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At least 793 records · Page 44

Mean Field Games for Stochastic Growth with Relative Utility

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.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Radiation-Induced Cataractogenesis: A Critical Literature Review for the Interventional Radiologist

Extensive research supports an association between radiation exposure and cataractogenesis. New data suggests that radiation-induced cataracts may form stochastically, without a threshold and at low radiation doses. We first review data linking cataractogenesis with interventional work. We then analyze the lens dose typical of various procedures, factors modulating dose, and predicted annual dosages. We conclude by critically evaluating the literature describing techniques for lens protection, finding that leaded eyeglasses may offer inadequate protection and exploring the available data on alternative strategies for cataract prevention.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Upscaling permeability for three-dimensional fractured porous rocks with the multiple boundary method

Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models.

58 GEOSCIENCES↗

Some Results of Multicriterial and Robust Optimization of Nuclear Power Systems Structure

The possibility of applying multicriterial and robust optimization methods as well as stochastic methods of determining the effect of uncertainties in the parameters of a system to structural optimization of nuclear power is discussed for the example of a hypothetical nuclear-power system consisting of thermal and fast reactors. It is shown that the optimal structures of nuclear power systems obtained by such methods are balanced in terms of conflicting criteria and technologically more diversified than those determined by single-criterion deterministic optimization. Cost-based innovative technologies, which can be adopted only by imposing additional external limitations in a single-criterion problem, appear in such structures. The examined methods make it possible to determine on a systematic basis the structures of nuclear power that are balanced in terms of a set of conflicting criteria, since factors having both positive and negative effects on the development of nuclear-power systems are included in the calculations, and to find economically efficient directions of structural changes in the system in order to improve stability and efficiency.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Risk Management of NPP Incidents

A diagnostic model for managing the risk of NPP incidents attending different irregularities of equipment operation is examined for the example of the oil delivery system of the main circulation pump. The model includes the construction of a graph of the operation of the oil system and ranking in order to obtain indices of priority for monitoring information flow that reflect the actuation probability of each form of protection. The results of the analysis can used as input data for predicting the duration of a stable state of a technological system in the course of operation on the basis of stochastic extrapolation of the parameters by means of single-channel queuing systems with finite storage – technological protection and blocking.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Simulation of the Quality Criterion of a Mixture in a Drum-Belt Apparatus

A method is proposed for calculating the inhomogeneity coefficient in the workspace of a drum-belt mixer of bulk components with brush elements in a three-stage batch mixing method with non-uniform proportioning. The method is based on a stochastic model of the motion of rarefied particle flows following interaction with flexible elements fixed along a helical line on the surface of the mixer drums. The principal coefficients affecting the quality of a bulk mixture are analyzed in the form of combined structural and regime complexes of parameters of the mixer and the characteristics of the physical and mechanical state of the mixed media are analyzed. The results obtained can be used to develop an engineering technique for calculating the parameters of a new drum-belt mixer of friable components.

42 ENGINEERING↗

Optimal Portfolio Management in a Modified Constant Elasticity of Variance Model

We investigate the optimal management of a portfolio consisting of a risk asset and a risk-free bond. The asset dynamics is specified by the M-CEV model. Assuming that the investor has a power utility function, we derive an explicit analytical portfolio-management formula that contains confluent hypergeometric functions. The asymptotic form of the proposed portfolio management strategy is obtained, as well as approximate formulas consisting only of elementary functions. We additionally present an application of our results in the context of algorithmic statistical-arbitrage strategies.

97 MATHEMATICS AND COMPUTING↗

Algorithms and Experience with Prediction of Technical Operating Failures in Nuclear Power Plant Equipment

The development of algorithms for the prediction of technological operating failure of nuclear power plant equipment based on stochastic extrapolation of the values of technical parameters is discussed. The algorithms are tested on real archived data on the operation of the oil circulation system of the main circulating pumps in a power generating unit at a nuclear power plant.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

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↗