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At least 721 records · Page 40

Assessment of the Time a Power System Remains in the Power Deficit Zone as a Function of the Scale Factor for Wind-Power Plants

The scale factor for the use of power plants of a certain type refers to the fraction of their use in the overall energy balance of the system. Energy production by wind power plants depends directly on the wind conditions in a particular location and is stochastic in character. Increasing the fraction of these installations in the overall balance of a system also requires an increase in the power reserve capacity. Here the time a power system remains in the power deficit zone is estimated as a function of the fraction of wind power plants in the system structure. Two approaches to the placement of wind power units within a power system are compared– individual components and a system of a set of components. It is concluded that even within a small power system, combining geographically distributed components with favorable and unfavorable wind conditions into a system can have a positive effect on all the components within certain ranges of the scale factor.

17 WIND ENERGY↗

Determination of the Coefficients of Heat Transfer and Friction in Supercritical-Pressure Nuclear Reactors with Account of the Intensity and Scale of Flow Turbulence on the Basis of the Theory of Stochastic Equations and Equivalence of Measures

New dependences of the coefficients of heat transfer and friction have been presented which are used for calculations in the reactor core at a supercritical water pressure by taking account of the parameters of perturbation in the coolant flow: of the intensity and scale of flow turbulence. These solutions have been obtained based on stochastic systems of equations for the turbulence and the equivalence of measures between deterministic (laminar) and random (turbulent) flows.

42 ENGINEERING↗

Eddy Current Probe Parameters Identification Using a Genetic Algorithm and Simultaneous Perturbation Stochastic Approximation

This study tries to identify the coil parameters using numerical methods. The eddy current testing (ECT) is used for evaluation of a crack with the aid of numerical simulations by utilizing the identification of these parameters. In this study, a comparison of the performance of the GA and SPSA algorithms to identify the parameter values of the coil sensors are presented. So, the optimization probe geometry is introduced in the simulation with Three-dimensional finite element simulations (FLUX finite element code) were conducted to obtain eddy current signals resulting from a crack in a plate made of aluminium. The simulation results are compared with experimental measurements for the defect present in a plate.

42 ENGINEERING↗

Dynamic Magnetic Hysteresis Behaviors in a Mixed Spin (3/2, 2) Bilayer System with Different Crystal-Field Interactions

Dynamic magnetic hysteresis (DMH) behaviors of the mixed spin-3/2 and spin-2 Ising bilayer system with different crystal-field interactions on a two-layer square lattice is studied by the use of dynamic mean field calculations based on the Glauber-type stochastic. The hysteresis loops are obtained for different reduced temperatures (T), magnetic field amplitudes (h), frequencies (w) and interlayer coupling constants (J{sub 3}). Influences of the T, h, w and J{sub 3} on the DMH properties are investigated. We also study the temperature, frequency and interlayer coupling interaction dependence of the coercive field and remanent magnetization. We compare our results with some theoretical and experimental works and observe a quantitatively good agreement with some theoretical and experimental results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Kinetic Phase Transition in the Semi-infinite Spin-1 Ising Model Under a Periodically Oscillating Magnetic Field

The kinetics of the semi-infinite Ising model in the presence of a time-dependent oscillating external field is studied within the framework of the mean-field approach. We use the Glauber-type stochastic dynamics to describe the evolution time of this system. We present a variety of phase in a semi-infinite cubic ferromagnet with spin-1 in two different, planes; phase diagrams contain (BF, S {sub 1}P, SP) phase, (BF, S {sub 1}F, SP) phase, completely ordered phase (BF, S {sub 1}F, SF) and completely disordered phase (BP, S {sub 1}P, SP), which strongly depend on interaction parameters. The nature first and second orders of the transitions is characterized by studying the thermal behaviors of the dynamic magnetizations. Furthermore, the system exhibits dynamical tricritical phenomenon and the reentrant behaviors. The magnetizations and phase space trajectories are given and discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Dynamic Magnetic Features of the Mixed Ising System on the Bilayer Square Lattice

In order to study the dynamic magnetic features of the mixed spin-1 and spin-5/2 Ising system, we have used the mean-field theory (MFT) based on the Glauber-type stochastic dynamics on the bilayer square lattice (BSL). By employing the Master equation, dynamic equations describing the behavior of the system are derived. The average order parameters and dynamic order parameters are studied for different values of exchange interactions, oscillating magnetic field, and temperature. The complete dynamic phase diagrams (DPDs) are obtained for the ferromagnetic/ferromagnetic (FM/FM), ferromagnetic/antiferromagnetic (FM/AFM), and antiferromagnetic/antiferromagnetic (AFM/AFM) interactions in the different planes, and the role of the interaction in the Hamiltonian on the DPDs is explored. It is found that the DPDs display richer dynamic behavior for this mixed Ising system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Random Crystal Field Effect on the Kinetic Spin-1 and Spin-3/2 Under a Time-Dependent Oscillating Field Phase Transitions

