procedure between the calculated and realistic reflectances is adopted in the near-field to optimize the VS parameters (intensities and locations). To be practically applicable, an explicit 2VS-DA model is established based on close-form derivations of the VS parameters for the typical ranges of the optical parameters. This parameterized scheme is proved to inherit the mathematical simplicity of the DA approximation while considerably extending its validity in modeling the near-field photon migration in low-albedo medium. The superiority of the proposed VS-DA method to the established ones is demonstrated in comparison with Monte-Carlo simulations over wide ranges of the source-detector separation and the medium optical properties.

Continual approach at T=0 in the mean field theory of incommensurate magnetic states in the frustrated Heisenberg ferromagnet with an easy axis anisotropy

NASA Astrophysics Data System (ADS)

Martynov, S. N.; Tugarinov, V. I.; Martynov, A. S.

2017-10-01

The algorithm of approximate solution was developed for the differential equation describing the anharmonical change of the spin orientation angle in the model of ferromagnet with the exchange competition between nearest and next nearest magnetic neighbors and the easy axis exchange anisotropy. The equation was obtained from the collinearity constraint on the discrete lattice. In the low anharmonicity approximation the equation is resulted to an autonomous form and is integrated in quadratures. The obvious dependence of the angle velocity and second derivative of angle from angle and initial condition was derived by expanding the first integral of the equation in the Taylor series in vicinity of initial condition. The ground state of the soliton solutions was calculated by a numerical minimization of the energy integral. The evaluation of the used approximation was made for a triple point of the phase diagram.

Core surface magnetic field evolution 2000-2010

NASA Astrophysics Data System (ADS)

Finlay, C. C.; Jackson, A.; Gillet, N.; Olsen, N.

2012-05-01

We present new dedicated core surface field models spanning the decade from 2000.0 to 2010.0. These models, called gufm-sat, are based on CHAMP, Ørsted and SAC-C satellite observations along with annual differences of processed observatory monthly means. A spatial parametrization of spherical harmonics up to degree and order 24 and a temporal parametrization of sixth-order B-splines with 0.25 yr knot spacing is employed. Models were constructed by minimizing an absolute deviation measure of misfit along with measures of spatial and temporal complexity at the core surface. We investigate traditional quadratic or maximum entropy regularization in space, and second or third time derivative regularization in time. Entropy regularization allows the construction of models with approximately constant spectral slope at the core surface, avoiding both the divergence characteristic of the crustal field and the unrealistic rapid decay typical of quadratic regularization at degrees above 12. We describe in detail aspects of the models that are relevant to core dynamics. Secular variation and secular acceleration are found to be of lower amplitude under the Pacific hemisphere where the core field is weaker. Rapid field evolution is observed under the eastern Indian Ocean associated with the growth and drift of an intense low latitude flux patch. We also find that the present axial dipole decay arises from a combination of subtle changes in the southern hemisphere field morphology.

Relation between lineal energy distribution and relative biological effectiveness for photon beams according to the microdosimetric kinetic model.

PubMed

Okamoto, Hiroyuki; Kanai, Tatsuaki; Kase, Yuki; Matsumoto, Yoshitaka; Furusawa, Yoshiya; Fujita, Yukio; Saitoh, Hidetoshi; Itami, Jun; Kohno, Toshiyuki

2011-01-01

Our cell survival data showed the obvious dependence of RBE on photon energy: The RBE value for 200 kV X-rays was approximately 10% greater than those for mega-voltage photon beams. In radiation therapy using mega-voltage photon beams, the photon energy distribution outside the field is different with that in the radiation field because of a large number of low energy scattering photons. Hence, the RBE values outside the field become greater. To evaluate the increase in RBE, the method of deriving the RBE using the Microdosimetric Kinetic model (MK model) was proposed in this study. The MK model has two kinds of the parameters, tissue-specific parameters and the dose-mean lineal energy derived from the lineal energy distributions measured with a Tissue-Equivalent Proportional Counter (TEPC). The lineal energy distributions with the same geometries of the cell irradiations for 200 kV X-rays, (60)Co γ-rays, and 6 MV X-rays were obtained with the TEPC and Monte Carlo code GEANT4. The measured lineal energy distribution for 200 kV X-rays was quite different from those for mega-voltage photon beams. The dose-mean lineal energy of 200 kV X-rays showed the greatest value, 4.51 keV/µm, comparing with 2.34 and 2.36 keV/µm for (60)Co γ-rays and 6 MV X-rays, respectively. By using the results of the TEPC and cell irradiations, the tissue-specific parameters in the MK model were determined. As a result, the RBE of the photon beams (y(D): 2~5 keV/µm) in arbitrary conditions can be derived by the measurements only or the calculations only of the dose-mean lineal energy.

Stochastic Models for Laser Propagation in Atmospheric Turbulence.

NASA Astrophysics Data System (ADS)

Leland, Robert Patton

In this dissertation, stochastic models for laser propagation in atmospheric turbulence are considered. A review of the existing literature on laser propagation in the atmosphere and white noise theory is presented, with a view toward relating the white noise integral and Ito integral approaches. The laser beam intensity is considered as the solution to a random Schroedinger equation, or forward scattering equation. This model is formulated in a Hilbert space context as an abstract bilinear system with a multiplicative white noise input, as in the literature. The model is also modeled in the Banach space of Fresnel class functions to allow the plane wave case and the application of path integrals. Approximate solutions to the Schroedinger equation of the Trotter-Kato product form are shown to converge for each white noise sample path. The product forms are shown to be physical random variables, allowing an Ito integral representation. The corresponding Ito integrals are shown to converge in mean square, providing a white noise basis for the Stratonovich correction term associated with this equation. Product form solutions for Ornstein -Uhlenbeck process inputs were shown to converge in mean square as the input bandwidth was expanded. A digital simulation of laser propagation in strong turbulence was used to study properties of the beam. Empirical distributions for the irradiance function were estimated from simulated data, and the log-normal and Rice-Nakagami distributions predicted by the classical perturbation methods were seen to be inadequate. A gamma distribution fit the simulated irradiance distribution well in the vicinity of the boresight. Statistics of the beam were seen to converge rapidly as the bandwidth of an Ornstein-Uhlenbeck process was expanded to its white noise limit. Individual trajectories of the beam were presented to illustrate the distortion and bending of the beam due to turbulence. Feynman path integrals were used to calculate an approximate expression for the mean of the beam intensity without using the Markov, or white noise, assumption, and to relate local variations in the turbulence field to the behavior of the beam by means of two approximations.

Modular model for Mercury's magnetospheric magnetic field confined within the average observed magnetopause.

PubMed

Korth, Haje; Tsyganenko, Nikolai A; Johnson, Catherine L; Philpott, Lydia C; Anderson, Brian J; Al Asad, Manar M; Solomon, Sean C; McNutt, Ralph L

2015-06-01

Accurate knowledge of Mercury's magnetospheric magnetic field is required to understand the sources of the planet's internal field. We present the first model of Mercury's magnetospheric magnetic field confined within a magnetopause shape derived from Magnetometer observations by the MErcury Surface, Space ENvironment, GEochemistry, and Ranging spacecraft. The field of internal origin is approximated by a dipole of magnitude 190 nT R M 3 , where R M is Mercury's radius, offset northward by 479 km along the spin axis. External field sources include currents flowing on the magnetopause boundary and in the cross-tail current sheet. The cross-tail current is described by a disk-shaped current near the planet and a sheet current at larger (≳ 5  R M ) antisunward distances. The tail currents are constrained by minimizing the root-mean-square (RMS) residual between the model and the magnetic field observed within the magnetosphere. The magnetopause current contributions are derived by shielding the field of each module external to the magnetopause by minimizing the RMS normal component of the magnetic field at the magnetopause. The new model yields improvements over the previously developed paraboloid model in regions that are close to the magnetopause and the nightside magnetic equatorial plane. Magnetic field residuals remain that are distributed systematically over large areas and vary monotonically with magnetic activity. Further advances in empirical descriptions of Mercury's magnetospheric external field will need to account for the dependence of the tail and magnetopause currents on magnetic activity and additional sources within the magnetosphere associated with Birkeland currents and plasma distributions near the dayside magnetopause.

Surface roughness effects on the solar reflectance of cool asphalt shingles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akbari, Hashem; Berdahl, Paul; Akbari, Hashem

2008-02-17

We analyze the solar reflectance of asphalt roofing shingles that are covered with pigmented mineral roofing granules. The reflecting surface is rough, with a total area approximately twice the nominal area. We introduce a simple analytical model that relates the 'micro-reflectance' of a small surface region to the 'macro-reflectance' of the shingle. This model uses a mean field approximation to account for multiple scattering effects. The model is then used to compute the reflectance of shingles with a mixture of different colored granules, when the reflectances of the corresponding mono-color shingles are known. Simple linear averaging works well, with smallmore » corrections to linear averaging derived for highly reflective materials. Reflective base granules and reflective surface coatings aid achievement of high solar reflectance. Other factors that influence the solar reflectance are the size distribution of the granules, coverage of the asphalt substrate, and orientation of the granules as affected by rollers during fabrication.« less

Extremal optimization for Sherrington-Kirkpatrick spin glasses

NASA Astrophysics Data System (ADS)

Boettcher, S.

2005-08-01

Extremal Optimization (EO), a new local search heuristic, is used to approximate ground states of the mean-field spin glass model introduced by Sherrington and Kirkpatrick. The implementation extends the applicability of EO to systems with highly connected variables. Approximate ground states of sufficient accuracy and with statistical significance are obtained for systems with more than N=1000 variables using ±J bonds. The data reproduces the well-known Parisi solution for the average ground state energy of the model to about 0.01%, providing a high degree of confidence in the heuristic. The results support to less than 1% accuracy rational values of ω=2/3 for the finite-size correction exponent, and of ρ=3/4 for the fluctuation exponent of the ground state energies, neither one of which has been obtained analytically yet. The probability density function for ground state energies is highly skewed and identical within numerical error to the one found for Gaussian bonds. But comparison with infinite-range models of finite connectivity shows that the skewness is connectivity-dependent.

Analytical model for the radio-frequency sheath

NASA Astrophysics Data System (ADS)

Czarnetzki, Uwe

2013-12-01

A simple analytical model for the planar radio-frequency (rf) sheath in capacitive discharges is developed that is based on the assumptions of a step profile for the electron front, charge exchange collisions with constant cross sections, negligible ionization within the sheath, and negligible ion dynamics. The continuity, momentum conservation, and Poisson equations are combined in a single integro-differential equation for the square of the ion drift velocity, the so called sheath equation. Starting from the kinetic Boltzmann equation, special attention is paid to the derivation and the validity of the approximate fluid equation for momentum balance. The integrals in the sheath equation appear in the screening function which considers the relative contribution of the temporal mean of the electron density to the space charge in the sheath. It is shown that the screening function is quite insensitive to variations of the effective sheath parameters. The two parameters defining the solution are the ratios of the maximum sheath extension to the ion mean free path and the Debye length, respectively. A simple general analytic expression for the screening function is introduced. By means of this expression approximate analytical solutions are obtained for the collisionless as well as the highly collisional case that compare well with the exact numerical solution. A simple transition formula allows application to all degrees of collisionality. In addition, the solutions are used to calculate all static and dynamic quantities of the sheath, e.g., the ion density, fields, and currents. Further, the rf Child-Langmuir laws for the collisionless as well as the collisional case are derived. An essential part of the model is the a priori knowledge of the wave form of the sheath voltage. This wave form is derived on the basis of a cubic charge-voltage relation for individual sheaths, considering both sheaths and the self-consistent self-bias in a discharge with arbitrary symmetry. The externally applied rf voltage is assumed to be sinusoidal, although the model can be extended to arbitrary wave forms, e.g., for dual-frequency discharges. The model calculates explicitly the cubic correction parameter in the charge-voltage relation for the case of highly asymmetric discharges. It is shown that the cubic correction is generally moderate but more pronounced in the collisionless case. The analytical results are compared to experimental data from the literature obtained by laser electric field measurements of the mean and dynamic fields in the capacitive sheath for various gases and pressures. Very good agreement is found throughout.

Analytical model for the radio-frequency sheath.

PubMed

Czarnetzki, Uwe

2013-12-01

A simple analytical model for the planar radio-frequency (rf) sheath in capacitive discharges is developed that is based on the assumptions of a step profile for the electron front, charge exchange collisions with constant cross sections, negligible ionization within the sheath, and negligible ion dynamics. The continuity, momentum conservation, and Poisson equations are combined in a single integro-differential equation for the square of the ion drift velocity, the so called sheath equation. Starting from the kinetic Boltzmann equation, special attention is paid to the derivation and the validity of the approximate fluid equation for momentum balance. The integrals in the sheath equation appear in the screening function which considers the relative contribution of the temporal mean of the electron density to the space charge in the sheath. It is shown that the screening function is quite insensitive to variations of the effective sheath parameters. The two parameters defining the solution are the ratios of the maximum sheath extension to the ion mean free path and the Debye length, respectively. A simple general analytic expression for the screening function is introduced. By means of this expression approximate analytical solutions are obtained for the collisionless as well as the highly collisional case that compare well with the exact numerical solution. A simple transition formula allows application to all degrees of collisionality. In addition, the solutions are used to calculate all static and dynamic quantities of the sheath, e.g., the ion density, fields, and currents. Further, the rf Child-Langmuir laws for the collisionless as well as the collisional case are derived. An essential part of the model is the a priori knowledge of the wave form of the sheath voltage. This wave form is derived on the basis of a cubic charge-voltage relation for individual sheaths, considering both sheaths and the self-consistent self-bias in a discharge with arbitrary symmetry. The externally applied rf voltage is assumed to be sinusoidal, although the model can be extended to arbitrary wave forms, e.g., for dual-frequency discharges. The model calculates explicitly the cubic correction parameter in the charge-voltage relation for the case of highly asymmetric discharges. It is shown that the cubic correction is generally moderate but more pronounced in the collisionless case. The analytical results are compared to experimental data from the literature obtained by laser electric field measurements of the mean and dynamic fields in the capacitive sheath for various gases and pressures. Very good agreement is found throughout.

Role of switching-on and -off effects in the vacuum instability

NASA Astrophysics Data System (ADS)

Adorno, T. C.; Ferreira, R.; Gavrilov, S. P.; Gitman, D. M.

2018-04-01

We find exact differential mean numbers of fermions and bosons created from the vacuum due to a composite electric field of special configuration. This configuration imitates a finite switching-on and -off regime and consists of fields that switch on exponentially from the infinitely remote past, remains constant during a certain interval T and switch off exponentially to the infinitely remote future. We show that calculations in the slowly varying field approximation are completely predictable in the framework of a locally constant field approximation. Beyond the slowly varying field approximation, we study effects of fast switching on and off in a number of cases when the size of the dimensionless parameter eET is either close or exceeds the threshold value that determines the transition from a regime sensitive to on-off parameters to the slowly varying regime for which these effects are secondary.

Two-dimensional Anderson-Hubbard model in the DMFT + {Sigma} approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuchinskii, E. Z., E-mail: kuchinsk@iep.uran.ru; Kuleeva, N. A.; Nekrasov, I. A.

The density of states, the dynamic (optical) conductivity, and the phase diagram of the paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean field theory (DMFT + {Sigma} approximation). Strong correlations are accounted by the DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular 'bare' density of states (DOS). The DMFT effective single-impurity problem is solved by numerical renormalization group (NRG). The 'correlated metal,' Mott insulator, and correlated Anderson insulator phases are identified from the evolution ofmore » the density of states, optical conductivity, and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of finite size, allowing us to construct the complete zero-temperature phase diagram of the paramagnetic Anderson-Hubbard model. The localization length in our approximation is practically independent of the strength of Hubbard correlations. But the divergence of the localization length in a finite-size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.« less

MHD Turbulence at Moderate Magnetic Reynolds Number

NASA Technical Reports Server (NTRS)

Knaepen, B.; Kassinos, S.; Carati, D.

2003-01-01

In the present article we will consider the decay of MHD turbulence under the influence of a strong external magnetic field at moderate magnetic Reynolds numbers. Typical values of R(sub m) that are considered here range from R(sub m) approx. 0.1 to R(sub m) approx. 20. As a comparison, the initial kinetic Reynolds number common to all our simulations is Re(sub L) = 199. This means that the range of Prandtl numbers explored is 5 x 10(exp -4) to 10(exp -1). Our motivation is mainly to exhibit how the transition from the QS approximation to FMHD occurs. At the lowest values of R(sub m) studied here, the QS approximation is shown to model the flow faithfully. However, for the higher values of R(sub m) considered, it is clearly inadequate but can be replaced by another approximation which will be referred to as the Quasi-Linear (QL) approximation. Another objective of the present study is to describe how variations in the magnetic Reynolds number (while maintaining all other parameters constant) affect the dynamics of the flow. This complements past studies where variations in either the strength of the external magnetic field or the kinetic Reynolds number were considered. This article is organized as follows. In section 2 we recall the definition of the quasi-static approximation. Section 3 is devoted to the description of the numerical experiments performed using the quasi-static approximation and full MHD. In section 4 we describe the quasi-linear approximation and test it numerically against full MHD. A concluding summary is given in section 5.

Quantum versus classical hyperfine-induced dynamics in a quantum dota)

NASA Astrophysics Data System (ADS)

Coish, W. A.; Loss, Daniel; Yuzbashyan, E. A.; Altshuler, B. L.

2007-04-01

In this article we analyze spin dynamics for electrons confined to semiconductor quantum dots due to the contact hyperfine interaction. We compare mean-field (classical) evolution of an electron spin in the presence of a nuclear field with the exact quantum evolution for the special case of uniform hyperfine coupling constants. We find that (in this special case) the zero-magnetic-field dynamics due to the mean-field approximation and quantum evolution are similar. However, in a finite magnetic field, the quantum and classical solutions agree only up to a certain time scale t <τc, after which they differ markedly.

A field data assessment of contemporary models of beach cusp formation

USGS Publications Warehouse

Allen, J.R.; Psuty, N.P.; Bauer, B.O.; Carter, R.W.G.

1996-01-01

Cusp formation was observed during an instrumented, daily profiled, time series of a reflective beach in Canaveral National Seashore, Florida on January 5, 1988. The monitored cusp embayment formed by erosion of the foreshore and the cusp series had a mean spacing of approximately 28 m. During this time, inshore fluid flows were dominated by two standing edge waves at frequencies of 0.06 Hz (primary) and 0.035 Hz (secondary) whereas incident waves were broadbanded at 0.12-0.16 Hz. Directly measured flows (and indirectly estimated swash excursion) data support both the standing wave subharmonic model and the self-organization model of cusp formation in this study.

One-dimensional model of interacting-step fluctuations on vicinal surfaces: Analytical formulas and kinetic Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Patrone, Paul N.; Einstein, T. L.; Margetis, Dionisios

2010-12-01

We study analytically and numerically a one-dimensional model of interacting line defects (steps) fluctuating on a vicinal crystal. Our goal is to formulate and validate analytical techniques for approximately solving systems of coupled nonlinear stochastic differential equations (SDEs) governing fluctuations in surface motion. In our analytical approach, the starting point is the Burton-Cabrera-Frank (BCF) model by which step motion is driven by diffusion of adsorbed atoms on terraces and atom attachment-detachment at steps. The step energy accounts for entropic and nearest-neighbor elastic-dipole interactions. By including Gaussian white noise to the equations of motion for terrace widths, we formulate large systems of SDEs under different choices of diffusion coefficients for the noise. We simplify this description via (i) perturbation theory and linearization of the step interactions and, alternatively, (ii) a mean-field (MF) approximation whereby widths of adjacent terraces are replaced by a self-consistent field but nonlinearities in step interactions are retained. We derive simplified formulas for the time-dependent terrace-width distribution (TWD) and its steady-state limit. Our MF analytical predictions for the TWD compare favorably with kinetic Monte Carlo simulations under the addition of a suitably conservative white noise in the BCF equations.

A Variational Approach to Simultaneous Image Segmentation and Bias Correction.

PubMed

Zhang, Kaihua; Liu, Qingshan; Song, Huihui; Li, Xuelong

2015-08-01

This paper presents a novel variational approach for simultaneous estimation of bias field and segmentation of images with intensity inhomogeneity. We model intensity of inhomogeneous objects to be Gaussian distributed with different means and variances, and then introduce a sliding window to map the original image intensity onto another domain, where the intensity distribution of each object is still Gaussian but can be better separated. The means of the Gaussian distributions in the transformed domain can be adaptively estimated by multiplying the bias field with a piecewise constant signal within the sliding window. A maximum likelihood energy functional is then defined on each local region, which combines the bias field, the membership function of the object region, and the constant approximating the true signal from its corresponding object. The energy functional is then extended to the whole image domain by the Bayesian learning approach. An efficient iterative algorithm is proposed for energy minimization, via which the image segmentation and bias field correction are simultaneously achieved. Furthermore, the smoothness of the obtained optimal bias field is ensured by the normalized convolutions without extra cost. Experiments on real images demonstrated the superiority of the proposed algorithm to other state-of-the-art representative methods.

Comparative DMFT study of the eg-orbital Hubbard model in thin films

NASA Astrophysics Data System (ADS)

Rüegg, Andreas; Hung, Hsiang-Hsuan; Gull, Emanuel; Fiete, Gregory A.

2014-02-01

Heterostructures of transition-metal oxides have emerged as a new route to engineer electronic systems with desired functionalities. Motivated by these developments, we study a two-orbital Hubbard model in a thin-film geometry confined along the cubic [001] direction using the dynamical mean-field theory. We contrast the results of two approximate impurity solvers (exact diagonalization and one-crossing approximation) to the results of the numerically exact continuous-time quantum Monte Carlo solver. Consistent with earlier studies, we find that the one-crossing approximation performs well in the insulating regime, while the advantage of the exact-diagonalization-based solver is more pronounced in the metallic regime. We then investigate various aspects of strongly correlated eg-orbital systems in thin-film geometries. In particular, we show how the interfacial orbital polarization dies off quickly a few layers from the interface and how the film thickness affects the location of the interaction-driven Mott transition. In addition, we explore the changes in the electronic structure with varying carrier concentration and identify large variations of the orbital polarization in the strongly correlated regime.

Fast summation of divergent series and resurgent transseries from Meijer-G approximants

NASA Astrophysics Data System (ADS)

Mera, Héctor; Pedersen, Thomas G.; Nikolić, Branislav K.

2018-05-01

We develop a resummation approach based on Meijer-G functions and apply it to approximate the Borel sum of divergent series and the Borel-Écalle sum of resurgent transseries in quantum mechanics and quantum field theory (QFT). The proposed method is shown to vastly outperform the conventional Borel-Padé and Borel-Padé-Écalle summation methods. The resulting Meijer-G approximants are easily parametrized by means of a hypergeometric ansatz and can be thought of as a generalization to arbitrary order of the Borel-hypergeometric method [Mera et al., Phys. Rev. Lett. 115, 143001 (2015), 10.1103/PhysRevLett.115.143001]. Here we demonstrate the accuracy of this technique in various examples from quantum mechanics and QFT, traditionally employed as benchmark models for resummation, such as zero-dimensional ϕ4 theory; the quartic anharmonic oscillator; the calculation of critical exponents for the N -vector model; ϕ4 with degenerate minima; self-interacting QFT in zero dimensions; and the summation of one- and two-instanton contributions in the quantum-mechanical double-well problem.

Interlayer tunneling in a strongly correlated electron-phonon system

NASA Astrophysics Data System (ADS)

Mierzejewski, M.; Zieliński, J.

1996-10-01

We discuss the role of interlayer tunneling for superconducting properties of strongly correlated (U-->∞ limit) two-layer Hubbard model coupled to phonons. Strong correlations are taken into account within the mean-field approximation for auxiliary boson fields. To consider phonon-mediated and interlayer tunneling contribution to superconductivity on equal footing we incorporate the tunneling term into the generalized Eliashberg equations. This leads to the modification of the phonon-induced pairing kernel and implies a pronounced enhancement of the superconducting transition temperature in the d-wave channel for moderate doping. In numerical calculations the two-dimensional band structure has been explicitly taken into account. The relevance of our results for high-temperature superconductors is briefly discussed.

Thermodynamically self-consistent theory for the Blume-Capel model.

PubMed

Grollau, S; Kierlik, E; Rosinberg, M L; Tarjus, G

2001-04-01

We use a self-consistent Ornstein-Zernike approximation to study the Blume-Capel ferromagnet on three-dimensional lattices. The correlation functions and the thermodynamics are obtained from the solution of two coupled partial differential equations. The theory provides a comprehensive and accurate description of the phase diagram in all regions, including the wing boundaries in a nonzero magnetic field. In particular, the coordinates of the tricritical point are in very good agreement with the best estimates from simulation or series expansion. Numerical and analytical analysis strongly suggest that the theory predicts a universal Ising-like critical behavior along the lambda line and the wing critical lines, and a tricritical behavior governed by mean-field exponents.

The nuclear contacts and short range correlations in nuclei

NASA Astrophysics Data System (ADS)

Weiss, R.; Cruz-Torres, R.; Barnea, N.; Piasetzky, E.; Hen, O.

2018-05-01

Atomic nuclei are complex strongly interacting systems and their exact theoretical description is a long-standing challenge. An approximate description of nuclei can be achieved by separating its short and long range structure. This separation of scales stands at the heart of the nuclear shell model and effective field theories that describe the long-range structure of the nucleus using a mean-field approximation. We present here an effective description of the complementary short-range structure using contact terms and stylized two-body asymptotic wave functions. The possibility to extract the nuclear contacts from experimental data is presented. Regions in the two-body momentum distribution dominated by high-momentum, close-proximity, nucleon pairs are identified and compared to experimental data. The amount of short-range correlated (SRC) nucleon pairs is determined and compared to measurements. Non-combinatorial isospin symmetry for SRC pairs is identified. The obtained one-body momentum distributions indicate dominance of SRC pairs above the nuclear Fermi-momentum.

Effects of dynamical paths on the energy gap and the corrections to the free energy in path integrals of mean-field quantum spin systems

NASA Astrophysics Data System (ADS)

Koh, Yang Wei

2018-03-01

In current studies of mean-field quantum spin systems, much attention is placed on the calculation of the ground-state energy and the excitation gap, especially the latter, which plays an important role in quantum annealing. In pure systems, the finite gap can be obtained by various existing methods such as the Holstein-Primakoff transform, while the tunneling splitting at first-order phase transitions has also been studied in detail using instantons in many previous works. In disordered systems, however, it remains challenging to compute the gap of large-size systems with specific realization of disorder. Hitherto, only quantum Monte Carlo techniques are practical for such studies. Recently, Knysh [Nature Comm. 7, 12370 (2016), 10.1038/ncomms12370] proposed a method where the exponentially large dimensionality of such systems is condensed onto a random potential of much lower dimension, enabling efficient study of such systems. Here we propose a slightly different approach, building upon the method of static approximation of the partition function widely used for analyzing mean-field models. Quantum effects giving rise to the excitation gap and nonextensive corrections to the free energy are accounted for by incorporating dynamical paths into the path integral. The time-dependence of the trace of the time-ordered exponential of the effective Hamiltonian is calculated by solving a differential equation perturbatively, yielding a finite-size series expansion of the path integral. Formulae for the first excited-state energy are proposed to aid in computing the gap. We illustrate our approach using the infinite-range ferromagnetic Ising model and the Hopfield model, both in the presence of a transverse field.

Poincare recurrence theorem and the strong CP problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalloniatis, Alex C.; Nedelko, Sergei N.; Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna

2006-02-01

The existence in the physical QCD vacuum of nonzero gluon condensates, such as , requires dominance of gluon fields with finite mean action density. This naturally allows any real number value for the unit 'topological charge' q characterizing the fields approximating the gluon configurations which should dominate the QCD partition function. If q is an irrational number then the critical values of the {theta} parameter for which CP is spontaneously broken are dense in R, which provides for a mechanism of resolving the strong CP problem simultaneously with a correct implementation of U{sub A}(1) symmetry. We present anmore » explicit realization of this mechanism within a QCD motivated domain model. Some model independent arguments are given that suggest the relevance of this mechanism also to genuine QCD.« less

Critical properties of the classical XY and classical Heisenberg models: A renormalization group study

NASA Astrophysics Data System (ADS)

de Sousa, J. Ricardo; de Albuquerque, Douglas F.

1997-02-01

By using two approaches of renormalization group (RG), mean field RG (MFRG) and effective field RG (EFRG), we study the critical properties of the simple cubic lattice classical XY and classical Heisenberg models. The methods are illustrated by employing its simplest approximation version in which small clusters with one ( N‧ = 1) and two ( N = 2) spins are used. The thermal and magnetic critical exponents, Yt and Yh, and the critical parameter Kc are numerically obtained and are compared with more accurate methods (Monte Carlo, series expansion and ε-expansion). The results presented in this work are in excellent agreement with these sophisticated methods. We have also shown that the exponent Yh does not depend on the symmetry n of the Hamiltonian, hence the criteria of universality for this exponent is only a function of the dimension d.

Nuclear deformation in the laboratory frame

NASA Astrophysics Data System (ADS)

Gilbreth, C. N.; Alhassid, Y.; Bertsch, G. F.

2018-01-01

We develop a formalism for calculating the distribution of the axial quadrupole operator in the laboratory frame within the rotationally invariant framework of the configuration-interaction shell model. The calculation is carried out using a finite-temperature auxiliary-field quantum Monte Carlo method. We apply this formalism to isotope chains of even-mass samarium and neodymium nuclei and show that the quadrupole distribution provides a model-independent signature of nuclear deformation. Two technical advances are described that greatly facilitate the calculations. The first is to exploit the rotational invariance of the underlying Hamiltonian to reduce the statistical fluctuations in the Monte Carlo calculations. The second is to determine quadruple invariants from the distribution of the axial quadrupole operator in the laboratory frame. This allows us to extract effective values of the intrinsic quadrupole shape parameters without invoking an intrinsic frame or a mean-field approximation.

Dynamics of a quantum spin liquid beyond integrability: The Kitaev-Heisenberg-Γ model in an augmented parton mean-field theory

NASA Astrophysics Data System (ADS)

Knolle, Johannes; Bhattacharjee, Subhro; Moessner, Roderich

2018-04-01

We present an augmented parton mean-field theory which (i) reproduces the exact ground state, spectrum, and dynamics of the quantum spin-liquid phase of Kitaev's honeycomb model, and (ii) is amenable to the inclusion of integrability breaking terms, allowing a perturbation theory from a controlled starting point. Thus, we exemplarily study dynamical spin correlations of the honeycomb Kitaev quantum spin liquid within the K -J -Γ model, which includes Heisenberg and symmetric-anisotropic (pseudodipolar) interactions. This allows us to trace changes of the correlations in the regime of slowly moving fluxes, where the theory captures the dominant deviations when integrability is lost. These include an asymmetric shift together with a broadening of the dominant peak in the response as a function of frequency, the generation of further-neighbor correlations and their structure in real and spin space, and a resulting loss of an approximate rotational symmetry of the structure factor in reciprocal space. We discuss the limitations of this approach and also view the neutron-scattering experiments on the putative proximate quantum spin-liquid material α -RuCl3 in the light of the results from this extended parton theory.

Impact of network topology on self-organized criticality

NASA Astrophysics Data System (ADS)

Hoffmann, Heiko

2018-02-01

The general mechanisms behind self-organized criticality (SOC) are still unknown. Several microscopic and mean-field theory approaches have been suggested, but they do not explain the dependence of the exponents on the underlying network topology of the SOC system. Here, we first report the phenomena that in the Bak-Tang-Wiesenfeld (BTW) model, sites inside an avalanche area largely return to their original state after the passing of an avalanche, forming, effectively, critically arranged clusters of sites. Then, we hypothesize that SOC relies on the formation process of these clusters, and present a model of such formation. For low-dimensional networks, we show theoretically and in simulation that the exponent of the cluster-size distribution is proportional to the ratio of the fractal dimension of the cluster boundary and the dimensionality of the network. For the BTW model, in our simulations, the exponent of the avalanche-area distribution matched approximately our prediction based on this ratio for two-dimensional networks, but deviated for higher dimensions. We hypothesize a transition from cluster formation to the mean-field theory process with increasing dimensionality. This work sheds light onto the mechanisms behind SOC, particularly, the impact of the network topology.

In Situ 3D Segmentation of Individual Plant Leaves Using a RGB-D Camera for Agricultural Automation.

PubMed

Xia, Chunlei; Wang, Longtan; Chung, Bu-Keun; Lee, Jang-Myung

2015-08-19

In this paper, we present a challenging task of 3D segmentation of individual plant leaves from occlusions in the complicated natural scene. Depth data of plant leaves is introduced to improve the robustness of plant leaf segmentation. The low cost RGB-D camera is utilized to capture depth and color image in fields. Mean shift clustering is applied to segment plant leaves in depth image. Plant leaves are extracted from the natural background by examining vegetation of the candidate segments produced by mean shift. Subsequently, individual leaves are segmented from occlusions by active contour models. Automatic initialization of the active contour models is implemented by calculating the center of divergence from the gradient vector field of depth image. The proposed segmentation scheme is tested through experiments under greenhouse conditions. The overall segmentation rate is 87.97% while segmentation rates for single and occluded leaves are 92.10% and 86.67%, respectively. Approximately half of the experimental results show segmentation rates of individual leaves higher than 90%. Nevertheless, the proposed method is able to segment individual leaves from heavy occlusions.

