Dependence of synchronization transitions on mean field approach in two-way coupled neural system
Shi, J. C.; Luo, M.; Huang, C. S.
2018-03-01
This work investigates the synchronization transitions in two-way coupled neural system by mean field approach. Results show that, there exists a critical noise intensity for the synchronization transitions, i.e., above (or below) the critical noise intensity, the synchronization transitions are decreased (or hardly change) with increasing the noise intensity. Meanwhile, the heterogeneity effect plays a negative role for the synchronization transitions, and above critical coupling strength, the heterogeneity effect on synchronization transitions can be negligible. Furthermore, when an external signal is introduced into the coupled system, the novel frequency-induced and amplitude-induced synchronization transitions are found, and there exist an optimal frequency and an optimal amplitude of external signal which makes the system to display the best synchronization transitions. In particular, it is observed that the synchronization transitions can not be further affected above critical frequency of external signal.
Noisy mean field game model for malware propagation in opportunistic networks
Tembine, Hamidou
2012-01-01
In this paper we present analytical mean field techniques that can be used to better understand the behavior of malware propagation in opportunistic large networks. We develop a modeling methodology based on stochastic mean field optimal control that is able to capture many aspects of the problem, especially the impact of the control and heterogeneity of the system on the spreading characteristics of malware. The stochastic large process characterizing the evolution of the total number of infected nodes is examined with a noisy mean field limit and compared to a deterministic one. The stochastic nature of the wireless environment make stochastic approaches more realistic for such types of networks. By introducing control strategies, we show that the fraction of infected nodes can be maintained below some threshold. In contrast to most of the existing results on mean field propagation models which focus on deterministic equations, we show that the mean field limit is stochastic if the second moment of the number of object transitions per time slot is unbounded with the size of the system. This allows us to compare one path of the fraction of infected nodes with the stochastic trajectory of its mean field limit. In order to take into account the heterogeneity of opportunistic networks, the analysis is extended to multiple types of nodes. Our numerical results show that the heterogeneity can help to stabilize the system. We verify the results through simulation showing how to obtain useful approximations in the case of very large systems. © 2012 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering.
On Social Optima of Non-Cooperative Mean Field Games
Energy Technology Data Exchange (ETDEWEB)
Li, Sen; Zhang, Wei; Zhao, Lin; Lian, Jianming; Kalsi, Karanjit
2016-12-12
This paper studies the social optima in noncooperative mean-field games for a large population of agents with heterogeneous stochastic dynamic systems. Each agent seeks to maximize an individual utility functional, and utility functionals of different agents are coupled through a mean field term that depends on the mean of the population states/controls. The paper has the following contributions. First, we derive a set of control strategies for the agents that possess *-Nash equilibrium property, and converge to the mean-field Nash equilibrium as the population size goes to infinity. Second, we study the social optimal in the mean field game. We derive the conditions, termed the socially optimal conditions, under which the *-Nash equilibrium of the mean field game maximizes the social welfare. Third, a primal-dual algorithm is proposed to compute the *-Nash equilibrium of the mean field game. Since the *-Nash equilibrium of the mean field game is socially optimal, we can compute the equilibrium by solving the social welfare maximization problem, which can be addressed by a decentralized primal-dual algorithm. Numerical simulations are presented to demonstrate the effectiveness of the proposed approach.
Halo nuclei studied by relativistic mean-field approach
International Nuclear Information System (INIS)
Gmuca, S.
1997-01-01
Density distributions of light neutron-rich nuclei are studied by using the relativistic mean-field approach. The effective interaction which parameterizes the recent Dirac-Brueckner-Hartree-Fock calculations of nuclear matter is used. The results are discussed and compared with the experimental observations with special reference to the neutron halo in the drip-line nuclei. (author)
A spectral k-means approach to bright-field cell image segmentation.
Bradbury, Laura; Wan, Justin W L
2010-01-01
Automatic segmentation of bright-field cell images is important to cell biologists, but difficult to complete due to the complex nature of the cells in bright-field images (poor contrast, broken halo, missing boundaries). Standard approaches such as level set segmentation and active contours work well for fluorescent images where cells appear as round shape, but become less effective when optical artifacts such as halo exist in bright-field images. In this paper, we present a robust segmentation method which combines the spectral and k-means clustering techniques to locate cells in bright-field images. This approach models an image as a matrix graph and segment different regions of the image by computing the appropriate eigenvectors of the matrix graph and using the k-means algorithm. We illustrate the effectiveness of the method by segmentation results of C2C12 (muscle) cells in bright-field images.
A versatile omnibus test for detecting mean and variance heterogeneity.
Cao, Ying; Wei, Peng; Bailey, Matthew; Kauwe, John S K; Maxwell, Taylor J
2014-01-01
Recent research has revealed loci that display variance heterogeneity through various means such as biological disruption, linkage disequilibrium (LD), gene-by-gene (G × G), or gene-by-environment interaction. We propose a versatile likelihood ratio test that allows joint testing for mean and variance heterogeneity (LRT(MV)) or either effect alone (LRT(M) or LRT(V)) in the presence of covariates. Using extensive simulations for our method and others, we found that all parametric tests were sensitive to nonnormality regardless of any trait transformations. Coupling our test with the parametric bootstrap solves this issue. Using simulations and empirical data from a known mean-only functional variant, we demonstrate how LD can produce variance-heterogeneity loci (vQTL) in a predictable fashion based on differential allele frequencies, high D', and relatively low r² values. We propose that a joint test for mean and variance heterogeneity is more powerful than a variance-only test for detecting vQTL. This takes advantage of loci that also have mean effects without sacrificing much power to detect variance only effects. We discuss using vQTL as an approach to detect G × G interactions and also how vQTL are related to relationship loci, and how both can create prior hypothesis for each other and reveal the relationships between traits and possibly between components of a composite trait.
Mean-field modeling approach for understanding epidemic dynamics in interconnected networks
International Nuclear Information System (INIS)
Zhu, Guanghu; Fu, Xinchu; Tang, Qinggan; Li, Kezan
2015-01-01
Modern systems (e.g., social, communicant, biological networks) are increasingly interconnected each other formed as ‘networks of networks’. Such complex systems usually possess inconsistent topologies and permit agents distributed in different subnetworks to interact directly/indirectly. Corresponding dynamics phenomena, such as the transmission of information, power, computer virus and disease, would exhibit complicated and heterogeneous tempo-spatial patterns. In this paper, we focus on the scenario of epidemic spreading in interconnected networks. We intend to provide a typical mean-field modeling framework to describe the time-evolution dynamics, and offer some mathematical skills to study the spreading threshold and the global stability of the model. Integrating the research with numerical analysis, we are able to quantify the effects of networks structure and epidemiology parameters on the transmission dynamics. Interestingly, we find that the diffusion transition in the whole network is governed by a unique threshold, which mainly depends on the most heterogenous connection patterns of network substructures. Further, the dynamics is highly sensitive to the critical values of cross infectivity with switchable phases.
A mean field approach to the Ising chain in a transverse magnetic field
Osácar, C.; Pacheco, A. F.
2017-07-01
We evaluate a mean field method to describe the properties of the ground state of the Ising chain in a transverse magnetic field. Specifically, a method of the Bethe-Peierls type is used by solving spin blocks with a self-consistency condition at the borders. The computations include the critical point for the phase transition, exponent of magnetisation and energy density. All results are obtained using basic quantum mechanics at an undergraduate level. The advantages and the limitations of the approach are emphasised.
RPA correlations and nuclear densities in relativistic mean field approach
International Nuclear Information System (INIS)
Van Giai, N.; Liang, H.Z.; Meng, J.
2007-02-01
The relativistic mean field approach (RMF) is well known for describing accurately binding energies and nucleon distributions in atomic nuclei throughout the nuclear chart. The random phase approximation (RPA) built on top of the RMF is also a good framework for the study of nuclear excitations. Here, we examine the consequences of long range correlations brought about by the RPA on the neutron and proton densities as given by the RMF approach. (authors)
Investigating heterogeneous nucleation in peritectic materials via the phase-field method
International Nuclear Information System (INIS)
Emmerich, Heike; Siquieri, Ricardo
2006-01-01
Here we propose a phase-field approach to investigate the influence of convection on peritectic growth as well as the heterogeneous nucleation kinetics of peritectic systems. For this purpose we derive a phase-field model for peritectic growth taking into account fluid flow in the melt, which is convergent to the underlying sharp interface problem in the thin interface limit (Karma and Rappel 1996 Phys. Rev. E 53 R3017). Moreover, we employ our new phase-field model to study the heterogeneous nucleation kinetics of peritectic material systems. Our approach is based on a similar approach towards homogeneous nucleation in Granasy et al (2003 Interface and Transport Dynamics (Springer Lecture Notes in Computational Science and Engineering vol 32) ed Emmerich et al (Berlin: Springer) p 190). We applied our model successfully to extend the nucleation rate predicted by classical nucleation theory for an additional morphological term relevant for peritectic growth. Further applications to understand the mechanisms and consequences of heterogeneous nucleation kinetics in more detail are discussed
A mean-field approach for an intercarrier interference canceller for OFDM
International Nuclear Information System (INIS)
Sakata, A; Kabashima, Y; Peleg, Y
2012-01-01
The similarity of the mathematical description of random-field spin systems to the orthogonal frequency-division multiplexing (OFDM) scheme for wireless communication is exploited in an intercarrier interference (ICI) canceller used in the demodulation of OFDM. The translational symmetry in the Fourier domain generically concentrates the major contribution of ICI from each subcarrier in the subcarrier’s neighbourhood. This observation in conjunction with the mean-field approach leads to the development of an ICI canceller whose necessary cost of computation scales linearly with respect to the number of subcarriers. It is also shown that the dynamics of the mean-field canceller are well captured by a discrete map of a single macroscopic variable, without taking the spatial and time correlations of estimated variables into account. (paper)
Integrating mean and variance heterogeneities to identify differentially expressed genes.
Ouyang, Weiwei; An, Qiang; Zhao, Jinying; Qin, Huaizhen
2016-12-06
In functional genomics studies, tests on mean heterogeneity have been widely employed to identify differentially expressed genes with distinct mean expression levels under different experimental conditions. Variance heterogeneity (aka, the difference between condition-specific variances) of gene expression levels is simply neglected or calibrated for as an impediment. The mean heterogeneity in the expression level of a gene reflects one aspect of its distribution alteration; and variance heterogeneity induced by condition change may reflect another aspect. Change in condition may alter both mean and some higher-order characteristics of the distributions of expression levels of susceptible genes. In this report, we put forth a conception of mean-variance differentially expressed (MVDE) genes, whose expression means and variances are sensitive to the change in experimental condition. We mathematically proved the null independence of existent mean heterogeneity tests and variance heterogeneity tests. Based on the independence, we proposed an integrative mean-variance test (IMVT) to combine gene-wise mean heterogeneity and variance heterogeneity induced by condition change. The IMVT outperformed its competitors under comprehensive simulations of normality and Laplace settings. For moderate samples, the IMVT well controlled type I error rates, and so did existent mean heterogeneity test (i.e., the Welch t test (WT), the moderated Welch t test (MWT)) and the procedure of separate tests on mean and variance heterogeneities (SMVT), but the likelihood ratio test (LRT) severely inflated type I error rates. In presence of variance heterogeneity, the IMVT appeared noticeably more powerful than all the valid mean heterogeneity tests. Application to the gene profiles of peripheral circulating B raised solid evidence of informative variance heterogeneity. After adjusting for background data structure, the IMVT replicated previous discoveries and identified novel experiment
Mean field approach to nuclear structure
International Nuclear Information System (INIS)
Nazarewicz, W.; Tennessee Univ., Knoxville, TN
1993-01-01
Several examples of mean-field calculations, relevant to the recent and planned low-spin experimental works, are presented. The perspectives for future studies (mainly related to spectroscopy of exotic nuclei) are reviewd
Constrained deterministic leader-follower mean field control
Möller, L.; Gentile, B.; Parise, F.; Grammatico, S.; Lygeros, J.
2016-01-01
We consider a mean field game among a large population of noncooperative agents divided into two categories: leaders and followers. Each agent is subject to heterogeneous convex constraints and minimizes a quadratic cost function; the cost of each leader is affected by the leaders' aggregate
Purchasing Power Parity and Heterogeneous Mean Reversion
C.G. Koedijk (Kees); B. Tims (Ben); M.A. van Dijk (Mathijs)
2005-01-01
textabstractThis paper analyzes the properties of multivariate tests of purchasing power parity (PPP) that fail to take heterogeneity in the speed of mean reversion across real exchange rates into account. We compare the performance of homogeneous and heterogeneous unit root testing methodologies.
A simplified BBGKY hierarchy for correlated fermions from a stochastic mean-field approach
International Nuclear Information System (INIS)
Lacroix, Denis; Tanimura, Yusuke; Ayik, Sakir; Yilmaz, Bulent
2016-01-01
The stochastic mean-field (SMF) approach allows to treat correlations beyond mean-field using a set of independent mean-field trajectories with appropriate choice of fluctuating initial conditions. We show here that this approach is equivalent to a simplified version of the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy between one-, two-,.., N -body degrees of freedom. In this simplified version, one-body degrees of freedom are coupled to fluctuations to all orders while retaining only specific terms of the general BBGKY hierarchy. The use of the simplified BBGKY is illustrated with the Lipkin-Meshkov-Glick (LMG) model. We show that a truncated version of this hierarchy can be useful, as an alternative to the SMF, especially in the weak coupling regime to get physical insight in the effect beyond mean-field. In particular, it leads to approximate analytical expressions for the quantum fluctuations both in the weak and strong coupling regime. In the strong coupling regime, it can only be used for short time evolution. In that case, it gives information on the evolution time-scale close to a saddle point associated to a quantum phase-transition. For long time evolution and strong coupling, we observed that the simplified BBGKY hierarchy cannot be truncated and only the full SMF with initial sampling leads to reasonable results. (orig.)
Green's Function and Stress Fields in Stochastic Heterogeneous Continua
Negi, Vineet
Many engineering materials used today are heterogenous in composition e.g. Composites - Polymer Matrix Composites, Metal Matrix Composites. Even, conventional engineering materials - metals, plastics, alloys etc. - may develop heterogeneities, like inclusions and residual stresses, during the manufacturing process. Moreover, these materials may also have intrinsic heterogeneities at a nanoscale in the form of grain boundaries in metals, crystallinity in amorphous polymers etc. While, the homogenized constitutive models for these materials may be satisfactory at a macroscale, recent studies of phenomena like fatigue failure, void nucleation, size-dependent brittle-ductile transition in polymeric nanofibers reveal a major play of micro/nanoscale physics in these phenomena. At this scale, heterogeneities in a material may no longer be ignored. Thus, this demands a study into the effects of various material heterogeneities. In this work, spatial heterogeneities in two material properties - elastic modulus and yield stress - have been investigated separately. The heterogeneity in the elastic modulus is studied in the context of Green's function. The Stochastic Finite Element method is adopted to get the mean statistics of the Green's function defined on a stochastic heterogeneous 2D infinite space. A study of the elastic-plastic transition in a domain having stochastic heterogenous yield stress was done using Mont-Carlo methods. The statistics for various stress and strain fields during the transition were obtained. Further, the effects of size of the domain and the strain-hardening rate on the stress fields during the heterogeneous elastic-plastic transition were investigated. Finally, a case is made for the role of the heterogenous elastic-plastic transition in damage nucleation and growth.
International Nuclear Information System (INIS)
Guerra, E.M. de
2001-01-01
In these talks, we review non relativistic selfconsistent mean field theories, their scope and limitations. We first discuss static and time dependent mean field approaches for particles and quasiparticles, together with applications. We then discuss extensions that go beyond the non-relativistic independent particle limit. On the one hand, we consider extensions concerned with restoration of symmetries and with the treatment of collective modes, particularly by means of quantized ATDHF. On the other hand, we consider extensions concerned with the relativistic dynamics of bound nucleons. We present data on nucleon momentum distributions that show the need for relativistic mean field approach and probe the limits of the mean field concept. Illustrative applications of various methods are presented stressing the role that selfconsistency plays in providing a unifying reliable framework to study all sorts of properties and phenomena. From global properties such as size, mass, lifetime,.., to detailed structure in excitation spectra (high spin, RPA modes,..), as well as charge, magnetization and velocity distributions. (orig.)
Non-equilibrium mean-field theories on scale-free networks
International Nuclear Information System (INIS)
Caccioli, Fabio; Dall'Asta, Luca
2009-01-01
Many non-equilibrium processes on scale-free networks present anomalous critical behavior that is not explained by standard mean-field theories. We propose a systematic method to derive stochastic equations for mean-field order parameters that implicitly account for the degree heterogeneity. The method is used to correctly predict the dynamical critical behavior of some binary spin models and reaction–diffusion processes. The validity of our non-equilibrium theory is further supported by showing its relation with the generalized Landau theory of equilibrium critical phenomena on networks
Direct Breakthrough Curve Prediction From Statistics of Heterogeneous Conductivity Fields
Hansen, Scott K.; Haslauer, Claus P.; Cirpka, Olaf A.; Vesselinov, Velimir V.
2018-01-01
This paper presents a methodology to predict the shape of solute breakthrough curves in heterogeneous aquifers at early times and/or under high degrees of heterogeneity, both cases in which the classical macrodispersion theory may not be applicable. The methodology relies on the observation that breakthrough curves in heterogeneous media are generally well described by lognormal distributions, and mean breakthrough times can be predicted analytically. The log-variance of solute arrival is thus sufficient to completely specify the breakthrough curves, and this is calibrated as a function of aquifer heterogeneity and dimensionless distance from a source plane by means of Monte Carlo analysis and statistical regression. Using the ensemble of simulated groundwater flow and solute transport realizations employed to calibrate the predictive regression, reliability estimates for the prediction are also developed. Additional theoretical contributions include heuristics for the time until an effective macrodispersion coefficient becomes applicable, and also an expression for its magnitude that applies in highly heterogeneous systems. It is seen that the results here represent a way to derive continuous time random walk transition distributions from physical considerations rather than from empirical field calibration.
Energy Technology Data Exchange (ETDEWEB)
Hamilton, D.S.; Raeuchle, S.K.; Holtz, M.H. [Bureau of Economic Geology, Austin, TX (United States)] [and others
1997-08-01
We applied an integrated geologic, geophysical, and engineering approach devised to identify heterogeneities in the subsurface that might lead to reserve growth opportunities in our analysis of the Oficina Formation at Budare field, Venezuela. The approach involves 4 key steps: (1) Determine geologic reservoir architecture; (2) Investigate trends in reservoir fluid flow; (3) Integrate fluid flow trends with reservoir architecture; and (4) Estimate original oil-in-place, residual oil saturation, and remaining mobile oil, to identify opportunities for reserve growth. There are three main oil-producing reservoirs in the Oficina Formation that were deposited in a bed-load fluvial system, an incised valley-fill, and a barrier-strandplain system. Reservoir continuity is complex because, in addition to lateral facies variability, the major Oficina depositional systems were internally subdivided by high-frequency stratigraphic surfaces. These surfaces define times of intermittent lacustrine and marine flooding events that punctuated the fluvial and marginal marine sedimentation, respectively. Syn and post depositional faulting further disrupted reservoir continuity. Trends in fluid flow established from initial fluid levels, response to recompletion workovers, and pressure depletion data demonstrated barriers to lateral and vertical fluid flow caused by a combination of reservoir facies pinchout, flooding shale markers, and the faults. Considerable reserve growth potential exists at Budare field because the reservoir units are highly compartment by the depositional heterogeneity and structural complexity. Numerous reserve growth opportunities were identified in attics updip of existing production, in untapped or incompletely drained compartments, and in field extensions.
Mean field theory of epidemic spreading with effective contacts on networks
International Nuclear Information System (INIS)
Wu, Qingchu; Chen, Shufang
2015-01-01
We present a general approach to the analysis of the susceptible-infected-susceptible model with effective contacts on networks, where each susceptible node will be infected with a certain probability only for effective contacts. In the network, each node has a given effective contact number. By using the one-vertex heterogenous mean-field (HMF) approximation and the pair HMF approximation, we obtain conditions for epidemic outbreak on degree-uncorrelated networks. Our results suggest that the epidemic threshold is closely related to the effective contact and its distribution. However, when the effective contact is only dependent of node degree, the epidemic threshold can be established by the degree distribution of networks.
From medium heterogeneity to flow and transport: A time-domain random walk approach
Hakoun, V.; Comolli, A.; Dentz, M.
2017-12-01
The prediction of flow and transport processes in heterogeneous porous media is based on the qualitative and quantitative understanding of the interplay between 1) spatial variability of hydraulic conductivity, 2) groundwater flow and 3) solute transport. Using a stochastic modeling approach, we study this interplay through direct numerical simulations of Darcy flow and advective transport in heterogeneous media. First, we study flow in correlated hydraulic permeability fields and shed light on the relationship between the statistics of log-hydraulic conductivity, a medium attribute, and the flow statistics. Second, we determine relationships between Eulerian and Lagrangian velocity statistics, this means, between flow and transport attributes. We show how Lagrangian statistics and thus transport behaviors such as late particle arrival times are influenced by the medium heterogeneity on one hand and the initial particle velocities on the other. We find that equidistantly sampled Lagrangian velocities can be described by a Markov process that evolves on the characteristic heterogeneity length scale. We employ a stochastic relaxation model for the equidistantly sampled particle velocities, which is parametrized by the velocity correlation length. This description results in a time-domain random walk model for the particle motion, whose spatial transitions are characterized by the velocity correlation length and temporal transitions by the particle velocities. This approach relates the statistical medium and flow properties to large scale transport, and allows for conditioning on the initial particle velocities and thus to the medium properties in the injection region. The approach is tested against direct numerical simulations.
Virtual-site correlation mean field approach to criticality in spin systems
International Nuclear Information System (INIS)
Sen, Aditi; Sen, Ujjwal
2013-01-01
We propose a virtual-site correlation mean field theory for dealing with interacting many-body systems. It involves a coarse-graining technique that terminates a step before the mean field theory: While mean field theory deals with only single-body physical parameters, the virtual-site correlation mean field theory deals with single- as well as two-body ones, and involves a virtual site for every interaction term in the Hamiltonian. We generalize the theory to a cluster virtual-site correlation mean field, that works with a fundamental unit of the lattice of the many-body system. We apply these methods to interacting Ising spin systems in several lattice geometries and dimensions, and show that the predictions of the onset of criticality of these models are generally much better in the proposed theories as compared to the corresponding ones in mean field theories
International Nuclear Information System (INIS)
Liu, Shuanglong; Feng, Yuan Ping; Zhang, Chun
2013-01-01
We show that when a molecular junction is under an external bias, its properties cannot be uniquely determined by the total electron density in the same manner as the density functional theory for ground state properties. In order to correctly incorporate bias-induced nonequilibrium effects, we present a dual mean field (DMF) approach. The key idea is that the total electron density together with the density of current-carrying electrons are sufficient to determine the properties of the system. Two mean fields, one for current-carrying electrons and the other one for equilibrium electrons can then be derived. Calculations for a graphene nanoribbon junction show that compared with the commonly used ab initio transport theory, the DMF approach could significantly reduce the electric current at low biases due to the non-equilibrium corrections to the mean field potential in the scattering region
Korres, Wolfgang; Montzka, Carsten; Fiener, Peter; Wilken, Florian; Stadler, Anja; Waldhoff, Guido; Schneider, Karl
2016-01-01
The ratio of leaf area to ground area (leaf area index, LAI) is an important state variable in ecosystem studies since it influences fluxes of matter and energy between the land surface and the atmosphere. As a basis for generating temporally continuous and spatially distributed datasets of LAI, the current study contributes an analysis of its spatial variability and spatial structure. Soil-vegetation-atmosphere fluxes of water, carbon and energy are nonlinearly related to LAI. Therefore, its spatial heterogeneity, i.e., the combination of spatial variability and structure, has an effect on simulations of these fluxes. To assess LAI spatial heterogeneity, we apply a Comprehensive Data Analysis Approach that combines data from remote sensing (5 m resolution) and simulation (150 m resolution) with field measurements and a detailed land use map. Test area is the arable land in the fertile loess plain of the Rur catchment on the Germany-Belgium-Netherlands border. LAI from remote sensing and simulation compares well with field measurements. Based on the simulation results, we describe characteristic crop-specific temporal patterns of LAI spatial variability. By means of these patterns, we explain the complex multimodal frequency distributions of LAI in the remote sensing data. In the test area, variability between agricultural fields is higher than within fields. Therefore, spatial resolutions less than the 5 m of the remote sensing scenes are sufficient to infer LAI spatial variability. Frequency distributions from the simulation agree better with the multimodal distributions from remote sensing than normal distributions do. The spatial structure of LAI in the test area is dominated by a short distance referring to field sizes. Longer distances that refer to soil and weather can only be derived from remote sensing data. Therefore, simulations alone are not sufficient to characterize LAI spatial structure. It can be concluded that a comprehensive picture of LAI spatial
Mean-field models and superheavy elements
International Nuclear Information System (INIS)
Reinhard, P.G.; Bender, M.; Maruhn, J.A.; Frankfurt Univ.
2001-03-01
We discuss the performance of two widely used nuclear mean-field models, the relativistic mean-field theory (RMF) and the non-relativistic Skyrme-Hartree-Fock approach (SHF), with particular emphasis on the description of superheavy elements (SHE). We provide a short introduction to the SHF and RMF, the relations between these two approaches and the relations to other nuclear structure models, briefly review the basic properties with respect to normal nuclear observables, and finally present and discuss recent results on the binding properties of SHE computed with a broad selection of SHF and RMF parametrisations. (orig.)
Many-Body Mean-Field Equations: Parallel implementation
International Nuclear Information System (INIS)
Vallieres, M.; Umar, S.; Chinn, C.; Strayer, M.
1993-01-01
We describe the implementation of Hartree-Fock Many-Body Mean-Field Equations on a Parallel Intel iPSC/860 hypercube. We first discuss the Nuclear Mean-Field approach in physical terms. Then we describe our parallel implementation of this approach on the Intel iPSC/860 hypercube. We discuss and compare the advantages and disadvantages of the domain partition versus the Hilbert space partition for this problem. We conclude by discussing some timing experiments on various computing platforms
Mean-field approximation minimizes relative entropy
International Nuclear Information System (INIS)
Bilbro, G.L.; Snyder, W.E.; Mann, R.C.
1991-01-01
The authors derive the mean-field approximation from the information-theoretic principle of minimum relative entropy instead of by minimizing Peierls's inequality for the Weiss free energy of statistical physics theory. They show that information theory leads to the statistical mechanics procedure. As an example, they consider a problem in binary image restoration. They find that mean-field annealing compares favorably with the stochastic approach
Nonasymptotic mean-field games
Tembine, Hamidou
2014-12-01
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networked systems with few entities. In this paper we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through a dynamic auction with asymmetric valuation distributions.
Nonasymptotic mean-field games
Tembine, Hamidou
2014-12-01
Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists of approximating large games by a stylized game model with a continuum of players. The approach has been shown to be useful in some applications. However, the stylized game model with continuum of decision-makers is rarely observed in practice and the approximation proposed in the asymptotic regime is meaningless for networks with few entities. In this paper, we propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through various examples including dynamic auction with asymmetric valuation distributions, and spiteful bidders.
Microscopic mean-field boson approach to the shape transition in Sm isotopes
International Nuclear Information System (INIS)
Kuchta, R.
1988-01-01
The phase transition from spherical to deformed shape in Sm 146-156 nuclei is analyzed within the mean-field approximation applied to the Dyson image of the shell-model Hamiltonian. No quasiparticle transformation is involved in the present approach and the Pauli principle in the physical boson subspace is properly taken into account. The low-lying spectra, B(E2; O 1 + →2 + ) probabilities and the corresponding densities of electromagnetic transitions are calculated. The results provide a reasonable explanation of the phase transition in the Sm isotopes. The role of bosons with different multipolarity is investigated and it is found that g-bosons (J=4) cannot be neglected in the transition region. Comparison of the present results with those of other approaches is given as well
Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach
DEFF Research Database (Denmark)
Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro
2013-01-01
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message passing fixed-point equations obtained with this combination...... correspond to stationary points of a constrained region-based free energy approximation. Moreover, we present a convergent implementation of these message passing fixed-point equations provided that the underlying factor graph fulfills certain technical conditions. In addition, we show how to include hard...
Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach
Chenavaz, Régis; Paraschiv, Corina; Turinici, Gabriel
2017-01-01
Dynamic pricing of new products has been extensively studied in monopolistic and oligopolistic markets. But, the optimal control and differential game tools used to investigate the pricing behavior on markets with a finite number of firms are not well-suited to model competitive markets with an infinity of firms. Using a mean-field games approach, this paper examines dynamic pricing policies in competitive markets, where no firm exerts market power. The theoretical setting is based on a diffu...
Zhao, Zhanfeng; Illman, Walter A.
2018-04-01
Previous studies have shown that geostatistics-based transient hydraulic tomography (THT) is robust for subsurface heterogeneity characterization through the joint inverse modeling of multiple pumping tests. However, the hydraulic conductivity (K) and specific storage (Ss) estimates can be smooth or even erroneous for areas where pumping/observation densities are low. This renders the imaging of interlayer and intralayer heterogeneity of highly contrasting materials including their unit boundaries difficult. In this study, we further test the performance of THT by utilizing existing and newly collected pumping test data of longer durations that showed drawdown responses in both aquifer and aquitard units at a field site underlain by a highly heterogeneous glaciofluvial deposit. The robust performance of the THT is highlighted through the comparison of different degrees of model parameterization including: (1) the effective parameter approach; (2) the geological zonation approach relying on borehole logs; and (3) the geostatistical inversion approach considering different prior information (with/without geological data). Results reveal that the simultaneous analysis of eight pumping tests with the geostatistical inverse model yields the best results in terms of model calibration and validation. We also find that the joint interpretation of long-term drawdown data from aquifer and aquitard units is necessary in mapping their full heterogeneous patterns including intralayer variabilities. Moreover, as geological data are included as prior information in the geostatistics-based THT analysis, the estimated K values increasingly reflect the vertical distribution patterns of permeameter-estimated K in both aquifer and aquitard units. Finally, the comparison of various THT approaches reveals that differences in the estimated K and Ss tomograms result in significantly different transient drawdown predictions at observation ports.
Two Numerical Approaches to Stationary Mean-Field Games
Almulla, Noha; Ferreira, Rita; Gomes, Diogo A.
2016-01-01
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Two Numerical Approaches to Stationary Mean-Field Games
Almulla, Noha
2016-10-04
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Tissue heterogeneity as a mechanism for localized neural stimulation by applied electric fields
International Nuclear Information System (INIS)
Miranda, P C; Correia, L; Salvador, R; Basser, P J
2007-01-01
We investigate the heterogeneity of electrical conductivity as a new mechanism to stimulate excitable tissues via applied electric fields. In particular, we show that stimulation of axons crossing internal boundaries can occur at boundaries where the electric conductivity of the volume conductor changes abruptly. The effectiveness of this and other stimulation mechanisms was compared by means of models and computer simulations in the context of transcranial magnetic stimulation. While, for a given stimulation intensity, the largest membrane depolarization occurred where an axon terminates or bends sharply in a high electric field region, a slightly smaller membrane depolarization, still sufficient to generate action potentials, also occurred at an internal boundary where the conductivity jumped from 0.143 S m -1 to 0.333 S m -1 , simulating a white-matter-grey-matter interface. Tissue heterogeneity can also give rise to local electric field gradients that are considerably stronger and more focal than those impressed by the stimulation coil and that can affect the membrane potential, albeit to a lesser extent than the two mechanisms mentioned above. Tissue heterogeneity may play an important role in electric and magnetic 'far-field' stimulation
Tissue heterogeneity as a mechanism for localized neural stimulation by applied electric fields
Energy Technology Data Exchange (ETDEWEB)
Miranda, P C [Institute of Biophysics and Biomedical Engineering, Faculty of Sciences, University of Lisbon, 1749-016 Lisbon (Portugal); Correia, L [Institute of Biophysics and Biomedical Engineering, Faculty of Sciences, University of Lisbon, 1749-016 Lisbon (Portugal); Salvador, R [Institute of Biophysics and Biomedical Engineering, Faculty of Sciences, University of Lisbon, 1749-016 Lisbon (Portugal); Basser, P J [Section on Tissue Biophysics and Biomimetics, NICHD, National Institutes of Health, Bethesda, MD 20892-1428 (United States)
2007-09-21
We investigate the heterogeneity of electrical conductivity as a new mechanism to stimulate excitable tissues via applied electric fields. In particular, we show that stimulation of axons crossing internal boundaries can occur at boundaries where the electric conductivity of the volume conductor changes abruptly. The effectiveness of this and other stimulation mechanisms was compared by means of models and computer simulations in the context of transcranial magnetic stimulation. While, for a given stimulation intensity, the largest membrane depolarization occurred where an axon terminates or bends sharply in a high electric field region, a slightly smaller membrane depolarization, still sufficient to generate action potentials, also occurred at an internal boundary where the conductivity jumped from 0.143 S m{sup -1} to 0.333 S m{sup -1}, simulating a white-matter-grey-matter interface. Tissue heterogeneity can also give rise to local electric field gradients that are considerably stronger and more focal than those impressed by the stimulation coil and that can affect the membrane potential, albeit to a lesser extent than the two mechanisms mentioned above. Tissue heterogeneity may play an important role in electric and magnetic 'far-field' stimulation.
Probabilistic theory of mean field games with applications
Carmona, René
2018-01-01
This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic...
Rinkevicius, Zilvinas; Li, Xin; Sandberg, Jaime A R; Mikkelsen, Kurt V; Ågren, Hans
2014-03-11
We introduce a density functional theory/molecular mechanical approach for computation of linear response properties of molecules in heterogeneous environments, such as metal surfaces or nanoparticles embedded in solvents. The heterogeneous embedding environment, consisting from metallic and nonmetallic parts, is described by combined force fields, where conventional force fields are used for the nonmetallic part and capacitance-polarization-based force fields are used for the metallic part. The presented approach enables studies of properties and spectra of systems embedded in or placed at arbitrary shaped metallic surfaces, clusters, or nanoparticles. The capability and performance of the proposed approach is illustrated by sample calculations of optical absorption spectra of thymidine absorbed on gold surfaces in an aqueous environment, where we study how different organizations of the gold surface and how the combined, nonadditive effect of the two environments is reflected in the optical absorption spectrum.
Correlations and fluctuations in static and dynamic mean-field approaches
International Nuclear Information System (INIS)
Balian, R.; Veneroni, M.
1991-01-01
Let the state of a many-body system at an initial time be specified, completely or partly; find the expectation values, correlations and fluctuations of single-particle observables at a later time. The characteristic function of these observables is optimized within a general variational scheme. The expansion of the optimal characteristic function provides the same results as the conventional mean-field approaches for the thermodynamic potentials and the expectation values: for fermions the best initial state is then the Hartree-Fock (HF) solution and the evolution is described by the time-dependent Hartree-Fock (TDHF) equation. Two special cases are investigated as preliminary steps. The first case deals with the evaluation of correlations for static problems, where the initial and final times coincide. In the second special case, the exact initial state is assumed to be an independent-particle one. (K.A.) 23 refs.; 1 fig
A family-based joint test for mean and variance heterogeneity for quantitative traits.
Cao, Ying; Maxwell, Taylor J; Wei, Peng
2015-01-01
Traditional quantitative trait locus (QTL) analysis focuses on identifying loci associated with mean heterogeneity. Recent research has discovered loci associated with phenotype variance heterogeneity (vQTL), which is important in studying genetic association with complex traits, especially for identifying gene-gene and gene-environment interactions. While several tests have been proposed to detect vQTL for unrelated individuals, there are no tests for related individuals, commonly seen in family-based genetic studies. Here we introduce a likelihood ratio test (LRT) for identifying mean and variance heterogeneity simultaneously or for either effect alone, adjusting for covariates and family relatedness using a linear mixed effect model approach. The LRT test statistic for normally distributed quantitative traits approximately follows χ(2)-distributions. To correct for inflated Type I error for non-normally distributed quantitative traits, we propose a parametric bootstrap-based LRT that removes the best linear unbiased prediction (BLUP) of family random effect. Simulation studies show that our family-based test controls Type I error and has good power, while Type I error inflation is observed when family relatedness is ignored. We demonstrate the utility and efficiency gains of the proposed method using data from the Framingham Heart Study to detect loci associated with body mass index (BMI) variability. © 2014 John Wiley & Sons Ltd/University College London.
Mass dispersions in a time-dependent mean-field approach
International Nuclear Information System (INIS)
Balian, R.; Bonche, P.; Flocard, H.; Veneroni, M.
1984-05-01
Characteristic functions for single-particle (s.p.) observables are evaluated by means of a time-dependent variational principle, which involves a state and an observable as conjugate variables. This provides a mean-field expression for fluctuations of s.p. observables, such as mass dispersions. The result differs from TDHF, it requires only the use of existing codes, and it presents attractive theoretical features. First numerical tests are encouraging. In particular, a calculation for 16 O + 16 O provides a significant increase of the predicted mass dispersion
Mean Field Games with a Dominating Player
Energy Technology Data Exchange (ETDEWEB)
Bensoussan, A., E-mail: axb046100@utdallas.edu [The University of Texas at Dallas, International Center for Decision and Risk Analysis, Jindal School of Management (United States); Chau, M. H. M., E-mail: michaelchaumanho@gmail.com; Yam, S. C. P., E-mail: scpyam@sta.cuhk.edu.hk [The Chinese University of Hong Kong, Department of Statistics (Hong Kong, People’s Republic of China) (China)
2016-08-15
In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the dominating player. We first provide the general theory and discuss the necessary condition for the optimal controls and equilibrium condition by adopting adjoint equation approach. We then present a special case in the context of linear-quadratic framework, in which a necessary and sufficient condition can be asserted by stochastic maximum principle; we finally establish the sufficient condition that guarantees the unique existence of the equilibrium control. The proof of the convergence result of finite player game to mean field counterpart is provided in Appendix.
Heterogeneous analysis of non-uniform neutron field formation
International Nuclear Information System (INIS)
Zagrebaev, A.M.; Fedosov, A.M.
1979-01-01
Investigated are the specific features of spatial-energy neutron distribution formation in the transient zone between regions, operating at different levels of energy release with accounting for the real structure of fuel element lattice and control elements in the channel reactors of high power. Presented are the calculation results, obtained by heterogeneous method in the two-group monopole approximation by means of the HETLAT code. The analysis, based on the homogeneous model shows, that the efficiency of the transient zone in forming neutron flux qradient can be increased by introducing an additional interlayer of moderator between the layers with extreme multiplying properties. It is stressed, that the most favourable from the point of view of energy release uniformity in zones and width of the transient zone is the variant in which neutron flux gradient is carried out by moving the control elements on the boundaries of regions while the internal rows of control elements create the conditions for flattening the energy release in the zones. The result obtained corresponds to the recommendation on optimal control, coming from the Pontryagin maximum principle. The analysis of neutron field formation using heterogeneous models mainly proves the conclusions following from homogeneous calculations using the maximum principle. At the same time quantitative results for the zones of small dimensions (less than 10 migration lengths) with a vividly expressed heterogeneous structure essentially differ from the forecast, obtained on the basis of the simplified homogeneous one-group model. The heterogeneous analysis shows possibilities for further optimization of the transient zone structure with account of the control element location
Mean-field approach to unconventional superconductivity
International Nuclear Information System (INIS)
Sacks, William; Mauger, Alain; Noat, Yves
2014-01-01
Highlights: • A model Hamiltonian for unconventional superconductivity (SC) is proposed. • The pseudogap (PG) state is described in terms of pair fluctuations. • SC coherence is restored by a new pair–pair interaction, which counteracts fluctuations. • Given the temperature dependence of the parameters, the SC to PG transition is examined. • The theory fits the ‘peak–dip–hump’ features of cuprate and pnictide excitation spectra. - Abstract: We propose a model that connects the quasiparticle spectral function of high-T c superconductors to the condensation energy. Given the evidence for pair correlations above T c , we consider a coarse-grain Hamiltonian of fluctuating pairs describing the incoherent pseudogap (PG) state, together with a novel pair–pair interaction term that restores long-range superconducting (SC) coherence below T c . A mean-field solution then leads to a self-consistent gap equation containing the new pair–pair coupling. The corresponding spectral function A(k,E) reveals the characteristic peak–dip–hump features of cuprates, now observed on iron pnictides (LiFeAs). The continuous transition from SC to PG states is discussed
Economic dynamics with financial fragility and mean-field interaction: A model
Di Guilmi, C.; Gallegati, M.; Landini, S.
2008-06-01
Following Aoki’s statistical mechanics methodology [Masanao Aoki, New Approaches to Macroeconomic Modeling, Cambridge University Press, 1996; Masanao Aoki, Modeling Aggregate Behaviour and Fluctuations in Economics, Cambridge University Press, 2002; Masanao Aoki, and Hiroshi Yoshikawa, Reconstructing Macroeconomics, Cambridge University Press, 2006], we provide some insights into the well-known works of [Bruce Greenwald, Joseph Stiglitz, Macroeconomic models with equity and credit rationing, in: R. Hubbard (Ed.), Information, Capital Markets and Investment, Chicago University Press, Chicago, 1990; Bruce Greenwald, Joseph Stiglitz, Financial markets imperfections and business cycles, Quarterly journal of Economics (1993)]. Specifically, we reach analytically a closed form solution of their models overcoming the aggregation problem. The key idea is to represent the economy as an evolving complex system, composed by heterogeneous interacting agents, that can be partitioned into a space of macroscopic states. This meso level of aggregation permits to adopt mean-field interaction modeling and master equation techniques.
3D Acoustic Modelling of Dissipative Silencers with Nonhomogeneous Properties and Mean Flow
Directory of Open Access Journals (Sweden)
E. M. Sánchez-Orgaz
2014-07-01
Full Text Available A finite element approach is proposed for the acoustic analysis of automotive silencers including a perforated duct with uniform axial mean flow and an outer chamber with heterogeneous absorbent material. This material can be characterized by means of its equivalent acoustic properties, considered coordinate-dependent via the introduction of a heterogeneous bulk density, and the corresponding material airflow resistivity variations. An approach has been implemented to solve the pressure wave equation for a nonmoving heterogeneous medium, associated with the problem of sound propagation in the outer chamber. On the other hand, the governing equation in the central duct has been solved in terms of the acoustic velocity potential considering the presence of a moving medium. The coupling between both regions and the corresponding acoustic fields has been carried out by means of a perforated duct and its acoustic impedance, adapted here to include absorbent material heterogeneities and mean flow effects simultaneously. It has been found that bulk density heterogeneities have a considerable influence on the silencer transmission loss.
Mean field games for cognitive radio networks
Tembine, Hamidou
2012-06-01
In this paper we study mobility effect and power saving in cognitive radio networks using mean field games. We consider two types of users: primary and secondary users. When active, each secondary transmitter-receiver uses carrier sensing and is subject to long-term energy constraint. We formulate the interaction between primary user and large number of secondary users as an hierarchical mean field game. In contrast to the classical large-scale approaches based on stochastic geometry, percolation theory and large random matrices, the proposed mean field framework allows one to describe the evolution of the density distribution and the associated performance metrics using coupled partial differential equations. We provide explicit formulas and algorithmic power management for both primary and secondary users. A complete characterization of the optimal distribution of energy and probability of success is given.
Fictive impurity approach to dynamical mean field theory
Energy Technology Data Exchange (ETDEWEB)
Fuhrmann, A.
2006-10-15
A new extension of the dynamical mean-field theory was investigated in the regime of large Coulomb repulsion. A number of physical quantities such as single-particle density of states, spin-spin correlation, internal energy and Neel temperature, were computed for a two-dimensional Hubbard model at half-filling. The numerical data were compared to our analytical results as well as to the results computed using the dynamical cluster approximation. In the second part of this work we consider a two-plane Hubbard model. The transport properties of the bilayer were investigated and the phase diagram was obtained. (orig.)
Fictive impurity approach to dynamical mean field theory
International Nuclear Information System (INIS)
Fuhrmann, A.
2006-10-01
A new extension of the dynamical mean-field theory was investigated in the regime of large Coulomb repulsion. A number of physical quantities such as single-particle density of states, spin-spin correlation, internal energy and Neel temperature, were computed for a two-dimensional Hubbard model at half-filling. The numerical data were compared to our analytical results as well as to the results computed using the dynamical cluster approximation. In the second part of this work we consider a two-plane Hubbard model. The transport properties of the bilayer were investigated and the phase diagram was obtained. (orig.)
Cluster Mean-Field Approach to the Steady-State Phase Diagram of Dissipative Spin Systems
Directory of Open Access Journals (Sweden)
Jiasen Jin
2016-07-01
Full Text Available We show that short-range correlations have a dramatic impact on the steady-state phase diagram of quantum driven-dissipative systems. This effect, never observed in equilibrium, follows from the fact that ordering in the steady state is of dynamical origin, and is established only at very long times, whereas in thermodynamic equilibrium it arises from the properties of the (free energy. To this end, by combining the cluster methods extensively used in equilibrium phase transitions to quantum trajectories and tensor-network techniques, we extend them to nonequilibrium phase transitions in dissipative many-body systems. We analyze in detail a model of spin-1/2 on a lattice interacting through an XYZ Hamiltonian, each of them coupled to an independent environment that induces incoherent spin flips. In the steady-state phase diagram derived from our cluster approach, the location of the phase boundaries and even its topology radically change, introducing reentrance of the paramagnetic phase as compared to the single-site mean field where correlations are neglected. Furthermore, a stability analysis of the cluster mean field indicates a susceptibility towards a possible incommensurate ordering, not present if short-range correlations are ignored.
Gomes, Diogo A.
2014-01-06
In this talk we will report on new results concerning the existence of smooth solutions for time dependent mean-field games. This new result is established through a combination of various tools including several a-priori estimates for time-dependent mean-field games combined with new techniques for the regularity of Hamilton-Jacobi equations.
Gomes, Diogo A.
2014-01-01
In this talk we will report on new results concerning the existence of smooth solutions for time dependent mean-field games. This new result is established through a combination of various tools including several a-priori estimates for time-dependent mean-field games combined with new techniques for the regularity of Hamilton-Jacobi equations.
Development of mean field theories in nuclear physics and in desordered media
International Nuclear Information System (INIS)
Orland, Henri.
1981-04-01
This work, in two parts, deals with the development of mean field theories in nuclear physics (nuclei in balance and collisions of heavy ions) as well as in disordered media. In the first part, two different ways of tackling the problem of developments around mean field theories are explained. Possessing an approach wave function for the system, the natural idea for including the correlations is to develop the exact wave function of the system around the mean field wave function. The first two chapters show two different ways of dealing with this problem: the perturbative approach - Hartree-Fock equations with two body collisions and functional methods. In the second part: mean field theory for spin glasses. The problem for spin glasses is to construct a physically acceptable mean field theory. The importance of this problem in statistical mechanics is linked to the fact that the mean field theory provides a qualitative description of the low temperature phase and is the starting point needed for using more sophisticated methods (renormalization group). Two approaches to this problem are presented, one based on the Sherrington-Kirkpatrick model and the other based on a model of spins with purely local disorder and competitive interaction between the spins [fr
An entropy approach to size and variance heterogeneity
Balasubramanyan, L.; Stefanou, S.E.; Stokes, J.R.
2012-01-01
In this paper, we investigate the effect of bank size differences on cost efficiency heterogeneity using a heteroskedastic stochastic frontier model. This model is implemented by using an information theoretic maximum entropy approach. We explicitly model both bank size and variance heterogeneity
Analytic equation of state for FCC C60 solid based on analytic mean-field potential approach
International Nuclear Information System (INIS)
Sun Jiuxun
2006-01-01
The analytic mean-field approach (AMFP) was applied to the FCC C60 solid. For the intermolecular forces the Girifalco potential has been utilized. The analytic expressions for the Helmholtz free energy, internal energy and equation of state have been derived. The numerical results of thermodynamic quantities are compared with the molecular dynamic (MD) simulations and the unsymmetrized self-consistent field approach (CUSF) in the literature. It is shown that our AMFP results are in good agreement with the MD data both at low and high temperatures. The results of CUSF are in accordance with the AMFP at low temperature, but at high temperature the difference becomes prominent. Especially the AMFP predicted that the FCC C60 solid is stable upto 2202 K, the spinodal temperature, in good agreement with 2320 K from the MD simulation. However, the CUST just gives 1916 K, a temperature evidently lower than the MD data. The AMFP qualifies as a useful approach that can reasonably consider the anharmonic effects at high temperature
On a mean field game optimal control approach modeling fast exit scenarios in human crowds
Burger, Martin; Di Francesco, Marco; Markowich, Peter A.; Wolfram, Marie Therese
2013-01-01
The understanding of fast exit and evacuation situations in crowd motion research has received a lot of scientific interest in the last decades. Security issues in larger facilities, like shopping malls, sports centers, or festivals necessitate a better understanding of the major driving forces in crowd dynamics. In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. The model is formulated in the framework of mean field games and based on a parabolic optimal control problem. We consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position and velocity, the overall density of people, and the time to exit. This microscopic setup leads in a mean-field formulation to a nonlinear macroscopic optimal control problem, which raises challenging questions for the analysis and numerical simulations.We discuss different aspects of the mathematical modeling and illustrate them with various computational results. ©2013 IEEE.
On a mean field game optimal control approach modeling fast exit scenarios in human crowds
Burger, Martin
2013-12-01
The understanding of fast exit and evacuation situations in crowd motion research has received a lot of scientific interest in the last decades. Security issues in larger facilities, like shopping malls, sports centers, or festivals necessitate a better understanding of the major driving forces in crowd dynamics. In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. The model is formulated in the framework of mean field games and based on a parabolic optimal control problem. We consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position and velocity, the overall density of people, and the time to exit. This microscopic setup leads in a mean-field formulation to a nonlinear macroscopic optimal control problem, which raises challenging questions for the analysis and numerical simulations.We discuss different aspects of the mathematical modeling and illustrate them with various computational results. ©2013 IEEE.
Mean-field approximation for spacing distribution functions in classical systems
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.
Air flow and pollution in a real, heterogeneous urban street canyon: A field and laboratory study
Karra, Styliani; Malki-Epshtein, Liora; Neophytou, Marina K.-A.
2017-09-01
In this work we investigate the influence of real world conditions, including heterogeneity and natural variability of background wind, on the air flow and pollutant concentrations in a heterogeneous urban street canyon using both a series of field measurements and controlled laboratory experiments. Field measurements of wind velocities and Carbon Monoxide (CO) concentrations were taken under field conditions in a heterogeneous street in a city centre at several cross-sections along the length of the street (each cross-section being of different aspect ratio). The real field background wind was in fact observed to be highly variable and thus different Intensive Observation Periods (IOPs) represented by a different mean wind velocity and different wind variability were defined. Observed pollution concentrations reveal high sensitivity to local parameters: there is a bias towards the side closer to the traffic lane; higher concentrations are found in the centre of the street as compared to cross-sections closer to the junctions; higher concentrations are found at 1.5 height from the ground than at 2.5 m height, all of which are of concern regarding pedestrian exposure to traffic-related pollution. A physical model of the same street was produced for the purpose of laboratory experiments, making some geometrical simplifications of complex volumes and extrusions. The physical model was tested in an Atmospheric Boundary Layer water channel, using simultaneously Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF), for flow visualisation as well as for quantitative measurement of concentrations and flow velocities. The wind field conditions were represented by a steady mean approach velocity in the laboratory simulation (essentially representing periods of near-zero wind variability). The laboratory investigations showed a clear sensitivity of the resulting flow field to the local geometry and substantial three-dimensional flow patterns were
Wang, Huai-Chun; Minh, Bui Quang; Susko, Edward; Roger, Andrew J
2018-03-01
Proteins have distinct structural and functional constraints at different sites that lead to site-specific preferences for particular amino acid residues as the sequences evolve. Heterogeneity in the amino acid substitution process between sites is not modeled by commonly used empirical amino acid exchange matrices. Such model misspecification can lead to artefacts in phylogenetic estimation such as long-branch attraction. Although sophisticated site-heterogeneous mixture models have been developed to address this problem in both Bayesian and maximum likelihood (ML) frameworks, their formidable computational time and memory usage severely limits their use in large phylogenomic analyses. Here we propose a posterior mean site frequency (PMSF) method as a rapid and efficient approximation to full empirical profile mixture models for ML analysis. The PMSF approach assigns a conditional mean amino acid frequency profile to each site calculated based on a mixture model fitted to the data using a preliminary guide tree. These PMSF profiles can then be used for in-depth tree-searching in place of the full mixture model. Compared with widely used empirical mixture models with $k$ classes, our implementation of PMSF in IQ-TREE (http://www.iqtree.org) speeds up the computation by approximately $k$/1.5-fold and requires a small fraction of the RAM. Furthermore, this speedup allows, for the first time, full nonparametric bootstrap analyses to be conducted under complex site-heterogeneous models on large concatenated data matrices. Our simulations and empirical data analyses demonstrate that PMSF can effectively ameliorate long-branch attraction artefacts. In some empirical and simulation settings PMSF provided more accurate estimates of phylogenies than the mixture models from which they derive.
