Relaxation time of processes driven by multiplicative noise

We consider systems described by nonlinear stochastic differential equations with multiplicative noise. We study the relaxation time of the steady-state correlation function as a function of noise parameters. We consider the white- and nonwhite-noise case for a prototype model for which numerical data are available. We discuss the validity of analytical approximation schemes. For the white-noise case we discuss the results of a projector-operator technique. This discussion allows us to give a generalization of the method to the non-white-noise case. Within this generalization, we account for the growth of the relaxation time as a function of the correlation time of the noise. This behavior is traced back to the existence of a non-Markovian term in the equation for the correlation function.

Quasilocal density functional theory and its application within the extended Thomas-Fermi approximation

In this paper we propose a generalization of the density functional theory. The theory leads to single-particle equations of motion with a quasilocal mean-field operator, which contains a quasiparticle position-dependent effective mass and a spin-orbit potential. The energy density functional is constructed using the extended Thomas-Fermi approximation and the ground-state properties of doubly magic nuclei are considered within the framework of this approach. Calculations were performed using the finite-range Gogny D1S forces and the results are compared with the exact Hartree-Fock calculations

System-level Support for Mobile Ad hoc Communications: an Algorithmic & Practical Approach

A mobile ad hoc network (MANET) is a decentralized and infrastructure-less network. This thesis aims to provide support at the system-level for developers of applications or protocols in such networks. To do this, we propose contributions in both the algorithmic realm and in the practical realm. In the algorithmic realm, we contribute to the field by proposing different context-aware broadcast and multicast algorithms in MANETs, namely six-shot broadcast, six-shot multicast, PLAN-B and ageneric algorithmic approach to optimize the power consumption of existing algorithms. For each algorithm we propose, we compare it to existing algorithms that are either probabilistic or context-aware, and then we evaluate their performance based on simulations. We demonstrate that in some cases, context-aware information, such as location or signal-strength, can improve the effciency. In the practical realm, we propose a testbed framework, namely ManetLab, to implement and to deploy MANET-specific protocols, and to evaluate their performance. This testbed framework aims to increase the accuracy of performance evaluation compared to simulations, while keeping the ease of use offered by the simulators to reproduce a performance evaluation. By evaluating the performance of different probabilistic algorithms with ManetLab, we observe that both simulations and testbeds should be used in a complementary way. In addition to the above original contributions, we also provide two surveys about system-level support for ad hoc communications in order to establish a state of the art. The first is about existing broadcast algorithms and the second is about existing middleware solutions and the way they deal with privacy and especially with location privacy. - Un réseau mobile ad hoc (MANET) est un réseau avec une architecture décentralisée et sans infrastructure. Cette thèse vise à fournir un support adéquat, au niveau système, aux développeurs d'applications ou de protocoles dans de tels réseaux. Dans ce but, nous proposons des contributions à la fois dans le domaine de l'algorithmique et dans celui de la pratique. Nous contribuons au domaine algorithmique en proposant différents algorithmes de diffusion dans les MANETs, algorithmes qui sont sensibles au contexte, à savoir six-shot broadcast,six-shot multicast, PLAN-B ainsi qu'une approche générique permettant d'optimiser la consommation d'énergie de ces algorithmes. Pour chaque algorithme que nous proposons, nous le comparons à des algorithmes existants qui sont soit probabilistes, soit sensibles au contexte, puis nous évaluons leurs performances sur la base de simulations. Nous montrons que, dans certains cas, des informations liées au contexte, telles que la localisation ou l'intensité du signal, peuvent améliorer l'efficience de ces algorithmes. Sur le plan pratique, nous proposons une plateforme logicielle pour la création de bancs d'essai, intitulé ManetLab, permettant d'implémenter, et de déployer des protocoles spécifiques aux MANETs, de sorte à évaluer leur performance. Cet outil logiciel vise à accroître la précision desévaluations de performance comparativement à celles fournies par des simulations, tout en conservant la facilité d'utilisation offerte par les simulateurs pour reproduire uneévaluation de performance. En évaluant les performances de différents algorithmes probabilistes avec ManetLab, nous observons que simulateurs et bancs d'essai doivent être utilisés de manière complémentaire. En plus de ces contributions principales, nous fournissons également deux états de l'art au sujet du support nécessaire pour les communications ad hoc. Le premier porte sur les algorithmes de diffusion existants et le second sur les solutions de type middleware existantes et la façon dont elles traitent de la confidentialité, en particulier celle de la localisation.