Mean-field study of correlation-induced antisymmetric spin-orbit coupling in a two-orbital honeycomb model

NASA Astrophysics Data System (ADS)

Hayami, Satoru; Kusunose, Hiroaki; Motome, Yukitoshi

2018-05-01

We investigate a two-orbital Hubbard model on a honeycomb structure, with a special focus on the antisymmetric spin-orbit coupling (ASOC) induced by symmetry breaking in the electronic degrees of freedom. By investigating the ground-state phase diagram by the mean-field approximation in addition to the analysis in the strong correlation limit, we obtain a variety of symmetry-broken phases that induce different types of effective ASOCs by breaking of spatial inversion symmetry. We find several unusual properties emergent from the ASOCs, such as a linear magnetoelectric effect in a spin-orbital ordered phase at 1/4 filling and a spin splitting in the band structure in charge ordered phases at 1/4 and 1/2 fillings. We also show that a staggered potential on the honeycomb structure leads to another type of ASOC, which gives rise to a valley splitting in the band structure at 1/2 filling. We discuss the experimental relevance of our results to candidate materials including transition metal dichalcogenides and trichalcogenides.

On the global well-posedness of BV weak solutions to the Kuramoto-Sakaguchi equation

NASA Astrophysics Data System (ADS)

Amadori, Debora; Ha, Seung-Yeal; Park, Jinyeong

2017-01-01

The Kuramoto model is a prototype phase model describing the synchronous behavior of weakly coupled limit-cycle oscillators. When the number of oscillators is sufficiently large, the dynamics of Kuramoto ensemble can be effectively approximated by the corresponding mean-field equation, namely "the Kuramoto-Sakaguchi (KS) equation". This KS equation is a kind of scalar conservation law with a nonlocal flux function due to the mean-field interactions among oscillators. In this paper, we provide a unique global solvability of bounded variation (BV) weak solutions to the kinetic KS equation for identical oscillators using the method of front-tracking in hyperbolic conservation laws. Moreover, we also show that our BV weak solutions satisfy local-in-time L1-stability with respect to BV-initial data. For the ensemble of identical Kuramoto oscillators, we explicitly construct an exponentially growing BV weak solution generated from BV perturbation of incoherent state for any positive coupling strength. This implies the nonlinear instability of incoherent state in a positive coupling strength regime. We provide several numerical examples and compare them with our analytical results.

In Situ 3D Segmentation of Individual Plant Leaves Using a RGB-D Camera for Agricultural Automation

PubMed Central

Xia, Chunlei; Wang, Longtan; Chung, Bu-Keun; Lee, Jang-Myung

2015-01-01

In this paper, we present a challenging task of 3D segmentation of individual plant leaves from occlusions in the complicated natural scene. Depth data of plant leaves is introduced to improve the robustness of plant leaf segmentation. The low cost RGB-D camera is utilized to capture depth and color image in fields. Mean shift clustering is applied to segment plant leaves in depth image. Plant leaves are extracted from the natural background by examining vegetation of the candidate segments produced by mean shift. Subsequently, individual leaves are segmented from occlusions by active contour models. Automatic initialization of the active contour models is implemented by calculating the center of divergence from the gradient vector field of depth image. The proposed segmentation scheme is tested through experiments under greenhouse conditions. The overall segmentation rate is 87.97% while segmentation rates for single and occluded leaves are 92.10% and 86.67%, respectively. Approximately half of the experimental results show segmentation rates of individual leaves higher than 90%. Nevertheless, the proposed method is able to segment individual leaves from heavy occlusions. PMID:26295395

Coagulation kinetics beyond mean field theory using an optimised Poisson representation.

PubMed

Burnett, James; Ford, Ian J

2015-05-21

Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics may be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants, but this can be a poor approximation when the mean populations are small. However, using the Poisson representation, it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy, and complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work, we encounter instabilities that can be eliminated using a suitable "gauge" transformation of the problem [P. D. Drummond, Eur. Phys. J. B 38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation.

Absence of Disorder-Driven Metal-Insulator Transitions in Simple Holographic Models

NASA Astrophysics Data System (ADS)

Grozdanov, Sašo; Lucas, Andrew; Sachdev, Subir; Schalm, Koenraad

2015-11-01

We study electrical transport in a strongly coupled strange metal in two spatial dimensions at finite temperature and charge density, holographically dual to the Einstein-Maxwell theory in an asymptotically four-dimensional anti-de Sitter space spacetime, with arbitrary spatial inhomogeneity, up to mild assumptions including emergent isotropy. In condensed matter, these are candidate models for exotic strange metals without long-lived quasiparticles. We prove that the electrical conductivity is bounded from below by a universal minimal conductance: the quantum critical conductivity of a clean, charge-neutral plasma. Beyond nonperturbatively justifying mean-field approximations to disorder, our work demonstrates the practicality of new hydrodynamic insight into holographic transport.

Extension of Ostwald Ripening Theory

NASA Technical Reports Server (NTRS)

Baird, J.; Naumann, R.

1985-01-01

The objective is to develop models based on the mean field approximation of Ostwald ripening to describe the growth of second phase droplets or crystallites. The models will include time variations in nucleation rate, control of saturation through addition of solute, precipitating agents, changes in temperature, and various surface kinetic effects. Numerical integration schemes have been developed and tested against the asymptotic solution of Liftshitz, Slyozov and Wagner (LSW). A second attractor (in addition to the LSW distribution) has been found and, contrary to the LSW theory, the final distribution is dependent on the initial distribution. A series of microgravity experiments is being planned to test this and other results from this work.

Propagation and Breaking at High Altitudes of Gravity Waves Excited by Tropospheric Forcing

NASA Technical Reports Server (NTRS)

Prusa, Joseph M.; Smolarkiewicz, Piotr K.; Garcia, Rolando R.

1996-01-01

An anelastic approximation is used with a time-variable coordinate transformation to formulate a two-dimensional numerical model that describes the evolution of gravity waves. The model is solved using a semi-Lagrangian method with monotone (nonoscillatory) interpolation of all advected fields. The time-variable transformation is used to generate disturbances at the lower boundary that approximate the effect of a traveling line of thunderstorms (a squall line) or of flow over a broad topographic obstacle. The vertical propagation and breaking of the gravity wave field (under conditions typical of summer solstice) is illustrated for each of these cases. It is shown that the wave field at high altitudes is dominated by a single horizontal wavelength; which is not always related simply to the horizontal dimension of the source. The morphology of wave breaking depends on the horizontal wavelength; for sufficiently short waves, breaking involves roughly one half of the wavelength. In common with other studies, it is found that the breaking waves undergo "self-acceleration," such that the zonal-mean intrinsic frequency remains approximately constant in spite of large changes in the background wind. It is also shown that many of the features obtained in the calculations can be understood in terms of linear wave theory. In particular, linear theory provides insights into the wavelength of the waves that break at high altitudes, the onset and evolution of breaking. the horizontal extent of the breaking region and its position relative to the forcing, and the minimum and maximum altitudes where breaking occurs. Wave breaking ceases at the altitude where the background dissipation rate (which in our model is a proxy for molecular diffusion) becomes greater than the rate of dissipation due to wave breaking, This altitude, in effect, the model turbopause, is shown to depend on a relatively small number of parameters that characterize the waves and the background state.

Comparison between two scalar field models using rotation curves of spiral galaxies

NASA Astrophysics Data System (ADS)

Fernández-Hernández, Lizbeth M.; Rodríguez-Meza, Mario A.; Matos, Tonatiuh

2018-04-01

Scalar fields have been used as candidates for dark matter in the universe, from axions with masses ∼ 10-5eV until ultra-light scalar fields with masses ∼ Axions behave as cold dark matter while the ultra-light scalar fields galaxies are Bose-Einstein condensate drops. The ultra-light scalar fields are also called scalar field dark matter model. In this work we study rotation curves for low surface brightness spiral galaxies using two scalar field models: the Gross-Pitaevskii Bose-Einstein condensate in the Thomas-Fermi approximation and a scalar field solution of the Klein-Gordon equation. We also used the zero disk approximation galaxy model where photometric data is not considered, only the scalar field dark matter model contribution to rotation curve is taken into account. From the best-fitting analysis of the galaxy catalog we use, we found the range of values of the fitting parameters: the length scale and the central density. The worst fitting results (values of χ red2 much greater than 1, on the average) were for the Thomas-Fermi models, i.e., the scalar field dark matter is better than the Thomas- Fermi approximation model to fit the rotation curves of the analysed galaxies. To complete our analysis we compute from the fitting parameters the mass of the scalar field models and two astrophysical quantities of interest, the dynamical dark matter mass within 300 pc and the characteristic central surface density of the dark matter models. We found that the value of the central mass within 300 pc is in agreement with previous reported results, that this mass is ≈ 107 M ⊙/pc2, independent of the dark matter model. And, on the contrary, the value of the characteristic central surface density do depend on the dark matter model.

Dynamical Vertex Approximation for the Hubbard Model

NASA Astrophysics Data System (ADS)

Toschi, Alessandro

A full understanding of correlated electron systems in the physically relevant situations of three and two dimensions represents a challenge for the contemporary condensed matter theory. However, in the last years considerable progress has been achieved by means of increasingly more powerful quantum many-body algorithms, applied to the basic model for correlated electrons, the Hubbard Hamiltonian. Here, I will review the physics emerging from studies performed with the dynamical vertex approximation, which includes diagrammatic corrections to the local description of the dynamical mean field theory (DMFT). In particular, I will first discuss the phase diagram in three dimensions with a special focus on the commensurate and incommensurate magnetic phases, their (quantum) critical properties, and the impact of fluctuations on electronic lifetimes and spectral functions. In two dimensions, the effects of non-local fluctuations beyond DMFT grow enormously, determining the appearance of a low-temperature insulating behavior for all values of the interaction in the unfrustrated model: Here the prototypical features of the Mott-Hubbard metal-insulator transition, as well as the existence of magnetically ordered phases, are completely overwhelmed by antiferromagnetic fluctuations of exponentially large extension, in accordance with the Mermin-Wagner theorem. Eventually, by a fluctuation diagnostics analysis of cluster DMFT self-energies, the same magnetic fluctuations are identified as responsible for the pseudogap regime in the holed-doped frustrated case, with important implications for the theoretical modeling of the cuprate physics.

A full-wave Helmholtz model for continuous-wave ultrasound transmission.

PubMed

Huttunen, Tomi; Malinen, Matti; Kaipio, Jari P; White, Phillip Jason; Hynynen, Kullervo

2005-03-01

A full-wave Helmholtz model of continuous-wave (CW) ultrasound fields may offer several attractive features over widely used partial-wave approximations. For example, many full-wave techniques can be easily adjusted for complex geometries, and multiple reflections of sound are automatically taken into account in the model. To date, however, the full-wave modeling of CW fields in general 3D geometries has been avoided due to the large computational cost associated with the numerical approximation of the Helmholtz equation. Recent developments in computing capacity together with improvements in finite element type modeling techniques are making possible wave simulations in 3D geometries which reach over tens of wavelengths. The aim of this study is to investigate the feasibility of a full-wave solution of the 3D Helmholtz equation for modeling of continuous-wave ultrasound fields in an inhomogeneous medium. The numerical approximation of the Helmholtz equation is computed using the ultraweak variational formulation (UWVF) method. In addition, an inverse problem technique is utilized to reconstruct the velocity distribution on the transducer which is used to model the sound source in the UWVF scheme. The modeling method is verified by comparing simulated and measured fields in the case of transmission of 531 kHz CW fields through layered plastic plates. The comparison shows a reasonable agreement between simulations and measurements at low angles of incidence but, due to mode conversion, the Helmholtz model becomes insufficient for simulating ultrasound fields in plates at large angles of incidence.

On effective temperature in network models of collective behavior

DOE Office of Scientific and Technical Information (OSTI.GOV)

Porfiri, Maurizio, E-mail: mporfiri@nyu.edu; Ariel, Gil, E-mail: arielg@math.biu.ac.il

Collective behavior of self-propelled units is studied analytically within the Vectorial Network Model (VNM), a mean-field approximation of the well-known Vicsek model. We propose a dynamical systems framework to study the stochastic dynamics of the VNM in the presence of general additive noise. We establish that a single parameter, which is a linear function of the circular mean of the noise, controls the macroscopic phase of the system—ordered or disordered. By establishing a fluctuation–dissipation relation, we posit that this parameter can be regarded as an effective temperature of collective behavior. The exact critical temperature is obtained analytically for systems withmore » small connectivity, equivalent to low-density ensembles of self-propelled units. Numerical simulations are conducted to demonstrate the applicability of this new notion of effective temperature to the Vicsek model. The identification of an effective temperature of collective behavior is an important step toward understanding order–disorder phase transitions, informing consistent coarse-graining techniques and explaining the physics underlying the emergence of collective phenomena.« less

Two-magnon excitations in resonant inelastic x-ray scattering studied within spin density wave formalism

NASA Astrophysics Data System (ADS)

Nomura, Takuji

2017-10-01

We study two-magnon excitations in resonant inelastic x-ray scattering (RIXS) at the transition-metal K edge. Instead of working with effective Heisenberg spin models, we work with a Hubbard-type model (d -p model) for a typical insulating cuprate La2CuO4 . For the antiferromagnetic ground state within the spin density wave (SDW) mean-field formalism, we calculate the dynamical correlation function within the random-phase approximation (RPA), and then obtain two-magnon excitation spectra by calculating the convolution of it. Coupling between the K -shell hole and the magnons in the intermediate state is calculated by means of diagrammatic perturbation expansion in the Coulomb interaction. The calculated momentum dependence of RIXS spectra agrees well with that of experiments. A notable difference from previous calculations based on the Heisenberg spin models is that RIXS spectra have a large two-magnon weight near the zone center, which may be confirmed by further careful high-resolution experiments.

Influence of periodic external fields in multiagent models with language dynamics

NASA Astrophysics Data System (ADS)

Palombi, Filippo; Ferriani, Stefano; Toti, Simona

2017-12-01

We investigate large-scale effects induced by external fields, phenomenologically interpreted as mass media, in multiagent models evolving with the microscopic dynamics of the binary naming game. In particular, we show that a single external field, broadcasting information at regular time intervals, can reverse the majority opinion of the population, provided the frequency and the effectiveness of the sent messages lie above well-defined thresholds. We study the phase structure of the model in the mean field approximation and in numerical simulations with several network topologies. We also investigate the influence on the agent dynamics of two competing external fields, periodically broadcasting different messages. In finite regions of the parameter space we observe periodic equilibrium states in which the average opinion densities are reversed with respect to naive expectations. Such equilibria occur in two cases: (i) when the frequencies of the competing messages are different but close to each other; (ii) when the frequencies are equal and the relative time shift of the messages does not exceed half a period. We interpret the observed phenomena as a result of the interplay between the external fields and the internal dynamics of the agents and conclude that, depending on the model parameters, the naming game is consistent with scenarios of first- or second-mover advantage (to borrow an expression from the jargon of business strategy).

Analysis And Validation of the Field Coupled Through an Aperture in an Avionics Enclosure

NASA Astrophysics Data System (ADS)

Bakore, Rahul

This work focused on accurately predicting the current response of an equipment under test (EUT) to a random electromagnetic field representing a threat source to model radio frequency directed energy weapons (RFDEWs). The modeled EUT consists of a single wire attached to the interior wall of a shielding enclosure that includes an aperture on one face. An in-house computational electromagnetic (CEM) code based on method of moments (MOM) and accelerated by the multi-level fast multipole algorithm (MLFMA), was enhanced through the implementation of first order vector basis functions that approximates the EUT surface current. The electric field integral equation (EFIE) is solved using MOM/MLFMA. Use of first-order basis functions gives a large savings in computational time over the previous implementation with zero-order Rao-Wilton-Glisson basis functions. A sample EUT was fabricated and tested within an anechoic chamber and a reverberation chamber over a wide frequency band. In the anechoic chamber measurements, the current response on the wire within the EUT due to a single uniform plane wave was found and compared with the numerical simulations. In the reverberation chamber measurements, the mean current magnitude excited on the wire within the EUT by a mechanically stirred random field was measured and compared with the numerical simulations. The measured scattering parameter between the source antenna and the EUT measurement port was used to derive the current response on the wire in both chambers. The numerically simulated currents agree very well with the measurements in both the anechoic and reverberation chambers over the measured frequency band, confirming the validity of the numerical approach for calculating EUT response due to a random field. An artificial neural network (ANN) was trained that can rapidly provide the mean induced current response of an EUT due to a random field under different aperture configurations arbitrarily placed on one face of an EUT. However, ANN proved no better than simple linear interpolation in approximating the induced currents on EUTs that give strong resonances and nulls in the response.

Predicting Statistical Response and Extreme Events in Uncertainty Quantification through Reduced-Order Models

NASA Astrophysics Data System (ADS)

Qi, D.; Majda, A.

2017-12-01

A low-dimensional reduced-order statistical closure model is developed for quantifying the uncertainty in statistical sensitivity and intermittency in principal model directions with largest variability in high-dimensional turbulent system and turbulent transport models. Imperfect model sensitivity is improved through a recent mathematical strategy for calibrating model errors in a training phase, where information theory and linear statistical response theory are combined in a systematic fashion to achieve the optimal model performance. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. A statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. Stringent models of barotropic and baroclinic turbulence are used to display the feasibility of the reduced-order methods. Principal statistical responses in mean and variance can be captured by the reduced-order models with accuracy and efficiency. Besides, the reduced-order models are also used to capture crucial passive tracer field that is advected by the baroclinic turbulent flow. It is demonstrated that crucial principal statistical quantities like the tracer spectrum and fat-tails in the tracer probability density functions in the most important large scales can be captured efficiently with accuracy using the reduced-order tracer model in various dynamical regimes of the flow field with distinct statistical structures.

Attitude Estimation for Large Field-of-View Sensors

NASA Technical Reports Server (NTRS)

Cheng, Yang; Crassidis, John L.; Markley, F. Landis

2005-01-01

The QUEST measurement noise model for unit vector observations has been widely used in spacecraft attitude estimation for more than twenty years. It was derived under the approximation that the noise lies in the tangent plane of the respective unit vector and is axially symmetrically distributed about the vector. For large field-of-view sensors, however, this approximation may be poor, especially when the measurement falls near the edge of the field of view. In this paper a new measurement noise model is derived based on a realistic noise distribution in the focal-plane of a large field-of-view sensor, which shows significant differences from the QUEST model for unit vector observations far away from the sensor boresight. An extended Kalman filter for attitude estimation is then designed with the new measurement noise model. Simulation results show that with the new measurement model the extended Kalman filter achieves better estimation performance using large field-of-view sensor observations.

Mean Field Analysis of Large-Scale Interacting Populations of Stochastic Conductance-Based Spiking Neurons Using the Klimontovich Method

NASA Astrophysics Data System (ADS)

Gandolfo, Daniel; Rodriguez, Roger; Tuckwell, Henry C.

2017-03-01

We investigate the dynamics of large-scale interacting neural populations, composed of conductance based, spiking model neurons with modifiable synaptic connection strengths, which are possibly also subjected to external noisy currents. The network dynamics is controlled by a set of neural population probability distributions (PPD) which are constructed along the same lines as in the Klimontovich approach to the kinetic theory of plasmas. An exact non-closed, nonlinear, system of integro-partial differential equations is derived for the PPDs. As is customary, a closing procedure leads to a mean field limit. The equations we have obtained are of the same type as those which have been recently derived using rigorous techniques of probability theory. The numerical solutions of these so called McKean-Vlasov-Fokker-Planck equations, which are only valid in the limit of infinite size networks, actually shows that the statistical measures as obtained from PPDs are in good agreement with those obtained through direct integration of the stochastic dynamical system for large but finite size networks. Although numerical solutions have been obtained for networks of Fitzhugh-Nagumo model neurons, which are often used to approximate Hodgkin-Huxley model neurons, the theory can be readily applied to networks of general conductance-based model neurons of arbitrary dimension.

Coherent states field theory in supramolecular polymer physics

NASA Astrophysics Data System (ADS)

Fredrickson, Glenn H.; Delaney, Kris T.

2018-05-01

In 1970, Edwards and Freed presented an elegant representation of interacting branched polymers that resembles the coherent states (CS) formulation of second-quantized field theory. This CS polymer field theory has been largely overlooked during the intervening period in favor of more conventional "auxiliary field" (AF) interacting polymer representations that form the basis of modern self-consistent field theory (SCFT) and field-theoretic simulation approaches. Here we argue that the CS representation provides a simpler and computationally more efficient framework than the AF approach for broad classes of reversibly bonding polymers encountered in supramolecular polymer science. The CS formalism is reviewed, initially for a simple homopolymer solution, and then extended to supramolecular polymers capable of forming reversible linkages and networks. In the context of the Edwards model of a non-reacting homopolymer solution and one and two-component models of telechelic reacting polymers, we discuss the structure of CS mean-field theory, including the equivalence to SCFT, and show how weak-amplitude expansions (random phase approximations) can be readily developed without explicit enumeration of all reaction products in a mixture. We further illustrate how to analyze CS field theories beyond SCFT at the level of Gaussian field fluctuations and provide a perspective on direct numerical simulations using a recently developed complex Langevin technique.

Comparison of Coarse-Grained Approaches in Predicting Polymer Nanocomposite Phase Behavior

DOE PAGES

Koski, Jason P.; Ferrier, Robert C.; Krook, Nadia M.; ...

2017-11-02

Because of the considerable parameter space, efficient theoretical and simulation methods are required to predict the morphology and guide experiments in polymer nanocomposites (PNCs). Unfortunately, theoretical and simulation methods are restricted in their ability to accurately map to experiments based on necessary approximations and numerical limitations. In this study, we provide direct comparisons of two recently developed coarse-grained approaches for modeling polymer nanocomposites (PNCs): polymer nanocomposite field theory (PNC-FT) and dynamic mean-field theory (DMFT). These methods are uniquely suited to efficiently capture mesoscale phase behavior of PNCs in comparison to other theoretical and simulation frameworks. We demonstrate the ability ofmore » both methods to capture macrophase separation and describe the thermodynamics of PNCs. We systematically test how the nanoparticle morphology in PNCs is affected by a uniform probability distribution of grafting sites, common in field-based methods, versus random discrete grafting sites on the nanoparticle surface. We also analyze the accuracy of the mean-field approximation in capturing the phase behavior of PNCs. Moreover, the DMFT method introduces the ability to describe nonequilibrium phase behavior while the PNC-FT method is strictly an equilibrium method. With the DMFT method we are able to show the evolution of nonequilibrium states toward their equilibrium state and a qualitative assessment of the dynamics in these systems. These simulations are compared to experiments consisting of polystyrene grafted gold nanorods in a poly(methyl methacrylate) matrix to ensure the model gives results that qualitatively agree with the experiments. This study reveals that nanoparticles in a relatively high matrix molecular weight are trapped in a nonequilibrium state and demonstrates the utility of the DMFT framework in capturing nonequilibrium phase behavior of PNCs. In conclusion, both the PNC-FT and DMFT framework are promising methods to describe the thermodynamic and nonequilibrium phase behavior of PNCs.« less

Comparison of Coarse-Grained Approaches in Predicting Polymer Nanocomposite Phase Behavior

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koski, Jason P.; Ferrier, Robert C.; Krook, Nadia M.

Because of the considerable parameter space, efficient theoretical and simulation methods are required to predict the morphology and guide experiments in polymer nanocomposites (PNCs). Unfortunately, theoretical and simulation methods are restricted in their ability to accurately map to experiments based on necessary approximations and numerical limitations. In this study, we provide direct comparisons of two recently developed coarse-grained approaches for modeling polymer nanocomposites (PNCs): polymer nanocomposite field theory (PNC-FT) and dynamic mean-field theory (DMFT). These methods are uniquely suited to efficiently capture mesoscale phase behavior of PNCs in comparison to other theoretical and simulation frameworks. We demonstrate the ability ofmore » both methods to capture macrophase separation and describe the thermodynamics of PNCs. We systematically test how the nanoparticle morphology in PNCs is affected by a uniform probability distribution of grafting sites, common in field-based methods, versus random discrete grafting sites on the nanoparticle surface. We also analyze the accuracy of the mean-field approximation in capturing the phase behavior of PNCs. Moreover, the DMFT method introduces the ability to describe nonequilibrium phase behavior while the PNC-FT method is strictly an equilibrium method. With the DMFT method we are able to show the evolution of nonequilibrium states toward their equilibrium state and a qualitative assessment of the dynamics in these systems. These simulations are compared to experiments consisting of polystyrene grafted gold nanorods in a poly(methyl methacrylate) matrix to ensure the model gives results that qualitatively agree with the experiments. This study reveals that nanoparticles in a relatively high matrix molecular weight are trapped in a nonequilibrium state and demonstrates the utility of the DMFT framework in capturing nonequilibrium phase behavior of PNCs. In conclusion, both the PNC-FT and DMFT framework are promising methods to describe the thermodynamic and nonequilibrium phase behavior of PNCs.« less

Approximate solution to the Callan-Giddings-Harvey-Strominger field equations for two-dimensional evaporating black holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ori, Amos

2010-11-15

Callan, Giddings, Harvey, and Strominger (CGHS) previously introduced a two-dimensional semiclassical model of gravity coupled to a dilaton and to matter fields. Their model yields a system of field equations which may describe the formation of a black hole in gravitational collapse as well as its subsequent evaporation. Here we present an approximate analytical solution to the semiclassical CGHS field equations. This solution is constructed using the recently introduced formalism of flux-conserving hyperbolic systems. We also explore the asymptotic behavior at the horizon of the evaporating black hole.

The Hofstadter Butterfly and some physical consequences

NASA Astrophysics Data System (ADS)

Claro, Francisco

Opening its beautiful wings for the first time four decades ago, the Hofstadter Butterfly emerged as a self-similar pattern of bands and gaps displaying the allowed energies for two dimensional crystalline electrons in a perpendicular magnetic field. Within the Harper model, as the external field parameter is varied well defined gaps traverse the spectrum, some closing at a Dirac point where two approaching bands touch. Such band edges degeneracy is lifted in more realistic models. Gaps have a unique label that determines the Hall conductivity of a noninteracting electron system, as observed in recent experiments. When the 2D electron assembly is allowed to interact in the absence of an underlying periodic potential, the mean field approximation predicts a liquid at integer filling fractions and electron density fluctuations otherwise, which if periodic may be represented again by a Harper equation. The intriguing odd denominator rule observed in experiment in the fractional quantum Hall regime is then a natural prediction of the model. Although I have an affiliation (lifetime Granted) I am actually retired (do not have a paid contract).

Theoretical evaluation of maximum electric field approximation of direct band-to-band tunneling Kane model for low bandgap semiconductors

NASA Astrophysics Data System (ADS)

Dang Chien, Nguyen; Shih, Chun-Hsing; Hoa, Phu Chi; Minh, Nguyen Hong; Thi Thanh Hien, Duong; Nhung, Le Hong

2016-06-01

The two-band Kane model has been popularly used to calculate the band-to-band tunneling (BTBT) current in tunnel field-effect transistor (TFET) which is currently considered as a promising candidate for low power applications. This study theoretically clarifies the maximum electric field approximation (MEFA) of direct BTBT Kane model and evaluates its appropriateness for low bandgap semiconductors. By analysing the physical origin of each electric field term in the Kane model, it has been elucidated in the MEFA that the local electric field term must be remained while the nonlocal electric field terms are assigned by the maximum value of electric field at the tunnel junction. Mathematical investigations have showed that the MEFA is more appropriate for low bandgap semiconductors compared to high bandgap materials because of enhanced tunneling probability in low field regions. The appropriateness of the MEFA is very useful for practical uses in quickly estimating the direct BTBT current in low bandgap TFET devices.

Scaling with System Size of the Lyapunov Exponents for the Hamiltonian Mean Field Model

NASA Astrophysics Data System (ADS)

Manos, Thanos; Ruffo, Stefano

2011-12-01

The Hamiltonian Mean Field model is a prototype for systems with long-range interactions. It describes the motion of N particles moving on a ring, coupled with an infinite-range potential. The model has a second-order phase transition at the energy density Uc =3/4 and its dynamics is exactly described by the Vlasov equation in the N→∞ limit. Its chaotic properties have been investigated in the past, but the determination of the scaling with N of the Lyapunov Spectrum (LS) of the model remains a challenging open problem. Here we show that the N -1/3 scaling of the Maximal Lyapunov Exponent (MLE), found in previous numerical and analytical studies, extends to the full LS; scaling is "precocious" for the LS, meaning that it becomes manifest for a much smaller number of particles than the one needed to check the scaling for the MLE. Besides that, the N -1/3 scaling appears to be valid not only for U>Uc , as suggested by theoretical approaches based on a random matrix approximation, but also below a threshold energy Ut ≈0.2. Using a recently proposed method (GALI) devised to rapidly check the chaotic or regular nature of an orbit, we find that Ut is also the energy at which a sharp transition from weak to strong chaos is present in the phase-space of the model. Around this energy the phase of the vector order parameter of the model becomes strongly time dependent, inducing a significant untrapping of particles from a nonlinear resonance.

The pressure coefficient of the Curie temperature of ferromagnetic superconductors

NASA Astrophysics Data System (ADS)

Konno, R.; Hatayama, N.

2012-12-01

The pressure coefficient of the Curie temperature of ferromagnetic superconductors is studied numerically. In our previous study the pressure coefficient of the Curie temperature and that of the superconducting transition temperature were shown based on the Hamiltonian derived by Linder et al. within the mean field approximation about the electron-electron interaction analytically. There have been no numerical results of the pressure coefficient of the Curie temperature derived from the microscopic model. In this study the numerical results are reported. These results are qualitatively consistent with the experimental data in UGe2.

The influence of the directional energy distribution on the nonlinear dispersion relation in a random gravity wave field

NASA Technical Reports Server (NTRS)

Huang, N. E.; Tung, C.-C.

1977-01-01

The influence of the directional distribution of wave energy on the dispersion relation is calculated numerically using various directional wave spectrum models. The results indicate that the dispersion relation varies both as a function of the directional energy distribution and the direction of propagation of the wave component under consideration. Furthermore, both the mean deviation and the random scatter from the linear approximation increase as the energy spreading decreases. Limited observational data are compared with the theoretical results. The agreement is favorable.

Approximate solutions of acoustic 3D integral equation and their application to seismic modeling and full-waveform inversion

NASA Astrophysics Data System (ADS)

Malovichko, M.; Khokhlov, N.; Yavich, N.; Zhdanov, M.

2017-10-01

Over the recent decades, a number of fast approximate solutions of Lippmann-Schwinger equation, which are more accurate than classic Born and Rytov approximations, were proposed in the field of electromagnetic modeling. Those developments could be naturally extended to acoustic and elastic fields; however, until recently, they were almost unknown in seismology. This paper presents several solutions of this kind applied to acoustic modeling for both lossy and lossless media. We evaluated the numerical merits of those methods and provide an estimation of their numerical complexity. In our numerical realization we use the matrix-free implementation of the corresponding integral operator. We study the accuracy of those approximate solutions and demonstrate, that the quasi-analytical approximation is more accurate, than the Born approximation. Further, we apply the quasi-analytical approximation to the solution of the inverse problem. It is demonstrated that, this approach improves the estimation of the data gradient, comparing to the Born approximation. The developed inversion algorithm is based on the conjugate-gradient type optimization. Numerical model study demonstrates that the quasi-analytical solution significantly reduces computation time of the seismic full-waveform inversion. We also show how the quasi-analytical approximation can be extended to the case of elastic wavefield.

Superconductivity in 2D and nearly 2D: A Conserving Description

NASA Astrophysics Data System (ADS)

Deisz, John; Hess, Daryl; Serene, Joe

1998-03-01

In a previous work,(J.J. Deisz, D.W. Hess, and J.W. Serene, Phys. Rev. Lett., to appear.) we used a 2D Hubbard model with an attractive interaction to explicitly show that a superconducting state in the fluctuation exchange approximation (FEA) could be detected from self-consistent calculations of the internal energy and free energy as a function of a threaded flux. The FEA is a conserving approximation beyond mean field theory that includes the exchange of Cooper pair, density, and spin fluctuations. Here, we present extensions of our previous calculations and show a phase diagram as a function of interaction strength and density. We discuss the nature of the FEA phase transition in 2D and focus on how it changes with increasing coupling between planes.

Impulsive EUV bursts observed in C IV with OSO-8. [UV solar spectra

NASA Technical Reports Server (NTRS)

Athay, R. G.; White, O. R.; Lites, B. W.; Bruner, E. C., Jr.

1980-01-01

Time sequences of profiles of the 1548 A line of C IV containing 51 EUV bursts observed in or near active regions are analyzed to determine the brightness, Doppler shift and line broadening characteristics of the bursts. The bursts have mean lifetimes of approximately 150 s, and mean increases in brightness at burst maximum of four-fold as observed with a field of view of 2 x 20 arc sec. Mean burst diameters are estimated to be 3 arc sec, or smaller. All but three of the bursts show Doppler shifts with velocities sometimes exceeding 75 km/s; 31 are dominated by red shifts and 17 are dominated by blue shifts. Approximately half of the latter group have red-shifted precursors. The bursts are interpreted as prominence material, such as surges and coronal rain, moving through the field of view of the spectrometer.

The role of large-scale eddies in the climate equilibrium. Part 2: Variable static stability

NASA Technical Reports Server (NTRS)

Zhou, Shuntai; Stone, Peter H.

1993-01-01

Lorenz's two-level model on a sphere is used to investigate how the results of Part 1 are modified when the interaction of the vertical eddy heat flux and static stability is included. In general, the climate state does not depend very much on whether or not this interaction is included, because the poleward eddy heat transport dominates the eddy forcing of mean temperature and wind fields. However, the climatic sensitivity is significantly affected. Compared to two-level model results with fixed static stability, the poleward eddy heat flux is less sensitive to the meridional temperature gradient and the gradient is more sensitive to the forcing. For example, the logarithmic derivative of the eddy flux with respect to the gradient has a slope that is reduced from approximately 15 on a beta-plane with fixed static stability and approximately 6 on a sphere with fixed static stability, to approximately 3 to 4 in the present model. This last result is more in line with analyses from observations. The present model also has a stronger baroclinic adjustment than that in Part 1, more like that in two-level beta-plane models with fixed static stability, that is, the midlatitude isentropic slope is very insensitive to the forcing, the diabatic heating, and the friction, unless the forcing is very weak.