Condition monitoring with Mean field independent components analysis
DEFF Research Database (Denmark)
Pontoppidan, Niels Henrik; Sigurdsson, Sigurdur; Larsen, Jan
2005-01-01
We discuss condition monitoring based on mean field independent components analysis of acoustic emission energy signals. Within this framework it is possible to formulate a generative model that explains the sources, their mixing and also the noise statistics of the observed signals. By using...... a novelty approach we may detect unseen faulty signals as indeed faulty with high precision, even though the model learns only from normal signals. This is done by evaluating the likelihood that the model generated the signals and adapting a simple threshold for decision. Acoustic emission energy signals...... from a large diesel engine is used to demonstrate this approach. The results show that mean field independent components analysis gives a better detection of fault compared to principal components analysis, while at the same time selecting a more compact model...
International Nuclear Information System (INIS)
Lü, Xiaoshu; Lu, Tao; Kibert, Charles J.; Viljanen, Martti
2015-01-01
Highlights: • This paper presents a new modeling method to forecast energy demands. • The model is based on physical–statistical approach to improving forecast accuracy. • A new method is proposed to address the heterogeneity challenge. • Comparison with measurements shows accurate forecasts of the model. • The first physical–statistical/heterogeneous building energy modeling approach is proposed and validated. - Abstract: Energy consumption forecasting is a critical and necessary input to planning and controlling energy usage in the building sector which accounts for 40% of the world’s energy use and the world’s greatest fraction of greenhouse gas emissions. However, due to the diversity and complexity of buildings as well as the random nature of weather conditions, energy consumption and loads are stochastic and difficult to predict. This paper presents a new methodology for energy demand forecasting that addresses the heterogeneity challenges in energy modeling of buildings. The new method is based on a physical–statistical approach designed to account for building heterogeneity to improve forecast accuracy. The physical model provides a theoretical input to characterize the underlying physical mechanism of energy flows. Then stochastic parameters are introduced into the physical model and the statistical time series model is formulated to reflect model uncertainties and individual heterogeneity in buildings. A new method of model generalization based on a convex hull technique is further derived to parameterize the individual-level model parameters for consistent model coefficients while maintaining satisfactory modeling accuracy for heterogeneous buildings. The proposed method and its validation are presented in detail for four different sports buildings with field measurements. The results show that the proposed methodology and model can provide a considerable improvement in forecasting accuracy
Selective pruning in pineapple plants as means to reduce heterogeneity in fruit quality
Fassinou Hotegni, V.N.; Lommen, W.J.M.; Struik, P.C.; Agbossou, E.K.
2015-01-01
Heterogeneity in fruit quality (size and taste) is a major problem in pineapple production chains. The possibilities were investigated of reducing the heterogeneity in pineapple in the field by pruning slips on selected plants, in order to promote the fruit growth on these plants. Slips are side
Mean-field learning for satisfactory solutions
Tembine, Hamidou
2013-12-01
One of the fundamental challenges in distributed interactive systems is to design efficient, accurate, and fair solutions. In such systems, a satisfactory solution is an innovative approach that aims to provide all players with a satisfactory payoff anytime and anywhere. In this paper we study fully distributed learning schemes for satisfactory solutions in games with continuous action space. Considering games where the payoff function depends only on own-action and an aggregate term, we show that the complexity of learning systems can be significantly reduced, leading to the so-called mean-field learning. We provide sufficient conditions for convergence to a satisfactory solution and we give explicit convergence time bounds. Then, several acceleration techniques are used in order to improve the convergence rate. We illustrate numerically the proposed mean-field learning schemes for quality-of-service management in communication networks. © 2013 IEEE.
Regadas Filho, J G L; Tedeschi, L O; Vieira, R A M; Rodrigues, M T
2014-03-01
The objectives of this study were to evaluate ruminal fiber stratification and to develop a mathematical approach for predicting the mean retention time (MRT) of forage and concentrates in goats. A dataset from 3 studies was used that contained information regarding fiber and lignin intake as well as ruminal content and the kinetics of fiber passage for forage and concentrates. The kinetic information was obtained through pulse dose and the fecal concentration measurement of forage and concentrate markers in the same animals that were used to measure ruminal content. The evaluation of heterogeneous fiber pools in the rumen was performed using the Lucas' test assumptions, and the marker excretion profiles were interpreted using a model known in the literature as GNG1. The GNG1 model assumes an age-dependent fractional rate for the transfer of particles from the raft to the escapable pool in the rumen (λ(r); h(-1)) and an age-independent fractional rate for the escape of particles from the escapable pool to the remaining parts of the stomach (k(e); h(-1)). The equations used to predict the MRT for forage and concentrate fiber were developed using stepwise regression. A sensitivity analysis was conducted using a Monte Carlo simulation to investigate the relationships between the dependent and independent variables and between forage and concentrate passage rates. The Lucas' test yields goodness-of-fit estimates for NDF analysis; however, the homogeneous fiber pool approach could not be applied because a positive intercept (P ruminal content. The stepwise regression model for MRT estimation had an approximate coefficient of determination and a root mean square error (RMSE) for forage of 0.53 and 9.78 h, respectively, and for concentrate of 0.49 and 5.86 h, respectively. The sensitivity analysis yielded a mean rate of passage (k(p)) value for forage of 0.0322 h(-1) (0.0158 to 0.0556 h(-1)) with 99% confidence interval. For the concentrate, the mean k(p) value was of 0
Optimal and Approximate Approaches for Deployment of Heterogeneous Sensing Devices
Directory of Open Access Journals (Sweden)
Rabie Ramadan
2007-04-01
Full Text Available A modeling framework for the problem of deploying a set of heterogeneous sensors in a field with time-varying differential surveillance requirements is presented. The problem is formulated as mixed integer mathematical program with the objective to maximize coverage of a given field. Two metaheuristics are used to solve this problem. The first heuristic adopts a genetic algorithm (GA approach while the second heuristic implements a simulated annealing (SA algorithm. A set of experiments is used to illustrate the capabilities of the developed models and to compare their performance. The experiments investigate the effect of parameters related to the size of the sensor deployment problem including number of deployed sensors, size of the monitored field, and length of the monitoring horizon. They also examine several endogenous parameters related to the developed GA and SA algorithms.
Risk-sensitive mean-field games
Tembine, Hamidou
2014-04-01
In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics. © 1963-2012 IEEE.
Risk-sensitive mean-field games
Tembine, Hamidou; Zhu, Quanyan; Başar, Tamer
2014-01-01
In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics. © 1963-2012 IEEE.
Linear–Quadratic Mean-Field-Type Games: A Direct Method
Directory of Open Access Journals (Sweden)
Tyrone E. Duncan
2018-02-01
Full Text Available In this work, a multi-person mean-field-type game is formulated and solved that is described by a linear jump-diffusion system of mean-field type and a quadratic cost functional involving the second moments, the square of the expected value of the state, and the control actions of all decision-makers. We propose a direct method to solve the game, team, and bargaining problems. This solution approach does not require solving the Bellman–Kolmogorov equations or backward–forward stochastic differential equations of Pontryagin’s type. The proposed method can be easily implemented by beginners and engineers who are new to the emerging field of mean-field-type game theory. The optimal strategies for decision-makers are shown to be in a state-and-mean-field feedback form. The optimal strategies are given explicitly as a sum of the well-known linear state-feedback strategy for the associated deterministic linear–quadratic game problem and a mean-field feedback term. The equilibrium cost of the decision-makers are explicitly derived using a simple direct method. Moreover, the equilibrium cost is a weighted sum of the initial variance and an integral of a weighted variance of the diffusion and the jump process. Finally, the method is used to compute global optimum strategies as well as saddle point strategies and Nash bargaining solution in state-and-mean-field feedback form.
Heterogeneity of cerebral blood flow: a fractal approach
International Nuclear Information System (INIS)
Kuikka, J.T.; Hartikainen, P.
2000-01-01
Aim: We demonstrate the heterogeneity of regional cerebral blood flow using a fractal approach and single-photon emission computed tomography (SPECT). Method: Tc-99m-labelled ethylcysteine dimer was injected intravenously in 10 healthy controls and in 10 patients with dementia of frontal lobe type. The head was imaged with a gamma camera and transaxial, sagittal and coronal slices were reconstructed. Two hundred fifty-six symmetrical regions of interest (ROIs) were drawn onto each hemisphere of functioning brain matter. Fractal analysis was used to examine the spatial heterogeneity of blood flow as a function of the number of ROIs. Results: Relative dispersion (=coefficient of variation of the regional flows) was fractal-like in healthy subjects and could be characterized by a fractal dimension of 1.17±0.05 (mean±SD) for the left hemisphere and 1.15±0.04 for the right hemisphere, respectively. The fractal dimension of 1.0 reflects completely homogeneous blood flow and 1.5 indicates a random blood flow distribution. Patients with dementia of frontal lobe type had a significantly lower fractal dimension of 1.04±0.03 than in healthy controls. (orig.) [de
Heterogeneous Face Attribute Estimation: A Deep Multi-Task Learning Approach.
Han, Hu; K Jain, Anil; Shan, Shiguang; Chen, Xilin
2017-08-10
Face attribute estimation has many potential applications in video surveillance, face retrieval, and social media. While a number of methods have been proposed for face attribute estimation, most of them did not explicitly consider the attribute correlation and heterogeneity (e.g., ordinal vs. nominal and holistic vs. local) during feature representation learning. In this paper, we present a Deep Multi-Task Learning (DMTL) approach to jointly estimate multiple heterogeneous attributes from a single face image. In DMTL, we tackle attribute correlation and heterogeneity with convolutional neural networks (CNNs) consisting of shared feature learning for all the attributes, and category-specific feature learning for heterogeneous attributes. We also introduce an unconstrained face database (LFW+), an extension of public-domain LFW, with heterogeneous demographic attributes (age, gender, and race) obtained via crowdsourcing. Experimental results on benchmarks with multiple face attributes (MORPH II, LFW+, CelebA, LFWA, and FotW) show that the proposed approach has superior performance compared to state of the art. Finally, evaluations on a public-domain face database (LAP) with a single attribute show that the proposed approach has excellent generalization ability.
Borgs, C.; Chayes, J.T.; Hofstad, van der R.W.; Slade, G.
1999-01-01
We introduce a mean-field model of lattice trees based on embeddings into d of abstract trees having a critical Poisson offspring distribution. This model provides a combinatorial interpretation for the self-consistent mean-field model introduced previously by Derbez and Slade [9], and provides an
Critical study of the dispersive n- 90Zr mean field by means of a new variational method
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
Mean field approximation versus exact treatment of collisions in few-body systems
International Nuclear Information System (INIS)
Lemm, J.; Weiguny, A.; Giraud, B.G.
1990-01-01
A variational principle for calculating matrix elements of the full resolvent operator for a many-body system is studied. Its mean field approximation results in non-linear equations of Hartree (-Fock) type, with initial and final channel wave functions as driving terms. The mean field equations will in general have many solutions whereas the exact problem being linear, has a unique solution. In a schematic model with separable forces the mean field equations are analytically soluble, and for the exact problem the resulting integral equations are solved numerically. Comparing exact and mean field results over a wide range of system parameters, the mean field approach proves to be a very reliable approximation, which is not plagued by the notorious problem of defining asymptotic channels in the time-dependent mean field method. (orig.)
Fiber Bundle Model Under Heterogeneous Loading
Roy, Subhadeep; Goswami, Sanchari
2018-03-01
The present work deals with the behavior of fiber bundle model under heterogeneous loading condition. The model is explored both in the mean-field limit as well as with local stress concentration. In the mean field limit, the failure abruptness decreases with increasing order k of heterogeneous loading. In this limit, a brittle to quasi-brittle transition is observed at a particular strength of disorder which changes with k. On the other hand, the model is hardly affected by such heterogeneity in the limit where local stress concentration plays a crucial role. The continuous limit of the heterogeneous loading is also studied and discussed in this paper. Some of the important results related to fiber bundle model are reviewed and their responses to our new scheme of heterogeneous loading are studied in details. Our findings are universal with respect to the nature of the threshold distribution adopted to assign strength to an individual fiber.
Non-local correlations within dynamical mean field theory
Energy Technology Data Exchange (ETDEWEB)
Li, Gang
2009-03-15
The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)
Non-local correlations within dynamical mean field theory
International Nuclear Information System (INIS)
Li, Gang
2009-03-01
The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)
Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul
2014-01-01
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple’s network on their feeling states and their well-being. PMID:24804835
Mean-field games for marriage.
Directory of Open Access Journals (Sweden)
Dario Bauso
Full Text Available This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being.
Bauso, Dario
2014-05-07
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple\\'s network on their feeling states and their well-being. © 2014 Bauso et al.
Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul
2014-01-01
This article examines mean-field games for marriage. The results support the argument that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being. © 2014 Bauso et al.
Mean Field Theory, Ginzburg Criterion, and Marginal Dimensionality of Phase-Transitions
DEFF Research Database (Denmark)
Als-Nielsen, Jens Aage; Birgenau, R. J.
1977-01-01
By applying a real space version of the Ginzburg criterion, the role of fluctuations and thence the self‐consistency of mean field theory are assessed in a simple fashion for a variety of phase transitions. It is shown that in using this approach the concept of ’’marginal dimensionality’’ emerges...... in a natural way. For example, it is shown that for many homogeneous structural transformations the marginal dimensionality is two, so that mean field theory will be valid for real three‐dimensional systems. It is suggested that this simple self‐consistent approach to Landau theory should be incorporated...
Merging Belief Propagation and the Mean Field Approximation
DEFF Research Database (Denmark)
Riegler, Erwin; Kirkelund, Gunvor Elisabeth; Manchón, Carles Navarro
2010-01-01
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence......) as a starting point. In this method message passing fixed point equations (which correspond to the update rules in a message passing algorithm) are then obtained by imposing different region-based approximations and constraints on the mean field and belief propagation parts of the corresponding factor graph....... Our results can be applied, for example, to algorithms that perform joint channel estimation and decoding in iterative receivers. This is demonstrated in a simple example....
Nuclear collective vibrations in extended mean-field theory
Energy Technology Data Exchange (ETDEWEB)
Lacroix, D. [Lab. de Physique Corpusculaire/ ENSICAEN, 14 - Caen (France); Ayik, S. [Tennessee Technological Univ., Cookeville, TN (United States); Chomaz, Ph. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France)
2003-07-01
The extended mean-field theory, which includes both the incoherent dissipation mechanism due to nucleon-nucleon collisions and the coherent dissipation mechanism due to coupling to low-lying surface vibrations, is briefly reviewed. Expressions of the strength functions for the collective excitations are presented in the small amplitude limit of this approach. This fully microscopic theory is applied by employing effective Skyrme forces to various giant resonance excitations at zero and finite temperature. The theory is able to describe the gross properties of giant resonance excitations, the fragmentation of the strength distributions as well as their fine structure. At finite temperature, the success and limitations of this extended mean-field description are discussed. (authors)
Bacterial Transport in Heterogeneous Porous Media: Laboratory and Field Experiments
Fuller, M. E.
2001-12-01
A fully instrumented research site for examining field-scale bacterial transport has been established on the eastern shore of Virginia. Studies employing intact sediment cores from the South Oyster site have been performed to examine the effects of physical and chemical heterogeneity, to derive transport parameters, and to aid in the selection of bacterial strains for use in field experiments. A variety of innovative methods for tracking bacteria were developed and evaluated under both laboratory and field conditions, providing the tools to detect target cell concentrations in groundwater down to effects of physical and chemical heterogeneity on field-scale bacterial transport. The results of this research not only contribute to the development of more effective bioremediation strategies, but also have implications for a better understanding of bacterial movement in the subsurface as it relates to public health microbiology and general microbial ecology.
Magnetic moments in present relativistic nuclear theories: a mean-field problem
International Nuclear Information System (INIS)
Desplanques, B.
1986-07-01
We show that the magnetic moments of LS closed shell nuclei plus or minus one nucleon derived from non-relativistic Hartree-Fock mean-fields are as bad as those obtained in relativistic approaches of nuclear structure. Deviations with respect to more complete results in both cases are ascribed to the mean-field approximation which neglects some degrees of freedom in the nucleus description. 18 refs
A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type Control
Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul
2015-01-01
In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends the risk-sensitive SMP (without mean-field coupling) of Lim and Zhou (2005), derived for feedback (or Markov) type optimal controls, to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. In our approach to the risk-sensitive SMP, the smoothness assumption on the value-function imposed in Lim and Zhou (2005) needs not be satisfied. For a general action space a Peng's type SMP is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type SMP under linear stochastic dynamics with exponential quadratic cost function. Explicit solutions are given for both mean-field free and mean-field models.
A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type Control
Djehiche, Boualem
2015-02-24
In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in which the drift and the diffusion coefficients as well as the performance functional depend not only on the state and the control but also on the mean of the distribution of the state. Our result extends the risk-sensitive SMP (without mean-field coupling) of Lim and Zhou (2005), derived for feedback (or Markov) type optimal controls, to optimal control problems for non-Markovian dynamics which may be time-inconsistent in the sense that the Bellman optimality principle does not hold. In our approach to the risk-sensitive SMP, the smoothness assumption on the value-function imposed in Lim and Zhou (2005) needs not be satisfied. For a general action space a Peng\\'s type SMP is derived, specifying the necessary conditions for optimality. Two examples are carried out to illustrate the proposed risk-sensitive mean-field type SMP under linear stochastic dynamics with exponential quadratic cost function. Explicit solutions are given for both mean-field free and mean-field models.
Extended Deterministic Mean-Field Games
Gomes, Diogo A.
2016-04-21
In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is particularly convenient for these problems. We prove an existence result for extended mean-field games and establish uniqueness conditions. In the last section, we consider the Master Equation and discuss properties of its solutions.
Extended Deterministic Mean-Field Games
Gomes, Diogo A.; Voskanyan, Vardan K.
2016-01-01
In this paper, we consider mean-field games where the interaction of each player with the mean field takes into account not only the states of the players but also their collective behavior. To do so, we develop a random variable framework that is particularly convenient for these problems. We prove an existence result for extended mean-field games and establish uniqueness conditions. In the last section, we consider the Master Equation and discuss properties of its solutions.
Time independent mean-field theory
International Nuclear Information System (INIS)
Negele, J.W.
1980-02-01
The physical and theoretical motivations for the time-dependent mean-field theory are presented, and the successes and limitations of the time-dependent Hartree-Fock initial-vaue problem are reviewed. New theoretical developments are described in the treatment of two-body correlations and the formulation of a quantum mean-field theory of large-amplitude collective motion and tunneling decay. Finally, the mean-field theory is used to obtain new insights into the phenomenon of pion condensation in finite nuclei. 18 figures
Mean field strategies induce unrealistic nonlinearities in calcium puffs
Directory of Open Access Journals (Sweden)
Guillermo eSolovey
2011-08-01
Full Text Available Mean field models are often useful approximations to biological systems, but sometimes, they can yield misleading results. In this work, we compare mean field approaches with stochastic models of intracellular calcium release. In particular, we concentrate on calcium signals generated by the concerted opening of several clustered channels (calcium puffs. To this end we simulate calcium puffs numerically and then try to reproduce features of the resulting calcium distribution using mean field models were all the channels open and close simultaneously. We show that an unrealistic nonlinear relationship between the current and the number of open channels is needed to reproduce the simulated puffs. Furthermore, a single channel current which is five times smaller than the one of the stochastic simulations is also needed. Our study sheds light on the importance of the stochastic kinetics of the calcium release channel activity to estimate the release fluxes.
International Nuclear Information System (INIS)
Bender, C.M.; Cooper, F.
1985-01-01
An apparent difference between formulating mean field perturbation theory for lambdaphi 4 field theory via path integrals or via functional differential equations when there are external sources present is shown not to exist when mean field theory is considered as the N = 1 limit of the 0(N)lambdaphi 4 field theory. A simply method is given for determining the 1/N expansion for the Green's functions in the presence of external sources by directly solving the functional differential equations order by order in 1/N. The 1/N expansion for the effective action GAMMA(phi,chi) is obtained by directly integrating the functional differential equations for the fields phi and chi (equivalent1/2lambda/Nphi/sub α/phi/sup α/-μ 2 ) in the presence of two external sources j = -deltaGAMMA/deltaphi, S = -deltaGAMMA/deltachi
Shapes and dynamics from the time-dependent mean field
International Nuclear Information System (INIS)
Stevenson, P.D.; Goddard, P.M.; Rios, A.
2015-01-01
Explaining observed properties in terms of underlying shape degrees of freedom is a well-established prism with which to understand atomic nuclei. Self-consistent mean-field models provide one tool to understand nuclear shapes, and their link to other nuclear properties and observables. We present examples of how the time-dependent extension of the mean-field approach can be used in particular to shed light on nuclear shape properties, particularly looking at the giant resonances built on deformed nuclear ground states, and at dynamics in highly-deformed fission isomers. Example calculations are shown of 28 Si in the first case, and 240 Pu in the latter case
Directory of Open Access Journals (Sweden)
Wilten eNicola
2016-02-01
Full Text Available A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF. The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networks
Nicola, Wilten; Tripp, Bryan; Scott, Matthew
2016-01-01
A fundamental question in computational neuroscience is how to connect a network of spiking neurons to produce desired macroscopic or mean field dynamics. One possible approach is through the Neural Engineering Framework (NEF). The NEF approach requires quantities called decoders which are solved through an optimization problem requiring large matrix inversion. Here, we show how a decoder can be obtained analytically for type I and certain type II firing rates as a function of the heterogeneity of its associated neuron. These decoders generate approximants for functions that converge to the desired function in mean-squared error like 1/N, where N is the number of neurons in the network. We refer to these decoders as scale-invariant decoders due to their structure. These decoders generate weights for a network of neurons through the NEF formula for weights. These weights force the spiking network to have arbitrary and prescribed mean field dynamics. The weights generated with scale-invariant decoders all lie on low dimensional hypersurfaces asymptotically. We demonstrate the applicability of these scale-invariant decoders and weight surfaces by constructing networks of spiking theta neurons that replicate the dynamics of various well known dynamical systems such as the neural integrator, Van der Pol system and the Lorenz system. As these decoders are analytically determined and non-unique, the weights are also analytically determined and non-unique. We discuss the implications for measured weights of neuronal networks.
Relativistic mean-field mass models
Energy Technology Data Exchange (ETDEWEB)
Pena-Arteaga, D.; Goriely, S.; Chamel, N. [Universite Libre de Bruxelles, Institut d' Astronomie et d' Astrophysique, CP-226, Brussels (Belgium)
2016-10-15
We present a new effort to develop viable mass models within the relativistic mean-field approach with density-dependent meson couplings, separable pairing and microscopic estimations for the translational and rotational correction energies. Two interactions, DD-MEB1 and DD-MEB2, are fitted to essentially all experimental masses, and also to charge radii and infinite nuclear matter properties as determined by microscopic models using realistic interactions. While DD-MEB1 includes the σ, ω and ρ meson fields, DD-MEB2 also considers the δ meson. Both mass models describe the 2353 experimental masses with a root mean square deviation of about 1.1 MeV and the 882 measured charge radii with a root mean square deviation of 0.029 fm. In addition, we show that the Pb isotopic shifts and moments of inertia are rather well reproduced, and the equation of state in pure neutron matter as well as symmetric nuclear matter are in relatively good agreement with existing realistic calculations. Both models predict a maximum neutron-star mass of more than 2.6 solar masses, and thus are able to accommodate the heaviest neutron stars observed so far. However, the new Lagrangians, like all previously determined RMF models, present the drawback of being characterized by a low effective mass, which leads to strong shell effects due to the strong coupling between the spin-orbit splitting and the effective mass. Complete mass tables have been generated and a comparison with other mass models is presented. (orig.)
The application of mean field theory to image motion estimation.
Zhang, J; Hanauer, G G
1995-01-01
Previously, Markov random field (MRF) model-based techniques have been proposed for image motion estimation. Since motion estimation is usually an ill-posed problem, various constraints are needed to obtain a unique and stable solution. The main advantage of the MRF approach is its capacity to incorporate such constraints, for instance, motion continuity within an object and motion discontinuity at the boundaries between objects. In the MRF approach, motion estimation is often formulated as an optimization problem, and two frequently used optimization methods are simulated annealing (SA) and iterative-conditional mode (ICM). Although the SA is theoretically optimal in the sense of finding the global optimum, it usually takes many iterations to converge. The ICM, on the other hand, converges quickly, but its results are often unsatisfactory due to its "hard decision" nature. Previously, the authors have applied the mean field theory to image segmentation and image restoration problems. It provides results nearly as good as SA but with much faster convergence. The present paper shows how the mean field theory can be applied to MRF model-based motion estimation. This approach is demonstrated on both synthetic and real-world images, where it produced good motion estimates.
Mean-field approximations of fixation time distributions of evolutionary game dynamics on graphs
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.
Geological entropy and solute transport in heterogeneous porous media
Bianchi, Marco; Pedretti, Daniele
2017-06-01
We propose a novel approach to link solute transport behavior to the physical heterogeneity of the aquifer, which we fully characterize with two measurable parameters: the variance of the log K values (σY2), and a new indicator (HR) that integrates multiple properties of the K field into a global measure of spatial disorder or geological entropy. From the results of a detailed numerical experiment considering solute transport in K fields representing realistic distributions of hydrofacies in alluvial aquifers, we identify empirical relationship between the two parameters and the first three central moments of the distributions of arrival times of solute particles at a selected control plane. The analysis of experimental data indicates that the mean and the variance of the solutes arrival times tend to increase with spatial disorder (i.e., HR increasing), while highly skewed distributions are observed in more orderly structures (i.e., HR decreasing) or at higher σY2. We found that simple closed-form empirical expressions of the bivariate dependency of skewness on HR and σY2 can be used to predict the emergence of non-Fickian transport in K fields considering a range of structures and heterogeneity levels, some of which based on documented real aquifers. The accuracy of these predictions and in general the results from this study indicate that a description of the global variability and structure of the K field in terms of variance and geological entropy offers a valid and broadly applicable approach for the interpretation and prediction of transport in heterogeneous porous media.
Pedestrian Flow in the Mean Field Limit
Haji Ali, Abdul Lateef
2012-11-01
We study the mean-field limit of a particle-based system modeling the behavior of many indistinguishable pedestrians as their number increases. The base model is a modified version of Helbing\\'s social force model. In the mean-field limit, the time-dependent density of two-dimensional pedestrians satisfies a four-dimensional integro-differential Fokker-Planck equation. To approximate the solution of the Fokker-Planck equation we use a time-splitting approach and solve the diffusion part using a Crank-Nicholson method. The advection part is solved using a Lax-Wendroff-Leveque method or an upwind Backward Euler method depending on the advection speed. Moreover, we use multilevel Monte Carlo to estimate observables from the particle-based system. We discuss these numerical methods, and present numerical results showing the convergence of observables that were calculated using the particle-based model as the number of pedestrians increases to those calculated using the probability density function satisfying the Fokker-Planck equation.
Dynamical Systems Approach to Endothelial Heterogeneity
Regan, Erzsébet Ravasz; Aird, William C.
2012-01-01
Rationale Objective Here we reexamine our current understanding of the molecular basis of endothelial heterogeneity. We introduce multistability as a new explanatory framework in vascular biology. Methods We draw on the field of non-linear dynamics to propose a dynamical systems framework for modeling multistability and its derivative properties, including robustness, memory, and plasticity. Conclusions Our perspective allows for both a conceptual and quantitative description of system-level features of endothelial regulation. PMID:22723222
Relativistic mean field calculations in neutron-rich nuclei
Energy Technology Data Exchange (ETDEWEB)
Gangopadhyay, G.; Bhattacharya, Madhubrata [Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Roy, Subinit [Saha Institute of Nuclear Physics, Block AF, Sector 1, Kolkata- 700 064 (India)
2014-08-14
Relativistic mean field calculations have been employed to study neutron rich nuclei. The Lagrange's equations have been solved in the co-ordinate space. The effect of the continuum has been effectively taken into account through the method of resonant continuum. It is found that BCS approximation performs as well as a more involved Relativistic Continuum Hartree Bogoliubov approach. Calculations reveal the possibility of modification of magic numbers in neutron rich nuclei. Calculation for low energy proton scattering cross sections shows that the present approach reproduces the density in very light neutron rich nuclei.
Autonomously responsive pumping by a bacterial flagellar forest: A mean-field approach
Martindale, James D.; Fu, Henry C.
2017-09-01
This study is motivated by a microfluidic device that imparts a magnetic torque on an array of bacterial flagella. Bacterial flagella can transform their helical geometry autonomously in response to properties of the background fluid, which provides an intriguing mechanism allowing their use as an engineered element for the regulation or transport of chemicals in microscale applications. The synchronization of flagellar phase has been widely studied in biological contexts, but here we examine the synchronization of flagellar tilt, which is necessary for effective pumping. We first examine the effects of helical geometry and tilt on the pumping flows generated by a single rotating flagellum. Next, we explore a mean-field model for an array of helical flagella to understand how collective tilt arises and influences pumping. The mean-field methodology allows us to take into account possible phase differences through a time-averaging procedure and to model an infinite array of flagella. We find array separation distances, magnetic field strengths, and rotation frequencies that produce nontrivial self-consistent pumping solutions. For individual flagella, pumping is reversed when helicity or rotation is reversed; in contrast, when collective effects are included, self-consistent tilted pumping solutions become untilted nonpumping solutions when helicity or rotation is reversed.
Emmerich, H.
2009-11-01
systems are investigated jointly by experimental scientists working with different experimental techniques together with theoreticians, whose expertise is likewise diverse, ranging from density functional theory (DFT), over molecular simulations (MC/MD) to the phase-field method and who at the same time aim at a rigorous connection of these methods. This sketch illustrates the different 'dimensions' of the interdisciplinary research setting of the Priority Program and thus underlying the articles in this issue. Still the comparison of these new approaches with experimental results leads to controversial conclusions [12, 16]. Hence the study and development of theoretical models for the understanding and in particular for the quantitative description of the heterogeneous nucleus- and microstructure-formation processes remains an open but successively more and more quantitatively approachable issue. The development of physically relevant models for nucleus- and initial microstructure-formation is based on reliable knowledge of key parameters as the interfacial energy between crystal nucleus and melt. The latter is still experimentally difficult to access in metallic systems due to limitations arising e.g. from non-transmittance of optical light. To accelerate the development of more quantitative models capable of addressing the open issues of heterogenous nucleation and microstructure formation further, it is therefore essential to find complementary experimental systems which are less limited in accessing the above key parameters than metals. For this reason, within the Priority Program 1296 'Heterogenous Nucleation and Microstructure Formation—a Scale- and System-Bridging Approach' [8], the emphasis is to investigate the energetics and kinetics of heterogeneous nucleation and microstructure-formation processes experimentally jointly with metals as well as colloids as mesoscopic model systems for these processes. Thereby the most comprehensive experimental picture shall
Aerosol processing: a wind of innovation in the field of advanced heterogeneous catalysts.
Debecker, Damien P; Le Bras, Solène; Boissière, Cédric; Chaumonnot, Alexandra; Sanchez, Clément
2018-04-16
Aerosol processing is long known and implemented industrially to obtain various types of divided materials and nanomaterials. The atomisation of a liquid solution or suspension produces a mist of aerosol droplets which can then be transformed via a diversity of processes including spray-drying, spray pyrolysis, flame spray pyrolysis, thermal decomposition, micronisation, gas atomisation, etc. The attractive technical features of these aerosol processes make them highly interesting for the continuous, large scale, and tailored production of heterogeneous catalysts. Indeed, during aerosol processing, each liquid droplet undergoes well-controlled physical and chemical transformations, allowing for example to dry and aggregate pre-existing solid particles or to synthesise new micro- or nanoparticles from mixtures of molecular or colloidal precursors. In the last two decades, more advanced reactive aerosol processes have emerged as innovative means to synthesise tailored-made nanomaterials with tunable surface properties, textures, compositions, etc. In particular, the "aerosol-assisted sol-gel" process (AASG) has demonstrated tremendous potential for the preparation of high-performance heterogeneous catalysts. The method is mainly based on the low-cost, scalable, and environmentally benign sol-gel chemistry process, often coupled with the evaporation-induced self-assembly (EISA) concept. It allows producing micronic or submicronic, inorganic or hybrid organic-inorganic particles bearing tuneable and calibrated porous structures at different scales. In addition, pre-formed nanoparticles can be easily incorporated or formed in a "one-pot" bottom-up approach within the porous inorganic or hybrid spheres produced by such spray drying method. Thus, multifunctional catalysts with tailored catalytic activities can be prepared in a relatively simple way. This account is an overview of aerosol processed heterogeneous catalysts which demonstrated interesting performance in
Mean field dynamics of networks of delay-coupled noisy excitable units
Energy Technology Data Exchange (ETDEWEB)
Franović, Igor, E-mail: franovic@ipb.ac.rs [Scientific Computing Laboratory, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade (Serbia); Todorović, Kristina; Burić, Nikola [Department of Physics and Mathematics, Faculty of Pharmacy, University of Belgrade, Vojvode Stepe 450, Belgrade (Serbia); Vasović, Nebojša [Department of Applied Mathematics, Faculty of Mining and Geology, University of Belgrade, PO Box 162, Belgrade (Serbia)
2016-06-08
We use the mean-field approach to analyze the collective dynamics in macroscopic networks of stochastic Fitzhugh-Nagumo units with delayed couplings. The conditions for validity of the two main approximations behind the model, called the Gaussian approximation and the Quasi-independence approximation, are examined. It is shown that the dynamics of the mean-field model may indicate in a self-consistent fashion the parameter domains where the Quasi-independence approximation fails. Apart from a network of globally coupled units, we also consider the paradigmatic setup of two interacting assemblies to demonstrate how our framework may be extended to hierarchical and modular networks. In both cases, the mean-field model can be used to qualitatively analyze the stability of the system, as well as the scenarios for the onset and the suppression of the collective mode. In quantitative terms, the mean-field model is capable of predicting the average oscillation frequency corresponding to the global variables of the exact system.
Measuring energy performance with sectoral heterogeneity: A non-parametric frontier approach
International Nuclear Information System (INIS)
Wang, H.; Ang, B.W.; Wang, Q.W.; Zhou, P.
2017-01-01
Evaluating economy-wide energy performance is an integral part of assessing the effectiveness of a country's energy efficiency policy. Non-parametric frontier approach has been widely used by researchers for such a purpose. This paper proposes an extended non-parametric frontier approach to studying economy-wide energy efficiency and productivity performances by accounting for sectoral heterogeneity. Relevant techniques in index number theory are incorporated to quantify the driving forces behind changes in the economy-wide energy productivity index. The proposed approach facilitates flexible modelling of different sectors' production processes, and helps to examine sectors' impact on the aggregate energy performance. A case study of China's economy-wide energy efficiency and productivity performances in its 11th five-year plan period (2006–2010) is presented. It is found that sectoral heterogeneities in terms of energy performance are significant in China. Meanwhile, China's economy-wide energy productivity increased slightly during the study period, mainly driven by the technical efficiency improvement. A number of other findings have also been reported. - Highlights: • We model economy-wide energy performance by considering sectoral heterogeneity. • The proposed approach can identify sectors' impact on the aggregate energy performance. • Obvious sectoral heterogeneities are identified in evaluating China's energy performance.
Field study of macrodispersion in a heterogeneous aquifer. I
International Nuclear Information System (INIS)
Boggs, J.M.; Young, S.C.; Waldrop, W.R.; Gelhar, L.W.; Adams, E.E.; Rehfeldt, K.R.
1990-01-01
A large-scale natural gradient tracer experiment has been conducted at a field site located at Columbus Air Force Base in northeastern Mississippi. The alluvial aquifer at the test site is composed of lenticular deposits of sand, gravel, silt and clay, and is quite heterogeneous with respect to its hydraulic properties. Ten cubic meters of a solution containing bromide and three organic tracers (pentafluorobenzoic acid, o-trifluoromethylbenzoic acid, and 2,6-difluorobenzoic acid) were injected into the aquifer at a uniform rate over a period of two days. The tracer plume was subsequently monitored in three dimensions over a 20-month period using a network of 258 multilevel sampling wells. The tracer concentration distribution of the plume at the conclusion of the experiment was highly asymmetric in the longitudinal direction. The peak tracer concentration was located only 7 m from the injection point, while the advancing side of the plume extended downgradient a distance of more than 260 m. The extreme skewness of the plume was caused by large scale spatial variations in the mean groundwater velocity along the plume travel path produced by the approximate two order-of-magnitude increase in the mean hydraulic conductivity between the near-field and far-field regions of the experimental site. The tracer mass balance during the experiment showed a declining trend between sampling events with approximately 50 percent of the injected tracer mass unaccounted for at the end of the experiment. Laboratory column experiments indicated that approximately 20 percent of the tracer mass was adsorbed to the aquifer matrix. The remaining 30 percent of the missing tracer mass was attributed to incomplete sampling coverage of the plume, particularly on the advancing side, and to a sampling bias produced by the multilevel samplers. (Author) (17 refs., 3 tabs., 11 figs.)
Field study of macrodispersion in a heterogeneous aquifer. 2
International Nuclear Information System (INIS)
Boggs, J.M.; Rehfeldt, K.R.
1990-01-01
Observations of the spatial variability of the hydraulic conductivity field at the site of a large-scale natural gradient tracer experiment located at Columbus Air Force Base in Mississippi are presented. Direct measurements of hydraulic conductivity of the heterogeneous alluvial aquifer at the site were made using a variety of methods including aquifer tests, borehole flowmeter logging, double-packer tests, slug tests, and a newly developed laboratory permeameter to test undisturbed soil cores. The borehole flowmeter method was shown to be the most effective method for measuring conductivity variability. Estimates of the log hydraulic conductivity variance (σ 2 lnL ) and the horizontal and vertical correlation sales, (λ h and λ v ) of 4.5, 12 m, and 1.5 m, respectively, were calculated assuming second order stationarity of the conductivity field. Large-scale spatial variations in the mean groundwater velocity indicated by the natural gradient tracer experiment, which were shown to be a direct result of contrasts in the mean hydraulic conductivity along the plume pathway, strongly suggested the presence of a conductivity trend. The measured hydraulic conductivity data were subsequently detrended using least-squares regression to remove three-dimensional polynomials. The third-order polynomial was judged the best representation of the conductivity drift based on its overall compatibility with the groundwater flow field inferred from the tracer plume observations. Significantly lower estimates for σ 2 lnK , λ h , and λ v of 2.8, 5.3 m, and 0.7 m, respectively, were obtained from the third-order log conductivity residuals. The experience with the borehole flowmeter technique shows the feasibility of observing the statistical parameters of the hydraulic conductivity variability required for stochastic models of macrodispersion. (Author) (20 refs., 3 figs., 10 tabs.)
Mean-field magnetohydrodynamics and dynamo theory
Krause, F
2013-01-01
Mean-Field Magnetohydrodynamics and Dynamo Theory provides a systematic introduction to mean-field magnetohydrodynamics and the dynamo theory, along with the results achieved. Topics covered include turbulence and large-scale structures; general properties of the turbulent electromotive force; homogeneity, isotropy, and mirror symmetry of turbulent fields; and turbulent electromotive force in the case of non-vanishing mean flow. The turbulent electromotive force in the case of rotational mean motion is also considered. This book is comprised of 17 chapters and opens with an overview of the gen
International Nuclear Information System (INIS)
Kundin, Julia; Pogorelov, Evgeny; Emmerich, Heike
2015-01-01
We have investigated the microstructure evolution during the isothermal and non-isothermal solidification of ternary Al–Cu–Ni alloys by means of a general multi-phase-field model for an arbitrary number of phases. The stability requirements for the model functions on every dual interface guarantee the absence of “ghost” phases. The aim was to generate a realistic microstructure by coupling the thermodynamic parameters of the phases and the thermodynamically consistent phase-field evolution equations. It is shown that the specially constructed thermal noise terms disturb the stability on the dual interfaces and can produce heterogeneous nucleation of product phases at energetically favorable points. Similar behavior can be observed in triple junctions where the heterogeneous nucleation of a fourth phase is more favorable. Finally, the model predicts the growth of a combined eutectic-like and peritectic-like structure that is comparable to the observed experimental microstructure in various alloys
Continuous Time Finite State Mean Field Games
International Nuclear Information System (INIS)
Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigão
2013-01-01
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games
Continuous Time Finite State Mean Field Games
Energy Technology Data Exchange (ETDEWEB)
Gomes, Diogo A., E-mail: dgomes@math.ist.utl.pt [Instituto Superior Tecnico, Center for Mathematical Analysis, Geometry, and Dynamical Systems, Departamento de Matematica (Portugal); Mohr, Joana, E-mail: joana.mohr@ufrgs.br; Souza, Rafael Rigao, E-mail: rafars@mat.ufrgs.br [UFRGS, Instituto de Matematica (Brazil)
2013-08-01
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N{yields}{infinity} of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games.
Heterogeneous network architectures
DEFF Research Database (Denmark)
Christiansen, Henrik Lehrmann
2006-01-01
is flexibility. This thesis investigates such heterogeneous network architectures and how to make them flexible. A survey of algorithms for network design is presented, and it is described how using heuristics can increase the speed. A hierarchical, MPLS based network architecture is described......Future networks will be heterogeneous! Due to the sheer size of networks (e.g., the Internet) upgrades cannot be instantaneous and thus heterogeneity appears. This means that instead of trying to find the olution, networks hould be designed as being heterogeneous. One of the key equirements here...... and it is discussed that it is advantageous to heterogeneous networks and illustrated by a number of examples. Modeling and simulation is a well-known way of doing performance evaluation. An approach to event-driven simulation of communication networks is presented and mixed complexity modeling, which can simplify...
Continuous time finite state mean field games
Gomes, Diogo A.; Mohr, Joana; Souza, Rafael Rigã o
2013-01-01
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.
Continuous time finite state mean field games
Gomes, Diogo A.
2013-04-23
In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary differential equations with initial-terminal data. For this mean field problem we prove a trend to equilibrium theorem, that is convergence, in an appropriate limit, to stationary solutions. Then we study an N+1-player problem, which the mean field model attempts to approximate. Our main result is the convergence as N→∞ of the mean field model and an estimate of the rate of convergence. We end the paper with some further examples for potential mean field games. © 2013 Springer Science+Business Media New York.
Nonequilibrium dynamical mean-field theory
Energy Technology Data Exchange (ETDEWEB)
Eckstein, Martin
2009-12-21
The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)
Nonequilibrium dynamical mean-field theory
International Nuclear Information System (INIS)
Eckstein, Martin
2009-01-01
The aim of this thesis is the investigation of strongly interacting quantum many-particle systems in nonequilibrium by means of the dynamical mean-field theory (DMFT). An efficient numerical implementation of the nonequilibrium DMFT equations within the Keldysh formalism is provided, as well a discussion of several approaches to solve effective single-site problem to which lattice models such as the Hubbard-model are mapped within DMFT. DMFT is then used to study the relaxation of the thermodynamic state after a sudden increase of the interaction parameter in two different models: the Hubbard model and the Falicov-Kimball model. In the latter case an exact solution can be given, which shows that the state does not even thermalize after infinite waiting times. For a slow change of the interaction, a transition to adiabatic behavior is found. The Hubbard model, on the other hand, shows a very sensitive dependence of the relaxation on the interaction, which may be called a dynamical phase transition. Rapid thermalization only occurs at the interaction parameter which corresponds to this transition. (orig.)
Mean field interaction in biochemical reaction networks
Tembine, Hamidou; Tempone, Raul; Vilanova, Pedro
2011-01-01
In this paper we establish a relationship between chemical dynamics and mean field game dynamics. We show that chemical reaction networks can be studied using noisy mean field limits. We provide deterministic, noisy and switching mean field limits
Flexible Grouping as a Means for Classroom Management in a Heterogeneous Classroom
Rytivaara, Anna
2011-01-01
This article concerns issues of classroom management in heterogeneous classrooms. Although research in the field of learning styles has yielded mixed results, there is a call for information about how they could be used to individualize instruction, especially in primary schools. This article is part of an ethnographic study aiming to examine…
Modeling energy fluxes in heterogeneous landscapes employing a mosaic approach
Klein, Christian; Thieme, Christoph; Priesack, Eckart
2015-04-01
Recent studies show that uncertainties in regional and global climate and weather simulations are partly due to inadequate descriptions of the energy flux exchanges between the land surface and the atmosphere. One major shortcoming is the limitation of the grid-cell resolution, which is recommended to be about at least 3x3 km² in most models due to limitations in the model physics. To represent each individual grid cell most models select one dominant soil type and one dominant land use type. This resolution, however, is often too coarse in regions where the spatial diversity of soil and land use types are high, e.g. in Central Europe. An elegant method to avoid the shortcoming of grid cell resolution is the so called mosaic approach. This approach is part of the recently developed ecosystem model framework Expert-N 5.0. The aim of this study was to analyze the impact of the characteristics of two managed fields, planted with winter wheat and potato, on the near surface soil moistures and on the near surface energy flux exchanges of the soil-plant-atmosphere interface. The simulated energy fluxes were compared with eddy flux tower measurements between the respective fields at the research farm Scheyern, North-West of Munich, Germany. To perform these simulations, we coupled the ecosystem model Expert-N 5.0 to an analytical footprint model. The coupled model system has the ability to calculate the mixing ratio of the surface energy fluxes at a given point within one grid cell (in this case at the flux tower between the two fields). This approach accounts for the differences of the two soil types, of land use managements, and of canopy properties due to footprint size dynamics. Our preliminary simulation results show that a mosaic approach can improve modeling and analyzing energy fluxes when the land surface is heterogeneous. In this case our applied method is a promising approach to extend weather and climate models on the regional and on the global scale.
Mean Field Games Models-A Brief Survey
Gomes, Diogo A.
2013-11-20
The mean-field framework was developed to study systems with an infinite number of rational agents in competition, which arise naturally in many applications. The systematic study of these problems was started, in the mathematical community by Lasry and Lions, and independently around the same time in the engineering community by P. Caines, Minyi Huang, and Roland Malhamé. Since these seminal contributions, the research in mean-field games has grown exponentially, and in this paper we present a brief survey of mean-field models as well as recent results and techniques. In the first part of this paper, we study reduced mean-field games, that is, mean-field games, which are written as a system of a Hamilton-Jacobi equation and a transport or Fokker-Planck equation. We start by the derivation of the models and by describing some of the existence results available in the literature. Then we discuss the uniqueness of a solution and propose a definition of relaxed solution for mean-field games that allows to establish uniqueness under minimal regularity hypothesis. A special class of mean-field games that we discuss in some detail is equivalent to the Euler-Lagrange equation of suitable functionals. We present in detail various additional examples, including extensions to population dynamics models. This section ends with a brief overview of the random variables point of view as well as some applications to extended mean-field games models. These extended models arise in problems where the costs incurred by the agents depend not only on the distribution of the other agents, but also on their actions. The second part of the paper concerns mean-field games in master form. These mean-field games can be modeled as a partial differential equation in an infinite dimensional space. We discuss both deterministic models as well as problems where the agents are correlated. We end the paper with a mean-field model for price impact. © 2013 Springer Science+Business Media New York.
Mean Field Games Models-A Brief Survey
Gomes, Diogo A.; Saú de, Joã o
2013-01-01
The mean-field framework was developed to study systems with an infinite number of rational agents in competition, which arise naturally in many applications. The systematic study of these problems was started, in the mathematical community by Lasry and Lions, and independently around the same time in the engineering community by P. Caines, Minyi Huang, and Roland Malhamé. Since these seminal contributions, the research in mean-field games has grown exponentially, and in this paper we present a brief survey of mean-field models as well as recent results and techniques. In the first part of this paper, we study reduced mean-field games, that is, mean-field games, which are written as a system of a Hamilton-Jacobi equation and a transport or Fokker-Planck equation. We start by the derivation of the models and by describing some of the existence results available in the literature. Then we discuss the uniqueness of a solution and propose a definition of relaxed solution for mean-field games that allows to establish uniqueness under minimal regularity hypothesis. A special class of mean-field games that we discuss in some detail is equivalent to the Euler-Lagrange equation of suitable functionals. We present in detail various additional examples, including extensions to population dynamics models. This section ends with a brief overview of the random variables point of view as well as some applications to extended mean-field games models. These extended models arise in problems where the costs incurred by the agents depend not only on the distribution of the other agents, but also on their actions. The second part of the paper concerns mean-field games in master form. These mean-field games can be modeled as a partial differential equation in an infinite dimensional space. We discuss both deterministic models as well as problems where the agents are correlated. We end the paper with a mean-field model for price impact. © 2013 Springer Science+Business Media New York.
Mean-field theory and solitonic matter
International Nuclear Information System (INIS)
Cohen, T.D.
1989-01-01
Finite density solitonic matter is considered in the context of quantum field theory. Mean-field theory, which provides a reasonable description for single-soliton properties gives rise to a crystalline description. A heuristic description of solitonic matter is given which shows that the low-density limit of solitonic matter (the limit which is presumably relevant for nuclear matter) does not commute with the mean-field theory limit and gives rise to a Fermi-gas description of the system. It is shown on the basis of a formal expansion of simple soliton models in terms of the coupling constant why one expects mean-field theory to fail at low densities and why the corrections to mean-field theory are nonperturbative. This heuristic description is tested against an exactly solvable 1+1 dimensional model (the sine-Gordon model) and found to give the correct behavior. The relevance of these results to the program of doing nuclear physics based on soliton models is discussed. (orig.)
Alagar, Ananda Giri Babu; Mani, Ganesh Kadirampatti; Karunakaran, Kaviarasu
2016-01-08
Small fields smaller than 4 × 4 cm2 are used in stereotactic and conformal treatments where heterogeneity is normally present. Since dose calculation accuracy in both small fields and heterogeneity often involves more discrepancy, algorithms used by treatment planning systems (TPS) should be evaluated for achieving better treatment results. This report aims at evaluating accuracy of four model-based algorithms, X-ray Voxel Monte Carlo (XVMC) from Monaco, Superposition (SP) from CMS-Xio, AcurosXB (AXB) and analytical anisotropic algorithm (AAA) from Eclipse are tested against the measurement. Measurements are done using Exradin W1 plastic scintillator in Solid Water phantom with heterogeneities like air, lung, bone, and aluminum, irradiated with 6 and 15 MV photons of square field size ranging from 1 to 4 cm2. Each heterogeneity is introduced individually at two different depths from depth-of-dose maximum (Dmax), one setup being nearer and another farther from the Dmax. The central axis percentage depth-dose (CADD) curve for each setup is measured separately and compared with the TPS algorithm calculated for the same setup. The percentage normalized root mean squared deviation (%NRMSD) is calculated, which represents the whole CADD curve's deviation against the measured. It is found that for air and lung heterogeneity, for both 6 and 15 MV, all algorithms show maximum deviation for field size 1 × 1 cm2 and gradually reduce when field size increases, except for AAA. For aluminum and bone, all algorithms' deviations are less for 15 MV irrespective of setup. In all heterogeneity setups, 1 × 1 cm2 field showed maximum deviation, except in 6MV bone setup. All algorithms in the study, irrespective of energy and field size, when any heterogeneity is nearer to Dmax, the dose deviation is higher compared to the same heterogeneity far from the Dmax. Also, all algorithms show maximum deviation in lower-density materials compared to high-density materials.
XML-based approaches for the integration of heterogeneous bio-molecular data.
Mesiti, Marco; Jiménez-Ruiz, Ernesto; Sanz, Ismael; Berlanga-Llavori, Rafael; Perlasca, Paolo; Valentini, Giorgio; Manset, David
2009-10-15
The today's public database infrastructure spans a very large collection of heterogeneous biological data, opening new opportunities for molecular biology, bio-medical and bioinformatics research, but raising also new problems for their integration and computational processing. In this paper we survey the most interesting and novel approaches for the representation, integration and management of different kinds of biological data by exploiting XML and the related recommendations and approaches. Moreover, we present new and interesting cutting edge approaches for the appropriate management of heterogeneous biological data represented through XML. XML has succeeded in the integration of heterogeneous biomolecular information, and has established itself as the syntactic glue for biological data sources. Nevertheless, a large variety of XML-based data formats have been proposed, thus resulting in a difficult effective integration of bioinformatics data schemes. The adoption of a few semantic-rich standard formats is urgent to achieve a seamless integration of the current biological resources.
