Exact correlation functions in particle-reaction models with immobile particles

Exact results on particle densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through pair annihilation where each particle interacts once at most throughout its entire history. The resulting large number of stationary states leads to a non-vanishing configurational entropy. Our results are established for arbitrary initial conditions and are derived via a generating function method. The single-species model is the dual of the 1D zero-temperature kinetic Ising model with Kimball-Deker-Haake dynamics. In this way, both in finite and semi-infinite chains and also the Bethe lattice can be analysed. The relationship with the random sequential adsorption of dimers and weakly tapped granular materials is discussed.

Nonlocal growth processes and conformal invariance

Up to now the raise-and-peel model was the single known example of a one-dimensional stochastic process where one can observe conformal invariance. The model has one parameter. Depending on its value one has a gapped phase, a critical point where one has conformal invariance, and a gapless phase with changing values of the dynamical critical exponent z. In this model, adsorption is local but desorption is not. The raise-and-strip model presented here, in which desorption is also nonlocal, has the same phase diagram. The critical exponents are different as are some physical properties of the model. Our study suggests the possible existence of a whole class of stochastic models in which one can observe conformal invariance.

Nonlocal asymmetric exclusion process on a ring and conformal invariance

We present a one-dimensional nonlocal hopping model with exclusion on a ring. The model is related to the Raise and Peel growth model. A nonnegative parameter u controls the ratio of the local backwards and nonlocal forwards hopping rates. The phase diagram, and consequently the values of the current, depend on u and the density of particles. In the special case of half-lling and u = 1 the system is conformal invariant and an exact value of the current for any size L of the system is conjectured and checked for large lattice sizes in Monte Carlo simulations. For u > 1 the current has a non-analytic dependence on the density when the latter approaches the half-lling value.

Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions

We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an exactly solvable high-spin asymmetric quantum Hamiltonian that is the infinitesimal generator of the zero range process. Generally, the critical dynamics of the interface fluctuations is in the Kardar-Parisi-Zhang universality class of critical behavior. We remark that a whole family of RSOS interface models similar to the Ising interface model investigated here can be described by exactly solvable restricted high-spin quantum XXZ-type Hamiltonians. (C) 2012 Elsevier B.V. All rights reserved.

Mathematical modeling and analysis of the particle interactions in the direct filtration using the colloidal theory

This work used the colloidal theory to describe forces and energy interactions of colloidal complexes in the water and those formed during filtration run in direct filtration. Many interactions of particle energy profiles between colloidal surfaces for three geometries are presented here in: spherical, plate and cylindrical; and four surface interactions arrangements: two cylinders, two spheres, two plates and a sphere and a plate. Two different situations were analyzed, before and after electrostatic destabilization by action of the alum sulfate as coagulant in water studies samples prepared with kaolin. In the case were used mathematical modeling by extended DLVO theory (from the names: Derjarguin-Landau-Verwey-Overbeek) or XDLVO, which include traditional approach of the electric double layer (EDL), surfaces attraction forces or London-van der Waals (LvdW), esteric forces and hydrophobic forces, additionally considering another forces in colloidal system, like molecular repulsion or Born Repulsion and Acid-Base (AB) chemical function forces from Lewis.

Dynamics of phytoplankton associations in three reservoirs in northeastern Brazil assessed using Reynolds' theory

The aim of the present study was to evaluate the influence of seasonality on the behavior of phytoplankton associations in eutrophic reservoirs with different depths in northeastern Brazil. Five collections were carried out at each of the reservoirs at two depths (0.1 m and near the sediment) at three-month intervals in each season (dry and rainy). The phytoplankton samples were preserved in Lugol's solution and quantified under an inverted microscope for the determination of density values, which were subsequently converted to biomass values based on cellular biovolume and classified in phytoplankton associations. The following abiotic variables were analyzed: water temperature, dissolved oxygen, pH, turbidity, water transparency, total phosphorus, total dissolved phosphorus, orthophosphate and total nitrogen. The data were investigated using canonical correspondence analysis. The influence of seasonality on the dynamics of the phytoplankton community was lesser in the deeper reservoirs. Depth affected the behavior of the algal associations. Variation in light availability was a determinant of changes in the phytoplankton structure. Urosolenia and Anabaena associations were more abundant in shallow ecosystems with a larger eutrophic zone, whereas the Microcystis association was more related to deep ecosystems with adequate availability of nutrients. The distribution of Cyclotella, Geitlerinema, Planktothrix, Pseudanabaena and Cylindrospermopsis associations was different from that seen in subtropical regions and the substitution of these associations was related to a reduction in the eutrophic zone rather than the mixture zone. Published by Elsevier GmbH.