Prediction of spectral acceleration response ordinates based on PGA attenuation

USGS Publications Warehouse

Graizer, V.; Kalkan, E.

2009-01-01

Developed herein is a new peak ground acceleration (PGA)-based predictive model for 5% damped pseudospectral acceleration (SA) ordinates of free-field horizontal component of ground motion from shallow-crustal earthquakes. The predictive model of ground motion spectral shape (i.e., normalized spectrum) is generated as a continuous function of few parameters. The proposed model eliminates the classical exhausted matrix of estimator coefficients, and provides significant ease in its implementation. It is structured on the Next Generation Attenuation (NGA) database with a number of additions from recent Californian events including 2003 San Simeon and 2004 Parkfield earthquakes. A unique feature of the model is its new functional form explicitly integrating PGA as a scaling factor. The spectral shape model is parameterized within an approximation function using moment magnitude, closest distance to the fault (fault distance) and VS30 (average shear-wave velocity in the upper 30 m) as independent variables. Mean values of its estimator coefficients were computed by fitting an approximation function to spectral shape of each record using robust nonlinear optimization. Proposed spectral shape model is independent of the PGA attenuation, allowing utilization of various PGA attenuation relations to estimate the response spectrum of earthquake recordings.

Modelling thermal radiation in buoyant turbulent diffusion flames

NASA Astrophysics Data System (ADS)

Consalvi, J. L.; Demarco, R.; Fuentes, A.

2012-10-01

This work focuses on the numerical modelling of radiative heat transfer in laboratory-scale buoyant turbulent diffusion flames. Spectral gas and soot radiation is modelled by using the Full-Spectrum Correlated-k (FSCK) method. Turbulence-Radiation Interactions (TRI) are taken into account by considering the Optically-Thin Fluctuation Approximation (OTFA), the resulting time-averaged Radiative Transfer Equation (RTE) being solved by the Finite Volume Method (FVM). Emission TRIs and the mean absorption coefficient are then closed by using a presumed probability density function (pdf) of the mixture fraction. The mean gas flow field is modelled by the Favre-averaged Navier-Stokes (FANS) equation set closed by a buoyancy-modified k-ɛ model with algebraic stress/flux models (ASM/AFM), the Steady Laminar Flamelet (SLF) model coupled with a presumed pdf approach to account for Turbulence-Chemistry Interactions, and an acetylene-based semi-empirical two-equation soot model. Two sets of experimental pool fire data are used for validation: propane pool fires 0.3 m in diameter with Heat Release Rates (HRR) of 15, 22 and 37 kW and methane pool fires 0.38 m in diameter with HRRs of 34 and 176 kW. Predicted flame structures, radiant fractions, and radiative heat fluxes on surrounding surfaces are found in satisfactory agreement with available experimental data across all the flames. In addition further computations indicate that, for the present flames, the gray approximation can be applied for soot with a minor influence on the results, resulting in a substantial gain in Computer Processing Unit (CPU) time when the FSCK is used to treat gas radiation.

Analytical Tools for Investigating and Modeling Agent-Based Systems

DTIC Science & Technology

2005-06-01

of Black Holes Cluster 10 : Juan M. Maldacena (1924), Journal of High Energy Physics Field theory models for tachyon and gauge field string dy...namics; Super-Poincare Invariant Superstring Field The- ory; Level Four Approximation to the Tachyon Potential in Superstring Field Theory; SO(32) Spinors

Influence of Mean-Density Gradient on Small-Scale Turbulence Noise

NASA Technical Reports Server (NTRS)

Khavaran, Abbas

2000-01-01

A physics-based methodology is described to predict jet-mixing noise due to small-scale turbulence. Both self- and shear-noise source teens of Lilley's equation are modeled and the far-field aerodynamic noise is expressed as an integral over the jet volume of the source multiplied by an appropriate Green's function which accounts for source convection and mean-flow refraction. Our primary interest here is to include transverse gradients of the mean density in the source modeling. It is shown that, in addition to the usual quadrupole type sources which scale to the fourth-power of the acoustic wave number, additional dipole and monopole sources are present that scale to lower powers of wave number. Various two-point correlations are modeled and an approximate solution to noise spectra due to multipole sources of various orders is developed. Mean flow and turbulence information is provided through RANS-k(epsilon) solution. Numerical results are presented for a subsonic jet at a range of temperatures and Mach numbers. Predictions indicated a decrease in high frequency noise with added heat, while changes in the low frequency noise depend on jet velocity and observer angle.

A Varifold Approach to Surface Approximation

NASA Astrophysics Data System (ADS)

Buet, Blanche; Leonardi, Gian Paolo; Masnou, Simon

2017-11-01

We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we introduce the notion of approximate mean curvature and show various convergence results that hold, in particular, for sequences of discrete varifolds associated with point clouds or pixel/voxel-type discretizations of d-surfaces in the Euclidean n-space, without restrictions on dimension and codimension. The variational nature of the approach also allows us to consider surfaces with singularities, and in that case the approximate mean curvature is consistent with the generalized mean curvature of the limit surface. A series of numerical tests are provided in order to illustrate the effectiveness and generality of the method.

Space-Time Data Fusion

NASA Technical Reports Server (NTRS)

Braverman, Amy; Nguyen, Hai; Olsen, Edward; Cressie, Noel

2011-01-01

Space-time Data Fusion (STDF) is a methodology for combing heterogeneous remote sensing data to optimally estimate the true values of a geophysical field of interest, and obtain uncertainties for those estimates. The input data sets may have different observing characteristics including different footprints, spatial resolutions and fields of view, orbit cycles, biases, and noise characteristics. Despite these differences all observed data can be linked to the underlying field, and therefore the each other, by a statistical model. Differences in footprints and other geometric characteristics are accounted for by parameterizing pixel-level remote sensing observations as spatial integrals of true field values lying within pixel boundaries, plus measurement error. Both spatial and temporal correlations in the true field and in the observations are estimated and incorporated through the use of a space-time random effects (STRE) model. Once the models parameters are estimated, we use it to derive expressions for optimal (minimum mean squared error and unbiased) estimates of the true field at any arbitrary location of interest, computed from the observations. Standard errors of these estimates are also produced, allowing confidence intervals to be constructed. The procedure is carried out on a fine spatial grid to approximate a continuous field. We demonstrate STDF by applying it to the problem of estimating CO2 concentration in the lower-atmosphere using data from the Atmospheric Infrared Sounder (AIRS) and the Japanese Greenhouse Gasses Observing Satellite (GOSAT) over one year for the continental US.

Turbulence in Electrically Conducting Fluids Driven by Rotating and Travelling Magnetic Fields

NASA Astrophysics Data System (ADS)

Stiller, Jörg; Koal, Kristina; Blackburn, Hugh M.

The turbulent flow driven by rotating and travelling magnetic fields in a closed cylinder is investigated by means of direct numerical simulations (DNS) and large eddy simulations (LES). Our model is based on the low-induction, low-frequency approximation and employs a spectral-element/Fourier method for discretisation. The spectral vanishing viscosity (SVV) technique was adopted for the LES. The study provides first insights into the developed turbulent flow. In the RMF case, Taylor-Görtler vortices remain the dominant turbulence mechanism, as already in the transitional regime. In contrast to previous predictions we found no evidence that the vortices are confined closer to the wall for higher forcing. In the TMF more than 50 percent of the kinetic energy is bound to the turbulent fluctuations, which renders this field an interesting candidate for mixing applications.

A Model for Backscattering from Quasi Periodic Corn Canopies at L-Band

NASA Technical Reports Server (NTRS)

Lang, R.; Utku, C.; Zhao, Q.; O'Neill, P.

2010-01-01

In this study, a model for backscattering at L-band from a corn canopy is proposed. The canopy consists of a quasi-periodic distribution of stalks and a random distribution of leaves. The Distorted Born Approximation (DBA) is employed to calculate the single scattered return from the corn field. The new feature of the method is that the coherence of the stalks in the row direction is incorporated in the model in a systematic fashion. Since the wavelength is on the order of the distance between corn stalks in a row, grating lobe behavior is observed at certain azimuth angles of incidence. The results are compared with experimental values measured in Huntsville, Alabama in 1998. The mean field and the effective dielectric constant of the canopy are obtained by using the Foldy approximation. The stalks are placed in the effective medium in a two dimensional lattice to simulate the row structure of a corn field. In order to mimic a real corn field, a quasi-periodic stalk distribution is assumed where the stalks are given small random perturbations about their lattice locations. Corn leaves are also embedded in the effective medium and the backscattered field from the stalks and the leaves is computed. The backscattering coefficient is calculated and averaged over successive stalk position perturbations. It is assumed that soil erosion has smoothed the soil sufficiently so that it can be assumed flat. Corn field backscatter data was collected from cornfields during the Huntsville 98 experimental campaign held at Alabama A&M University Research Station, Huntsville, Alabama in 1998 using the NASA/GW truck mounted radar. Extensive ground truth data was collected. This included soil moisture measurements and corn plant architectural data to be used in the model. In particular, the distances between the stalks in a single row have been measured. The L-band radar backscatter data was collected for both H and V polarizations and for look angles of 15o and 45o over a two week period under varying soil moisture conditions. These measured backscattering values will be compared with the model backscattering values and a discussion of the results will be presented.

Influence of xc functional on thermal-elastic properties of Ceria: A DFT-based Debye-Grüneisen model approach

NASA Astrophysics Data System (ADS)

Lee, Ji-Hwan; Tak, Youngjoo; Lee, Taehun; Soon, Aloysius

Ceria (CeO2-x) is widely studied as a choice electrolyte material for intermediate-temperature (~ 800 K) solid oxide fuel cells. At this temperature, maintaining its chemical stability and thermal-mechanical integrity of this oxide are of utmost importance. To understand their thermal-elastic properties, we firstly test the influence of various approximations to the density-functional theory (DFT) xc functionals on specific thermal-elastic properties of both CeO2 and Ce2O3. Namely, we consider the local-density approximation (LDA), the generalized gradient approximation (GGA-PBE) with and without additional Hubbard U as applied to the 4 f electron of Ce, as well as the recently popularized hybrid functional due to Heyd-Scuseria-Ernzehof (HSE06). Next, we then couple this to a volume-dependent Debye-Grüneisen model to determine the thermodynamic quantities of ceria at arbitrary temperatures. We find an explicit description of the strong correlation (e.g. via the DFT + U and hybrid functional approach) is necessary to have a good agreement with experimental values, in contrast to the mean-field treatment in standard xc approximations (such as LDA or GGA-PBE). We acknowledge support from Samsung Research Funding Center of Samsung Electronics (SRFC-MA1501-03).

Dynamical behaviors of inter-out-of-equilibrium state intervals in Korean futures exchange markets

NASA Astrophysics Data System (ADS)

Lim, Gyuchang; Kim, SooYong; Kim, Kyungsik; Lee, Dong-In; Scalas, Enrico

2008-05-01

A recently discovered feature of financial markets, the two-phase phenomenon, is utilized to categorize a financial time series into two phases, namely equilibrium and out-of-equilibrium states. For out-of-equilibrium states, we analyze the time intervals at which the state is revisited. The power-law distribution of inter-out-of-equilibrium state intervals is shown and we present an analogy with discrete-time heat bath dynamics, similar to random Ising systems. In the mean-field approximation, this model reduces to a one-dimensional multiplicative process. By varying global and local model parameters, the relevance between volatilities in financial markets and the interaction strengths between agents in the Ising model are investigated and discussed.

Geomagnetic main field modeling using magnetohydrodynamic constraints

NASA Technical Reports Server (NTRS)

Estes, R. H.

1985-01-01

The influence of physical constraints are investigated which may be approximately satisfied by the Earth's liquid core on models of the geomagnetic main field and its secular variation. A previous report describes the methodology used to incorporate nonlinear equations of constraint into the main field model. The application of that methodology to the GSFC 12/83 field model to test the frozen-flux hypothesis and the usefulness of incorporating magnetohydrodynamic constraints for obtaining improved geomagnetic field models is described.

Intercomparison and validation of the mixed layer depth fields of global ocean syntheses

NASA Astrophysics Data System (ADS)

Toyoda, Takahiro; Fujii, Yosuke; Kuragano, Tsurane; Kamachi, Masafumi; Ishikawa, Yoichi; Masuda, Shuhei; Sato, Kanako; Awaji, Toshiyuki; Hernandez, Fabrice; Ferry, Nicolas; Guinehut, Stéphanie; Martin, Matthew J.; Peterson, K. Andrew; Good, Simon A.; Valdivieso, Maria; Haines, Keith; Storto, Andrea; Masina, Simona; Köhl, Armin; Zuo, Hao; Balmaseda, Magdalena; Yin, Yonghong; Shi, Li; Alves, Oscar; Smith, Gregory; Chang, You-Soon; Vernieres, Guillaume; Wang, Xiaochun; Forget, Gael; Heimbach, Patrick; Wang, Ou; Fukumori, Ichiro; Lee, Tong

2017-08-01

Intercomparison and evaluation of the global ocean surface mixed layer depth (MLD) fields estimated from a suite of major ocean syntheses are conducted. Compared with the reference MLDs calculated from individual profiles, MLDs calculated from monthly mean and gridded profiles show negative biases of 10-20 m in early spring related to the re-stratification process of relatively deep mixed layers. Vertical resolution of profiles also influences the MLD estimation. MLDs are underestimated by approximately 5-7 (14-16) m with the vertical resolution of 25 (50) m when the criterion of potential density exceeding the 10-m value by 0.03 kg m-3 is used for the MLD estimation. Using the larger criterion (0.125 kg m-3) generally reduces the underestimations. In addition, positive biases greater than 100 m are found in wintertime subpolar regions when MLD criteria based on temperature are used. Biases of the reanalyses are due to both model errors and errors related to differences between the assimilation methods. The result shows that these errors are partially cancelled out through the ensemble averaging. Moreover, the bias in the ensemble mean field of the reanalyses is smaller than in the observation-only analyses. This is largely attributed to comparably higher resolutions of the reanalyses. The robust reproduction of both the seasonal cycle and interannual variability by the ensemble mean of the reanalyses indicates a great potential of the ensemble mean MLD field for investigating and monitoring upper ocean processes.

Model of a thin film optical fiber fluorosensor

NASA Technical Reports Server (NTRS)

Egalon, Claudio O.; Rogowski, Robert S.

1991-01-01

The efficiency of core-light injection from sources in the cladding of an optical fiber is modeled analytically by means of the exact field solution of a step-profile fiber. The analysis is based on the techniques by Marcuse (1988) in which the sources are treated as infinitesimal electric currents with random phase and orientation that excite radiation fields and bound modes. Expressions are developed based on an infinite cladding approximation which yield the power efficiency for a fiber coated with fluorescent sources in the core/cladding interface. Marcuse's results are confirmed for the case of a weakly guiding cylindrical fiber with fluorescent sources uniformly distributed in the cladding, and the power efficiency is shown to be practically constant for variable wavelengths and core radii. The most efficient fibers have the thin film located at the core/cladding boundary, and fibers with larger differences in the indices of refraction are shown to be the most efficient.

Exploring precipitation pattern scaling methodologies and robustness among CMIP5 models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kravitz, Ben; Lynch, Cary; Hartin, Corinne

Pattern scaling is a well-established method for approximating modeled spatial distributions of changes in temperature by assuming a time-invariant pattern that scales with changes in global mean temperature. We compare two methods of pattern scaling for annual mean precipitation (regression and epoch difference) and evaluate which method is better in particular circumstances by quantifying their robustness to interpolation/extrapolation in time, inter-model variations, and inter-scenario variations. Both the regression and epoch-difference methods (the two most commonly used methods of pattern scaling) have good absolute performance in reconstructing the climate model output, measured as an area-weighted root mean square error. We decomposemore » the precipitation response in the RCP8.5 scenario into a CO 2 portion and a non-CO 2 portion. Extrapolating RCP8.5 patterns to reconstruct precipitation change in the RCP2.6 scenario results in large errors due to violations of pattern scaling assumptions when this CO 2-/non-CO 2-forcing decomposition is applied. As a result, the methodologies discussed in this paper can help provide precipitation fields to be utilized in other models (including integrated assessment models or impacts assessment models) for a wide variety of scenarios of future climate change.« less

Exploring precipitation pattern scaling methodologies and robustness among CMIP5 models

DOE PAGES

Kravitz, Ben; Lynch, Cary; Hartin, Corinne; ...

2017-05-12

Pattern scaling is a well-established method for approximating modeled spatial distributions of changes in temperature by assuming a time-invariant pattern that scales with changes in global mean temperature. We compare two methods of pattern scaling for annual mean precipitation (regression and epoch difference) and evaluate which method is better in particular circumstances by quantifying their robustness to interpolation/extrapolation in time, inter-model variations, and inter-scenario variations. Both the regression and epoch-difference methods (the two most commonly used methods of pattern scaling) have good absolute performance in reconstructing the climate model output, measured as an area-weighted root mean square error. We decomposemore » the precipitation response in the RCP8.5 scenario into a CO 2 portion and a non-CO 2 portion. Extrapolating RCP8.5 patterns to reconstruct precipitation change in the RCP2.6 scenario results in large errors due to violations of pattern scaling assumptions when this CO 2-/non-CO 2-forcing decomposition is applied. As a result, the methodologies discussed in this paper can help provide precipitation fields to be utilized in other models (including integrated assessment models or impacts assessment models) for a wide variety of scenarios of future climate change.« less

Two-Dimensional Quantum Model of a Nanotransistor

NASA Technical Reports Server (NTRS)

Govindan, T. R.; Biegel, B.; Svizhenko, A.; Anantram, M. P.

2009-01-01

A mathematical model, and software to implement the model, have been devised to enable numerical simulation of the transport of electric charge in, and the resulting electrical performance characteristics of, a nanotransistor [in particular, a metal oxide/semiconductor field-effect transistor (MOSFET) having a channel length of the order of tens of nanometers] in which the overall device geometry, including the doping profiles and the injection of charge from the source, gate, and drain contacts, are approximated as being two-dimensional. The model and software constitute a computational framework for quantitatively exploring such device-physics issues as those of source-drain and gate leakage currents, drain-induced barrier lowering, and threshold voltage shift due to quantization. The model and software can also be used as means of studying the accuracy of quantum corrections to other semiclassical models.

Empirical Model Development for Predicting Shock Response on Composite Materials Subjected to Pyroshock Loading. Volume 2, Part 1; Appendices

NASA Technical Reports Server (NTRS)

Gentz, Steven J.; Ordway, David O.; Parsons, David S.; Garrison, Craig M.; Rodgers, C. Steven; Collins, Brian W.

2015-01-01

The NASA Engineering and Safety Center (NESC) received a request to develop an analysis model based on both frequency response and wave propagation analyses for predicting shock response spectrum (SRS) on composite materials subjected to pyroshock loading. The model would account for near-field environment (approximately 9 inches from the source) dominated by direct wave propagation, mid-field environment (approximately 2 feet from the source) characterized by wave propagation and structural resonances, and far-field environment dominated by lower frequency bending waves in the structure. This document contains appendices to the Volume I report.

Magnetic properties of a quasi-two-dimensional S =1/2 Heisenberg antiferromagnet with distorted square lattice

NASA Astrophysics Data System (ADS)

Yamaguchi, Hironori; Tamekuni, Yusuke; Iwasaki, Yoshiki; Otsuka, Rei; Hosokoshi, Yuko; Kida, Takanori; Hagiwara, Masayuki

2017-06-01

We successfully synthesize single crystals of the verdazyl radical α -2 ,3 ,5 -Cl3 -V. Ab initio molecular orbital calculations indicate that the two dominant antiferromagnetic interactions, J1 and J2 (α =J2/J1≃0.56 ), form an S =1 /2 distorted square lattice. We explain the magnetic properties based on the S =1 /2 square lattice Heisenberg antiferromagnet using the quantum Monte Carlo method, and examine the effects of the lattice distortion and the interplane interaction contribution. In the low-temperature regions below 6.4 K, we observe anisotropic magnetic behavior accompanied by a phase transition to a magnetically ordered state. The electron spin resonance signals exhibit anisotropic behavior in the temperature dependence of the resonance field and the linewidth. We explain the frequency dependence of the resonance fields in the ordered phase using a mean-field approximation with out-of-plane easy-axis anisotropy, which causes a spin-flop phase transition at approximately 0.4 T for the field perpendicular to the plane. Furthermore, the anisotropic dipole field provides supporting information regarding the presence of the easy-axis anisotropy. These results demonstrate that the lattice distortion, anisotropy, and interplane interaction of this model are sufficiently small that they do not affect the intrinsic behavior of the S =1 /2 square lattice Heisenberg antiferromagnet.

Adiabatic cooling processes in frustrated magnetic systems with pyrochlore structure

NASA Astrophysics Data System (ADS)

Jurčišinová, E.; Jurčišin, M.

2017-11-01

We investigate in detail the process of adiabatic cooling in the framework of the exactly solvable antiferromagnetic spin-1/2 Ising model in the presence of the external magnetic field on an approximate lattice with pyrochlore structure. The behavior of the entropy of the model is studied and exact values of the residual entropies of all ground states are found. The temperature variation of the system under adiabatic (de)magnetization is investigated and the central role of the macroscopically degenerated ground states in cooling processes is explicitly demonstrated. It is shown that the model parameter space of the studied geometrically frustrated system is divided into five disjunct regions with qualitatively different processes of the adiabatic cooling. The effectiveness of the adiabatic (de)magnetization cooling in the studied model is compared to the corresponding processes in paramagnetic salts. It is shown that the processes of the adiabatic cooling in the antiferromagnetic frustrated systems are much more effective especially in nonzero external magnetic fields. It means that the frustrated magnetic materials with pyrochlore structure can be considered as very promising refrigerants mainly in the situations with nonzero final values of the magnetic field.

Adiabatic cooling processes in frustrated magnetic systems with pyrochlore structure.

PubMed

Jurčišinová, E; Jurčišin, M

2017-11-01

We investigate in detail the process of adiabatic cooling in the framework of the exactly solvable antiferromagnetic spin-1/2 Ising model in the presence of the external magnetic field on an approximate lattice with pyrochlore structure. The behavior of the entropy of the model is studied and exact values of the residual entropies of all ground states are found. The temperature variation of the system under adiabatic (de)magnetization is investigated and the central role of the macroscopically degenerated ground states in cooling processes is explicitly demonstrated. It is shown that the model parameter space of the studied geometrically frustrated system is divided into five disjunct regions with qualitatively different processes of the adiabatic cooling. The effectiveness of the adiabatic (de)magnetization cooling in the studied model is compared to the corresponding processes in paramagnetic salts. It is shown that the processes of the adiabatic cooling in the antiferromagnetic frustrated systems are much more effective especially in nonzero external magnetic fields. It means that the frustrated magnetic materials with pyrochlore structure can be considered as very promising refrigerants mainly in the situations with nonzero final values of the magnetic field.

Using the WSA Model to Test the Parker Spiral Approximation for SEP Event Magnetic Connections

NASA Astrophysics Data System (ADS)

Kahler, S. W.; Arge, C. N.; Smith, D. A.

2016-08-01

In studies of solar energetic (E > 10 MeV) particle (SEP) events the Parker spiral (PS) field approximation, based only on the measured 1 AU solar wind (SW) speed Vsw, is nearly always used to determine the coronal or photospheric source locations of the 1 AU magnetic fields. There is no objective way to validate that approximation, but here we seek guidelines for optimizing its application. We first review recent SEP studies showing the extensive use of the PS approximation with various assumptions about coronal and photospheric source fields. We then run the Wang-Sheeley-Arge (WSA) model over selected Carrington rotations (CRs) to track both the photospheric and 5 R_{⊙} source locations of the forecasted 1 AU SW, allowing us to compare those WSA sources with the PS sources inferred from the WSA Vsw forecast. We compile statistics of the longitude differences (WSA-PS) for all the CRs and discuss the limitations of using the WSA model to validate the PS approximation. Over nearly all of each CR the PS and WSA source longitudes agree to within several degrees. The agreement is poor only in the slow-fast SW interaction regions characterized by high-speed events (HSEs), where the longitude differences can reach several tens of degrees. This result implies that SEP studies should limit use of the PS approximation around HSEs and use magnetic field polarities as an additional check of solar source connections.

Analysis of atmospheric flow over a surface protrusion using the turbulence kinetic energy equation

NASA Technical Reports Server (NTRS)

Frost, W.; Harper, W. L.; Fichtl, G. H.

1975-01-01

Atmospheric flow fields resulting from a semi-elliptical surface obstruction in an otherwise horizontally homogeneous statistically stationary flow are modelled with the boundary-layer/Boussinesq-approximation of the governing equation of fluid mechanics. The turbulence kinetic energy equation is used to determine the dissipative effects of turbulent shear on the mean flow. Mean-flow results are compared with those given in a previous paper where the same problem was attacked using a Prandtl mixing-length hypothesis. Iso-lines of turbulence kinetic energy and turbulence intensity are plotted in the plane of the flow. They highlight regions of high turbulence intensity in the stagnation zone and sharp gradients in intensity along the transition from adverse to favourable pressure gradient.

Forecasting experiments of a dynamical-statistical model of the sea surface temperature anomaly field based on the improved self-memorization principle

NASA Astrophysics Data System (ADS)

Hong, Mei; Chen, Xi; Zhang, Ren; Wang, Dong; Shen, Shuanghe; Singh, Vijay P.

2018-04-01

With the objective of tackling the problem of inaccurate long-term El Niño-Southern Oscillation (ENSO) forecasts, this paper develops a new dynamical-statistical forecast model of the sea surface temperature anomaly (SSTA) field. To avoid single initial prediction values, a self-memorization principle is introduced to improve the dynamical reconstruction model, thus making the model more appropriate for describing such chaotic systems as ENSO events. The improved dynamical-statistical model of the SSTA field is used to predict SSTA in the equatorial eastern Pacific and during El Niño and La Niña events. The long-term step-by-step forecast results and cross-validated retroactive hindcast results of time series T1 and T2 are found to be satisfactory, with a Pearson correlation coefficient of approximately 0.80 and a mean absolute percentage error (MAPE) of less than 15 %. The corresponding forecast SSTA field is accurate in that not only is the forecast shape similar to the actual field but also the contour lines are essentially the same. This model can also be used to forecast the ENSO index. The temporal correlation coefficient is 0.8062, and the MAPE value of 19.55 % is small. The difference between forecast results in spring and those in autumn is not high, indicating that the improved model can overcome the spring predictability barrier to some extent. Compared with six mature models published previously, the present model has an advantage in prediction precision and length, and is a novel exploration of the ENSO forecast method.

Comparison of the near field/far field model and the advanced reach tool (ART) model V1.5: exposure estimates to benzene during parts washing with mineral spirits.

PubMed

LeBlanc, Mallory; Allen, Joseph G; Herrick, Robert F; Stewart, James H

2018-03-01

The Advanced Reach Tool V1.5 (ART) is a mathematical model for occupational exposures conceptually based on, but implemented differently than, the "classic" Near Field/Far Field (NF/FF) exposure model. The NF/FF model conceptualizes two distinct exposure "zones"; the near field, within approximately 1m of the breathing zone, and the far field, consisting of the rest of the room in which the exposure occurs. ART has been reported to provide "realistic and reasonable worst case" estimates of the exposure distribution. In this study, benzene exposure during the use of a metal parts washer was modeled using ART V1.5, and compared to actual measured workers samples and to NF/FF model results from three previous studies. Next, the exposure concentrations expected to be exceeded 25%, 10% and 5% of the time for the exposure scenario were calculated using ART. Lastly, ART exposure estimates were compared with and without Bayesian adjustment. The modeled parts washing benzene exposure scenario included distinct tasks, e.g. spraying, brushing, rinsing and soaking/drying. Because ART can directly incorporate specific types of tasks that are part of the exposure scenario, the present analysis identified each task's determinants of exposure and performance time, thus extending the work of the previous three studies where the process of parts washing was modeled as one event. The ART 50th percentile exposure estimate for benzene (0.425ppm) more closely approximated the reported measured mean value of 0.50ppm than the NF/FF model estimates of 0.33ppm, 0.070ppm or 0.2ppm obtained from other modeling studies of this exposure scenario. The ART model with the Bayesian analysis provided the closest estimate to the measured value (0.50ppm). ART (with Bayesian adjustment) was then used to assess the 75th, the 90th and 95th percentile exposures, predicting that on randomly selected days during this parts washing exposure scenario, 25% of the benzene exposures would be above 0.70ppm; 10% above 0.95ppm; and 5% above 1.15ppm. These exposure estimates at the three different percentiles of the ART exposure distribution refer to the modeled exposure scenario not a specific workplace or worker. This study provides a detailed comparison of modeling tools currently available to occupational hygienists and other exposure assessors. Possible applications are considered. Copyright © 2017 Elsevier GmbH. All rights reserved.

Spatially structured superinfection and the evolution of disease virulence.

PubMed

Caraco, Thomas; Glavanakov, Stephan; Li, Shengua; Maniatty, William; Szymanski, Boleslaw K

2006-06-01

When pathogen strains differing in virulence compete for hosts, spatial structuring of disease transmission can govern both evolved levels of virulence and patterns in strain coexistence. We develop a spatially detailed model of superinfection, a form of contest competition between pathogen strains; the probability of superinfection depends explicitly on the difference in levels of virulence. We apply methods of adaptive dynamics to address the interplay of spatial dynamics and evolution. The mean-field approximation predicts evolution to criticality; any small increase in virulence capable of dynamical persistence is favored. Both pair approximation and simulation of the detailed model indicate that spatial structure constrains disease virulence. Increased spatial clustering reduces the maximal virulence capable of single-strain persistence and, more importantly, reduces the convergent-stable virulence level under strain competition. The spatially detailed model predicts that increasing the probability of superinfection, for given difference in virulence, increases the likelihood of between-strain coexistence. When strains differing in virulence can coexist ecologically, our results may suggest policies for managing diseases with localized transmission. Comparing equilibrium densities from the pair approximation, we find that introducing a more virulent strain into a host population infected by a less virulent strain can sometimes reduce total host mortality and increase global host density.

The effect of driven electron-phonon coupling on the electronic conductance of a polar nanowire

NASA Astrophysics Data System (ADS)

Mardaani, Mohammad; Rabani, Hassan; Esmaili, Esmat; Shariati, Ashrafalsadat

2015-08-01

A semi-classical model is proposed to explore the effect of electron-phonon coupling on the coherent electronic transport of a polar chain which is confined between two rigid leads in the presence of an external electric field. To this end, we construct the model by means of Green's function technique within the nearest neighbor tight-binding and harmonic approximations. For a time-periodic electric field, the atomic displacements from the equilibrium positions are obtained precisely. The result is then used to compute the electronic transport properties of the chain within the Peierls-type model. The numerical results indicate that the conductance of the system shows interesting behavior in some special frequencies. For each special frequency, there is an electronic quasi-state in which the scattering of electrons by vibrating atoms reaches maximum. The system electronic conductance decreases dramatically at the strong electron-phonon couplings and low electron energies. In the presence of damping forces, the electron-phonon interaction has a less significant effect on the conductance.

Coagulation kinetics beyond mean field theory using an optimised Poisson representation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burnett, James; Ford, Ian J.

Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics may be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants, but this can be a poor approximation when the mean populations are small. However, using the Poisson representation, it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy, andmore » complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work, we encounter instabilities that can be eliminated using a suitable “gauge” transformation of the problem [P. D. Drummond, Eur. Phys. J. B 38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation.« less

Nature of phase transitions in Axelrod-like coupled Potts models in two dimensions

NASA Astrophysics Data System (ADS)

Gandica, Yerali; Chiacchiera, Silvia

2016-03-01

We study F coupled q -state Potts models in a two-dimensional square lattice. The interaction between the different layers is attractive to favor a simultaneous alignment in all of them, and its strength is fixed. The nature of the phase transition for zero field is numerically determined for F =2 ,3 . Using the Lee-Kosterlitz method, we find that it is continuous for F =2 and q =2 , whereas it is abrupt for higher values of q and/or F . When a continuous or a weakly first-order phase transition takes place, we also analyze the properties of the geometrical clusters. This allows us to determine the fractal dimension D of the incipient infinite cluster and to examine the finite-size scaling of the cluster number density via data collapse. A mean-field approximation of the model, from which some general trends can be determined, is presented too. Finally, since this lattice model has been recently considered as a thermodynamic counterpart of the Axelrod model of social dynamics, we discuss our results in connection with this one.

Nature of phase transitions in Axelrod-like coupled Potts models in two dimensions.

PubMed

Gandica, Yerali; Chiacchiera, Silvia

2016-03-01

We study F coupled q-state Potts models in a two-dimensional square lattice. The interaction between the different layers is attractive to favor a simultaneous alignment in all of them, and its strength is fixed. The nature of the phase transition for zero field is numerically determined for F = 2,3. Using the Lee-Kosterlitz method, we find that it is continuous for F = 2 and q = 2, whereas it is abrupt for higher values of q and/or F. When a continuous or a weakly first-order phase transition takes place, we also analyze the properties of the geometrical clusters. This allows us to determine the fractal dimension D of the incipient infinite cluster and to examine the finite-size scaling of the cluster number density via data collapse. A mean-field approximation of the model, from which some general trends can be determined, is presented too. Finally, since this lattice model has been recently considered as a thermodynamic counterpart of the Axelrod model of social dynamics, we discuss our results in connection with this one.

Spatial averaging of fields from half-wave dipole antennas and corresponding SAR calculations in the NORMAN human voxel model between 65 MHz and 2 GHz.