Mean field interaction in biochemical reaction networks
Tembine, Hamidou
2011-09-01
In this paper we establish a relationship between chemical dynamics and mean field game dynamics. We show that chemical reaction networks can be studied using noisy mean field limits. We provide deterministic, noisy and switching mean field limits and illustrate them with numerical examples. © 2011 IEEE.
Field heritability of a plant adaptation to fire in heterogeneous landscapes.
Castellanos, M C; González-Martínez, S C; Pausas, J G
2015-11-01
The strong association observed between fire regimes and variation in plant adaptations to fire suggests a rapid response to fire as an agent of selection. It also suggests that fire-related traits are heritable, a precondition for evolutionary change. One example is serotiny, the accumulation of seeds in unopened fruits or cones until the next fire, an important strategy for plant population persistence in fire-prone ecosystems. Here, we evaluate the potential of this trait to respond to natural selection in its natural setting. For this, we use a SNP marker approach to estimate genetic variance and heritability of serotiny directly in the field for two Mediterranean pine species. Study populations were large and heterogeneous in climatic conditions and fire regime. We first estimated the realized relatedness among trees from genotypes, and then partitioned the phenotypic variance in serotiny using Bayesian animal models that incorporated environmental predictors. As expected, field heritability was smaller (around 0.10 for both species) than previous estimates under common garden conditions (0.20). An estimate on a subset of stands with more homogeneous environmental conditions was not different from that in the complete set of stands, suggesting that our models correctly captured the environmental variation at the spatial scale of the study. Our results highlight the importance of measuring quantitative genetic parameters in natural populations, where environmental heterogeneity is a critical aspect. The heritability of serotiny, although not high, combined with high phenotypic variance within populations, confirms the potential of this fire-related trait for evolutionary change in the wild. © 2015 John Wiley & Sons Ltd.
Mean-field potential approach for thermodynamic properties of lanthanide: Europium as a prototype
Kumar, Priyank; Bhatt, N. K.; Vyas, P. R.; Gohel, V. B.
2018-03-01
In the present paper, a simple conjunction scheme [mean-field potential (MFP) + local pseudopotential] is used to study the thermodynamic properties of divalent lanthanide europium (Eu) at extreme environment. Present study has been carried out due to the fact that divalent nature of Eu arises because of stable half-filled 4f-shell at ambient condition, which has great influence on the thermodynamic properties at extreme environment. Due to such electronic structure, it is different from remaining lanthanides having incomplete 4f-shell. The presently computed results of thermodynamic properties of Eu are in good agreement with the experimental results. Looking to such success, it seems that the concept of MFP approach is successful to account contribution due to nuclear motion to the total Helmholtz free energy at finite temperatures and pressure-induced inter-band transfer of electrons for condensed state of matter. The local pseudopotential is used to evaluate cold energy and hence MFP accounts the s-p-d-f hybridization properly. Looking to the reliability and transferability along with its computational and conceptual simplicity, we would like to extend the present scheme for the study of thermodynamic properties of remaining lanthanides and actinides at extreme environment.
International Nuclear Information System (INIS)
Bellonzi, Nicole; Jain, Amber; Subotnik, Joseph E.
2016-01-01
We study several recent mean-field semiclassical dynamics methods, focusing on the ability to recover detailed balance for long time (equilibrium) populations. We focus especially on Miller and Cotton’s [J. Phys. Chem. A 117, 7190 (2013)] suggestion to include both zero point electronic energy and windowing on top of Ehrenfest dynamics. We investigate three regimes: harmonic surfaces with weak electronic coupling, harmonic surfaces with strong electronic coupling, and anharmonic surfaces with weak electronic coupling. In most cases, recent additions to Ehrenfest dynamics are a strong improvement upon mean-field theory. However, for methods that include zero point electronic energy, we show that anharmonic potential energy surfaces often lead to numerical instabilities, as caused by negative populations and forces. We also show that, though the effect of negative forces can appear hidden in harmonic systems, the resulting equilibrium limits do remain dependent on any windowing and zero point energy parameters.
Ontology-based knowledge representation for resolution of semantic heterogeneity in GIS
Liu, Ying; Xiao, Han; Wang, Limin; Han, Jialing
2017-07-01
Lack of semantic interoperability in geographical information systems has been identified as the main obstacle for data sharing and database integration. The new method should be found to overcome the problems of semantic heterogeneity. Ontologies are considered to be one approach to support geographic information sharing. This paper presents an ontology-driven integration approach to help in detecting and possibly resolving semantic conflicts. Its originality is that each data source participating in the integration process contains an ontology that defines the meaning of its own data. This approach ensures the automation of the integration through regulation of semantic integration algorithm. Finally, land classification in field GIS is described as the example.
Noisy mean field game model for malware propagation in opportunistic networks
Tembine, Hamidou; Vilanova, Pedro; Debbah, Mé roú ane
2012-01-01
nodes is examined with a noisy mean field limit and compared to a deterministic one. The stochastic nature of the wireless environment make stochastic approaches more realistic for such types of networks. By introducing control strategies, we show
Effect of Electromagnetic Fields on Transfer Processes in Heterogeneous Systems
Czech Academy of Sciences Publication Activity Database
Levdansky, V.V.; Kim, H. Y.; Kim, H. C.; Smolík, Jiří; Moravec, Pavel
2001-01-01
Roč. 44, č. 5 (2001), s. 1065-1071 ISSN 0017-9310 Institutional research plan: CEZ:AV0Z4072921 Keywords : electromagnetic field * transfer processes * heterogeneous system Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.240, year: 2001
The surface compression of nuclei in relativistic mean-field approach
International Nuclear Information System (INIS)
Sharma, M.M.
1991-01-01
The surface compression properties of nuclei have been studied in the framework of the relativistic non-linear σ-ω model. Using the Thomas-Fermi approximation for semi-infinite nuclear matter, it is shown that by varying the σ-meson mass one can change the surface compression as relative to the bulk compression. This fact is in contrast with the known properties of the phenomenological Skyrme interactions, where the ratio of the surface to the bulk incompressibility (-K S /K V ) is nearly 1 in the scaling mode of compression. The results suggest that the relativistic mean-field model may provide an interaction with the essential ingredients different from those of the Skyrme interactions. (author) 23 refs., 2 figs., 1 tab
Capturing heterogeneity: The role of a study area's extent for estimating mean throughfall
Zimmermann, Alexander; Voss, Sebastian; Metzger, Johanna Clara; Hildebrandt, Anke; Zimmermann, Beate
2016-11-01
The selection of an appropriate spatial extent of a sampling plot is one among several important decisions involved in planning a throughfall sampling scheme. In fact, the choice of the extent may determine whether or not a study can adequately characterize the hydrological fluxes of the studied ecosystem. Previous attempts to optimize throughfall sampling schemes focused on the selection of an appropriate sample size, support, and sampling design, while comparatively little attention has been given to the role of the extent. In this contribution, we investigated the influence of the extent on the representativeness of mean throughfall estimates for three forest ecosystems of varying stand structure. Our study is based on virtual sampling of simulated throughfall fields. We derived these fields from throughfall data sampled in a simply structured forest (young tropical forest) and two heterogeneous forests (old tropical forest, unmanaged mixed European beech forest). We then sampled the simulated throughfall fields with three common extents and various sample sizes for a range of events and for accumulated data. Our findings suggest that the size of the study area should be carefully adapted to the complexity of the system under study and to the required temporal resolution of the throughfall data (i.e. event-based versus accumulated). Generally, event-based sampling in complex structured forests (conditions that favor comparatively long autocorrelations in throughfall) requires the largest extents. For event-based sampling, the choice of an appropriate extent can be as important as using an adequate sample size.
The mean field theory in EM procedures for blind Markov random field image restoration.
Zhang, J
1993-01-01
A Markov random field (MRF) model-based EM (expectation-maximization) procedure for simultaneously estimating the degradation model and restoring the image is described. The MRF is a coupled one which provides continuity (inside regions of smooth gray tones) and discontinuity (at region boundaries) constraints for the restoration problem which is, in general, ill posed. The computational difficulty associated with the EM procedure for MRFs is resolved by using the mean field theory from statistical mechanics. An orthonormal blur decomposition is used to reduce the chances of undesirable locally optimal estimates. Experimental results on synthetic and real-world images show that this approach provides good blur estimates and restored images. The restored images are comparable to those obtained by a Wiener filter in mean-square error, but are most visually pleasing.
Why Panel Tests of Purchasing Power Parity Should Allow for Heterogeneous Mean Reversion
C.G. Koedijk (Kees); B. Tims (Ben); M.A. van Dijk (Mathijs)
2010-01-01
textabstractAbstract Recent studies of purchasing power parity (PPP) use panel tests that fail to take into account heterogeneity in the speed of mean reversion across real exchange rates. In contrast to several other severe restrictions of panel models and tests of PPP, the assumption of
International Nuclear Information System (INIS)
Suyama, Yasuhiro; Toida, Masaru; Yanagizawa, Koichi
2009-01-01
The geological environment has spatially heterogeneous characteristics with varied host rock types, fractures and so on. In this case the generic disposal tunnel layout, which has been designed by JNC, is not the most suitable for HLW disposal in Japan. The existence of spatially heterogeneous characteristics means that in the repository region there exist sub-regions that are more favourable from the perspective of long-term safety and ones that are less favourable. In order that the spatially heterogeneous environment itself may be utilized most effectively as a natural barrier system, an alternative design of disposal tunnel layout is required. Focusing on the geological environment with spatially heterogeneous characteristics, the authors have developed an alternative design of disposal tunnel layout. The alternative design adopts an optimization approach using a variable disposal tunnel layout. The optimization approach minimizes the number of locations where major water-conducting fractures are intersected, and maximizes the number of emplacement locations for waste packages. This paper will outline the variable disposal tunnel layout and its applicability.
How heterogeneous susceptibility and recovery rates affect the spread of epidemics on networks
Directory of Open Access Journals (Sweden)
Wei Gou
2017-08-01
Full Text Available In this paper, an extended heterogeneous SIR model is proposed, which generalizes the heterogeneous mean-field theory. Different from the traditional heterogeneous mean-field model only taking into account the heterogeneity of degree, our model considers not only the heterogeneity of degree but also the heterogeneity of susceptibility and recovery rates. Then, we analytically study the basic reproductive number and the final epidemic size. Combining with numerical simulations, it is found that the basic reproductive number depends on the mean of distributions of susceptibility and disease course when both of them are independent. If the mean of these two distributions is identical, increasing the variance of susceptibility may block the spread of epidemics, while the corresponding increase in the variance of disease course has little effect on the final epidemic size. It is also shown that positive correlations between individual susceptibility, course of disease and the square of degree make the population more vulnerable to epidemic and avail to the epidemic prevalence, whereas the negative correlations make the population less vulnerable and impede the epidemic prevalence. Keywords: Networks, Heterogeneity, Susceptibility, Recovery rates, Correlation, The basic reproductive number, The final epidemic size
About soil cover heterogeneity of agricultural research stations' experimental fields
Rannik, Kaire; Kõlli, Raimo; Kukk, Liia
2013-04-01
Depending on local pedo-ecological conditions (topography, (geo) diversity of soil parent material, meteorological conditions) the patterns of soil cover and plant cover determined by soils are very diverse. Formed in the course of soil-plant mutual relationship, the natural ecosystems are always influenced to certain extent by the other local soil forming conditions or they are site specific. The agricultural land use or the formation of agro-ecosystems depends foremost on the suitability of soils for the cultivation of feed and food crops. As a rule, the most fertile or the best soils of the area, which do not present any or present as little as possible constraints for agricultural land use, are selected for this purpose. Compared with conventional field soils, the requirements for the experimental fields' soil cover quality are much higher. Experimental area soils and soil cover composition should correspond to local pedo-ecological conditions and, in addition to that, represent the soil types dominating in the region, whereas the fields should be as homogeneous as possible. The soil cover heterogeneity of seven arable land blocks of three research stations (Jõgeva, Kuusiku and Olustvere) was studied 1) by examining the large scale (1:10 000) digital soil map (available via the internet), and 2) by field researches using the transect method. The stages of soils litho-genetic and moisture heterogeneities were estimated by using the Estonian normal soils matrix, however, the heterogeneity of top- and subsoil texture by using the soil texture matrix. The quality and variability of experimental fields' soils humus status, was studied more thoroughly from the aspect of humus concentration (g kg-1), humus cover thickness (cm) and humus stocks (Mg ha-1). The soil cover of Jõgeva experimental area, which presents an accumulative drumlin landscape (formed during the last glacial period), consist from loamy Luvisols and associated to this Cambisols. In Kuusiku area
Dynamical Mean Field Approximation Applied to Quantum Field Theory
Akerlund, Oscar; Georges, Antoine; Werner, Philipp
2013-12-04
We apply the Dynamical Mean Field (DMFT) approximation to the real, scalar phi^4 quantum field theory. By comparing to lattice Monte Carlo calculations, perturbation theory and standard mean field theory, we test the quality of the approximation in two, three, four and five dimensions. The quantities considered in these tests are the critical coupling for the transition to the ordered phase and the associated critical exponents nu and beta. We also map out the phase diagram in four dimensions. In two and three dimensions, DMFT incorrectly predicts a first order phase transition for all bare quartic couplings, which is problematic, because the second order nature of the phase transition of lattice phi^4-theory is crucial for taking the continuum limit. Nevertheless, by extrapolating the behaviour away from the phase transition, one can obtain critical couplings and critical exponents. They differ from those of mean field theory and are much closer to the correct values. In four dimensions the transition is sec...
Fan, Weihua; Hancock, Gregory R.
2012-01-01
This study proposes robust means modeling (RMM) approaches for hypothesis testing of mean differences for between-subjects designs in order to control the biasing effects of nonnormality and variance inequality. Drawing from structural equation modeling (SEM), the RMM approaches make no assumption of variance homogeneity and employ robust…
Mean-field dynamics of a population of stochastic map neurons
Franović, Igor; Maslennikov, Oleg V.; Bačić, Iva; Nekorkin, Vladimir I.
2017-07-01
We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis. It is demonstrated that the mean-field model can qualitatively account for stability and bifurcations of the exact system, capturing all the generic forms of collective behavior, including macroscopic excitability, subthreshold oscillations, periodic or chaotic spiking, and chaotic bursting dynamics. Apart from qualitative analogies, we find a substantial quantitative agreement between the exact and the approximate system, as reflected in matching of the parameter domains admitting the different dynamical regimes, as well as the characteristic properties of the associated time series. The effective model is further shown to reproduce with sufficient accuracy the phase response curves of the exact system and the assembly's response to external stimulation of finite amplitude and duration.
Mean-field models and exotic nuclei
Energy Technology Data Exchange (ETDEWEB)
Bender, M; Buervenich, T; Maruhn, J A; Greiner, W [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany); Rutz, K [Inst. fuer Theoretische Physik, Univ. Frankfurt (Germany); [Gesellschaft fuer Schwerionenforschung mbH, Darmstadt (Germany); Reinhard, P G [Inst. fuer Theoretische Physik, Univ. Erlangen (Germany)
1998-06-01
We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei. Test cases are superheavy nuclei and neutron-rich Sn isotopes. New information in this regime helps to fix hitherto loosely determined aspects of the models. (orig.)
Mean-field models and exotic nuclei
International Nuclear Information System (INIS)
Bender, M.; Buervenich, T.; Maruhn, J.A.; Greiner, W.; Rutz, K.; Reinhard, P.G.
1998-01-01
We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei. Test cases are superheavy nuclei and neutron-rich Sn isotopes. New information in this regime helps to fix hitherto loosely determined aspects of the models. (orig.)
Study of two-proton radioactivity within the relativistic mean-field plus BCS approach
International Nuclear Information System (INIS)
Singh, D.; Saxena, G.
2012-01-01
Inspired by recent experimental studies of two-proton radioactivity in the light-medium mass region, we have employed relativistic mean-field plus state-dependent BCS approach (RMF+BCS) to study the ground state properties of selected even-Z nuclei in the region 20 ≤ Z ≤ 40. It is found that the effective potential barrier provided by the Coulomb interaction and that due to centrifugal force may cause a long delay in the decay of some of the nuclei even with small negative proton separation energy. This may cause the existence of proton-rich nuclei beyond the proton drip-line. Nuclei 38 Ti, 42 Cr, 45 Fe, 48 Ni, 55 Zn, 60 Ge, 63, 64 Se, 68 Kr, 72 Sr and 76 Zr are found to be the potential candidates for exhibiting two-proton radioactivity in the region 20 ≤ Z ≤ 40. The reliability of these predictions is further strengthened by the agreement of the calculated results for the ground state properties such as binding energy, one- and two-proton separation energy, proton and neutron radii, and deformation with the available experimental data for the entire chain of the isotopes of the nuclei in the region 20 ≤ Z ≤ 40. (author)
Influence of Magnetic Field on the Rectification Process of Binary Heterogeneous Azeotrope
Institute of Scientific and Technical Information of China (English)
JIA Shaoyi; WU Songhai; LI Zhen; JIA Liang
2005-01-01
To improve separate effect of binary heterogeneous azeotrope in the magnetic field with different magnetic induction intensity, the influence of magnetic field on the rectification process of binary heterogeneous azeotrope was investigated with 1-butanol-water system. The results show that the composition of liquid-liquid phase equilibrium of 1-butanol-water system has definitely changed, the composition of 1-butanol in light phase (1-butanol layer) increases by 1.17%-1.63% and the composition of water in heavy phase (water layer) increases by 1.21%-1.58% under the influence of magnetic field. By separation of magnetization, the composition of 1-butanol increases by 0.8%-1.2% and the recovery ratio of 1-butanol increases by 1.6%-2.5%. Magnetic field has positive effect, however, the magnetized effect is not in proportion to magnetic induction intensity and has an optimum condition, in the range of 0.25 T-0.3 T.
Field verification of advanced transport models of radionuclides in heterogeneous soils
International Nuclear Information System (INIS)
Visser, W.; Meurs, G.A.M.; Weststrate, F.A.
1991-01-01
This report deals with a verification study of advanced transport models of radionuclides in heterogeneous soils. The study reported here is the third phase of a research program carried out by Delft Geotechnics concerning the influence of soil heterogeneities on the migration of radionuclides in the soil and soil-water system. Phases 1 and 2 have been reported earlier in the EC Nuclear Science and technology series (EUR 12111 EN, 1989). The verification study involves the predictive modelling of a field tracer experiment carried out by the British Geological Survey (BGS) at Drigg, Cumbria (UK). Conservative (I 131 , Cl-, H 3 ) as well as non-conservative (Co-EDTA) tracers were used. The inverse modelling shows that micro dispersion may be considered as a soil constant related to grainsize. Micro dispersion shows a slow increase with distance from the source. This increase is caused by mass transfer between adjacent layers of different permeability. Macro dispersion is observed when sampling over a larger interval then permitted by the detail with which the heterogeneity is described in the model. The prediction of the migration of radionuclides through heterogeneous soils is possible. The advection dispersion equation seems to be an adequate description of the migration of conservative tracers. The models based on this equation give comparable results on a small field test scale (3.5 m). The prediction of the migration of adsorbing species is more difficult. The mathematical descriptions seem appropriate, but the heterogeneity in soils seems to create a higher order of uncertainty which can not be described as yet with calculation strategies available at this moment
Directory of Open Access Journals (Sweden)
Saeed Balouchi
2013-01-01
Full Text Available Fractured reservoirs contain about 85 and 90 percent of oil and gas resources respectively in Iran. A comprehensive study and investigation of fractures as the main factor affecting fluid flow or perhaps barrier seems necessary for reservoir development studies. High degrees of heterogeneity and sparseness of data have incapacitated conventional deterministic methods in fracture network modeling. Recently, simulated annealing (SA has been applied to generate stochastic realizations of spatially correlated fracture networks by assuming that the elastic energy of fractures follows Boltzmann distribution. Although SA honors local variability, the objective function of geometrical fracture modeling is defined for homogeneous conditions. In this study, after the introduction of SA and the derivation of the energy function, a novel technique is presented to adjust the model with highly heterogeneous data for a fractured field from the southwest of Iran. To this end, the regular object-based model is combined with a grid-based technique to cover the heterogeneity of reservoir properties. The original SA algorithm is also modified by being constrained in different directions and weighting the energy function to make it appropriate for heterogeneous conditions. The simulation results of the presented approach are in good agreement with the observed field data.
International Nuclear Information System (INIS)
McCallum, R. William
2005-01-01
For a uniaxial nanocrystalline magnetic material, the determination of the saturation magnetization, M s , requires measurements of the magnetization at fields which exceed the anisotropy field. For a typical RE-Tm compound, where RE=rare earth and Tm=transition metal, this may require fields above 7 T if the approach to saturation law is used. However for an isotropic material composed of a random distribution of non-interacting uniaxial grains, both M s and the anisotropy filed, H a , may be determined by fitting the Stoner-Wohlfarth (SW) model (Philos. Trans. Roy. Soc. 240 (1948) 599) to the reversible part of the demagnetization curve in the first quadrant. Furthermore, using the mean field interaction model of Callen, Liu and Cullen [2], a quantitative measure of the interaction strength for interacting particles may be determined. In conjunction with an analytical fit to the first quadrant demagnetization curve of the SW model, this allows M s , H a and the mean field interaction constant of a nanocrystalline magnet to be determined from measurements below 5 T. Furthermore, comparison of the model solution for the reversible magnetization with experimental data in the 2nd and 3rd quadrants allows the accurate determination of the switching field distribution. In many cases the hysteresis loop may be accurately described by a normal distribution of switching fields
Liu, Gaisheng; Lu, Zhiming; Zhang, Dongxiao
2007-01-01
A new approach has been developed for solving solute transport problems in randomly heterogeneous media using the Karhunen‐Loève‐based moment equation (KLME) technique proposed by Zhang and Lu (2004). The KLME approach combines the Karhunen‐Loève decomposition of the underlying random conductivity field and the perturbative and polynomial expansions of dependent variables including the hydraulic head, flow velocity, dispersion coefficient, and solute concentration. The equations obtained in this approach are sequential, and their structure is formulated in the same form as the original governing equations such that any existing simulator, such as Modular Three‐Dimensional Multispecies Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems (MT3DMS), can be directly applied as the solver. Through a series of two‐dimensional examples, the validity of the KLME approach is evaluated against the classical Monte Carlo simulations. Results indicate that under the flow and transport conditions examined in this work, the KLME approach provides an accurate representation of the mean concentration. For the concentration variance, the accuracy of the KLME approach is good when the conductivity variance is 0.5. As the conductivity variance increases up to 1.0, the mismatch on the concentration variance becomes large, although the mean concentration can still be accurately reproduced by the KLME approach. Our results also indicate that when the conductivity variance is relatively large, neglecting the effects of the cross terms between velocity fluctuations and local dispersivities, as done in some previous studies, can produce noticeable errors, and a rigorous treatment of the dispersion terms becomes more appropriate.
DEFF Research Database (Denmark)
Opper, Manfred; Winther, Ole
2001-01-01
We develop an advanced mean held method for approximating averages in probabilistic data models that is based on the Thouless-Anderson-Palmer (TAP) approach of disorder physics. In contrast to conventional TAP. where the knowledge of the distribution of couplings between the random variables...... is required. our method adapts to the concrete couplings. We demonstrate the validity of our approach, which is so far restricted to models with nonglassy behavior? by replica calculations for a wide class of models as well as by simulations for a real data set....
Nonasymptotic mean-field games
Tembine, Hamidou
2014-01-01
a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through various examples including dynamic auction with asymmetric
Heterogeneous grain-scale response in ferroic polycrystals under electric field
DEFF Research Database (Denmark)
Daniels, John E.; Majkut, Marta; Cao, Qingua
2016-01-01
-ray diffraction (3D-XRD) is used to resolve the non-180° ferroelectric domain switching strain components of 191 grains from the bulk of a polycrystalline electro-ceramic that has undergone an electric-field-induced phase transformation. It is found that while the orientation of a given grain relative...... to the field direction has a significant influence on the phase and resultant domain texture, there are large deviations from the average behaviour at the grain scale. It is suggested that these deviations arise from local strain and electric field neighbourhoods being highly heterogeneous within the bulk...
Directory of Open Access Journals (Sweden)
Mauro Regi
2017-01-01
Full Text Available The magnetic field satellite data are usually referred to geocentric coordinate reference frame. Conversely, the magnetohydrodynamic waves modes in magnetized plasma depend on the ambient magnetic field, and is then useful to rotate the magnetic field measurements into the mean field aligned (MFA coordinate system. This reference frame is useful to study the ultra low frequency magnetic field variations along the direction of the mean field and perpendicularly to it. In order to identify the mean magnetic field the classical moving average (MAVG approach is usually adopted but, under particular conditions, this procedure induces undesired features, such as spectral alteration in the rotated components. We discuss these aspects promoting an alternative and more efficient method for mean field aligned projection, based on the empirical mode decomposition (EMD.
Mean-field theory of nuclear structure and dynamics
International Nuclear Information System (INIS)
Negele, J.W.
1982-01-01
The physical and theoretical foundations are presented for the mean-field theory of nuclear structure and dynamics. Salient features of the many-body theory of stationary states are reviewed to motivate the time-dependent mean-field approximation. The time-dependent Hartree-Fock approximation and its limitations are discussed and general theoretical formulations are presented which yield time-dependent mean-field equations in lowest approximation and provide suitable frameworks for overcoming various conceptual and practical limitations of the mean-field theory. Particular emphasis is placed on recent developments utilizing functional integral techniques to obtain a quantum mean-field theory applicable to quantized eigenstates, spontaneous fission, the nuclear partition function, and scattering problems. Applications to a number of simple, idealized systems are presented to verify the approximations for solvable problems and to elucidate the essential features of mean-field dynamics. Finally, calculations utilizing moderately realistic geometries and interactions are reviewed which address heavy-ion collisions, fusion, strongly damped collisions, and fission
Mean field limit for bosons with compact kernels interactions by Wigner measures transportation
International Nuclear Information System (INIS)
Liard, Quentin; Pawilowski, Boris
2014-01-01
We consider a class of many-body Hamiltonians composed of a free (kinetic) part and a multi-particle (potential) interaction with a compactness assumption on the latter part. We investigate the mean field limit of such quantum systems following the Wigner measures approach. We prove in particular the propagation of these measures along the flow of a nonlinear (Hartree) field equation. This enhances and complements some previous results of the same type shown in Z. Ammari and F. Nier and Fröhlich et al. [“Mean field limit for bosons and propagation of Wigner measures,” J. Math. Phys. 50(4), 042107 (2009); Z. Ammari and F. Nier and Fröhlich et al., “Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states,” J. Math. Pures Appl. 95(6), 585–626 (2011); Z. Ammari and F. Nier and Fröhlich et al., “Mean-field- and classical limit of many-body Schrödinger dynamics for bosons,” Commun. Math. Phys. 271(3), 681–697 (2007)
Nonasymptotic mean-field games
Tembine, Hamidou
2014-01-01
propose a mean-field framework that is suitable not only for large systems but also for a small world with few number of entities. The applicability of the proposed framework is illustrated through a dynamic auction with asymmetric valuation distributions.
Khlyupin, Aleksey; Aslyamov, Timur
2017-06-01
Realistic fluid-solid interaction potentials are essential in description of confined fluids especially in the case of geometric heterogeneous surfaces. Correlated random field is considered as a model of random surface with high geometric roughness. We provide the general theory of effective coarse-grained fluid-solid potential by proper averaging of the free energy of fluid molecules which interact with the solid media. This procedure is largely based on the theory of random processes. We apply first passage time probability problem and assume the local Markov properties of random surfaces. General expression of effective fluid-solid potential is obtained. In the case of small surface irregularities analytical approximation for effective potential is proposed. Both amorphous materials with large surface roughness and crystalline solids with several types of fcc lattices are considered. It is shown that the wider the lattice spacing in terms of molecular diameter of the fluid, the more obtained potentials differ from classical ones. A comparison with published Monte-Carlo simulations was discussed. The work provides a promising approach to explore how the random geometric heterogeneity affects on thermodynamic properties of the fluids.
Energy Technology Data Exchange (ETDEWEB)
Graber, P. Jameson, E-mail: jameson-graber@baylor.edu [Baylor University, Department of Mathematics (United States)
2016-12-15
We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources.
Surface incompressibility from semiclassical relativistic mean field calculations
International Nuclear Information System (INIS)
Patra, S.K.; Centelles, M.; Vinas, X.; Estal, M. del
2002-01-01
By using the scaling method and the Thomas-Fermi and extended Thomas-Fermi approaches to relativistic mean field theory the surface contribution to the leptodermous expansion of the finite nuclei incompressibility K A has been self-consistently computed. The validity of the simplest expansion, which contains volume, volume-symmetry, surface, and Coulomb terms, is examined by comparing it with self-consistent results of K A for some currently used nonlinear σ-ω parameter sets. A numerical estimate of higher-order contributions to the leptodermous expansion, namely, the curvature and surface-symmetry terms, is made
Mean fields and self consistent normal ordering of lattice spin and gauge field theories
International Nuclear Information System (INIS)
Ruehl, W.
1986-01-01
Classical Heisenberg spin models on lattices possess mean field theories that are well defined real field theories on finite lattices. These mean field theories can be self consistently normal ordered. This leads to a considerable improvement over standard mean field theory. This concept is carried over to lattice gauge theories. We construct first an appropriate real mean field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean field theory are derived. (orig.)
International Nuclear Information System (INIS)
Tsang, Chin-Fu.
1989-02-01
Many current development and utilization of groundwater resources include a study of their flow and transport properties. These properties are needed in evaluating possible changes in groundwater quality and potential transport of hazardous solutes through the groundwater system. Investigation of transport properties of fractured rocks is an active area of research. Most of the current approaches to the study of flow and transport in fractured rocks cannot be easily used for analysis of tracer transport field data. A new approach is proposed based on a detailed study of transport through a fracture of variable aperture. This is a two-dimensional strongly heterogeneous permeable system. It is suggested that tracer breakthrough curves can be analyzed based on an aperture or permeability probability distribution function that characterizes the tracer flow through the fracture. The results are extended to a multi-fracture system and can be equally applied to a strongly heterogeneous porous medium. Finally, the need for multi-point or line and areal tracer injection and observation tests is indicated as a way to avoid the sensitive dependence of point measurements on local permeability variability. 30 refs., 15 figs
Self-diffusion measurements in heterogeneous systems using NMR pulsed field gradient technique
International Nuclear Information System (INIS)
Heink, W.; Kaerger, J.; Walter, A.
1978-01-01
The experimental pecularities of the NMR pulsed field gradient technique are critical surveyed in its application to zeolite adsorbate adsorbent systems. After a presentation of the different transport parameters accessible by this technique, the consequences of the existence of inner field gradients being inherent to heterogeneous systems are analyzed. Experimental conditions and consequences of an application of pulsed field gradients of high intensity which are necessary for the measurement of small intracrystalline self-diffusion coefficients, are discussed. Gradient pulses of 0.15 Tcm -1 with pulse widths of 2 ms maximum and relative deviations of less than 0.01 per mille can be realized. Since for a number of adsorbate adsorbent systems a distinct dependence of the intracrystalline self-diffusion coeffcients on adsorbate concentration is observed, determination of zeolite pore fiiling factor is of considerable importance for the interpretation of the diffusivities obtained. It is demonstrated that also this information can be obtained by NMR technique in a straightforward way with a mean error of less than 5 to 10 %. Applying this new method and using an optimum experimental device as described, pore filling factor dependences of the self-diffusion coefficients of alkanes in NaX zeolites can be followed over more than two orders of magnitude. (author)
Obstacle mean-field game problem
Gomes, Diogo A.; Patrizi, Stefania
2015-01-01
In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations. Finally, we prove uniqueness of solutions. © European Mathematical Society 2015.
Coagulation kinetics beyond mean field theory using an optimised Poisson representation
Energy Technology Data Exchange (ETDEWEB)
Burnett, James [Department of Mathematics, UCL, Gower Street, London WC1E 6BT (United Kingdom); Ford, Ian J. [Department of Physics and Astronomy, UCL, Gower Street, London WC1E 6BT (United Kingdom)
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.
Bent dark soliton dynamics in two spatial dimensions beyond the mean field approximation
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''.
Retardation and dispersive effects in the nuclear mean field
International Nuclear Information System (INIS)
Mahaux, C.; Davies, K.T.R.; Satchler, G.R.
1993-01-01
We consider several parametrizations of the energy dependence of the imaginary part of the mean field, for nucleons as well as heavy ions. These parametrizations specify the energy dependence of the corresponding real part, because the real and imaginary parts are connected by a dispersion relation. The latter can be viewed as equivalent to the causality property. Since Hilbert transforms appear in the dispersion relation and since Fourier transforms give the correspondence between energy dependence and temporal nonlocality, we derive several properties of these transforms which are of particular interest in the present context. The most useful one is that the Fourier transform of a function F(E) which is analytic in the upper half of the complex E-plane can be expressed in terms of the Fourier transform of the imaginary part of F(E) alone. We investigate several schematic models for the mean field. They fall into two main categories. These correspond to the two main definitions which have been proposed for the mean field, namely the self-energy and Feshbach's potential. Both of these definitions can be used for the nucleon-nucleus system, in which case they correspond to two different ways of handling the combined influence of ground state correlations and antisymmetrization. The resulting two mean fields have different energy dependences and, correspondingly, temporal nonlocalities. Feshbach's approach can also be applied to the nucleus-nucleus system. Our schematic models are semi-realistic, in the sense that they all take account of the 'Fermi surface anomaly' for the nucleon-nucleus system or of the 'threshold anomaly' for the nucleus-nucleus case. The temporal nonlocality is investigated for each model. A physical interpretation of this nonlocality is given in terms delay of the response of the medium, in which an incident wave is partially trapped in nonelastic channels and subsequently reemitted. (orig./HSI)
Soltanian, Mohamad Reza; Ritzi, Robert W; Dai, Zhenxue; Huang, Chao Cheng
2015-03-01
Physical and chemical heterogeneities have a large impact on reactive transport in porous media. Examples of heterogeneous attributes affecting reactive mass transport are the hydraulic conductivity (K), and the equilibrium sorption distribution coefficient (Kd). This paper uses the Deng et al. (2013) conceptual model for multimodal reactive mineral facies and a Lagrangian-based stochastic theory in order to analyze the reactive solute dispersion in three-dimensional anisotropic heterogeneous porous media with hierarchical organization of reactive minerals. An example based on real field data is used to illustrate the time evolution trends of reactive solute dispersion. The results show that the correlation between the hydraulic conductivity and the equilibrium sorption distribution coefficient does have a significant effect on reactive solute dispersion. The anisotropy ratio does not have a significant effect on reactive solute dispersion. Furthermore, through a sensitivity analysis we investigate the impact of changing the mean, variance, and integral scale of K and Kd on reactive solute dispersion. Copyright © 2014 Elsevier Ltd. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Kretz, V.
2002-11-01
The prediction of oil recovery or pollutant dispersion requires an accurate knowledge of the permeability field distribution. Available data are usually measurements in well bores, and, since a few years, 4D-seismic data (seismic mappings repeated in time). Such measurements allow to evaluate fluids displacements fronts evolution. The purpose of the thesis is to evaluate the possibility to determinate permeability fields from fluid displacement measurements in heterogeneous porous media. At the laboratory scale, experimental studies are made on a model and on numerical simulations. The system uses blocks of granular materials whose individual geometries and permeabilities are controlled. The fluids displacements are detected with an acoustical. The key parameters of the study are the size and spatial correlation of the permeability heterogeneity distribution, and the influence of viscosity and gravity contrasts between the injected ant displaced fluid. Then the inverse problem - evaluating the permeability field from concentration fronts evolution - is approached. At the reservoir scale, the work will mainly be focused on the integration of 4D-seismic data into inversion programs on a 3D synthetic case. A particular importance will be given to the calculation of gradients, in order to obtain a complementary information about the sensitivity of data. The information provided by 4D-seismic data consists in maps showing the vertical average of oil saturation or the presence of gas. The purpose is to integrate this qualitative information in the inversion process and to evaluate the impact on the reservoir characterization. Comparative studies - with or without 4D-seismic data - will be realized on a synthetic case. (author)
Quark number density and susceptibility calculation with one correction in mean field potential
International Nuclear Information System (INIS)
Singh, S. Somorendro
2016-01-01
We calculate quark number density and susceptibility of a model which has one loop correction in mean field potential. The calculation shows continuous increasing in the number density and susceptibility up to the temperature T = 0.4 GeV. Then the value of number density and susceptibility approach to the lattice result for higher value of temperature. The result indicates that the calculated values of the model fit well and the result increase the temperature to reach the lattice data with the one loop correction in the mean field potential. (author)
A model-based approach to studying changes in compositional heterogeneity
Baeten, L.; Warton, D.; Calster, van H.; Frenne, De P.; Verstraeten, G.; Bonte, D.; Bernhardt-Romermann, M.; Cornelis, R.; Decocq, G.; Eriksson, O.; Hommel, P.W.F.M.
2014-01-01
1. Non-random species loss and gain in local communities change the compositional heterogeneity between communities over time, which is traditionally quantified with dissimilarity-based approaches. Yet, dissimilarities summarize the multivariate species data into a univariate index and obscure the
Upscaling of permeability heterogeneities in reservoir rocks; an integrated approach
Mikes, D.
2002-01-01
This thesis presents a hierarchical and geologically constrained deterministic approach to incorporate small-scale heterogeneities into reservoir flow simulators. We use a hierarchical structure to encompass all scales from laminae to an entire depositional system. For the geological models under
A self-consistent mean-field approach to the dynamical symmetry breaking
International Nuclear Information System (INIS)
Kunihiro, Teiji; Hatsuda, Tetsuo.
1984-01-01
The dynamical symmetry breaking phenomena in the Nambu and Jona-Lasimio model are reexamined in the framework of a self-consistent mean-field (SCMF) theory. First, we formulate the SCMF theory in a lucid manner based on a successful decomposition of the Lagrangian into semiclassical and residual interaction parts by imposing a condition that ''the dangerous term'' in Bogoliubov's sense should vanish. Then, we show that the difference of the energy density between the super and normal phases, the correct expression of which the original authors failed to give, can be readily obtained by applying the SCMF theory. Futhermore, it is shown that the expression thus obtained is identical to that of the effective potential (E.P.) given by the path-integral method with an auxiliary field up to the one loop order in the loop expansion, then one finds a new and simple way to get the E.P. Some numerical results of the E.P. and the dynamically generated mass of fermion are also shown. As another demonstration of the powerfulness of the SCMF theory, we derive, in the Appendix, the energy density of the O(N)-phi 4 model including the higher order corrections in the sense of large N expansion. (author)
An open, object-based modeling approach for simulating subsurface heterogeneity
Bennett, J.; Ross, M.; Haslauer, C. P.; Cirpka, O. A.
2017-12-01
Characterization of subsurface heterogeneity with respect to hydraulic and geochemical properties is critical in hydrogeology as their spatial distribution controls groundwater flow and solute transport. Many approaches of characterizing subsurface heterogeneity do not account for well-established geological concepts about the deposition of the aquifer materials; those that do (i.e. process-based methods) often require forcing parameters that are difficult to derive from site observations. We have developed a new method for simulating subsurface heterogeneity that honors concepts of sequence stratigraphy, resolves fine-scale heterogeneity and anisotropy of distributed parameters, and resembles observed sedimentary deposits. The method implements a multi-scale hierarchical facies modeling framework based on architectural element analysis, with larger features composed of smaller sub-units. The Hydrogeological Virtual Reality simulator (HYVR) simulates distributed parameter models using an object-based approach. Input parameters are derived from observations of stratigraphic morphology in sequence type-sections. Simulation outputs can be used for generic simulations of groundwater flow and solute transport, and for the generation of three-dimensional training images needed in applications of multiple-point geostatistics. The HYVR algorithm is flexible and easy to customize. The algorithm was written in the open-source programming language Python, and is intended to form a code base for hydrogeological researchers, as well as a platform that can be further developed to suit investigators' individual needs. This presentation will encompass the conceptual background and computational methods of the HYVR algorithm, the derivation of input parameters from site characterization, and the results of groundwater flow and solute transport simulations in different depositional settings.
Naturalness of Nonlinear Scalar Self-Couplings in a Relativistic Mean Field Theory for Neutron Stars
International Nuclear Information System (INIS)
Maekawa, Claudio; Razeira, Moises; Vasconcellos, Cesar A. Z.; Dillig, Manfred; Bodmann, Bardo E. J.
2004-01-01
We investigate the role of naturalness in effective field theory. We focus on dense hadronic matter using a generalized relativistic multi-baryon lagrangian density mean field approach which contains nonlinear self-couplings of the σ, δ meson fields and the fundamental baryon octet. We adjust the model parameters to describe bulk static properties of ordinary nuclear matter. Then, we show that our approach represents a natural modelling of nuclear matter under the extreme conditions of density as the ones found in the interior of neutron stars
Energy Technology Data Exchange (ETDEWEB)
Haertle, Rainer [Institut fuer Theoretische Physik, Georg-August-Universitaet Goettingen, Goettingen (Germany); Millis, Andrew J. [Department of Physics, Columbia University, New York (United States)
2016-07-01
We present a new impurity solver for real-time and nonequilibrium dynamical mean field theory applications, based on the recently developed hierarchical quantum master equation approach. Our method employs a hybridization expansion of the time evolution operator, including an advanced, systematic truncation scheme. Convergence to exact results for not too low temperatures has been demonstrated by a direct comparison to quantum Monte Carlo simulations. The approach is time-local, which gives us access to slow dynamics such as, e.g., in the presence of magnetic fields or exchange interactions and to nonequilibrium steady states. Here, we present first results of this new scheme for the description of strongly correlated materials in the framework of dynamical mean field theory, including benchmark and new results for the Hubbard and periodic Anderson model.
DEFF Research Database (Denmark)
List, Nanna Holmgaard; Jensen, Hans Jørgen Aagaard; Kongsted, Jacob
2016-01-01
chemical reference calculations. For the lowest π → π∗ transition in DsRed, inclusion of effective external field effects gives rise to a 1.9- and 3.5-fold reduction in the 1PA and 2PA cross-sections, respectively. The effective external field is, however, strongly influenced by the heterogeneity...... (1PA and 2PA, respectively) properties of PRODAN-methanol clusters as well as the fluorescent protein DsRed. Our results demonstrate the necessity of accounting for both the dynamical reaction field and effective external field contributions to the local field in order to reproduce full quantum...
Characterizing hydrogeologic heterogeneity using lithologic data
International Nuclear Information System (INIS)
Flach, G.P.; Hamm, L.L.; Harris, M.K.; Thayer, P.A.; Haselow, J.S.; Smits, A.D.
1995-01-01
Large-scale (> 1 m) variability in hydraulic conductivity is usually the main influence on field-scale groundwater flow patterns and dispersive transport. Sediment lithologic descriptions and geophysical logs typically offer finer spatial resolution, and therefore more potential information about site-scale heterogeneity, than other site characterization data. In this study, a technique for generating a heterogeneous, three-dimensional hydraulic conductivity field from sediment lithologic descriptions is presented. The approach involves creating a three-dimensional, fine-scale representation of mud (silt + clay) percentage using a stratified interpolation algorithm. Mud percentage is then translated into horizontal and vertical conductivity using direct correlations derived from measured data and inverse groundwater flow modeling. Lastly, the fine-scale conductivity fields are averaged to create a coarser grid for use in groundwater flow and transport modeling. The approach is demonstrated using a finite-element groundwater flow model of a Savannah River Site solid radioactive and hazardous waste burial ground. Hydrostratigraphic units in the area consist of fluvial, deltaic, and shallow marine sand, mud and calcareous sediment that exhibit abrupt facies changes over short distances
Pineda, M.; Stamatakis, M.
2017-07-01
Modeling the kinetics of surface catalyzed reactions is essential for the design of reactors and chemical processes. The majority of microkinetic models employ mean-field approximations, which lead to an approximate description of catalytic kinetics by assuming spatially uncorrelated adsorbates. On the other hand, kinetic Monte Carlo (KMC) methods provide a discrete-space continuous-time stochastic formulation that enables an accurate treatment of spatial correlations in the adlayer, but at a significant computation cost. In this work, we use the so-called cluster mean-field approach to develop higher order approximations that systematically increase the accuracy of kinetic models by treating spatial correlations at a progressively higher level of detail. We further demonstrate our approach on a reduced model for NO oxidation incorporating first nearest-neighbor lateral interactions and construct a sequence of approximations of increasingly higher accuracy, which we compare with KMC and mean-field. The latter is found to perform rather poorly, overestimating the turnover frequency by several orders of magnitude for this system. On the other hand, our approximations, while more computationally intense than the traditional mean-field treatment, still achieve tremendous computational savings compared to KMC simulations, thereby opening the way for employing them in multiscale modeling frameworks.
On the design of innovative heterogeneous tests using a shape optimization approach
Aquino, J.; Campos, A. Andrade; Souto, N.; Thuillier, S.
2018-05-01
The development of full-field measurement methods enabled a new trend of mechanical tests. By providing the inhomogeneous strain field from the tests, these techniques are being widely used in sheet metal identification strategies, through heterogeneous mechanical tests. In this work, a heterogeneous mechanical test with an innovative tool/specimen shape, capable of producing rich heterogeneous strain paths providing extensive information on material behavior, is aimed. The specimen is found using a shape optimization process where a dedicated indicator that evaluates the richness of strain information is used. The methodology and results here presented are extended to non-specimen geometry dependence and to the non-dependence of the geometry parametrization through the use of the Ritz method for boundary value problems. Different curve models, such as Splines, B-Splines and NURBS, are used and C1 continuity throughout the specimen is guaranteed. Moreover, various optimization methods are used, deterministic and stochastic, in order to find the method or a combination of methods able to effectively minimize the cost function.
Quantum noise in the mirror–field system: A field theoretic approach
International Nuclear Information System (INIS)
Hsiang, Jen-Tsung; Wu, Tai-Hung; Lee, Da-Shin; King, Sun-Kun; Wu, Chun-Hsien
2013-01-01
We revisit the quantum noise problem in the mirror–field system by a field-theoretic approach. Here a perfectly reflecting mirror is illuminated by a single-mode coherent state of the massless scalar field. The associated radiation pressure is described by a surface integral of the stress-tensor of the field. The read-out field is measured by a monopole detector, from which the effective distance between the detector and mirror can be obtained. In the slow-motion limit of the mirror, this field-theoretic approach allows to identify various sources of quantum noise that all in all leads to uncertainty of the read-out measurement. In addition to well-known sources from shot noise and radiation pressure fluctuations, a new source of noise is found from field fluctuations modified by the mirror’s displacement. Correlation between different sources of noise can be established in the read-out measurement as the consequence of interference between the incident field and the field reflected off the mirror. In the case of negative correlation, we found that the uncertainty can be lowered than the value predicted by the standard quantum limit. Since the particle-number approach is often used in quantum optics, we compared results obtained by both approaches and examine its validity. We also derive a Langevin equation that describes the stochastic dynamics of the mirror. The underlying fluctuation–dissipation relation is briefly mentioned. Finally we discuss the backreaction induced by the radiation pressure. It will alter the mean displacement of the mirror, but we argue this backreaction can be ignored for a slowly moving mirror. - Highlights: ► The quantum noise problem in the mirror–field system is re-visited by a field-theoretic approach. ► Other than the shot noise and radiation pressure noise, we show there are new sources of noise and correlation between them. ► The noise correlations can be used to suppress the overall quantum noise on the mirror.
Quantum noise in the mirror-field system: A field theoretic approach
Energy Technology Data Exchange (ETDEWEB)
Hsiang, Jen-Tsung, E-mail: cosmology@gmail.com [Department of Physics, National Dong-Hwa University, Hua-lien, Taiwan, ROC (China); Wu, Tai-Hung [Department of Physics, National Dong-Hwa University, Hua-lien, Taiwan, ROC (China); Lee, Da-Shin, E-mail: dslee@mail.ndhu.edu.tw [Department of Physics, National Dong-Hwa University, Hua-lien, Taiwan, ROC (China); King, Sun-Kun [Institutes of Astronomy and Astrophysics, Academia Sinica, Taipei, Taiwan, ROC (China); Wu, Chun-Hsien [Department of Physics, Soochow University, Taipei, Taiwan, ROC (China)
2013-02-15
We revisit the quantum noise problem in the mirror-field system by a field-theoretic approach. Here a perfectly reflecting mirror is illuminated by a single-mode coherent state of the massless scalar field. The associated radiation pressure is described by a surface integral of the stress-tensor of the field. The read-out field is measured by a monopole detector, from which the effective distance between the detector and mirror can be obtained. In the slow-motion limit of the mirror, this field-theoretic approach allows to identify various sources of quantum noise that all in all leads to uncertainty of the read-out measurement. In addition to well-known sources from shot noise and radiation pressure fluctuations, a new source of noise is found from field fluctuations modified by the mirror's displacement. Correlation between different sources of noise can be established in the read-out measurement as the consequence of interference between the incident field and the field reflected off the mirror. In the case of negative correlation, we found that the uncertainty can be lowered than the value predicted by the standard quantum limit. Since the particle-number approach is often used in quantum optics, we compared results obtained by both approaches and examine its validity. We also derive a Langevin equation that describes the stochastic dynamics of the mirror. The underlying fluctuation-dissipation relation is briefly mentioned. Finally we discuss the backreaction induced by the radiation pressure. It will alter the mean displacement of the mirror, but we argue this backreaction can be ignored for a slowly moving mirror. - Highlights: Black-Right-Pointing-Pointer The quantum noise problem in the mirror-field system is re-visited by a field-theoretic approach. Black-Right-Pointing-Pointer Other than the shot noise and radiation pressure noise, we show there are new sources of noise and correlation between them. Black-Right-Pointing-Pointer The noise
Two Populations Mean-Field Monomer-Dimer Model
Alberici, Diego; Mingione, Emanuele
2018-04-01
A two populations mean-field monomer-dimer model including both hard-core and attractive interactions between dimers is considered. The pressure density in the thermodynamic limit is proved to satisfy a variational principle. A detailed analysis is made in the limit of one population is much smaller than the other and a ferromagnetic mean-field phase transition is found.
Zhang, Hua; Harter, Thomas; Sivakumar, Bellie
2006-06-01
Facies-based geostatistical models have become important tools for analyzing flow and mass transport processes in heterogeneous aquifers. Yet little is known about the relationship between these latter processes and the parameters of facies-based geostatistical models. In this study, we examine the transport of a nonpoint source solute normal (perpendicular) to the major bedding plane of an alluvial aquifer medium that contains multiple geologic facies, including interconnected, high-conductivity (coarse textured) facies. We also evaluate the dependence of the transport behavior on the parameters of the constitutive facies model. A facies-based Markov chain geostatistical model is used to quantify the spatial variability of the aquifer system's hydrostratigraphy. It is integrated with a groundwater flow model and a random walk particle transport model to estimate the solute traveltime probability density function (pdf) for solute flux from the water table to the bottom boundary (the production horizon) of the aquifer. The cases examined include two-, three-, and four-facies models, with mean length anisotropy ratios for horizontal to vertical facies, ek, from 25:1 to 300:1 and with a wide range of facies volume proportions (e.g., from 5 to 95% coarse-textured facies). Predictions of traveltime pdfs are found to be significantly affected by the number of hydrostratigraphic facies identified in the aquifer. Those predictions of traveltime pdfs also are affected by the proportions of coarse-textured sediments, the mean length of the facies (particularly the ratio of length to thickness of coarse materials), and, to a lesser degree, the juxtapositional preference among the hydrostratigraphic facies. In transport normal to the sedimentary bedding plane, traveltime is not lognormally distributed as is often assumed. Also, macrodispersive behavior (variance of the traveltime) is found not to be a unique function of the conductivity variance. For the parameter range
Mean field games with nonlinear mobilities in pedestrian dynamics
Burger, Martin; Di Francesco, Marco; Markowich, Peter A.; Wolfram, Marie Therese
2014-01-01
In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to the Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.
Mean field games with nonlinear mobilities in pedestrian dynamics
Burger, Martin
2014-04-01
In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to the Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.