Binding energy and momentum distribution of nuclear matter using Green's functions methods

The influence of hole-hole (h-h) propagation in addition to the conventional particle-particle (p-p) propagation, on the energy per particle and the momentum distribution is investigated for the v2 central interaction which is derived from Reid¿s soft-core potential. The results are compared to Brueckner-Hartree-Fock calculations with a continuous choice for the single-particle (SP) spectrum. Calculation of the energy from a self-consistently determined SP spectrum leads to a lower saturation density. This result is not corroborated by calculating the energy from the hole spectral function, which is, however, not self-consistent. A generalization of previous calculations of the momentum distribution, based on a Goldstone diagram expansion, is introduced that allows the inclusion of h-h contributions to all orders. From this result an alternative calculation of the kinetic energy is obtained. In addition, a direct calculation of the potential energy is presented which is obtained from a solution of the ladder equation containing p-p and h-h propagation to all orders. These results can be considered as the contributions of selected Goldstone diagrams (including p-p and h-h terms on the same footing) to the kinetic and potential energy in which the SP energy is given by the quasiparticle energy. The results for the summation of Goldstone diagrams leads to a different momentum distribution than the one obtained from integrating the hole spectral function which in general gives less depletion of the Fermi sea. Various arguments, based partly on the results that are obtained, are put forward that a self-consistent determination of the spectral functions including the p-p and h-h ladder contributions (using a realistic interaction) will shed light on the question of nuclear saturation at a nonrelativistic level that is consistent with the observed depletion of SP orbitals in finite nuclei.

Interfacial growth in driven diffusive systems

We have studied the growth of interfaces in driven diffusive systems well below the critical temperature by means of Monte Carlo simulations. We consider the region beyond the linear regime and of large values of the external field which has not been explored before. The simulations support the existence of interfacial traveling waves when asymmetry is introduced in the model, a result previously predicted by a linear-stability analysis. Furthermore, the generalization of the Gibbs-Thomson relation is discussed. The results provide evidence that the external field is a stabilizing effect which can be considered as effectively increasing the surface tension.

Is Tsallis thermodynamics nonextensive?

Within the Tsallis thermodynamics framework, and using scaling properties of the entropy, we derive a generalization of the Gibbs-Duhem equation. The analysis suggests a transformation of variables that allows standard thermodynamics to be recovered. Moreover, we also generalize Einsteins formula for the probability of a fluctuation to occur by means of the maximum statistical entropy method. The use of the proposed transformation of variables also shows that fluctuations within Tsallis statistics can be mapped to those of standard statistical mechanics.

Diffusion in spatially and temporarily inhomogeneous media

In this paper we consider diffusion of a passive substance C in a temporarily and spatially inhomogeneous two-dimensional medium. As a realization for the latter we choose a phase-separating medium consisting of two substances A and B, whose dynamics is determined by the Cahn-Hilliard equation. Assuming different diffusion coefficients of C in A and B, we find that the variance of the distribution function of the said substance grows less than linearly in time. We derive a simple identity for the variance using a probabilistic ansatz and are then able to identify the interface between A and B as the main cause for this nonlinear dependence. We argue that, finally, for very large times the here temporarily dependent diffusion "constant" goes like t-1/3 to a constant asymptotic value D¿. The latter is calculated approximately by employing the effective-medium approximation and by fitting the simulation data to the said time dependence.

Reply to Comment on 'Two-finger selection theory in the Saffman-Taylor problem

We clarify the meaning of the results of Phys. Rev. E 60, R5013 (1999). We discuss the use and implications of periodic boundary conditions, as opposed to rigid-wall ones. We briefly argue that the solutions of the paper above are physically relevant as part of a more general issue, namely the possible generalization to dynamics, of the microscopic solvability scenario of selection.

New perspectives in the use of ink evidence in forensic science: Part III: Operational applications and evaluation

The research reported in this series of article aimed at (1) automating the search of questioned ink specimens in ink reference collections and (2) at evaluating the strength of ink evidence in a transparent and balanced manner. These aims require that ink samples are analysed in an accurate and reproducible way and that they are compared in an objective and automated way. This latter requirement is due to the large number of comparisons that are necessary in both scenarios. A research programme was designed to (a) develop a standard methodology for analysing ink samples in a reproducible way, (b) comparing automatically and objectively ink samples and (c) evaluate the proposed methodology in forensic contexts. This report focuses on the last of the three stages of the research programme. The calibration and acquisition process and the mathematical comparison algorithms were described in previous papers [C. Neumann, P. Margot, New perspectives in the use of ink evidence in forensic science-Part I: Development of a quality assurance process for forensic ink analysis by HPTLC, Forensic Sci. Int. 185 (2009) 29-37; C. Neumann, P. Margot, New perspectives in the use of ink evidence in forensic science- Part II: Development and testing of mathematical algorithms for the automatic comparison of ink samples analysed by HPTLC, Forensic Sci. Int. 185 (2009) 38-50]. In this paper, the benefits and challenges of the proposed concepts are tested in two forensic contexts: (1) ink identification and (2) ink evidential value assessment. The results show that different algorithms are better suited for different tasks. This research shows that it is possible to build digital ink libraries using the most commonly used ink analytical technique, i.e. high-performance thin layer chromatography, despite its reputation of lacking reproducibility. More importantly, it is possible to assign evidential value to ink evidence in a transparent way using a probabilistic model. It is therefore possible to move away from the traditional subjective approach, which is entirely based on experts' opinion, and which is usually not very informative. While there is room for the improvement, this report demonstrates the significant gains obtained over the traditional subjective approach for the search of ink specimens in ink databases, and the interpretation of their evidential value.