PubMed

Findlay, R P; Dimbylow, P J

2009-04-21

If an antenna is located close to a person, the electric and magnetic fields produced by the antenna will vary in the region occupied by the human body. To obtain a mean value of the field for comparison with reference levels, the Institute of Electrical and Electronic Engineers (IEEE) and International Commission on Non-Ionizing Radiation Protection (ICNIRP) recommend spatially averaging the squares of the field strength over the height the body. This study attempts to assess the validity and accuracy of spatial averaging when used for half-wave dipoles at frequencies between 65 MHz and 2 GHz and distances of lambda/2, lambda/4 and lambda/8 from the body. The differences between mean electric field values calculated using ten field measurements and that of the true averaged value were approximately 15% in the 600 MHz to 2 GHz range. The results presented suggest that the use of modern survey equipment, which takes hundreds rather than tens of measurements, is advisable to arrive at a sufficiently accurate mean field value. Whole-body averaged and peak localized SAR values, normalized to calculated spatially averaged fields, were calculated for the NORMAN voxel phantom. It was found that the reference levels were conservative for all whole-body SAR values, but not for localized SAR, particularly in the 1-2 GHz region when the dipole was positioned very close to the body. However, if the maximum field is used for normalization of calculated SAR as opposed to the lower spatially averaged value, the reference levels provide a conservative estimate of the localized SAR basic restriction for all frequencies studied.

The diagram of phase-field crystal structures: an influence of model parameters in a two-mode approximation

NASA Astrophysics Data System (ADS)

Ankudinov, V.; Galenko, P. K.

2017-04-01

Effect of phase-field crystal model (PFC-model) parameters on the structure diagram is analyzed. The PFC-model is taken in a two-mode approximation and the construction of structure diagram follows from the free energy minimization and Maxwell thermodynamic rule. The diagram of structure’s coexistence for three dimensional crystal structures [Body-Centered-Cubic (BCC), Face-Centered-Cubic (FCC) and homogeneous structures] are constructed. An influence of the model parameters, including the stability parameters, are discussed. A question about the structure diagram construction using the two-mode PFC-model with the application to real materials is established.

Random versus maximum entropy models of neural population activity

NASA Astrophysics Data System (ADS)

Ferrari, Ulisse; Obuchi, Tomoyuki; Mora, Thierry

2017-04-01

The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions underlying maximum entropy are intuitive and appealing, its adequacy for describing complex empirical data has been little studied in comparison to alternative approaches. Here, data from the collective spiking activity of retinal neurons is reanalyzed. The accuracy of the maximum entropy distribution constrained by mean firing rates and pairwise correlations is compared to a random ensemble of distributions constrained by the same observables. For most of the tested networks, maximum entropy approximates the true distribution better than the typical or mean distribution from that ensemble. This advantage improves with population size, with groups as small as eight being almost always better described by maximum entropy. Failure of maximum entropy to outperform random models is found to be associated with strong correlations in the population.

Phonon and magnetic structure in δ-plutonium from density-functional theory

DOE PAGES

Söderlind, Per; Zhou, F.; Landa, A.; ...

2015-10-30

We present phonon properties of plutonium metal obtained from a combination of density-functional-theory (DFT) electronic structure and the recently developed compressive sensing lattice dynamics (CSLD). The CSLD model is here trained on DFT total energies of several hundreds of quasi-random atomic configurations for best possible accuracy of the phonon properties. The calculated phonon dispersions compare better with experiment than earlier results obtained from dynamical mean-field theory. The density-functional model of the electronic structure consists of disordered magnetic moments with all relativistic effects and explicit orbital-orbital correlations. The magnetic disorder is approximated in two ways: (i) a special quasi-random structure andmore » (ii) the disordered-local-moment (DLM) method within the coherent potential approximation. Magnetism in plutonium has been debated intensely, However, the present magnetic approach for plutonium is validated by the close agreement between the predicted magnetic form factor and that of recent neutron-scattering experiments.« less

Remote sensing of mesospheric electric fields using MF radars

NASA Astrophysics Data System (ADS)

Meek, C. E.; Manson, A. H.; Martynenko, S. I.; Rozumenko, V. T.; Tyrnov, O. F.

2004-07-01

Large mesospheric electric fields can play an essential role in middle atmospheric electrodynamics (see, e.g., Goldberg, R. A., Middle Atmospheric Electrodynamics during MAP, Adv. Space Res. 10 (10) (1990) 209). The V/m electric fields of atmospheric origin can be the possible cause of large variations in the electron collision frequency at mesospheric altitudes, and this provides a unique opportunity to take measurements of electric fields in the lower ionosphere by using remote sensing instruments employing radiowave techniques. A technique has been proposed for making estimates of large mesospheric electric field intensities on the lower edge of the ionosphere by using MF radar data and the inherent effective electron collision frequency. To do this, data collected in Canada and Ukraine were utilized. The developed technique permits the changes in mesospheric electric field intensities to be derived from MF radar data in real time. The statistical analysis of data consistent with large mesospheric electric field intensities in the 60-67km region resulted in the following inferences. There are at least two mechanisms for the generation of large mesospheric electric fields in the mesosphere. The most likely mechanism, with a probability of 60-70%, is the summation of random fields from a large number of elementary small-scale mesospheric generators, which results in a one-parameter Rayleigh distribution of the total large mesospheric electric field intensity E with a mean value of approximately 0.7-0.9V/m in the 60-67km altitude region, or in the corresponding one-parameter exponential distribution of the intensity squared E2 of large mesospheric electric fields. The second mechanism of unknown nature, with 5-15% probability, gives rise to the sporadic appearance of large mesospheric electric field intensities E>2.5V/m with a mean of 4V/m. Statistically significant seasonal differences in the averaged large mesospheric electric field parameters have not been revealed. The probability of the absence of local large mesospheric electric fields amounts to approximately 25% for Ukraine and approximately 30% for Canada. A comparison of the Ukrainian and Canadian data indicates the possible existence of a latitudinal dependence in mean large mesospheric electric field features. Hence, the large electric fields are an additional source of electron heating that must be taken into account in studying a disturbed lower ionosphere and radio wave propagation within it.

A kinetic model of the formation of organic monolayers on hydrogen-terminated silicon by hydrosilation of alkenes.

PubMed

Woods, M; Carlsson, S; Hong, Q; Patole, S N; Lie, L H; Houlton, A; Horrocks, B R

2005-12-22

We have analyzed a kinetic model for the formation of organic monolayers based on a previously suggested free radical chain mechanism for the reaction of unsaturated molecules with hydrogen-terminated silicon surfaces (Linford, M. R.; Fenter, P. M.; Chidsey, C. E. D. J. Am. Chem. Soc 1995, 117, 3145). A direct consequence of this mechanism is the nonexponential growth of the monolayer, and this has been observed spectroscopically. In the model, the initiation of silyl radicals on the surface is pseudo first order with rate constant, ki, and the rate of propagation is determined by the concentration of radicals and unreacted Si-H nearest neighbor sites with a rate constant, kp. This propagation step determines the rate at which the monolayer forms by addition of alkene molecules to form a track of molecules that constitute a self-avoiding random walk on the surface. The initiation step describes how frequently new random walks commence. A termination step by which the radicals are destroyed is also included. The solution of the kinetic equations yields the fraction of alkylated surface sites and the mean length of the random walks as a function of time. In mean-field approximation we show that (1) the average length of the random walk is proportional to (kp/ki)1/2, (2) the monolayer surface coverage grows exponentially only after an induction period, (3) the effective first-order rate constant describing the growth of the monolayer and the induction period (kt) is k = (2ki kp)1/2, (4) at long times the effective first-order rate constant drops to ki, and (5) the overall activation energy for the growth kinetics is the mean of the activation energies for the initiation and propagation steps. Monte Carlo simulations of the mechanism produce qualitatively similar kinetic plots, but the mean random walk length (and effective rate constant) is overestimated by the mean field approximation and when kp > ki, we find k approximately ki0.7kp0.3 and Ea = (0.7Ei+ 0.3Ep). However the most striking prediction of the Monte Carlo simulations is that at long times, t > 1/k, the effective first-order rate constant decreases to ki even in the absence of a chemical termination step. Experimental kinetic data for the reaction of undec-1-ene with hydrogen-terminated porous silicon under thermal reflux in toluene and ethylbenzene gave a value of k = 0.06 min(-1) and an activation energy of 107 kJ mol(-1). The activation energy is in reasonable agreement with density functional calculations of the transition state energies for the initiation and propagation steps.

[Study of cefuroxime in pediatric field (author's transl)].

PubMed

Iwai, N; Sasaki, A; Miyazu, M; Osuga, T; Inaguma, K

1979-11-01

1. Cefuroxime (CXM) was studied for absorption and excretion in 4 pediatric patients given one shot intravenous injection of 20 approximately 25 mg/kg. The following serum levels were determined: 24.5 approximately 38.0 micrograms/ml at 30 minutes (mean 33.3 +/- 6.1 micrograms/ml), 10.0 approximately 17.0 micrograms/ml at 1 hours (mean 13.9 +/- 3.3 micrograms/ml), 3.4 approximately 7.6 micrograms/ml at 2 hours (mean 5.2 +/- 1.9 micrograms/ml, 0.7 approximately 2.1 micrograms/ml at 4 hours (mean 1.3 +/- 0.6 micrograms/ml, 0.1 approximately 0.3 microgram/ml at 6 hours (mean 0.2 +/- 0.1 microgram microgram/ml). Half-life (T 1/2) was 0.65 approximately 0.88 hour (mean 0.75 +/- 0.10 hour). Urinary levels were 1,280 approximately 7,100 micrograms/ml at 0 approximately 2 hours, 96 approximately 3,400 micrograms/ml at 2 approximately 4 hours, 68 approximately 250 micrograms/ml at 4 approximately 6 hours. Urinary recovery rate at 0 approximately 6 hours was 54.1 approximately 74.4% (mean 61.8 +/- 9.4%). 2. From the study on spinal fluid concentration in pediatric patients with Haemophilus influenzae-induced meningitis, the dose of CXM 52.2 mg/kg was given to 1 pediatric case with this disease by one shot intravenous injection. Spinal fluid levels were presumed as 9.0 micrograms/ml at 30 minutes, 6.8 micrograms/ml at 1 hour, 3.8 micrograms/ml at 2 hours and 1.2 micrograms/ml at 4 hours. 3. CXM was studied in 19 pediatric patients with bacterial infection for clinical efficacy, bacteriological effect and side effect. Clinical result was found good in 1 with purulent meningitis; excellent in 9 out of 15 with acute lobar pneumonia or acute bronchopneumonia, and good in remaining 6 cases; good in 2 with acute bronchitis; excellent in 1 with acute pyelonephritis. This represents efficacy ("excellent" plus "good") rate of 100%. Of 5 strains of H. influenzae presumed as causative organisms, 4 were disappeared and 1 was reduced. Two strains of Streptococcus pneumoniae and 1 strain of Escherichia coli were disappeared. No side effect was noted in terms of clinical symptom. Laboratory examination showed elevation of GOT and GPT in 1 case, but these elevated values returned to normal after the end of the CXM treatment.

Self-diffusion in dense granular shear flows.

PubMed

Utter, Brian; Behringer, R P

2004-03-01

Diffusivity is a key quantity in describing velocity fluctuations in granular materials. These fluctuations are the basis of many thermodynamic and hydrodynamic models which aim to provide a statistical description of granular systems. We present experimental results on diffusivity in dense, granular shear flows in a two-dimensional Couette geometry. We find that self-diffusivities D are proportional to the local shear rate gamma; with diffusivities along the direction of the mean flow approximately twice as large as those in the perpendicular direction. The magnitude of the diffusivity is D approximately gamma;a(2), where a is the particle radius. However, the gradient in shear rate, coupling to the mean flow, and strong drag at the moving boundary lead to particle displacements that can appear subdiffusive or superdiffusive. In particular, diffusion appears to be superdiffusive along the mean flow direction due to Taylor dispersion effects and subdiffusive along the perpendicular direction due to the gradient in shear rate. The anisotropic force network leads to an additional anisotropy in the diffusivity that is a property of dense systems and has no obvious analog in rapid flows. Specifically, the diffusivity is suppressed along the direction of the strong force network. A simple random walk simulation reproduces the key features of the data, such as the apparent superdiffusive and subdiffusive behavior arising from the mean velocity field, confirming the underlying diffusive motion. The additional anisotropy is not observed in the simulation since the strong force network is not included. Examples of correlated motion, such as transient vortices, and Lévy flights are also observed. Although correlated motion creates velocity fields which are qualitatively different from collisional Brownian motion and can introduce nondiffusive effects, on average the system appears simply diffusive.

Progress in the Determination of the Earth's Gravity Field

NASA Technical Reports Server (NTRS)

Rapp, Richard H. (Editor)

1989-01-01

Topics addressed include: global gravity model development; methods for approximation of the gravity field; gravity field measuring techniques; global gravity field applications and requirements in geophysics and oceanography; and future gravity missions.

Theoretical exploration of optical response of Fe3O4-reduced graphene oxide nanoparticle system within dynamical mean-field theory

NASA Astrophysics Data System (ADS)

Majidi, M. A.; Kusumaatmadja, R.; Fauzi, A. D.; Phan, W. Y.; Taufik, A.; Saleh, R.; Rusydi, A.

2017-04-01

We theoretically investigate the optical conductivity and its related optical response of Fe3O4-reduced graphene oxide (rGO) nanoparticle system. Experimental data of magnetization of the Fe3O4-rGO nanoparticle system have shown that the saturation magnetization can be enhanced by controlling the rGO content with the maximum enhancement reached at the optimal rGO content of about 5 weight percentage. We hypothesize that the magnetization enhancement is due to spin-flipping of Fe ions at tetrahedral sites induced by oxygen vacancies at the Fe3O4 nanoparticle boundaries. These oxygen vacancies are formed due to adsorption of oxygen atoms by rGO flakes around the Fe3O4 nanoparticle. In this study, we aim to explore the implications of this effect to the optical response of the system as a function of the rGO content. Our model incorporates Hubbard-repulsive interactions between electrons occupying the e g orbitals of Fe3+ and Heisenberg-like interactions between electron spins and spins of Fe3+ ions. We treat the relevant interactions within mean-field and dynamical mean-field approximations. Our results are to be compared with the existing experimental reflectance data of Fe3O4 nanoparticle system.

Complexity of Quantum Impurity Problems

NASA Astrophysics Data System (ADS)

Bravyi, Sergey; Gosset, David

2017-12-01

We give a quasi-polynomial time classical algorithm for estimating the ground state energy and for computing low energy states of quantum impurity models. Such models describe a bath of free fermions coupled to a small interacting subsystem called an impurity. The full system consists of n fermionic modes and has a Hamiltonian {H=H_0+H_{imp}}, where H 0 is quadratic in creation-annihilation operators and H imp is an arbitrary Hamiltonian acting on a subset of O(1) modes. We show that the ground energy of H can be approximated with an additive error {2^{-b}} in time {n^3 \\exp{[O(b^3)]}}. Our algorithm also finds a low energy state that achieves this approximation. The low energy state is represented as a superposition of {\\exp{[O(b^3)]}} fermionic Gaussian states. To arrive at this result we prove several theorems concerning exact ground states of impurity models. In particular, we show that eigenvalues of the ground state covariance matrix decay exponentially with the exponent depending very mildly on the spectral gap of H 0. A key ingredient of our proof is Zolotarev's rational approximation to the {√{x}} function. We anticipate that our algorithms may be used in hybrid quantum-classical simulations of strongly correlated materials based on dynamical mean field theory. We implemented a simplified practical version of our algorithm and benchmarked it using the single impurity Anderson model.

Critical Slowing Down in Time-to-Extinction: An Example of Critical Phenomena in Ecology

NASA Technical Reports Server (NTRS)

Gandhi, Amar; Levin, Simon; Orszag, Steven

1998-01-01

We study a model for two competing species that explicitly accounts for effects due to discreteness, stochasticity and spatial extension of populations. The two species are equally preferred by the environment and do better when surrounded by others of the same species. We observe that the final outcome depends on the initial densities (uniformly distributed in space) of the two species. The observed phase transition is a continuous one and key macroscopic quantities like the correlation length of clusters and the time-to-extinction diverge at a critical point. Away from the critical point, the dynamics can be described by a mean-field approximation. Close to the critical point, however, there is a crossover to power-law behavior because of the gross mismatch between the largest and smallest scales in the system. We have developed a theory based on surface effects, which is in good agreement with the observed behavior. The course-grained reaction-diffusion system obtained from the mean-field dynamics agrees well with the particle system.

Neutrality and evolvability of designed protein sequences

NASA Astrophysics Data System (ADS)

Bhattacherjee, Arnab; Biswas, Parbati

2010-07-01

The effect of foldability on protein’s evolvability is analyzed by a two-prong approach consisting of a self-consistent mean-field theory and Monte Carlo simulations. Theory and simulation models representing protein sequences with binary patterning of amino acid residues compatible with a particular foldability criteria are used. This generalized foldability criterion is derived using the high temperature cumulant expansion approximating the free energy of folding. The effect of cumulative point mutations on these designed proteins is studied under neutral condition. The robustness, protein’s ability to tolerate random point mutations is determined with a selective pressure of stability (ΔΔG) for the theory designed sequences, which are found to be more robust than that of Monte Carlo and mean-field-biased Monte Carlo generated sequences. The results show that this foldability criterion selects viable protein sequences more effectively compared to the Monte Carlo method, which has a marked effect on how the selective pressure shapes the evolutionary sequence space. These observations may impact de novo sequence design and its applications in protein engineering.

The local phase transitions of the solvent in the neighborhood of a solvophobic polymer at high pressures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Budkov, Yu. A., E-mail: urabudkov@rambler.ru; National Research University Higher School of Economics, Moscow; Department of Chemistry, Lomonosov Moscow State University, Moscow

2014-11-28

We investigate local phase transitions of the solvent in the neighborhood of a solvophobic polymer chain which is induced by a change of the polymer-solvent repulsion and the solvent pressure in the bulk solution. We describe the polymer in solution by the Edwards model, where the conditional partition function of the polymer chain at a fixed radius of gyration is described by a mean-field theory. The contributions of the polymer-solvent and the solvent-solvent interactions to the total free energy are described within the mean-field approximation. We obtain the total free energy of the solution as a function of the radiusmore » of gyration and the average solvent number density within the gyration volume. The resulting system of coupled equations is solved varying the polymer-solvent repulsion strength at high solvent pressure in the bulk. We show that the coil-globule (globule-coil) transition occurs accompanied by a local solvent evaporation (condensation) within the gyration volume.« less

WE-AB-209-07: Explicit and Convex Optimization of Plan Quality Metrics in Intensity-Modulated Radiation Therapy Treatment Planning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Engberg, L; KTH Royal Institute of Technology, Stockholm; Eriksson, K

Purpose: To formulate objective functions of a multicriteria fluence map optimization model that correlate well with plan quality metrics, and to solve this multicriteria model by convex approximation. Methods: In this study, objectives of a multicriteria model are formulated to explicitly either minimize or maximize a dose-at-volume measure. Given the widespread agreement that dose-at-volume levels play important roles in plan quality assessment, these objectives correlate well with plan quality metrics. This is in contrast to the conventional objectives, which are to maximize clinical goal achievement by relating to deviations from given dose-at-volume thresholds: while balancing the new objectives means explicitlymore » balancing dose-at-volume levels, balancing the conventional objectives effectively means balancing deviations. Constituted by the inherently non-convex dose-at-volume measure, the new objectives are approximated by the convex mean-tail-dose measure (CVaR measure), yielding a convex approximation of the multicriteria model. Results: Advantages of using the convex approximation are investigated through juxtaposition with the conventional objectives in a computational study of two patient cases. Clinical goals of each case respectively point out three ROI dose-at-volume measures to be considered for plan quality assessment. This is translated in the convex approximation into minimizing three mean-tail-dose measures. Evaluations of the three ROI dose-at-volume measures on Pareto optimal plans are used to represent plan quality of the Pareto sets. Besides providing increased accuracy in terms of feasibility of solutions, the convex approximation generates Pareto sets with overall improved plan quality. In one case, the Pareto set generated by the convex approximation entirely dominates that generated with the conventional objectives. Conclusion: The initial computational study indicates that the convex approximation outperforms the conventional objectives in aspects of accuracy and plan quality.« less

Performance of FFT methods in local gravity field modelling

NASA Technical Reports Server (NTRS)

Forsberg, Rene; Solheim, Dag

1989-01-01

Fast Fourier transform (FFT) methods provide a fast and efficient means of processing large amounts of gravity or geoid data in local gravity field modelling. The FFT methods, however, has a number of theoretical and practical limitations, especially the use of flat-earth approximation, and the requirements for gridded data. In spite of this the method often yields excellent results in practice when compared to other more rigorous (and computationally expensive) methods, such as least-squares collocation. The good performance of the FFT methods illustrate that the theoretical approximations are offset by the capability of taking into account more data in larger areas, especially important for geoid predictions. For best results good data gridding algorithms are essential. In practice truncated collocation approaches may be used. For large areas at high latitudes the gridding must be done using suitable map projections such as UTM, to avoid trivial errors caused by the meridian convergence. The FFT methods are compared to ground truth data in New Mexico (xi, eta from delta g), Scandinavia (N from delta g, the geoid fits to 15 cm over 2000 km), and areas of the Atlantic (delta g from satellite altimetry using Wiener filtering). In all cases the FFT methods yields results comparable or superior to other methods.

On the effect of the degeneracy among dark energy parameters

NASA Astrophysics Data System (ADS)

Gong, Yungui; Gao, Qing

2014-01-01

The dynamics of scalar fields as dark energy is well approximated by some general relations between the equation of state parameter and the fractional energy density . Based on the approximation, for slowly rolling scalar fields, we derived the analytical expressions of which reduce to the popular Chevallier-Polarski-Linder parametrization with an explicit degeneracy relation between and . The models approximate the dynamics of scalar fields well and help eliminate the degeneracies among , , and . With the explicit degeneracy relations, we test their effects on the constraints of the cosmological parameters. We find that: (1) The analytical relations between and for the two models are consistent with observational data. (2) The degeneracies have little effect on . (3) The error of was reduced about 30 % with the degeneracy relations.

Self-consistent field calculations of conductance through conjugated molecules at finite bias

NASA Astrophysics Data System (ADS)

Paulsson, Magnus; Stafström, Sven

2001-03-01

Conductance through conjugated molecules have previously been calculated for a large number of systems using the Landauer formula but only a few calculations have included charging effects. In this study we present calculations in the mean field approximation of the conductance of metal-molecule-metal systems using two different kinds of molecules for a large number of configurations and applied biases. The molecules are described in the Pariser-Parr Pople model. Current-voltage (I-V) characteristics and charge distribution of the molecule connected by one dimensional leads to reservoirs is solved within the Hartree-Fock approximation. Charging of the molecule occurs when the chemical potential of the reservoirs approach the resonant tunneling levels. The ensuing potential difference, due to the charging, shifts the tunneling peaks which affects the I-V curves considerably. Asymmetrical interaction with the metal leads, e.g. molecule on a metal surface contacted with an STM-tip, also give asymmetrical I-V curves where the potential of the molecule is shown to more closely follow the potential of the surface. Negative differential conductance is discussed in systems consisting of two weakly coupled molecules.

Point spread functions and deconvolution of ultrasonic images.

PubMed

Dalitz, Christoph; Pohle-Fröhlich, Regina; Michalk, Thorsten

2015-03-01

This article investigates the restoration of ultrasonic pulse-echo C-scan images by means of deconvolution with a point spread function (PSF). The deconvolution concept from linear system theory (LST) is linked to the wave equation formulation of the imaging process, and an analytic formula for the PSF of planar transducers is derived. For this analytic expression, different numerical and analytic approximation schemes for evaluating the PSF are presented. By comparing simulated images with measured C-scan images, we demonstrate that the assumptions of LST in combination with our formula for the PSF are a good model for the pulse-echo imaging process. To reconstruct the object from a C-scan image, we compare different deconvolution schemes: the Wiener filter, the ForWaRD algorithm, and the Richardson-Lucy algorithm. The best results are obtained with the Richardson-Lucy algorithm with total variation regularization. For distances greater or equal twice the near field distance, our experiments show that the numerically computed PSF can be replaced with a simple closed analytic term based on a far field approximation.

Feedback control of an interacting Bose-Einstein condensate using phase-contrast imaging

NASA Astrophysics Data System (ADS)

Szigeti, S. S.; Hush, M. R.; Carvalho, A. R. R.; Hope, J. J.

2010-10-01

The linewidth of an atom laser is limited by density fluctuations in the Bose-Einstein condensate (BEC) from which the atom laser beam is outcoupled. In this paper we show that a stable spatial mode for an interacting BEC can be generated using a realistic control scheme that includes the effects of the measurement backaction. This model extends the feedback theory, based on a phase-contrast imaging setup, presented by Szigeti, Hush, Carvalho, and Hope [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.80.013614 80, 013614 (2009)]. In particular, it is applicable to a BEC with large interatomic interactions and solves the problem of inadequacy of the mean-field (coherent state) approximation by utilizing a fixed number state approximation. Our numerical analysis shows the control to be more effective for a condensate with a large nonlinearity.

Contribution of Twinning to Low Strain Deformation in a Mg Alloy

NASA Astrophysics Data System (ADS)

Barnett, Matthew R.; Ghaderi, Alireza; Robson, Joseph D.

2014-07-01

Deformation twinning plays an important role in the yielding of extruded magnesium alloys, especially when loaded in compression along the extrusion axis. The magnitude of this contribution is not accurately known. The present study employs electron backscatter diffraction to reveal the influence of grain orientation on twin-volume fraction for alloy AZ31 tested in compression to strains between 0.008 and 0.015. For these strains, it is seen that approximately 45 pct of the deformation can be attributed to "tensile" twinning. The variation of twin-volume fraction over different orientation classes correlates closely with the maximum Schmid factors for both tensile twinning and basal slip. These effects are readily explained quantitatively using a mean field crystal plasticity model without recourse to stochastic effects. Encouraged by this, we introduce an analytical approximation based on the uniformity of (axial) work.

Epidemic thresholds for bipartite networks

NASA Astrophysics Data System (ADS)

Hernández, D. G.; Risau-Gusman, S.

2013-11-01

It is well known that sexually transmitted diseases (STD) spread across a network of human sexual contacts. This network is most often bipartite, as most STD are transmitted between men and women. Even though network models in epidemiology have quite a long history now, there are few general results about bipartite networks. One of them is the simple dependence, predicted using the mean field approximation, between the epidemic threshold and the average and variance of the degree distribution of the network. Here we show that going beyond this approximation can lead to qualitatively different results that are supported by numerical simulations. One of the new features, that can be relevant for applications, is the existence of a critical value for the infectivity of each population, below which no epidemics can arise, regardless of the value of the infectivity of the other population.

A new equation of state Based on Nuclear Statistical Equilibrium for Core-Collapse Simulations

NASA Astrophysics Data System (ADS)

Furusawa, Shun; Yamada, Shoichi; Sumiyoshi, Kohsuke; Suzuki, Hideyuki

2012-09-01

We calculate a new equation of state for baryons at sub-nuclear densities for the use in core-collapse simulations of massive stars. The formulation is the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by relativistic mean field theory for nucleons and the mass formula for nuclei with atomic number up to ~ 1000. We have also taken into account the pasta phase. We find that the free energy and other thermodynamical quantities are not very different from those given in the standard EOSs that adopt the single nucleus approximation. On the other hand, the average mass is systematically different, which may have an important effect on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores.

Low-Energy Excitation Spectra in the Excitonic Phase of Cobalt Oxides

NASA Astrophysics Data System (ADS)

Yamaguchi, Tomoki; Sugimoto, Koudai; Ohta, Yukinori

2017-04-01

We study the excitonic phase and low-energy excitation spectra of perovskite cobalt oxides. Constructing the five-orbital Hubbard model defined on the three-dimensional cubic lattice for the 3d bands of Pr0.5Ca0.5CoO3, we calculate the excitonic susceptibility in the normal state in the random-phase approximation (RPA) to show the presence of the instability toward excitonic condensation. On the basis of the excitonic ground state with a magnetic multipole obtained in the mean-field approximation, we calculate the dynamical susceptibility of the excitonic phase in the RPA and find that there appear a gapless collective excitation in the spin-transverse mode (Goldstone mode) and a gapful collective excitation in the spin-longitudinal mode (Higgs mode). The experimental relevance of our results is discussed.

A classical density functional theory for the asymmetric restricted primitive model of ionic liquids

NASA Astrophysics Data System (ADS)

Lu, Hongduo; Nordholm, Sture; Woodward, Clifford E.; Forsman, Jan

2018-05-01

A new three-parameter (valency, ion size, and charge asymmetry) model, the asymmetric restricted primitive model (ARPM) of ionic liquids, has recently been proposed. Given that ionic liquids generally are composed of monovalent species, the ARPM effectively reduces to a two-parameter model. Monte Carlo (MC) simulations have demonstrated that the ARPM is able to reproduce key properties of room temperature ionic liquids (RTILs) in bulk and at charged surfaces. The relatively modest complexity of the model raises the possibility, which is explored here, that a classical density functional theory (DFT) could resolve its properties. This is relevant because it might generate great improvements in terms of both numerical efficiency and understanding in the continued research of RTILs and their applications. In this report, a DFT for rod-like molecules is proposed as an approximate theoretical tool for an ARPM fluid. Borrowing data on the ion pair fraction from a single bulk simulation, the ARPM is modelled as a mixture of dissociated ions and connected ion pairs. We have specifically studied an ARPM where the hard-sphere diameter is 5 Å, with the charge located 1 Å from the hard-sphere centre. We focus on fluid structure and electrochemical behaviour of this ARPM fluid, into which a model electrode is immersed. The latter is modelled as a perfect conductor, and surface polarization is handled by the method of image charges. Approximate methods, which were developed in an earlier study, to take image interactions into account, are also incorporated in the DFT. We make direct numerical comparisons between DFT predictions and corresponding simulation data. The DFT theory is implemented both in the normal mean field form with respect to the electrostatic interactions and in a correlated form based on hole formation by both steric repulsions and ion-ion Coulomb interactions. The results clearly show that ion-ion correlations play a very important role in the screening of the charged surfaces by our ARPM ionic liquid. We have studied electrostatic potentials and ion density profiles as well the differential capacitance. The mean-field DFT fails to reproduce these properties, but the inclusion of ion-ion correlation by a simple approximate treatment yields quite reasonable agreement with the corresponding simulation results. An interesting finding is that there appears to be a surface phase transition at relatively low surface charge which is readily explored by DFT, but seen also in the MC simulations at somewhat higher asymmetry.

Statistical simulations of the dust foreground to cosmic microwave background polarization

NASA Astrophysics Data System (ADS)

Vansyngel, F.; Boulanger, F.; Ghosh, T.; Wandelt, B.; Aumont, J.; Bracco, A.; Levrier, F.; Martin, P. G.; Montier, L.

2017-07-01

The characterization of the dust polarization foreground to the cosmic microwave background (CMB) is a necessary step toward the detection of the B-mode signal associated with primordial gravitational waves. We present a method to simulate maps of polarized dust emission on the sphere that is similar to the approach used for CMB anisotropies. This method builds on the understanding of Galactic polarization stemming from the analysis of Planck data. It relates the dust polarization sky to the structure of the Galactic magnetic field and its coupling with interstellar matter and turbulence. The Galactic magnetic field is modeled as a superposition of a mean uniform field and a Gaussian random (turbulent) component with a power-law power spectrum of exponent αM. The integration along the line of sight carried out to compute Stokes maps is approximated by a sum over a small number of emitting layers with different realizations of the random component of the magnetic field. The model parameters are constrained to fit the power spectra of dust polarization EE, BB, and TE measured using Planck data. We find that the slopes of the E and B power spectra of dust polarization are matched for αM = -2.5, an exponent close to that measured for total dust intensity but larger than the Kolmogorov exponent - 11/3. The model allows us to compute multiple realizations of the Stokes Q and U maps for different realizations of the random component of the magnetic field, and to quantify the variance of dust polarization spectra for any given sky area outside of the Galactic plane. The simulations reproduce the scaling relation between the dust polarization power and the mean total dust intensity including the observed dispersion around the mean relation. We also propose a method to carry out multifrequency simulations, including the decorrelation measured recently by Planck, using a given covariance matrix of the polarization maps. These simulations are well suited to optimize component separation methods and to quantify the confidence with which the dust and CMB B-modes can be separated in present and future experiments. We also provide an astrophysical perspective on our phenomenological modeling of the dust polarization spectra.

A new baryonic equation of state at sub-nuclear densities for core-collapse simulations

NASA Astrophysics Data System (ADS)

Furusawa, Shun; Yamada, Shoichi; Sumiyoshi, Kohsuke; Suzuki, Hideyuki

2012-11-01

We construct a new equation of state for baryons at sub-nuclear densities for the use in core-collapse simulations of massive stars. The formulation is based on the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by using relativistic mean field theory for nucleons and the mass formula for nuclei with atomic number up to ~ 1000. We have also taken into account the pasta phase. We find that the free energy and other thermodynamical quantities are not very different from those given in the standard EOSs that adopt the single nucleus approximation. On the other hand, the average mass is systematically different, which may have an important effect to the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. It is also interesting that the root mean square of the mass number is not very different from the average mass number, since the former is important for the evaluation of coherent scattering rates on nuclei but has been unavailable so far.

Steady induction effects in geomagnetism. Part 1C: Geomagnetic estimation of steady surficial core motions: Application to the definitive geomagnetic reference field models

NASA Technical Reports Server (NTRS)

Voorhies, Coerte V.