A Bayesian mean field game approach to supply demand analysis of the smart grid
Kamgarpour, Maryam
2013-07-01
We explore a game theoretic framework for multiple energy producers competing in energy market. Each producer, referred to as a player, optimizes its own objective function given the demand utility. The equilibrium strategy of each player depends on the production cost, referred to as type, of the other players. We show that as the number of players increases, the mean of the types is sufficient for finding the equilibrium. For finite number of players, we design a mean field distributed learning algorithm that converges to equilibrium. We discuss extensions of our model to include several realistic aspects of the energy market. © 2013 IEEE.
Regularity theory for mean-field game systems
Gomes, Diogo A; Voskanyan, Vardan
2016-01-01
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Regularity Theory for Mean-Field Game Systems
Gomes, Diogo A.
2016-09-14
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Regularity Theory for Mean-Field Game Systems
Gomes, Diogo A.; Pimentel, Edgard A.; Voskanyan, Vardan K.
2016-01-01
Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.
Quark self-energy beyond the mean field at finite temperature
International Nuclear Information System (INIS)
Zhuang, P.
1995-01-01
The Nambu--Jona-Lasinio model, an effective low-energy model of QCD, is extended to the next to the leading order in the 1/N c expansion at finite temperature and density. The contributions to the quark self-energy and the constituent quark mass from the meson dressing are considered in a perturbative approach about the mean field. In particular, the temperature dependence of the quark mass is shown numerically at zero chemical potential. The correction to the quark mass from the meson dressing amounts to 20% compared to the result of the leading order at low temperature, and rapidly approaches zero at high temperature
Band mixing effects in mean field theories
International Nuclear Information System (INIS)
Kuyucak, S.; Morrison, I.
1989-01-01
The 1/N expansion method, which is an angular momentum projected mean field theory, is used to investigate the nature of electromagnetic transitions in the interacting boson model (IBM). Conversely, comparison with the exact IBM results sheds light on the range of validity of the mean field theory. It is shown that the projected mean field results for the E2 transitions among the ground, β and γ bands are incomplete for the spin dependent terms and it is essential to include band mixing effect for a correct (Mikhailov) analysis of E2 data. The algebraic expressions derived are general and will be useful in the analysis of experimental data in terms of both the sd and sdg boson models. 17 refs., 7 figs., 8 tabs
Constitutive modeling of two phase materials using the Mean Field method for homogenization
Perdahcioglu, Emin Semih; Geijselaers, Hubertus J.M.
2010-01-01
A Mean-Field homogenization framework for constitutive modeling of materials involving two distinct elastic-plastic phases is presented. With this approach it is possible to compute the macroscopic mechanical behavior of this type of materials based on the constitutive models of the constituent
Directory of Open Access Journals (Sweden)
Akanda Md. Abdus Salam
2017-03-01
Full Text Available Individual heterogeneity in capture probabilities and time dependence are fundamentally important for estimating the closed animal population parameters in capture-recapture studies. A generalized estimating equations (GEE approach accounts for linear correlation among capture-recapture occasions, and individual heterogeneity in capture probabilities in a closed population capture-recapture individual heterogeneity and time variation model. The estimated capture probabilities are used to estimate animal population parameters. Two real data sets are used for illustrative purposes. A simulation study is carried out to assess the performance of the GEE estimator. A Quasi-Likelihood Information Criterion (QIC is applied for the selection of the best fitting model. This approach performs well when the estimated population parameters depend on the individual heterogeneity and the nature of linear correlation among capture-recapture occasions.
A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type
Energy Technology Data Exchange (ETDEWEB)
Hosking, John Joseph Absalom, E-mail: j.j.a.hosking@cma.uio.no [University of Oslo, Centre of Mathematics for Applications (CMA) (Norway)
2012-12-15
We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966-979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197-216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.
A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type
International Nuclear Information System (INIS)
Hosking, John Joseph Absalom
2012-01-01
We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966–979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197–216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.
Pape-Haugaard, Louise; Frank, Lars
2011-01-01
A major obstacle in ensuring ubiquitous information is the utilization of heterogeneous systems in eHealth. The objective in this paper is to illustrate how an architecture for distributed eHealth databases can be designed without lacking the characteristic features of traditional sustainable databases. The approach is firstly to explain traditional architecture in central and homogeneous distributed database computing, followed by a possible approach to use an architectural framework to obtain sustainability across disparate systems i.e. heterogeneous databases, concluded with a discussion. It is seen that through a method of using relaxed ACID properties on a service-oriented architecture it is possible to achieve data consistency which is essential when ensuring sustainable interoperability.
Back-reaction beyond the mean field approximation
International Nuclear Information System (INIS)
Kluger, Y.
1993-01-01
A method for solving an initial value problem of a closed system consisting of an electromagnetic mean field and its quantum fluctuations coupled to fermions is presented. By tailoring the large N f expansion method to the Schwinger-Keldysh closed time path (CTP) formulation of the quantum effective action, causality of the resulting equations of motion is ensured, and a systematic energy conserving and gauge invariant expansion about the electromagnetic mean field in powers of 1/N f is developed. The resulting equations may be used to study the quantum nonequilibrium effects of pair creation in strong electric fields and the scattering and transport processes of a relativistic e + e - plasma. Using the Bjorken ansatz of boost invariance initial conditions in which the initial electric mean field depends on the proper time only, we show numerical results for the case in which the N f expansion is truncated in the lowest order, and compare them with those of a phenomenological transport equation
Siebert, Janet C; Munsil, Wes; Rosenberg-Hasson, Yael; Davis, Mark M; Maecker, Holden T
2012-03-28
Systems-level approaches are increasingly common in both murine and human translational studies. These approaches employ multiple high information content assays. As a result, there is a need for tools to integrate heterogeneous types of laboratory and clinical/demographic data, and to allow the exploration of that data by aggregating and/or segregating results based on particular variables (e.g., mean cytokine levels by age and gender). Here we describe the application of standard data warehousing tools to create a novel environment for user-driven upload, integration, and exploration of heterogeneous data. The system presented here currently supports flow cytometry and immunoassays performed in the Stanford Human Immune Monitoring Center, but could be applied more generally. Users upload assay results contained in platform-specific spreadsheets of a defined format, and clinical and demographic data in spreadsheets of flexible format. Users then map sample IDs to connect the assay results with the metadata. An OLAP (on-line analytical processing) data exploration interface allows filtering and display of various dimensions (e.g., Luminex analytes in rows, treatment group in columns, filtered on a particular study). Statistics such as mean, median, and N can be displayed. The views can be expanded or contracted to aggregate or segregate data at various levels. Individual-level data is accessible with a single click. The result is a user-driven system that permits data integration and exploration in a variety of settings. We show how the system can be used to find gender-specific differences in serum cytokine levels, and compare them across experiments and assay types. We have used the tools and techniques of data warehousing, including open-source business intelligence software, to support investigator-driven data integration and mining of diverse immunological data.
Directory of Open Access Journals (Sweden)
Siebert Janet C
2012-03-01
Full Text Available Abstract Background Systems-level approaches are increasingly common in both murine and human translational studies. These approaches employ multiple high information content assays. As a result, there is a need for tools to integrate heterogeneous types of laboratory and clinical/demographic data, and to allow the exploration of that data by aggregating and/or segregating results based on particular variables (e.g., mean cytokine levels by age and gender. Methods Here we describe the application of standard data warehousing tools to create a novel environment for user-driven upload, integration, and exploration of heterogeneous data. The system presented here currently supports flow cytometry and immunoassays performed in the Stanford Human Immune Monitoring Center, but could be applied more generally. Results Users upload assay results contained in platform-specific spreadsheets of a defined format, and clinical and demographic data in spreadsheets of flexible format. Users then map sample IDs to connect the assay results with the metadata. An OLAP (on-line analytical processing data exploration interface allows filtering and display of various dimensions (e.g., Luminex analytes in rows, treatment group in columns, filtered on a particular study. Statistics such as mean, median, and N can be displayed. The views can be expanded or contracted to aggregate or segregate data at various levels. Individual-level data is accessible with a single click. The result is a user-driven system that permits data integration and exploration in a variety of settings. We show how the system can be used to find gender-specific differences in serum cytokine levels, and compare them across experiments and assay types. Conclusions We have used the tools and techniques of data warehousing, including open-source business intelligence software, to support investigator-driven data integration and mining of diverse immunological data.
International Nuclear Information System (INIS)
Mil'shtejn, R.S.
1988-01-01
Analysis of dose fields in a heterogeneous tissue equivalent medium has shown that dose distributions have radial symmetry and can be described by a curve of axial distribution with renormalization of maximum ionization depth. A method of the calculation of a dose field in a heterogeneous medium using the principle of radial symmetry is presented
Ohm's law for mean magnetic fields
International Nuclear Information System (INIS)
Boozer, A.H.
1986-05-01
The magnetic fields associated with plasmas frequently exhibit small amplitude MHD fluctuations. It is useful to have equations for the magnetic field averaged over these fluctuations, the so-called mean field equations. Under very general assumptions it is shown that the effect of MHD fluctuations on a force-free plasma can be represented by one parameter in Ohm's law, which is effectively the coefficient of electric current viscosity
Ohm's law for mean magnetic fields
International Nuclear Information System (INIS)
Boozer, A.H.
1986-01-01
The magnetic fields associated with plasmas frequently exhibit small-amplitude MHD fluctuations. It is useful to have equations for the magnetic field averaged over these fluctuations, the so-called mean field equations. Under very general assumptions, it is shown that the effect of MHD fluctuations on a force-free plasma can be represented by one parameter in Ohm's law, which is effectively the coefficient of electric current viscosity. (author)
Identification of transmissivity fields using a Bayesian strategy and perturbative approach
Zanini, Andrea; Tanda, Maria Giovanna; Woodbury, Allan D.
2017-10-01
The paper deals with the crucial problem of the groundwater parameter estimation that is the basis for efficient modeling and reclamation activities. A hierarchical Bayesian approach is developed: it uses the Akaike's Bayesian Information Criteria in order to estimate the hyperparameters (related to the covariance model chosen) and to quantify the unknown noise variance. The transmissivity identification proceeds in two steps: the first, called empirical Bayesian interpolation, uses Y* (Y = lnT) observations to interpolate Y values on a specified grid; the second, called empirical Bayesian update, improve the previous Y estimate through the addition of hydraulic head observations. The relationship between the head and the lnT has been linearized through a perturbative solution of the flow equation. In order to test the proposed approach, synthetic aquifers from literature have been considered. The aquifers in question contain a variety of boundary conditions (both Dirichelet and Neuman type) and scales of heterogeneities (σY2 = 1.0 and σY2 = 5.3). The estimated transmissivity fields were compared to the true one. The joint use of Y* and head measurements improves the estimation of Y considering both degrees of heterogeneity. Even if the variance of the strong transmissivity field can be considered high for the application of the perturbative approach, the results show the same order of approximation of the non-linear methods proposed in literature. The procedure allows to compute the posterior probability distribution of the target quantities and to quantify the uncertainty in the model prediction. Bayesian updating has advantages related both to the Monte-Carlo (MC) and non-MC approaches. In fact, as the MC methods, Bayesian updating allows computing the direct posterior probability distribution of the target quantities and as non-MC methods it has computational times in the order of seconds.
DEFF Research Database (Denmark)
Ilkhchi, Rahim Kadkhodaie; Rezaee, Reza; Harami, Reza Moussavi
2014-01-01
Tight gas sands in Whicher Range Field of Perth Basin show large heterogeneity in reservoir characteristics and production behavior related to depositional and diagenetic features. Diagenetic events (compaction and cementation) have severely affected the pore system. In order to investigate...... the petrophysical characteristics, reservoir sandstone facies were correlated with core porosity and permeability and their equivalent well log responses to describe hydraulic flow units and electrofacies, respectively. Thus, very tight, tight, and sub-tight sands were differentiated. To reveal the relationship...... between pore system properties and depositional and diagenetic characteristics in each sand type, reservoir rock types were extracted. The identified reservoir rock types are in fact a reflection of internal reservoir heterogeneity related to pore system properties. All reservoir rock types...
QCD Sum Rule External Field Approach and Vacuum Susceptibilities
Institute of Scientific and Technical Information of China (English)
ZONG Hong-Shi; PING Jia-Lun; CHANG Chao-His; WANG Fan; ZHAO En-Guang
2002-01-01
Based on QCD sum rule three-point and two-point external field formulas respectively, the vector vacuumsusceptibilities are calculated at the mean-field level in the framework of the global color symmetry model. It is shownthat the above two approaches of determination of the vector vacuum susceptibility may lead to different results. Thereason of this contradiction is discussed.
Lessons learned from IOR steamflooding in a bitumen-light oil heterogeneous reservoir
Al Mudhafar, W.J.M.; Hosseini Nasab, S.M.
2015-01-01
The Steamflooding was considered in this research to extract the discontinuous bitumen layers that are located at the oil-water contact for the heterogeneous light oil sandstone reservoir of South Rumaila Field. The reservoir heterogeneity and the bitumen layers impede water aquifer approaching into
Identical bands at normal deformation: Necessity of going beyond the mean-field approach
International Nuclear Information System (INIS)
Sun, Y.; Wu, C.; Feng, D.H.; Egido, J.L.; Guidry, M.
1996-01-01
The validity of BCS theory has been questioned because the appearance of normally deformed identical bands in odd and even nuclei seems to contradict the conventional understanding of the blocking effect. This problem is examined with the projected shell model (PSM), which projects good angular momentum states and includes many-body correlations in both deformation and pairing channels. Satisfactory reproduction of identical band data by the PSM suggests that it may be necessary to go beyond the mean field to obtain a quantitative account of identical bands. copyright 1996 The American Physical Society
Mean-field Ensemble Kalman Filter
Law, Kody; Tembine, Hamidou; Tempone, Raul
2015-01-01
A proof of convergence of the standard EnKF generalized to non-Gaussian state space models is provided. A density-based deterministic approximation of the mean-field limiting EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature
Exotic nuclei in self-consistent mean-field models
International Nuclear Information System (INIS)
Bender, M.; Rutz, K.; Buervenich, T.; Reinhard, P.-G.; Maruhn, J. A.; Greiner, W.
1999-01-01
We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei with emphasis on neutron-rich tin isotopes and superheavy nuclei. (c) 1999 American Institute of Physics
International Nuclear Information System (INIS)
Rodrigues, Serafim; Terry, John R.; Breakspear, Michael
2006-01-01
In this Letter, the genesis of spike-wave activity-a hallmark of many generalized epileptic seizures-is investigated in a reduced mean-field model of human neural activity. Drawing upon brain modelling and dynamical systems theory, we demonstrate that the thalamic circuitry of the system is crucial for the generation of these abnormal rhythms, observing that the combination of inhibition from reticular nuclei and excitation from the cortical signal, interplay to generate the spike-wave oscillation. The mechanism revealed provides an explanation of why approaches based on linear stability and Heaviside approximations to the activation function have failed to explain the phenomena of spike-wave behaviour in mean-field models. A mathematical understanding of this transition is a crucial step towards relating spiking network models and mean-field approaches to human brain modelling
Delange, Pascal; Backes, Steffen; van Roekeghem, Ambroise; Pourovskii, Leonid; Jiang, Hong; Biermann, Silke
2018-04-01
The most intriguing properties of emergent materials are typically consequences of highly correlated quantum states of their electronic degrees of freedom. Describing those materials from first principles remains a challenge for modern condensed matter theory. Here, we review, apply and discuss novel approaches to spectral properties of correlated electron materials, assessing current day predictive capabilities of electronic structure calculations. In particular, we focus on the recent Screened Exchange Dynamical Mean-Field Theory scheme and its relation to generalized Kohn-Sham Theory. These concepts are illustrated on the transition metal pnictide BaCo2As2 and elemental zinc and cadmium.
Energy Technology Data Exchange (ETDEWEB)
Kelly, Aaron; Markland, Thomas E., E-mail: tmarkland@stanford.edu [Department of Chemistry, Stanford University, Stanford, California 94305 (United States); Brackbill, Nora [Department of Physics, Stanford University, Stanford, California 94305 (United States)
2015-03-07
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
Kelly, Aaron; Brackbill, Nora; Markland, Thomas E
2015-03-07
In this article, we show how Ehrenfest mean field theory can be made both a more accurate and efficient method to treat nonadiabatic quantum dynamics by combining it with the generalized quantum master equation framework. The resulting mean field generalized quantum master equation (MF-GQME) approach is a non-perturbative and non-Markovian theory to treat open quantum systems without any restrictions on the form of the Hamiltonian that it can be applied to. By studying relaxation dynamics in a wide range of dynamical regimes, typical of charge and energy transfer, we show that MF-GQME provides a much higher accuracy than a direct application of mean field theory. In addition, these increases in accuracy are accompanied by computational speed-ups of between one and two orders of magnitude that become larger as the system becomes more nonadiabatic. This combination of quantum-classical theory and master equation techniques thus makes it possible to obtain the accuracy of much more computationally expensive approaches at a cost lower than even mean field dynamics, providing the ability to treat the quantum dynamics of atomistic condensed phase systems for long times.
Quantum correlated cluster mean-field theory applied to the transverse Ising model.
Zimmer, F M; Schmidt, M; Maziero, Jonas
2016-06-01
Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there has been a surge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.
Uncertainty quantification for mean field games in social interactions
Dia, Ben Mansour
2016-01-09
We present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (marriage). However , if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.
Uncertainty quantification for mean field games in social interactions
Dia, Ben Mansour
2016-01-01
We present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (marriage). However , if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.
International Nuclear Information System (INIS)
Nastar, M.
2008-01-01
When an alloy is irradiated, atomic transport can occur through the two types of defects which are created: vacancies and interstitials. Recent developments of the self-consistent mean field (SCMF) kinetic theory could treat within the same formalism diffusion due to vacancies and interstitials in a multi-component alloy. It starts from a microscopic model of the atomic transport via vacancies and interstitials and yields the fluxes with a complete Onsager matrix of the phenomenological coefficients. The jump frequencies depend on the local environment through a 'broken bond model' such that the large range of frequencies involved in concentrated alloys is produced by a small number of thermodynamic and kinetic parameters. Kinetic correlations are accounted for through a set of time-dependent effective interactions within a non-equilibrium distribution function of the system. The different approximations of the SCMF theory recover most of the previous diffusion models. Recent improvements of the theory were to extend the multi-frequency approach usually restricted to dilute alloys to diffusion in concentrated alloys with jump frequencies depending on local concentrations and to generalize the formalism first developed for the vacancy diffusion mechanism to the more complex diffusion mechanism of the interstitial in the dumbbell configuration. (author)
Finite-State Mean-Field Games, Crowd Motion Problems, and its Numerical Methods
Machado Velho, Roberto
2017-09-10
In this dissertation, we present two research projects, namely finite-state mean-field games and the Hughes model for the motion of crowds. In the first part, we describe finite-state mean-field games and some applications to socio-economic sciences. Examples include paradigm shifts in the scientific community and the consumer choice behavior in a free market. The corresponding finite-state mean-field game models are hyperbolic systems of partial differential equations, for which we propose and validate a new numerical method. Next, we consider the dual formulation to two-state mean-field games, and we discuss numerical methods for these problems. We then depict different computational experiments, exhibiting a variety of behaviors, including shock formation, lack of invertibility, and monotonicity loss. We conclude the first part of this dissertation with an investigation of the shock structure for two-state problems. In the second part, we consider a model for the movement of crowds proposed by R. Hughes in [56] and describe a numerical approach to solve it. This model comprises a Fokker-Planck equation coupled with an Eikonal equation with Dirichlet or Neumann data. We first establish a priori estimates for the solutions. Next, we consider radial solutions, and we identify a shock formation mechanism. Subsequently, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. We also propose a new numerical method for the solution of Fokker-Planck equations and then to systems of PDEs composed by a Fokker-Planck equation and a potential type equation. Finally, we illustrate the use of the numerical method both to the Hughes model and mean-field games. We also depict cases such as the evacuation of a room and the movement of persons around Kaaba (Saudi Arabia).
An ab initio approach to free-energy reconstruction using logarithmic mean force dynamics
International Nuclear Information System (INIS)
Nakamura, Makoto; Obata, Masao; Morishita, Tetsuya; Oda, Tatsuki
2014-01-01
We present an ab initio approach for evaluating a free energy profile along a reaction coordinate by combining logarithmic mean force dynamics (LogMFD) and first-principles molecular dynamics. The mean force, which is the derivative of the free energy with respect to the reaction coordinate, is estimated using density functional theory (DFT) in the present approach, which is expected to provide an accurate free energy profile along the reaction coordinate. We apply this new method, first-principles LogMFD (FP-LogMFD), to a glycine dipeptide molecule and reconstruct one- and two-dimensional free energy profiles in the framework of DFT. The resultant free energy profile is compared with that obtained by the thermodynamic integration method and by the previous LogMFD calculation using an empirical force-field, showing that FP-LogMFD is a promising method to calculate free energy without empirical force-fields
Nurbekyan, Levon
2017-01-01
Here, we study a one-dimensional, non-local mean-field game model with congestion. When the kernel in the non-local coupling is a trigonometric polynomial we reduce the problem to a finite dimensional system. Furthermore, we treat the general case by approximating the kernel with trigonometric polynomials. Our technique is based on Fourier expansion methods.
Nurbekyan, Levon
2017-03-11
Here, we study a one-dimensional, non-local mean-field game model with congestion. When the kernel in the non-local coupling is a trigonometric polynomial we reduce the problem to a finite dimensional system. Furthermore, we treat the general case by approximating the kernel with trigonometric polynomials. Our technique is based on Fourier expansion methods.
Probing water motion in heterogenous systems : a multi-parameter NMR approach
Dusschoten, van D.
1996-01-01
In this Thesis a practical approach is presented to study water mobility in heterogeneous systems by a number of novel NMR sequences. The major part of this Thesis describes how the reliability of diffusion measurements can be improved using some of the novel NMR sequences. The
Derivation of mean-field dynamics for fermions
International Nuclear Information System (INIS)
Petrat, Soeren
2014-01-01
In this work, we derive the time-dependent Hartree(-Fock) equations as an effective dynamics for fermionic many-particle systems. Our main results are the first for a quantum mechanical mean-field dynamics for fermions; in previous works, the mean-field limit is usually either coupled to a semiclassical limit, or the interaction is scaled down so much, that the system behaves freely for large particle number N. We mainly consider systems with total kinetic energy bounded by const.N and long-range interaction potentials, e.g., Coulomb interaction. Examples for such systems are large molecules or certain solid states. Our analysis also applies to attractive interactions, as, e.g., in fermionic stars. The fermionic Hartree(-Fock) equations are a standard tool to describe, e.g., excited states or chemical reactions of large molecules (like proteins). A deeper understanding of these equations as an approximation to the time evolution of a many body quantum system is thus highly relevant. We consider the fermionic Hartree equations (i.e., the Hartree-Fock equations without exchange term) in this work, since the exchange term is subleading in our setting. The main result is that the fermionic Hartree dynamics approximates the Schroedinger dynamics well for large N. This statement becomes exact in the thermodynamic limit N→∞. We give explicit values for the rates of convergence. We prove two types of results. The first type is very general and concerns arbitrary free Hamiltonians (e.g., relativistic, non-relativistic, with external fields) and arbitrary interactions. The theorems give explicit conditions on the solutions to the fermionic Hartree equations under which a derivation of the mean-field dynamics succeeds. The second type of results scrutinizes situations where the conditions are fulfilled. These results are about non-relativistic free Hamiltonians with external fields, systems with total kinetic energy bounded by const.N and with long-range interactions of
International Nuclear Information System (INIS)
Grasso, M.
2009-10-01
This document is a summary of the author's research activities whose common topic is the N-body problem. The first chapter introduces the N-body issue through models based on the mean-field theory and on the Hartree-Fock-Bogoliubov equations. The second chapter presents the understanding of exotic nuclei features within the mean-field approach. Exotic phenomena like nuclear bubble structure, pairing correlations and pairing violations, giant neutron halos, non-standard terms in the Skyrme interactions are reviewed. The chapter 3 is dedicated to some extensions of the RPA (random phase approximation). For instance the computation of the shell structure far from the stability valley requires a more accurate assessment of the energy of the individual states through the introduction of a particle-vibration coupling. Different RPA extensions are described: first the self-consistent extension enlarged beyond particle-hole configurations, then the boson-mapping-based extension in a 3-level Lipkin model and also the second random-phase approximation. The chapter 4 gathers some studies concerning ultra-cold gases of trapped atoms. These systems are the only structures that allow the study of the correlations associated to superfluidity in terms of interaction intensity, temperature or system size. The mean-field approach is adequate for these studies. The last chapter draws a perspective for the mean-field-based models, their limits are assessed and ways of improvement are proposed. (A.C.)
A Simple Approach for Local Contact Angle Determination on a Heterogeneous Surface
Wu, Jinbo; Zhang, Mengying; Wang, Xiang; Li, Shunbo; Wen, Weijia
2011-01-01
We report a simple approach for measuring the local contact angle of liquids on a heterogeneous surface consisting of intersected hydrophobic and hydrophilic patch arrays, specifically by employing confocal microscopy and the addition of a very low
Variance heterogeneity in Saccharomyces cerevisiae expression data: trans-regulation and epistasis.
Nelson, Ronald M; Pettersson, Mats E; Li, Xidan; Carlborg, Örjan
2013-01-01
Here, we describe the results from the first variance heterogeneity Genome Wide Association Study (VGWAS) on yeast expression data. Using this forward genetics approach, we show that the genetic regulation of gene-expression in the budding yeast, Saccharomyces cerevisiae, includes mechanisms that can lead to variance heterogeneity in the expression between genotypes. Additionally, we performed a mean effect association study (GWAS). Comparing the mean and variance heterogeneity analyses, we find that the mean expression level is under genetic regulation from a larger absolute number of loci but that a higher proportion of the variance controlling loci were trans-regulated. Both mean and variance regulating loci cluster in regulatory hotspots that affect a large number of phenotypes; a single variance-controlling locus, mapping close to DIA2, was found to be involved in more than 10% of the significant associations. It has been suggested in the literature that variance-heterogeneity between the genotypes might be due to genetic interactions. We therefore screened the multi-locus genotype-phenotype maps for several traits where multiple associations were found, for indications of epistasis. Several examples of two and three locus genetic interactions were found to involve variance-controlling loci, with reports from the literature corroborating the functional connections between the loci. By using a new analytical approach to re-analyze a powerful existing dataset, we are thus able to both provide novel insights to the genetic mechanisms involved in the regulation of gene-expression in budding yeast and experimentally validate epistasis as an important mechanism underlying genetic variance-heterogeneity between genotypes.
Maurits, NM; Zvelindovsky, AV; Fraaije, JGEM
1998-01-01
In the present paper, we extend the dynamic mean-field density functional method which describes microphase separation phenomena in polymer liquids, to account for viscoelastic effects. The effect of simple steady shear on polymer orientation and elongation is taken into account by adapting the
Self-consistent mean-field models for nuclear structure
International Nuclear Information System (INIS)
Bender, Michael; Heenen, Paul-Henri; Reinhard, Paul-Gerhard
2003-01-01
The authors review the present status of self-consistent mean-field (SCMF) models for describing nuclear structure and low-energy dynamics. These models are presented as effective energy-density functionals. The three most widely used variants of SCMF's based on a Skyrme energy functional, a Gogny force, and a relativistic mean-field Lagrangian are considered side by side. The crucial role of the treatment of pairing correlations is pointed out in each case. The authors discuss other related nuclear structure models and present several extensions beyond the mean-field model which are currently used. Phenomenological adjustment of the model parameters is discussed in detail. The performance quality of the SCMF model is demonstrated for a broad range of typical applications
Probabilistic models for reactive behaviour in heterogeneous condensed phase media
Baer, M. R.; Gartling, D. K.; DesJardin, P. E.
2012-02-01
This work presents statistically-based models to describe reactive behaviour in heterogeneous energetic materials. Mesoscale effects are incorporated in continuum-level reactive flow descriptions using probability density functions (pdfs) that are associated with thermodynamic and mechanical states. A generalised approach is presented that includes multimaterial behaviour by treating the volume fraction as a random kinematic variable. Model simplifications are then sought to reduce the complexity of the description without compromising the statistical approach. Reactive behaviour is first considered for non-deformable media having a random temperature field as an initial state. A pdf transport relationship is derived and an approximate moment approach is incorporated in finite element analysis to model an example application whereby a heated fragment impacts a reactive heterogeneous material which leads to a delayed cook-off event. Modelling is then extended to include deformation effects associated with shock loading of a heterogeneous medium whereby random variables of strain, strain-rate and temperature are considered. A demonstrative mesoscale simulation of a non-ideal explosive is discussed that illustrates the joint statistical nature of the strain and temperature fields during shock loading to motivate the probabilistic approach. This modelling is derived in a Lagrangian framework that can be incorporated in continuum-level shock physics analysis. Future work will consider particle-based methods for a numerical implementation of this modelling approach.
Effects of upper mantle heterogeneities on the lithospheric stress field and dynamic topography
Osei Tutu, Anthony; Steinberger, Bernhard; Sobolev, Stephan V.; Rogozhina, Irina; Popov, Anton A.
2018-05-01
The orientation and tectonic regime of the observed crustal/lithospheric stress field contribute to our knowledge of different deformation processes occurring within the Earth's crust and lithosphere. In this study, we analyze the influence of the thermal and density structure of the upper mantle on the lithospheric stress field and topography. We use a 3-D lithosphere-asthenosphere numerical model with power-law rheology, coupled to a spectral mantle flow code at 300 km depth. Our results are validated against the World Stress Map 2016 (WSM2016) and the observation-based residual topography. We derive the upper mantle thermal structure from either a heat flow model combined with a seafloor age model (TM1) or a global S-wave velocity model (TM2). We show that lateral density heterogeneities in the upper 300 km have a limited influence on the modeled horizontal stress field as opposed to the resulting dynamic topography that appears more sensitive to such heterogeneities. The modeled stress field directions, using only the mantle heterogeneities below 300 km, are not perturbed much when the effects of lithosphere and crust above 300 km are added. In contrast, modeled stress magnitudes and dynamic topography are to a greater extent controlled by the upper mantle density structure. After correction for the chemical depletion of continents, the TM2 model leads to a much better fit with the observed residual topography giving a good correlation of 0.51 in continents, but this correction leads to no significant improvement of the fit between the WSM2016 and the resulting lithosphere stresses. In continental regions with abundant heat flow data, TM1 results in relatively small angular misfits. For example, in western Europe the misfit between the modeled and observation-based stress is 18.3°. Our findings emphasize that the relative contributions coming from shallow and deep mantle dynamic forces are quite different for the lithospheric stress field and dynamic
Classification of networks of automata by dynamical mean field theory
International Nuclear Information System (INIS)
Burda, Z.; Jurkiewicz, J.; Flyvbjerg, H.
1990-01-01
Dynamical mean field theory is used to classify the 2 24 =65,536 different networks of binary automata on a square lattice with nearest neighbour interactions. Application of mean field theory gives 700 different mean field classes, which fall in seven classes of different asymptotic dynamics characterized by fixed points and two-cycles. (orig.)
Eivazy, Hesameddin; Esmaieli, Kamran; Jean, Raynald
2017-12-01
An accurate characterization and modelling of rock mass geomechanical heterogeneity can lead to more efficient mine planning and design. Using deterministic approaches and random field methods for modelling rock mass heterogeneity is known to be limited in simulating the spatial variation and spatial pattern of the geomechanical properties. Although the applications of geostatistical techniques have demonstrated improvements in modelling the heterogeneity of geomechanical properties, geostatistical estimation methods such as Kriging result in estimates of geomechanical variables that are not fully representative of field observations. This paper reports on the development of 3D models for spatial variability of rock mass geomechanical properties using geostatistical conditional simulation method based on sequential Gaussian simulation. A methodology to simulate the heterogeneity of rock mass quality based on the rock mass rating is proposed and applied to a large open-pit mine in Canada. Using geomechanical core logging data collected from the mine site, a direct and an indirect approach were used to model the spatial variability of rock mass quality. The results of the two modelling approaches were validated against collected field data. The study aims to quantify the risks of pit slope failure and provides a measure of uncertainties in spatial variability of rock mass properties in different areas of the pit.
Symplectic manifolds, coadjoint orbits, and Mean Field Theory
International Nuclear Information System (INIS)
Rosensteel, G.
1986-01-01
Mean field theory is given a geometrical interpretation as a Hamiltonian dynamical system. The Hartree-Fock phase space is the Grassmann manifold, a symplectic submanifold of the projective space of the full many-fermion Hilbert space. The integral curves of the Hartree-Fock vector field are the time-dependent Hartree-Fock solutions, while the critical points of the energy function are the time-independent states. The mean field theory is generalized beyond determinants to coadjoint orbit spaces of the unitary group; the Grassmann variety is the minimal coadjoint orbit
On the validity of effective formulations for transport through heterogeneous porous media
de Dreuzy, Jean-Raynald; Carrera, Jesus
2016-04-01
Geological heterogeneity enhances spreading of solutes and causes transport to be anomalous (i.e., non-Fickian), with much less mixing than suggested by dispersion. This implies that modeling transport requires adopting either stochastic approaches that model heterogeneity explicitly or effective transport formulations that acknowledge the effects of heterogeneity. A number of such formulations have been developed and tested as upscaled representations of enhanced spreading. However, their ability to represent mixing has not been formally tested, which is required for proper reproduction of chemical reactions and which motivates our work. We propose that, for an effective transport formulation to be considered a valid representation of transport through heterogeneous porous media (HPM), it should honor mean advection, mixing and spreading. It should also be flexible enough to be applicable to real problems. We test the capacity of the multi-rate mass transfer (MRMT) model to reproduce mixing observed in HPM, as represented by the classical multi-Gaussian log-permeability field with a Gaussian correlation pattern. Non-dispersive mixing comes from heterogeneity structures in the concentration fields that are not captured by macrodispersion. These fine structures limit mixing initially, but eventually enhance it. Numerical results show that, relative to HPM, MRMT models display a much stronger memory of initial conditions on mixing than on dispersion because of the sensitivity of the mixing state to the actual values of concentration. Because MRMT does not restitute the local concentration structures, it induces smaller non-dispersive mixing than HPM. However long-lived trapping in the immobile zones may sustain the deviation from dispersive mixing over much longer times. While spreading can be well captured by MRMT models, in general non-dispersive mixing cannot.
Landscape evaluation of heterogeneous areas using fuzzy sets
Directory of Open Access Journals (Sweden)
Ralf-Uwe Syrbe
1998-02-01
Full Text Available Landscape evaluation is an interesting field for fuzzy approaches, because it happens on the transition line between natural and social systems. Both are very complex. Therefore, transformation of scientific results to politically significant statements on environmental problems demands intelligent support. Particularly landscape planners need methods to gather natural facts of an area and assess them in consideration of its meaning to society as a whole. Since each land unit is heterogeneous, a special methodology is necessary. Such an evaluation technique was developed within a Geographical Information System (ARC/INFO. The methodology combines several known methods with fuzzy approaches to catch the intrinsic fuzziness of ecological systems as well as the heterogeneity of landscape. Additionally, a way will be discussed to vary the fuzzy inference in order to consider spatial relations of various landscape elements. Fuzzy logic is used to process the data uncertainty, to simulate the vagueness of knowledge about ecological functionality, and to model the spatial structure of landscape. Fuzzy sets describe the attributes of thematically defined land units and their assessment results. In this way, the available information will be preserved in their full diversity. The fuzzy operations are executed by AML-programs (ARC/INFO Macro Language. With such a tight coupling, it is possible to use the geographical functions (neighbourhoods, distances, etc. of GIS within the fuzzy system directly.
Adaptive and self-averaging Thouless-Anderson-Palmer mean-field theory for probabilistic modeling
DEFF Research Database (Denmark)
Opper, Manfred; Winther, Ole
2001-01-01
We develop a generalization of the Thouless-Anderson-Palmer (TAP) mean-field approach of disorder physics. which makes the method applicable to the computation of approximate averages in probabilistic models for real data. In contrast to the conventional TAP approach, where the knowledge...... of the distribution of couplings between the random variables is required, our method adapts to the concrete set of couplings. We show the significance of the approach in two ways: Our approach reproduces replica symmetric results for a wide class of toy models (assuming a nonglassy phase) with given disorder...... distributions in the thermodynamic limit. On the other hand, simulations on a real data model demonstrate that the method achieves more accurate predictions as compared to conventional TAP approaches....
Weakly coupled mean-field game systems
Gomes, Diogo A.; Patrizi, Stefania
2016-01-01
Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized problem
Boccia, E.; Luther, S.
2017-01-01
In cardiac tissue, electrical spiral waves pinned to a heterogeneity can be unpinned (and eventually terminated) using electric far field pulses and recruiting the heterogeneity as a virtual electrode. While for isotropic media the process of unpinning is much better understood, the case of an anisotropic substrate with different conductivities in different directions still needs intensive investigation. To study the impact of anisotropy on the unpinning process, we present numerical simulations based on the bidomain formulation of the phase I of the Luo and Rudy action potential model modified due to the occurrence of acute myocardial ischaemia. Simulating a rotating spiral wave pinned to an ischaemic heterogeneity, we compare the success of sequences of far field pulses in the isotropic and the anisotropic case for spirals still in transient or in steady rotation states. Our results clearly indicate that the range of pacing parameters resulting in successful termination of pinned spiral waves is larger in anisotropic tissue than in an isotropic medium. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’. PMID:28507234
Spatial heterogeneity study of vegetation coverage at Heihe River Basin
Wu, Lijuan; Zhong, Bo; Guo, Liyu; Zhao, Xiangwei
2014-11-01
Spatial heterogeneity of the animal-landscape system has three major components: heterogeneity of resource distributions in the physical environment, heterogeneity of plant tissue chemistry, heterogeneity of movement modes by the animal. Furthermore, all three different types of heterogeneity interact each other and can either reinforce or offset one another, thereby affecting system stability and dynamics. In previous studies, the study areas are investigated by field sampling, which costs a large amount of manpower. In addition, uncertain in sampling affects the quality of field data, which leads to unsatisfactory results during the entire study. In this study, remote sensing data is used to guide the sampling for research on heterogeneity of vegetation coverage to avoid errors caused by randomness of field sampling. Semi-variance and fractal dimension analysis are used to analyze the spatial heterogeneity of vegetation coverage at Heihe River Basin. The spherical model with nugget is used to fit the semivariogram of vegetation coverage. Based on the experiment above, it is found, (1)there is a strong correlation between vegetation coverage and distance of vegetation populations within the range of 0-28051.3188m at Heihe River Basin, but the correlation loses suddenly when the distance greater than 28051.3188m. (2)The degree of spatial heterogeneity of vegetation coverage at Heihe River Basin is medium. (3)Spatial distribution variability of vegetation occurs mainly on small scales. (4)The degree of spatial autocorrelation is 72.29% between 25% and 75%, which means that spatial correlation of vegetation coverage at Heihe River Basin is medium high.
Energy Technology Data Exchange (ETDEWEB)
Peru, S. [CEA, DAM, DIF, Arpajon (France); Martini, M. [Ghent University, Department of Physics and Astronomy, Gent (Belgium); CEA, DAM, DIF, Arpajon (France); Universite Libre de Bruxelles, Institut d' Astronomie et d' Astrophysique, CP-226, Brussels (Belgium)
2014-05-15
We present a review of several works using the finite-range Gogny interaction in mean field approaches and beyond to explore the most striking nuclear structure features. Shell evolution along the N = 16, 20, 28, 40 isotopic chains is investigated. The static deformation obtained in the mean field description are shown to be often in disagreement with the one experimentally determined. Dynamics is addressed in a GCM-like method, including rotational degrees of freedom, namely the five-dimension collective Hamiltonian (5DCH). This framework allows the description of the low-energy collective excitations. Nevertheless, some data cannot be reproduced with the collective Hamiltonian approach. Thus the QRPA formalism is introduced and used to simultaneously describe high- and low-energy spectroscopy as well as collective and individual excitations. After the description of giant resonances in doubly magic exotic nuclei, the role of the intrinsic deformation in giant resonances is presented. The appearance of low-energy dipole resonances in light nuclei is also discussed. In particular the isoscalar or isovector nature of Pygmy states is debated. Then, the first microscopic fully coherent description of the multipole spectrum of heavy deformed nucleus {sup 238}U is presented. Finally, a comparison of the low-energy spectrum obtained within the two extensions of the static mean field, namely QRPA and 5DCH, is performed for 2{sup +} states in N = 16 isotones, nickel and tin isotopes. For the first time the different static and dynamic factors involved in the generation of the 2{sup +} states in the nickel isotopic chain, from drip line to drip line, can be analysed in only one set of coherent approaches, free of adjustable parameters, using the same two-body interaction D1S and the resulting HFB mean field. (orig.)
Heterogeneity in pineapple fruit quality results from plant heterogeneity at flower induction
Fassinou Hotegni, V.N.; Lommen, W.J.M.; Agbossou, E.K.; Struik, P.C.
2014-01-01
Heterogeneity in fruit quality constitutes a major constraint in agri-food chains. In this paper the sources of the heterogeneity in pineapple in the field were studied in four experiments in commercial pineapple fields. The aims were to determine (a) whether differences in pineapple fruit quality
General Relativistic Mean Field Theory for rotating nuclei
Energy Technology Data Exchange (ETDEWEB)
Madokoro, Hideki [Kyushu Univ., Fukuoka (Japan). Dept. of Physics; Matsuzaki, Masayuki
1998-03-01
The {sigma}-{omega} model Lagrangian is generalized to an accelerated frame by using the technique of general relativity which is known as tetrad formalism. We apply this model to the description of rotating nuclei within the mean field approximation, which we call General Relativistic Mean Field Theory (GRMFT) for rotating nuclei. The resulting equations of motion coincide with those of Munich group whose formulation was not based on the general relativistic transformation property of the spinor fields. Some numerical results are shown for the yrast states of the Mg isotopes and the superdeformed rotational bands in the A {approx} 60 mass region. (author)
Bauso, Dario; Dia, Ben Mansour; Djehiche, Boualem; Tembine, Hamidou; Tempone, Raul
2014-01-01
The myth of marriage has been and is still a fascinating historical societal phenomenon. Paradoxically, the empirical divorce rates are at an all-time high. This work describes a unique paradigm for preserving relationships and marital stability from mean-field game theory. We show that optimizing the long-term well-being via effort and society feeling state distribution will help in stabilizing relationships.
Bauso, Dario
2014-01-06
The myth of marriage has been and is still a fascinating historical societal phenomenon. Paradoxically, the empirical divorce rates are at an all-time high. This work describes a unique paradigm for preserving relationships and marital stability from mean-field game theory. We show that optimizing the long-term well-being via effort and society feeling state distribution will help in stabilizing relationships.
Reprocessed and combined thorium fuel cycles in a PER system with a micro heterogeneous approaches
International Nuclear Information System (INIS)
Monteiro, Fabiana B.A.; Castro, Victor F.; Faria, Rochkhudson B. de; Pereira, Claubia; Fortini, Angela
2015-01-01
A micro heterogeneous approaches were used to study the behavior of reprocessed fuel spiked with thorium in a PWR fuel element considering (TRU-Th) cycle. The goal is to achieve a higher burnup using three different configurations to model the fuel element using SCALE 6.0. The reprocessed fuels were obtained using the ORIGEN 2.1 code from a spent PWR standard fuel (33,000 MWd/tHM burned), with 3.1% of initial enrichment. The spent fuel remained in the cooling pool for five years and then reprocessed using the UREX+ technique. Three configurations of micro heterogeneous approaches were analyzed, and the k inf and plutonium evolution during the burnup were evaluated. The preliminary results show that the behavior of advanced fuel based on transuranic elements spiked with thorium, and micro heterogeneous approach are satisfactory in PWRs, and the configuration that use a combination of Th and TRU (configuration 1) seems to be the most promising once has higher values for k inf during the burnup, compared with other configurations. (author)
Mean Field Games for Stochastic Growth with Relative Utility
Energy Technology Data Exchange (ETDEWEB)
Huang, Minyi, E-mail: mhuang@math.carleton.ca [Carleton University, School of Mathematics and Statistics (Canada); Nguyen, Son Luu, E-mail: sonluu.nguyen@upr.edu [University of Puerto Rico, Department of Mathematics (United States)
2016-12-15
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 error estimate.
Mean Field Games for Stochastic Growth with Relative Utility
International Nuclear Information System (INIS)
Huang, Minyi; Nguyen, Son Luu
2016-01-01
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 error estimate.
A Method to Represent Heterogeneous Materials for Rapid Prototyping: The Matryoshka Approach
Lei, Shuangyan; Frank, Matthew C.; Anderson, Donald D.; Brown, Thomas D.
2015-01-01
Purpose The purpose of this paper is to present a new method for representing heterogeneous materials using nested STL shells, based, in particular, on the density distributions of human bones. Design/methodology/approach Nested STL shells, called Matryoshka models, are described, based on their namesake Russian nesting dolls. In this approach, polygonal models, such as STL shells, are “stacked” inside one another to represent different material regions. The Matryoshka model addresses the challenge of representing different densities and different types of bone when reverse engineering from medical images. The Matryoshka model is generated via an iterative process of thresholding the Hounsfield Unit (HU) data using computed tomography (CT), thereby delineating regions of progressively increasing bone density. These nested shells can represent regions starting with the medullary (bone marrow) canal, up through and including the outer surface of the bone. Findings The Matryoshka approach introduced can be used to generate accurate models of heterogeneous materials in an automated fashion, avoiding the challenge of hand-creating an assembly model for input to multi-material additive or subtractive manufacturing. Originality/Value This paper presents a new method for describing heterogeneous materials: in this case, the density distribution in a human bone. The authors show how the Matryoshka model can be used to plan harvesting locations for creating custom rapid allograft bone implants from donor bone. An implementation of a proposed harvesting method is demonstrated, followed by a case study using subtractive rapid prototyping to harvest a bone implant from a human tibia surrogate. PMID:26120277
Modification of linear response theory for mean-field approximations
Hütter, M.; Öttinger, H.C.
1996-01-01
In the framework of statistical descriptions of many particle systems, the influence of mean-field approximations on the linear response theory is studied. A procedure, analogous to one where no mean-field approximation is involved, is used in order to determine the first order response of the
Stochastic description of heterogeneities of permeability within groundwater flow models
International Nuclear Information System (INIS)
Cacas, M.C.; Lachassagne, P.; Ledoux, E.; Marsily, G. de
1991-01-01
In order to model radionuclide migration in the geosphere realistically at the field scale, the hydrogeologist needs to be able to simulate groundwater flow in heterogeneous media. Heterogeneity of the medium can be described using a stochastic approach, that affects the way in which a flow model is formulated. In this paper, we discuss the problems that we have encountered in modelling both continuous and fractured media. The stochastic approach leads to a methodology that enables local measurements of permeability to be integrated into a model which gives a good prediction of groundwater flow on a regional scale. 5 Figs.; 8 Refs
Dynamics of epidemics outbreaks in heterogeneous populations
Brockmann, Dirk; Morales-Gallardo, Alejandro; Geisel, Theo
2007-03-01
The dynamics of epidemic outbreaks have been investigated in recent years within two alternative theoretical paradigms. The key parameter of mean field type of models such as the SIR model is the basic reproduction number R0, the average number of secondary infections caused by one infected individual. Recently, scale free network models have received much attention as they account for the high variability in the number of social contacts involved. These models predict an infinite basic reproduction number in some cases. We investigate the impact of heterogeneities of contact rates in a generic model for epidemic outbreaks. We present a system in which both the time periods of being infectious and the time periods between transmissions are Poissonian processes. The heterogeneities are introduced by means of strongly variable contact rates. In contrast to scale free network models we observe a finite basic reproduction number and, counterintuitively a smaller overall epidemic outbreak as compared to the homogeneous system. Our study thus reveals that heterogeneities in contact rates do not necessarily facilitate the spread to infectious disease but may well attenuate it.
Hydrodynamic mean-field solutions of 1D exclusion processes with spatially varying hopping rates
Energy Technology Data Exchange (ETDEWEB)
Lakatos, Greg; O' Brien, John; Chou, Tom [Department of Biomathematics and Institute for Pure and Applied Mathematics, UCLA, Los Angeles, CA 90095 (United States)
2006-03-10
We analyse the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean-field limit. The mean-field equations for particle densities are written in terms of Ricatti equations with the steady-state current J as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents J are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for J from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean-field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions.
Hydrodynamic mean-field solutions of 1D exclusion processes with spatially varying hopping rates
International Nuclear Information System (INIS)
Lakatos, Greg; O'Brien, John; Chou, Tom
2006-01-01
We analyse the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean-field limit. The mean-field equations for particle densities are written in terms of Ricatti equations with the steady-state current J as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents J are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for J from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean-field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions
Fluorescent lamp with static magnetic field generating means
Moskowitz, P.E.; Maya, J.
1987-09-08
A fluorescent lamp wherein magnetic field generating means (e.g., permanent magnets) are utilized to generate a static magnetic field across the respective electrode structures of the lamp such that maximum field strength is located at the electrode's filament. An increase in efficacy during operation has been observed. 2 figs.
Neutron fraction and neutrino mean free path predictions in relativistic mean field models
International Nuclear Information System (INIS)
Hutauruk, P.T.P.; Williams, C.K.; Sulaksono, A.; Mart, T.
2004-01-01
The equation of state (EOS) of dense matter and neutrino mean free path (NMFP) in a neutron star have been studied by using relativistic mean field models motivated by effective field theory. It is found that the models predict too large proton fractions, although one of the models (G2) predicts an acceptable EOS. This is caused by the isovector terms. Except G2, the other two models predict anomalous NMFP's. In order to minimize the anomaly, besides an acceptable EOS, a large M* is favorable. A model with large M* retains the regularity in the NMFP even for a small neutron fraction
International Nuclear Information System (INIS)
Madani, Tarik
2015-01-01
The present work follows a first approach where a strategy for identifying the shape and the parameters of cohesive-zone laws has been developed for homogeneous materials. The extension of this method to heterogeneous material requires the knowledge of the local stress state. The study aims at developing a local characterization method for mechanical properties and stresses. This method is based on the constitutive equation gap principles and relies on the knowledge of mechanical kinematic fields and particularly of the strain fields. These fields are obtained by the numerical differentiation of displacement fields measured by digital image correlation. This identification method is based on the iterative minimization of an energy norm involving the secant elastoplastic tensor. Various numerical simulations were used to illustrate the performances of the procedure for locally identifying heterogeneous property fields, and to characterize its robustness and its stability with respect to noise to the values of the algorithm initialization parameter and to the mesh refinement. Finally, various experimental tests with different specimen geometries were performed and a test has been developed to obtain a controlled heterogeneous initial state. The multilinear elastoplastic identification results showed the ability of the method to identify the local behavior properties on heterogeneous materials. (author)
Mean-field theory of active electrolytes: Dynamic adsorption and overscreening
Frydel, Derek; Podgornik, Rudolf
2018-05-01
We investigate active electrolytes within the mean-field level of description. The focus is on how the double-layer structure of passive, thermalized charges is affected by active dynamics of constituting ions. One feature of active dynamics is that particles adhere to hard surfaces, regardless of chemical properties of a surface and specifically in complete absence of any chemisorption or physisorption. To carry out the mean-field analysis of the system that is out of equilibrium, we develop the "mean-field simulation" technique, where the simulated system consists of charged parallel sheets moving on a line and obeying active dynamics, with the interaction strength rescaled by the number of sheets. The mean-field limit becomes exact in the limit of an infinite number of movable sheets.
Heterogeneous propellant internal ballistics: criticism and regeneration
Glick, R. L.
2011-10-01
Although heterogeneous propellant and its innately nondeterministic, chemically discrete morphology dominates applications, ballisticcharacterization deterministic time-mean burning rate and acoustic admittance measures' absence of explicit, nondeterministic information requires homogeneous propellant with a smooth, uniformly regressing burning surface: inadequate boundary conditions for heterogeneous propellant grained applications. The past age overcame this dichotomy with one-dimensional (1D) models and empirical knowledge from numerous, adequately supported motor developments and supplementary experiments. However, current cost and risk constraints inhibit this approach. Moreover, its fundamental science approach is more sensitive to incomplete boundary condition information (garbage-in still equals garbage-out) and more is expected. This work critiques this situation and sketches a path forward based on enhanced ballistic and motor characterizations in the workplace and approximate model and apparatus developments mentored by CSAR DNS capabilities (or equivalent).
International Nuclear Information System (INIS)
Gengembre, N.