The effect of random crystal field on the stationary states of the kinetic spin-1 and spin-3/2 Blume-Capel model is investigated within the framework of the mean field approach. The Glauber-type stochastic dynamics is used to describe the time evolution of the system which is subjected to a time-dependent oscillating external magnetic field. The model exhibits first- and second-order transitions as well as dynamical tricritical, triple and an isolated critical end points. We found that the system displays reentrant phenomenon for both α = 0 and α > 0. Moreover, the system exhibits in the phase space a fixed points and limit cycles with circle, elliptic and parallelogram shapes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nonlinear Dynamic Characteristics and Control of Giant Magnetostrictive Ultrasonic Transducer

The nonlinear dynamic characteristics of giant magnetostrictive ultrasonic transducer (GMUT) are researched in this paper, and the optimal control strategy is proposed. New nonlinear differential terms are introduced to explain the hysteretic phenomena of giant magnetostrictive materials (GMM), and the nonlinear dynamic model of a giant magnetostrictive ultrasonic transducer subjected to harmonic magnetic field and stochastic disturbance is developed. The system’s nonlinear dynamic responses are discussed, and the optimal control strategy is proposed to improve the system’s accuracy. Numerical simulation and experiment results show that there are abundant nonlinear dynamic behaviors in the system; the stability of the system varies with the parameters, which causes stochastic bifurcation; the system’s accuracy is improved through stochastic optimal control. The results of this study are helpful for the application of giant magnetostrictive ultrasonic transducer in engineering fields.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

On the Small Mass Limit of Quantum Brownian Motion with Inhomogeneous Damping and Diffusion

We study the small mass limit (or: the Smoluchowski–Kramers limit) of a class of quantum Brownian motions with inhomogeneous damping and diffusion. For Ohmic bath spectral density with a Lorentz–Drude cutoff, we derive the Heisenberg–Langevin equations for the particle’s observables using a quantum stochastic calculus approach. We set the mass of the particle to equal m=m{sub 0}ϵ, the reduced Planck constant to equal ℏ=ϵ and the cutoff frequency to equal Λ=E{sub Λ}/ϵ, where m{sub 0} and E{sub Λ} are positive constants, so that the particle’s de Broglie wavelength and the largest energy scale of the bath are fixed as ϵ→0. We study the limit as ϵ→0 of the rescaled model and derive a limiting equation for the (slow) particle’s position variable. We find that the limiting equation contains several drift correction terms, the quantum noise-induced drifts, including terms of purely quantum nature, with no classical counterparts.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Stochastic Spatial Models in Ecology: A Statistical Physics Approach

Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions accounting for general empirical patterns in communities of competing species. However, while neutral theory in well-mixed ecosystems is mathematically well understood, spatial models still present several open problems, limiting the quantitative understanding of spatial biodiversity. In this review, we discuss the state of the art in spatial neutral theory. We emphasize the connection between spatial ecological models and the physics of non-equilibrium phase transitions and how concepts developed in statistical physics translate in population dynamics, and vice versa. We focus on non-trivial scaling laws arising at the critical dimension D=2 of spatial neutral models, and their relevance for biological populations inhabiting two-dimensional environments. We conclude by discussing models incorporating non-neutral effects in the form of spatial and temporal disorder, and analyze how their predictions deviate from those of purely neutral theories.

54 ENVIRONMENTAL SCIENCES↗

Density Large Deviations for Multidimensional Stochastic Hyperbolic Conservation Laws

We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law. When the mobility and diffusivity matrices are proportional, i.e. an Einstein-like relation is satisfied, the problem has been solved in Bellettini and Mariani (Bull Greek Math Soc 57:31–45, 2010). When this proportionality does not hold, we compute explicitly the large deviation function for a step-like density profile, and we show that the associated optimal current has a non trivial structure. We also derive a lower bound for the large deviation function, valid for a more general weak solution, and leave the general large deviation function upper bound as a conjecture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Universality Classes of Interaction Structures for NK Fitness Landscapes