1993-01-01

In the source-free mantle/frozen-flux core magnetic earth model, the non-linear inverse steady motional induction problem was solved using the method presented in Part 1B. How that method was applied to estimate steady, broad-scale fluid velocity fields near the top of Earth's core that induce the secular change indicated by the Definitive Geomagnetic Reference Field (DGRF) models from 1945 to 1980 are described. Special attention is given to the derivation of weight matrices for the DGRF models because the weights determine the apparent significance of the residual secular change. The derived weight matrices also enable estimation of the secular change signal-to-noise ratio characterizing the DGRF models. Two types of weights were derived in 1987-88: radial field weights for fitting the evolution of the broad-scale portion of the radial geomagnetic field component at Earth's surface implied by the DGRF's, and general weights for fitting the evolution of the broad-scale portion of the scalar potential specified by these models. The difference is non-trivial because not all the geomagnetic data represented by the DGRF's constrain the radial field component. For radial field weights (or general weights), a quantitatively acceptable explication of broad-scale secular change relative to the 1980 Magsat epoch must account for 99.94271 percent (or 99.98784 percent) of the total weighted variance accumulated therein. Tolerable normalized root-mean-square weighted residuals of 2.394 percent (or 1.103 percent) are less than the 7 percent errors expected in the source-free mantle/frozen-flux core approximation.

Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models.

PubMed

Antonov, N V; Gulitskiy, N M; Kostenko, M M; Malyshev, A V

2018-03-01

In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time. This indicates that the Galilean symmetry of the model violated by the "colored" random force is restored in the inertial range. This regime corresponds to the only nontrivial fixed point of the renormalization group equation. The stability of this point depends on the relation between the exponents in the energy spectrum E∝k^{1-y} and the dispersion law ω∝k^{2-η}. The second analyzed problem is the passive advection of a scalar field by this velocity ensemble. Correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. We demonstrate that in accordance with Kolmogorov's hypothesis of the local symmetry restoration the main contribution to the operator product expansion is given by the isotropic operator, while anisotropic terms should be considered only as corrections.

Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Malyshev, A. V.

2018-03-01

In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time. This indicates that the Galilean symmetry of the model violated by the "colored" random force is restored in the inertial range. This regime corresponds to the only nontrivial fixed point of the renormalization group equation. The stability of this point depends on the relation between the exponents in the energy spectrum E ∝k1 -y and the dispersion law ω ∝k2 -η . The second analyzed problem is the passive advection of a scalar field by this velocity ensemble. Correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. We demonstrate that in accordance with Kolmogorov's hypothesis of the local symmetry restoration the main contribution to the operator product expansion is given by the isotropic operator, while anisotropic terms should be considered only as corrections.

Electrodiffusion Models of Neurons and Extracellular Space Using the Poisson-Nernst-Planck Equations—Numerical Simulation of the Intra- and Extracellular Potential for an Axon Model

PubMed Central

Pods, Jurgis; Schönke, Johannes; Bastian, Peter

2013-01-01

In neurophysiology, extracellular signals—as measured by local field potentials (LFP) or electroencephalography—are of great significance. Their exact biophysical basis is, however, still not fully understood. We present a three-dimensional model exploiting the cylinder symmetry of a single axon in extracellular fluid based on the Poisson-Nernst-Planck equations of electrodiffusion. The propagation of an action potential along the axonal membrane is investigated by means of numerical simulations. Special attention is paid to the Debye layer, the region with strong concentration gradients close to the membrane, which is explicitly resolved by the computational mesh. We focus on the evolution of the extracellular electric potential. A characteristic up-down-up LFP waveform in the far-field is found. Close to the membrane, the potential shows a more intricate shape. A comparison with the widely used line source approximation reveals similarities and demonstrates the strong influence of membrane currents. However, the electrodiffusion model shows another signal component stemming directly from the intracellular electric field, called the action potential echo. Depending on the neuronal configuration, this might have a significant effect on the LFP. In these situations, electrodiffusion models should be used for quantitative comparisons with experimental data. PMID:23823244

Density functional plus dynamical mean-field theory of the metal-insulator transition in early transition-metal oxides

NASA Astrophysics Data System (ADS)

Dang, Hung T.; Ai, Xinyuan; Millis, Andrew J.; Marianetti, Chris A.

2014-09-01

The combination of density functional theory and single-site dynamical mean-field theory, using both Hartree and full continuous-time quantum Monte Carlo impurity solvers, is used to study the metal-insulator phase diagram of perovskite transition-metal oxides of the form ABO3 with a rare-earth ion A =Sr, La, Y and transition metal B =Ti, V, Cr. The correlated subspace is constructed from atomiclike d orbitals defined using maximally localized Wannier functions derived from the full p-d manifold; for comparison, results obtained using a projector method are also given. Paramagnetic DFT + DMFT computations using full charge self-consistency along with the standard "fully localized limit" (FLL) double counting are shown to incorrectly predict that LaTiO3, YTiO3, LaVO3, and SrMnO3 are metals. A more general examination of the dependence of physical properties on the mean p-d energy splitting, the occupancy of the correlated d states, the double-counting correction, and the lattice structure demonstrates the importance of charge-transfer physics even in the early transition-metal oxides and elucidates the factors underlying the failure of the standard approximations. If the double counting is chosen to produce a p-d splitting consistent with experimental spectra, single-site dynamical mean-field theory provides a reasonable account of the materials properties. The relation of the results to those obtained from "d-only" models in which the correlation problem is based on the frontier orbital p-d antibonding bands is determined. It is found that if an effective interaction U is properly chosen the d-only model provides a good account of the physics of the d1 and d2 materials.

Spatiotemporal characterization of soil moisture fields in agricultural areas using cosmic-ray neutron probes and data fusion

NASA Astrophysics Data System (ADS)

Franz, Trenton; Wang, Tiejun

2015-04-01

Approximately 40% of global food production comes from irrigated agriculture. With the increasing demand for food even greater pressures will be placed on water resources within these systems. In this work we aimed to characterize the spatial and temporal patterns of soil moisture at the field-scale (~500 m) using the newly developed cosmic-ray neutron rover near Waco, NE USA. Here we mapped soil moisture of 144 quarter section fields (a mix of maize, soybean, and natural areas) each week during the 2014 growing season (May to September). The 12 by 12 km study domain also contained three stationary cosmic-ray neutron probes for independent validation of the rover surveys. Basic statistical analysis of the domain indicated a strong relationship between the mean and variance of soil moisture at several averaging scales. The relationships between the mean and higher order moments were not significant. Scaling analysis indicated strong power law behavior between the variance of soil moisture and averaging area with minimal dependence of mean soil moisture on the slope of the power law function. In addition, we combined the data from the three stationary cosmic-ray neutron probes and mobile surveys using linear regression to derive a daily soil moisture product at 1, 3, and 12 km spatial resolutions for the entire growing season. The statistical relationships derived from the rover dataset offer a novel set of observations that will be useful in: 1) calibrating and validating land surface models, 2) calibrating and validating crop models, 3) soil moisture covariance estimates for statistical downscaling of remote sensing products such as SMOS and SMAP, and 4) provide daily center-pivot scale mean soil moisture data for optimal irrigation timing and volume amounts.

Active matter beyond mean-field: ring-kinetic theory for self-propelled particles.

PubMed

Chou, Yen-Liang; Ihle, Thomas

2015-02-01

Recently, Hanke et al. [Phys. Rev. E 88, 052309 (2013)] showed that mean-field kinetic theory fails to describe collective motion in soft active colloids and that correlations must not be neglected. Correlation effects are also expected to be essential in systems of biofilaments driven by molecular motors and in swarms of midges. To obtain correlations in an active matter system from first principles, we derive a ring-kinetic theory for Vicsek-style models of self-propelled agents from the exact N-particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle precollisional correlations and cluster formation, which are both important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small-density expansion of the collision operator and derive the first two equations of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. An algorithm is presented that numerically solves the evolution equation for the two-particle correlations on a lattice. Agent-based simulations are performed and informative quantities such as orientational and density correlation functions are compared with those obtained by ring-kinetic theory. Excellent quantitative agreement between simulations and theory is found at not-too-small noises and mean free paths. This shows that there are parameter ranges in Vicsek-like models where the correlated closure of the BBGKY hierarchy gives correct and nontrivial results. We calculate the dependence of the orientational correlations on distance in the disordered phase and find that it seems to be consistent with a power law with an exponent around -1.8, followed by an exponential decay. General limitations of the kinetic theory and its numerical solution are discussed.

Exactly solvable relativistic model with the anomalous interaction

NASA Astrophysics Data System (ADS)

Ferraro, Elena; Messina, Antonino; Nikitin, A. G.

2010-04-01

A special class of Dirac-Pauli equations with time-like vector potentials of an external field is investigated. An exactly solvable relativistic model describing the anomalous interaction of a neutral Dirac fermion with a cylindrically symmetric external electromagnetic field is presented. The related external field is a superposition of the electric field generated by a charged infinite filament and the magnetic field generated by a straight line current. In the nonrelativistic approximation the considered model is reduced to the integrable Pron’ko-Stroganov model.

Schlieren imaging of the standing wave field in an ultrasonic acoustic levitator

NASA Astrophysics Data System (ADS)

Rendon, Pablo Luis; Boullosa, Ricardo R.; Echeverria, Carlos; Porta, David

2015-11-01

We consider a model of a single axis acoustic levitator consisting of two cylinders immersed in air and directed along the same axis. The first cylinder has a flat termination and functions as a sound emitter, and the second cylinder, which is simply a refector, has the side facing the first cylinder cut out by a spherical surface. By making the first cylinder vibrate at ultrasonic frequencies a standing wave is produced in the air between the cylinders which makes it possible, by means of the acoustic radiation pressure, to levitate one or several small objects of different shapes, such as spheres or disks. We use schlieren imaging to observe the acoustic field resulting from the levitation of one or several objects, and compare these results to previous numerical approximations of the field obtained using a finite element method. The authors acknowledge financial support from DGAPA-UNAM through project PAPIIT IN109214.

Multiscale Analysis of Rapidly Rotating Dynamo Simulations

NASA Astrophysics Data System (ADS)

Orvedahl, R.; Calkins, M. A.; Featherstone, N. A.

2017-12-01

The magnetic field of the planets and stars are generated by dynamo action in their electrically conducting fluid interiors. Numerical models of this process solve the fundamental equations of magnetohydrodynamics driven by convection in a rotating spherical shell. Rotation plays an important role in modifying the resulting convective flows and the self-generated magnetic field. We present results of simulating rapidly rotating systems that are unstable to dynamo action. We use the pseudo-spectral code Rayleigh to generate a suite of direct numerical simulations. Each simulation uses the Boussinesq approximation and is characterized by an Ekman number (Ek=ν /Ω L2) of 10-5. We vary the degree of convective forcing to obtain a range of convective Rossby numbers. The resulting flows and magnetic structures are analyzed using a Reynolds decomposition. We determine the relative importance of each term in the scale-separated governing equations and estimate the relevant spatial scales responsible for generating the mean magnetic field.

An atomic mean-field spin-orbit approach within exact two-component theory for a non-perturbative treatment of spin-orbit coupling

NASA Astrophysics Data System (ADS)

Liu, Junzi; Cheng, Lan

2018-04-01

An atomic mean-field (AMF) spin-orbit (SO) approach within exact two-component theory (X2C) is reported, thereby exploiting the exact decoupling scheme of X2C, the one-electron approximation for the scalar-relativistic contributions, the mean-field approximation for the treatment of the two-electron SO contribution, and the local nature of the SO interactions. The Hamiltonian of the proposed SOX2CAMF scheme comprises the one-electron X2C Hamiltonian, the instantaneous two-electron Coulomb interaction, and an AMF SO term derived from spherically averaged Dirac-Coulomb Hartree-Fock calculations of atoms; no molecular relativistic two-electron integrals are required. Benchmark calculations for bond lengths, harmonic frequencies, dipole moments, and electric-field gradients for a set of diatomic molecules containing elements across the periodic table show that the SOX2CAMF scheme offers a balanced treatment for SO and scalar-relativistic effects and appears to be a promising candidate for applications to heavy-element containing systems. SOX2CAMF coupled-cluster calculations of molecular properties for bismuth compounds (BiN, BiP, BiF, BiCl, and BiI) are also presented and compared with experimental results to further demonstrate the accuracy and applicability of the SOX2CAMF scheme.

Self-consistent mean-field approach to the statistical level density in spherical nuclei

NASA Astrophysics Data System (ADS)

Kolomietz, V. M.; Sanzhur, A. I.; Shlomo, S.

2018-06-01

A self-consistent mean-field approach within the extended Thomas-Fermi approximation with Skyrme forces is applied to the calculations of the statistical level density in spherical nuclei. Landau's concept of quasiparticles with the nucleon effective mass and the correct description of the continuum states for the finite-depth potentials are taken into consideration. The A dependence and the temperature dependence of the statistical inverse level-density parameter K is obtained in a good agreement with experimental data.

Combining global and local approximations

NASA Technical Reports Server (NTRS)

Haftka, Raphael T.

1991-01-01

A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model.

Accurate estimates of 3D Ising critical exponents using the coherent-anomaly method

NASA Astrophysics Data System (ADS)

Kolesik, Miroslav; Suzuki, Masuo

1995-02-01

An analysis of the critical behavior of the three-dimensional Ising model using the coherent-anomaly method (CAM) is presented. Various sources of errors in CAM estimates of critical exponents are discussed, and an improved scheme for the CAM data analysis is tested. Using a set of mean-field type approximations based on the variational series expansion approach, accuracy comparable to the most precise conventional methods has been achieved. Our results for the critical exponents are given by α = 0.108(5), β = 0.327(4), γ = 1.237(4) and δ = 4.77(5).

Pressure and Temperature Sensors Using Two Spin Crossover Materials.

PubMed

Jureschi, Catalin-Maricel; Linares, Jorge; Boulmaali, Ayoub; Dahoo, Pierre Richard; Rotaru, Aurelian; Garcia, Yann

2016-02-02

The possibility of a new design concept for dual spin crossover based sensors for concomitant detection of both temperature and pressure is presented. It is conjectured from numerical results obtained by mean field approximation applied to a Ising-like model that using two different spin crossover compounds containing switching molecules with weak elastic interactions it is possible to simultaneously measure P and T. When the interaction parameters are optimized, the spin transition is gradual and for each spin crossover compounds, both temperature and pressure values being identified from their optical densities. This concept offers great perspectives for smart sensing devices.

Multipole ordering and collective excitations in the excitonic phase of Pr0.5Ca0.5CoO3

NASA Astrophysics Data System (ADS)

Yamaguchi, Tomoki; Sugimoto, Koudai; Ohta, Yukinori

2018-05-01

As an extension of our previous paper (Yamaguchi et al., 2017) [24], we study the carrier doping dependence of the excitonic condensation in Pr0.5Ca0.5CoO3 using the random-phase and mean-field approximations for the realistic five-orbital Hubbard model. We show that the spin-triplet excitonic phase with a magnetic multipole ordering is stable against the doping of carriers in a considerable range around Co3+ (or 3d6). We discuss experimental relevance of our results.

Mean-field dynamo action in renovating shearing flows.

PubMed

Kolekar, Sanved; Subramanian, Kandaswamy; Sridhar, S

2012-08-01

We study mean-field dynamo action in renovating flows with finite and nonzero correlation time (τ) in the presence of shear. Previous results obtained when shear was absent are generalized to the case with shear. The question of whether the mean magnetic field can grow in the presence of shear and nonhelical turbulence, as seen in numerical simulations, is examined. We show in a general manner that, if the motions are strictly nonhelical, then such mean-field dynamo action is not possible. This result is not limited to low (fluid or magnetic) Reynolds numbers nor does it use any closure approximation; it only assumes that the flow renovates itself after each time interval τ. Specifying to a particular form of the renovating flow with helicity, we recover the standard dispersion relation of the α(2)Ω dynamo, in the small τ or large wavelength limit. Thus mean fields grow even in the presence of rapidly growing fluctuations, surprisingly, in a manner predicted by the standard quasilinear closure, even though such a closure is not strictly justified. Our work also suggests the possibility of obtaining mean-field dynamo growth in the presence of helicity fluctuations, although having a coherent helicity will be more efficient.

Parameterized source term in the diffusion approximation for enhanced near-field modeling of collimated light

NASA Astrophysics Data System (ADS)

Jia, Mengyu; Wang, Shuang; Chen, Xueying; Gao, Feng; Zhao, Huijuan

2016-03-01

Most analytical methods for describing light propagation in turbid medium exhibit low effectiveness in the near-field of a collimated source. Motivated by the Charge Simulation Method in electromagnetic theory as well as the established discrete source based modeling, we have reported on an improved explicit model, referred to as "Virtual Source" (VS) diffuse approximation (DA), to inherit the mathematical simplicity of the DA while considerably extend its validity in modeling the near-field photon migration in low-albedo medium. In this model, the collimated light in the standard DA is analogously approximated as multiple isotropic point sources (VS) distributed along the incident direction. For performance enhancement, a fitting procedure between the calculated and realistic reflectances is adopted in the nearfield to optimize the VS parameters (intensities and locations). To be practically applicable, an explicit 2VS-DA model is established based on close-form derivations of the VS parameters for the typical ranges of the optical parameters. The proposed VS-DA model is validated by comparing with the Monte Carlo simulations, and further introduced in the image reconstruction of the Laminar Optical Tomography system.

Applications of the PUFF model to forecasts of volcanic clouds dispersal from Etna and Vesuvio

NASA Astrophysics Data System (ADS)

Daniele, P.; Lirer, L.; Petrosino, P.; Spinelli, N.; Peterson, R.

2009-05-01

PUFF is a numerical volcanic ash tracking model developed to simulate the behaviour of ash clouds in the atmosphere. The model uses wind field data provided by meteorological models and adds dispersion and sedimentation physics to predict the evolution of the cloud once it reaches thermodynamic equilibrium with the atmosphere. The software is intended for use in emergency response situations during an eruption to quickly forecast the position and trajectory of the ash cloud in the near (˜1-72 h) future. In this paper, we describe the first application of the PUFF model in forecasting volcanic ash dispersion from the Etna and Vesuvio volcanoes. We simulated the daily occurrence of an eruptive event of Etna utilizing ash cloud parameters describing the paroxysm of 22nd July 1998 and wind field data for the 1st September 2005-31st December 2005 time span from the Global Forecast System (GFS) model at the approximate location of the Etna volcano (38N 15E). The results show that volcanic ash particles are dispersed in a range of directions in response to changing wind field at various altitudes and that the ash clouds are mainly dispersed toward the east and southeast, although the exact trajectory is highly variable, and can change within a few hours. We tested the sensitivity of the model to the mean particle grain size and found that an increased concentration of ash particles in the atmosphere results when the mean grain size is decreased. Similarly, a dramatic variation in dispersion results when the logarithmic standard deviation of the particle-size distribution is changed. Additionally, we simulated the occurrence of an eruptive event at both Etna and Vesuvio, using the same parameters describing the initial volcanic plume, and wind field data recorded for 1st September 2005, at approximately 38N 15E for Etna and 41N 14E for Vesuvio. The comparison of the two simulations indicates that identical eruptions occurring at the same time at the two volcanic centres display significantly different dispersal axes as a consequence of the different local wind field acting at the respective eruptive vents. At the Vesuvio the volcano, a plinian eruptive event with the dynamical parameters of the 79 A.D. eruption was simulated daily for one year, from 1st July 2005 to 30th June 2006. The statistical processing of results points out that, although in most cases the ash cloud dispersal encompasses many different areas, generally the easterly southeasterly direction is preferred. Our results highlight the significant role of wind field trends in influencing the distribution of ash particles from eruptive columns and prove that the dynamical parameters that most influence the variability of plume dispersal are the duration of the eruption and the maximum column height. Finally, the possible use of cloud simulations for refining hazard maps of areas exposed to volcanic ash dispersal is proposed.

Model of non-stationary, inhomogeneous turbulence

DOE PAGES

Bragg, Andrew D.; Kurien, Susan; Clark, Timothy T.

2016-07-08

Here, we compare results from a spectral model for non-stationary, inhomogeneous turbulence (Besnard et al. in Theor Comp Fluid Dyn 8:1–35, 1996) with direct numerical simulation (DNS) data of a shear-free mixing layer (SFML) (Tordella et al. in Phys Rev E 77:016309, 2008). The SFML is used as a test case in which the efficacy of the model closure for the physical-space transport of the fluid velocity field can be tested in a flow with inhomogeneity, without the additional complexity of mean-flow coupling. The model is able to capture certain features of the SFML quite well for intermediate to longmore » times, including the evolution of the mixing-layer width and turbulent kinetic energy. At short-times, and for more sensitive statistics such as the generation of the velocity field anisotropy, the model is less accurate. We propose two possible causes for the discrepancies. The first is the local approximation to the pressure-transport and the second is the a priori spherical averaging used to reduce the dimensionality of the solution space of the model, from wavevector to wavenumber space. DNS data are then used to gauge the relative importance of both possible deficiencies in the model.« less

Generalization of the Last Scattering Approximation for the Second Solar Spectrum Modeling: The Ca I 4227 Å Line as a Case Study

NASA Astrophysics Data System (ADS)

Anusha, L. S.; Nagendra, K. N.; Stenflo, J. O.; Bianda, M.; Sampoorna, M.; Frisch, H.; Holzreuter, R.; Ramelli, R.

2010-08-01

To model the second solar spectrum (the linearly polarized spectrum of the Sun that is due to coherent scattering processes), one needs to solve the polarized radiative transfer (RT) equation. For strong resonance lines, partial frequency redistribution (PRD) effects must be accounted for, which make the problem computationally demanding. The "last scattering approximation" (LSA) is a concept that has been introduced to make this highly complex problem more tractable. An earlier application of a simple LSA version could successfully model the wings of the strong Ca I 4227 Å resonance line in Stokes Q/I (fractional linear polarization), but completely failed to reproduce the observed Q/I peak in the line core. Since the magnetic field signatures from the Hanle effect only occur in the line core, we need to generalize the existing LSA approach if it is to be useful for the diagnostics of chromospheric and turbulent magnetic fields. In this paper, we explore three different approximation levels for LSA and compare each of them with the benchmark represented by the solution of the full polarized RT, including PRD effects. The simplest approximation level is LSA-1, which uses the observed center-to-limb variation of the intensity profile to obtain the anisotropy of the radiation field at the surface, without solving any transfer equation. In contrast, the next two approximation levels use the solution of the unpolarized transfer equation to derive the anisotropy of the incident radiation field and use it as an input. In the case of LSA-2, the anisotropy at level τλ = μ, the atmospheric level from which an observed photon is most likely to originate, is used. LSA-3, on the other hand, makes use of the full depth dependence of the radiation anisotropy. The Q/I formula for LSA-3 is obtained by keeping the first term in a series expansion of the Q-source function in powers of the mean number of scattering events. Computationally, LSA-1 is 21 times faster than LSA-2, which is 5 times faster than the more general LSA-3, which itself is 8 times faster than the polarized RT approach. A comparison of the calculated Q/I spectra with the RT benchmark shows excellent agreement for LSA-3, including good modeling of the Q/I core region with its PRD effects. In contrast, both LSA-1 and LSA-2 fail to model the core region. The RT and LSA-3 approaches are then applied to model the recently observed Q/I profile of the Ca I 4227 Å line in quiet regions of the Sun. Apart from a global scale factor both give a very good fit to the Q/I spectra for all the wavelengths, including the core peak and blend line depolarizations. We conclude that LSA-3 is an excellent substitute for the full polarized RT and can be used to interpret the second solar spectrum, including the Hanle effect with PRD. It also allows the techniques developed for unpolarized three-dimensional RT to be applied to the modeling of the second solar spectrum.

Role of spin-orbit coupling in the Kugel-Khomskii model on the honeycomb lattice

NASA Astrophysics Data System (ADS)

Koga, Akihisa; Nakauchi, Shiryu; Nasu, Joji

2018-03-01

We study the effective spin-orbital model for honeycomb-layered transition metal compounds, applying the second-order perturbation theory to the three-orbital Hubbard model with the anisotropic hoppings. This model is reduced to the Kitaev model in the strong spin-orbit coupling limit. Combining the cluster mean-field approximations with the exact diagonalization, we treat the Kugel-Khomskii type superexchange interaction and spin-orbit coupling on an equal footing to discuss ground-state properties. We find that a zigzag ordered state is realized in the model within nearest-neighbor interactions. We clarify how the ordered state competes with the nonmagnetic state, which is adiabatically connected to the quantum spin liquid state realized in a strong spin-orbit coupling limit. Thermodynamic properties are also addressed. The present paper should provide another route to account for the Kitaev-based magnetic properties in candidate materials.

Fisher waves and front roughening in a two-species invasion model with preemptive competition.

PubMed

O'Malley, L; Kozma, B; Korniss, G; Rácz, Z; Caraco, T

2006-10-01

We study front propagation when an invading species competes with a resident; we assume nearest-neighbor preemptive competition for resources in an individual-based, two-dimensional lattice model. The asymptotic front velocity exhibits an effective power-law dependence on the difference between the two species' clonal propagation rates (key ecological parameters). The mean-field approximation behaves similarly, but the power law's exponent slightly differs from the individual-based model's result. We also study roughening of the front, using the framework of nonequilibrium interface growth. Our analysis indicates that initially flat, linear invading fronts exhibit Kardar-Parisi-Zhang (KPZ) roughening in one transverse dimension. Further, this finding implies, and is also confirmed by simulations, that the temporal correction to the asymptotic front velocity is of O(t(-2/3)).

A numerical circulation model with topography for the Martian Southern Hemisphere

NASA Technical Reports Server (NTRS)

Mass, C.; Sagan, C.

1975-01-01

A quasi-geostrophic numerical model, including friction, radiation, and the observed planetary topography, is applied to the general circulation of the Martian atmosphere in the Southern Hemisphere at latitudes south of about 35 deg. Near equilibrium weather systems developed after about 5 model days. To avoid violating the quasi-geostrophic approximation, only 0.8 of the already smoothed relief was employed. Weather systems and velocity fields are strikingly tied to topography. A 2mb middle latitude jet stream is found of remarkably terrestrial aspect. Highest surface velocities, both horizontal and vertical, are predicted in western Hellas Planitia and eastern Argyre Planitia, which are observed to be preferred sites of origin of major Martian dust storms. Mean horizontal velocities and vertical velocities are found just above the surface velocity boundary layer.

Front dynamics and entanglement in the XXZ chain with a gradient

NASA Astrophysics Data System (ADS)

Eisler, Viktor; Bauernfeind, Daniel

2017-11-01

We consider the XXZ spin chain with a magnetic field gradient and study the profiles of the magnetization as well as the entanglement entropy. For a slowly varying field, it is shown that, by means of a local density approximation, the ground-state magnetization profile can be obtained with standard Bethe ansatz techniques. Furthermore, it is argued that the low-energy description of the theory is given by a Luttinger liquid with slowly varying parameters. This allows us to obtain a very good approximation of the entanglement profile using a recently introduced technique of conformal field theory in curved spacetime. Finally, the front dynamics is also studied after the gradient field has been switched off, following arguments of generalized hydrodynamics for integrable systems. While for the XX chain the hydrodynamic solution can be found analytically, the XXZ case appears to be more complicated and the magnetization profiles are recovered only around the edge of the front via an approximate numerical solution.

A semi-analytical study of positive corona discharge in wire-plane electrode configuration

NASA Astrophysics Data System (ADS)

Yanallah, K.; Pontiga, F.; Chen, J. H.

2013-08-01

Wire-to-plane positive corona discharge in air has been studied using an analytical model of two species (electrons and positive ions). The spatial distributions of electric field and charged species are obtained by integrating Gauss's law and the continuity equations of species along the Laplacian field lines. The experimental values of corona current intensity and applied voltage, together with Warburg's law, have been used to formulate the boundary condition for the electron density on the corona wire. To test the accuracy of the model, the approximate electric field distribution has been compared with the exact numerical solution obtained from a finite element analysis. A parametrical study of wire-to-plane corona discharge has then been undertaken using the approximate semi-analytical solutions. Thus, the spatial distributions of electric field and charged particles have been computed for different values of the gas pressure, wire radius and electrode separation. Also, the two dimensional distribution of ozone density has been obtained using a simplified plasma chemistry model. The approximate semi-analytical solutions can be evaluated in a negligible computational time, yet provide precise estimates of corona discharge variables.

Approximate analytic expression for the Skyrmions crystal

NASA Astrophysics Data System (ADS)

Grandi, Nicolás; Sturla, Mauricio

2018-01-01

We find approximate solutions for the two-dimensional nonlinear Σ-model with Dzyalioshinkii-Moriya term, representing magnetic Skyrmions. They are built in an analytic form, by pasting different approximate solutions found in different regions of space. We verify that our construction reproduces the phenomenology known from numerical solutions and Monte Carlo simulations, giving rise to a Skyrmion lattice at an intermediate range of magnetic field, flanked by spiral and spin-polarized phases for low and high magnetic fields, respectively.

Safe uses of Hill's model: an exact comparison with the Adair-Klotz model

PubMed Central

2011-01-01

Background The Hill function and the related Hill model are used frequently to study processes in the living cell. There are very few studies investigating the situations in which the model can be safely used. For example, it has been shown, at the mean field level, that the dose response curve obtained from a Hill model agrees well with the dose response curves obtained from a more complicated Adair-Klotz model, provided that the parameters of the Adair-Klotz model describe strongly cooperative binding. However, it has not been established whether such findings can be extended to other properties and non-mean field (stochastic) versions of the same, or other, models. Results In this work a rather generic quantitative framework for approaching such a problem is suggested. The main idea is to focus on comparing the particle number distribution functions for Hill's and Adair-Klotz's models instead of investigating a particular property (e.g. the dose response curve). The approach is valid for any model that can be mathematically related to the Hill model. The Adair-Klotz model is used to illustrate the technique. One main and two auxiliary similarity measures were introduced to compare the distributions in a quantitative way. Both time dependent and the equilibrium properties of the similarity measures were studied. Conclusions A strongly cooperative Adair-Klotz model can be replaced by a suitable Hill model in such a way that any property computed from the two models, even the one describing stochastic features, is approximately the same. The quantitative analysis showed that boundaries of the regions in the parameter space where the models behave in the same way exhibit a rather rich structure. PMID:21521501

Nonperturbative interpretation of the Bloch vector's path beyond the rotating-wave approximation

NASA Astrophysics Data System (ADS)

Benenti, Giuliano; Siccardi, Stefano; Strini, Giuliano

2013-09-01

The Bloch vector's path of a two-level system exposed to a monochromatic field exhibits, in the regime of strong coupling, complex corkscrew trajectories. By considering the infinitesimal evolution of the two-level system when the field is treated as a classical object, we show that the Bloch vector's rotation speed oscillates between zero and twice the rotation speed predicted by the rotating wave approximation. Cusps appear when the rotation speed vanishes. We prove analytically that in correspondence to cusps the curvature of the Bloch vector's path diverges. On the other hand, numerical data show that the curvature is very large even for a quantum field in the deep quantum regime with mean number of photons n¯≲1. We finally compute numerically the typical error size in a quantum gate when the terms beyond rotating wave approximation are neglected.

A probabilistic cellular automata model for the dynamics of a population driven by logistic growth and weak Allee effect

NASA Astrophysics Data System (ADS)

Mendonça, J. R. G.

2018-04-01

We propose and investigate a one-parameter probabilistic mixture of one-dimensional elementary cellular automata under the guise of a model for the dynamics of a single-species unstructured population with nonoverlapping generations in which individuals have smaller probability of reproducing and surviving in a crowded neighbourhood but also suffer from isolation and dispersal. Remarkably, the first-order mean field approximation to the dynamics of the model yields a cubic map containing terms representing both logistic and weak Allee effects. The model has a single absorbing state devoid of individuals, but depending on the reproduction and survival probabilities can achieve a stable population. We determine the critical probability separating these two phases and find that the phase transition between them is in the directed percolation universality class of critical behaviour.

Microwave vector radiative transfer equation of a sea foam layer by the second-order Rayleigh approximation

NASA Astrophysics Data System (ADS)

Wei, En-Bo

2011-10-01

The microwave vector radiative transfer (VRT) equation of a coated spherical bubble layer is derived by means of the second-order Rayleigh approximation field when the microwave wavelength is larger than the coated spherical particle diameter. Meanwhile, the perturbation method is developed to solve the second-order Rayleigh VRT equation for the small ratio of the volume scattering coefficient to the extinction coefficient. As an example, the emissive properties of a sea surface foam layer, which consists of seawater coated bubbles, are investigated. The extinction, absorption, and scattering coefficients of sea foam are obtained by the second-order Rayleigh approximation fields and discussed for the different microwave frequencies and the ratio of inner radius to outer radius of a coated bubble. Our results show that in the dilute limit, the volume scattering coefficient decreases with increasing the ratio of inner radius to outer radius and decreasing the frequencies. It is also found that the microwave emissivity and the extinction coefficient have a peak at very thin seawater coating and its peak value decreases with frequency decrease. Furthermore, with the VRT equation and effective medium approximation of densely coated bubbles, the mechanism of sea foam enhancing the emissivity of a sea surface is disclosed. In addition, excellent agreement is obtained by comparing our VRT results with the experimental data of microwave emissivities of sea surface covered by a sea foam layer at L-band (1.4 GHz) and the Camps' model.

Nuclear dipole polarizability from mean-field modeling constrained by chiral effective field theory

NASA Astrophysics Data System (ADS)

Zhang, Zhen; Lim, Yeunhwan; Holt, Jeremy W.; Ko, Che Ming

2018-02-01

We construct a new Skyrme interaction Skχm* by fitting the equation of state and nucleon effective masses in asymmetric nuclear matter from chiral two- and three-body forces as well as the binding energies of finite nuclei. Employing this interaction to study the electric dipole polarizabilities of 48Ca, 68Ni, 120Sn, and 208Pb in the random-phase approximation, we find that the theoretical predictions are in good agreement with experimentally measured values without additional fine tuning of the Skyrme interaction, thus confirming the usefulness of the new Skyrme interaction in studying the properties of nuclei. We further use this interaction to study the neutron skin thicknesses of 48Ca and 208Pb, and they are found to be consistent with the experimental data.

Polarizable Force Field for DNA Based on the Classical Drude Oscillator: I. Refinement Using Quantum Mechanical Base Stacking and Conformational Energetics.