2000-01-01
A model for the field radiated by an ultrasonic transducer into anisotropic and heterogeneous media is developed in this thesis. This work aims at improving the settings and interpretations of non destructive tests in welded structures. Since the shape of the transducer is assumed arbitrary, its emitting surface is divided into small elementary sources. The overall field at an observation point in the medium is derived by a summation of the elementary contributions of these point sources. An accurate and numerically efficient model is developed using the Geometrical Optics approximation to evaluate these elementary contributions. Two different forms of this approximation are used: The stationary phase method and the pencil method. The first one is based on an exact formulation of the field and is used for fields into anisotropic and homogeneous media. It allows to emphasize specific configurations for which additional developments are required; this need arises for calculation points in the vicinity of caustics (zones of high intensity). This problem is solved for both harmonic and transient fields, for points laying on caustics or in their neighborhood. The pencil method is used for the calculation of fields in heterogeneous media, although it does not permit to overcome the problem of caustics. It is also advantageous for the implementation of the model. A comparison of both above-mentioned methods is drawn, and their equivalence is proved for some cases. The calculation of fields in anisotropic and heterogeneous media is performed using both methods together, and then the problem of caustics is also treated. Calculated fields into welded components are shown and compared with experiments or with a numerical model, in order to validate the developments. (author)
A Maximum Principle for SDEs of Mean-Field Type
Energy Technology Data Exchange (ETDEWEB)
Andersson, Daniel, E-mail: danieand@math.kth.se; Djehiche, Boualem, E-mail: boualem@math.kth.se [Royal Institute of Technology, Department of Mathematics (Sweden)
2011-06-15
We study the optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state of the process. Moreover the cost functional is also of mean-field type, which makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. Under the assumption of a convex action space a maximum principle of local form is derived, specifying the necessary conditions for optimality. These are also shown to be sufficient under additional assumptions. This maximum principle differs from the classical one, where the adjoint equation is a linear backward SDE, since here the adjoint equation turns out to be a linear mean-field backward SDE. As an illustration, we apply the result to the mean-variance portfolio selection problem.
A Maximum Principle for SDEs of Mean-Field Type
International Nuclear Information System (INIS)
Andersson, Daniel; Djehiche, Boualem
2011-01-01
We study the optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state of the process. Moreover the cost functional is also of mean-field type, which makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. Under the assumption of a convex action space a maximum principle of local form is derived, specifying the necessary conditions for optimality. These are also shown to be sufficient under additional assumptions. This maximum principle differs from the classical one, where the adjoint equation is a linear backward SDE, since here the adjoint equation turns out to be a linear mean-field backward SDE. As an illustration, we apply the result to the mean-variance portfolio selection problem.
Dark-Bright Soliton Dynamics Beyond the Mean-Field Approximation
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''.
ENERGETIC PARTICLE TRANSPORT ACROSS THE MEAN MAGNETIC FIELD: BEFORE DIFFUSION
International Nuclear Information System (INIS)
Laitinen, T.; Dalla, S.
2017-01-01
Current particle transport models describe the propagation of charged particles across the mean field direction in turbulent plasmas as diffusion. However, recent studies suggest that at short timescales, such as soon after solar energetic particle (SEP) injection, particles remain on turbulently meandering field lines, which results in nondiffusive initial propagation across the mean magnetic field. In this work, we use a new technique to investigate how the particles are displaced from their original field lines, and we quantify the parameters of the transition from field-aligned particle propagation along meandering field lines to particle diffusion across the mean magnetic field. We show that the initial decoupling of the particles from the field lines is slow, and particles remain within a Larmor radius from their initial meandering field lines for tens to hundreds of Larmor periods, for 0.1–10 MeV protons in turbulence conditions typical of the solar wind at 1 au. Subsequently, particles decouple from their initial field lines and after hundreds to thousands of Larmor periods reach time-asymptotic diffusive behavior consistent with particle diffusion across the mean field caused by the meandering of the field lines. We show that the typical duration of the prediffusive phase, hours to tens of hours for 10 MeV protons in 1 au solar wind turbulence conditions, is significant for SEP propagation to 1 au and must be taken into account when modeling SEP propagation in the interplanetary space.
ENERGETIC PARTICLE TRANSPORT ACROSS THE MEAN MAGNETIC FIELD: BEFORE DIFFUSION
Energy Technology Data Exchange (ETDEWEB)
Laitinen, T.; Dalla, S., E-mail: tlmlaitinen@uclan.ac.uk [Jeremiah Horrocks Institute, University of Central Lancashire, Preston (United Kingdom)
2017-01-10
Current particle transport models describe the propagation of charged particles across the mean field direction in turbulent plasmas as diffusion. However, recent studies suggest that at short timescales, such as soon after solar energetic particle (SEP) injection, particles remain on turbulently meandering field lines, which results in nondiffusive initial propagation across the mean magnetic field. In this work, we use a new technique to investigate how the particles are displaced from their original field lines, and we quantify the parameters of the transition from field-aligned particle propagation along meandering field lines to particle diffusion across the mean magnetic field. We show that the initial decoupling of the particles from the field lines is slow, and particles remain within a Larmor radius from their initial meandering field lines for tens to hundreds of Larmor periods, for 0.1–10 MeV protons in turbulence conditions typical of the solar wind at 1 au. Subsequently, particles decouple from their initial field lines and after hundreds to thousands of Larmor periods reach time-asymptotic diffusive behavior consistent with particle diffusion across the mean field caused by the meandering of the field lines. We show that the typical duration of the prediffusive phase, hours to tens of hours for 10 MeV protons in 1 au solar wind turbulence conditions, is significant for SEP propagation to 1 au and must be taken into account when modeling SEP propagation in the interplanetary space.
Jiancheng, Shi; Min, Luo; Chusheng, Huang
2017-08-01
The cooperative effect of random coupling strength and time-periodic coupling strengh on synchronization transitions in one-way coupled neural system has been investigated by mean field approach. Results show that cooperative coupling strength (CCS) plays an active role for the enhancement of synchronization transitions. There exist an optimal frequency of CCS which makes the system display the best CCS-induced synchronization transitions, a critical frequency of CCS which can not further affect the CCS-induced synchronization transitions, and a critical amplitude of CCS which can not occur the CCS-induced synchronization transitions. Meanwhile, noise intensity plays a negative role for the CCS-induced synchronization transitions. Furthermore, it is found that the novel CCS amplitude-induced synchronization transitions and CCS frequency-induced synchronization transitions are found.
Variational approach to gravity field theories from Newton to Einstein and beyond
Vecchiato, Alberto
2017-01-01
This book offers a detailed and stimulating account of the Lagrangian, or variational, approach to general relativity and beyond. The approach more usually adopted when describing general relativity is to introduce the required concepts of differential geometry and derive the field and geodesic equations from purely geometrical properties. Demonstration of the physical meaning then requires the weak field approximation of these equations to recover their Newtonian counterparts. The potential downside of this approach is that it tends to suit the mathematical mind and requires the physicist to study and work in a completely unfamiliar environment. In contrast, the approach to general relativity described in this book will be especially suited to physics students. After an introduction to field theories and the variational approach, individual sections focus on the variational approach in relation to special relativity, general relativity, and alternative theories of gravity. Throughout the text, solved exercis...
A Stochastic Maximum Principle for General Mean-Field Systems
International Nuclear Information System (INIS)
Buckdahn, Rainer; Li, Juan; Ma, Jin
2016-01-01
In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.
A Stochastic Maximum Principle for General Mean-Field Systems
Energy Technology Data Exchange (ETDEWEB)
Buckdahn, Rainer, E-mail: Rainer.Buckdahn@univ-brest.fr [Université de Bretagne-Occidentale, Département de Mathématiques (France); Li, Juan, E-mail: juanli@sdu.edu.cn [Shandong University, Weihai, School of Mathematics and Statistics (China); Ma, Jin, E-mail: jinma@usc.edu [University of Southern California, Department of Mathematics (United States)
2016-12-15
In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.
Estimating field-scale soil water dynamics at a heterogeneous site using multi-channel GPR
Directory of Open Access Journals (Sweden)
X. Pan
2012-11-01
Full Text Available We explore the feasibility to quantify the field-scale soil water dynamics through time series of GPR (ground-penetrating radar measurements, which bridge the gap between point measurements and field measurements. Working on a 40 m × 50 m area in a heterogeneous agricultural field, we obtain a time series of radargrams after a heavy rainfall event. The data are analysed to simultaneously yield (i a three-dimensional representation of the subsurface architecture and (ii the total soil water volume between the surface and a reflection boundary associated with the presence of paleo sand dunes or clay inclusions in a rather uniform sand matrix. We assess the precision and the accuracy of these quantities and conclude that the method is sensitive enough to capture the spatial structure of the changing soil water content in a three-dimensional heterogeneous soil during a short-duration infiltration event. While the sensitivity of the method needs to be improved, it already produced useful information to understand the observed patterns in crop height and it yielded insight into the dynamics of soil water content at this site including the effect of evaporation.
Transverse dispersion in heterogeneous fractures
International Nuclear Information System (INIS)
Dershowitz, Bill; Shuttle, Dawn; Klise, Kate; Outters, Nils; Hermanson, Jan
2004-12-01
This report evaluates the significance of transverse dispersion processes for solute transport in a single fracture. Transverse dispersion is a potentially significant process because it increases the fracture surface area available for sorptive and diffusive properties, and has the potential to transport solute between what would otherwise be distinctive, streamline pathways. Transverse dispersion processes are generally ignored in one-dimensional repository performance assessment approaches. This report provides an initial assessment of the magnitude of transverse dispersion effect in a single heterogeneous fracture on repository safety assessment. This study builds on a previous report which considered the network effects on transport dispersion including streamline routing and mixing at fracture intersections. The project uses FracMan software. This platform has been extensively used by SKB in other projects. FracMan software is designed to generate and analyze DFN's as well as to compute fluid flow in DFN's with the MAFIC Finite element method (FEM) code. Solute transport was modeled using the particle tracking inside MAFIC, the 2-D Laplace Transform Galerkin inside PAWorks/LTG, and the 1-D Laplace Transform approach designed to replicate FARF31 inside GoldSim.The study reported here focuses on a single, 20-meter scale discrete fracture, with simplified boundary conditions intended to represent the position of this fracture within a fracture network. The range of assumptions made regarding fracture heterogeneity were as follows: Base case, Heterogeneous fracture, geostatistical field, correlation length 0.01 m. Case 1a, Homogeneous fracture, transmissivity = 10 -7 m 2 /s. Case 1b, Heterogeneous fracture, non-channeled geostatistical field correlation length 5 m. Case 1c, Heterogeneous fracture, channeled, anisotropic geostatistical field. Case 1d, Heterogeneous fracture, fracture intersection zone (FIZ) permeability enhanced. Case 5, Simple channelized
Comolli, Alessandro; Hakoun, Vivien; Dentz, Marco
2017-04-01
Achieving the understanding of the process of solute transport in heterogeneous porous media is of crucial importance for several environmental and social purposes, ranging from aquifers contamination and remediation, to risk assessment in nuclear waste repositories. The complexity of this aim is mainly ascribable to the heterogeneity of natural media, which can be observed at all the scales of interest, from pore scale to catchment scale. In fact, the intrinsic heterogeneity of porous media is responsible for the arising of the well-known non-Fickian footprints of transport, including heavy-tailed breakthrough curves, non-Gaussian spatial density profiles and the non-linear growth of the mean squared displacement. Several studies investigated the processes through which heterogeneity impacts the transport properties, which include local modifications to the advective-dispersive motion of solutes, mass exchanges between some mobile and immobile phases (e.g. sorption/desorption reactions or diffusion into solid matrix) and spatial correlation of the flow field. In the last decades, the continuous time random walk (CTRW) model has often been used to describe solute transport in heterogenous conditions and to quantify the impact of point heterogeneity, spatial correlation and mass transfer on the average transport properties [1]. Open issues regarding this approach are the possibility to relate measurable properties of the medium to the parameters of the model, as well as its capability to provide predictive information. In a recent work [2] the authors have shed new light on understanding the relationship between Lagrangian and Eulerian dynamics as well as on their evolution from arbitrary initial conditions. On the basis of these results, we derive a CTRW model for the description of Darcy-scale transport in d-dimensional media characterized by spatially random permeability fields. The CTRW approach models particle velocities as a spatial Markov process, which is
Kirchner, J. W.
2016-01-01
Environmental heterogeneity is ubiquitous, but environmental systems are often analyzed as if they were homogeneous instead, resulting in aggregation errors that are rarely explored and almost never quantified. Here I use simple benchmark tests to explore this general problem in one specific context: the use of seasonal cycles in chemical or isotopic tracers (such as Cl-, δ18O, or δ2H) to estimate timescales of storage in catchments. Timescales of catchment storage are typically quantified by the mean transit time, meaning the average time that elapses between parcels of water entering as precipitation and leaving again as streamflow. Longer mean transit times imply greater damping of seasonal tracer cycles. Thus, the amplitudes of tracer cycles in precipitation and streamflow are commonly used to calculate catchment mean transit times. Here I show that these calculations will typically be wrong by several hundred percent, when applied to catchments with realistic degrees of spatial heterogeneity. This aggregation bias arises from the strong nonlinearity in the relationship between tracer cycle amplitude and mean travel time. I propose an alternative storage metric, the young water fraction in streamflow, defined as the fraction of runoff with transit times of less than roughly 0.2 years. I show that this young water fraction (not to be confused with event-based "new water" in hydrograph separations) is accurately predicted by seasonal tracer cycles within a precision of a few percent, across the entire range of mean transit times from almost zero to almost infinity. Importantly, this relationship is also virtually free from aggregation error. That is, seasonal tracer cycles also accurately predict the young water fraction in runoff from highly heterogeneous mixtures of subcatchments with strongly contrasting transit-time distributions. Thus, although tracer cycle amplitudes yield biased and unreliable estimates of catchment mean travel times in heterogeneous
Mean field theory of dynamic phase transitions in ferromagnets
International Nuclear Information System (INIS)
Idigoras, O.; Vavassori, P.; Berger, A.
2012-01-01
We have studied the second order dynamic phase transition (DPT) of the two-dimensional kinetic Ising model by means of numerical calculations. While it is well established that the order parameter Q of the DPT is the average magnetization per external field oscillation cycle, the possible identity of the conjugate field has been addressed only recently. In this work, we demonstrate that our entire set of numerical data is fully consistent with the applied bias field H b being the conjugate field of order parameter Q. For this purpose, we have analyzed the Q(H b )-dependence and we have found that it follows the expected power law behavior with the same critical exponent as the mean field equilibrium case.
Momentum and density dependence of the nuclear mean field
International Nuclear Information System (INIS)
Behera, B.; Routray, T.R.
1999-01-01
The purpose of this is to analyse the momentum, density and temperature dependence of the mean field in nuclear matter derived from finite range effective interactions and to examine the influence of the functional form of the interaction on the high momentum behaviour of the mean field. Emphasis will be given to use very simple parametrizations of the effective interaction with a minimum number of adjustable parameters and yet capable of giving a good description of the mean field in nuclear matter over a wide range of momentum, density and temperature. As an application of the calculated equation of state of nuclear matter, phase transitions to quark-gluon plasma is studied where the quark phase is described by a zeroth order bag model equation of state
Nonergodicity, fluctuations, and criticality in heterogeneous diffusion processes.
Cherstvy, A G; Metzler, R
2014-07-01
We study the stochastic behavior of heterogeneous diffusion processes with the power-law dependence D(x) ∼ |x|(α) of the generalized diffusion coefficient encompassing sub- and superdiffusive anomalous diffusion. Based on statistical measures such as the amplitude scatter of the time-averaged mean-squared displacement of individual realizations, the ergodicity breaking and non-Gaussianity parameters, as well as the probability density function P(x,t), we analyze the weakly nonergodic character of the heterogeneous diffusion process and, particularly, the degree of irreproducibility of individual realizations. As we show, the fluctuations between individual realizations increase with growing modulus |α| of the scaling exponent. The fluctuations appear to diverge when the critical value α = 2 is approached, while for even larger α the fluctuations decrease, again. At criticality, the power-law behavior of the mean-squared displacement changes to an exponentially fast growth, and the fluctuations of the time-averaged mean-squared displacement do not converge for increasing number of realizations. From a systematic comparison we observe some striking similarities of the heterogeneous diffusion process with the familiar subdiffusive continuous time random walk process with power-law waiting time distribution and diverging characteristic waiting time.
A Practical Approach to Tumor Heterogeneity in Clinical Research and Diagnostics.
Stanta, Giorgio; Bonin, Serena
2018-01-01
This Pathobiology issue tries to better define the complex phenomenon of intratumor heterogeneity (ITH), mostly from a practical point of view. This topic has been chosen because ITH is a central issue in tumor development and has to be investigated directly in patient tissue and immediately applied in the treatment of the presenting patient. Different types of ITH should be considered: clonal genetic and epigenetic evolution, morphological heterogeneity, and tumor sampling, heterogeneity resulting from microenvironmental autocrine and paracrine interaction, and stochastic plasticity related to different functional cell efficiencies. For a higher level of reproducibility in clinical research and diagnostics, it is necessary to establish standardized analytical methods, including microdissection. In situ techniques can be pivotal to explore tumor microenvironment and can be improved with associated digital analysis. Liquid biopsies for plasma DNA analysis are at present the best method to study recurrent tumors with treatment adaptation, and widespread clinical use could be beneficial. The different types of tumor genomic instabilities could have pragmatic applications to rank ITH for clinical applications: treatment approaches differ in patients with a high nucleotide mutation rate and patients with high copy number alterations. © 2017 S. Karger AG, Basel.
Mean field with corrections in lattice gauge theory
International Nuclear Information System (INIS)
Flyvbjerg, H.; Zuber, J.B.; Lautrup, B.
1981-12-01
A systematic expansion of the path integral for lattice gauge theory is performed around the mean field solution. In this letter the authors present the results for the pure gauge groups Z(2), SU(2) and SO(3). The agreement with Monte Carlo calculations is excellent. For the discrete group the calculation is performed with and without gauge fixing, whereas for the continuous groups gauge fixing is mandatory. In the case of SU(2) the absence of a phase transition is correctly signalled by mean field theory. (Auth.)
Configuration mixing of mean-field states
International Nuclear Information System (INIS)
Bender, M; Heenen, P-H
2005-01-01
Starting from self-consistent mean-field models, we discuss how to include correlations from fluctuations in collective degrees of freedom through symmetry restoration and configuration mixing, which give access to ground-state correlations and collective excitations. As an example for the method, we discuss the spectroscopy of neutron-deficient Pb isotopes
Mean Field Type Control with Congestion
Energy Technology Data Exchange (ETDEWEB)
Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Laurière, Mathieu [Univ. Paris Diderot, Sorbonne Paris Cité, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS (France)
2016-06-15
We analyze some systems of partial differential equations arising in the theory of mean field type control with congestion effects. We look for weak solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as the optima of two optimal control problems in duality.
Real-space, mean-field algorithm to numerically calculate long-range interactions
Cadilhe, A.; Costa, B. V.
2016-02-01
Long-range interactions are known to be of difficult treatment in statistical mechanics models. There are some approaches that introduce a cutoff in the interactions or make use of reaction field approaches. However, those treatments suffer the illness of being of limited use, in particular close to phase transitions. The use of open boundary conditions allows the sum of the long-range interactions over the entire system to be done, however, this approach demands a sum over all degrees of freedom in the system, which makes a numerical treatment prohibitive. Techniques like the Ewald summation or fast multipole expansion account for the exact interactions but are still limited to a few thousands of particles. In this paper we introduce a novel mean-field approach to treat long-range interactions. The method is based in the division of the system in cells. In the inner cell, that contains the particle in sight, the 'local' interactions are computed exactly, the 'far' contributions are then computed as the average over the particles inside a given cell with the particle in sight for each of the remaining cells. Using this approach, the large and small cells limits are exact. At a fixed cell size, the method also becomes exact in the limit of large lattices. We have applied the procedure to the two-dimensional anisotropic dipolar Heisenberg model. A detailed comparison between our method, the exact calculation and the cutoff radius approximation were done. Our results show that the cutoff-cell approach outperforms any cutoff radius approach as it maintains the long-range memory present in these interactions, contrary to the cutoff radius approximation. Besides that, we calculated the critical temperature and the critical behavior of the specific heat of the anisotropic Heisenberg model using our method. The results are in excellent agreement with extensive Monte Carlo simulations using Ewald summation.
Püthe, Christoph; Manoj, Chandrasekharan; Kuvshinov, Alexey
2015-04-01
Electric fields induced in the conducting Earth during magnetic storms drive currents in power transmission grids, telecommunication lines or buried pipelines. These geomagnetically induced currents (GIC) can cause severe service disruptions. The prediction of GIC is thus of great importance for public and industry. A key step in the prediction of the hazard to technological systems during magnetic storms is the calculation of the geoelectric field. To address this issue for mid-latitude regions, we developed a method that involves 3-D modelling of induction processes in a heterogeneous Earth and the construction of a model of the magnetospheric source. The latter is described by low-degree spherical harmonics; its temporal evolution is derived from observatory magnetic data. Time series of the electric field can be computed for every location on Earth's surface. The actual electric field however is known to be perturbed by galvanic effects, arising from very local near-surface heterogeneities or topography, which cannot be included in the conductivity model. Galvanic effects are commonly accounted for with a real-valued time-independent distortion matrix, which linearly relates measured and computed electric fields. Using data of various magnetic storms that occurred between 2000 and 2003, we estimated distortion matrices for observatory sites onshore and on the ocean bottom. Strong correlations between modellings and measurements validate our method. The distortion matrix estimates prove to be reliable, as they are accurately reproduced for different magnetic storms. We further show that 3-D modelling is crucial for a correct separation of galvanic and inductive effects and a precise prediction of electric field time series during magnetic storms. Since the required computational resources are negligible, our approach is suitable for a real-time prediction of GIC. For this purpose, a reliable forecast of the source field, e.g. based on data from satellites
Mapping soil heterogeneity using RapidEye satellite images
Piccard, Isabelle; Eerens, Herman; Dong, Qinghan; Gobin, Anne; Goffart, Jean-Pierre; Curnel, Yannick; Planchon, Viviane
2016-04-01
In the frame of BELCAM, a project funded by the Belgian Science Policy Office (BELSPO), researchers from UCL, ULg, CRA-W and VITO aim to set up a collaborative system to develop and deliver relevant information for agricultural monitoring in Belgium. The main objective is to develop remote sensing methods and processing chains able to ingest crowd sourcing data, provided by farmers or associated partners, and to deliver in return relevant and up-to-date information for crop monitoring at the field and district level based on Sentinel-1 and -2 satellite imagery. One of the developments within BELCAM concerns an automatic procedure to detect soil heterogeneity within a parcel using optical high resolution images. Such heterogeneity maps can be used to adjust farming practices according to the detected heterogeneity. This heterogeneity may for instance be caused by differences in mineral composition of the soil, organic matter content, soil moisture or soil texture. Local differences in plant growth may be indicative for differences in soil characteristics. As such remote sensing derived vegetation indices may be used to reveal soil heterogeneity. VITO started to delineate homogeneous zones within parcels by analyzing a series of RapidEye images acquired in 2015 (as a precursor for Sentinel-2). Both unsupervised classification (ISODATA, K-means) and segmentation techniques were tested. Heterogeneity maps were generated from images acquired at different moments during the season (13 May, 30 June, 17 July, 31 August, 11 September and 1 November 2015). Tests were performed using blue, green, red, red edge and NIR reflectances separately and using derived indices such as NDVI, fAPAR, CIrededge, NDRE2. The results for selected winter wheat, maize and potato fields were evaluated together with experts from the collaborating agricultural research centers. For a few fields UAV images and/or yield measurements were available for comparison.
Diffusion with finite-helicity field tensor: A mechanism of generating heterogeneity
Sato, N.; Yoshida, Z.
2018-02-01
Topological constraints on a dynamical system often manifest themselves as breaking of the Hamiltonian structure; well-known examples are nonholonomic constraints on Lagrangian mechanics. The statistical mechanics under such topological constraints is the subject of this study. Conventional arguments based on phase spaces, Jacobi identity, invariant measure, or the H theorem are no longer applicable since all these notions stem from the symplectic geometry underlying canonical Hamiltonian systems. Remembering that Hamiltonian systems are endowed with field tensors (canonical 2-forms) that have zero helicity, our mission is to extend the scope toward the class of systems governed by finite-helicity field tensors. Here, we introduce a class of field tensors that are characterized by Beltrami vectors. We prove an H theorem for this Beltrami class. The most general class of energy-conserving systems are non-Beltrami, for which we identify the "field charge" that prevents the entropy to maximize, resulting in creation of heterogeneous distributions. The essence of the theory can be delineated by classifying three-dimensional dynamics. We then generalize to arbitrary (finite) dimensions.
Mean-field inference of Hawkes point processes
International Nuclear Information System (INIS)
Bacry, Emmanuel; Gaïffas, Stéphane; Mastromatteo, Iacopo; Muzy, Jean-François
2016-01-01
We propose a fast and efficient estimation method that is able to accurately recover the parameters of a d-dimensional Hawkes point-process from a set of observations. We exploit a mean-field approximation that is valid when the fluctuations of the stochastic intensity are small. We show that this is notably the case in situations when interactions are sufficiently weak, when the dimension of the system is high or when the fluctuations are self-averaging due to the large number of past events they involve. In such a regime the estimation of a Hawkes process can be mapped on a least-squares problem for which we provide an analytic solution. Though this estimator is biased, we show that its precision can be comparable to the one of the maximum likelihood estimator while its computation speed is shown to be improved considerably. We give a theoretical control on the accuracy of our new approach and illustrate its efficiency using synthetic datasets, in order to assess the statistical estimation error of the parameters. (paper)
Field scale heterogeneity of redox conditions in till-upscaling to a catchment nitrate model
DEFF Research Database (Denmark)
Hansen, J.R.; Erntsen, V.; Refsgaard, J.C.
2008-01-01
Point scale studies in different settings of glacial geology show a large local variation of redox conditions. There is a need to develop an upscaling methodology for catchment scale models. This paper describes a study of field-scale heterogeneity of redox-interfaces in a till aquitard within an...
Mechanism of spiral formation in heterogeneous discretized excitable media.
Kinoshita, Shu-ichi; Iwamoto, Mayuko; Tateishi, Keita; Suematsu, Nobuhiko J; Ueyama, Daishin
2013-06-01
Spiral waves on excitable media strongly influence the functions of living systems in both a positive and negative way. The spiral formation mechanism has thus been one of the major themes in the field of reaction-diffusion systems. Although the widely believed origin of spiral waves is the interaction of traveling waves, the heterogeneity of an excitable medium has recently been suggested as a probable cause. We suggest one possible origin of spiral waves using a Belousov-Zhabotinsky reaction and a discretized FitzHugh-Nagumo model. The heterogeneity of the reaction field is shown to stochastically generate unidirectional sites, which can induce spiral waves. Furthermore, we found that the spiral wave vanished with only a small reduction in the excitability of the reaction field. These results reveal a gentle approach for controlling the appearance of a spiral wave on an excitable medium.
Scherrer, P. H.; Wilcox, J. M.; Kotov, V.; Severnyi, A. B.; Howard, R.
1977-01-01
The mean solar magnetic field as measured in integrated light has been observed since 1968. Since 1970 it has been observed both at Hale Observatories and at the Crimean Astrophysical Observatory. The observing procedures at both observatories and their implications for mean field measurements are discussed. A comparison of the two sets of daily observations shows that similar results are obtained at both observatories. A comparison of the mean field with the interplanetary magnetic polarity shows that the IMF sector structure has the same pattern as the mean field polarity.
International Nuclear Information System (INIS)
Rockhold, M.L.
1993-02-01
A field-scale, unsaturated flow and solute transport experiment at the Las Cruces trench site in New Mexico was simulated as part of a ''blind'' modeling exercise to demonstrate the ability or inability of uncalibrated models to predict unsaturated flow and solute transport in spatially variable porous media. Simulations were conducted using a recently developed multiphase flow and transport simulator. Uniform and heterogeneous soil models were tested, and data from a previous experiment at the site were used with an inverse procedure to estimate water retention parameters. A spatial moment analysis was used to provide a quantitative basis for comparing the mean observed and simulated flow and transport behavior. The results of this study suggest that defensible predictions of waste migration and fate at low-level waste sites will ultimately require site-specific data for model calibration
Orbital effect of the magnetic field in dynamical mean-field theory
Acheche, S.; Arsenault, L.-F.; Tremblay, A.-M. S.
2017-12-01
The availability of large magnetic fields at international facilities and of simulated magnetic fields that can reach the flux-quantum-per-unit-area level in cold atoms calls for systematic studies of orbital effects of the magnetic field on the self-energy of interacting systems. Here we demonstrate theoretically that orbital effects of magnetic fields can be treated within single-site dynamical mean-field theory with a translationally invariant quantum impurity problem. As an example, we study the one-band Hubbard model on the square lattice using iterated perturbation theory as an impurity solver. We recover the expected quantum oscillations in the scattering rate, and we show that the magnetic fields allow the interaction-induced effective mass to be measured through the single-particle density of states accessible in tunneling experiments. The orbital effect of magnetic fields on scattering becomes particularly important in the Hofstadter butterfly regime.
A Method to Represent Heterogeneous Materials for Rapid Prototyping: The Matryoshka Approach.
Lei, Shuangyan; Frank, Matthew C; Anderson, Donald D; Brown, Thomas D
The purpose of this paper is to present a new method for representing heterogeneous materials using nested STL shells, based, in particular, on the density distributions of human bones. Nested STL shells, called Matryoshka models, are described, based on their namesake Russian nesting dolls. In this approach, polygonal models, such as STL shells, are "stacked" inside one another to represent different material regions. The Matryoshka model addresses the challenge of representing different densities and different types of bone when reverse engineering from medical images. The Matryoshka model is generated via an iterative process of thresholding the Hounsfield Unit (HU) data using computed tomography (CT), thereby delineating regions of progressively increasing bone density. These nested shells can represent regions starting with the medullary (bone marrow) canal, up through and including the outer surface of the bone. The Matryoshka approach introduced can be used to generate accurate models of heterogeneous materials in an automated fashion, avoiding the challenge of hand-creating an assembly model for input to multi-material additive or subtractive manufacturing. This paper presents a new method for describing heterogeneous materials: in this case, the density distribution in a human bone. The authors show how the Matryoshka model can be used to plan harvesting locations for creating custom rapid allograft bone implants from donor bone. An implementation of a proposed harvesting method is demonstrated, followed by a case study using subtractive rapid prototyping to harvest a bone implant from a human tibia surrogate.
Weakly coupled mean-field game systems
Gomes, Diogo A.
2016-07-14
Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized problem. Finally, by a limiting procedure, we obtain solutions to the MFG problem. © 2016 Elsevier Ltd
Phase diagram of the mean field model of simplicial gravity
International Nuclear Information System (INIS)
Bialas, P.; Burda, Z.; Johnston, D.
1999-01-01
We discuss the phase diagram of the balls in boxes model, with a varying number of boxes. The model can be regarded as a mean-field model of simplicial gravity. We analyse in detail the case of weights of the form p(q) = q -β , which correspond to the measure term introduced in the simplicial quantum gravity simulations. The system has two phases: elongated (fluid) and crumpled. For β ε (2, ∞) the transition between these two phases is first-order, while for β ε (1, 2) it is continuous. The transition becomes softer when β approaches unity and eventually disappears at β = 1. We then generalise the discussion to an arbitrary set of weights. Finally, we show that if one introduces an additional kinematic bound on the average density of balls per box then a new condensed phase appears in the phase diagram. It bears some similarity to the crinkled phase of simplicial gravity discussed recently in models of gravity interacting with matter fields
Oscillations of oblate drop between heterogeneous plates under uniform electric field
Kashina, M. A.; Alabuzhev, A. A.
2018-01-01
The forced oscillations of the incompressible fluid drop under the action of the uniform electric field are considered. In equilibrium, the drop has the form of a circular cylinder bounded axially by the parallel solid planes; the contact angle is right. An incompressible fluid of different density surrounds the drop. The external electric field acts as an external force that causes motion of the contact line. In order to describe this contact line motion, the modified Hocking boundary condition is applied: the velocity of the contact line is proportional to the deviation of the contact angle and the speed of the fast relaxation processes, whose frequency is proportional to twice the frequency of the electric field. The case of heterogeneous plates is investigated. We assume that the Hocking parameter depends on the polar angle in this case. The function describing the change in the coefficient of the interaction between the plate and the fluid (the contact line) is expanded in a series of the Laplace operator eigenfunctions.
An estimating function approach to linkage heterogeneity
Indian Academy of Sciences (India)
Testing linkage heterogeneity between two loci is an important issue in genetics. Currently, there are ... on linkage heterogeneity can help people to better understand complex .... χ2(F − 2) + cχ2 (1), where c is a constant (see Appendix). Here, it can be ..... gin, ancestry, gender, age, etc., for purpose of dividing sub- groups to ...
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.
DIGITAL ONCOLOGY PATIENT RECORD - HETEROGENEOUS FILE BASED APPROACH
Directory of Open Access Journals (Sweden)
Nikolay Sapundzhiev
2010-12-01
Full Text Available Introduction: Oncology patients need extensive follow-up and meticulous documentation. The aim of this study was to introduce a simple, platform independent file based system for documentation of diagnostic and therapeutic procedures in oncology patients and test its function.Material and methods: A file-name based system of the type M1M2M3.F2 was introduced, where M1 is a unique identifier for the patient, M2 is the date of the clinical intervention/event, M3 is an identifier for the author of the medical record and F2 is the specific software generated file-name extension.Results: This system is in use at 5 institutions, where a total of 11 persons on 14 different workstations inputted 16591 entries (files for 2370. The merge process was tested on 2 operating systems - when copied together all files sort up as expected by patient, and for each patient in a chronological order, providing a digital cumulative patient record, which contains heterogeneous file formats.Conclusion: The file based approach for storing heterogeneous digital patient related information is an reliable system, which can handle open-source, proprietary, general and custom file formats and seems to be easily scalable. Further development of software for automatic checks of the integrity and searching and indexing of the files is expected to produce a more user-friendly environment
Mean-field theory and self-consistent dynamo modeling
International Nuclear Information System (INIS)
Yoshizawa, Akira; Yokoi, Nobumitsu
2001-12-01
Mean-field theory of dynamo is discussed with emphasis on the statistical formulation of turbulence effects on the magnetohydrodynamic equations and the construction of a self-consistent dynamo model. The dynamo mechanism is sought in the combination of the turbulent residual-helicity and cross-helicity effects. On the basis of this mechanism, discussions are made on the generation of planetary magnetic fields such as geomagnetic field and sunspots and on the occurrence of flow by magnetic fields in planetary and fusion phenomena. (author)
A mean field theory of coded CDMA systems
International Nuclear Information System (INIS)
Yano, Toru; Tanaka, Toshiyuki; Saad, David
2008-01-01
We present a mean field theory of code-division multiple-access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean-field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems
A mean field theory of coded CDMA systems
Energy Technology Data Exchange (ETDEWEB)
Yano, Toru [Graduate School of Science and Technology, Keio University, Hiyoshi, Kohoku-ku, Yokohama-shi, Kanagawa 223-8522 (Japan); Tanaka, Toshiyuki [Graduate School of Informatics, Kyoto University, Yoshida Hon-machi, Sakyo-ku, Kyoto-shi, Kyoto 606-8501 (Japan); Saad, David [Neural Computing Research Group, Aston University, Birmingham B4 7ET (United Kingdom)], E-mail: yano@thx.appi.keio.ac.jp
2008-08-15
We present a mean field theory of code-division multiple-access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean-field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.
Explaining the heterogeneous scrapie surveillance figures across Europe: a meta-regression approach
Directory of Open Access Journals (Sweden)
Ru Giuseppe
2007-06-01
Full Text Available Abstract Background Two annual surveys, the abattoir and the fallen stock, monitor the presence of scrapie across Europe. A simple comparison between the prevalence estimates in different countries reveals that, in 2003, the abattoir survey appears to detect more scrapie in some countries. This is contrary to evidence suggesting the greater ability of the fallen stock survey to detect the disease. We applied meta-analysis techniques to study this apparent heterogeneity in the behaviour of the surveys across Europe. Furthermore, we conducted a meta-regression analysis to assess the effect of country-specific characteristics on the variability. We have chosen the odds ratios between the two surveys to inform the underlying relationship between them and to allow comparisons between the countries under the meta-regression framework. Baseline risks, those of the slaughtered populations across Europe, and country-specific covariates, available from the European Commission Report, were inputted in the model to explain the heterogeneity. Results Our results show the presence of significant heterogeneity in the odds ratios between countries and no reduction in the variability after adjustment for the different risks in the baseline populations. Three countries contributed the most to the overall heterogeneity: Germany, Ireland and The Netherlands. The inclusion of country-specific covariates did not, in general, reduce the variability except for one variable: the proportion of the total adult sheep population sampled as fallen stock by each country. A large residual heterogeneity remained in the model indicating the presence of substantial effect variability between countries. Conclusion The meta-analysis approach was useful to assess the level of heterogeneity in the implementation of the surveys and to explore the reasons for the variation between countries.
Isospin-symmetry-breaking effects in A∼70 nuclei within beyond-mean-field approach
Energy Technology Data Exchange (ETDEWEB)
Petrovici, A.; Andrei, O. [National Institute for Physics and Nuclear Engineering, R-077125 Bucharest (Romania)
2015-02-24
Particular isospin-symmetry-breaking probes including Coulomb energy differences (CED), mirror energy differences (MED), and triplet energy differences (TED) manifest anomalies in the A∼70 isovector triplets of nuclei. The structure of proton-rich nuclei in the A∼70 mass region suggests shape coexistence and competition between pairing correlations in different channels. Recent results concerning the interplay between isospin-mixing and shape-coexistence effects on exotic phenomena in A∼70 nuclei obtained within the beyond-mean-field complex Excited Vampir variational model with symmetry projection before variation using a realistic effective interaction in a relatively large model space are presented. Excited Vampir predictions concerning the Gamow-Teller β decay to the odd-odd N=Z {sup 66}As and {sup 70}Br nuclei correlated with the pair structure analysis in the T=1 and T=0 channel of the involved wave functions are discussed.
International Nuclear Information System (INIS)
Kuchinskii, E. Z.; Nekrasov, I. A.; Sadovskii, M. V.
2008-01-01
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 + Σ 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 dynamic 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
Field theory approach to gravitation
International Nuclear Information System (INIS)
Yilmaz, H.
1978-01-01
A number of authors considered the possibility of formulating a field-theory approach to gravitation with the claim that such an approach would uniquely lead to Einstein's theory of general relativity. In this article it is shown that the field theory approach is more generally applicable and uniqueness cannot be claimed. Theoretical and experimental reasons are given showing that the Einsteinian limit appears to be unviable
Mean field games for cognitive radio networks
Tembine, Hamidou; Tempone, Raul; Vilanova, Pedro
2012-01-01
In this paper we study mobility effect and power saving in cognitive radio networks using mean field games. We consider two types of users: primary and secondary users. When active, each secondary transmitter-receiver uses carrier sensing
Magnetic properties of mixed Ni–Cu ferrites calculated using mean field approach
Energy Technology Data Exchange (ETDEWEB)
Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, 63, 46000 Safi (Morocco); LMPHE, URAC 12, Faculté des Sciences, Université Mohamed V-Agdal, Rabat (Morocco); Hamedoun, M. [Institute for Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Benyoussef, A. [LMPHE, URAC 12, Faculté des Sciences, Université Mohamed V-Agdal, Rabat (Morocco); Institute for Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Academie Hassan II des Sciences et Techniques, Rabat (Morocco); Hlil, E.K. [Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble cedex 9 (France)
2014-08-01
The magnetic properties of spinel ferrites [Fe{sub 1−(1−x)y}{sup 3+}Cu{sub (1−x)y}{sup 2+}]{sub A}[Ni{sub x}{sup 2+}Cu{sub (1−x)(1−y)}{sup 2+}Fe{sub 1+(1−x)y}{sup 3+}]{sub B}O{sub 4} have been studied by the mean field theory (MFT) and high temperature series expansions (HTSEs) combined with the Padé approximants. The critical temperature, the saturation magnetisation (M{sub S}) and the intra-sublattice exchanges interactions (J{sub AA}(x,y), J{sub BB}(x,y) and J{sub AB}(x,y)) are obtained by using a probability distribution law. The critical exponents associate with the magnetic susceptibility have been obtained. The effect of copper doping on the magnetic properties of nickel ferrites has been examined. - Highlights: • The exchange and constants interactions of CuFe{sub 2}O{sub 4} material are obtained. • The saturation magnetisation, the critical temperature, the Curie Weiss temperature and the Curie constant of CuFe{sub 2}O{sub 4} are obtained. • The critical exponent associated with the magnetic susceptibility is given.
International Nuclear Information System (INIS)
Hatanaka, Koichiro; Umeki, Hiroyuki.
1995-01-01
Generally, geological media is modelled as porous or fractured media depending on their characteristics. Since the channels of groundwater flow and the transport paths are determined by the heterogeneity of the geological media, quantitative understanding of the heterogeneity is an important issue for modelling flow and transport processes through them. Therefore, it becomes popular way to develop statistical identification approaches of the heterogeneous field by using data from in-situ test and conduct validation studies of flow and transport models through the field by comparing with observed data. In this report, the theories of the identification approach and the concept on groundwater flow and mass transport are explained briefly and the application to tracer tests conducted at Grimsel test site, Switzerland, are described. (author)
The Meaning of Out-of-Field Teaching for Educational Leadership
du Plessis, Anna E.; Carroll, Annemaree; Gillies, Robyn M.
2017-01-01
Assigning teachers to a position for which they are not suitably qualified influences effective educational leadership. The paper reveals assumptions and misconceptions about the lived experiences of teachers in out-of-field positions and what it means for effective educational leadership. The multilayered meaning of out-of-field teaching for…
The finite state projection approach to analyze dynamics of heterogeneous populations
Johnson, Rob; Munsky, Brian
2017-06-01
Population modeling aims to capture and predict the dynamics of cell populations in constant or fluctuating environments. At the elementary level, population growth proceeds through sequential divisions of individual cells. Due to stochastic effects, populations of cells are inherently heterogeneous in phenotype, and some phenotypic variables have an effect on division or survival rates, as can be seen in partial drug resistance. Therefore, when modeling population dynamics where the control of growth and division is phenotype dependent, the corresponding model must take account of the underlying cellular heterogeneity. The finite state projection (FSP) approach has often been used to analyze the statistics of independent cells. Here, we extend the FSP analysis to explore the coupling of cell dynamics and biomolecule dynamics within a population. This extension allows a general framework with which to model the state occupations of a heterogeneous, isogenic population of dividing and expiring cells. The method is demonstrated with a simple model of cell-cycle progression, which we use to explore possible dynamics of drug resistance phenotypes in dividing cells. We use this method to show how stochastic single-cell behaviors affect population level efficacy of drug treatments, and we illustrate how slight modifications to treatment regimens may have dramatic effects on drug efficacy.
Simple Theory for the Dynamics of Mean-Field-Like Models of Glass-Forming Fluids
Szamel, Grzegorz
2017-10-01
We propose a simple theory for the dynamics of model glass-forming fluids, which should be solvable using a mean-field-like approach. The theory is based on transparent physical assumptions, which can be tested in computer simulations. The theory predicts an ergodicity-breaking transition that is identical to the so-called dynamic transition predicted within the replica approach. Thus, it can provide the missing dynamic component of the random first order transition framework. In the large-dimensional limit the theory reproduces the result of a recent exact calculation of Maimbourg et al. [Phys. Rev. Lett. 116, 015902 (2016), 10.1103/PhysRevLett.116.015902]. Our approach provides an alternative, physically motivated derivation of this result.
Ali, Ghaffar
2018-09-01
Climate change is a multidimensional phenomenon, which has various implications for the environment and socio-economic conditions of the people. Its effects are deeper in an agrarian economy which is susceptible to the vagaries of nature. Therefore, climate change directly impacts the society in different ways, and society must pay the cost. Focusing on this truth, the main objective of this research was to investigate the empirical changes and spatial heterogeneity in the climate of Pakistan in real terms using time series data. Climate change and variability in Pakistan, over time, were estimated from 1961 to 2014 using all the climate variables for the very first time. Several studies were available on climate change impacts, mitigation, and adaptation; however, it was difficult to observe exactly how much change occurred in which province and when. A multidisciplinary approach was utilized to estimate the absolute change through a combination of environmental, econometric, and remote sensing methods. Moreover, the Autoregressive Distributed Lag (ARDL) model was used to ascertain the extent of variability in climate change and information was digitalized through ground truthing. Results showed that the average temperature of Pakistan increased by 2°C between 1960 and 1987 and 4°C between 1988 and 2014, and R 2 was 0.978. The rate of temperature increased 0.09°C between 1960 and 2014. The mean annual precipitation of Pakistan increased by 478mm, and its R 2 were 0.34-0.64. The mean annual humidity of Pakistan increased by 2.94%, and the rate of humidity has been increased by 0.97% from 1988 to 2014. Notably, Sindh and Balochistan provinces have shown a significant spatial heterogeneity regarding the increase in precipitation. Statistically all variables are significant. This would serve as a baseline information for climate change-related studies in Pakistan and its application in different sectors. This would also serve the plant breeders and policymakers of
A regularized stationary mean-field game
Yang, Xianjin
2016-01-01
In the thesis, we discuss the existence and numerical approximations of solutions of a regularized mean-field game with a low-order regularization. In the first part, we prove a priori estimates and use the continuation method to obtain the existence of a solution with a positive density. Finally, we introduce the monotone flow method and solve the system numerically.
A regularized stationary mean-field game
Yang, Xianjin
2016-04-19
In the thesis, we discuss the existence and numerical approximations of solutions of a regularized mean-field game with a low-order regularization. In the first part, we prove a priori estimates and use the continuation method to obtain the existence of a solution with a positive density. Finally, we introduce the monotone flow method and solve the system numerically.
Mittra, R.; Rushdi, A.
1979-01-01
An approach for computing the geometrical optic fields reflected from a numerically specified surface is presented. The approach includes the step of deriving a specular point and begins with computing the reflected rays off the surface at the points where their coordinates, as well as the partial derivatives (or equivalently, the direction of the normal), are numerically specified. Then, a cluster of three adjacent rays are chosen to define a 'mean ray' and the divergence factor associated with this mean ray. Finally, the ampilitude, phase, and vector direction of the reflected field at a given observation point are derived by associating this point with the nearest mean ray and determining its position relative to such a ray.
Study of bubble structure in N = 20 isotones within relativistic mean-field plus BCS approach
International Nuclear Information System (INIS)
Kumawat, M.; Singh, U.K.; Jain, S.K.; Saxena, G.; Aggarwal, Mamta; Singh, S. Somorendro; Kaushik, M.
2017-01-01
Guided by various theoretical studies and encouraged with recent first experimental evidence of proton density depletion in "3"4Si, we have applied relativistic mean field plus BCS approach for systematic study of bubble structure in magic nuclei with N = 20 isotones. Our present investigations include single particle energies, deformations, separation energies as well as neutron and proton densities etc. It is found that proton sd shells (1d_5_/_2,2s_1_/_2,1d_3_/_2) in N = 20 isotones play very important role in the formation of bubble structure. The unoccupied 2s_1_/_2 state gives rise to bubble since this 2s_1_/_2 state does not have any centrifugal barrier, therefore for Z = 8 - 14 in the isotonic chain radial distributions of such state is found with peak in the interior of the nucleus with corresponding wave functions extending into the surface region. Consequently, in these nuclei with unoccupied s-state the central density found depleted as compared to the nucleus wherein this state is fully occupied. It is important to note here that in these nuclei depletion in proton density for "3"4Si is found with most significance which is in accord with the recent experiment. Moving further for higher Z value, Z = 16 and Z = 18 the 2s_1_/_2 state remains semi-occupied and contributing partially in the depletion of central density resulting semi-bubble structure for Z = 16 and 18. For Z≥20, 2s_1_/_2 state get fully occupied and no sign of bubble structures are seen for higher isotones
Flow field investigations in rotating facilities by means of stationary PIV systems
International Nuclear Information System (INIS)
Armellini, A; Mucignat, C; Casarsa, L; Giannattasio, P
2012-01-01
The flow field inside rotating test sections can be investigated by means of particle image velocimetry (PIV) operated in the phase-locked mode. With this experimental approach, the measurement system is kept fixed and it is synchronized with the periodical passage of the test section. Therefore, the direct output of the PIV measurements is the absolute velocity field, while the relative one is indirectly obtained from proper data processing that relies on accurate knowledge of the peripheral velocity field. This work provides an uncertainty analysis about the evaluation of the peripheral displacement field in phase-locked PIV measurements. The analysis leads to the detection of the levels of accuracy required in the estimation of both the angular velocity and the position of the center of rotation to ensure correct evaluation of the peripheral displacement field. In this regard, a simple methodology is proposed to evaluate the center of rotation position with an accuracy below 1 px. Finally, a procedure to pre-process the PIV images by subtracting the peripheral displacement is described. The advantages of its implementation are highlighted by the comparison with the performance of a more standard methodology where the peripheral field is subtracted from the absolute velocity field and not directly from the PIV raw data
A mean-field game economic growth model
Gomes, Diogo A.; Lafleche, Laurent; Nurbekyan, Levon
2016-01-01
Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative, rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent seeks
Mining Functional Modules in Heterogeneous Biological Networks Using Multiplex PageRank Approach.
Li, Jun; Zhao, Patrick X
2016-01-01
Identification of functional modules/sub-networks in large-scale biological networks is one of the important research challenges in current bioinformatics and systems biology. Approaches have been developed to identify functional modules in single-class biological networks; however, methods for systematically and interactively mining multiple classes of heterogeneous biological networks are lacking. In this paper, we present a novel algorithm (called mPageRank) that utilizes the Multiplex PageRank approach to mine functional modules from two classes of biological networks. We demonstrate the capabilities of our approach by successfully mining functional biological modules through integrating expression-based gene-gene association networks and protein-protein interaction networks. We first compared the performance of our method with that of other methods using simulated data. We then applied our method to identify the cell division cycle related functional module and plant signaling defense-related functional module in the model plant Arabidopsis thaliana. Our results demonstrated that the mPageRank method is effective for mining sub-networks in both expression-based gene-gene association networks and protein-protein interaction networks, and has the potential to be adapted for the discovery of functional modules/sub-networks in other heterogeneous biological networks. The mPageRank executable program, source code, the datasets and results of the presented two case studies are publicly and freely available at http://plantgrn.noble.org/MPageRank/.
International Nuclear Information System (INIS)
Ertaş, Mehmet; Keskin, Mustafa
2012-01-01
The dynamic magnetic behavior of the mixed Ising bilayer system (σ=2 and S=5/2), with a crystal-field interaction in an oscillating field are studied, within the mean-field approach, by using the Glauber-type stochastic dynamics for both ferromagnetic/ferromagnetic and antiferromagnetic/ferromagnetic interactions. The time variations of average magnetizations and the temperature dependence of the dynamic magnetizations are investigated. The dynamic phase diagrams are presented in the reduced temperature and magnetic field amplitude plane and they exhibit several ordered phases, coexistence phase regions and critical points as well as a re-entrant behavior depending on interaction parameters. -- Highlights: ► Dynamic magnetic behavior of the mixed Ising bilayer system is investigated within the Glauber-type stochastic dynamics. ► The time variations of average magnetizations are studied to find the phases. ► The temperature dependence of the dynamic magnetizations is investigated to obtain the dynamic phase transition points. ► The dynamic phase diagrams are presented and they exhibit several ordered phases, coexistence phase regions and critical points as well as a re-entrant behavior.
Energy Technology Data Exchange (ETDEWEB)
Ertaş, Mehmet [Department of Physics, Erciyes University, 38039 Kayseri (Turkey); Keskin, Mustafa, E-mail: keskin@erciyes.edu.tr [Department of Physics, Erciyes University, 38039 Kayseri (Turkey)
2012-07-23
The dynamic magnetic behavior of the mixed Ising bilayer system (σ=2 and S=5/2), with a crystal-field interaction in an oscillating field are studied, within the mean-field approach, by using the Glauber-type stochastic dynamics for both ferromagnetic/ferromagnetic and antiferromagnetic/ferromagnetic interactions. The time variations of average magnetizations and the temperature dependence of the dynamic magnetizations are investigated. The dynamic phase diagrams are presented in the reduced temperature and magnetic field amplitude plane and they exhibit several ordered phases, coexistence phase regions and critical points as well as a re-entrant behavior depending on interaction parameters. -- Highlights: ► Dynamic magnetic behavior of the mixed Ising bilayer system is investigated within the Glauber-type stochastic dynamics. ► The time variations of average magnetizations are studied to find the phases. ► The temperature dependence of the dynamic magnetizations is investigated to obtain the dynamic phase transition points. ► The dynamic phase diagrams are presented and they exhibit several ordered phases, coexistence phase regions and critical points as well as a re-entrant behavior.