Kauffman’s NK-model is a paradigmatic example of a class of stochastic models of genotypic fitness landscapes that aim to capture generic features of epistatic interactions in multilocus systems. Genotypes are represented as sequences of L binary loci. The fitness assigned to a genotype is a sum of contributions, each of which is a random function defined on a subset of k≤L loci. These subsets or neighborhoods determine the genetic interactions of the model. Whereas earlier work on the NK model suggested that most of its properties are robust with regard to the choice of neighborhoods, recent work has revealed an important and sometimes counter-intuitive influence of the interaction structure on the properties of NK fitness landscapes. Here we review these developments and present new results concerning the number of local fitness maxima and the statistics of selectively accessible (that is, fitness-monotonic) mutational pathways. In particular, we develop a unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of L, and identify two different universality classes of interaction structures that display different asymptotics of this quantity for large k. Moreover, we show that the probability that the fitness landscape can be traversed along an accessible path decreases exponentially in L for a large class of interaction structures that we characterize as locally bounded. Finally, we discuss the impact of the NK interaction structures on the dynamics of evolution using adaptive walk models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On a Homogenization Problem

We study the average Green’s function of stochastic, uniformly elliptic operators of divergence form on Zdℤ{sup d}. When the randomness is independent and has small variance, we prove regularity of the Fourier transform of the self-energy. The proof relies on the Schur complement formula and the analysis of singular integral operators combined with a Steinhaus system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Convergence and Efficiency of Adaptive Importance Sampling Techniques with Partial Biasing

We propose a new Monte Carlo method to efficiently sample a multimodal distribution (known up to a normalization constant). We consider a generalization of the discrete-time Self Healing Umbrella Sampling method, which can also be seen as a generalization of well-tempered metadynamics. The dynamics is based on an adaptive importance technique. The importance function relies on the weights (namely the relative probabilities) of disjoint sets which form a partition of the space. These weights are unknown but are learnt on the fly yielding an adaptive algorithm. In the context of computational statistical physics, the logarithm of these weights is, up to an additive constant, the free-energy, and the discrete valued function defining the partition is called the collective variable. The algorithm falls into the general class of Wang–Landau type methods, and is a generalization of the original Self Healing Umbrella Sampling method in two ways: (i) the updating strategy leads to a larger penalization strength of already visited sets in order to escape more quickly from metastable states, and (ii) the target distribution is biased using only a fraction of the free-energy, in order to increase the effective sample size and reduce the variance of importance sampling estimators. We prove the convergence of the algorithm and analyze numerically its efficiency on a toy example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Flocking of the Motsch–Tadmor Model with a Cut-Off Interaction Function

In this paper, we study the flocking behavior of the Motsch–Tadmor model with a cut-off interaction function. Our analysis shows that connectedness is important for flocking of this kind of model. Fortunately, we get a sufficient condition imposed only on the model parameters and initial data to guarantee the connectedness of the neighbor graph associated with the system. Then we present a theoretical analysis for flocking, and show that the system achieves consensus at an exponential rate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Stochastic Resonance and First Arrival Time for Excitable Systems

We study the noise induced thermally activated barrier crossing of Brownian particles that hop in a piecewise linear potential. Using the exact analytic solutions and via numerical simulations not only we explore the dependence for the first passage time of a single particle but also we calculate the first arrival time for one particle out of N particles. The first arrival time decreases as the number of particles increases as expected. We then explore the thermally activated barrier crossing rate of the system in the presence of time varying signal. The dependence of signal to noise ratio SNR as well as the power amplification (η) on model parameters is explored. η and SNR depict a pronounced peak at particular noise strength. In the presence of N particles, η is considerably amplified as N steps up showing the weak periodic signal plays a vital role in controlling the noise induced dynamics of the system. Moreover, for the sake of generality, the viscous friction γ is considered to decrease exponentially when the temperature T of the medium increases (γ=Be{sup −AT}) as proposed originally by Reynolds (Philos Trans R Soc Lond 177:157, 1886).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Tightness of the Ising–Kac Model on the Two-Dimensional Torus

We consider the sequence of Gibbs measures of Ising models with Kac interaction defined on a periodic two-dimensional discrete torus near criticality. Using the convergence of the Glauber dynamic proven by Mourrat and Weber (Commun Pure Appl Math 70:717–812, 2017) and a method by Tsatsoulis and Weber employed in ( arXiv:1609.08447 2016), we show tightness for the sequence of Gibbs measures of the Ising–Kac model near criticality and characterise the law of the limit as the Φ{sub 2}{sup 4} measure on the torus. Our result is very similar to the one obtained by Cassandro et al. (J Stat Phys 78(3):1131–1138, 1995) on ℤ{sup 2}, but our strategy takes advantage of the dynamic, instead of correlation inequalities. In particular, our result covers the whole critical regime and does not require the large temperature/large mass/small coupling assumption present in earlier results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