Stochastic competitive learning in complex networks

Competitive learning is an important machine learning approach which is widely employed in artificial neural networks. In this paper, we present a rigorous definition of a new type of competitive learning scheme realized on large-scale networks. The model consists of several particles walking within the network and competing with each other to occupy as many nodes as possible, while attempting to reject intruder particles. The particle's walking rule is composed of a stochastic combination of random and preferential movements. The model has been applied to solve community detection and data clustering problems. Computer simulations reveal that the proposed technique presents high precision of community and cluster detections, as well as low computational complexity. Moreover, we have developed an efficient method for estimating the most likely number of clusters by using an evaluator index that monitors the information generated by the competition process itself. We hope this paper will provide an alternative way to the study of competitive learning.

Particle Acceleration in Turbulence and Weakly Stochastic Reconnection

In this Letter we analyze the energy distribution evolution of test particles injected in three dimensional (3D) magnetohydrodynamic (MHD) simulations of different magnetic reconnection configurations. When considering a single Sweet-Parker topology, the particles accelerate predominantly through a first-order Fermi process, as predicted in [3] and demonstrated numerically in [8]. When turbulence is included within the current sheet, the acceleration rate is highly enhanced, because reconnection becomes fast and independent of resistivity [4,11] and allows the formation of a thick volume filled with multiple simultaneously reconnecting magnetic fluxes. Charged particles trapped within this volume suffer several head-on scatterings with the contracting magnetic fluctuations, which significantly increase the acceleration rate and results in a first-order Fermi process. For comparison, we also tested acceleration in MHD turbulence, where particles suffer collisions with approaching and receding magnetic irregularities, resulting in a reduced acceleration rate. We argue that the dominant acceleration mechanism approaches a second order Fermi process in this case.

Bacterial and phytoplankton dynamics in a sub-tropical estuary

Heterotrophic bacterial and biomass, production, specific growth rates and growth efficiencies were studied in July 2001 and January 2002 during both spring and neap tides, along a tidal cycle, at three sites in a subtropical estuary. Major freshwater inputs located in the Northern region led to differences in both and bacterioplankton biomass and activity along the estuary. While in the Northern region is light-limited, with mean production (PP) between 1.1 and 1.9 mu g C l(-1) h(-1) and mean specific growth rates (PSG) between 0.14 and 0.16 d(-1), the Southern region registered values as high as 24.7 mu g C l(-1) h(-1) for PP and 2.45 d(-1) (mean PP between 3.4 and 7.3 mu g C l(-1) h(-1); mean PSG between 0.28 and 0.57 d(-1)). On the other hand, maximum bacterial production (BP: 63.8 mu g C l(-1) h(-1)) and specific growth rate (BSG: 32.26 d(-1)) were observed in the Northern region (mean BP between 3.4 and 12.8 mu g C l(-1) h(-1); mean BSG between 1.98 and 6.67 day(-1)). These bacterial activity rates are among the highest recorded rates in estuarine and coastal waters, indicating that this system can be highly heterotrophic, due to high loads of allochthonous carbon (mainly derived from mangrove forest). Our results also showed that, despite that BP rates usually exceeded PP, in the Southern region BP may be partially supported (similar to 45%) by PP, since a significant regression was observed between BP and PP (r = 0.455, P < 0.001).

Connections between the Sznajd model with general confidence rules and graph theory

The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabasi-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q > 2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).

Analytic perturbation theory for bound states in the transfer matrix spectrum of weakly correlated lattice ferromagnetic spin systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region ('beta' << 1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter 'alfa' = ('S POT.4') - 3 '(S POT.2') POT.2' > 0, i.e. in the region which we call Gaussian subjugation, where ('S POT.K') denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass -ln 'beta' and a bound state below the two-particle threshold. We develop a 'beta' analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in 'beta'.