Statistical mechanics in the extended Gaussian ensemble

The extended Gaussian ensemble (EGE) is introduced as a generalization of the canonical ensemble. This ensemble is a further extension of the Gaussian ensemble introduced by Hetherington [J. Low Temp. Phys. 66, 145 (1987)]. The statistical mechanical formalism is derived both from the analysis of the system attached to a finite reservoir and from the maximum statistical entropy principle. The probability of each microstate depends on two parameters ß and ¿ which allow one to fix, independently, the mean energy of the system and the energy fluctuations, respectively. We establish the Legendre transform structure for the generalized thermodynamic potential and propose a stability criterion. We also compare the EGE probability distribution with the q-exponential distribution. As an example, an application to a system with few independent spins is presented.

On the many-time formulation of classical particle dynamics

Starting from the standard one-time dynamics of n nonrelativistic particles, the n-time equations of motion are inferred, and a variational principle is formulated. A suitable generalization of the classical LieKnig theorem is demonstrated, which allows the determination of all the associated presymplectic structures. The conditions under which the action of an invariance group is canonical are studied, and a corresponding Noether theorem is deduced. A formulation of the theory in terms of n first-class constraints is recovered by means of coisotropic imbeddings. The proposed approach also provides for a better understanding of the relativistic particle dynamics, since it shows that the different roles of the physical positions and the canonical variables is not peculiar to special relativity, but rather to any n-time approach: indeed a nonrelativistic no-interaction theorem is deduced.

Theory for correlation functions of processes driven by external colored noise

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.

Automatic Mapping and Classification of Spatial Environmental Data

The paper deals with the development and application of the generic methodology for automatic processing (mapping and classification) of environmental data. General Regression Neural Network (GRNN) is considered in detail and is proposed as an efficient tool to solve the problem of spatial data mapping (regression). The Probabilistic Neural Network (PNN) is considered as an automatic tool for spatial classifications. The automatic tuning of isotropic and anisotropic GRNN/PNN models using cross-validation procedure is presented. Results are compared with the k-Nearest-Neighbours (k-NN) interpolation algorithm using independent validation data set. Real case studies are based on decision-oriented mapping and classification of radioactively contaminated territories.

Fragile-glass behavior of a short-range p-spin model

We propose a short-range generalization of the p-spin interaction spin-glass model. The model is well suited to test the idea that an entropy collapse is at the bottom line of the dynamical singularity encountered in structural glasses. The model is studied in three dimensions through Monte Carlo simulations, which put in evidence fragile glass behavior with stretched exponential relaxation and super-Arrhenius behavior of the relaxation time. Our data are in favor of a Vogel-Fulcher behavior of the relaxation time, related to an entropy collapse at the Kauzmann temperature. We, however, encounter difficulties analogous to those found in experimental systems when extrapolating thermodynamical data at low temperatures. We study the spin-glass susceptibility, investigating the behavior of the correlation length in the system. We find that the increase of the relaxation time is accompanied by a very slow growth of the correlation length. We discuss the scaling properties of off-equilibrium dynamics in the glassy regime, finding qualitative agreement with the mean-field theory.

Stochastic semiclassical gravity

In the first part of this paper, we show that the semiclassical Einstein-Langevin equation, introduced in the framework of a stochastic generalization of semiclassical gravity to describe the back reaction of matter stress-energy fluctuations, can be formally derived from a functional method based on the influence functional of Feynman and Vernon. In the second part, we derive a number of results for background solutions of semiclassical gravity consisting of stationary and conformally stationary spacetimes and scalar fields in thermal equilibrium states. For these cases, fluctuation-dissipation relations are derived. We also show that particle creation is related to the vacuum stress-energy fluctuations and that it is enhanced by the presence of stochastic metric fluctuations.