PubMed

Lemkul, Justin A; MacKerell, Alexander D

2017-05-09

Empirical force fields seek to relate the configuration of a set of atoms to its energy, thus yielding the forces governing its dynamics, using classical physics rather than more expensive quantum mechanical calculations that are computationally intractable for large systems. Most force fields used to simulate biomolecular systems use fixed atomic partial charges, neglecting the influence of electronic polarization, instead making use of a mean-field approximation that may not be transferable across environments. Recent hardware and software developments make polarizable simulations feasible, and to this end, polarizable force fields represent the next generation of molecular dynamics simulation technology. In this work, we describe the refinement of a polarizable force field for DNA based on the classical Drude oscillator model by targeting quantum mechanical interaction energies and conformational energy profiles of model compounds necessary to build a complete DNA force field. The parametrization strategy employed in the present work seeks to correct weak base stacking in A- and B-DNA and the unwinding of Z-DNA observed in the previous version of the force field, called Drude-2013. Refinement of base nonbonded terms and reparametrization of dihedral terms in the glycosidic linkage, deoxyribofuranose rings, and important backbone torsions resulted in improved agreement with quantum mechanical potential energy surfaces. Notably, we expand on previous efforts by explicitly including Z-DNA conformational energetics in the refinement.

Study of the Influence of the Orientation of a 50-Hz Magnetic Field on Fetal Exposure Using Polynomial Chaos Decomposition

PubMed Central

Liorni, Ilaria; Parazzini, Marta; Fiocchi, Serena; Ravazzani, Paolo

2015-01-01

Human exposure modelling is a complex topic, because in a realistic exposure scenario, several parameters (e.g., the source, the orientation of incident fields, the morphology of subjects) vary and influence the dose. Deterministic dosimetry, so far used to analyze human exposure to electromagnetic fields (EMF), is highly time consuming if the previously-mentioned variations are considered. Stochastic dosimetry is an alternative method to build analytical approximations of exposure at a lower computational cost. In this study, it was used to assess the influence of magnetic flux density (B) orientation on fetal exposure at 50 Hz by polynomial chaos (PC). A PC expansion of induced electric field (E) in each fetal tissue at different gestational ages (GA) was built as a function of B orientation. Maximum E in each fetal tissue and at each GA was estimated for different exposure configurations and compared with the limits of the International Commission of Non-Ionising Radiation Protection (ICNIRP) Guidelines 2010. PC theory resulted in an efficient tool to build accurate approximations of E in each fetal tissue. B orientation strongly influenced E, with a variability across tissues from 10% to 43% with respect to the mean value. However, varying B orientation, maximum E in each fetal tissue was below the limits of ICNIRP 2010 at all GAs. PMID:26024363

Study of the influence of the orientation of a 50-Hz magnetic field on fetal exposure using polynomial chaos decomposition.

PubMed

Liorni, Ilaria; Parazzini, Marta; Fiocchi, Serena; Ravazzani, Paolo

2015-05-27

Human exposure modelling is a complex topic, because in a realistic exposure scenario, several parameters (e.g., the source, the orientation of incident fields, the morphology of subjects) vary and influence the dose. Deterministic dosimetry, so far used to analyze human exposure to electromagnetic fields (EMF), is highly time consuming if the previously-mentioned variations are considered. Stochastic dosimetry is an alternative method to build analytical approximations of exposure at a lower computational cost. In this study, it was used to assess the influence of magnetic flux density (B) orientation on fetal exposure at 50 Hz by polynomial chaos (PC). A PC expansion of induced electric field (E) in each fetal tissue at different gestational ages (GA) was built as a function of B orientation. Maximum E in each fetal tissue and at each GA was estimated for different exposure configurations and compared with the limits of the International Commission of Non-Ionising Radiation Protection (ICNIRP) Guidelines 2010. PC theory resulted in an efficient tool to build accurate approximations of E in each fetal tissue. B orientation strongly influenced E, with a variability across tissues from 10% to 43% with respect to the mean value. However, varying B orientation, maximum E in each fetal tissue was below the limits of ICNIRP 2010 at all GAs.

Symmetry restoration and quantumness reestablishment.

PubMed

Zeng, Guo-Mo; Wu, Lian-Ao; Xing, Hai-Jun

2014-09-18

A realistic quantum many-body system, characterized by a generic microscopic Hamiltonian, is accessible only through approximation methods. The mean field theories, as the simplest practices of approximation methods, commonly serve as a powerful tool, but unfortunately often violate the symmetry of the Hamiltonian. The conventional BCS theory, as an excellent mean field approach, violates the particle number conservation and completely erases quantumness characterized by concurrence and quantum discord between different modes. We restore the symmetry by using the projected BCS theory and the exact numerical solution and find that the lost quantumness is synchronously reestablished. We show that while entanglement remains unchanged with the particle numbers, quantum discord behaves as an extensive quantity with respect to the system size. Surprisingly, discord is hardly dependent on the interaction strengths. The new feature of discord offers promising applications in modern quantum technologies.

The Complexity of Dynamics in Small Neural Circuits

PubMed Central

Panzeri, Stefano

2016-01-01

Mean-field approximations are a powerful tool for studying large neural networks. However, they do not describe well the behavior of networks composed of a small number of neurons. In this case, major differences between the mean-field approximation and the real behavior of the network can arise. Yet, many interesting problems in neuroscience involve the study of mesoscopic networks composed of a few tens of neurons. Nonetheless, mathematical methods that correctly describe networks of small size are still rare, and this prevents us to make progress in understanding neural dynamics at these intermediate scales. Here we develop a novel systematic analysis of the dynamics of arbitrarily small networks composed of homogeneous populations of excitatory and inhibitory firing-rate neurons. We study the local bifurcations of their neural activity with an approach that is largely analytically tractable, and we numerically determine the global bifurcations. We find that for strong inhibition these networks give rise to very complex dynamics, caused by the formation of multiple branching solutions of the neural dynamics equations that emerge through spontaneous symmetry-breaking. This qualitative change of the neural dynamics is a finite-size effect of the network, that reveals qualitative and previously unexplored differences between mesoscopic cortical circuits and their mean-field approximation. The most important consequence of spontaneous symmetry-breaking is the ability of mesoscopic networks to regulate their degree of functional heterogeneity, which is thought to help reducing the detrimental effect of noise correlations on cortical information processing. PMID:27494737

Dispersal of spores following a persistent random walk.

PubMed

Bicout, D J; Sache, I

2003-03-01

A model of a persistent random walk is used to describe the transport and deposition of the spore dispersal process. In this model, the spore particle flies along straight line trajectories, with constant speed v, which are interrupted by scattering, originating from interaction of spores with the field and wind variations, which randomly change its direction. To characterize the spore dispersal gradients, we have derived analytical expressions of the deposition probability epsilon (r|v) of airborne spores as a function of the distance r from the spore source in an infinite free space and in a disk of radius R with an absorbing edge that mimics an agricultural field surrounded with fields of nonhost plants and bare land. It is found in the free space that epsilon (r|v) approximately e(-alphar/l), with alpha a function of l(d)/l, where l and l(d) are the scattering and deposition mean free paths, respectively. In the disk, however, epsilon (r|v) is an infinite series of Bessel functions and, exhibits three regimes: absorbing (Rl(d)).

Analytical approximations for effective relative permeability in the capillary limit

NASA Astrophysics Data System (ADS)

Rabinovich, Avinoam; Li, Boxiao; Durlofsky, Louis J.

2016-10-01

We present an analytical method for calculating two-phase effective relative permeability, krjeff, where j designates phase (here CO2 and water), under steady state and capillary-limit assumptions. These effective relative permeabilities may be applied in experimental settings and for upscaling in the context of numerical flow simulations, e.g., for CO2 storage. An exact solution for effective absolute permeability, keff, in two-dimensional log-normally distributed isotropic permeability (k) fields is the geometric mean. We show that this does not hold for krjeff since log normality is not maintained in the capillary-limit phase permeability field (Kj=k·krj) when capillary pressure, and thus the saturation field, is varied. Nevertheless, the geometric mean is still shown to be suitable for approximating krjeff when the variance of ln⁡k is low. For high-variance cases, we apply a correction to the geometric average gas effective relative permeability using a Winsorized mean, which neglects large and small Kj values symmetrically. The analytical method is extended to anisotropically correlated log-normal permeability fields using power law averaging. In these cases, the Winsorized mean treatment is applied to the gas curves for cases described by negative power law exponents (flow across incomplete layers). The accuracy of our analytical expressions for krjeff is demonstrated through extensive numerical tests, using low-variance and high-variance permeability realizations with a range of correlation structures. We also present integral expressions for geometric-mean and power law average krjeff for the systems considered, which enable derivation of closed-form series solutions for krjeff without generating permeability realizations.

The multiscale coarse-graining method. II. Numerical implementation for coarse-grained molecular models

PubMed Central

Noid, W. G.; Liu, Pu; Wang, Yanting; Chu, Jhih-Wei; Ayton, Gary S.; Izvekov, Sergei; Andersen, Hans C.; Voth, Gregory A.

2008-01-01

The multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B 109, 2469 (2005);J. Chem. Phys. 123, 134105 (2005)] employs a variational principle to determine an interaction potential for a CG model from simulations of an atomically detailed model of the same system. The companion paper proved that, if no restrictions regarding the form of the CG interaction potential are introduced and if the equilibrium distribution of the atomistic model has been adequately sampled, then the MS-CG variational principle determines the exact many-body potential of mean force (PMF) governing the equilibrium distribution of CG sites generated by the atomistic model. In practice, though, CG force fields are not completely flexible, but only include particular types of interactions between CG sites, e.g., nonbonded forces between pairs of sites. If the CG force field depends linearly on the force field parameters, then the vector valued functions that relate the CG forces to these parameters determine a set of basis vectors that span a vector subspace of CG force fields. The companion paper introduced a distance metric for the vector space of CG force fields and proved that the MS-CG variational principle determines the CG force force field that is within that vector subspace and that is closest to the force field determined by the many-body PMF. The present paper applies the MS-CG variational principle for parametrizing molecular CG force fields and derives a linear least squares problem for the parameter set determining the optimal approximation to this many-body PMF. Linear systems of equations for these CG force field parameters are derived and analyzed in terms of equilibrium structural correlation functions. Numerical calculations for a one-site CG model of methanol and a molecular CG model of the EMIM+∕NO3− ionic liquid are provided to illustrate the method. PMID:18601325

Attosecond polarization control in atomic RABBITT-like experiments assisted by a circularly polarized laser

NASA Astrophysics Data System (ADS)

Boll, D. I. R.; Fojón, O. A.

2017-12-01

We study theoretically the single ionization of noble gas atoms by the combined action of an attosecond pulse train with linear polarization and an assistant laser field with circular polarization. We employ a non-perturbative model that under certain approximations gives closed-form expressions for the angular distributions of photoelectrons. Interestingly, our model allow us to interpret these angular distributions as two-centre interferences where the orientation and the modulus of the separation vector between the virtual emitters is governed by the assistant laser field. Additionally, we show that such a configuration of light fields is similar to the polarization control technique, where both the attosecond pulse train and the assistant laser field have linear polarizations whose relative orientation may be controlled. Moreover, in order to compare our results with the available experimental data, we obtain analytical expressions for the cross sections integrated over the photoelectron emission angles. By means of these expressions, we define the ‘magic time’ as the delay for which the total cross sections for atomic targets exhibit the same functional form as the one of the monochromatic photoionization of diatomic molecular targets.

Doubly self-consistent field theory of grafted polymers under simple shear in steady state.

PubMed

Suo, Tongchuan; Whitmore, Mark D

2014-03-21

We present a generalization of the numerical self-consistent mean-field theory of polymers to the case of grafted polymers under simple shear. The general theoretical framework is presented, and then applied to three different chain models: rods, Gaussian chains, and finitely extensible nonlinear elastic (FENE) chains. The approach is self-consistent at two levels. First, for any flow field, the polymer density profile and effective potential are calculated self-consistently in a manner similar to the usual self-consistent field theory of polymers, except that the calculation is inherently two-dimensional even for a laterally homogeneous system. Second, through the use of a modified Brinkman equation, the flow field and the polymer profile are made self-consistent with respect to each other. For all chain models, we find that reasonable levels of shear cause the chains to tilt, but it has very little effect on the overall thickness of the polymer layer, causing a small decrease for rods, and an increase of no more than a few percent for the Gaussian and FENE chains. Using the FENE model, we also probe the individual bond lengths, bond correlations, and bond angles along the chains, the effects of the shear on them, and the solvent and bonded stress profiles. We find that the approximations needed within the theory for the Brinkman equation affect the bonded stress, but none of the other quantities.

Supplemental computational phantoms to estimate out-of-field absorbed dose in photon radiotherapy

NASA Astrophysics Data System (ADS)

Gallagher, Kyle J.; Tannous, Jaad; Nabha, Racile; Feghali, Joelle Ann; Ayoub, Zeina; Jalbout, Wassim; Youssef, Bassem; Taddei, Phillip J.

2018-01-01

The purpose of this study was to develop a straightforward method of supplementing patient anatomy and estimating out-of-field absorbed dose for a cohort of pediatric radiotherapy patients with limited recorded anatomy. A cohort of nine children, aged 2-14 years, who received 3D conformal radiotherapy for low-grade localized brain tumors (LBTs), were randomly selected for this study. The extent of these patients’ computed tomography simulation image sets were cranial only. To approximate their missing anatomy, we supplemented the LBT patients’ image sets with computed tomography images of patients in a previous study with larger extents of matched sex, height, and mass and for whom contours of organs at risk for radiogenic cancer had already been delineated. Rigid fusion was performed between the LBT patients’ data and that of the supplemental computational phantoms using commercial software and in-house codes. In-field dose was calculated with a clinically commissioned treatment planning system, and out-of-field dose was estimated with a previously developed analytical model that was re-fit with parameters based on new measurements for intracranial radiotherapy. Mean doses greater than 1 Gy were found in the red bone marrow, remainder, thyroid, and skin of the patients in this study. Mean organ doses between 150 mGy and 1 Gy were observed in the breast tissue of the girls and lungs of all patients. Distant organs, i.e. prostate, bladder, uterus, and colon, received mean organ doses less than 150 mGy. The mean organ doses of the younger, smaller LBT patients (0-4 years old) were a factor of 2.4 greater than those of the older, larger patients (8-12 years old). Our findings demonstrated the feasibility of a straightforward method of applying supplemental computational phantoms and dose-calculation models to estimate absorbed dose for a set of children of various ages who received radiotherapy and for whom anatomies were largely missing in their original computed tomography simulations.

How to Define the Mean Square Amplitude of Solar Wind Fluctuations With Respect to the Local Mean Magnetic Field

NASA Astrophysics Data System (ADS)

Podesta, John J.

2017-12-01

Over the last decade it has become popular to analyze turbulent solar wind fluctuations with respect to a coordinate system aligned with the local mean magnetic field. This useful analysis technique has provided new information and new insights about the nature of solar wind fluctuations and provided some support for phenomenological theories of MHD turbulence based on the ideas of Goldreich and Sridhar. At the same time it has drawn criticism suggesting that the use of a scale-dependent local mean field is somehow inconsistent or irreconcilable with traditional analysis techniques based on second-order structure functions and power spectra that, for stationary time series, are defined with respect to the constant (scale-independent) ensemble average magnetic field. Here it is shown that for fluctuations with power law spectra, such as those observed in solar wind turbulence, it is possible to define the local mean magnetic field in a special way such that the total mean square amplitude (trace amplitude) of turbulent fluctuations is approximately the same, scale by scale, as that obtained using traditional second-order structure functions or power spectra. This fact should dispel criticism concerning the physical validity or practical usefulness of the local mean magnetic field in these applications.

Consistent parameter fixing in the quark-meson model with vacuum fluctuations

NASA Astrophysics Data System (ADS)

Carignano, Stefano; Buballa, Michael; Elkamhawy, Wael

2016-08-01

We revisit the renormalization prescription for the quark-meson model in an extended mean-field approximation, where vacuum quark fluctuations are included. At a given cutoff scale the model parameters are fixed by fitting vacuum quantities, typically including the sigma-meson mass mσ and the pion decay constant fπ. In most publications the latter is identified with the expectation value of the sigma field, while for mσ the curvature mass is taken. When quark loops are included, this prescription is however inconsistent, and the correct identification involves the renormalized pion decay constant and the sigma pole mass. In the present article we investigate the influence of the parameter-fixing scheme on the phase structure of the model at finite temperature and chemical potential. Despite large differences between the model parameters in the two schemes, we find that in homogeneous matter the effect on the phase diagram is relatively small. For inhomogeneous phases, on the other hand, the choice of the proper renormalization prescription is crucial. In particular, we show that if renormalization effects on the pion decay constant are not considered, the model does not even present a well-defined renormalized limit when the cutoff is sent to infinity.

A hybrid phase-space and histogram source model for GPU-based Monte Carlo radiotherapy dose calculation

NASA Astrophysics Data System (ADS)

Townson, Reid W.; Zavgorodni, Sergei

2014-12-01

In GPU-based Monte Carlo simulations for radiotherapy dose calculation, source modelling from a phase-space source can be an efficiency bottleneck. Previously, this has been addressed using phase-space-let (PSL) sources, which provided significant efficiency enhancement. We propose that additional speed-up can be achieved through the use of a hybrid primary photon point source model combined with a secondary PSL source. A novel phase-space derived and histogram-based implementation of this model has been integrated into gDPM v3.0. Additionally, a simple method for approximately deriving target photon source characteristics from a phase-space that does not contain inheritable particle history variables (LATCH) has been demonstrated to succeed in selecting over 99% of the true target photons with only ~0.3% contamination (for a Varian 21EX 18 MV machine). The hybrid source model was tested using an array of open fields for various Varian 21EX and TrueBeam energies, and all cases achieved greater than 97% chi-test agreement (the mean was 99%) above the 2% isodose with 1% / 1 mm criteria. The root mean square deviations (RMSDs) were less than 1%, with a mean of 0.5%, and the source generation time was 4-5 times faster. A seven-field intensity modulated radiation therapy patient treatment achieved 95% chi-test agreement above the 10% isodose with 1% / 1 mm criteria, 99.8% for 2% / 2 mm, a RMSD of 0.8%, and source generation speed-up factor of 2.5. Presented as part of the International Workshop on Monte Carlo Techniques in Medical Physics

An econometric investigation of the sunspot number record since the year 1700 and its prediction into the 22nd century

NASA Astrophysics Data System (ADS)

Travaglini, Guido

2015-09-01

Solar activity, as measured by the yearly revisited time series of sunspot numbers (SSN) for the period 1700-2014 (Clette et al., 2014), undergoes in this paper a triple statistical and econometric checkup. The conclusions are that the SSN sequence: (1) is best modeled as a signal that features nonlinearity in mean and variance, long memory, mean reversion, 'threshold' symmetry, and stationarity; (2) is best described as a discrete damped harmonic oscillator which linearly approximates the flux-transport dynamo model; (3) its prediction well into the 22nd century testifies of a substantial fall of the SSN centered around the year 2030. In addition, the first and last Gleissberg cycles show almost the same peak number and height during the period considered, yet the former slightly prevails when measured by means of the estimated smoother. All of these conclusions are achieved by making use of modern tools developed in the field of Financial Econometrics and of two new proposed procedures for signal smoothing and prediction.

Giant Dipole Resonance in light and heavy nuclei beyond selfconsistent mean field theory

NASA Astrophysics Data System (ADS)

Krewald, Siegfried; Lyutorovich, Nikolay; Tselyaev, Victor; Speth, Josef; Gruemmer, Frank; Reinhard, Paul-Gerhard

2012-10-01

While bulk properties of stable nuclei are successfully reproduced by mean-field theories employing effective interactions, the dependence of the centroid energy of the electric giant dipole resonance on the nucleon number A is not. This problem is cured by considering many-particle correlations beyond mean-field theory, which we do within a selfconsistent generalization of the Quasiparticle Time Blocking Approximation [1,2]. The electric giant dipole resonances in ^16O, ^40Ca, and ^208Pb are calculated using two new Skyrme interactions. Perspectives for an extension to effective field theories[3] are discussed.[4pt] [1] V. Tselyaev et al., Phys.Rev.C75, 014315(2007).[0pt] [2] N. Lyutorovich et al., submitted to Phys.Rev.Lett.[0pt] [3] S. Krewald et al., Prog.Part.Nucl.Phys.67, 322(2012).

Collective Traffic-like Movement of Ants on a Trail: Dynamical Phases and Phase Transitions

NASA Astrophysics Data System (ADS)

Kunwar, Ambarish; John, Alexander; Nishinari, Katsuhiro; Schadschneider, Andreas; Chowdhury, Debashish

2004-11-01

The traffic-like collective movement of ants on a trail can be described by a stochastic cellular automaton model. We have earlier investigated its unusual flow-density relation by using various mean field approximations and computer simulations. In this paper, we study the model following an alternative approach based on the analogy with the zero range process, which is one of the few known exactly solvable stochastic dynamical models. We show that our theory can quantitatively account for the unusual non-monotonic dependence of the average speed of the ants on their density for finite lattices with periodic boundary conditions. Moreover, we argue that the model exhibits a continuous phase transition at the critial density only in a limiting case. Furthermore, we investigate the phase diagram of the model by replacing the periodic boundary conditions by open boundary conditions.

Lyapunov exponent and criticality in the Hamiltonian mean field model

NASA Astrophysics Data System (ADS)

Filho, L. H. Miranda; Amato, M. A.; Rocha Filho, T. M.

2018-03-01

We investigate the dependence of the largest Lyapunov exponent (LLE) of an N-particle self-gravitating ring model at equilibrium with respect to the number of particles and its dependence on energy. This model has a continuous phase-transition from a ferromagnetic to homogeneous phase, and we numerically confirm with large scale simulations the existence of a critical exponent associated to the LLE, although at variance with the theoretical estimate. The existence of strong chaos in the magnetized state evidenced by a positive Lyapunov exponent is explained by the coupling of individual particle oscillations to the diffusive motion of the center of mass of the system and also results in a change of the scaling of the LLE with the number of particles. We also discuss thoroughly for the model the validity and limits of the approximations made by a geometrical model for their analytic estimate.

Synchronization scenarios in the Winfree model of coupled oscillators

NASA Astrophysics Data System (ADS)

Gallego, Rafael; Montbrió, Ernest; Pazó, Diego

2017-10-01

Fifty years ago Arthur Winfree proposed a deeply influential mean-field model for the collective synchronization of large populations of phase oscillators. Here we provide a detailed analysis of the model for some special, analytically tractable cases. Adopting the thermodynamic limit, we derive an ordinary differential equation that exactly describes the temporal evolution of the macroscopic variables in the Ott-Antonsen invariant manifold. The low-dimensional model is then thoroughly investigated for a variety of pulse types and sinusoidal phase response curves (PRCs). Two structurally different synchronization scenarios are found, which are linked via the mutation of a Bogdanov-Takens point. From our results, we infer a general rule of thumb relating pulse shape and PRC offset with each scenario. Finally, we compare the exact synchronization threshold with the prediction of the averaging approximation given by the Kuramoto-Sakaguchi model. At the leading order, the discrepancy appears to behave as an odd function of the PRC offset.

First principles cable braid electromagnetic penetration model

DOE PAGES

Warne, Larry Kevin; Langston, William L.; Basilio, Lorena I.; ...

2016-01-01

The model for penetration of a wire braid is rigorously formulated. Integral formulas are developed from energy principles for both self and transfer immittances in terms of potentials for the fields. The detailed boundary value problem for the wire braid is also set up in a very efficient manner; the braid wires act as sources for the potentials in the form of a sequence of line multi-poles with unknown coefficients that are determined by means of conditions arising from the wire surface boundary conditions. Approximations are introduced to relate the local properties of the braid wires to a simplified infinitemore » periodic planar geometry. Furthermore, this is used to treat nonuniform coaxial geometries including eccentric interior coaxial arrangements and an exterior ground plane.« less

Magnetic Field Line Random Walk in Arbitrarily Stretched Isotropic Turbulence

NASA Astrophysics Data System (ADS)

Wongpan, P.; Ruffolo, D.; Matthaeus, W. H.; Rowlands, G.

2006-12-01

Many types of space and laboratory plasmas involve turbulent fluctuations with an approximately uniform mean magnetic field B_0, and the field line random walk plays an important role in guiding particle motions. Much of the relevant literature concerns isotropic turbulence, and has mostly been perturbative, i.e., for small fluctuations, or based on numerical simulations for specific conditions. On the other hand, solar wind turbulence is apparently anisotropic, and has been modeled as a sum of idealized two-dimensional and one dimensional (slab) components, but with the deficiency of containing no oblique wave vectors. In the present work, we address the above issues with non-perturbative analytic calculations of diffusive field line random walks for unpolarized, arbitrarily stretched isotropic turbulence, including the limits of nearly one-dimensional (highly stretched) and nearly two-dimensional (highly squashed) turbulence. We develop implicit analytic formulae for the diffusion coefficients D_x and D_z, two coupled integral equations in which D_x and D_z appear inside 3-dimensional integrals over all k-space, are solved numerically with the aid of Mathematica routines for specific cases. We can vary the parameters B0 and β, the stretching along z for constant turbulent energy. Furthermore, we obtain analytic closed-form solutions in all extreme cases. We obtain 0.54 < D_z/D_x < 2, indicating an approximately isotropic random walk even for very anisotropic (unpolarized) turbulence, a surprising result. For a given β, the diffusion coefficient vs. B0 can be described by a Padé approximant. We find quasilinear behavior at high B0 and percolative behavior at low B_0. Partially supported by a Sritrangthong Scholarship from the Faculty of Science, Mahidol University; the Thailand Research Fund; NASA Grant NNG05GG83G; and Thailand's Commission for Higher Education.

Noise is the new signal: Moving beyond zeroth-order geomorphology (Invited)

NASA Astrophysics Data System (ADS)

Jerolmack, D. J.

2010-12-01

The last several decades have witnessed a rapid growth in our understanding of landscape evolution, led by the development of geomorphic transport laws - time- and space-averaged equations relating mass flux to some physical process(es). In statistical mechanics this approach is called mean field theory (MFT), in which complex many-body interactions are replaced with an external field that represents the average effect of those interactions. Because MFT neglects all fluctuations around the mean, it has been described as a zeroth-order fluctuation model. The mean field approach to geomorphology has enabled the development of landscape evolution models, and led to a fundamental understanding of many landform patterns. Recent research, however, has highlighted two limitations of MFT: (1) The integral (averaging) time and space scales in geomorphic systems are sometimes poorly defined and often quite large, placing the mean field approximation on uncertain footing, and; (2) In systems exhibiting fractal behavior, an integral scale does not exist - e.g., properties like mass flux are scale-dependent. In both cases, fluctuations in sediment transport are non-negligible over the scales of interest. In this talk I will synthesize recent experimental and theoretical work that confronts these limitations. Discrete element models of fluid and grain interactions show promise for elucidating transport mechanics and pattern-forming instabilities, but require detailed knowledge of micro-scale processes and are computationally expensive. An alternative approach is to begin with a reasonable MFT, and then add higher-order terms that capture the statistical dynamics of fluctuations. In either case, moving beyond zeroth-order geomorphology requires a careful examination of the origins and structure of transport “noise”. I will attempt to show how studying the signal in noise can both reveal interesting new physics, and also help to formalize the applicability of geomorphic transport laws. Flooding on an experimental alluvial fan. Intensity is related to the cumulative amount of time flow has visited an area of the fan over the experiment. Dark areas represent an emergent channel network resulting from stochastic migration of river channels.

Dynamical arrest with zero complexity: The unusual behavior of the spherical Blume-Emery-Griffiths disordered model

NASA Astrophysics Data System (ADS)

Rainone, Corrado; Ferrari, Ulisse; Paoluzzi, Matteo; Leuzzi, Luca

2015-12-01

The short- and long-time dynamics of model systems undergoing a glass transition with apparent inversion of Kauzmann and dynamical arrest glass transition lines is investigated. These models belong to the class of the spherical mean-field approximation of a spin-1 model with p -body quenched disordered interaction, with p >2 , termed spherical Blume-Emery-Griffiths models. Depending on temperature and chemical potential the system is found in a paramagnetic or in a glassy phase and the transition between these phases can be of a different nature. In specific regions of the phase diagram coexistence of low-density and high-density paramagnets can occur, as well as the coexistence of spin-glass and paramagnetic phases. The exact static solution for the glassy phase is known to be obtained by the one-step replica symmetry breaking ansatz. Different scenarios arise for both the dynamic and the thermodynamic transitions. These include: (i) the usual random first-order transition (Kauzmann-like) for mean-field glasses preceded by a dynamic transition, (ii) a thermodynamic first-order transition with phase coexistence and latent heat, and (iii) a regime of apparent inversion of static transition line and dynamic transition lines, the latter defined as a nonzero complexity line. The latter inversion, though, turns out to be preceded by a dynamical arrest line at higher temperature. Crossover between different regimes is analyzed by solving mode-coupling-theory equations near the boundaries of paramagnetic solutions and the relationship with the underlying statics is discussed.

The Hubble Space Telescope Medium Deep Survey with the Wide Field and Planetary Camera. 1: Methodology and results on the field near 3C 273

NASA Technical Reports Server (NTRS)

Griffiths, R. E.; Ratnatunga, K. U.; Neuschaefer, L. W.; Casertano, S.; Im, M.; Wyckoff, E. W.; Ellis, R. S.; Gilmore, G. F.; Elson, R. A. W.; Glazebrook, K.

1994-01-01

We present results from the Medium Deep Survey (MDS), a Key Project using the Hubble Space Telescope (HST). Wide Field Camera (WFC) images of random fields have been taken in 'parallel mode' with an effective resolution of 0.2 sec full width at half maximum (FWHM) in the V(F555W) and I(F785LP) filters. The exposures presented here were targeted on a field away from 3C 273, and resulted in approximately 5 hr integration time in each filter. Detailed morphological structure is seen in galaxy images with total integrated magnitudes down to V approximately = 22.5 and I approximately = 21.5. Parameters are estimated that best fit the observed galaxy images, and 143 objects are identified (including 23 stars) in the field to a fainter limiting magnitude of I approximately = 23.5. We outline the extragalactic goals of the HST Medium Deep Survey, summarize our basic data reduction procedures, and present number (magnitude) counts, a color-magnitude diagram for the field, surface brightness profiles for the brighter galaxies, and best-fit half-light radii for the fainter galaxies as a function of apparent magnitude. A median galaxy half-light radius of 0.4 sec is measured, and the distribution of galaxy sizes versus magnitude is presented. We observe an apparent deficit of galaxies with half-light radii between approximately 0.6 sec and 1.5 sec, with respect to standard no-evolution or mild evolution cosmological models. An apparent excess of compact objects (half-light radii approximately 0.1 sec) is also observed with respect to those models. Finally, we find a small excess in the number of faint galaxy pairs and groups with respect to a random low-redshift field sample.

Stormtime ring current and radiation belt ion transport: Simulations and interpretations

NASA Technical Reports Server (NTRS)

Lyons, Larry R.; Gorney, David J.; Chen, Margaret W.; Schulz, Michael

1995-01-01

We use a dynamical guiding-center model to investigate the stormtime transport of ring current and radiation-belt ions. We trace the motion of representative ions' guiding centers in response to model substorm-associated impulses in the convection electric field for a range of ion energies. Our simple magnetospheric model allows us to compare our numerical results quantitatively with analytical descriptions of particle transport, (e.g., with the quasilinear theory of radial diffusion). We find that 10-145-keV ions gain access to L approximately 3, where they can form the stormtime ring current, mainly from outside the (trapping) region in which particles execute closed drift paths. Conversely, the transport of higher-energy ions (approximately greater than 145 keV at L approximately 3) turns out to resemble radial diffusion. The quasilinear diffusion coefficient calculated for our model storm does not vary smoothly with particle energy, since our impulses occur at specific (although randomly determined) times. Despite the spectral irregularity, quasilinear theory provides a surprisingly accurate description of the transport process for approximately greater than 145-keV ions, even for the case of an individual storm. For 4 different realizations of our model storm, the geometric mean discrepancies between diffusion coefficients D(sup sim, sub LL) obtained from the simulations and the quasilinear diffusion coefficient D(sup ql, sub LL) amount to factors of 2.3, 2.3, 1.5, and 3.0, respectively. We have found that these discrepancies between D(sup sim, sub LL) and D(sup ql, sub LL) can be reduced slightly by invoking drift-resonance broadening to smooth out the sharp minima and maxima in D(sup ql, sub LL). The mean of the remaining discrepancies between D(sup sim, sub LL) and D(sup ql, sub LL) for the 4 different storms then amount to factors of 1.9, 2.1, 1.5, and 2.7, respectively. We find even better agreement when we reduce the impulse amplitudes systematically in a given model storm (e.g., reduction of all the impulse amplitudes by half reduces the discrepancy factor by at least its square root) and also when we average our results over an ensemble of 20 model storms (agreement is within a factor of 1.2 without impulse-amplitude reduction). We use our simulation results also to map phase-space densities f in accordance with Liouville's theorem. We find that the stormtime transport of approximately greater than 145-keV ions produces little change in f-bar the drift-averaged phase-space density on any drift shell of interest. However, the stormtime transport produces a major enhancement from the pre-storm phase-space density at energies approximately 30-145 keV, which are representative of the stormtime ring current.

On the effective field theory for quasi-single field inflation

NASA Astrophysics Data System (ADS)

Tong, Xi; Wang, Yi; Zhou, Siyi

2017-11-01

We study the effective field theory (EFT) description of the virtual particle effects in quasi-single field inflation, which unifies the previous results on large mass and large mixing cases. By using a horizon crossing approximation and matching with known limits, approximate expressions for the power spectrum and the spectral index are obtained. The error of the approximate solution is within 10% in dominate parts of the parameter space, which corresponds to less-than-0.1% error in the ns-r diagram. The quasi-single field corrections on the ns-r diagram are plotted for a few inflation models. Especially, the quasi-single field correction drives m2phi2 inflation to the best fit region on the ns-r diagram, with an amount of equilateral non-Gaussianity which can be tested in future experiments.