Influence of the magnetization damping on dynamic hysteresis loops in single domain particles

This article reports on the influence of the magnetization damping on dynamic hysteresis loops in single-domain particles with uniaxial anisotropy. The approach is based on the Neel-Brown theory and the hierarchy of differential recurrence relations, which follow from averaging over the realizations of the stochastic Landau-Lifshitz equation. A new method of solution is proposed, where the resulting system of differential equations is solved directly using optimized algorithms to explore its sparsity. All parameters involved in uniaxial systems are treated in detail, with particular attention given to the frequency dependence. It is shown that in the ferromagnetic resonance region, novel phenomena are observed for even moderately low values of the damping. The hysteresis loops assume remarkably unusual shapes, which are also followed by a pronounced reduction of their heights. Also demonstrated is that these features remain for randomly oriented ensembles and, moreover, are approximately independent of temperature and particle size. (C) 2012 American Institute of Physics. [doi:10.1063/1.3684629]

Integrable Models: from Dynamical Solutions to String Theory

We review the status of integrable models from the point of view of their dynamics and integrability conditions. A few integrable models are discussed in detail. We comment on the use it is made of them in string theory. We also discuss the SO(6) symmetric Hamiltonian with SO(6) boundary. This work is especially prepared for the 70th anniversaries of Andr, Swieca (in memoriam) and Roland Koberle.

Inconsistent-tolerant base revision through Argument Theory Change

Reasoning and change over inconsistent knowledge bases (KBs) is of utmost relevance in areas like medicine and law. Argumentation may bring the possibility to cope with both problems. Firstly, by constructing an argumentation framework (AF) from the inconsistent KB, we can decide whether to accept or reject a certain claim through the interplay among arguments and counterarguments. Secondly, by handling dynamics of arguments of the AF, we might deal with the dynamics of knowledge of the underlying inconsistent KB. Dynamics of arguments has recently attracted attention and although some approaches have been proposed, a full axiomatization within the theory of belief revision was still missing. A revision arises when we want the argumentation semantics to accept an argument. Argument Theory Change (ATC) encloses the revision operators that modify the AF by analyzing dialectical trees-arguments as nodes and attacks as edges-as the adopted argumentation semantics. In this article, we present a simple approach to ATC based on propositional KBs. This allows to manage change of inconsistent KBs by relying upon classical belief revision, although contrary to it, consistency restoration of the KB is avoided. Subsequently, a set of rationality postulates adapted to argumentation is given, and finally, the proposed model of change is related to the postulates through the corresponding representation theorem. Though we focus on propositional logic, the results can be easily extended to more expressive formalisms such as first-order logic and description logics, to handle evolution of ontologies.

Alfven eigenmode properties and dynamics in the TJ-II stellarator

Alfven eigenmodes (AEs) were studied in neutral beam injection (NBI) heated plasmas in the TJ-II stellarator using a heavy ion beam probe (HIBP) in the core, and by Langmuir (LP) and Mirnov probes (MP) at the edge. AEs were detected over the whole plasma radius by the HIBP with a spatial resolution of about 1 cm. AE-induced oscillations were detected in the plasma density n(e), electric potential phi and poloidal magnetic field B-pol with frequencies 50 kHz < f(AE) < 300 kHz. The LP, MP and HIBP data showed a high level of coherency for specific branches of AEs. Poloidal mode wave-vectors k(theta), mode numbers m (m < 8) and propagation velocities V-theta similar to 30 km s(-1) were detected for various branches of AEs, having different radial locations. When the density rose due to NBI fuelling, the AE frequency decreased as predicted by the Alfven law f(AE) similar to n(e)(-1/2). During the AE frequency decay the following new AE features were observed: (i) the poloidal wave-vector k(theta) and mode number m remained constant, (ii) the cross-phases between the oscillations in B-pol, n(e) and electric potential remained constant, having an individual value for each AE branch, (iii) V-theta decreased proportional to the AE frequency. The interaction of the AEs with the bulk (thermal) plasma resulted in clearly pronounced quasi-coherent peaks in the electrostatic turbulent particle flux spectra. Various AE branches exhibited different contributions to the particle flux: outward, inward and also zero, depending on the phase relations between the oscillations in E-pol and n(e), which are specific for each branch. A comparison with MHD mode modelling indicated that some of the more prominent frequency branches can be identified as radially extended helical AEs.