The relativistic mean-field description of nuclei and nuclear dynamics
International Nuclear Information System (INIS)
Reinhard, P.G.
1989-01-01
The relativistic mean-field model of the nucleus is reviewed. It describes the nucleus as a system of Dirac-Nucleons which interact in a relativistic covariant manner via meson fields. The meson fields are treated as mean fields, i.e. as non quantal c-number fields. The effects of the Dirac sea of the nucleons is neglected. The model is interpreted as a phenomenological ansatz providing a selfconsistent relativistic description of nuclei and nuclear dynamics. It is viewed, so to say, as the relativistic generalisation of the Skyrme-Hartree-Fock ansatz. The capability and the limitations of the model to describe nuclear properties are discussed. Recent applications to spherical and deformed nuclei and to nuclear dynamics are presented. (orig.)
The effects of floodplain soil heterogeneity on meander planform shape
Motta, D.; Abad, J. D.; Langendoen, E. J.; GarcíA, M. H.
2012-09-01
Past analytical studies of meander planform development have mostly focused on the complexity of the governing equations, i.e., hydrodynamics, and less so on the stream bank resistance to erosion, whose spatial heterogeneity is difficult to describe deterministically. This motivated the use of a Monte Carlo approach to examine the effects of floodplain soils and their distribution on planform development, with the goal of including bank erosion properties in the analysis. Simulated bank erosion rates are controlled by the resistance to hydraulic erosion of the bank soils using an excess shear stress approach. The spatial distribution of critical shear stress across the floodplain is delineated on a rectangular, equidistant grid with varying degrees of variability. The corresponding erodibility coefficient is computed using a field-derived empirical relation. For a randomly disturbed distribution, in which the mean resistance to erosion exponentially increases away from the valley centerline, two relevant parameters are identified: the standard deviation of the critical shear stress distribution, which controls skewness and variability of the channel centerline, and the cross-valley increase in soil resistance, which constrains lateral migration and also affects bend skewness. For a purely random distribution, migrated centerlines exhibit larger variability for increasing spatial scales of floodplain soil heterogeneity. For equal stochastic variability of the corresponding governing parameters, relating meander migration to hydraulic erosion of the bank soils produces more variability and shape complexity than the "classic" bank migration approach of Ikeda et al. (1981), which relates migration rate to excess velocity at the outer bank. Finally, the proposed stochastic approach provides a foundation for estimating a suitable spatial density of measurements to characterize the physical properties of floodplain soils and vegetation.
Saggar, Manish; Zanesco, Anthony P; King, Brandon G; Bridwell, David A; MacLean, Katherine A; Aichele, Stephen R; Jacobs, Tonya L; Wallace, B Alan; Saron, Clifford D; Miikkulainen, Risto
2015-07-01
Meditation training has been shown to enhance attention and improve emotion regulation. However, the brain processes associated with such training are poorly understood and a computational modeling framework is lacking. Modeling approaches that can realistically simulate neurophysiological data while conforming to basic anatomical and physiological constraints can provide a unique opportunity to generate concrete and testable hypotheses about the mechanisms supporting complex cognitive tasks such as meditation. Here we applied the mean-field computational modeling approach using the scalp-recorded electroencephalogram (EEG) collected at three assessment points from meditating participants during two separate 3-month-long shamatha meditation retreats. We modeled cortical, corticothalamic, and intrathalamic interactions to generate a simulation of EEG signals recorded across the scalp. We also present two novel extensions to the mean-field approach that allow for: (a) non-parametric analysis of changes in model parameter values across all channels and assessments; and (b) examination of variation in modeled thalamic reticular nucleus (TRN) connectivity over the retreat period. After successfully fitting whole-brain EEG data across three assessment points within each retreat, two model parameters were found to replicably change across both meditation retreats. First, after training, we observed an increased temporal delay between modeled cortical and thalamic cells. This increase provides a putative neural mechanism for a previously observed reduction in individual alpha frequency in these same participants. Second, we found decreased inhibitory connection strength between the TRN and secondary relay nuclei (SRN) of the modeled thalamus after training. This reduction in inhibitory strength was found to be associated with increased dynamical stability of the model. Altogether, this paper presents the first computational approach, taking core aspects of physiology and
Stochastic quantization and mean field approximation
International Nuclear Information System (INIS)
Jengo, R.; Parga, N.
1983-09-01
In the context of the stochastic quantization we propose factorized approximate solutions for the Fokker-Planck equation for the XY and Zsub(N) spin systems in D dimensions. The resulting differential equation for a factor can be solved and it is found to give in the limit of t→infinity the mean field or, in the more general case, the Bethe-Peierls approximation. (author)
Effects of anisotropies in turbulent magnetic diffusion in mean-field solar dynamo models
Energy Technology Data Exchange (ETDEWEB)
Pipin, V. V. [Institute of Solar-Terrestrial Physics, Russian Academy of Sciences, Irkutsk 664033 (Russian Federation); Kosovichev, A. G. [Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305 (United States)
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 of 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.
Mean-field theory of anyons near Bose statistics
International Nuclear Information System (INIS)
McCabe, J.; MacKenzie, R.
1992-01-01
The validity of a mean-field approximation for a boson-based free anyon gas near Bose statistics is shown. The magnetic properties of the system is discussed in the approximation that the statistical magnetic field is uniform. It is proved that the anyon gas does not exhibit a Meissner effect in the domain of validity the approximation. (K.A.) 7 refs
Time-Dependent Mean-Field Games in the Subquadratic Case
Gomes, Diogo A.; Pimentel, Edgard A.; Sá nchez-Morgado, Hé ector
2014-01-01
In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the growth of the Hamiltonian and the dimension. This is done by combining regularity estimates for the Hamilton-Jacobi equation based on the Gagliardo-Nirenberg interpolation inequality with polynomial estimates for the Fokker-Planck equation. This technique improves substantially the previous results on the regularity of time-dependent mean-field games.
Time-Dependent Mean-Field Games in the Subquadratic Case
Gomes, Diogo A.
2014-10-14
In this paper we consider time-dependent mean-field games with subquadratic Hamiltonians and power-like local dependence on the measure. We establish existence of classical solutions under a certain set of conditions depending on both the growth of the Hamiltonian and the dimension. This is done by combining regularity estimates for the Hamilton-Jacobi equation based on the Gagliardo-Nirenberg interpolation inequality with polynomial estimates for the Fokker-Planck equation. This technique improves substantially the previous results on the regularity of time-dependent mean-field games.
Stochastic mean-field dynamics for fermions in the weak coupling limit
International Nuclear Information System (INIS)
Lacroix, D.
2005-09-01
Assuming that the effect of the residual interaction beyond mean-field is weak and can be treated as a statistical ensemble of two-body interactions, a Markovian quantum jump theory is developed for fermionic systems. In this theory, jumps occur between many-body densities formed of pairs of states D |Φ a > b | / b | |Φ a > where |Φ a > and |Φ b > are anti-symmetrized products of single-particle states. The underlying Stochastic Mean-Field (SMF) theory is discussed and applied to the monopole vibration of a spherical 40 Ca nucleus under the influence of a statistical ensemble of two-body contact interactions. In this example, the mean-field evolution of one-body observables is recovered by averaging over different stochastic trajectories while fluctuations beyond mean-field are observed. Finally, the nature of the fluctuations is discussed. (author)
International Nuclear Information System (INIS)
Zozoulenko, I V; Ihnatsenka, S
2008-01-01
We have developed a mean-field first-principles approach for studying electronic and transport properties of low dimensional lateral structures in the integer quantum Hall regime. The electron interactions and spin effects are included within the spin density functional theory in the local density approximation where the conductance, the density, the effective potentials and the band structure are calculated on the basis of the Green's function technique. In this paper we present a systematic review of the major results obtained on the energetics, spin polarization, effective g factor, magnetosubband and edge state structure of split-gate and cleaved-edge overgrown quantum wires as well as on the conductance of quantum point contacts (QPCs) and open quantum dots. In particular, we discuss how the spin-resolved subband structure, the current densities, the confining potentials, as well as the spin polarization of the electron and current densities in quantum wires and antidots evolve when an applied magnetic field varies. We also discuss the role of the electron interaction and spin effects in the conductance of open systems focusing our attention on the 0.7 conductance anomaly in the QPCs. Special emphasis is given to the effect of the electron interaction on the conductance oscillations and their statistics in open quantum dots as well as to interpretation of the related experiments on the ultralow temperature saturation of the coherence time in open dots
A Dynamic BI–Orthogonal Field Equation Approach to Efficient Bayesian Inversion
Directory of Open Access Journals (Sweden)
Tagade Piyush M.
2017-06-01
Full Text Available This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen-Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.
Applicability of self-consistent mean-field theory
International Nuclear Information System (INIS)
Guo Lu; Sakata, Fumihiko; Zhao Enguang
2005-01-01
Within the constrained Hartree-Fock (CHF) theory, an analytic condition is derived to estimate whether a concept of the self-consistent mean field is realized in the level repulsive region. The derived condition states that an iterative calculation of the CHF equation does not converge when the quantum fluctuations coming from two-body residual interaction and quadrupole deformation become larger than a single-particle energy difference between two avoided crossing orbits. By means of numerical calculation, it is shown that the analytic condition works well for a realistic case
Socio-economic applications of finite state mean field games
Gomes, Diogo A.
2014-10-06
In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments,which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems.
Stochastic mean-field dynamics for fermions in the weak coupling limit
Energy Technology Data Exchange (ETDEWEB)
Lacroix, D
2005-09-15
Assuming that the effect of the residual interaction beyond mean-field is weak and can be treated as a statistical ensemble of two-body interactions, a Markovian quantum jump theory is developed for fermionic systems. In this theory, jumps occur between many-body densities formed of pairs of states D |{phi}{sub a}> <|{phi}{sub b}| / <|{phi}{sub b} | |{phi} {sub a}> where |{phi}{sub a}> and |{phi}{sub b}> are anti-symmetrized products of single-particle states. The underlying Stochastic Mean-Field (SMF) theory is discussed and applied to the monopole vibration of a spherical {sup 40}Ca nucleus under the influence of a statistical ensemble of two-body contact interactions. In this example, the mean-field evolution of one-body observables is recovered by averaging over different stochastic trajectories while fluctuations beyond mean-field are observed. Finally, the nature of the fluctuations is discussed. (author)
Stable oscillations of a predator-prey probabilistic cellular automaton: a mean-field approach
International Nuclear Information System (INIS)
Tome, Tania; Carvalho, Kelly C de
2007-01-01
We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator-prey system. The individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired by the processes of the Lotka-Volterra model. Two levels of mean-field approximations are set up. The simple approximation is equivalent to an extended patch model, a simple metapopulation model with patches colonized by prey, patches colonized by predators and empty patches. This approximation is capable of describing the limited available space for species occupancy. The pair approximation is moreover able to describe two types of coexistence of prey and predators: one where population densities are constant in time and another displaying self-sustained time oscillations of the population densities. The oscillations are associated with limit cycles and arise through a Hopf bifurcation. They are stable against changes in the initial conditions and, in this sense, they differ from the Lotka-Volterra cycles which depend on initial conditions. In this respect, the present model is biologically more realistic than the Lotka-Volterra model
Heavy-ion interactions in relativistic mean-field models
International Nuclear Information System (INIS)
Rashdan, M.
1996-01-01
The interaction potential between spherical nuclei and the elastic scattering cross section are calculated within relativistic mean-field (linear and non-linear) models, using a generalized relativistic local density approximation. The nuclear densities are calculated self-consistently from the solution of the relativistic mean-field equations. It is found that both the linear and non-linear models predict the characteristic switching-over phenomenon of the heavy-ion nuclear potential, where the potential gets attraction with increasing energy up to some value where it reverses this behaviour. The non-linear NLC model predicts a deeper potential than the linear LW model. The elastic scattering cross section calculated within the non-linear NLC model is in better agreement with experiments than that calculated within the linear LW model. (orig.)
A simple network agreement-based approach for combining evidences in a heterogeneous sensor network
Directory of Open Access Journals (Sweden)
Raúl Eusebio-Grande
2015-12-01
Full Text Available In this research we investigate how the evidences provided by both static and mobile nodes that are part of a heterogenous sensor network can be combined to have trustworthy results. A solution relying on a network agreement-based approach was implemented and tested.
DEFF Research Database (Denmark)
Yue, Yuanzheng; Zhang, Yanfei
Structural heterogeneity plays a crucial role in determining functionality of glasses. In this work we have found that the sub-Tg enthalpy relaxation pattern in a hyperquenched glass is highly sensitive to structural heterogeneity. As a consequence, the former can be used as an effective approach...... to detect and quantify the structural heterogeneity in glass-forming liquids. However, the chemical nature of structural heterogeneity should be revealed by other means such as high resolution microscopic and spectroscopic methods. To study the impact of the structural heterogeneity on the sub-Tg relaxation...... chemical features and degrees of structural heterogeneity in glass-forming liquids. This finding contributes to the microscopic origin of both the primary and secondary relaxation in terms of structural heterogeneity. Finally the results provide insights into the relation between structural heterogeneity...
Laube, G.; Schmidt, C.; Fleckenstein, J. H.
2014-12-01
The hyporheic zone (HZ) contributes significantly to whole stream biogeochemical cycling. Biogeochemical reactions within the HZ are often transport limited, thus, understanding these reactions requires knowledge about the magnitude of hyporheic fluxes (HF) and the residence time (RT) of these fluxes within the HZ. While the hydraulics of HF are relatively well understood, studies addressing the influence of permeability heterogeneity lack systematic analysis and have even produced contradictory results (e.g. [1] vs. [2]). In order to close this gap, this study uses a statistical numerical approach to elucidate the influence of permeability heterogeneity on HF and RT. We simulated and evaluated 3750 2D-scenarios of sediment heterogeneity by means of Gaussian random fields with focus on total HF and RT distribution. The scenarios were based on ten realizations of each of all possible combinations of 15 different correlation lengths, 5 dipping angles and 5 permeability variances. Roughly 500 hyporheic stream traces were analyzed per simulation, for a total of almost two million stream traces analyzed for correlations between permeability heterogeneity, HF, and RT. Total HF and the RT variance positively correlated with permeability variance while the mean RT negatively correlated with permeability variance. In contrast, changes in correlation lengths and dipping angles had little effect on the examined properties RT and HF. These results provide a possible explanation of the seemingly contradictory conclusions of recent studies, given that the permeability variances in these studies differ by several orders of magnitude. [1] Bardini, L., Boano, F., Cardenas, M.B, Sawyer, A.H, Revelli, R. and Ridolfi, L. "Small-Scale Permeability Heterogeneity Has Negligible Effects on Nutrient Cycling in Streambeds." Geophysical Research Letters, 2013. doi:10.1002/grl.50224. [2] Zhou, Y., Ritzi, R. W., Soltanian, M. R. and Dominic, D. F. "The Influence of Streambed Heterogeneity on
On the existence of classical solutions for stationary extended mean field games
Gomes, Diogo A.; Patrizi, Stefania; Voskanyan, Vardan
2014-01-01
In this paper we consider extended stationary mean-field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean-field games in Gomes et al. (2012). In addition we use adjoint method techniques to obtain higher regularity bounds. Then we establish the existence of smooth solutions under fairly general conditions by applying the continuity method. When applied to standard stationary mean-field games as in Lasry and Lions (2006), Gomes and Sanchez-Morgado (2011) or Gomes et al. (2012) this paper yields various new estimates and regularity properties not available previously. We discuss additionally several examples where the existence of classical solutions can be proved. © 2013 Elsevier Ltd. All rights reserved.
On the existence of classical solutions for stationary extended mean field games
Gomes, Diogo A.
2014-04-01
In this paper we consider extended stationary mean-field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean-field games in Gomes et al. (2012). In addition we use adjoint method techniques to obtain higher regularity bounds. Then we establish the existence of smooth solutions under fairly general conditions by applying the continuity method. When applied to standard stationary mean-field games as in Lasry and Lions (2006), Gomes and Sanchez-Morgado (2011) or Gomes et al. (2012) this paper yields various new estimates and regularity properties not available previously. We discuss additionally several examples where the existence of classical solutions can be proved. © 2013 Elsevier Ltd. All rights reserved.
A mobile-mobile transport model for simulating reactive transport in connected heterogeneous fields
Lu, Chunhui; Wang, Zhiyuan; Zhao, Yue; Rathore, Saubhagya Singh; Huo, Jinge; Tang, Yuening; Liu, Ming; Gong, Rulan; Cirpka, Olaf A.; Luo, Jian
2018-05-01
Mobile-immobile transport models can be effective in reproducing heavily tailed breakthrough curves of concentration. However, such models may not adequately describe transport along multiple flow paths with intermediate velocity contrasts in connected fields. We propose using the mobile-mobile model for simulating subsurface flow and associated mixing-controlled reactive transport in connected fields. This model includes two local concentrations, one in the fast- and the other in the slow-flow domain, which predict both the concentration mean and variance. The normalized total concentration variance within the flux is found to be a non-monotonic function of the discharge ratio with a maximum concentration variance at intermediate values of the discharge ratio. We test the mobile-mobile model for mixing-controlled reactive transport with an instantaneous, irreversible bimolecular reaction in structured and connected random heterogeneous domains, and compare the performance of the mobile-mobile to the mobile-immobile model. The results indicate that the mobile-mobile model generally predicts the concentration breakthrough curves (BTCs) of the reactive compound better. Particularly, for cases of an elliptical inclusion with intermediate hydraulic-conductivity contrasts, where the travel-time distribution shows bimodal behavior, the prediction of both the BTCs and maximum product concentration is significantly improved. Our results exemplify that the conceptual model of two mobile domains with diffusive mass transfer in between is in general good for predicting mixing-controlled reactive transport, and particularly so in cases where the transfer in the low-conductivity zones is by slow advection rather than diffusion.
Mean-field Ohm's law and coaxial helicity injection in force-free plasmas
International Nuclear Information System (INIS)
Weening, R. H.
2011-01-01
A theoretical analysis of steady-state coaxial helicity injection (CHI) in force-free plasmas is presented using a parallel mean-field Ohm's law that includes resistivity η and hyper-resistivity Λ terms. Using Boozer coordinates, a partial differential equation is derived for the time evolution of the mean-field poloidal magnetic flux, or magnetic Hamiltonian function, from the parallel mean-field Ohm's law. A general expression is obtained from the mean-field theory for the efficiency of CHI current drive in force-free plasmas. Inductances of internal energy, magnetic helicity, and poloidal magnetic flux are used to characterize axisymmetric plasma equilibria that have a model current profile. Using the model current profile, a method is suggested to determine the level of magnetohydrodynamic activity at the magnetic axis and the consequent deviation from the completely relaxed Taylor state. The mean-field Ohm's law model suggests that steady-state CHI can be viewed most simply as a boundary layer problem.
Time-odd mean fields in covariant density functional theory: Rotating systems
International Nuclear Information System (INIS)
Afanasjev, A. V.; Abusara, H.
2010-01-01
Time-odd mean fields (nuclear magnetism) and their impact on physical observables in rotating nuclei are studied in the framework of covariant density functional theory (CDFT). It is shown that they have profound effect on the dynamic and kinematic moments of inertia. Particle number, configuration, and rotational frequency dependencies of their impact on the moments of inertia have been analyzed in a systematic way. Nuclear magnetism can also considerably modify the band crossing features such as crossing frequencies and the properties of the kinematic and dynamic moments of inertia in the band crossing region. The impact of time-odd mean fields on the moments of inertia in the regions away from band crossing only weakly depends on the relativistic mean-field parametrization, reflecting good localization of the properties of time-odd mean fields in CDFT. The moments of inertia of normal-deformed nuclei considerably deviate from the rigid-body value. On the contrary, superdeformed and hyperdeformed nuclei have the moments of inertia which are close to rigid-body value. The structure of the currents in rotating frame, their microscopic origin, and the relations to the moments of inertia have been systematically analyzed. The phenomenon of signature separation in odd-odd nuclei, induced by time-odd mean fields, has been analyzed in detail.
Experimental oligopolies modeling: A dynamic approach based on heterogeneous behaviors
Cerboni Baiardi, Lorenzo; Naimzada, Ahmad K.
2018-05-01
In the rank of behavioral rules, imitation-based heuristics has received special attention in economics (see [14] and [12]). In particular, imitative behavior is considered in order to understand the evidences arising in experimental oligopolies which reveal that the Cournot-Nash equilibrium does not emerge as unique outcome and show that an important component of the production at the competitive level is observed (see e.g.[1,3,9] or [7,10]). By considering the pioneering groundbreaking approach of [2], we build a dynamical model of linear oligopolies where heterogeneous decision mechanisms of players are made explicit. In particular, we consider two different types of quantity setting players characterized by different decision mechanisms that coexist and operate simultaneously: agents that adaptively adjust their choices towards the direction that increases their profit are embedded with imitator agents. The latter ones use a particular form of proportional imitation rule that considers the awareness about the presence of strategic interactions. It is noteworthy that the Cournot-Nash outcome is a stationary state of our models. Our thesis is that the chaotic dynamics arousing from a dynamical model, where heterogeneous players are considered, are capable to qualitatively reproduce the outcomes of experimental oligopolies.
Energy Technology Data Exchange (ETDEWEB)
Gengembre, N
2000-07-01
A model for the field radiated by an ultrasonic transducer into anisotropic and heterogeneous media is developed in this thesis. This work aims at improving the settings and interpretations of non destructive tests in welded structures. Since the shape of the transducer is assumed arbitrary, its emitting surface is divided into small elementary sources. The overall field at an observation point in the medium is derived by a summation of the elementary contributions of these point sources. An accurate and numerically efficient model is developed using the Geometrical Optics approximation to evaluate these elementary contributions. Two different forms of this approximation are used: The stationary phase method and the pencil method. The first one is based on an exact formulation of the field and is used for fields into anisotropic and homogeneous media. It allows to emphasize specific configurations for which additional developments are required; this need arises for calculation points in the vicinity of caustics (zones of high intensity). This problem is solved for both harmonic and transient fields, for points laying on caustics or in their neighborhood. The pencil method is used for the calculation of fields in heterogeneous media, although it does not permit to overcome the problem of caustics. It is also advantageous for the implementation of the model. A comparison of both above-mentioned methods is drawn, and their equivalence is proved for some cases. The calculation of fields in anisotropic and heterogeneous media is performed using both methods together, and then the problem of caustics is also treated. Calculated fields into welded components are shown and compared with experiments or with a numerical model, in order to validate the developments. (author)
Scalable and fast heterogeneous molecular simulation with predictive parallelization schemes
International Nuclear Information System (INIS)
Guzman, Horacio V.; Junghans, Christoph; Kremer, Kurt; Stuehn, Torsten
2017-01-01
Multiscale and inhomogeneous molecular systems are challenging topics in the field of molecular simulation. In particular, modeling biological systems in the context of multiscale simulations and exploring material properties are driving a permanent development of new simulation methods and optimization algorithms. In computational terms, those methods require parallelization schemes that make a productive use of computational resources for each simulation and from its genesis. Here, we introduce the heterogeneous domain decomposition approach, which is a combination of an heterogeneity-sensitive spatial domain decomposition with an a priori rearrangement of subdomain walls. Within this approach and paper, the theoretical modeling and scaling laws for the force computation time are proposed and studied as a function of the number of particles and the spatial resolution ratio. We also show the new approach capabilities, by comparing it to both static domain decomposition algorithms and dynamic load-balancing schemes. Specifically, two representative molecular systems have been simulated and compared to the heterogeneous domain decomposition proposed in this work. Finally, these two systems comprise an adaptive resolution simulation of a biomolecule solvated in water and a phase-separated binary Lennard-Jones fluid.
Scalable and fast heterogeneous molecular simulation with predictive parallelization schemes
Guzman, Horacio V.; Junghans, Christoph; Kremer, Kurt; Stuehn, Torsten
2017-11-01
Multiscale and inhomogeneous molecular systems are challenging topics in the field of molecular simulation. In particular, modeling biological systems in the context of multiscale simulations and exploring material properties are driving a permanent development of new simulation methods and optimization algorithms. In computational terms, those methods require parallelization schemes that make a productive use of computational resources for each simulation and from its genesis. Here, we introduce the heterogeneous domain decomposition approach, which is a combination of an heterogeneity-sensitive spatial domain decomposition with an a priori rearrangement of subdomain walls. Within this approach, the theoretical modeling and scaling laws for the force computation time are proposed and studied as a function of the number of particles and the spatial resolution ratio. We also show the new approach capabilities, by comparing it to both static domain decomposition algorithms and dynamic load-balancing schemes. Specifically, two representative molecular systems have been simulated and compared to the heterogeneous domain decomposition proposed in this work. These two systems comprise an adaptive resolution simulation of a biomolecule solvated in water and a phase-separated binary Lennard-Jones fluid.
Impacts of Streambed Heterogeneity and Anisotropy on Residence Time of Hyporheic Zone.
Liu, Suning; Chui, Ting Fong May
2018-05-01
The hyporheic zone (HZ), which is the region beneath or alongside a streambed, plays an important role in the stream's ecology. The duration that a water molecule or a solute remains within the HZ, or residence time (RT), is one of the most common metrics used to evaluate the function of the HZ. The RT is greatly influenced by the streambed's hydraulic conductivity (K), which is intrinsically difficult to characterize due to its heterogeneity and anisotropy. Many laboratory and numerical studies of the HZ have simplified the streambed K to a constant, thus producing RT values that may differ from those gathered from the field. Some studies have considered the heterogeneity of the HZ, but very few have accounted for anisotropy or the natural K distributions typically found in real streambeds. This study developed numerical models in MODFLOW to examine the influence of heterogeneity and anisotropy, and that of the natural K distribution in a streambed, on the RT of the HZ. Heterogeneity and anisotropy were both found to shorten the mean and median RTs while increasing the range of the RTs. Moreover, heterogeneous K fields arranged in a more orderly pattern had longer RTs than those with random K distributions. These results could facilitate the design of streambed K values and distributions to achieve the desired RT during river restoration. They could also assist the translation of results from the more commonly considered homogeneous and/or isotropic conditions into heterogeneous and anisotropic field situations. © 2017, National Ground Water Association.
Quantum mean-field approximations for nuclear bound states and tunneling
International Nuclear Information System (INIS)
Negele, J.W.; Levit, S.; Paltiel, Z.; Massachusetts Inst. of Tech., Cambridge
1979-01-01
A conceptual framework has been presented in which observables are approximated in terms of a self-consistent quantum mean-field theory. Since the SPA (Stationary Phase Approximation) determines the optimal mean field to approximate a given observable, it is natural that when one changes the observable, the best mean field to describe it changes as well. Although the theory superficially appears applicable to any observable expressible in terms of an evolution operator, for example an S-matrix element, one would have to go far beyond the SPA to adequately approximate the overlap of two many-body wave functions. The most salient open problems thus concern quantitative assessment of the accuracy of the SPA, reformulation of the theory to accomodate hard cores, and selection of sensible expectation values of few-body operators to address in scattering problems
Particle Production and Effective Thermalization in Inhomogeneous Mean Field Theory
Aarts, G.; Smit, J.
2000-01-01
As a toy model for dynamics in nonequilibrium quantum field theory we consider the abelian Higgs model in 1+1 dimensions with fermions. In the approximate dynamical equations, inhomogeneous classical (mean) Bose fields are coupled to quantized fermion fields, which are treated with a mode function
Out-of-equilibrium dynamical mean-field equations for the perceptron model
Agoritsas, Elisabeth; Biroli, Giulio; Urbani, Pierfrancesco; Zamponi, Francesco
2018-02-01
Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their applicability and importance, a detailed study of their Langevin dynamics has never been performed yet. Here we derive the mean-field dynamical equations that describe the continuous random perceptron in the thermodynamic limit, in a very general setting with arbitrary noise and friction kernels, not necessarily related by equilibrium relations. We derive the equations in two ways: via a dynamical cavity method, and via a path-integral approach in its supersymmetric formulation. The end point of both approaches is the reduction of the dynamics of the system to an effective stochastic process for a representative dynamical variable. Because the perceptron is formally very close to a system of interacting particles in a high dimensional space, the methods we develop here can be transferred to the study of liquid and glasses in high dimensions. Potentially interesting applications are thus the study of the glass transition in active matter, the study of the dynamics around the jamming transition, and the calculation of rheological properties in driven systems.
σ-SCF: A direct energy-targeting method to mean-field excited states.
Ye, Hong-Zhou; Welborn, Matthew; Ricke, Nathan D; Van Voorhis, Troy
2017-12-07
The mean-field solutions of electronic excited states are much less accessible than ground state (e.g., Hartree-Fock) solutions. Energy-based optimization methods for excited states, like Δ-SCF (self-consistent field), tend to fall into the lowest solution consistent with a given symmetry-a problem known as "variational collapse." In this work, we combine the ideas of direct energy-targeting and variance-based optimization in order to describe excited states at the mean-field level. The resulting method, σ-SCF, has several advantages. First, it allows one to target any desired excited state by specifying a single parameter: a guess of the energy of that state. It can therefore, in principle, find all excited states. Second, it avoids variational collapse by using a variance-based, unconstrained local minimization. As a consequence, all states-ground or excited-are treated on an equal footing. Third, it provides an alternate approach to locate Δ-SCF solutions that are otherwise hardly accessible by the usual non-aufbau configuration initial guess. We present results for this new method for small atoms (He, Be) and molecules (H 2 , HF). We find that σ-SCF is very effective at locating excited states, including individual, high energy excitations within a dense manifold of excited states. Like all single determinant methods, σ-SCF shows prominent spin-symmetry breaking for open shell states and our results suggest that this method could be further improved with spin projection.
σ-SCF: A direct energy-targeting method to mean-field excited states
Ye, Hong-Zhou; Welborn, Matthew; Ricke, Nathan D.; Van Voorhis, Troy
2017-12-01
The mean-field solutions of electronic excited states are much less accessible than ground state (e.g., Hartree-Fock) solutions. Energy-based optimization methods for excited states, like Δ-SCF (self-consistent field), tend to fall into the lowest solution consistent with a given symmetry—a problem known as "variational collapse." In this work, we combine the ideas of direct energy-targeting and variance-based optimization in order to describe excited states at the mean-field level. The resulting method, σ-SCF, has several advantages. First, it allows one to target any desired excited state by specifying a single parameter: a guess of the energy of that state. It can therefore, in principle, find all excited states. Second, it avoids variational collapse by using a variance-based, unconstrained local minimization. As a consequence, all states—ground or excited—are treated on an equal footing. Third, it provides an alternate approach to locate Δ-SCF solutions that are otherwise hardly accessible by the usual non-aufbau configuration initial guess. We present results for this new method for small atoms (He, Be) and molecules (H2, HF). We find that σ-SCF is very effective at locating excited states, including individual, high energy excitations within a dense manifold of excited states. Like all single determinant methods, σ-SCF shows prominent spin-symmetry breaking for open shell states and our results suggest that this method could be further improved with spin projection.
International Nuclear Information System (INIS)
Frank, T D; Mongkolsakulvong, S
2015-01-01
In a previous study strongly nonlinear autoregressive (SNAR) models have been introduced as a generalization of the widely-used time-discrete autoregressive models that are known to apply both to Markov and non-Markovian systems. In contrast to conventional autoregressive models, SNAR models depend on process mean values. So far, only linear dependences have been studied. We consider the case in which process mean values can have a nonlinear impact on the processes under consideration. It is shown that such models describe Markov and non-Markovian many-body systems with mean field forces that exhibit a nonlinear impact on single subsystems. We exemplify that such nonlinear dependences can describe order-disorder phase transitions of time-discrete Markovian and non-Markovian many-body systems. The relevant order parameter equations are derived and issues of stability and stationarity are studied. (paper)
Low pressure arc discharge lamp apparatus with magnetic field generating means
Grossman, Mark W.; George, William A.; Maya, Jakob
1987-01-01
A low-pressure arc discharge apparatus having a magnetic field generating means for increasing the output of a discharge lamp is disclosed. The magnetic field generating means, which in one embodiment includes a plurality of permanent magnets, is disposed along the lamp for applying a constant transverse magnetic field over at least a portion of the positive discharge column produced in the arc discharge lamp operating at an ambient temperature greater than about 25.degree. C.
Low pressure arc discharge lamp apparatus with magnetic field generating means
Grossman, M.W.; George, W.A.; Maya, J.
1987-10-06
A low-pressure arc discharge apparatus having a magnetic field generating means for increasing the output of a discharge lamp is disclosed. The magnetic field generating means, which in one embodiment includes a plurality of permanent magnets, is disposed along the lamp for applying a constant transverse magnetic field over at least a portion of the positive discharge column produced in the arc discharge lamp operating at an ambient temperature greater than about 25 C. 3 figs.
Explicit Solutions for One-Dimensional Mean-Field Games
Prazeres, Mariana
2017-01-01
In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested
Two numerical methods for mean-field games
Gomes, Diogo A.
2016-01-01
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Two numerical methods for mean-field games
Gomes, Diogo A.
2016-01-09
Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.
Rädler, K.-H.
This article elucidates the basic ideas of electrodynamics and magnetohydrodynamics of mean fields in turbulently moving conducting fluids. It is stressed that the connection of the mean electromotive force with the mean magnetic field and its first spatial derivatives is in general neither local nor instantaneous and that quite a few claims concerning pretended failures of the mean-field concept result from ignoring this aspect. In addition to the mean-field dynamo mechanisms of α2 and α Ω type several others are considered. Much progress in mean-field electrodynamics and magnetohydrodynamics results from the test-field method for calculating the coefficients that determine the connection of the mean electromotive force with the mean magnetic field. As an important example the memory effect in homogeneous isotropic turbulence is explained. In magnetohydrodynamic turbulence there is the possibility of a mean electromotive force that is primarily independent of the mean magnetic field and labeled as Yoshizawa effect. Despite of many efforts there is so far no convincing comprehensive theory of α quenching, that is, the reduction of the α effect with growing mean magnetic field, and of the saturation of mean-field dynamos. Steps toward such a theory are explained. Finally, some remarks on laboratory experiments with dynamos are made.
Isospin-dependent properties of asymmetric nuclear matter in relativistic mean-field models
Chen, Lie-Wen; Ko, Che Ming; Li, Bao-An
2007-01-01
Using various relativistic mean-field models, including the nonlinear ones with meson field self-interactions, those with density-dependent meson-nucleon couplings, and the point-coupling models without meson fields, we have studied the isospin-dependent bulk and single-particle properties of asymmetric nuclear matter. In particular, we have determined the density dependence of nuclear symmetry energy from these different relativistic mean-field models and compare the results with the constra...
Understanding and exploiting nanoscale surface heterogeneity for particle and cell manipulation
Kalasin, Surachate
surface region sufficiently attractive for capture. Though neglecting hydrodynamics, the resulting (kappa-1a)1/2 power law scaling for the density of patches at the adhesion threshold roughly captures the general shape of the data. The study also reveals that at high ionic strength, particle-surface interactions are most influenced by the patchy surface heterogeneity; however, at low ionic strengths, the system becomes most sensitive to the average system properties. Thus for heterogeneous interfaces, the extent to which heterogeneity is influential depends on other factors (particle size, ionic strength). While this comprises a crossover from heterogeneity-dominated to mean field behavior, it is worth noting that even in the mean field regime, the spacing between patches always exceeds the Debye length, making the regions of different surface charge always distinct. Comparison with the simulations of Duffadar and Davis reveals that the criterion for particle capture is a nearly constant number of cationic patches per unit area of contact between a particle and a heterogeneous collector. The heterogeneous surface model displays a shear crossover seen with bacteria and other complex systems: At low shear, particle capture is enhanced, while at higher shears it is reduced. This behavior, sometimes rationalized in terms of the complex energy landscapes of biological bonds, is clearly explained in the heterogeneity model. For weakly adhesive systems engaging only a few adhesive elements or receptors, shear compromises the ability of a few bonds to capture particles. For more strongly adhesive systems, shear increases particle transport. The convolution of this competition leads to the non-monotonic effect of shear seen in biology. The complex variety of particle behaviors combined with the large number of independently variable parameters, each with different scaling of interfacial forces, necessitates a state-space approach to mapping regimes interactions and motion
Socio-economic applications of finite state mean field games.
Gomes, Diogo; Velho, Roberto M; Wolfram, Marie-Therese
2014-11-13
In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments, which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
Self-consistent mean field forces in turbulent plasmas: Current and momentum relaxation
International Nuclear Information System (INIS)
Hegna, C.C.
1997-08-01
The properties of turbulent plasmas are described using the two-fluid equations. Under some modest assumptions, global constraints for the turbulent mean field forces that act on the ion and electron fluids are derived. These constraints imply a functional form for the parallel mean field forces in the Ohm's law and the momentum balance equation. These forms suggest that the fluctuations attempt to relax the plasma to a state where both the current and the bulk plasma momentum are aligned along the mean magnetic field with proportionality constants that are global constants. Observations of flow profile evolution during discrete dynamo activity in reversed field pinch experiments are interpreted
Indirect estimation of signal-dependent noise with nonadaptive heterogeneous samples.
Azzari, Lucio; Foi, Alessandro
2014-08-01
We consider the estimation of signal-dependent noise from a single image. Unlike conventional algorithms that build a scatterplot of local mean-variance pairs from either small or adaptively selected homogeneous data samples, our proposed approach relies on arbitrarily large patches of heterogeneous data extracted at random from the image. We demonstrate the feasibility of our approach through an extensive theoretical analysis based on mixture of Gaussian distributions. A prototype algorithm is also developed in order to validate the approach on simulated data as well as on real camera raw images.
Dynamic characterization of oil fields, complex stratigraphically using genetic algorithms
International Nuclear Information System (INIS)
Gonzalez, Santiago; Hidrobo, Eduardo A
2004-01-01
A novel methodology is presented in this paper for the characterization of highly heterogeneous oil fields by integration of the oil fields dynamic information to the static updated model. The objective of the oil field's characterization process is to build an oil field model, as realistic as possible, through the incorporation of all the available information. The classical approach consists in producing a model based in the oil field's static information, having as the process final stage the validation model with the dynamic information available. It is important to clarify that the term validation implies a punctual process by nature, generally intended to secure the required coherence between productive zones and petrophysical properties. The objective of the proposed methodology is to enhance the prediction capacity of the oil field's model by previously integrating, parameters inherent to the oil field's fluid dynamics by a process of dynamic data inversion through an optimization procedure based on evolutionary computation. The proposed methodology relies on the construction of the oil field's high-resolution static model, escalated by means of hybrid techniques while aiming to preserve the oil field's heterogeneity. Afterwards, using an analytic simulator as reference, the scaled model is methodically modified by means of an optimization process that uses genetic algorithms and production data as conditional information. The process's final product is a model that observes the static and dynamic conditions of the oil field with the capacity to minimize the economic impact that generates production historical adjustments to the simulation tasks. This final model features some petrophysical properties (porosity, permeability and water saturation), as modified to achieve a better adjustment of the simulated production's history versus the real one history matching. Additionally, the process involves a slight modification of relative permeability, which has
Dispersivity in heterogeneous permeable media
International Nuclear Information System (INIS)
Chesnut, D.A.
1994-01-01
When one fluid displaces another through a one-dimensional porous medium, the composition changes from pure displacing fluid at the inlet to pure displaced fluid some distance downstream. The distance over which an arbitrary percentage of this change occurs is defined as the mixing zone length, which increases with increasing average distance traveled by the displacement front. For continuous injection, the mixing zone size can be determined from a breakthrough curve as the time required for the effluent displacing fluid concentration to change from, say, 10% to 90%. In classical dispersion theory, the mixing zone grows in proportion to the square root of the mean distance traveled, or, equivalently, to the square root of the mean breakthrough time. In a multi-dimensional heterogeneous medium, especially at field scales, the size of the mixing zone grows almost linearly with mean distance or travel time. If an observed breakthrough curve is forced to fit the, clinical theory, the resulting effective dispersivity, instead of being constant, also increases almost linearly with the spatial or temporal scale of the problem. This occurs because the heterogeneity in flow properties creates a corresponding velocity distribution along the different flow pathways from the inlet to the outlet of the system. Mixing occurs mostly at the outlet, or wherever the fluid is sampled, rather than within the medium. In this paper, we consider the effects. of this behavior on radionuclide or other contaminant migration
Dispersivity in heterogeneous permeable media
International Nuclear Information System (INIS)
Chesnut, D.A.
1994-01-01
When one fluid displaces another through a one-dimensional porous medium, the composition changes from pure displacing fluid at the inlet to pure displaced fluid some distance downstream. The distance over which an arbitrary percentage (typically 80%) of this change occurs is defined as the mixing zone length, which increases with increasing average distance traveled by the displacement front. Alternatively, for continuous injection, the mixing zone size can be determined from a breakthrough curve as the time required for the effluent displacing fluid concentration to change from, say, 10% to 90%. In classical dispersion theory, the mixing zone grows in proportion to the square root of the mean distance traveled, or, equivalently, to the square root of the mean breakthrough time. In a multi-dimensional heterogeneous medium, especially at field scales, the size of the mixing zone grows almost linearly with mean distance or travel time. If an observed breakthrough curve is forced to fit the classical theory, the resulting effective dispersivity, instead of being constant, also increases almost linearly with the spatial or temporal scale of the problem. This occurs because the heterogeneity in flow properties creates a corresponding velocity distribution along the different flow pathways from the inlet to the outlet of the system. Mixing occurs mostly at the outlet, or wherever the fluid is sampled, rather than within the medium. In this paper, we consider the effects of this behavior on radionuclide or other contaminant migration
Nuclear matter in relativistic mean field theory with isovector scalar meson.
Energy Technology Data Exchange (ETDEWEB)
Kubis, S.; Kutschera, M. [Institute of Nuclear Physics, Cracow (Poland)
1996-12-01
Relativistic mean field (RMF) theory of nuclear matter with the isovector scalar mean field corresponding to the {delta}-meson [a{sub 0}(980)] is studied. While the {delta}-meson field vanishes in symmetric nuclear matter, it can influence properties of asymmetric nuclear matter in neutron stars. The RMF contribution due to {delta}-field to the nuclear symmetry energy is negative. To fit the empirical value, E{sub s}{approx}30 MeV, a stronger {rho}-meson coupling is required than in absence of the {delta}-field. The energy per particle of neutron star matter is than larger at high densities than the one with no {delta}-field included. Also, the proton fraction of {beta}-stable matter increases. Splitting of proton and neutron effective masses due to the {delta}-field can affect transport properties of neutron star matter. (author). 4 refs, 6 figs.
Nuclear matter in relativistic mean field theory with isovector scalar meson
International Nuclear Information System (INIS)
Kubis, S.; Kutschera, M.
1996-12-01
Relativistic mean field (RMF) theory of nuclear matter with the isovector scalar mean field corresponding to the δ-meson [a 0 (980)] is studied. While the δ-meson field vanishes in symmetric nuclear matter, it can influence properties of asymmetric nuclear matter in neutron stars. The RMF contribution due to δ-field to the nuclear symmetry energy is negative. To fit the empirical value, E s ∼30 MeV, a stronger ρ-meson coupling is required than in absence of the δ-field. The energy per particle of neutron star matter is than larger at high densities than the one with no δ-field included. Also, the proton fraction of β-stable matter increases. Splitting of proton and neutron effective masses due to the δ-field can affect transport properties of neutron star matter. (author). 4 refs, 6 figs
Generalized quantum mean-field systems and their application to ultracold atoms
International Nuclear Information System (INIS)
Trimborn-Witthaut, Friederike Annemarie
2011-01-01
Strongly interacting many-body systems consisting of a large number of indistinguishable particles play an important role in many areas of physics. Though such systems are hard to deal with theoretically since the dimension of the respective Hilbert space increases exponentially both in the particle number and in the number of system modes. Therefore, approximations are of considerable interest. The mean-field approximation describes the behaviour in the macroscopic limit N→∞, which leads to an effective nonlinear single-particle problem. Although this approximation is widely used, rigorous results on the applicability and especially on finite size corrections are extremely rare. One prominent example of strongly interacting many-body systems are ultracold atoms in optical lattices, which are a major subject of this thesis. Typically these systems consist of a large but well-defined number of particles, such that corrections to the mean-field limit can be systematically studied. This thesis is divided into two parts: In the first part we study generalized quantum mean-field systems in a C * -algebraic framework. These systems are characterized by their intrinsic permutation symmetry. In the limit of infinite system size, N→∞, the intensive observables converge to the commutative algebra of weak * -continuous functions on the single particle state space. To quantify the deviations from the meanfield prediction for large but finite N, we establish a differential calculus for state space functions and provide a generalized Taylor expansion around the mean-field limit. Furthermore, we introduce the algebra of macroscopic fluctuations around the mean-field limit and prove a quantum version of the central limit theorem. On the basis of these results, we give a detailed study of the finite size corrections to the ground state energy and establish bounds, for both the quantum and the classical case. Finally, we restrict ourselves to the subspace of Bose
Detection of structural heterogeneity of glass melts
DEFF Research Database (Denmark)
Yue, Yuanzheng
2004-01-01
The structural heterogeneity of both supercooled liquid and molten states of silicate has been studied using calorimetric method. The objects of this study are basaltic glasses and liquids. Two experimental approaches are taken to detect the structural heterogeneity of the liquids. One is the hyp......The structural heterogeneity of both supercooled liquid and molten states of silicate has been studied using calorimetric method. The objects of this study are basaltic glasses and liquids. Two experimental approaches are taken to detect the structural heterogeneity of the liquids. One...... is the hyperquench-anneal-calorimetric scan approach, by which the structural information of a basaltic supercooled liquid and three binary silicate liquids is acquired. Another is the calorimetrically repeated up- and downscanning approach, by which the structural heterogeneity, the intermediate range order...... is discussed. The ordered structure of glass melts above the liquidus temperature is indirectly characterized by use of X-ray diffraction method. The new approaches are of importance for monitoring the glass melting and forming process and for improving the physical properties of glasses and glass fibers....
Generating functional of the mean field in quantum electrodynamics with non-stable vacuum
International Nuclear Information System (INIS)
Gitman, D.M.; Kuchin, V.A.
1981-01-01
Generating functional for calculating a mean field, in the case of unstable vacuum, in quantum field theory has been suggested. Continual representation for the generating functional of the mean field has been found in the case of quantum electrodynamics with an external field. Generating electron-positron pairs from vacuum [ru
The impact of heterogeneous response on coupled spreading dynamics in multiplex networks
Nie, Xiaoyu; Tang, Ming; Zou, Yong; Guan, Shuguang; Zhou, Jie
2017-10-01
Many recent studies have demonstrated that individual awareness of disease may significantly affect the spreading process of infectious disease. In the majority of these studies, the response of the awareness is generally treated homogeneously. Considering of diversity and heterogeneity in the human behavior which widely exist under different circumstances, in this paper we study heterogeneous response when people are aware of the prevalence of infectious diseases. Specifically, we consider that an individual with more neighbors may take more preventive measures as a reaction when he is aware of the disease. A suppression strength is introduced to describe such heterogeneity, and we find that a more evident heterogeneity may cause a more effective suppressing effect to the spreading of epidemics. A mean-field theory is developed to support the results which are verified on the multiplex networks with different interlayer degree correlation.
An XML-based loose-schema approach to managing diagnostic data in heterogeneous formats
Energy Technology Data Exchange (ETDEWEB)
Naito, O., E-mail: naito.osamu@jaea.go.j [Japan Atomic Energy Agency, 801-1 Mukouyama, Naka, Ibaraki 311-0193 (Japan)
2010-07-15
An approach to managing diagnostic data in heterogenous formats by using XML-based (eXtensible Markup Language) tag files is discussed. The tag file functions like header information in ordinary data formats but it is separate from the main body of data, human readable, and self-descriptive. Thus all the necessary information for reading the contents of data can be obtained without prior information or reading the data body itself. In this paper, modeling of diagnostic data and its representation in XML are studied and a very primitive implementation of this approach in C++ is presented. The overhead of manipulating XML in a proof-of-principle code was found to be small. The merits, demerits, and possible extensions of this approach are also discussed.
An XML-based loose-schema approach to managing diagnostic data in heterogeneous formats
International Nuclear Information System (INIS)
Naito, O.
2010-01-01
An approach to managing diagnostic data in heterogenous formats by using XML-based (eXtensible Markup Language) tag files is discussed. The tag file functions like header information in ordinary data formats but it is separate from the main body of data, human readable, and self-descriptive. Thus all the necessary information for reading the contents of data can be obtained without prior information or reading the data body itself. In this paper, modeling of diagnostic data and its representation in XML are studied and a very primitive implementation of this approach in C++ is presented. The overhead of manipulating XML in a proof-of-principle code was found to be small. The merits, demerits, and possible extensions of this approach are also discussed.
Spectral Gap Estimates in Mean Field Spin Glasses
Ben Arous, Gérard; Jagannath, Aukosh
2018-05-01
We show that mixing for local, reversible dynamics of mean field spin glasses is exponentially slow in the low temperature regime. We introduce a notion of free energy barriers for the overlap, and prove that their existence imply that the spectral gap is exponentially small, and thus that mixing is exponentially slow. We then exhibit sufficient conditions on the equilibrium Gibbs measure which guarantee the existence of these barriers, using the notion of replicon eigenvalue and 2D Guerra Talagrand bounds. We show how these sufficient conditions cover large classes of Ising spin models for reversible nearest-neighbor dynamics and spherical models for Langevin dynamics. Finally, in the case of Ising spins, Panchenko's recent rigorous calculation (Panchenko in Ann Probab 46(2):865-896, 2018) of the free energy for a system of "two real replica" enables us to prove a quenched LDP for the overlap distribution, which gives us a wider criterion for slow mixing directly related to the Franz-Parisi-Virasoro approach (Franz et al. in J Phys I 2(10):1869-1880, 1992; Kurchan et al. J Phys I 3(8):1819-1838, 1993). This condition holds in a wider range of temperatures.
Contradiction analysis: towards a dialectical approach in ergonomics field interventions
Directory of Open Access Journals (Sweden)
Dimitris Nathanael
2015-03-01
Full Text Available The present paper is a methodological contribution to the ergonomics field intervention process. It proposes a perspective on work analysis based on the dialectics notion of contradictions. Contradiction analysis is proposed as being complementary to more established work decomposition methods. The aim of including such an analysis is to frame various heterogeneous determinants of a work activity in practical terms, swiftly and in a manner that preserves its multifaceted unity and essence. Such framing is of particular value when considering alternative design solutions because it provides a practical means for anticipating the effects and side effects of proposed changes. The proposed method is inspired by two theoretical constructs: (i contradiction, as used in Cultural Historical Activity Theory, and (ii regulation, as developed and used by the francophone tradition of the ergonomics of activity. Two brief examples of its use are presented, and its usefulness, possible pitfalls and need for further developments are discussed.
Isotopes in heterogeneous catalysis
Hargreaves, Justin SJ
2006-01-01
The purpose of this book is to review the current, state-of-the-art application of isotopic methods to the field of heterogeneous catalysis. Isotopic studies are arguably the ultimate technique in in situ methods for heterogeneous catalysis. In this review volume, chapters have been contributed by experts in the field and the coverage includes both the application of specific isotopes - Deuterium, Tritium, Carbon-14, Sulfur-35 and Oxygen-18 - as well as isotopic techniques - determination of surface mobility, steady state transient isotope kinetic analysis, and positron emission profiling.
A heterogeneous computing environment to solve the 768-bit RSA challenge
Kleinjung, Thorsten; Bos, Joppe Willem; Lenstra, Arjen K.; Osvik, Dag Arne; Aoki, Kazumaro; Contini, Scott; Franke, Jens; Thomé, Emmanuel; Jermini, Pascal; Thiémard, Michela; Leyland, Paul; Montgomery, Peter L.; Timofeev, Andrey; Stockinger, Heinz
2010-01-01
In December 2009 the 768-bit, 232-digit number RSA-768 was factored using the number field sieve. Overall, the computational challenge would take more than 1700 years on a single, standard core. In the article we present the heterogeneous computing approach, involving different compute clusters and Grid computing environments, used to solve this problem.