Evaporation of 2-dimensional black holes

NASA Astrophysics Data System (ADS)

Ramazanoglu, Fethi M.

We present a detailed analysis of results from a new study of the quantum evaporation of Callan-Giddings-Harvey-Strominger (CGHS) black holes within the mean-field approximation. The CGHS model is a two dimensional model of quantum gravity which has been extensively investigated in the last two decades. Moreover, Ashtekar, Taveras and Varadarajan have recently proposed a solution to the information loss paradox within the context of this model, which has rekindled the interest in it. However, many aspects of black hole evaporation in this model has been overlooked because of lack of a solution for black holes with macroscopic mass. We show that this was due to, in part, limited numerical precision and, in part, misinterpretation of certain properties and symmetries of the model. By addressing these issues, we were, for the first time, able to numerically evolve macroscopic-mass black hole spacetimes of the CGHS model within the mean-field approximation, up to the vicinity of the singularity. Our calculations show that, while some of the assumptions underlying the standard evaporation paradigm are borne out, several are not. One of the anticipated properties we confirm is that the semi-classical space-time is asymptotically flat at right future null infinity, I+R , yet incomplete in the sense that null observers reach a future Cauchy horizon in finite affine time. Unexpected behavior includes that the Bondi mass traditionally used in the literature can become negative even when the area of the horizon is macroscopic; an improved Bondi mass remains positive until the end of semi-classical evaporation, yet the final value can be arbitrarily large relative to the Planck mass; and the flux of the quantum radiation at I+R is non-thermal even when the horizon area is large compared to the Planck scale. Furthermore, if the black hole is initially macroscopic, the evaporation process exhibits remarkable universal properties, which offer problems to attack to the mathematical relativity and geometric analysis communities. Our results also provide support for the full quantum scenario developed by Ashtekar et al.

Technical note: A method for assigning animals to treatment groups with unequal count per group that equalizes mean animal weight among groups.

PubMed

Epplin, F M; Haankuku, C; Horn, G W

2015-09-01

Pastures available for grazing studies may be of unequal size and may have heterogeneous carrying capacity necessitating the assignment of unequal numbers of animals per pasture. To reduce experimental error, it is often desirable that the initial mean BW be similar among experimental units. The objective of this note is to present and illustrate the use of a method for assignment of animals to experimental units of different sizes such that the initial mean weight of animals in each unit is approximately the same as the overall mean. Two alternative models were developed and solved to assign each of 231 weaned steers () to 1 of 12 pastures with carrying capacity ranging from 5 to 26 animals per pasture. A solution to Model 1 was obtained in which the mean weights among pastures were approximately the same but the variances among pastures were heteroskedastic, meaning that weight variances across pens were different (-value < 0.05). An alternative model was developed (Model 2) and used to derive assignments with nearly equal mean weights and homoskedastic variances among pastures.

A low-dimensional analogue of holographic baryons

NASA Astrophysics Data System (ADS)

Bolognesi, Stefano; Sutcliffe, Paul

2014-04-01

Baryons in holographic QCD correspond to topological solitons in the bulk. The most prominent example is the Sakai-Sugimoto model, where the bulk soliton in the five-dimensional spacetime of AdS-type can be approximated by the flat space self-dual Yang-Mills instanton with a small size. Recently, the validity of this approximation has been verified by comparison with the numerical field theory solution. However, multi-solitons and solitons with finite density are currently beyond numerical field theory computations. Various approximations have been applied to investigate these important issues and have led to proposals for finite density configurations that include dyonic salt and baryonic popcorn. Here we introduce and investigate a low-dimensional analogue of the Sakai-Sugimoto model, in which the bulk soliton can be approximated by a flat space sigma model instanton. The bulk theory is a baby Skyrme model in a three-dimensional spacetime with negative curvature. The advantage of the lower-dimensional theory is that numerical simulations of multi-solitons and finite density solutions can be performed and compared with flat space instanton approximations. In particular, analogues of dyonic salt and baryonic popcorn configurations are found and analysed.

Weber's gravitational force as static weak field approximation

NASA Astrophysics Data System (ADS)

Tiandho, Yuant

2016-02-01

Weber's gravitational force (WGF) is one of gravitational model that can accommodate a non-static system because it depends not only on the distance but also on the velocity and the acceleration. Unlike Newton's law of gravitation, WGF can predict the anomalous of Mercury and gravitational bending of light near massive object very well. Then, some researchers use WGF as an alternative model of gravitation and propose a new mechanics theory namely the relational mechanics theory. However, currently we have known that the theory of general relativity which proposed by Einstein can explain gravity with very accurate. Through the static weak field approximation for the non-relativistic object, we also have known that the theory of general relativity will reduce to Newton's law of gravity. In this work, we expand the static weak field approximation that compatible with relativistic object and we obtain a force equation which correspond to WGF. Therefore, WGF is more precise than Newton's gravitational law. The static-weak gravitational field that we used is a solution of the Einstein's equation in the vacuum that satisfy the linear field approximation. The expression of WGF with ξ = 1 and satisfy the requirement of energy conservation are obtained after resolving the geodesic equation. By this result, we can conclude that WGF can be derived from the general relativity.

γ-decay of {}_{8}^{16}{{\\rm{O}}}_{8}\\,{and}\\,{}_{7}^{16}{{\\rm{N}}}_{9} in proton-neutron Tamm-Dancoff and random phase approximations with optimized surface δ interaction

NASA Astrophysics Data System (ADS)

Pahlavani, M. R.; Firoozi, B.

2016-09-01

γ-ray transitions from excited states of {}16{{N}} and {}16{{O}} isomers that appear in the γ spectrum of the {}616{{{C}}}10\\to {}716{{{N}}}9\\to {}816{{{O}}}8 beta decay chain are investigated. The theoretical approach used in this research starts with a mean-field potential consisting of a phenomenological Woods-Saxon potential including spin-orbit and Coulomb terms (for protons) in order to obtain single-particle energies and wave functions for nucleons in a nucleus. A schematic residual surface delta interaction is then employed on the top of the mean field and is treated within the proton-neutron Tamm-Dancoff approximation (pnTDA) and the proton-neutron random phase approximation. The goal is to use an optimized surface delta interaction interaction, as a residual interaction, to improve the results. We have used artificial intelligence algorithms to establish a good agreement between theoretical and experimental energy spectra. The final results of the ‘optimized’ calculations are reasonable via this approach.

Issues related to the Fermion mass problem

NASA Astrophysics Data System (ADS)

Murakowski, Janusz Adam

1998-09-01

This thesis is divided into three parts. Each illustrates a different aspect of the fermion mass issue in elementary particle physics. In the first part, the possibility of chiral symmetry breaking in the presence of uniform magnetic and electric fields is investigated. The system is studied nonperturbatively with the use of basis functions compatible with the external field configuration, the parabolic cylinder functions. It is found that chiral symmetry, broken by a uniform magnetic field, is restored by electric field. Obtained result is nonperturbative in nature: even the tiniest deviation of the electric field from zero restores chiral symmetry. In the second part, heavy quarkonium systems are investigated. To study these systems, a phenomenological nonrelativistic model is built. Approximate solutions to this model are found with the use of a specially designed Pade approximation and by direct numerical integration of Schrodinger equation. The results are compared with experimental measurements of respective meson masses. Good agreement between theoretical calculations and experimental results is found. Advantages and shortcommings of the new approximation method are analysed. In the third part, an extension of the standard model of elementary particles is studied. The extension, called the aspon model, was originally introduced to cure the so called strong CP problem. In addition to fulfilling its original purpose, the aspon model modifies the couplings of the standard model quarks to the Z boson. As a result, the decay rates of the Z boson to quarks are altered. By using the recent precise measurements of the decay rates Z → bb and Z /to [/it c/=c], new constraints on the aspon model parameters are found.

Harmonic generation beyond the Strong-Field Approximation: the physics behind the short-wave-infrared scaling laws.

PubMed

Pérez-Hernández, J A; Roso, L; Plaja, L

2009-06-08

The physics of laser-mater interactions beyond the perturbative limit configures the field of extreme non-linear optics. Although most experiments have been done in the near infrared ( lambda

Quantitative vs. subjective portal verification using digital portal images.

PubMed

Bissett, R; Leszczynski, K; Loose, S; Boyko, S; Dunscombe, P

1996-01-15

Off-line, computer-aided prescription (simulator) and treatment (portal) image registration using chamfer matching has been implemented on PC based viewing station. The purposes of this study were (a) to evaluate the performance of interactive anatomy and field edge extraction and subsequent registration, and (b) to compare observer's perceptions of field accuracy with measured discrepancies following anatomical registration. Prescription-treatment image pairs for 48 different patients were examined in this study. Digital prescription images were produced with the aid of a television camera and a digital frame grabber, while the treatment images were obtained directly from an on-line portal imaging system. To facilitate perception of low contrast anatomical detail, on-line portal images were enhanced with selective adaptive histogram equalization prior to extraction of anatomical edges. Following interactive extraction of anatomical and field border information by an experienced observer, the identified anatomy was registered using chamfer matching. The degree of conformity between the prescription and treatment fields was quantified using several parameters, which included relative prescription field coverage and overcoverage, as well as the translational and rotational displacements as measured by chamfer matching applied to the boundaries of the two fields. These quantitative measures were compared with subjective evaluations made by four radiation oncologists. All the images in this series that included a range of the most commonly seen treatment sites were registered and the conformity parameters were found. The mean treatment/prescription field coverage and overcoverage were approximately 95 and 7%, respectively before registration. The mean translational displacement in the transverse and cranio-caudal directions were 2.9 and 3.4 mm, respectively. The mean rotational displacement was approximately 2 degrees. For all four oncologists, the portals classified as unacceptable, in terms of the field placement, exhibited significantly higher (p < 0.03) translational errors in the transverse direction. The field coverages were significantly lower (p < 0.05) and the translational errors in the cranio-caudal direction were significantly higher (p < 0.05) for the portals rated as unacceptable by two of the oncologists. From the parameters that were used to quantify the degree of conformity between the prescription and treatment fields, the translational error in the transverse direction correlated best with the oncologists' assessments on the field placement. Field coverage and translational error in the cranio-caudal direction correlated well with assessments of only two out of the four participating oncologists. This can be explained by the fact that for the majority of treatment sites included in the study the positioning of field borders was more critical for the transverse direction. A conclusion for the design of future quantitative and automated on-line portal verification systems is that they will have to model different perceived significances of different types of localization errors intrinsic to oncologist evaluation of portal images.

Structural versus dynamical origins of mean-field behavior in a self-organized critical model of neuronal avalanches

NASA Astrophysics Data System (ADS)

Moosavi, S. Amin; Montakhab, Afshin

2015-11-01

Critical dynamics of cortical neurons have been intensively studied over the past decade. Neuronal avalanches provide the main experimental as well as theoretical tools to consider criticality in such systems. Experimental studies show that critical neuronal avalanches show mean-field behavior. There are structural as well as recently proposed [Phys. Rev. E 89, 052139 (2014), 10.1103/PhysRevE.89.052139] dynamical mechanisms that can lead to mean-field behavior. In this work we consider a simple model of neuronal dynamics based on threshold self-organized critical models with synaptic noise. We investigate the role of high-average connectivity, random long-range connections, as well as synaptic noise in achieving mean-field behavior. We employ finite-size scaling in order to extract critical exponents with good accuracy. We conclude that relevant structural mechanisms responsible for mean-field behavior cannot be justified in realistic models of the cortex. However, strong dynamical noise, which can have realistic justifications, always leads to mean-field behavior regardless of the underlying structure. Our work provides a different (dynamical) origin than the conventionally accepted (structural) mechanisms for mean-field behavior in neuronal avalanches.

Ion radial diffusion in an electrostatic impulse model for stormtime ring current formation

NASA Technical Reports Server (NTRS)

Chen, Margaret W.; Schulz, Michael; Lyons, Larry R.; Gorney, David J.

1992-01-01

Guiding-center simulations of stormtime transport of ring-current and radiation-belt ions having first adiabatic invariants mu is approximately greater than 15 MeV/G (E is approximately greater than 165 keV at L is approximately 3) are surprisingly well described (typically within a factor of approximately less than 4) by the quasilinear theory of radial diffusion. This holds even for the case of an individual model storm characterized by substorm-associated impulses in the convection electric field, provided that the actual spectrum of the electric field is incorporated in the quasilinear theory. Correction of the quasilinear diffusion coefficient D(sub LL)(sup ql) for drift-resonance broadening (so as to define D(sub LL)(sup ql)) reduced the typical discrepancy with the diffusion coefficients D(sub LL)(sup sim) deduced from guiding-center simulations of representative-particle trajectories to a factor of approximately 3. The typical discrepancy was reduced to a factor of approximately 1.4 by averaging D(sub LL)(sup sim), D(sub LL)(sup ql), and D(sub LL)(sup rb) over an ensemble of model storms characterized by different (but statistically equivalent) sets of substorm-onset times.

Pion properties at finite isospin chemical potential with isospin symmetry breaking

NASA Astrophysics Data System (ADS)

Wu, Zuqing; Ping, Jialun; Zong, Hongshi

2017-12-01

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI <0 and μI >0 in the phase diagram, and different values for the charged pion mass (or decay constant) and neutral pion mass (or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses. Supported by National Natural Science Foundation of China (11175088, 11475085, 11535005, 11690030) and the Fundamental Research Funds for the Central Universities (020414380074)

Non-Gaussianity from self-ordering scalar fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Figueroa, Daniel G.; Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, 28049 Madrid; Caldwell, Robert R.

The Universe may harbor relics of the post-inflationary epoch in the form of a network of self-ordered scalar fields. Such fossils, while consistent with current cosmological data at trace levels, may leave too weak an imprint on the cosmic microwave background and the large-scale distribution of matter to allow for direct detection. The non-Gaussian statistics of the density perturbations induced by these fields, however, permit a direct means to probe for these relics. Here we calculate the bispectrum that arises in models of self-ordered scalar fields. We find a compact analytic expression for the bispectrum, evaluate it numerically, and providemore » a simple approximation that may be useful for data analysis. The bispectrum is largest for triangles that are aligned (have edges k{sub 1{approx_equal}}2k{sub 2{approx_equal}}2k{sub 3}) as opposed to the local-model bispectrum, which peaks for squeezed triangles (k{sub 1{approx_equal}}k{sub 2}>>k{sub 3}), and the equilateral bispectrum, which peaks at k{sub 1{approx_equal}}k{sub 2{approx_equal}}k{sub 3}. We estimate that this non-Gaussianity should be detectable by the Planck satellite if the contribution from self-ordering scalar fields to primordial perturbations is near the current upper limit.« less

Axisymmetric simulations of magnetorotational core collapse: approximate inclusion of general relativistic effects

NASA Astrophysics Data System (ADS)

Obergaulinger, M.; Aloy, M. A.; Dimmelmeier, H.; Müller, E.

2006-10-01

We continue our investigations of the magnetorotational collapse of stellar cores by discussing simulations performed with a modified Newtonian gravitational potential that mimics general relativistic effects. The approximate TOV gravitational potential used in our simulations captures several basic features of fully relativistic simulations quite well. In particular, it is able to correctly reproduce the behavior of models that show a qualitative change both of the dynamics and the gravitational wave signal when switching from Newtonian to fully relativistic simulations. For models where the dynamics and gravitational wave signals are already captured qualitatively correctly by a Newtonian potential, the results of the Newtonian and the approximate TOV models differ quantitatively. The collapse proceeds to higher densities with the approximate TOV potential, allowing for a more efficient amplification of the magnetic field by differential rotation. The strength of the saturation fields (˜ 1015 ~ G at the surface of the inner core) is a factor of two to three higher than in Newtonian gravity. Due to the more efficient field amplification, the influence of magnetic fields is considerably more pronounced than in the Newtonian case for some of the models. As in the Newtonian case, sufficiently strong magnetic fields slow down the core's rotation and trigger a secular contraction phase to higher densities. More clearly than in Newtonian models, the collapsed cores of these models exhibit two different kinds of shock generation. Due to magnetic braking, a first shock wave created during the initial centrifugal bounce at subnuclear densities does not suffice for ejecting any mass, and the temporarily stabilized core continues to collapse to supranuclear densities. Another stronger shock wave is generated during the second bounce as the core exceeds nuclear matter density. The gravitational wave signal of these models does not fit into the standard classification. Therefore, in the first paper of this series we introduced a new type of gravitational wave signal, which we call type IV or “magnetic type”. This signal type is more frequent for the approximate relativistic potential than for the Newtonian one. Most of our weak-field models are marginally detectable with the current LIGO interferometer for a source located at a distance of 10 kpc. Strongly magnetized models emit a substantial fraction of their GW power at very low frequencies. A flat spectrum between 10 Hz and ⪉ 100 kHz denotes the generation of a jet-like hydromagnetic outflow.

A unified model of density limit in fusion plasmas

NASA Astrophysics Data System (ADS)

Zanca, P.; Sattin, F.; Escande, D. F.; Pucella, G.; Tudisco, O.

2017-05-01

In this work we identify by analytical and numerical means the conditions for the existence of a magnetic and thermal equilibrium of a cylindrical plasma, in the presence of Ohmic and/or additional power sources, heat conduction and radiation losses by light impurities. The boundary defining the solutions’ space having realistic temperature profile with small edge value takes mathematically the form of a density limit (DL). Compared to previous similar analyses the present work benefits from dealing with a more accurate set of equations. This refinement is elementary, but decisive, since it discloses a tenuous dependence of the DL on the thermal transport for configurations with an applied electric field. Thanks to this property, the DL scaling law is recovered almost identical for two largely different devices such as the ohmic tokamak and the reversed field pinch. In particular, they have in common a Greenwald scaling, linearly depending on the plasma current, quantitatively consistent with experimental results. In the tokamak case the DL dependence on any additional heating approximately follows a 0.5 power law, which is compatible with L-mode experiments. For a purely externally heated configuration, taken as a cylindrical approximation of the stellarator, the DL dependence on transport is found stronger. By adopting suitable transport models, DL takes on a Sudo-like form, in fair agreement with LHD experiments. Overall, the model provides a good zeroth-order quantitative description of the DL, applicable to widely different configurations.

Methodological study of computational approaches to address the problem of strong correlations

NASA Astrophysics Data System (ADS)

Lee, Juho

The main focus of this thesis is the detailed investigation of computational methods to tackle strongly correlated materials in which a rich variety of exotic phenomena are found. A many-body problem with sizable electronic correlations can no longer be explained by independent-particle approximations such as density functional theory (DFT) or tight-binding approaches. The influence of an electron to the others is too strong for each electron to be treated as an independent quasiparticle and consequently those standard band-structure methods fail even at a qualitative level. One of the most powerful approaches for strong correlations is the dynamical mean-field theory (DMFT), which has enlightened the understanding of the Mott transition based on the Hubbard model. For realistic applications, the dynamical mean-field theory is combined with various independent-particles approaches. The most widely used one is the DMFT combined with the DFT in the local density approximation (LDA), so-called LDA+DMFT. In this approach, the electrons in the weakly correlated orbitals are calculated by LDA while others in the strongly correlated orbitals are treated by DMFT. Recently, the method combining DMFT with Hedin's GW approximation was also developed, in which the momentum-dependent self-energy is also added. In this thesis, we discuss the application of those methodologies based on DMFT. First, we apply the dynamical mean-field theory to solve the 3-dimensional Hubbard model in Chap. 3. In this application, we model the interface between the thermodynamically coexisting metal and Mott insulator. We show how to model the required slab geometry and extract the electronic spectra. We construct an effective Landau free energy and compute the variation of its parameters across the phase diagram. Finally, using a linear mixture of the density and double-occupancy, we identify a natural Ising order parameter which unifies the treatment of the bandwidth and filling controlled Mott transitions. Secondly, we study the double-counting problem, a subtle issue that arises in LDA+DMFT. We propose a highly precise double-counting functional, in which the intersection of LDA and DMFT is calculated exactly, and implement a parameter-free version of the LDA+DMFT that is tested on one of the simplest strongly correlated systems, the H2 molecule. We show that the exact double-counting treatment along with a good DMFT projector leads to very accurate and total energy and excitation spectrum of H2 molecule. Finally, we implement various versions of GW+DMFT, in its fully self-consistent way, one shot GW approximation, and quasiparticle self-consistent scheme, and studied how well these combined methods perform on H2 molecule as compared to more established methods such as LDA+DMFT. We found that most flavors of GW+DMFT break down in strongly correlated regime due to causality violation. Among GW+DMFT methods, only the self-consistent quasiparticle GW+DMFT with static double-counting, and a new method with causal double-counting, correctly recover the atomic limit at large H-atom separation. While some flavors of GW+DMFT improve the single-electron spectra of LDA+DMFT, the total energy is best predicted by LDA+DMFT, for which the exact double-counting is known, and is static.

Comparison Of The Global Analytic Models Of The Main Geomagnetic Field With The Stratospheric Balloon Magnetic Data 335

NASA Astrophysics Data System (ADS)

Tsvetkov, Yu.; Filippov, S.; Frunze, A.

2013-12-01

Three global analytical models of a main geomagnetic field constructed by satellite data are used: model IGRF, Daily Mean Spherical Harmonic Models (DMSHM), and model EMM/2010, and also scalar data of geomagnetic field and its gradients, received in stratospheric balloon gradient magnetic surveys at altitudes of ~30 km. At these altitudes the regional magnetic field is formed from all sources of the Earth's crust. It enables to receive along lengthy routes of surveys the fullest data on regional and longwave-lenght magnetic anomalies. Model DMSHM is used at extracting of magnetic anomalies for elimination of a secular variation up to significant value 0,2 nT. The model can be constructed within the limits of ± 1 months from the moment stratospheric balloon surveys with beneficial day terms with magnetic activity up to Kp <20, that leads to an error of representation of main MFE equal ±5 нТл. It is possible at presence acting for the period of stratospheric balloon magnetic survey of the satellite, for example, Swarm. On stratospheric balloon data it is shown, that model EMM/2010 unsatisfactorily displays MFE at altitude of 30 km. Hence, the qualitative model of the constant (main and anomaly) magnetic field cannot be constructed only with use of satellite and ground data. The improved model constant MFE, constructed according to satellite and stratospheric balloon magnetic surveys, developed up to a degree and the order m=n=720, will have a reliable data about regional crust magnetic field, hence, and about deep magnetic structure of the Earth's crust. The use gradient magnetic surveys aboard stratospheric balloons allows to find the places alternating approximately through 3000 km in which there are no magnetic anomalies. In these places probably to supervise satellite magnetic models for a range of altitude of 20-40 km, timed to stratospheric balloon magnetic surveys.

JOURNAL SCOPE GUIDELINES: Paper classification scheme

NASA Astrophysics Data System (ADS)

2005-06-01

This scheme is used to clarify the journal's scope and enable authors and readers to more easily locate the appropriate section for their work. For each of the sections listed in the scope statement we suggest some more detailed subject areas which help define that subject area. These lists are by no means exhaustive and are intended only as a guide to the type of papers we envisage appearing in each section. We acknowledge that no classification scheme can be perfect and that there are some papers which might be placed in more than one section. We are happy to provide further advice on paper classification to authors upon request (please email jphysa@iop.org). 1. Statistical physics numerical and computational methods statistical mechanics, phase transitions and critical phenomena quantum condensed matter theory Bose-Einstein condensation strongly correlated electron systems exactly solvable models in statistical mechanics lattice models, random walks and combinatorics field-theoretical models in statistical mechanics disordered systems, spin glasses and neural networks nonequilibrium systems network theory 2. Chaotic and complex systems nonlinear dynamics and classical chaos fractals and multifractals quantum chaos classical and quantum transport cellular automata granular systems and self-organization pattern formation biophysical models 3. Mathematical physics combinatorics algebraic structures and number theory matrix theory classical and quantum groups, symmetry and representation theory Lie algebras, special functions and orthogonal polynomials ordinary and partial differential equations difference and functional equations integrable systems soliton theory functional analysis and operator theory inverse problems geometry, differential geometry and topology numerical approximation and analysis geometric integration computational methods 4. Quantum mechanics and quantum information theory coherent states eigenvalue problems supersymmetric quantum mechanics scattering theory relativistic quantum mechanics semiclassical approximations foundations of quantum mechanics and measurement theory entanglement and quantum nonlocality geometric phases and quantum tomography quantum tunnelling decoherence and open systems quantum cryptography, communication and computation theoretical quantum optics 5. Classical and quantum field theory quantum field theory gauge and conformal field theory quantum electrodynamics and quantum chromodynamics Casimir effect integrable field theory random matrix theory applications in field theory string theory and its developments classical field theory and electromagnetism metamaterials 6. Fluid and plasma theory turbulence fundamental plasma physics kinetic theory magnetohydrodynamics and multifluid descriptions strongly coupled plasmas one-component plasmas non-neutral plasmas astrophysical and dusty plasmas

Finite size induces crossover temperature in growing spin chains

NASA Astrophysics Data System (ADS)

Sienkiewicz, Julian; Suchecki, Krzysztof; Hołyst, Janusz A.

2014-01-01

We introduce a growing one-dimensional quenched spin model that bases on asymmetrical one-side Ising interactions in the presence of external field. Numerical simulations and analytical calculations based on Markov chain theory show that when the external field is smaller than the exchange coupling constant J there is a nonmonotonous dependence of the mean magnetization on the temperature in a finite system. The crossover temperature Tc corresponding to the maximal magnetization decays with system size, approximately as the inverse of the Lambert W function. The observed phenomenon can be understood as an interplay between the thermal fluctuations and the presence of the first cluster determined by initial conditions. The effect exists also when spins are not quenched but fully thermalized after the attachment to the chain. By performing tests on real data we conceive the model is in part suitable for a qualitative description of online emotional discussions arranged in a chronological order, where a spin in every node conveys emotional valence of a subsequent post.

Finite size induces crossover temperature in growing spin chains.

PubMed

Sienkiewicz, Julian; Suchecki, Krzysztof; Hołyst, Janusz A

2014-01-01

We introduce a growing one-dimensional quenched spin model that bases on asymmetrical one-side Ising interactions in the presence of external field. Numerical simulations and analytical calculations based on Markov chain theory show that when the external field is smaller than the exchange coupling constant J there is a nonmonotonous dependence of the mean magnetization on the temperature in a finite system. The crossover temperature Tc corresponding to the maximal magnetization decays with system size, approximately as the inverse of the Lambert W function. The observed phenomenon can be understood as an interplay between the thermal fluctuations and the presence of the first cluster determined by initial conditions. The effect exists also when spins are not quenched but fully thermalized after the attachment to the chain. By performing tests on real data we conceive the model is in part suitable for a qualitative description of online emotional discussions arranged in a chronological order, where a spin in every node conveys emotional valence of a subsequent post.

Attenuation of the NMR signal in a field gradient due to stochastic dynamics with memory

NASA Astrophysics Data System (ADS)

Lisý, Vladimír; Tóthová, Jana

2017-03-01

The attenuation function S(t) for an ensemble of spins in a magnetic-field gradient is calculated by accumulation of the phase shifts in the rotating frame resulting from the displacements of spin-bearing particles. The found S(t), expressed through the particle mean square displacement, is applicable for any kind of stationary stochastic motion of spins, including their non-markovian dynamics with memory. The known expressions valid for normal and anomalous diffusion are obtained as special cases in the long time approximation. The method is also applicable to the NMR pulse sequences based on the refocusing principle. This is demonstrated by describing the Hahn spin echo experiment. The attenuation of the NMR signal is also evaluated providing that the random motion of particle is modeled by the generalized Langevin equation with the memory kernel exponentially decaying in time. The models considered in our paper assume massive particles driven by much smaller particles.

Numerical evaluation of electromagnetic fields due to dipole antennas in the presence of stratified media

NASA Technical Reports Server (NTRS)

Tsang, L.; Brown, R.; Kong, J. A.; Simmons, G.

1974-01-01

Two numerical methods are used to evaluate the integrals that express the em fields due to dipole antennas radiating in the presence of a stratified medium. The first method is a direct integration by means of Simpson's rule. The second method is indirect and approximates the kernel of the integral by means of the fast Fourier transform. In contrast to previous analytical methods that applied only to two-layer cases the numerical methods can be used for any arbitrary number of layers with general properties.

Two-dimensional Fermi gas in spin-dependent magnetic fields

NASA Astrophysics Data System (ADS)

Anzai, Takaaki; Nishida, Yusuke

Experimental techniques in ultracold atoms allow us to tune parameters of the system at will. In particular, synthetic magnetic fields have been created by using the atom-light coupling and, therefore, it is interesting to study what kinds of quantum phenomena appear in correlated ultracold atoms subjected to synthetic magnetic fields. In this work, we consider a two-dimensional Fermi gas with two spin states in spin-dependent magnetic fields which are assumed to be antiparallel for different spin states. By studying the ground-state phase diagram within the mean-field approximation, we find quantum spin Hall and superfluid phases separated by a second-order phase transition. We also show that there are regions where the superfluid gap parameter is proportional to the attractive coupling, which is in marked contrast to the usual exponential dependence. Moreover, we elucidate that the universality class of the phase transition belongs to that of the XY model at special points of the phase boundary, while it belongs to that of a dilute Bose gas anywhere else. International Research Center for Nanoscience and Quantum Physics, Tokyo Institute of Technology.

On the frequency spectra of the core magnetic field Gauss coefficients

NASA Astrophysics Data System (ADS)

Lesur, Vincent; Wardinski, Ingo; Baerenzung, Julien; Holschneider, Matthias

2018-03-01

From monthly mean observatory data spanning 1957-2014, geomagnetic field secular variation values were calculated by annual differences. Estimates of the spherical harmonic Gauss coefficients of the core field secular variation were then derived by applying a correlation based modelling. Finally, a Fourier transform was applied to the time series of the Gauss coefficients. This process led to reliable temporal spectra of the Gauss coefficients up to spherical harmonic degree 5 or 6, and down to periods as short as 1 or 2 years depending on the coefficient. We observed that a k-2 slope, where k is the frequency, is an acceptable approximation for these spectra, with possibly an exception for the dipole field. The monthly estimates of the core field secular variation at the observatory sites also show that large and rapid variations of the latter happen. This is an indication that geomagnetic jerks are frequent phenomena and that significant secular variation signals at short time scales - i.e. less than 2 years, could still be extracted from data to reveal an unexplored part of the core dynamics.

Unified TeV scale picture of baryogenesis and dark matter.

PubMed

Babu, K S; Mohapatra, R N; Nasri, Salah

2007-04-20

We present a simple extension of the minimal supersymmetric standard model which provides a unified picture of cosmological baryon asymmetry and dark matter. Our model introduces a gauge singlet field N and a color triplet field X which couple to the right-handed quark fields. The out-of-equilibrium decay of the Majorana fermion N mediated by the exchange of the scalar field X generates adequate baryon asymmetry for MN approximately 100 GeV and MX approximately TeV. The scalar partner of N (denoted N1) is naturally the lightest SUSY particle as it has no gauge interactions and plays the role of dark matter. The model is experimentally testable in (i) neutron-antineutron oscillations with a transition time estimated to be around 10(10)sec, (ii) discovery of colored particles X at LHC with mass of order TeV, and (iii) direct dark matter detection with a predicted cross section in the observable range.

The 1D Richards' equation in two layered soils: a Filippov approach to treat discontinuities

NASA Astrophysics Data System (ADS)

Berardi, Marco; Difonzo, Fabio; Vurro, Michele; Lopez, Luciano

2018-05-01

The infiltration process into the soil is generally modeled by the Richards' partial differential equation (PDE). In this paper a new approach for modeling the infiltration process through the interface of two different soils is proposed, where the interface is seen as a discontinuity surface defined by suitable state variables. Thus, the original 1D Richards' PDE, enriched by a particular choice of the boundary conditions, is first approximated by means of a time semidiscretization, that is by means of the transversal method of lines (TMOL). In such a way a sequence of discontinuous initial value problems, described by a sequence of second order differential systems in the space variable, is derived. Then, Filippov theory on discontinuous dynamical systems may be applied in order to study the relevant dynamics of the problem. The numerical integration of the semidiscretized differential system will be performed by using a one-step method, which employs an event driven procedure to locate the discontinuity surface and to adequately change the vector field.

Subtraction method in the Second Random Phase Approximation

NASA Astrophysics Data System (ADS)

Gambacurta, Danilo

2018-02-01

We discuss the subtraction method applied to the Second Random Phase Approximation (SRPA). This method has been proposed to overcome double counting and stability issues appearing in beyond mean-field calculations. We show that the subtraction procedure leads to a considerable reduction of the SRPA downwards shift with respect to the random phase approximation (RPA) spectra and to results that are weakly cutoff dependent. Applications to the isoscalar monopole and quadrupole response in 16O and to the low-lying dipole response in 48Ca are shown and discussed.

The environmental effect on the radial breathing mode of carbon nanotubes. II. Shell model approximation for internally and externally adsorbed fluids

NASA Astrophysics Data System (ADS)

Longhurst, M. J.; Quirke, N.

2006-11-01

We have previously shown that the upshift in the radial breathing mode (RBM) of closed (or infinite) carbon nanotubes in solution is almost entirely due to coupling of the RBM with an adsorbed layer of fluid on the nanotube surface. The upshift can be modeled analytically by considering the adsorbed fluid as an infinitesimally thin shell, which interacts with the nanotube via a continuum Lennard-Jones potential. Here we extend the model to include internally as well as externally adsorbed waterlike molecules, and find that filling the nanotubes leads to an additional upshift of two to six wave numbers. We show that using molecular dynamics, the RBM can be accurately reproduced by replacing the fluid molecules with a mean field harmonic shell potential, greatly reducing simulation times.

Electromotive force and large-scale magnetic dynamo in a turbulent flow with a mean shear.