International Nuclear Information System (INIS)
Morales P, J.R.; Avila P, P.
1996-01-01
If we have consider the maximum permissible levels showed for the case of oysters, it results forbidding to collect oysters at the four stations of the El Chijol Channel ( Veracruz, Mexico), as well as along the channel itself, because the metal concentrations studied exceed these limits. In this case the application of Welch tests were not necessary. For the water hyacinth the means of the treatments were unequal in Fe, Cu, Ni, and Zn. This case is more illustrative, for the conclusion has been reached through the application of the Welch tests to treatments with heterogeneous variances. (Author)
Pairing gaps from nuclear mean-field models
International Nuclear Information System (INIS)
Bender, M.; Rutz, K.; Maruhn, J.A.
2000-01-01
We discuss the pairing gap, a measure for nuclear pairing correlations, in chains of spherical, semi-magic nuclei in the framework of self-consistent nuclear mean-field models. The equations for the conventional BCS model and the approximate projection-before-variation Lipkin-Nogami method are formulated in terms of local density functionals for the effective interaction. We calculate the Lipkin-Nogami corrections of both the mean-field energy and the pairing energy. Various definitions of the pairing gap are discussed as three-point, four-point and five-point mass-difference formulae, averaged matrix elements of the pairing potential, and single-quasiparticle energies. Experimental values for the pairing gap are compared with calculations employing both a delta pairing force and a density-dependent delta interaction in the BCS and Lipkin-Nogami model. Odd-mass nuclei are calculated in the spherical blocking approximation which neglects part of the the core polarization in the odd nucleus. We find that the five-point mass difference formula gives a very robust description of the odd-even staggering, other approximations for the gap may differ from that up to 30% for certain nuclei. (orig.)
Decision support tool for soil sampling of heterogeneous pesticide (chlordecone) pollution.
Clostre, Florence; Lesueur-Jannoyer, Magalie; Achard, Raphaël; Letourmy, Philippe; Cabidoche, Yves-Marie; Cattan, Philippe
2014-02-01
When field pollution is heterogeneous due to localized pesticide application, as is the case of chlordecone (CLD), the mean level of pollution is difficult to assess. Our objective was to design a decision support tool to optimize soil sampling. We analyzed the CLD heterogeneity of soil content at 0-30- and 30-60-cm depth. This was done within and between nine plots (0.4 to 1.8 ha) on andosol and ferralsol. We determined that 20 pooled subsamples per plot were a satisfactory compromise with respect to both cost and accuracy. Globally, CLD content was greater for andosols and the upper soil horizon (0-30 cm). Soil organic carbon cannot account for CLD intra-field variability. Cropping systems and tillage practices influence the CLD content and distribution; that is CLD pollution was higher under intensive banana cropping systems and, while upper soil horizon was more polluted than the lower one with shallow tillage (pollution in the soil profile. The decision tool we proposed compiles and organizes these results to better assess CLD soil pollution in terms of sampling depth, distance, and unit at field scale. It accounts for sampling objectives, farming practices (cropping system, tillage), type of soil, and topographical characteristics (slope) to design a relevant sampling plan. This decision support tool is also adaptable to other types of heterogeneous agricultural pollution at field level.
IDENTIFIABILITY VERSUS HETEROGENEITY IN GROUNDWATER MODELING SYSTEMS
Directory of Open Access Journals (Sweden)
A M BENALI
2003-06-01
Full Text Available Review of history matching of reservoirs parameters in groundwater flow raises the problem of identifiability of aquifer systems. Lack of identifiability means that there exists parameters to which the heads are insensitive. From the guidelines of the study of the homogeneous case, we inspect the identifiability of the distributed transmissivity field of heterogeneous groundwater aquifers. These are derived from multiple realizations of a random function Y = log T whose probability distribution function is normal. We follow the identifiability of the autocorrelated block transmissivities through the measure of the sensitivity of the local derivatives DTh = (∂hi ∕ ∂Tj computed for each sample of a population N (0; σY, αY. Results obtained from an analysis of Monte Carlo type suggest that the more a system is heterogeneous, the less it is identifiable.
The signal and comprehension approach: decoding and meaning building
Directory of Open Access Journals (Sweden)
Rajaa Aquil
2013-01-01
Full Text Available This paper discusses Egyptian colloquial Arabic connected speech as a listening problem. The paper proposes a modified approach for teaching listening: The Signal and Comprehension Approach. It is an approach that enhances listening as a skill to attain comprehension in any listening task. The approach focuses on signals laden with linguistic phonological changes that make deciphering connected speech very difficult. By adopting the proposed approach, learners can develop not only their listening skills but also their listening strategies and meaning building. It trains the language learner to crack the code in order to construct meaning. The approach includes pedagogical listening tasks that are based on topdown or world knowledge as well as bottom-up or data driven processes. The discussed tasks use songs as a venue of connected speech. These tasks come from an online course offered through the Georgia Institute of Technology (Georgia Tech that uses songs to teach Arabic language, culture and history.
Mean-field Ensemble Kalman Filter
Law, Kody
2015-01-07
A proof of convergence of the standard EnKF generalized to non-Gaussian state space models is provided. A density-based deterministic approximation of the mean-field limiting EnKF (MFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for d < 2 . The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which arises in both deterministic and standard EnKF. Numerical results support and extend the theory.
Temperature dependence of magnetic anisotropy and magnetostriction: Beyond the mean-field theory
International Nuclear Information System (INIS)
Millev, Y.; Faehnle, M.
1994-05-01
The first nonvanishing magnetic anisotropy coefficient is calculated as a function of temperature for any spin quantum number and all temperatures below the Curie temperature for the case of face-centred cubic symmetry within the random-phase approximation (RPA). A detailed and instructive comparison between the mean-field and the RPA predictions is carried out. The RPA magnetization curves are also given for the first time for spins S>1/2. Most of the theoretical considerations are quite general as regard lattice type and even decoupling scheme and can thus be applied straightforwardly to other cases of interest. The progress reported here has been attained with the help of a new simplified and improved parametric approach and of a recent calculation of the average occupation number of magnons within the RPA. In particular, the new approach makes unnecessary the solving of integral equations so that the proposed procedure is especially simple and practically versatile in applications to any particular anisotropic material. (author). Refs, 6 figs
Directory of Open Access Journals (Sweden)
Chen Zeng
2012-01-01
Full Text Available Knowledge of soil hydraulic parameters for the van Genuchten function is important to characterize soil water movement for watershed management. Accurate and rapid prediction of soil water flow in heterogeneous gravel soil has become a hot topic in recent years. However, it is difficult to precisely estimate hydraulic parameters in a heterogeneous soil with rock fragments. In this study, the HYDRUS-2D numerical model was used to evaluate hydraulic parameters for heterogeneous gravel soil that was irregularly embedded with rock fragments in a grape production base. The centrifugal method (CM, tensiometer method (TM and inverse solution method (ISM were compared for various parameters in the van Genuchten function. The soil core method (SCM, disc infiltration method (DIM and inverse solution method (ISM were also investigated for measuring saturated hydraulic conductivity. Simulation with the DIM approach revealed a problem of overestimating soil water infiltration whereas simulation with the SCM approach revealed a problem of underestimating water movement as compared to actual field observation. The ISM approach produced the best simulation result even though this approach slightly overestimated soil moisture by ignoring the impact of rock fragments. This study provides useful information on the overall evaluation of soil hydraulic parameters attained with different measurement methods for simulating soil water movement and distribution in heterogeneous gravel soil.
On the initial conditions of time-dependent mean-field equations of evolution. Pt. 2
International Nuclear Information System (INIS)
Troudet, T.; Paris-11 Univ., 91 - Orsay
1986-01-01
We analyze the problem so far untouched of determining the initial mean-field wavefunction in the context of zero-temperature mean-field descriptions of time-dependent expectation values and quantum fluctuations of nuclear observables. The nucleus, at zero temperature, is taken to be in a low-lying excited many-body eigenstate and is approximated by the corresponding RPA wavefunction as a continuous superposition of coherent states (i.e. Slater determinants). A generating function Gsub(A)(lambda) for time-dependent expectation values and quantum fluctuations is constructed within the formalism of functional integration. By applying the saddle-point method to the functional action of Gsub(A)(lambda) and then taking its lambda-derivatives, we recover the well-known TDHF theory and propose a simple determination of the initial Slater determinant for an appropriate mean-field description of time-dependent expectation values. The analog mean-field description of quadratic-quantum fluctuations proceeds similarly and in addition includes the contribution of the uncorrelated TDHF-RPA phonons coupled to collective excitations of the initial (static) mean-field configuration. When the collective TDHF-RPA excitations are solely taken into account, we obtain an improved version of the Balian-Veneroni dispersion formula by showing how to determine the initial mean-field wavefunction. By first taking the lambda-derivatives of Gsub(A)(lambda) before applying the saddle-point method, the initial mean-field wavefunction is found to be non-linearly coupled to the mean-field dynamics themselves. In return, and in contrast to the first quantization scheme, these both depend non-trivially upon the observable A being measured so that approximations must be proposed to simplify the resulting mean-field equations. (orig.)
Availability analysis for heterogeneous nucleation in a uniform electric field
Saidi, M H
2003-01-01
Industrial demands for more compact heat exchangers are a motivation to find new technology features. Electrohydrodynamics (EHD) is introduced as a promising phenomenon for heat transfer enhancement mechanisms. Similar to any new technology, EHD has not been understood completely yet and require more fundamental studies. In boiling phase change phenomena, nucleation is the dominant mechanism in heat transfer. Because of higher performance in heat transfer, nucleate boiling is considered as the main regime in thermal components. Hence, bubble dynamic investigation is a means to evaluate heat transfer. This study investigate bubble formation, including homogeneous and heterogeneous nucleation, from a thermodynamic point of view. Change in availability due to bubble embryo nucleation is discussed. Stability criteria for these systems are theoretically studied and results are discussed considering experimental data. In addition, a conceptual discussion on entropy generation in a thermodynamic system under electri...
Evaluation of an energy-based fatigue approach considering mean stress effects
Energy Technology Data Exchange (ETDEWEB)
Kabir, S. M. Humayun [Chittagong University of Engineering and Technology, Chittagong (Bangladesh); Yeo, Tae In [University of Ulsan, Ulsan (Korea, Republic of)
2014-04-15
In this paper, an attempt is made to extend the total strain energy approach for predicting the fatigue life subjected to mean stress under uniaxial state. The effects of means stress on the fatigue failure of a ferritic stainless steel and high pressure tube steel are studied under strain-controlled low cycle fatigue condition. Based on the fatigue results from different strain ratios, modified total strain energy density approach is proposed to account for the mean stress effects. The proposed damage parameter provides convenient means of evaluating fatigue life with mean stress effects considering the fact that the definitions used for measuring strain energies are the same as in the fully-reversed cycling (R = -1). A good agreement is observed between experimental life and predicted life using proposed approach. Two other mean stress models (Smith-Watson-Topper model and Morrow model) are also used to evaluate the low cycle fatigue data. Based on a simple statistical estimator, the proposed approach is compared with these models and is found realistic.
Evaluation of an energy-based fatigue approach considering mean stress effects
International Nuclear Information System (INIS)
Kabir, S. M. Humayun; Yeo, Tae In
2014-01-01
In this paper, an attempt is made to extend the total strain energy approach for predicting the fatigue life subjected to mean stress under uniaxial state. The effects of means stress on the fatigue failure of a ferritic stainless steel and high pressure tube steel are studied under strain-controlled low cycle fatigue condition. Based on the fatigue results from different strain ratios, modified total strain energy density approach is proposed to account for the mean stress effects. The proposed damage parameter provides convenient means of evaluating fatigue life with mean stress effects considering the fact that the definitions used for measuring strain energies are the same as in the fully-reversed cycling (R = -1). A good agreement is observed between experimental life and predicted life using proposed approach. Two other mean stress models (Smith-Watson-Topper model and Morrow model) are also used to evaluate the low cycle fatigue data. Based on a simple statistical estimator, the proposed approach is compared with these models and is found realistic.
Yu, Huai-Zhong; Yin, Xiang-Chu; Zhu, Qing-Yong; Yan, Yu-Ding
2006-12-01
The concept of state vector stems from statistical physics, where it is usually used to describe activity patterns of a physical field in its manner of coarsegrain. In this paper, we propose an approach by which the state vector was applied to describe quantitatively the damage evolution of the brittle heterogeneous systems, and some interesting results are presented, i.e., prior to the macro-fracture of rock specimens and occurrence of a strong earthquake, evolutions of the four relevant scalars time series derived from the state vectors changed anomalously. As retrospective studies, some prominent large earthquakes occurred in the Chinese Mainland (e.g., the M 7.4 Haicheng earthquake on February 4, 1975, and the M 7.8 Tangshan earthquake on July 28, 1976, etc) were investigated. Results show considerable promise that the time-dependent state vectors could serve as a kind of precursor to predict earthquakes.
International Nuclear Information System (INIS)
Niksic, T.; Vretenar, D.; Ring, P.
2006-01-01
The framework of relativistic self-consistent mean-field models is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum and particle-number projected relativistic wave functions. The geometry is restricted to axially symmetric shapes, and the intrinsic wave functions are generated from the solutions of the relativistic mean-field+Lipkin-Nogami BCS equations, with a constraint on the mass quadrupole moment. The model employs a relativistic point-coupling (contact) nucleon-nucleon effective interaction in the particle-hole channel, and a density-independent δ-interaction in the pairing channel. Illustrative calculations are performed for 24 Mg, 32 S, and 36 Ar, and compared with results obtained employing the model developed in the first part of this work, i.e., without particle-number projection, as well as with the corresponding nonrelativistic models based on Skyrme and Gogny effective interactions
A General Stochastic Maximum Principle for SDEs of Mean-field Type
International Nuclear Information System (INIS)
Buckdahn, Rainer; Djehiche, Boualem; Li Juan
2011-01-01
We study the optimal control for stochastic differential equations (SDEs) of mean-field type, in which the coefficients depend on the state of the solution process as well as of its expected value. Moreover, the cost functional is also of mean-field type. This makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. For a general action space a Peng’s-type stochastic maximum principle (Peng, S.: SIAM J. Control Optim. 2(4), 966–979, 1990) is derived, specifying the necessary conditions for optimality. This maximum principle differs from the classical one in the sense that here the first order adjoint equation turns out to be a linear mean-field backward SDE, while the second order adjoint equation remains the same as in Peng’s stochastic maximum principle.
Characterizing heterogeneous cellular responses to perturbations.
Slack, Michael D; Martinez, Elisabeth D; Wu, Lani F; Altschuler, Steven J
2008-12-09
Cellular populations have been widely observed to respond heterogeneously to perturbation. However, interpreting the observed heterogeneity is an extremely challenging problem because of the complexity of possible cellular phenotypes, the large dimension of potential perturbations, and the lack of methods for separating meaningful biological information from noise. Here, we develop an image-based approach to characterize cellular phenotypes based on patterns of signaling marker colocalization. Heterogeneous cellular populations are characterized as mixtures of phenotypically distinct subpopulations, and responses to perturbations are summarized succinctly as probabilistic redistributions of these mixtures. We apply our method to characterize the heterogeneous responses of cancer cells to a panel of drugs. We find that cells treated with drugs of (dis-)similar mechanism exhibit (dis-)similar patterns of heterogeneity. Despite the observed phenotypic diversity of cells observed within our data, low-complexity models of heterogeneity were sufficient to distinguish most classes of drug mechanism. Our approach offers a computational framework for assessing the complexity of cellular heterogeneity, investigating the degree to which perturbations induce redistributions of a limited, but nontrivial, repertoire of underlying states and revealing functional significance contained within distinct patterns of heterogeneous responses.
Heterogeneity in pineapple fruit quality results from plant heterogeneity at flower induction.
Fassinou Hotegni, V Nicodème; Lommen, Willemien J M; Agbossou, Euloge K; Struik, Paul C
2014-01-01
Heterogeneity in fruit quality constitutes a major constraint in agri-food chains. In this paper the sources of the heterogeneity in pineapple in the field were studied in four experiments in commercial pineapple fields. The aims were to determine (a) whether differences in pineapple fruit quality among individual fruits are associated with differences in vigor of the individual plants within the crop at the time of artificial flower induction; and (b) whether the side shoots produced by the plant during the generative phase account for the fruit quality heterogeneity. Two pineapple cultivars were considered: cv. Sugarloaf and cv. Smooth Cayenne. Plant vigor at the time of artificial flower induction was measured by three variates: the number of functional leaves, the D-leaf length and their cross product. Fruit quality attributes measured at harvest time included external attributes (weight and height of fruit, infructescence and crown) and internal quality attributes [total soluble solids (TSS), pH, translucent flesh]. Results showed that the heterogeneity in fruit weight was a consequence of the heterogeneity in vigor of the plants at the moment of flower induction; that effect was mainly on the infructescence weight and less or not on the crown weight. The associations between plant vigor variates at flower induction and the internal quality attributes of the fruit were poor and/or not consistent across experiments. The weight of the slips (side shoots) explained part of the heterogeneity in fruit weight, infructescence weight and fruit height in cv. Sugarloaf. Possibilities for reducing the variation in fruit quality by precise cultural practices are discussed.
Heterogeneity in pineapple fruit quality results from plant heterogeneity at flower induction
Directory of Open Access Journals (Sweden)
V. Nicodeme eFassinou Hotegni
2014-12-01
Full Text Available Heterogeneity in fruit quality constitutes a major constraint in agri-food chains. In this paper the sources of the heterogeneity in pineapple in the field were studied in four experiments in commercial pineapple fields. The aims were to determine (a whether differences in pineapple fruit quality among individual fruits are associated with differences in vigor of the individual plants within the crop at the time of artificial flower induction; and (b whether the side shoots produced by the plant during the generative phase account for the fruit quality heterogeneity. Two pineapple cultivars were considered: cv. Sugarloaf and cv. Smooth Cayenne. Plant vigor at the time of artificial flower induction was measured by three variates: the number of functional leaves, the D-leaf length and their cross product. Fruit quality attributes measured at harvest time included external attributes (weight and height of fruit, infructescence and crown and internal quality attributes (total soluble solids, pH, translucent flesh. Results showed that the heterogeneity in fruit weight was a consequence of the heterogeneity in vigor of the plants at the moment of flower induction; that effect was mainly on the infructescence weight and less or not on the crown weight. The association between plant vigor variates at flower induction and the internal quality attributes of the fruit were poor and/or not consistent across experiments. The weight of the slips (side shoots, explained part of the heterogeneity in fruit weight, infructescence weight and fruit height in cv. Sugarloaf. Possibilities for reducing the variation in fruit quality by precise cultural practices are discussed.
International Nuclear Information System (INIS)
Lin, Boqiang; Du, Kerui
2014-01-01
The importance of technology heterogeneity in estimating economy-wide energy efficiency has been emphasized by recent literature. Some studies use the metafrontier analysis approach to estimate energy efficiency. However, for such studies, some reliable priori information is needed to divide the sample observations properly, which causes a difficulty in unbiased estimation of energy efficiency. Moreover, separately estimating group-specific frontiers might lose some common information across different groups. In order to overcome these weaknesses, this paper introduces a latent class stochastic frontier approach to measure energy efficiency under heterogeneous technologies. An application of the proposed model to Chinese energy economy is presented. Results show that the overall energy efficiency of China's provinces is not high, with an average score of 0.632 during the period from 1997 to 2010. - Highlights: • We introduce a latent class stochastic frontier approach to measure energy efficiency. • Ignoring technological heterogeneity would cause biased estimates of energy efficiency. • An application of the proposed model to Chinese energy economy is presented. • There is still a long way for China to develop an energy efficient regime
Energy Technology Data Exchange (ETDEWEB)
Matsuzaki, M. [Fukuoka Univ. of Education, Dept. of Physics, Munakata, Fukuoka (Japan); Tanigawa, T.
1999-08-01
We propose a simple method to reproduce the {sup 1}S{sub 0} pairing properties of nuclear matter, which are obtained by a sophisticated model, by introducing a density-independent cutoff into the relativistic mean field model. This applies well to the physically relevant density range. (author)
Interactive macroeconomics stochastic aggregate dynamics with heterogeneous and interacting agents
Di Guilmi, Corrado
2017-01-01
One of the major problems of macroeconomic theory is the way in which the people exchange goods in decentralized market economies. There are major disagreements among macroeconomists regarding tools to influence required outcomes. Since the mainstream efficient market theory fails to provide an internal coherent framework, there is a need for an alternative theory. The book provides an innovative approach for the analysis of agent based models, populated by the heterogeneous and interacting agents in the field of financial fragility. The text is divided in two parts; the first presents analytical developments of stochastic aggregation and macro-dynamics inference methods. The second part introduces macroeconomic models of financial fragility for complex systems populated by heterogeneous and interacting agents. The concepts of financial fragility and macroeconomic dynamics are explained in detail in separate chapters. The statistical physics approach is applied to explain theories of macroeconomic modelling a...
Molson, J W; Frind, E O
2012-01-01
Protection and sustainability of water supply wells requires the assessment of vulnerability to contamination and the delineation of well capture zones. Capture zones, or more generally, time-of-travel zones corresponding to specific contaminant travel times, are most commonly delineated using advective particle tracking. More recently, the capture probability approach has been used in which a probability of capture of P=1 is assigned to the well and the growth of a probability-of-capture plume is tracked backward in time using an advective-dispersive transport model. This approach accounts for uncertainty due to local-scale heterogeneities through the use of macrodispersion. In this paper, we develop an alternative approach to capture zone delineation by applying the concept of mean life expectancy E (time remaining before being captured by the well), and we show how life expectancy E is related to capture probability P. Either approach can be used to delineate time-of-travel zones corresponding to specific travel times, as well as the ultimate capture zone. The related concept of mean groundwater age A (time since recharge) can also be applied in the context of defining the vulnerability of a pumped aquifer. In the same way as capture probability, mean life expectancy and groundwater age account for local-scale uncertainty or unresolved heterogeneities through macrodispersion, which standard particle tracking neglects. The approach is tested on 2D and 3D idealized systems, as well as on several watershed-scale well fields within the Regional Municipality of Waterloo, Ontario, Canada. Copyright © 2011 Elsevier B.V. All rights reserved.
Biomarker discovery in heterogeneous tissue samples -taking the in-silico deconfounding approach
Directory of Open Access Journals (Sweden)
Parida Shreemanta K
2010-01-01
Full Text Available Abstract Background For heterogeneous tissues, such as blood, measurements of gene expression are confounded by relative proportions of cell types involved. Conclusions have to rely on estimation of gene expression signals for homogeneous cell populations, e.g. by applying micro-dissection, fluorescence activated cell sorting, or in-silico deconfounding. We studied feasibility and validity of a non-negative matrix decomposition algorithm using experimental gene expression data for blood and sorted cells from the same donor samples. Our objective was to optimize the algorithm regarding detection of differentially expressed genes and to enable its use for classification in the difficult scenario of reversely regulated genes. This would be of importance for the identification of candidate biomarkers in heterogeneous tissues. Results Experimental data and simulation studies involving noise parameters estimated from these data revealed that for valid detection of differential gene expression, quantile normalization and use of non-log data are optimal. We demonstrate the feasibility of predicting proportions of constituting cell types from gene expression data of single samples, as a prerequisite for a deconfounding-based classification approach. Classification cross-validation errors with and without using deconfounding results are reported as well as sample-size dependencies. Implementation of the algorithm, simulation and analysis scripts are available. Conclusions The deconfounding algorithm without decorrelation using quantile normalization on non-log data is proposed for biomarkers that are difficult to detect, and for cases where confounding by varying proportions of cell types is the suspected reason. In this case, a deconfounding ranking approach can be used as a powerful alternative to, or complement of, other statistical learning approaches to define candidate biomarkers for molecular diagnosis and prediction in biomedicine, in
Predicting Upscaled Behavior of Aqueous Reactants in Heterogeneous Porous Media
Wright, E. E.; Hansen, S. K.; Bolster, D.; Richter, D. H.; Vesselinov, V. V.
2017-12-01
When modeling reactive transport, reaction rates are often overestimated due to the improper assumption of perfect mixing at the support scale of the transport model. In reality, fronts tend to form between participants in thermodynamically favorable reactions, leading to segregation of reactants into islands or fingers. When such a configuration arises, reactions are limited to the interface between the reactive solutes. Closure methods for estimating control-volume-effective reaction rates in terms of quantities defined at the control volume scale do not presently exist, but their development is crucial for effective field-scale modeling. We attack this problem through a combination of analytical and numerical means. Specifically, we numerically study reactive transport through an ensemble of realizations of two-dimensional heterogeneous porous media. We then employ regression analysis to calibrate an analytically-derived relationship between reaction rate and various dimensionless quantities representing conductivity-field heterogeneity and the respective strengths of diffusion, reaction and advection.
Smouse, P E; Dyer, R J; Westfall, R D; Sork, V L
2001-02-01
Gene flow is a key factor in the spatial genetic structure in spatially distributed species. Evolutionary biologists interested in microevolutionary processess and conservation biologists interested in the impact of landscape change require a method that measures the real time process of gene movement. We present a novel two-generation (parent-offspring) approach to the study of genetic structure (TwoGener) that allows us to quantify heterogeneity among the male gamete pools sampled by maternal trees scattered across the landscape and to estimate mean pollination distance and effective neighborhood size. First, we describe the model's elements: genetic distance matrices to estimate intergametic distances, molecular analysis of variance to determine whether pollen profiles differ among mothers, and optimal sampling considerations. Second, we evaluate the model's effectiveness by simulating spatially distributed populations. Spatial heterogeneity in male gametes can be estimated by phiFT, a male gametic analogue of Wright's F(ST) and an inverse function of mean pollination distance. We illustrate TwoGener in cases where the male gamete can be categorically or ambiguously determined. This approach does not require the high level of genetic resolution needed by parentage analysis, but the ambiguous case is vulnerable to bias in the absence of adequate genetic resolution. Finally, we apply TwoGener to an empirical study of Quercus alba in Missouri Ozark forests. We find that phiFT = 0.06, translating into about eight effective pollen donors per female and an effective pollination neighborhood as a circle of radius about 17 m. Effective pollen movement in Q. alba is more restricted than previously realized, even though pollen is capable of moving large distances. This case study illustrates that, with a modest investment in field survey and laboratory analysis, the TwoGener approach permits inferences about landscape-level gene movements.
Malpetti, Daniele; Roscilde, Tommaso
2017-02-01
The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical
The implications of heterogeneity for repository performance assessments
International Nuclear Information System (INIS)
Jackson, C.P.; Porter, J.D.; Morris, S.T.; Herbert, A.W.
1991-01-01
We outline the current views of the Nirex Disposal Safety Assessment Team on heterogeneity, we describe the pragmatic approach to modelling the consequences of heterogeneity that is being currently used, we present work that is being undertaken in the Nirex Safety Assessment Research Programme to develop improved models and we discuss the implications of heterogeneity for site investigation. We point out the need to develop simple models for use in probabilistic analyses. Heterogeneity leads to dispersion, which is currently modelled using a simple diffusion-like model. We discuss the differences between structured heterogeneity, such as fracture zones, and random heterogeneity. We consider that the geostatistical approach to modelling random heterogeneity is probably that most suitable for the needs of Nirex. More measurements are needed in order to characterize heterogeneous media than to characterize homogeneous media. 18 refs., 4 figs
Socio-economic applications of finite state mean field games
Gomes, Diogo A.; Machado Velho, Roberto; Wolfram, Marie Therese
2014-01-01
In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite
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.
Mean-field theory of differential rotation in density stratified turbulent convection
Rogachevskii, I.
2018-04-01
A mean-field theory of differential rotation in a density stratified turbulent convection has been developed. This theory is based on the combined effects of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. A coupled system of dynamical budget equations consisting in the equations for the Reynolds stress, the entropy fluctuations and the turbulent heat flux has been solved. To close the system of these equations, the spectral approach, which is valid for large Reynolds and Péclet numbers, has been applied. The adopted model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with the rotation rate. This theory yields the radial profile of the differential rotation which is in agreement with that for the solar differential rotation.
Parity doubling structure of nucleon at non-zero density in the holographic mean field theory
Directory of Open Access Journals (Sweden)
He Bing-Ran
2014-06-01
Full Text Available We summarize our recent work in which we develope the holographic mean field approach to study the dense baryonic matter in a bottom-up holographic QCD model including baryons and scalar mesons in addition to vector mesons. We first show that, at zero density, the rate of the chiral invariant mass of nucleon is controlled by the ratio of the infrared boundary values of two baryon fields included in the model. Then, at non-zero density, we find that the chiral condensate decreases with the increasing density indicating the partial restoration of the chiral symmetry. Our result shows that the more amount of the proton mass comes from the chiral symmetry breaking, the faster the effective nucleon mass decrease with density.
Non-degeneracy, Mean Field Equations and the Onsager Theory of 2D Turbulence
Bartolucci, Daniele; Jevnikar, Aleks; Lee, Youngae; Yang, Wen
2018-04-01
The understanding of some large energy, negative specific heat states in the Onsager description of 2D turbulence seem to require the analysis of a subtle open problem about bubbling solutions of the mean field equation. Motivated by this application we prove that, under suitable non-degeneracy assumptions on the associated m-vortex Hamiltonian, the m-point bubbling solutions of the mean field equation are non-degenerate as well. Then we deduce that the Onsager mean field equilibrium entropy is smooth and strictly convex in the high energy regime on domains of second kind.
Instability in relativistic mean-field theories of nuclear matter
International Nuclear Information System (INIS)
Friman, B.L.; Henning, P.A.
1988-01-01
We investigate the stability of the nuclear matter ground state with respect to small-perturbations of the meson fields in relativistic mean-field theories. The popular σ-ω model is shown to have an instability at about twice the nuclear density, which gives rise to a new ground state with periodic spin alignment. Taking into account the contributions of the Dirac sea properly, this instability vanishes. Consequences for relativistic heavy-ion-collisions are discussed briefly. (orig.)
Instability in relativistic mean-field theories of nuclear matter
International Nuclear Information System (INIS)
Friman, B.L.; Henning, P.A.
1988-01-01
We investigate the stability of the nuclear matter ground state with respect to small perturbations of the meson fields in relativistic mean-field theories. The popular σ-ω model is shown to have an instability at about twice the nuclear density, which gives rise to a new ground state with periodic spin alignment. Taking into account the contributions of the Dirac sea properly, this instability vanishes. Consequences for relativistic heavy-ion collisions are discussed briefly. (orig.)
Vector solution for the mean electromagnetic fields in a layer of random particles
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.
A Ranking Approach on Large-Scale Graph With Multidimensional Heterogeneous Information.
Wei, Wei; Gao, Bin; Liu, Tie-Yan; Wang, Taifeng; Li, Guohui; Li, Hang
2016-04-01
Graph-based ranking has been extensively studied and frequently applied in many applications, such as webpage ranking. It aims at mining potentially valuable information from the raw graph-structured data. Recently, with the proliferation of rich heterogeneous information (e.g., node/edge features and prior knowledge) available in many real-world graphs, how to effectively and efficiently leverage all information to improve the ranking performance becomes a new challenging problem. Previous methods only utilize part of such information and attempt to rank graph nodes according to link-based methods, of which the ranking performances are severely affected by several well-known issues, e.g., over-fitting or high computational complexity, especially when the scale of graph is very large. In this paper, we address the large-scale graph-based ranking problem and focus on how to effectively exploit rich heterogeneous information of the graph to improve the ranking performance. Specifically, we propose an innovative and effective semi-supervised PageRank (SSP) approach to parameterize the derived information within a unified semi-supervised learning framework (SSLF-GR), then simultaneously optimize the parameters and the ranking scores of graph nodes. Experiments on the real-world large-scale graphs demonstrate that our method significantly outperforms the algorithms that consider such graph information only partially.
Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model
Erban, Radek
2009-01-01
A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs, for example, in the modeling of cell-cycle regulation. It is shown that the stochastic system possesses oscillatory solutions even for parameter values for which the mean-field model does not oscillate. The dependence of the mean period of these oscillations on the parameters of the model (kinetic rate constants) and the size of the system (number of molecules present) are studied. Our approach is based on the chemical Fokker-Planck equation. To gain some insight into the advantages and disadvantages of the method, a simple one-dimensional chemical switch is first analyzed, and then the chemical SNIPER problem is studied in detail. First, results obtained by solving the Fokker-Planck equation numerically are presented. Then an asymptotic analysis of the Fokker-Planck equation is used to derive explicit formulae for the period of oscillation as a function of the rate constants and as a function of the system size. © 2009 Society for Industrial and Applied Mathematics.
Mean field theory of nuclei and shell model. Present status and future outlook
International Nuclear Information System (INIS)
Nakada, Hitoshi
2003-01-01
Many of the recent topics of the nuclear structure are concerned on the problems of unstable nuclei. It has been revealed experimentally that the nuclear halos and the neutron skins as well as the cluster structures or the molecule-like structures can be present in the unstable nuclei, and the magic numbers well established in the stable nuclei disappear occasionally while new ones appear. The shell model based on the mean field approximation has been successfully applied to stable nuclei to explain the nuclear structure as the finite many body system quantitatively and it is considered as the standard model at present. If the unstable nuclei will be understood on the same model basis or not is a matter related to fundamental principle of nuclear structure theories. In this lecture, the fundamental concept and the framework of the theory of nuclear structure based on the mean field theory and the shell model are presented to make clear the problems and to suggest directions for future researches. At first fundamental properties of nuclei are described under the subtitles: saturation and magic numbers, nuclear force and effective interactions, nuclear matter, and LS splitting. Then the mean field theory is presented under subtitles: the potential model, the mean field theory, Hartree-Fock approximation for nuclear matter, density dependent force, semiclassical mean field theory, mean field theory and symmetry, Skyrme interaction and density functional, density matrix expansion, finite range interactions, effective masses, and motion of center of mass. The subsequent section is devoted to the shell model with the subtitles: beyond the mean field approximation, core polarization, effective interaction of shell model, one-particle wave function, nuclear deformation and shell model, and shell model of cross shell. Finally structure of unstable nuclei is discussed with the subtitles: general remark on the study of unstable nuclear structure, asymptotic behavior of wave
Sanyal, Soumya; Jain, Amit; Das, Sajal K.; Biswas, Rupak
2003-01-01
In this paper, we propose a distributed approach for mapping a single large application to a heterogeneous grid environment. To minimize the execution time of the parallel application, we distribute the mapping overhead to the available nodes of the grid. This approach not only provides a fast mapping of tasks to resources but is also scalable. We adopt a hierarchical grid model and accomplish the job of mapping tasks to this topology using a scheduler tree. Results show that our three-phase algorithm provides high quality mappings, and is fast and scalable.
Shieh, Gwowen; Jan, Show-Li
2015-01-01
The general formulation of a linear combination of population means permits a wide range of research questions to be tested within the context of ANOVA. However, it has been stressed in many research areas that the homogeneous variances assumption is frequently violated. To accommodate the heterogeneity of variance structure, the…
Engdahl, N.B.; Vogler, E.T.; Weissmann, G.S.
2010-01-01
River-aquifer exchange is considered within a transition probability framework along the Rio Grande in Albuquerque, New Mexico, to provide a stochastic estimate of aquifer heterogeneity and river loss. Six plausible hydrofacies configurations were determined using categorized drill core and wetland survey data processed through the TPROGS geostatistical package. A base case homogeneous model was also constructed for comparison. River loss was simulated for low, moderate, and high Rio Grande stages and several different riverside drain stage configurations. Heterogeneity effects were quantified by determining the mean and variance of the K field for each realization compared to the root-mean-square (RMS) error of the observed groundwater head data. Simulation results showed that the heterogeneous models produced smaller estimates of loss than the homogeneous approximation. Differences between heterogeneous and homogeneous model results indicate that the use of a homogeneous K in a regional-scale model may result in an overestimation of loss but comparable RMS error. We find that the simulated river loss is dependent on the aquifer structure and is most sensitive to the volumetric proportion of fines within the river channel. Copyright 2010 by the American Geophysical Union.
Energy Technology Data Exchange (ETDEWEB)
Farajzadeh, R. [Shell International Exploration and Production, Houston, TX (United States); Ranganathan, P.; Zitha, P.L.J.; Bruining, J. [Delft Univ. of Technology, Delft (Netherlands)
2010-07-01
This paper investigated the effect of heterogeneity on the character of natural-convection flow of carbon dioxide (CO{sub 2}) in aquifers and on the dissolution rate of CO{sub 2} in brine, contributing to a better understanding of the effect of heterogeneity on CO{sub 2} mass transfer in aquifers, which is necessary for efficient storage of CO{sub 2} in aquifers. The aquifer permeability, which is in practice heterogeneous, largely governs the efficiency of mixing in density-driven natural convection. The aquifer's degree of permeability variance and the correlation length informs the character of flow-driven mixing processes. Numerical simulation was used to identify different flow regimes of a density-driven natural flow regime. Heterogeneous fields were generated using a spectral method that allows the use of power-law variograms. From the simulations it was observed that the rate of mass transfer of carbon dioxide (CO{sub 2}) into water is higher for heterogeneous media. The formulation of the physical model and related equations and the method for generating the permeability fields were described. The simulation results indicated that gravity-induced fingering is the dominant pattern in low heterogeneity, but fingering will not occur in realistic porous media. The results also showed that the permeability field structure dominates at moderate heterogeneity, and that the flow is dispersive at high heterogeneity when the correlation length of the field is small. Heterogeneous media facilitate a larger rate of CO{sub 2} dissolution than homogenous media, which means that the former can store larger volumes of CO{sub 2}. 49 refs., 3 tabs., 13 figs.
Automation of multi-agent control for complex dynamic systems in heterogeneous computational network
Oparin, Gennady; Feoktistov, Alexander; Bogdanova, Vera; Sidorov, Ivan
2017-01-01
The rapid progress of high-performance computing entails new challenges related to solving large scientific problems for various subject domains in a heterogeneous distributed computing environment (e.g., a network, Grid system, or Cloud infrastructure). The specialists in the field of parallel and distributed computing give the special attention to a scalability of applications for problem solving. An effective management of the scalable application in the heterogeneous distributed computing environment is still a non-trivial issue. Control systems that operate in networks, especially relate to this issue. We propose a new approach to the multi-agent management for the scalable applications in the heterogeneous computational network. The fundamentals of our approach are the integrated use of conceptual programming, simulation modeling, network monitoring, multi-agent management, and service-oriented programming. We developed a special framework for an automation of the problem solving. Advantages of the proposed approach are demonstrated on the parametric synthesis example of the static linear regulator for complex dynamic systems. Benefits of the scalable application for solving this problem include automation of the multi-agent control for the systems in a parallel mode with various degrees of its detailed elaboration.
Maqsood, Najwa; Mustafa, M.; Khan, Junaid Ahmad
This study provides a numerical treatment for rotating flow of viscoelastic (Maxwell) fluid bounded by a linearly deforming elastic surface. Mass transfer analysis is carried out in the existence of homogeneous-heterogeneous reactions. By means of usual transformation, the governing equations are changed into global similarity equations which have been tackled by an expedient shooting approach. A contemporary numerical routine bvp4c of software MATLAB is also opted to develop numerical approximations. Both methods of solution are found in complete agreement in all the cases. Velocity and concentration profiles are computed and elucidated for certain range of viscoelastic fluid parameter. The solutions contain a rotation-strength parameter λ that has a considerable impact on the flow fields. For sufficiently large value of λ , the velocity fields are oscillatory decaying function of the non-dimensional vertical distance. Concentration distribution at the surface is found to decrease upon increasing the strengths of chemical reactions. A comparison of present computations is made with those of already published ones and such comparison appears convincing.
A Multimetric Approach for Handoff Decision in Heterogeneous Wireless Networks
Kustiawan, I.; Purnama, W.
2018-02-01
Seamless mobility and service continuity anywhere at any time are an important issue in the wireless Internet. This research proposes a scheme to make handoff decisions effectively in heterogeneous wireless networks using a fuzzy system. Our design lies in an inference engine which takes RSS (received signal strength), data rate, network latency, and user preference as strategic determinants. The logic of our engine is realized on a UE (user equipment) side in faster reaction to network dynamics while roaming across different radio access technologies. The fuzzy system handles four metrics jointly to deduce a moderate decision about when to initiate handoff. The performance of our design is evaluated by simulating move-out mobility scenarios. Simulation results show that our scheme outperforms other approaches in terms of reducing unnecessary handoff.
Directory of Open Access Journals (Sweden)
Martin Cupal
2017-01-01
Full Text Available The article focuses on heterogeneity of goods, namely real estate and consequently deals with market valuation accuracy. The heterogeneity of real estate property is, in particular, that every unit is unique in terms of its construction, condition, financing and mainly location and thus assessing the value must necessarily be difficult. This research also indicates the rate of efficiency of markets across the types based on their level of variability. The research is based on two databases consisting of various types of real estate with specific market parameters. These parameters determine the differences across the types and reveal heterogeneity. The first database has been set on valuations by sales comparison approach and the second one on data of real properties offered on the market. The methodology is based on univariate and multivariate statistics of key variables of those databases. The multivariate analysis is performed by Hotelling T2 control chart and statistics with appropriate numerical characteristics. The results of both databases were joint by weights with regard to the dependence criterion of the variables. The final results indicate potential valuation accuracy across the types. The main contribution of the research is that the evaluation was not only derived from the price deviation or distribution, but it also draws from causes of real property heterogeneity as a whole.
Continuous spin mean-field models : Limiting kernels and Gibbs properties of local transforms
Kulske, Christof; Opoku, Alex A.
2008-01-01
We extend the notion of Gibbsianness for mean-field systems to the setup of general (possibly continuous) local state spaces. We investigate the Gibbs properties of systems arising from an initial mean-field Gibbs measure by application of given local transition kernels. This generalizes previous
Global mean-field phase diagram of the spin-1 Ising ferromagnet in a random crystal field
Borelli, M. E. S.; Carneiro, C. E. I.
1996-02-01
We study the phase diagram of the mean-field spin-1 Ising ferromagnet in a uniform magnetic field H and a random crystal field Δi, with probability distribution P( Δi) = pδ( Δi - Δ) + (1 - p) δ( Δi). We analyse the effects of randomness on the first-order surfaces of the Δ- T- H phase diagram for different values of the concentration p and show how these surfaces are affected by the dilution of the crystal field.
Shoff, Carla; Chen, Vivian Yi-Ju; Yang, Tse-Chuan
2014-01-01
Using geographically weighted regression (GWR), a recent study by Shoff and colleagues (2012) investigated the place-specific risk factors for prenatal care utilization in the US and found that most of the relationships between late or not prenatal care and its determinants are spatially heterogeneous. However, the GWR approach may be subject to the confounding effect of spatial homogeneity. The goal of this study is to address this concern by including both spatial homogeneity and heterogeneity into the analysis. Specifically, we employ an analytic framework where a spatially lagged (SL) effect of the dependent variable is incorporated into the GWR model, which is called GWR-SL. Using this innovative framework, we found evidence to argue that spatial homogeneity is neglected in the study by Shoff et al. (2012) and the results are changed after considering the spatially lagged effect of prenatal care utilization. The GWR-SL approach allows us to gain a place-specific understanding of prenatal care utilization in US counties. In addition, we compared the GWR-SL results with the results of conventional approaches (i.e., OLS and spatial lag models) and found that GWR-SL is the preferred modeling approach. The new findings help us to better estimate how the predictors are associated with prenatal care utilization across space, and determine whether and how the level of prenatal care utilization in neighboring counties matters. PMID:24893033
Heterogeneity of postpartum depression: a latent class analysis
2016-01-01
Summary Background Maternal depression in the postpartum period confers substantial morbidity and mortality, but the definition of postpartum depression remains controversial. We investigated the heterogeneity of symptoms with the aim of identifying clinical subtypes of postpartum depression. Methods Data were aggregated from the international perinatal psychiatry consortium Postpartum Depression: Action Towards Causes and Treatment, which represents 19 institutions in seven countries. 17 912 unique subject records with phenotypic data were submitted. We applied latent class analyses in a two-tiered approach to assess the validity of empirically defined subtypes of postpartum depression. Tier one assessed heterogeneity in women with complete data on the Edinburgh postnatal depression scale (EPDS) and tier two in those with postpartum depression case status. Findings 6556 individuals were assessed in tier one and 4245 in tier two. A final model with three latent classes was optimum for both tiers. The most striking characteristics associated with postpartum depression were severity, timing of onset, comorbid anxiety, and suicidal ideation. Women in class 1 had the least severe symptoms (mean EPDS score 10·5), followed by those in class 2 (mean EPDS score 14·8) and those in class 3 (mean EPDS score 20·1). The most severe symptoms of postpartum depression were significantly associated with poor mood (mean EPDS score 20·1), increased anxiety, onset of symptoms during pregnancy, obstetric complications, and suicidal ideation. In class 2, most women (62%) reported symptom onset within 4 weeks postpartum and had more pregnancy complications than in other two classes (69% vs 67% in class 1 and 29% in class 3). Interpretation PPD seems to have several distinct phenotypes. Further assessment of PPD heterogeneity to identify more precise phenotypes will be important for future biological and genetic investigations. Funding Sources of funding are listed at the end of the
Murali K. Mantrala; Prabhakant Sinha; Andris A. Zoltners
1994-01-01
This paper presents an agency theoretic model-based approach that assists sales managers in determining the profit-maximizing structure of a common multiproduct sales quota-bonus plan for a geographically specialized heterogeneous sales force operating in a repetitive buying environment. This approach involves estimating each salesperson's utility function for income and effort and using these models to predict individual sales achievements and the associated aggregate profit for the firm und...
International Nuclear Information System (INIS)
Hojsik, M.; Gmuca, S.
1998-01-01
Relativistic microscopic calculations are presented for proton elastic scattering from 40 Ca at 500 MeV. The underlying target densities are calculated within the framework of the relativistic mean-field theory with several parameter sets commonly in use. The self consistency of the scalar and vector densities (and thus to relativistic mean-field parameters) is investigated. Recently, the relativistic impulse approximation (RIA) has been widely and repeatedly used for the calculations of proton-nucleus scattering at intermediate energies. These calculations have exhibited significant improvements over the nonrelativistic approaches. The relativistic impulse approximation calculations. in particular, provide a dramatically better description of the spin observables, namely the analyzing power, A y , and the spin-rotation function, Q, at least for energies higher than 400 MeV. In the relativistic impulse approximation, the Dirac optical potential is obtained by folding of the local Lorentz-invariant amplitudes with the corresponding nuclear densities. For the spin zero targets the scalar and vector terms give the dominant contributions. Thus the scalar and vector nuclear densities (both, proton and neutron ones) play the dominant role in the relativistic impulse approximation. While the proton vector densities can be obtained by unfolding from the empirically known charge densities, all other densities used rely to a great extent on theoretical models. The various recipes are used to construct the neutron vector densities and the scalar densities for both, neutrons and protons. In this paper we will study the sensitivity of the relativistic impulse approximation results on the various sets of relativistic mean-field parameters currently in use
Heterogeneous Computing in Economics: A Simplified Approach
DEFF Research Database (Denmark)
Dziubinski, Matt P.; Grassi, Stefano
This paper shows the potential of heterogeneous computing in solving dynamic equilibrium models in economics. We illustrate the power and simplicity of the C++ Accelerated Massive Parallelism recently introduced by Microsoft. Starting from the same exercise as Aldrich et al. (2011) we document a ...
Partial discharge transients: The field theoretical approach
DEFF Research Database (Denmark)
McAllister, Iain Wilson; Crichton, George C
1998-01-01
Up until the mid-1980s the theory of partial discharge transients was essentially static. This situation had arisen because of the fixation with the concept of void capacitance and the use of circuit theory to address what is in essence a field problem. Pedersen rejected this approach and instead...... began to apply field theory to the problem of partial discharge transients. In the present paper, the contributions of Pedersen using the field theoretical approach will be reviewed and discussed....
Elastic Rock Heterogeneity Controls Brittle Rock Failure during Hydraulic Fracturing
Langenbruch, C.; Shapiro, S. A.
2014-12-01
For interpretation and inversion of microseismic data it is important to understand, which properties of the reservoir rock control the occurrence probability of brittle rock failure and associated seismicity during hydraulic stimulation. This is especially important, when inverting for key properties like permeability and fracture conductivity. Although it became accepted that seismic events are triggered by fluid flow and the resulting perturbation of the stress field in the reservoir rock, the magnitude of stress perturbations, capable of triggering failure in rocks, can be highly variable. The controlling physical mechanism of this variability is still under discussion. We compare the occurrence of microseismic events at the Cotton Valley gas field to elastic rock heterogeneity, obtained from measurements along the treatment wells. The heterogeneity is characterized by scale invariant fluctuations of elastic properties. We observe that the elastic heterogeneity of the rock formation controls the occurrence of brittle failure. In particular, we find that the density of events is increasing with the Brittleness Index (BI) of the rock, which is defined as a combination of Young's modulus and Poisson's ratio. We evaluate the physical meaning of the BI. By applying geomechanical investigations we characterize the influence of fluctuating elastic properties in rocks on the probability of brittle rock failure. Our analysis is based on the computation of stress fluctuations caused by elastic heterogeneity of rocks. We find that elastic rock heterogeneity causes stress fluctuations of significant magnitude. Moreover, the stress changes necessary to open and reactivate fractures in rocks are strongly related to fluctuations of elastic moduli. Our analysis gives a physical explanation to the observed relation between elastic heterogeneity of the rock formation and the occurrence of brittle failure during hydraulic reservoir stimulations. A crucial factor for understanding
Mean Field Analysis of Quantum Annealing Correction.
Matsuura, Shunji; Nishimori, Hidetoshi; Albash, Tameem; Lidar, Daniel A
2016-06-03
Quantum annealing correction (QAC) is a method that combines encoding with energy penalties and decoding to suppress and correct errors that degrade the performance of quantum annealers in solving optimization problems. While QAC has been experimentally demonstrated to successfully error correct a range of optimization problems, a clear understanding of its operating mechanism has been lacking. Here we bridge this gap using tools from quantum statistical mechanics. We study analytically tractable models using a mean-field analysis, specifically the p-body ferromagnetic infinite-range transverse-field Ising model as well as the quantum Hopfield model. We demonstrate that for p=2, where the phase transition is of second order, QAC pushes the transition to increasingly larger transverse field strengths. For p≥3, where the phase transition is of first order, QAC softens the closing of the gap for small energy penalty values and prevents its closure for sufficiently large energy penalty values. Thus QAC provides protection from excitations that occur near the quantum critical point. We find similar results for the Hopfield model, thus demonstrating that our conclusions hold in the presence of disorder.
Effective field renormalization group approach for Ising lattice spin systems
Fittipaldi, Ivon P.
1994-03-01
A new applicable real-space renormalization group framework (EFRG) for computing the critical properties of Ising lattice spin systems is presented. The method, which follows up the same strategy of the mean-field renormalization group scheme (MFRG), is based on rigorous Ising spin identities and utilizes a convenient differential operator expansion technique. Within this scheme, in contrast with the usual mean-field type of equation of state, all the relevant self-spin correlations are taken exactly into account. The results for the critical coupling and the critical exponent v, for the correlation length, are very satisfactory and it is shown that this technique leads to rather accurate results which represent a remarkable improvement on those obtained from the standard MFRG method. In particular, it is shown that the present EFRG approach correctly distinguishes the geometry of the lattice structure even when employing its simplest size-cluster version. Owing to its simplicity we also comment on the wide applicability of the present method to problems in crystalline and disordered Ising spin systems.
Applying Mean-Field Approximation to Continuous Time Markov Chains
Kolesnichenko, A.V.; Senni, Valerio; Pourranjabar, Alireza; Remke, A.K.I.; Stoelinga, M.I.A.
2014-01-01
The mean-field analysis technique is used to perform analysis of a system with a large number of components to determine the emergent deterministic behaviour and how this behaviour modifies when its parameters are perturbed. The computer science performance modelling and analysis community has found
Real-Space Application of the Mean-Field Description of Spin-Glass Dynamics
International Nuclear Information System (INIS)
Barrat, Alain; Berthier, Ludovic
2001-01-01
The out of equilibrium dynamics of finite dimensional spin glasses is considered from a point of view going beyond the standard 'mean-field theory' versus 'droplet picture' debate of the past decades. The main predictions of both theories concerning the spin-glass dynamics are discussed. It is shown, in particular, that predictions originating from mean-field ideas concerning the violations of the fluctuation-dissipation theorem apply quantitatively, provided one properly takes into account the role of a spin-glass coherence length, which plays a central role in the droplet picture. Dynamics in a uniform magnetic field is also briefly discussed
Generic evolution of mixing in heterogeneous media
De Dreuzy, J.; Carrera, J.; Dentz, M.; Le Borgne, T.