PubMed

Rogachevskii, Igor; Kleeorin, Nathan

2003-09-01

An effect of sheared large-scale motions on a mean electromotive force in a nonrotating turbulent flow of a conducting fluid is studied. It is demonstrated that in a homogeneous divergence-free turbulent flow the alpha effect does not exist, however a mean magnetic field can be generated even in a nonrotating turbulence with an imposed mean velocity shear due to a "shear-current" effect. A mean velocity shear results in an anisotropy of turbulent magnetic diffusion. A contribution to the electromotive force related to the symmetric parts of the gradient tensor of the mean magnetic field (the kappa effect) is found in nonrotating turbulent flows with a mean shear. The kappa effect and turbulent magnetic diffusion reduce the growth rate of the mean magnetic field. It is shown that a mean magnetic field can be generated when the exponent of the energy spectrum of the background turbulence (without the mean velocity shear) is less than 2. The shear-current effect was studied using two different methods: the tau approximation (the Orszag third-order closure procedure) and the stochastic calculus (the path integral representation of the solution of the induction equation, Feynman-Kac formula, and Cameron-Martin-Girsanov theorem). Astrophysical applications of the obtained results are discussed.

A high speed model-based approach for wavefront sensorless adaptive optics systems

NASA Astrophysics Data System (ADS)

Lianghua, Wen; Yang, Ping; Shuai, Wang; Wenjing, Liu; Shanqiu, Chen; Xu, Bing

2018-02-01

To improve temporal-frequency property of wavefront sensorless adaptive optics (AO) systems, a fast general model-based aberration correction algorithm is presented. The fast general model-based approach is based on the approximately linear relation between the mean square of the aberration gradients and the second moment of far-field intensity distribution. The presented model-based method is capable of completing a mode aberration effective correction just applying one disturbing onto the deformable mirror(one correction by one disturbing), which is reconstructed by the singular value decomposing the correlation matrix of the Zernike functions' gradients. Numerical simulations of AO corrections under the various random and dynamic aberrations are implemented. The simulation results indicate that the equivalent control bandwidth is 2-3 times than that of the previous method with one aberration correction after applying N times disturbing onto the deformable mirror (one correction by N disturbing).

M2, S2, K1 models of the global ocean tide

NASA Technical Reports Server (NTRS)

Parke, M. E.; Hendershott, M. C.

1979-01-01

Ocean tidal signals appear in many geophysical measurements. Geophysicists need realistic tidal models to aid in interpretation of their data. Because of the closeness to resonance of dissipationless ocean tides, it is difficult for numerical models to correctly represent the actual open ocean tide. As an approximate solution to this problem, test functions derived by solving Laplace's Tidal Equations with ocean loading and self gravitation are used as a basis for least squares dynamic interpolation of coastal and island tidal data for the constituents M2, S2, and Kl. The resulting representations of the global tide are stable over at least a ?5% variation in the mean depth of the model basin, and they conserve mass. Maps of the geocentric tide, the induced free space potential, the induced vertical component of the solid earth tide, and the induced vertical component of the gravitational field for each contituent are presented.

Two-population dynamics in a growing network model

NASA Astrophysics Data System (ADS)

Ivanova, Kristinka; Iordanov, Ivan

2012-02-01

We introduce a growing network evolution model with nodal attributes. The model describes the interactions between potentially violent V and non-violent N agents who have different affinities in establishing connections within their own population versus between the populations. The model is able to generate all stable triads observed in real social systems. In the framework of rate equations theory, we employ the mean-field approximation to derive analytical expressions of the degree distribution and the local clustering coefficient for each type of nodes. Analytical derivations agree well with numerical simulation results. The assortativity of the potentially violent network qualitatively resembles the connectivity pattern in terrorist networks that was recently reported. The assortativity of the network driven by aggression shows clearly different behavior than the assortativity of the networks with connections of non-aggressive nature in agreement with recent empirical results of an online social system.

When push comes to shove: Exclusion processes with nonlocal consequences

NASA Astrophysics Data System (ADS)

Almet, Axel A.; Pan, Michael; Hughes, Barry D.; Landman, Kerry A.

2015-11-01

Stochastic agent-based models are useful for modelling collective movement of biological cells. Lattice-based random walk models of interacting agents where each site can be occupied by at most one agent are called simple exclusion processes. An alternative motility mechanism to simple exclusion is formulated, in which agents are granted more freedom to move under the compromise that interactions are no longer necessarily local. This mechanism is termed shoving. A nonlinear diffusion equation is derived for a single population of shoving agents using mean-field continuum approximations. A continuum model is also derived for a multispecies problem with interacting subpopulations, which either obey the shoving rules or the simple exclusion rules. Numerical solutions of the derived partial differential equations compare well with averaged simulation results for both the single species and multispecies processes in two dimensions, while some issues arise in one dimension for the multispecies case.

Modeling mesoscopic cortical dynamics using a mean-field model of conductance-based networks of adaptive exponential integrate-and-fire neurons.

PubMed

Zerlaut, Yann; Chemla, Sandrine; Chavane, Frederic; Destexhe, Alain

2018-02-01

Voltage-sensitive dye imaging (VSDi) has revealed fundamental properties of neocortical processing at macroscopic scales. Since for each pixel VSDi signals report the average membrane potential over hundreds of neurons, it seems natural to use a mean-field formalism to model such signals. Here, we present a mean-field model of networks of Adaptive Exponential (AdEx) integrate-and-fire neurons, with conductance-based synaptic interactions. We study a network of regular-spiking (RS) excitatory neurons and fast-spiking (FS) inhibitory neurons. We use a Master Equation formalism, together with a semi-analytic approach to the transfer function of AdEx neurons to describe the average dynamics of the coupled populations. We compare the predictions of this mean-field model to simulated networks of RS-FS cells, first at the level of the spontaneous activity of the network, which is well predicted by the analytical description. Second, we investigate the response of the network to time-varying external input, and show that the mean-field model predicts the response time course of the population. Finally, to model VSDi signals, we consider a one-dimensional ring model made of interconnected RS-FS mean-field units. We found that this model can reproduce the spatio-temporal patterns seen in VSDi of awake monkey visual cortex as a response to local and transient visual stimuli. Conversely, we show that the model allows one to infer physiological parameters from the experimentally-recorded spatio-temporal patterns.

LES study of microphysical variability bias in shallow cumulus

NASA Astrophysics Data System (ADS)

Kogan, Yefim

2017-05-01

Subgrid-scale (SGS) variability of cloud microphysical variables over the mesoscale numerical weather prediction (NWP) model has been evaluated by means of joint probability distribution functions (JPDFs). The latter were obtained using dynamically balanced Large Eddy Simulation (LES) model dataset from a case of marine trade cumulus initialized with soundings from Rain in Cumulus Over the Ocean (RICO) field project. Bias in autoconversion and accretion rates from different formulations of the JPDFs was analyzed. Approximating the 2-D PDF using a generic (fixed-in-time), but variable-in-height JPDFs give an acceptable level of accuracy, whereas neglecting the SGS variability altogether results in a substantial underestimate of the grid-mean total conversion rate and producing negative bias in rain water. Nevertheless the total effect on rain formation may be uncertain in the long run due to the fact that the negative bias in rain water may be counterbalanced by the positive bias in cloud water. Consequently, the overall effect of SGS neglect needs to be investigated in direct simulations with a NWP model.

Bulk viscosity of strongly interacting matter in the relaxation time approximation

DOE PAGES

Czajka, Alina; Hauksson, Sigtryggur; Shen, Chun; ...

2018-04-24

Here, we show how thermal mean field effects can be incorporated consistently in the hydrodynamical modeling of heavy-ion collisions. The nonequilibrium correction to the distribution function resulting from a temperature-dependent mass is obtained in a procedure which automatically satisfies the Landau matching condition and is thermodynamically consistent. The physics of the bulk viscosity is studied here for Boltzmann and Bose-Einstein gases within the Chapman-Enskog and 14-moment approaches in the relaxation time approximation. Constant and temperature-dependent masses are considered in turn. It is shown that, in the small mass limit, both methods lead to the same value of the ratio ofmore » the bulk viscosity to its relaxation time. The inclusion of a temperature-dependent mass leads to the emergence of the β λ function in that ratio, and it is of the expected parametric form for the Boltzmann gas, while for the Bose-Einstein case it is affected by the infrared cutoff. This suggests that the relaxation time approximation may be too crude to obtain a reliable form of ς/τ R for gases obeying Bose-Einstein statistics.« less

Bulk viscosity of strongly interacting matter in the relaxation time approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Czajka, Alina; Hauksson, Sigtryggur; Shen, Chun

Here, we show how thermal mean field effects can be incorporated consistently in the hydrodynamical modeling of heavy-ion collisions. The nonequilibrium correction to the distribution function resulting from a temperature-dependent mass is obtained in a procedure which automatically satisfies the Landau matching condition and is thermodynamically consistent. The physics of the bulk viscosity is studied here for Boltzmann and Bose-Einstein gases within the Chapman-Enskog and 14-moment approaches in the relaxation time approximation. Constant and temperature-dependent masses are considered in turn. It is shown that, in the small mass limit, both methods lead to the same value of the ratio ofmore » the bulk viscosity to its relaxation time. The inclusion of a temperature-dependent mass leads to the emergence of the β λ function in that ratio, and it is of the expected parametric form for the Boltzmann gas, while for the Bose-Einstein case it is affected by the infrared cutoff. This suggests that the relaxation time approximation may be too crude to obtain a reliable form of ς/τ R for gases obeying Bose-Einstein statistics.« less

Bulk viscosity of strongly interacting matter in the relaxation time approximation

NASA Astrophysics Data System (ADS)

Czajka, Alina; Hauksson, Sigtryggur; Shen, Chun; Jeon, Sangyong; Gale, Charles

2018-04-01

We show how thermal mean field effects can be incorporated consistently in the hydrodynamical modeling of heavy-ion collisions. The nonequilibrium correction to the distribution function resulting from a temperature-dependent mass is obtained in a procedure which automatically satisfies the Landau matching condition and is thermodynamically consistent. The physics of the bulk viscosity is studied here for Boltzmann and Bose-Einstein gases within the Chapman-Enskog and 14-moment approaches in the relaxation time approximation. Constant and temperature-dependent masses are considered in turn. It is shown that, in the small mass limit, both methods lead to the same value of the ratio of the bulk viscosity to its relaxation time. The inclusion of a temperature-dependent mass leads to the emergence of the βλ function in that ratio, and it is of the expected parametric form for the Boltzmann gas, while for the Bose-Einstein case it is affected by the infrared cutoff. This suggests that the relaxation time approximation may be too crude to obtain a reliable form of ζ /τR for gases obeying Bose-Einstein statistics.

Gravity Wave Mixing and Effective Diffusivity for Minor Chemical Constituents in the Mesosphere/Lower Thermosphere

NASA Astrophysics Data System (ADS)

Grygalashvyly, M.; Becker, E.; Sonnemann, G. R.

2012-06-01

The influence of gravity waves (GWs) on the distributions of minor chemical constituents in the mesosphere-lower thermosphere (MLT) is studied on the basis of the effective diffusivity concept. The mixing ratios of chemical species used for calculations of the effective diffusivity are obtained from numerical experiments with an off-line coupled model of the dynamics and chemistry abbreviated as KMCM-MECTM (Kuehlungsborn Mechanistic general Circulation Model—MEsospheric Chemistry-Transport Model). In our control simulation the MECTM is driven with the full dynamical fields from an annual cycle simulation with the KMCM, where mid-frequency GWs down to horizontal wavelengths of 350 km are resolved and their wave-mean flow interaction is self-consistently induced by an advanced turbulence model. A perturbation simulation with the MECTM is defined by eliminating all meso-scale variations with horizontal wavelengths shorter than 1000 km from the dynamical fields by means of spectral filtering before running the MECTM. The response of the MECTM to GWs perturbations reveals strong effects on the minor chemical constituents. We show by theoretical arguments and numerical diagnostics that GWs have direct, down-gradient mixing effects on all long-lived minor chemical species that possess a mean vertical gradient in the MLT. Introducing the term wave diffusion (WD) and showing that wave mixing yields approximately the same WD coefficient for different chemical constituents, we argue that it is a useful tool for diagnostic irreversible transport processes. We also present a detailed discussion of the gravity-wave mixing effects on the photochemistry and highlight the consequences for the general circulation of the MLT.

Transport toward a well in highly heterogeneous aquifer

NASA Astrophysics Data System (ADS)

Di Dato, Mariaines; de Barros, Felipe P. J.; Bellin, Alberto; Fiori, Aldo

2017-04-01

Solute transport toward a well is a challenging subject in subsurface hydrology since the complexity of the mathematical model is tremendously increased by the non-uniformity of the mean flow and heterogeneity of the formation. Up to date, analytical solutions for such flow configurations are limited to low heterogeneous conditions. On the other hand, numerical simulations in 3D highly heterogeneous formations are computationally expensive and plagued by numerical errors. In this work we propose an analytical solution for the Breakthrough Curve (BTC) at the well for an instantaneous linear injection across the aquifer's thickness for any degree of heterogeneity of the porous medium. Our solution makes use of the Multi Indicator Model-Self Consistent Approximation (MIMSCA), by which the aquifer is conceptualized as an ensemble of blocks of constant hydraulic conductivity K randomly drawn from a lognormal distribution. In order to apply MIMSCA, we assume the flow as locally uniform, given that K is uniform within the block. With this approximation, the travel time to the well is equal to the superposition of the time spent by the solute particle within each block. We emphasize that, despite the approximations introduced, the model is able to reproduce the laboratory experiment of [1] without the need to fit any transport parameters. In this work, we present results for two different injection modes: a resident injection (e.g., residual DNAPL) and a flux proportional injection (e.g., leakage from a passive well). The proposed methodology allows to quantify the BTC at the well as a function of few parameters such as the injection mode and the statistical structure of the aquifer (geometric mean, variance and integral scale of the hydraulic conductivity field). Results illustrate that the release condition has a strong impact on the shape of the BTC. Furthermore, the difference between different injection modes increases with the heterogeneity of the K-field. The importance of the both injection mode and heterogeneity degree are also elucidated on the early and late solute arrival times at the well. Finally, we show how travel times become ergodic only for very thick aquifers, even in case of mild heterogeneity. We emphasize that the present framework has a practical validity, giving an affordable, although approximated, first estimation of mass arrival at an extraction well. References [1] Fernàndez-Garcia, D., T. H. Illangasekare, and H. Rajaram (2004), Conservative and sorptive forced-gradient and uniform flow tracer tests in a three-dimensional laboratory test aquifer, Water Resour. Res., 40, W10103, doi:10.1029/2004WR003112.

Semiclassical Models for Virtual Antiparticle Pairs, the Unit of Charge e, and the QCD Coupling alpha(sub s)

NASA Technical Reports Server (NTRS)

Batchelor, David; Zukor, Dorothy (Technical Monitor)

2001-01-01

New semiclassical models of virtual antiparticle pairs are used to compute the pair lifetimes, and good agreement with the Heisenberg lifetimes from quantum field theory (QFT) is found. The modeling method applies to both the electromagnetic and color forces. Evaluation of the action integral of potential field fluctuation for each interaction potential yields approximately Planck's constant/2 for both electromagnetic and color fluctuations, in agreement with QFT. Thus each model is a quantized semiclassical representation for such virtual antiparticle pairs, to good approximation. When the results of the new models and QFT are combined, formulae for e and alpha(sub s)(q) are derived in terms of only Planck's constant and c.

Fierz Convergence Criterion: A Controlled Approach to Strongly Interacting Systems with Small Embedded Clusters.

PubMed

Ayral, Thomas; Vučičević, Jaksa; Parcollet, Olivier

2017-10-20

We present an embedded-cluster method, based on the triply irreducible local expansion formalism. It turns the Fierz ambiguity, inherent to approaches based on a bosonic decoupling of local fermionic interactions, into a convergence criterion. It is based on the approximation of the three-leg vertex by a coarse-grained vertex computed from a self-consistently determined cluster impurity model. The computed self-energies are, by construction, continuous functions of momentum. We show that, in three interaction and doping regimes of the two-dimensional Hubbard model, self-energies obtained with clusters of size four only are very close to numerically exact benchmark results. We show that the Fierz parameter, which parametrizes the freedom in the Hubbard-Stratonovich decoupling, can be used as a quality control parameter. By contrast, the GW+extended dynamical mean field theory approximation with four cluster sites is shown to yield good results only in the weak-coupling regime and for a particular decoupling. Finally, we show that the vertex has spatially nonlocal components only at low Matsubara frequencies.

Techniques of Global analysis applied to gravitation theories: A cosmological black hole?

NASA Technical Reports Server (NTRS)

Debney, G.

1977-01-01

An elementary model of freely falling observers and emitters within a black hole's radius is examined to determine the redshift spectrum reaching a typical observer. The model is independent of scale, the fundamental unit being the radius (mass) of the black hole. The observers/emitters all follow the same kinds of trajectories: radially inward and starting from rest at spatial infinity. The test-particle role is assumed throughout; i.e., the observers/emitters do not themselves contribute to the gravitational field of the system. By means of redshift formulas and luminosity distance to the emitters, a picture of actual redshifts and blueshifts, with their intensities, emerges for an observer within the black hole's radius. No luminosity distances greater than approximately one-half the radius are considered in this particular study; nevertheless, redshifts and blueshifts up to approximately 0.6 are seen in portions of the observer's celestial sphere. An exotic application can be made, as a curiosity, to a black hole the size of the universe, resulting in a particular anisotropic "cosmology."

Critical space-time networks and geometric phase transitions from frustrated edge antiferromagnetism

NASA Astrophysics Data System (ADS)

Trugenberger, Carlo A.

2015-12-01

Recently I proposed a simple dynamical network model for discrete space-time that self-organizes as a graph with Hausdorff dimension dH=4 . The model has a geometric quantum phase transition with disorder parameter (dH-ds) , where ds is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean-field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions.

Quasi-analytical treatment of spatially averaged radiation transfer in complex terrain

NASA Astrophysics Data System (ADS)

LöWe, H.; Helbig, N.

2012-10-01

We provide a new quasi-analytical method to compute the subgrid topographic influences on the shortwave radiation fluxes and the effective albedo in complex terrain as required for large-scale meteorological, land surface, or climate models. We investigate radiative transfer in complex terrain via the radiosity equation on isotropic Gaussian random fields. Under controlled approximations we derive expressions for domain-averaged fluxes of direct, diffuse, and terrain radiation and the sky view factor. Domain-averaged quantities can be related to a type of level-crossing probability of the random field, which is approximated by long-standing results developed for acoustic scattering at ocean boundaries. This allows us to express all nonlocal horizon effects in terms of a local terrain parameter, namely, the mean-square slope. Emerging integrals are computed numerically, and fit formulas are given for practical purposes. As an implication of our approach, we provide an expression for the effective albedo of complex terrain in terms of the Sun elevation angle, mean-square slope, the area-averaged surface albedo, and the ratio of atmospheric direct beam to diffuse radiation. For demonstration we compute the decrease of the effective albedo relative to the area-averaged albedo in Switzerland for idealized snow-covered and clear-sky conditions at noon in winter. We find an average decrease of 5.8% and spatial patterns which originate from characteristics of the underlying relief. Limitations and possible generalizations of the method are discussed.

An analytical method to calculate equivalent fields to irregular symmetric and asymmetric photon fields.

PubMed

Tahmasebi Birgani, Mohamad J; Chegeni, Nahid; Zabihzadeh, Mansoor; Hamzian, Nima

2014-01-01

Equivalent field is frequently used for central axis depth-dose calculations of rectangular- and irregular-shaped photon beams. As most of the proposed models to calculate the equivalent square field are dosimetry based, a simple physical-based method to calculate the equivalent square field size was used as the basis of this study. The table of the sides of the equivalent square or rectangular fields was constructed and then compared with the well-known tables by BJR and Venselaar, et al. with the average relative error percentage of 2.5 ± 2.5% and 1.5 ± 1.5%, respectively. To evaluate the accuracy of this method, the percentage depth doses (PDDs) were measured for some special irregular symmetric and asymmetric treatment fields and their equivalent squares for Siemens Primus Plus linear accelerator for both energies, 6 and 18MV. The mean relative differences of PDDs measurement for these fields and their equivalent square was approximately 1% or less. As a result, this method can be employed to calculate equivalent field not only for rectangular fields but also for any irregular symmetric or asymmetric field. © 2013 American Association of Medical Dosimetrists Published by American Association of Medical Dosimetrists All rights reserved.

Approximate ground states of the random-field Potts model from graph cuts

NASA Astrophysics Data System (ADS)

Kumar, Manoj; Kumar, Ravinder; Weigel, Martin; Banerjee, Varsha; Janke, Wolfhard; Puri, Sanjay

2018-05-01

While the ground-state problem for the random-field Ising model is polynomial, and can be solved using a number of well-known algorithms for maximum flow or graph cut, the analog random-field Potts model corresponds to a multiterminal flow problem that is known to be NP-hard. Hence an efficient exact algorithm is very unlikely to exist. As we show here, it is nevertheless possible to use an embedding of binary degrees of freedom into the Potts spins in combination with graph-cut methods to solve the corresponding ground-state problem approximately in polynomial time. We benchmark this heuristic algorithm using a set of quasiexact ground states found for small systems from long parallel tempering runs. For a not-too-large number q of Potts states, the method based on graph cuts finds the same solutions in a fraction of the time. We employ the new technique to analyze the breakup length of the random-field Potts model in two dimensions.

Equivalent source modeling of the core magnetic field using magsat data

NASA Technical Reports Server (NTRS)

Mayhew, M. A.; Estes, R. H.

1983-01-01

Experiments are carried out on fitting the main field using different numbers of equivalent sources arranged in equal area at fixed radii at and inside the core-mantle boundary. In fixing the radius for a given series of runs, the convergence problems that result from the extreme nonlinearity of the problem when dipole positions are allowed to vary are avoided. Results are presented from a comparison between this approach and the standard spherical harmonic approach for modeling the main field in terms of accuracy and computational efficiency. The modeling of the main field with an equivalent dipole representation is found to be comparable to the standard spherical harmonic approach in accuracy. The 32 deg dipole density (42 dipoles) corresponds approximately to an eleventh degree/order spherical harmonic expansion (143 parameters), whereas the 21 dipole density (92 dipoles) corresponds to approximately a seventeenth degree and order expansion (323 parameters). It is pointed out that fixing the dipole positions results in rapid convergence of the dipole solutions for single-epoch models.

Phenomenological picture of fluctuations in branching random walks

NASA Astrophysics Data System (ADS)

Mueller, A. H.; Munier, S.

2014-10-01

We propose a picture of the fluctuations in branching random walks, which leads to predictions for the distribution of a random variable that characterizes the position of the bulk of the particles. We also interpret the 1 /√{t } correction to the average position of the rightmost particle of a branching random walk for large times t ≫1 , computed by Ebert and Van Saarloos, as fluctuations on top of the mean-field approximation of this process with a Brunet-Derrida cutoff at the tip that simulates discreteness. Our analytical formulas successfully compare to numerical simulations of a particular model of a branching random walk.

Pasta phases in core-collapse supernova matter

NASA Astrophysics Data System (ADS)

Pais, Helena; Chiacchiera, Silvia; Providência, Constança

2016-04-01

The pasta phase in core-collapse supernova matter (finite temperatures and fixed proton fractions) is studied within relativistic mean field models. Three different calculations are used for comparison, the Thomas-Fermi (TF), the Coexisting Phases (CP) and the Compressible Liquid Drop (CLD) approximations. The effects of including light clusters in nuclear matter and the densities at which the transitions between pasta configurations and to uniform matter occur are also investigated. The free energy and pressure, in the space of particle number densities and temperatures expected to cover the pasta region, are calculated. Finally, a comparison with a finite temperature Skyrme-Hartree-Fock calculation is drawn.

Formation of plasmon pulses in the cooperative decay of excitons of quantum dots near a metal surface

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shesterikov, A. B.; Gubin, M. Yu.; Gladush, M. G.

The formation of pulses of surface electromagnetic waves at a metal–dielectric boundary is considered in the process of cooperative decay of excitons of quantum dots distributed near a metal surface in a dielectric layer. It is shown that the efficiency of exciton energy transfer to excited plasmons can, in principle, be increased by selecting the dielectric material with specified values of the complex permittivity. It is found that in the mean field approximation, the semiclassical model of formation of plasmon pulses in the system under study is reduced to the pendulum equation with the additional term of nonlinear losses.

A quasi-steady state cosmological model with creation of matter

NASA Technical Reports Server (NTRS)

Hoyle, F.; Burbidge, G.; Narlikar, J. V.

1993-01-01

A universe is envisioned in which there was a major creation episode when the mean universal density was about 10 to the -27 g/cu cm. Explicit equations are given for the creation of matter; in a cosmological approximation, these equations lead to expressions for the time-dependence of the cosmological scale factor S(t), but do not entail, as big bang cosmology does, that S(t) tend to zero at some finite time t. The equations therefore possess a universality that is absent from big bang cosmology. Creation occurs when certain conservation equations involving the gradient of a scalar field C(i) are satisfied.

Shape study of the N =Z nucleus 72Kr via β decay

NASA Astrophysics Data System (ADS)

Briz, J. A.; Nácher, E.; Borge, M. J. G.; Algora, A.; Rubio, B.; Dessagne, Ph.; Maira, A.; Cano-Ott, D.; Courtin, S.; Escrig, D.; Fraile, L. M.; Gelletly, W.; Jungclaus, A.; Le Scornet, G.; Maréchal, F.; Miehé, Ch.; Poirier, E.; Poves, A.; Sarriguren, P.; Taín, J. L.; Tengblad, O.

2015-11-01

The β decay of the N =Z nucleus 72Kr has been studied with the total absorption spectroscopy technique at ISOLDE (CERN). A total B (GT) =0.79 (4 ) gA2/4 π has been found up to an excitation energy of 2.7 MeV. The B (GT) distribution obtained is compared with predictions from state-of-the-art theoretical calculations to learn about the ground state deformation of 72Kr. Although a dominant oblate deformation is suggested by direct comparison with quasiparticle random phase approximation (QRPA) calculations, beyond-mean-field and shell-model calculations favor a large oblate-prolate mixing in the ground state.

Soybean canopy reflectance as a function of view and illumination geometry

NASA Technical Reports Server (NTRS)

Ranson, K. J.; Vanderbilt, V. C.; Biehl, L. L.; Robinson, B. F.; Bauer, M. E.

1981-01-01

Reflectances were calculated from measurements at four wavelength bands through eight view azimuth and seven view zenith directions, for various solar zenith and azimuth angles over portions of three days, in an experimental characterization of a soybean field by means of its reflectances and physical and agronomic attributes. Results indicate that the distribution of reflectance from a soybean field is a function of the solar illumination and viewing geometry, wavelength, and row direction, as well as the state of canopy development. Shadows between rows were found to affect visible wavelength band reflectance to a greater extent than near-IR reflectance. A model describing reflectance variation as a function of projected solar and viewing angles is proposed, which approximates the visible wavelength band reflectance variations of a canopy with a well-defined row structure.

Non-integrable dynamics of matter-wave solitons in a density-dependent gauge theory

NASA Astrophysics Data System (ADS)

Dingwall, R. J.; Edmonds, M. J.; Helm, J. L.; Malomed, B. A.; Öhberg, P.

2018-04-01

We study interactions between bright matter-wave solitons which acquire chiral transport dynamics due to an optically-induced density-dependent gauge potential. Through numerical simulations, we find that the collision dynamics feature several non-integrable phenomena, from inelastic collisions including population transfer and radiation losses to the formation of short-lived bound states and soliton fission. An effective quasi-particle model for the interaction between the solitons is derived by means of a variational approximation, which demonstrates that the inelastic nature of the collision arises from a coupling of the gauge field to velocities of the solitons. In addition, we derive a set of interaction potentials which show that the influence of the gauge field appears as a short-range potential, that can give rise to both attractive and repulsive interactions.

Laws of Large Numbers and Langevin Approximations for Stochastic Neural Field Equations

PubMed Central

2013-01-01

In this study, we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson–Cowan equation can be obtained as the limit in uniform convergence on compacts in probability for a sequence of microscopic models when the number of neuron populations distributed in space and the number of neurons per population tend to infinity. This result also allows to obtain limits for qualitatively different stochastic convergence concepts, e.g., convergence in the mean. Further, we present a central limit theorem for the martingale part of the microscopic models which, suitably re-scaled, converges to a centred Gaussian process with independent increments. These two results provide the basis for presenting the neural field Langevin equation, a stochastic differential equation taking values in a Hilbert space, which is the infinite-dimensional analogue of the chemical Langevin equation in the present setting. On a technical level, we apply recently developed law of large numbers and central limit theorems for piecewise deterministic processes taking values in Hilbert spaces to a master equation formulation of stochastic neuronal network models. These theorems are valid for processes taking values in Hilbert spaces, and by this are able to incorporate spatial structures of the underlying model. Mathematics Subject Classification (2000): 60F05, 60J25, 60J75, 92C20. PMID:23343328

Modelling of induced electric fields based on incompletely known magnetic fields

NASA Astrophysics Data System (ADS)

Laakso, Ilkka; De Santis, Valerio; Cruciani, Silvano; Campi, Tommaso; Feliziani, Mauro

2017-08-01

Determining the induced electric fields in the human body is a fundamental problem in bioelectromagnetics that is important for both evaluation of safety of electromagnetic fields and medical applications. However, existing techniques for numerical modelling of induced electric fields require detailed information about the sources of the magnetic field, which may be unknown or difficult to model in realistic scenarios. Here, we show how induced electric fields can accurately be determined in the case where the magnetic fields are known only approximately, e.g. based on field measurements. The robustness of our approach is shown in numerical simulations for both idealized and realistic scenarios featuring a personalized MRI-based head model. The approach allows for modelling of the induced electric fields in biological bodies directly based on real-world magnetic field measurements.

Model of reversible vesicular transport with exclusion

NASA Astrophysics Data System (ADS)

Bressloff, Paul C.; Karamched, Bhargav R.

2016-08-01

A major question in neurobiology concerns the mechanics behind the motor-driven transport and delivery of vesicles to synaptic targets along the axon of a neuron. Experimental evidence suggests that the distribution of vesicles along the axon is relatively uniform and that vesicular delivery to synapses is reversible. A recent modeling study has made explicit the crucial role that reversibility in vesicular delivery to synapses plays in achieving uniformity in vesicle distribution, so called synaptic democracy (Bressloff et al 2015 Phys. Rev. Lett. 114 168101). In this paper we generalize the previous model by accounting for exclusion effects (hard-core repulsion) that may occur between molecular motor-cargo complexes (particles) moving along the same microtubule track. The resulting model takes the form of an exclusion process with four internal states, which distinguish between motile and stationary particles, and whether or not a particle is carrying vesicles. By applying a mean field approximation and an adiabatic approximation we reduce the system of ODEs describing the evolution of occupation numbers of the sites on a 1D lattice to a system of hydrodynamic equations in the continuum limit. We find that reversibility in vesicular delivery allows for synaptic democracy even in the presence of exclusion effects, although exclusion does exacerbate nonuniform distributions of vesicles in an axon when compared with a model without exclusion. We also uncover the relationship between our model and other models of exclusion processes with internal states.

Revisiting the time until fixation of a neutral mutant in a finite population - A coalescent theory approach.

PubMed

Greenbaum, Gili

2015-09-07

Evaluation of the time scale of the fixation of neutral mutations is crucial to the theoretical understanding of the role of neutral mutations in evolution. Diffusion approximations of the Wright-Fisher model are most often used to derive analytic formulations of genetic drift, as well as for the time scales of the fixation of neutral mutations. These approximations require a set of assumptions, most notably that genetic drift is a stochastic process in a continuous allele-frequency space, an assumption appropriate for large populations. Here equivalent approximations are derived using a coalescent theory approach which relies on a different set of assumptions than the diffusion approach, and adopts a discrete allele-frequency space. Solutions for the mean and variance of the time to fixation of a neutral mutation derived from the two approaches converge for large populations but slightly differ for small populations. A Markov chain analysis of the Wright-Fisher model for small populations is used to evaluate the solutions obtained, showing that both the mean and the variance are better approximated by the coalescent approach. The coalescence approximation represents a tighter upper-bound for the mean time to fixation than the diffusion approximation, while the diffusion approximation and coalescence approximation form an upper and lower bound, respectively, for the variance. The converging solutions and the small deviations of the two approaches strongly validate the use of diffusion approximations, but suggest that coalescent theory can provide more accurate approximations for small populations. Copyright © 2015 Elsevier Ltd. All rights reserved.

Monte Carlo based investigation of berry phase for depth resolved characterization of biomedical scattering samples

NASA Astrophysics Data System (ADS)

Baba, J. S.; Koju, V.; John, D.

2015-03-01

The propagation of light in turbid media is an active area of research with relevance to numerous investigational fields, e.g., biomedical diagnostics and therapeutics. The statistical random-walk nature of photon propagation through turbid media is ideal for computational based modeling and simulation. Ready access to super computing resources provide a means for attaining brute force solutions to stochastic light-matter interactions entailing scattering by facilitating timely propagation of sufficient (>107) photons while tracking characteristic parameters based on the incorporated physics of the problem. One such model that works well for isotropic but fails for anisotropic scatter, which is the case for many biomedical sample scattering problems, is the diffusion approximation. In this report, we address this by utilizing Berry phase (BP) evolution as a means for capturing anisotropic scattering characteristics of samples in the preceding depth where the diffusion approximation fails. We extend the polarization sensitive Monte Carlo method of Ramella-Roman, et al., to include the computationally intensive tracking of photon trajectory in addition to polarization state at every scattering event. To speed-up the computations, which entail the appropriate rotations of reference frames, the code was parallelized using OpenMP. The results presented reveal that BP is strongly correlated to the photon penetration depth, thus potentiating the possibility of polarimetric depth resolved characterization of highly scattering samples, e.g., biological tissues.