2011-12-01
Mixing in heterogeneous media results from the competition bewteen flow fluctuations and local scale diffusion. Flow fluctuations quickly create concentration contrasts and thus heterogeneity of the concentration field, which is slowly homogenized by local scale diffusion. Mixing first deviates from Gaussian mixing, which represents the potential mixing induced by spreading before approaching it. This deviation fundamentally expresses the evolution of the interaction between spreading and local scale diffusion. We characterize it by the ratio γ of the non-Gaussian to the Gaussian mixing states. We define the Gaussian mixing state as the integrated squared concentration of the Gaussian plume that has the same longitudinal dispersion as the real plume. The non-Gaussian mixing state is the difference between the overall mixing state defined as the integrated squared concentration and the Gaussian mixing state. The main advantage of this definition is to use the full knowledge previously acquired on dispersion for characterizing mixing even when the solute concentration field is highly non Gaussian. Using high precision numerical simulations, we show that γ quickly increases, peaks and slowly decreases. γ can be derived from two scales characterizing spreading and local mixing, at least for large flux-weighted solute injection conditions into classically log-normal Gaussian correlated permeability fields. The spreading scale is directly related to the longitudinal dispersion. The local mixing scale is the largest scale over which solute concentrations can be considered locally uniform. More generally, beyond the characteristics of its maximum, γ turns out to have a highly generic scaling form. Its fast increase and slow decrease depend neither on the heterogeneity level, nor on the ratio of diffusion to advection, nor on the injection conditions. They might even not depend on the particularities of the flow fields as the same generic features also prevail for
Mean-field approach to evolving spatial networks, with an application to osteocyte network formation
Taylor-King, Jake P.; Basanta, David; Chapman, S. Jonathan; Porter, Mason A.
2017-07-01
We consider evolving networks in which each node can have various associated properties (a state) in addition to those that arise from network structure. For example, each node can have a spatial location and a velocity, or it can have some more abstract internal property that describes something like a social trait. Edges between nodes are created and destroyed, and new nodes enter the system. We introduce a "local state degree distribution" (LSDD) as the degree distribution at a particular point in state space. We then make a mean-field assumption and thereby derive an integro-partial differential equation that is satisfied by the LSDD. We perform numerical experiments and find good agreement between solutions of the integro-differential equation and the LSDD from stochastic simulations of the full model. To illustrate our theory, we apply it to a simple model for osteocyte network formation within bones, with a view to understanding changes that may take place during cancer. Our results suggest that increased rates of differentiation lead to higher densities of osteocytes, but with a smaller number of dendrites. To help provide biological context, we also include an introduction to osteocytes, the formation of osteocyte networks, and the role of osteocytes in bone metastasis.
Superheavy nuclei: a relativistic mean field outlook
International Nuclear Information System (INIS)
Afanasjev, A.V.
2006-01-01
The analysis of quasi-particle spectra in the heaviest A∼250 nuclei with spectroscopic data provides an additional constraint for the choice of effective interaction for the description of superheavy nuclei. It strongly suggests that only the parametrizations which predict Z = 120 and N = 172 as shell closures are reliable for superheavy nuclei within the relativistic mean field theory. The influence of the central depression in the density distribution of spherical superheavy nuclei on the shell structure is studied. A large central depression produces large shell gaps at Z = 120 and N = 172. The shell gaps at Z = 126 and N = 184 are favoured by a flat density distribution in the central part of the nucleus. It is shown that approximate particle number projection (PNP) by means of the Lipkin-Nogami (LN) method removes pairing collapse seen at these gaps in the calculations without PNP
Thin inclusion approach for modelling of heterogeneous conducting materials
Lavrov, Nikolay; Smirnova, Alevtina; Gorgun, Haluk; Sammes, Nigel
Experimental data show that heterogeneous nanostructure of solid oxide and polymer electrolyte fuel cells could be approximated as an infinite set of fiber-like or penny-shaped inclusions in a continuous medium. Inclusions can be arranged in a cluster mode and regular or random order. In the newly proposed theoretical model of nanostructured material, the most attention is paid to the small aspect ratio of structural elements as well as to some model problems of electrostatics. The proposed integral equation for electric potential caused by the charge distributed over the single circular or elliptic cylindrical conductor of finite length, as a single unit of a nanostructured material, has been asymptotically simplified for the small aspect ratio and solved numerically. The result demonstrates that surface density changes slightly in the middle part of the thin domain and has boundary layers localized near the edges. It is anticipated, that contribution of boundary layer solution to the surface density is significant and cannot be governed by classic equation for smooth linear charge. The role of the cross-section shape is also investigated. Proposed approach is sufficiently simple, robust and allows extension to either regular or irregular system of various inclusions. This approach can be used for the development of the system of conducting inclusions, which are commonly present in nanostructured materials used for solid oxide and polymer electrolyte fuel cell (PEMFC) materials.
The influence of idealized surface heterogeneity on virtual turbulent flux measurements
De Roo, Frederik; Mauder, Matthias
2018-04-01
The imbalance of the surface energy budget in eddy-covariance measurements is still an unsolved problem. A possible cause is the presence of land surface heterogeneity, which affects the boundary-layer turbulence. To investigate the impact of surface variables on the partitioning of the energy budget of flux measurements in the surface layer under convective conditions, we set up a systematic parameter study by means of large-eddy simulation. For the study we use a virtual control volume approach, which allows the determination of advection by the mean flow, flux-divergence and storage terms of the energy budget at the virtual measurement site, in addition to the standard turbulent flux. We focus on the heterogeneity of the surface fluxes and keep the topography flat. The surface fluxes vary locally in intensity and these patches have different length scales. Intensity and length scales can vary for the two horizontal dimensions but follow an idealized chessboard pattern. Our main focus lies on surface heterogeneity of the kilometer scale, and one order of magnitude smaller. For these two length scales, we investigate the average response of the fluxes at a number of virtual towers, when varying the heterogeneity length within the length scale and when varying the contrast between the different patches. For each simulation, virtual measurement towers were positioned at functionally different positions (e.g., downdraft region, updraft region, at border between domains, etc.). As the storage term is always small, the non-closure is given by the sum of the advection by the mean flow and the flux-divergence. Remarkably, the missing flux can be described by either the advection by the mean flow or the flux-divergence separately, because the latter two have a high correlation with each other. For kilometer scale heterogeneity, we notice a clear dependence of the updrafts and downdrafts on the surface heterogeneity and likewise we also see a dependence of the energy
International Nuclear Information System (INIS)
Mathieu, J.Ph.
2006-10-01
Reactor Pressure Vessel is the second containment barrier between nuclear fuel and the environment. Electricite de France's reactors are made with french 16MND5 low-alloyed steel (equ. ASTM A508 Cl.3). Various experimental techniques (scanning electron microscopy, X-ray diffraction...) are set up in order to characterize mechanical heterogeneities inside material microstructure during tensile testing at different low temperatures [-150 C;-60 C]. Heterogeneities can be seen as the effect of both 'polycrystalline' and 'composite' microstructural features. Interphase (until 150 MPa in average between ferritic and bainitic macroscopic stress state) and intra-phase (until 100 MPa in average between ferritic orientations) stress variations are highlighted. Modelling involves micro-mechanical description of plastic glide, mean fields models and realistic three-dimensional aggregates, all put together inside a multi-scale approach. Calibration is done on macroscopic stress-strain curves at different low temperatures, and modelling reproduces experimental stress heterogeneities. This modelling allows to apply a local micro-mechanical fracture criterion for crystallographic cleavage. Deterministic computations of time to fracture for different carbides random selection provide a way to express probability of fracture for the elementary volume. Results are in good agreement with hypothesis made by local approach to fracture. Hence, the main difference is that no dependence to loading nor microstructure features is supposed for probability of fracture on the representative volume: this dependence is naturally introduced by modelling. (author)
Conserving gapless mean-field theory for weakly interacting Bose gases
International Nuclear Information System (INIS)
Kita, Takafumi
2006-01-01
This paper presents a conserving gapless mean-field theory for weakly interacting Bose gases. We first construct a mean-field Luttinger-Ward thermodynamic functional in terms of the condensate wave function Ψ and the Nambu Green's function G for the quasiparticle field. Imposing its stationarity respect to Ψ and G yields a set of equations to determine the equilibrium for general non-uniform systems. They have a plausible property of satisfying the Hugenholtz-Pines theorem to provide a gapless excitation spectrum. Also, the corresponding dynamical equations of motion obey various conservation laws. Thus, the present mean-field theory shares two important properties with the exact theory: 'conserving' and 'gapless'. The theory is then applied to a homogeneous weakly interacting Bose gas with s-wave scattering length a and particle mass m to clarify its basic thermodynamic properties under two complementary conditions of constant density n and constant pressure p. The superfluid transition is predicted to be first-order because of the non-analytic nature of the order-parameter expansion near T c inherent in Bose systems, i.e., the Landau-Ginzburg expansion is not possible here. The transition temperature T c shows quite a different interaction dependence between the n-fixed and p-fixed cases. In the former case T c increases from the ideal gas value T 0 as T c /T 0 =1+2.33an 1/3 , whereas it decreases in the latter as T c /T 0 =1-3.84a(mp/2πℎ 2 ) 1/5 . Temperature dependences of basic thermodynamic quantities are clarified explicitly. (author)
DEFF Research Database (Denmark)
Haustein, Sonja
2012-01-01
The western population is ageing. Based on the assumption that the elderly are a quite heterogeneous population group with an increasing impact on the transport system, mobility types of the elderly were identified. By means of 1,500 standardized telephone interviews, mobility behavior and possib...... of the diverse lifestyles, attitudes, travel behavior and needs of the elderly. Furthermore, it identifies starting points for the reduction of car use....
A philosophical approach to quantum field theory
Öttinger, Hans Christian
2015-01-01
This text presents an intuitive and robust mathematical image of fundamental particle physics based on a novel approach to quantum field theory, which is guided by four carefully motivated metaphysical postulates. In particular, the book explores a dissipative approach to quantum field theory, which is illustrated for scalar field theory and quantum electrodynamics, and proposes an attractive explanation of the Planck scale in quantum gravity. Offering a radically new perspective on this topic, the book focuses on the conceptual foundations of quantum field theory and ontological questions. It also suggests a new stochastic simulation technique in quantum field theory which is complementary to existing ones. Encouraging rigor in a field containing many mathematical subtleties and pitfalls this text is a helpful companion for students of physics and philosophers interested in quantum field theory, and it allows readers to gain an intuitive rather than a formal understanding.
Hubbard interaction in the arbitrary Chern number insulator: A mean-field study
Energy Technology Data Exchange (ETDEWEB)
Wang, Yi-Xiang, E-mail: wangyixiang@jiangnan.edu.cn [School of Science, Jiangnan University, Wuxi 214122 (China); Cao, Jie [College of Science, Hohai University, Nanjing 210098 (China)
2017-05-10
The low-dimensional electron gas owing topological property has attracted many interests recently. In this work, we study the influence of the electron-electron interaction on the arbitrary Chern number insulator. Using the mean-field method, we approximately solve the Hubbard model in the half-filling case and obtain the phase diagrams in different parametric spaces. We further verify the results by calculating the entanglement spectrum, which contains C chiral modes and corresponds to a real space partitioning. - Highlights: • In this work, we made a mean-field study of the Hubbard interaction in the arbitrary Chern number insulator. • We point out that how the Zeeman splitting, the local magnetization and the Hubbard interaction are intimately related. • The mean-field phase diagrams are obtained in different parametric spaces. • The Chern number phase is demonstrated by calculating the entanglement spectrum.
Massively Parallel Geostatistical Inversion of Coupled Processes in Heterogeneous Porous Media
Ngo, A.; Schwede, R. L.; Li, W.; Bastian, P.; Ippisch, O.; Cirpka, O. A.
2012-04-01
The quasi-linear geostatistical approach is an inversion scheme that can be used to estimate the spatial distribution of a heterogeneous hydraulic conductivity field. The estimated parameter field is considered to be a random variable that varies continuously in space, meets the measurements of dependent quantities (such as the hydraulic head, the concentration of a transported solute or its arrival time) and shows the required spatial correlation (described by certain variogram models). This is a method of conditioning a parameter field to observations. Upon discretization, this results in as many parameters as elements of the computational grid. For a full three dimensional representation of the heterogeneous subsurface it is hardly sufficient to work with resolutions (up to one million parameters) of the model domain that can be achieved on a serial computer. The forward problems to be solved within the inversion procedure consists of the elliptic steady-state groundwater flow equation and the formally elliptic but nearly hyperbolic steady-state advection-dominated solute transport equation in a heterogeneous porous medium. Both equations are discretized by Finite Element Methods (FEM) using fully scalable domain decomposition techniques. Whereas standard conforming FEM is sufficient for the flow equation, for the advection dominated transport equation, which rises well known numerical difficulties at sharp fronts or boundary layers, we use the streamline diffusion approach. The arising linear systems are solved using efficient iterative solvers with an AMG (algebraic multigrid) pre-conditioner. During each iteration step of the inversion scheme one needs to solve a multitude of forward and adjoint problems in order to calculate the sensitivities of each measurement and the related cross-covariance matrix of the unknown parameters and the observations. In order to reduce interprocess communications and to improve the scalability of the code on larger clusters
Engineering Microbial Metabolite Dynamics and Heterogeneity.
Schmitz, Alexander C; Hartline, Christopher J; Zhang, Fuzhong
2017-10-01
As yields for biological chemical production in microorganisms approach their theoretical maximum, metabolic engineering requires new tools, and approaches for improvements beyond what traditional strategies can achieve. Engineering metabolite dynamics and metabolite heterogeneity is necessary to achieve further improvements in product titers, productivities, and yields. Metabolite dynamics, the ensemble change in metabolite concentration over time, arise from the need for microbes to adapt their metabolism in response to the extracellular environment and are important for controlling growth and productivity in industrial fermentations. Metabolite heterogeneity, the cell-to-cell variation in a metabolite concentration in an isoclonal population, has a significant impact on ensemble productivity. Recent advances in single cell analysis enable a more complete understanding of the processes driving metabolite heterogeneity and reveal metabolic engineering targets. The authors present an overview of the mechanistic origins of metabolite dynamics and heterogeneity, why they are important, their potential effects in chemical production processes, and tools and strategies for engineering metabolite dynamics and heterogeneity. The authors emphasize that the ability to control metabolite dynamics and heterogeneity will bring new avenues of engineering to increase productivity of microbial strains. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Mean field methods for cortical network dynamics
DEFF Research Database (Denmark)
Hertz, J.; Lerchner, Alexander; Ahmadi, M.
2004-01-01
We review the use of mean field theory for describing the dynamics of dense, randomly connected cortical circuits. For a simple network of excitatory and inhibitory leaky integrate- and-fire neurons, we can show how the firing irregularity, as measured by the Fano factor, increases...... with the strength of the synapses in the network and with the value to which the membrane potential is reset after a spike. Generalizing the model to include conductance-based synapses gives insight into the connection between the firing statistics and the high- conductance state observed experimentally in visual...
Quantum mean-field theory of collective dynamics and tunneling
International Nuclear Information System (INIS)
Negele, J.W.
1981-01-01
A fundamental problem in quantum many-body theory is formulation of a microscopic theory of collective motion. For self-bound, saturating systems like finite nuclei described in the context of nonrelativistic quantum mechanics with static interactions, the essential problem is how to formulate a systematic quantal theory in which the relevant collective variables and their dynamics arise directly and naturally from the Hamiltonian and the system under consideration. Significant progress has been made recently in formulating the quantum many-body problem in terms of an expansion about solutions to time-dependent mean-field equations. The essential ideas, principal results, and illustrative examples are summarized. An exact expression for an observable of interest is written using a functional integral representation for the evolution operator, and tractable time-dependent mean field equations are obtained by application of the stationary-phase approximation (SPA) to the functional integral. Corrections to the lowest-order theory may be systematically enumerated. 6 figures
Single-chain-in-mean-field simulations of weak polyelectrolyte brushes
Léonforte, F.; Welling, U.; Müller, M.
2016-12-01
Structural properties of brushes which are composed of weak acidic and basic polyelectrolytes are studied in the framework of a particle-based approach that implicitly accounts for the solvent quality. Using a semi-grandcanonical partition function in the framework of the Single-Chain-in-Mean-Field (SCMF) algorithm, the weak polyelectrolyte is conceived as a supramolecular mixture of polymers in different dissociation states, which are explicitly treated in the partition function and sampled by the SCMF procedure. One obtains a local expression for the equilibrium acid-base reaction responsible for the regulation of the charged groups that is also incorporated to the SCMF sampling. Coupled to a simultaneous treatment of the electrostatics, the approach is shown to capture the main features of weak polyelectrolyte brushes as a function of the bulk pH in the solution, the salt concentration, and the grafting density. Results are compared to experimental and theoretical works from the literature using coarse-grained representations of poly(acrylic acid) (PAA) and poly(2-vinyl pyridine) (P2VP) polymer-based brushes. As the Born self-energy of ions can be straightforwardly included in the numerical approach, we also study its effect on the local charge regulation mechanism of the brush. We find that its effect becomes significant when the brush is dense and exposed to high salt concentrations. The numerical methodology is then applied (1) to the study of the kinetics of collapse/swelling of a P2VP brush and (2) to the ability of an applied voltage to induce collapse/swelling of a PAA brush in a pH range close to the pKa value of the polymer.
Semiclassical approximations in a mean-field theory with collision terms
International Nuclear Information System (INIS)
Galetti, D.
1986-01-01
Semiclassical approximations in a mean-field theory with collision terms are discussed taking the time dependent Hartree-Fock method as framework in the obtainment of the relevant parameters.(L.C.) [pt
Neutron stars in relativistic mean field theory with isovector scalar meson
International Nuclear Information System (INIS)
Kubis, S.; Kutschera, M.; Stachniewicz, S.
1996-12-01
We study the equation of state (EOS) of neutron star matter in a relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the δ-meson [a 0 (980)]. A range of values of the δ-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E s ∼ 30 MeV. We find that proton fraction of neutron star matter is higher in the presence of the δ-field whereas the energy per particle is lower. The EOS becomes slightly stiffer and the maximum mass of the neutron star increased with increasing δmeson coupling. The effect is stronger for soft EOS. (author). 7 refs, 6 figs, 1 tab
Neutron stars in relativistic mean field theory with isovector scalar meson
International Nuclear Information System (INIS)
Kubis, S.; Kutschera, M.; Stachniewicz, S.
1998-01-01
We study the equation of state (EOS) of β-stable dense matter and models of neutron stars in the relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the δ-meson (a 0 (980)). A range of values of the δ-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E s ∼30 MeV. We find that the quantity most sensitive to the δ-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the δ-field. The energy per baryon also increases but the effect is smaller. The EOS becomes slightly stiffer and the maximum neutron star mass increases for stronger δ-meson coupling. (author)
Neutron stars in relativistic mean field theory with isovector scalar meson
Energy Technology Data Exchange (ETDEWEB)
Kubis, S.; Kutschera, M.; Stachniewicz, S. [Institute of Nuclear Physics, Cracow (Poland)
1996-12-01
We study the equation of state (EOS) of neutron star matter in a relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the {delta}-meson [a{sub 0}(980)]. A range of values of the {delta}-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E{sub s} {approx} 30 MeV. We find that proton fraction of neutron star matter is higher in the presence of the {delta}-field whereas the energy per particle is lower. The EOS becomes slightly stiffer and the maximum mass of the neutron star increased with increasing {delta}meson coupling. The effect is stronger for soft EOS. (author). 7 refs, 6 figs, 1 tab.
Energy Technology Data Exchange (ETDEWEB)
Juillet, O.; Gulminelli, F. [Caen Univ., Lab. de Physique Corpusculaire (LPC/ENSICAEN), 14 (France); Chomaz, Ph. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France)
2003-11-01
The canonical thermodynamic properties of a one-dimensional system of interacting spin-1/2 fermions with an attractive zero-range pseudo-potential are investigated within an exact approach. The density operator is evaluated as the statistical average of dyadics formed from a stochastic mean-field propagation of independent Slater determinants. For an harmonically trapped Fermi gas and for fermions confined in a 1D-like torus, we observe the transition to a quasi-BCS state with Cooper-like momentum correlations and an algebraic long-range order. For few trapped fermions in a rotating torus, a dominant superfluid component with quantized circulation can be isolated. (author)
Complexity Reduction of Multiphase Flows in Heterogeneous Porous Media
Ghommem, Mehdi
2015-04-22
In this paper, we apply mode decomposition and interpolatory projection methods to speed up simulations of two-phase flows in heterogeneous porous media. We propose intrusive and nonintrusive model-reduction approaches that enable a significant reduction in the size of the subsurface flow problem while capturing the behavior of the fully resolved solutions. In one approach, we use the dynamic mode decomposition. This approach does not require any modification of the reservoir simulation code but rather post-processes a set of global snapshots to identify the dynamically relevant structures associated with the flow behavior. In the second approach, we project the governing equations of the velocity and the pressure fields on the subspace spanned by their proper-orthogonal-decomposition modes. Furthermore, we use the discrete empirical interpolation method to approximate the mobility-related term in the global-system assembly and then reduce the online computational cost and make it independent of the fine grid. To show the effectiveness and usefulness of the aforementioned approaches, we consider the SPE-10 benchmark permeability field, and present a numerical example in two-phase flow. One can efficiently use the proposed model-reduction methods in the context of uncertainty quantification and production optimization.
Stochastic modeling of catalytic processes in nanoporous materials: Beyond mean-field approach
Energy Technology Data Exchange (ETDEWEB)
Garcia, Andres [Iowa State Univ., Ames, IA (United States)
2017-08-05
Transport and reaction in zeolites and other porous materials, such as mesoporous silica particles, has been a focus of interest in recent years. This is in part due to the possibility of anomalous transport effects (e.g. single-file diffusion) and its impact in the reaction yield in catalytic processes. Computational simulations are often used to study these complex nonequilibrium systems. Computer simulations using Molecular Dynamics (MD) techniques are prohibitive, so instead coarse grained one-dimensional models with the aid of Kinetic Monte Carlo (KMC) simulations are used. Both techniques can be computationally expensive, both time and resource wise. These coarse-grained systems can be exactly described by a set of coupled stochastic master equations, that describe the reaction-diffusion kinetics of the system. The equations can be written exactly, however, coupling between the equations and terms within the equations make it impossible to solve them exactly; approximations must be made. One of the most common methods to obtain approximate solutions is to use Mean Field (MF) theory. MF treatments yield reasonable results at high ratios of reaction rate k to hop rate h of the particles, but fail completely at low k=h due to the over-estimation of fluxes of particles within the pore. We develop a method to estimate fluxes and intrapore diffusivity in simple one- dimensional reaction-diffusion models at high and low k=h, where the pores are coupled to an equilibrated three-dimensional fluid. We thus successfully describe analytically these simple reaction-diffusion one-dimensional systems. Extensions to models considering behavior with long range steric interactions and wider pores require determination of multiple boundary conditions. We give a prescription to estimate the required parameters for these simulations. For one dimensional systems, if single-file diffusion is relaxed, additional parameters to describe particle exchange have to be introduced. We use
Epidemic spreading in weighted networks: an edge-based mean-field solution.
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.
Quantum mean-field theory of collective dynamics and tunneling
International Nuclear Information System (INIS)
Negele, J.W.; Massachusetts Inst. of Tech., Cambridge
1981-01-01
In collaboration with Shimon Levit and Zvi Paltiel, significant progress has been made recently in formulating the quantum many-body problem in terms of an expansion about solutions to time-dependent mean-field equations. The essential ideas, principal results, and illustrative examples will be summarized here. (orig./HSI)
Frampton, A.; Hyman, J.; Zou, L.
2017-12-01
Analysing flow and transport in sparsely fractured media is important for understanding how crystalline bedrock environments function as barriers to transport of contaminants, with important applications towards subsurface repositories for storage of spent nuclear fuel. Crystalline bedrocks are particularly favourable due to their geological stability, low advective flow and strong hydrogeochemical retention properties, which can delay transport of radionuclides, allowing decay to limit release to the biosphere. There are however many challenges involved in quantifying and modelling subsurface flow and transport in fractured media, largely due to geological complexity and heterogeneity, where the interplay between advective and dispersive flow strongly impacts both inert and reactive transport. A key to modelling transport in a Lagrangian framework involves quantifying pathway travel times and the hydrodynamic control of retention, and both these quantities strongly depend on heterogeneity of the fracture network at different scales. In this contribution, we present recent analysis of flow and transport considering fracture networks with single-fracture heterogeneity described by different multivariate normal distributions. A coherent triad of fields with identical correlation length and variance are created but which greatly differ in structure, corresponding to textures with well-connected low, medium and high permeability structures. Through numerical modelling of multiple scales in a stochastic setting we quantify the relative impact of texture type and correlation length against network topological measures, and identify key thresholds for cases where flow dispersion is controlled by single-fracture heterogeneity versus network-scale heterogeneity. This is achieved by using a recently developed novel numerical discrete fracture network model. Furthermore, we highlight enhanced flow channelling for cases where correlation structure continues across
Lehermeier, Christina; Schön, Chris-Carolin; de Los Campos, Gustavo
2015-09-01
Plant breeding populations exhibit varying levels of structure and admixture; these features are likely to induce heterogeneity of marker effects across subpopulations. Traditionally, structure has been dealt with as a potential confounder, and various methods exist to "correct" for population stratification. However, these methods induce a mean correction that does not account for heterogeneity of marker effects. The animal breeding literature offers a few recent studies that consider modeling genetic heterogeneity in multibreed data, using multivariate models. However, these methods have received little attention in plant breeding where population structure can have different forms. In this article we address the problem of analyzing data from heterogeneous plant breeding populations, using three approaches: (a) a model that ignores population structure [A-genome-based best linear unbiased prediction (A-GBLUP)], (b) a stratified (i.e., within-group) analysis (W-GBLUP), and (c) a multivariate approach that uses multigroup data and accounts for heterogeneity (MG-GBLUP). The performance of the three models was assessed on three different data sets: a diversity panel of rice (Oryza sativa), a maize (Zea mays L.) half-sib panel, and a wheat (Triticum aestivum L.) data set that originated from plant breeding programs. The estimated genomic correlations between subpopulations varied from null to moderate, depending on the genetic distance between subpopulations and traits. Our assessment of prediction accuracy features cases where ignoring population structure leads to a parsimonious more powerful model as well as others where the multivariate and stratified approaches have higher predictive power. In general, the multivariate approach appeared slightly more robust than either the A- or the W-GBLUP. Copyright © 2015 by the Genetics Society of America.
Directory of Open Access Journals (Sweden)
W. Kurtz
2013-10-01
-resolution characterization of L fields with EnKF is still feasible. For less heterogeneous river bed hydraulic conductivities, a high-resolution characterization of L is less important. When uncertainties in the hydraulic parameters of the aquifer are also regarded in the assimilation, the errors in state and flux predictions increase, but the ensemble with a high spatial resolution for L still outperforms the ensembles with effective L values. We conclude that for strongly heterogeneous river beds the commonly applied simplified representation of the streambed, with spatially homogeneous parameters or constant parameters for a few zones, might yield significant biases in the characterization of the water balance. For strongly heterogeneous river beds, we suggest adopting a stochastic field approach to model the spatially heterogeneous river beds geostatistically. The paper illustrates that EnKF is able to calibrate such heterogeneous streambeds on the basis of hydraulic head measurements, outperforming zonation approaches.
Armstrong, Joshua J; Zhu, Mu; Hirdes, John P; Stolee, Paul
2012-12-01
To examine the heterogeneity of home care clients who use rehabilitation services by using the K-means algorithm to identify previously unknown patterns of clinical characteristics. Observational study of secondary data. Home care system. Assessment information was collected on 150,253 home care clients using the provincially mandated Resident Assessment Instrument-Home Care (RAI-HC) data system. Not applicable. Assessment information from every long-stay (>60 d) home care client that entered the home care system between 2005 and 2008 and used rehabilitation services within 3 months of their initial assessment was analyzed. The K-means clustering algorithm was applied using 37 variables from the RAI-HC assessment. The K-means cluster analysis resulted in the identification of 7 relatively homogeneous subgroups that differed on characteristics such as age, sex, cognition, and functional impairment. Client profiles were created to illustrate the diversity of this geriatric population. The K-means algorithm provided a useful way to segment a heterogeneous rehabilitation client population into more homogeneous subgroups. This analysis provides an enhanced understanding of client characteristics and needs, and could enable more appropriate targeting of rehabilitation services for home care clients. Copyright © 2012 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.
Isospin-dependent properties of asymmetric nuclear matter in relativistic mean field models
Chen, Lie-Wen; Ko, Che Ming; Li, Bao-An
2007-11-01
Using various relativistic mean-field models, including nonlinear ones with meson field self-interactions, models with density-dependent meson-nucleon couplings, and point-coupling models without meson fields, we have studied the isospin-dependent bulk and single-particle properties of asymmetric nuclear matter. In particular, we have determined the density dependence of nuclear symmetry energy from these different relativistic mean-field models and compared the results with the constraints recently extracted from analyses of experimental data on isospin diffusion and isotopic scaling in intermediate energy heavy-ion collisions as well as from measured isotopic dependence of the giant monopole resonances in even-A Sn isotopes. Among the 23 parameter sets in the relativistic mean-field model that are commonly used for nuclear structure studies, only a few are found to give symmetry energies that are consistent with the empirical constraints. We have also studied the nuclear symmetry potential and the isospin splitting of the nucleon effective mass in isospin asymmetric nuclear matter. We find that both the momentum dependence of the nuclear symmetry potential at fixed baryon density and the isospin splitting of the nucleon effective mass in neutron-rich nuclear matter depend not only on the nuclear interactions but also on the definition of the nucleon optical potential.
A network of spiking neurons that can represent interval timing: mean field analysis.
Gavornik, Jeffrey P; Shouval, Harel Z
2011-04-01
Despite the vital importance of our ability to accurately process and encode temporal information, the underlying neural mechanisms are largely unknown. We have previously described a theoretical framework that explains how temporal representations, similar to those reported in the visual cortex, can form in locally recurrent cortical networks as a function of reward modulated synaptic plasticity. This framework allows networks of both linear and spiking neurons to learn the temporal interval between a stimulus and paired reward signal presented during training. Here we use a mean field approach to analyze the dynamics of non-linear stochastic spiking neurons in a network trained to encode specific time intervals. This analysis explains how recurrent excitatory feedback allows a network structure to encode temporal representations.
Some approximate calculations in SU2 lattice mean field theory
International Nuclear Information System (INIS)
Hari Dass, N.D.; Lauwers, P.G.
1981-12-01
Approximate calculations are performed for small Wilson loops of SU 2 lattice gauge theory in mean field approximation. Reasonable agreement is found with Monte Carlo data. Ways of improving these calculations are discussed. (Auth.)
International Nuclear Information System (INIS)
Suyama, Yasuhiro; Toida, Masaru; Yanagizawa, Koichi
2007-01-01
The geological environment has spatially heterogeneous characteristics with varied host rock types, fractures and so on. In this case the generic disposal tunnel layout, which has been designed by JNC, is not the most suitable for HLW disposal in Japan. The existence of spatially heterogeneous characteristics means that in the repository region there exist sub-regions that are more favorable from the perspective of long-term safety and ones that are less favorable. In order that the spatially heterogeneous environment itself may be utilized most effectively as an NBS, an alternative design of disposal tunnel layout is required. Focusing on the geological environment with spatially heterogeneous characteristics, the authors have developed an alternative design of disposal tunnel layout. The alternative design adopts an optimization approach using a 'variable disposal tunnel layout'. The optimization approach minimizes the number of locations where major water conducting fractures are intersected, and maximizes the number of emplacement locations for waste packages. This paper will outline the variable disposal tunnel layout and its applicability. (author)
Nonlinear mean field theory for nuclear matter and surface properties
International Nuclear Information System (INIS)
Boguta, J.; Moszkowski, S.A.
1983-01-01
Nuclear matter properties are studied in a nonlinear relativistic mean field theory. We determine the parameters of the model from bulk properties of symmetric nuclear matter and a reasonable value of the effective mass. In this work, we stress the nonrelativistic limit of the theory which is essentially equivalent to a Skyrme hamiltonian, and we show that most of the results can be obtained, to a good approximation, analytically. The strength of the required parameters is determined from the binding energy and density of nuclear matter and the effective nucleon mass. For realistic values of the parameters, the nonrelativistic approximation turns out to be quite satisfactory. Using reasonable values of the parameters, we can account for other key properties of nuclei, such as the spin-orbit coupling, surface energy, and diffuseness of the nuclear surface. Also the energy dependence of the nucleon-nucleus optical model is accounted for reasonably well except near the Fermi surface. It is found, in agreement with empirical results, that the Landau parameter F 0 is quite small in normal nuclear matter. Both density dependence and momentum dependence of the NN interaction, but especially the former, are important for nuclear saturation. The required scalar and vector coupling constants agree fairly well with those obtained from analyses of NN scattering phase shifts with one-boson-exchange models. The mean field theory provides a semiquantitative justification for the weak Skyrme interaction in odd states. The strength of the required nonlinear term is roughly consistent with that derived using a new version of the chiral mean field theory in which the vector mass as well as the nucleon mass is generated by the sigma-field. (orig.)
Neutron stars in relativistic mean field theory with isovector scalar meson
Energy Technology Data Exchange (ETDEWEB)
Kubis, S.; Kutschera, M.; Stachniewicz, S. [H. Niewodniczanski Institute of Nuclear Physics, Cracow (Poland)
1998-03-01
We study the equation of state (EOS) of {beta}-stable dense matter and models of neutron stars in the relativistic mean field (RMF) theory with the isovector scalar mean field corresponding to the {delta}-meson (a{sub 0}(980)). A range of values of the {delta}-meson coupling compatible with the Bonn potentials is explored. Parameters of the model in the isovector sector are constrained to fit the nuclear symmetry energy, E{sub s}{approx}30 MeV. We find that the quantity most sensitive to the {delta}-meson coupling is the proton fraction of neutron star matter. It increases significantly in the presence of the {delta}-field. The energy per baryon also increases but the effect is smaller. The EOS becomes slightly stiffer and the maximum neutron star mass increases for stronger {delta}-meson coupling. (author) 8 refs, 6 figs, 2 tabs
Bureick, Johannes; Alkhatib, Hamza; Neumann, Ingo
2016-03-01
In many geodetic engineering applications it is necessary to solve the problem of describing a measured data point cloud, measured, e. g. by laser scanner, by means of free-form curves or surfaces, e. g., with B-Splines as basis functions. The state of the art approaches to determine B-Splines yields results which are seriously manipulated by the occurrence of data gaps and outliers. Optimal and robust B-Spline fitting depend, however, on optimal selection of the knot vector. Hence we combine in our approach Monte-Carlo methods and the location and curvature of the measured data in order to determine the knot vector of the B-Spline in such a way that no oscillating effects at the edges of data gaps occur. We introduce an optimized approach based on computed weights by means of resampling techniques. In order to minimize the effect of outliers, we apply robust M-estimators for the estimation of control points. The above mentioned approach will be applied to a multi-sensor system based on kinematic terrestrial laserscanning in the field of rail track inspection.
A matrix approach to the statistics of longevity in heterogeneous frailty models
Directory of Open Access Journals (Sweden)
Hal Caswell
2014-09-01
Full Text Available Background: The gamma-Gompertz model is a fixed frailty model in which baseline mortality increasesexponentially with age, frailty has a proportional effect on mortality, and frailty at birth follows a gamma distribution. Mortality selects against the more frail, so the marginal mortality rate decelerates, eventually reaching an asymptote. The gamma-Gompertz is one of a wider class of frailty models, characterized by the choice of baseline mortality, effects of frailty, distributions of frailty, and assumptions about the dynamics of frailty. Objective: To develop a matrix model to compute all the statistical properties of longevity from thegamma-Gompertz and related models. Methods: I use the vec-permutation matrix formulation to develop a model in which individuals are jointly classified by age and frailty. The matrix is used to project the age and frailty dynamicsof a cohort and the fundamental matrix is used to obtain the statistics of longevity. Results: The model permits calculation of the mean, variance, coefficient of variation, skewness and all moments of longevity, the marginal mortality and survivorship functions, the dynamics of the frailty distribution, and other quantities. The matrix formulation extends naturally to other frailty models. I apply the analysis to the gamma-Gompertz model (for humans and laboratory animals, the gamma-Makeham model, and the gamma-Siler model, and to a hypothetical dynamic frailty model characterized by diffusion of frailty with reflecting boundaries.The matrix model permits partitioning the variance in longevity into components due to heterogeneity and to individual stochasticity. In several published human data sets, heterogeneity accounts for less than 10Š of the variance in longevity. In laboratory populations of five invertebrate animal species, heterogeneity accounts for 46Š to 83Š ofthe total variance in longevity.
The crossover from mean-field to 3D-Ising critical behaviour in a 3-component microemulsion
DEFF Research Database (Denmark)
Seto, H.; Schwahn, D.; Yokoi, E.
1995-01-01
Density fluctuations and associated critical phenomena of water droplets in a water-in-oil microemulsion system have been studied, We have recently found a mean-field behavior in the ''near-critical region'', and this evidence suggested that a crossover from mean-field to non-mean-field behavior...
A mean-field game economic growth model
Gomes, Diogo A.
2016-08-05
Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative, rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent seeks to maximize his/her utility by taking into account statistical data about the whole population. The individual actions drive the evolution of the players, and a market-clearing condition determines the relative price of capital and consumer goods. We study the existence and uniqueness of optimal strategies of the agents and develop numerical methods to compute these strategies and the equilibrium price.
Liu, Zhaolun; AlTheyab, Abdullah; Hanafy, Sherif M.; Schuster, Gerard T.
2017-01-01
We have developed a methodology for detecting the presence of near-surface heterogeneities by naturally migrating backscattered surface waves in controlled-source data. The near-surface heterogeneities must be located within a depth of approximately one-third the dominant wavelength λ of the strong surface-wave arrivals. This natural migration method does not require knowledge of the near-surface phase-velocity distribution because it uses the recorded data to approximate the Green’s functions for migration. Prior to migration, the backscattered data are separated from the original records, and the band-passed filtered data are migrated to give an estimate of the migration image at a depth of approximately one-third λ. Each band-passed data set gives a migration image at a different depth. Results with synthetic data and field data recorded over known faults validate the effectiveness of this method. Migrating the surface waves in recorded 2D and 3D data sets accurately reveals the locations of known faults. The limitation of this method is that it requires a dense array of receivers with a geophone interval less than approximately one-half λ.
Liu, Zhaolun
2017-03-06
We have developed a methodology for detecting the presence of near-surface heterogeneities by naturally migrating backscattered surface waves in controlled-source data. The near-surface heterogeneities must be located within a depth of approximately one-third the dominant wavelength λ of the strong surface-wave arrivals. This natural migration method does not require knowledge of the near-surface phase-velocity distribution because it uses the recorded data to approximate the Green’s functions for migration. Prior to migration, the backscattered data are separated from the original records, and the band-passed filtered data are migrated to give an estimate of the migration image at a depth of approximately one-third λ. Each band-passed data set gives a migration image at a different depth. Results with synthetic data and field data recorded over known faults validate the effectiveness of this method. Migrating the surface waves in recorded 2D and 3D data sets accurately reveals the locations of known faults. The limitation of this method is that it requires a dense array of receivers with a geophone interval less than approximately one-half λ.
Mean field theories and dual variation mathematical structures of the mesoscopic model
Suzuki, Takashi
2015-01-01
Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.
A symmetrical approach to mammal cancer: heterogeneity, regulation and embodiment
Directory of Open Access Journals (Sweden)
Jorge Leandro Castillo Sepúlveda
2012-11-01
Full Text Available Cancer is commonly described as the uncontrolled reproduction of abnormal cells in the body. This definition enacts the disease as a local process, whose temporality is linear. In this article we challenge this approach, from a case study on breast cancer, analysed from the actor-network theory. Starting from the conception of disease as a material-semiotic trajectory, we establish the role of regulation and the processes of pre-symptomatic diagnosis in the materiality of cancer. Echoing the proposal of Alfred North Whitehead, we define cancer as a potential object. Then, we describe how propositions are articulated in biomedical patients, affect their anatomy and establish an authentic embodiment, which acts as a socio-material assemblage. We conclude that it is necessary to think about interventions that consider the heterogeneity of the material aspects that come with cancer, conceived from this perspective.
In-situ characterization of heterogeneous catalysts
Rodriguez, Jose A; Chupas, Peter J
2013-01-01
Helps researchers develop new catalysts for sustainable fuel and chemical production Reviewing the latest developments in the field, this book explores the in-situ characterization of heterogeneous catalysts, enabling readers to take full advantage of the sophisticated techniques used to study heterogeneous catalysts and reaction mechanisms. In using these techniques, readers can learn to improve the selectivity and the performance of catalysts and how to prepare catalysts as efficiently as possible, with minimum waste. In-situ Characterization of Heterogeneous Catalysts feat
Optimal Premium Pricing for a Heterogeneous Portfolio of Insurance Risks
Pantelous, Athanasios A.; Frangos, Nicholas E.; Zimbidis, Alexandros A.
2009-01-01
The paper revisits the classical problem of premium rating within a heterogeneous portfolio of insurance risks using a continuous stochastic control framework. The portfolio is divided into several classes where each class interacts with the others. The risks are modelled dynamically by the means of a Brownian motion. This dynamic approach is also transferred to the design of the premium process. The premium is not constant but equals the drift of the Brownian motion plus a controlled percent...
Integration of crosswell seismic data for simulating porosity in a heterogeneous carbonate aquifer
Emery, Xavier; Parra, Jorge
2013-11-01
A challenge for the geostatistical simulation of subsurface properties in mining, petroleum and groundwater applications is the integration of well logs and seismic measurements, which can provide information on geological heterogeneities at a wide range of scales. This paper presents a case study conducted at the Port Mayaca aquifer, located in western Martin County, Florida, in which it is of interest to simulate porosity, based on porosity logs at two wells and high-resolution crosswell seismic measurements of P-wave impedance. To this end, porosity and impedance are transformed into cross-correlated Gaussian random fields, using local transformations. The model parameters (transformation functions, mean values and correlation structure of the transformed fields) are inferred and checked against the data. Multiple realizations of porosity can then be constructed conditionally to the impedance information in the interwell region, which allow identifying one low-porosity structure and two to three flow units that connect the two wells, mapping heterogeneities within these units and visually assessing fluid paths in the aquifer. In particular, the results suggest that the paths in the lower flow units, formed by a network of heterogeneous conduits, are not as smooth as in the upper flow unit.
Interconnecting heterogeneous database management systems
Gligor, V. D.; Luckenbaugh, G. L.
1984-01-01
It is pointed out that there is still a great need for the development of improved communication between remote, heterogeneous database management systems (DBMS). Problems regarding the effective communication between distributed DBMSs are primarily related to significant differences between local data managers, local data models and representations, and local transaction managers. A system of interconnected DBMSs which exhibit such differences is called a network of distributed, heterogeneous DBMSs. In order to achieve effective interconnection of remote, heterogeneous DBMSs, the users must have uniform, integrated access to the different DBMs. The present investigation is mainly concerned with an analysis of the existing approaches to interconnecting heterogeneous DBMSs, taking into account four experimental DBMS projects.
Jones, A. A.; Holt, R. M.
2017-12-01
Image capturing in flow experiments has been used for fluid mechanics research since the early 1970s. Interactions of fluid flow between the vadose zone and permanent water table are of great interest because this zone is responsible for all recharge waters, pollutant transport and irrigation efficiency for agriculture. Griffith, et al. (2011) developed an approach where constructed reproducible "geologically realistic" sand configurations are deposited in sandfilled experimental chambers for light-transmitted flow visualization experiments. This method creates reproducible, reverse graded, layered (stratified) thin-slab sand chambers for point source experiments visualizing multiphase flow through porous media. Reverse-graded stratification of sand chambers mimic many naturally occurring sedimentary deposits. Sandfilled chambers use light as nonintrusive tools for measuring water saturation in two-dimensions (2-D). Homogeneous and heterogeneous sand configurations can be produced to visualize the complex physics of the unsaturated zone. The experimental procedure developed by Griffith, et al. (2011) was designed using now outdated and obsolete equipment. We have modernized this approach with new Parker Deadel linear actuator and programed projects/code for multiple configurations. We have also updated the Roper CCD software and image processing software with the latest in industry standards. Modernization of transmitted-light source, robotic equipment, redesigned experimental chambers, and newly developed analytical procedures have greatly reduced time and cost per experiment. We have verified the ability of the new equipment to generate reproducible heterogeneous sand-filled chambers and demonstrated the functionality of the new equipment and procedures by reproducing several gravity-driven fingering experiments conducted by Griffith (2008).
Tang, Jian; Jiang, Xiaoliang
2017-01-01
Image segmentation has always been a considerable challenge in image analysis and understanding due to the intensity inhomogeneity, which is also commonly known as bias field. In this paper, we present a novel region-based approach based on local entropy for segmenting images and estimating the bias field simultaneously. Firstly, a local Gaussian distribution fitting (LGDF) energy function is defined as a weighted energy integral, where the weight is local entropy derived from a grey level distribution of local image. The means of this objective function have a multiplicative factor that estimates the bias field in the transformed domain. Then, the bias field prior is fully used. Therefore, our model can estimate the bias field more accurately. Finally, minimization of this energy function with a level set regularization term, image segmentation, and bias field estimation can be achieved. Experiments on images of various modalities demonstrated the superior performance of the proposed method when compared with other state-of-the-art approaches.
On the convergence of finite state mean-field games through Γ-convergence
Ferreira, Rita C.; Gomes, Diogo A.
2014-01-01
In this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ-convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler-Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ-convergence problem. Our results generalize previous results related to long-term convergence for finite state problems. © 2014 Elsevier Inc.
On the convergence of finite state mean-field games through Γ-convergence
Ferreira, Rita C.
2014-10-01
In this study, we consider the long-term convergence (trend toward an equilibrium) of finite state mean-field games using Γ-convergence. Our techniques are based on the observation that an important class of mean-field games can be viewed as the Euler-Lagrange equation of a suitable functional. Therefore, using a scaling argument, one can convert a long-term convergence problem into a Γ-convergence problem. Our results generalize previous results related to long-term convergence for finite state problems. © 2014 Elsevier Inc.
EDUCATIONAL OPPORTUNITIES OF COLLAGE AS A DIDACTIC MEANS: INTERDISCIPLINARY APPROACH
Directory of Open Access Journals (Sweden)
I. B. Ryzhkina
2014-01-01
Full Text Available The research aim is to examine the functions and educational opportunities of collage as a didactic means.The methodology and methods involve the multilateral theoretical data analysis and generalization; activity approach to pupils’ perception analysis; communicative approach to finding the interrelation between the perception and speech act; lingua-cultural approach to collage consideration as a sign, information vehicle and communication subject; and developmental teaching approach.The author undertakes the cross-disciplinary analysis, including the scientific works on philosophy, psychology, semiotics and culture studies, and proves the collage adequacy to the cognitive specificity of modern pupils’perception and foreign-language teaching. The concept of collage is specified, its semiotic characteristics and unique features as a didactic means discussed.The research novelty involves developing a new frame of reference to collage as a didactic tool and cultural phenomenon with educational and developmental opportunities.The research findings, including the methodology basis for content structuring and selecting a collage type, can be used for educational problem solving.
Discrete Feature Approach for Heterogeneous Reservoir Production Enhancement
Energy Technology Data Exchange (ETDEWEB)
Dershowitz, William S.; Curran, Brendan; Einstein, Herbert; LaPointe, Paul; Shuttle, Dawn; Klise, Kate
2002-07-26
The report presents summaries of technology development for discrete feature modeling in support of the improved oil recovery (IOR) for heterogeneous reservoirs. In addition, the report describes the demonstration of these technologies at project study sites.
Deconstructing stem cell population heterogeneity: Single-cell analysis and modeling approaches
Wu, Jincheng; Tzanakakis, Emmanuel S.
2014-01-01
Isogenic stem cell populations display cell-to-cell variations in a multitude of attributes including gene or protein expression, epigenetic state, morphology, proliferation and proclivity for differentiation. The origins of the observed heterogeneity and its roles in the maintenance of pluripotency and the lineage specification of stem cells remain unclear. Addressing pertinent questions will require the employment of single-cell analysis methods as traditional cell biochemical and biomolecular assays yield mostly population-average data. In addition to time-lapse microscopy and flow cytometry, recent advances in single-cell genomic, transcriptomic and proteomic profiling are reviewed. The application of multiple displacement amplification, next generation sequencing, mass cytometry and spectrometry to stem cell systems is expected to provide a wealth of information affording unprecedented levels of multiparametric characterization of cell ensembles under defined conditions promoting pluripotency or commitment. Establishing connections between single-cell analysis information and the observed phenotypes will also require suitable mathematical models. Stem cell self-renewal and differentiation are orchestrated by the coordinated regulation of subcellular, intercellular and niche-wide processes spanning multiple time scales. Here, we discuss different modeling approaches and challenges arising from their application to stem cell populations. Integrating single-cell analysis with computational methods will fill gaps in our knowledge about the functions of heterogeneity in stem cell physiology. This combination will also aid the rational design of efficient differentiation and reprogramming strategies as well as bioprocesses for the production of clinically valuable stem cell derivatives. PMID:24035899
On transport in formations of large heterogeneity scales
International Nuclear Information System (INIS)
Dagan, Gedeon
1990-01-01
It has been suggested that in transport through heterogeneous aquifers, the effective dispersivity increases with the travel distance, since plumes encounter heterogeneity of increasing scales. This conclusion is underlain, however, by the assumption of ergodicity. If the plume is viewed as made up of different particles, this means that these particles move independently from a statistical point of view. To satisfy ergodicity the solute body has to be of a much larger extent than heterogeneity scales. Thus, if the latter are increasing for ever and the solute body is finite, ergodicity cannot be obeyed. To demonstrate this thesis we relate to the two-dimensional heterogeneity associated with transmissivity variations in the horizontal plane. First, the effective dispersion coefficient is defined as half the rate of change of the expected value of the solute body second spatial moment relative to its centroid. Subsequently the asymptotic large time limit of dispersivity is evaluated in terms of the log transmissivity integral scale and of the dimensions of the initial solute body in the direction of mean flow and normal to it. It is shown that for a thin plume aligned with the mean flow the effective dispersivity is zero and the effect of heterogeneity is a slight and finite expansion determined solely by the solute body size. In the case of a solute body transverse to the mean flow the effective dispersivity is different from zero, but has a maximal value which is again dependent on the solute body size and not on the heterogeneity scale. It is concluded that from a theoretical standpoint and for the definition of dispersivity adopted here for non-ergodic conditions, the claim of ever-increasing dispersivity with travel distance is not valid for the scale of heterogeneity analyzed here. (Author) (21 refs., 6 figs.)
Afshari, Saied; Hejazi, S. Hossein; Kantzas, Apostolos
2018-05-01
Miscible displacement of fluids in porous media is often characterized by the scaling of the mixing zone length with displacement time. Depending on the viscosity contrast of fluids, the scaling law varies between the square root relationship, a sign for dispersive transport regime during stable displacement, and the linear relationship, which represents the viscous fingering regime during an unstable displacement. The presence of heterogeneities in a porous medium significantly affects the scaling behavior of the mixing length as it interacts with the viscosity contrast to control the mixing of fluids in the pore space. In this study, the dynamics of the flow and transport during both unit and adverse viscosity ratio miscible displacements are investigated in heterogeneous packings of circular grains using pore-scale numerical simulations. The pore-scale heterogeneity level is characterized by the variations of the grain diameter and velocity field. The growth of mixing length is employed to identify the nature of the miscible transport regime at different viscosity ratios and heterogeneity levels. It is shown that as the viscosity ratio increases to higher adverse values, the scaling law of mixing length gradually shifts from dispersive to fingering nature up to a certain viscosity ratio and remains almost the same afterwards. In heterogeneous media, the mixing length scaling law is observed to be generally governed by the variations of the velocity field rather than the grain size. Furthermore, the normalization of mixing length temporal plots with respect to the governing parameters of viscosity ratio, heterogeneity, medium length, and medium aspect ratio is performed. The results indicate that mixing length scales exponentially with log-viscosity ratio and grain size standard deviation while the impact of aspect ratio is insignificant. For stable flows, mixing length scales with the square root of medium length, whereas it changes linearly with length during