On stochastic heating of electrons by intense laser radiation in the presence of electrostatic potential well
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Krasheninnikov, S. I.↗
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Results for “stochastic processes”
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Synchronizing spatio-temporal chaos with imperfect models: A stochastic surface growth picture
We study the synchronization of two spatially extended dynamical systems where the models have imperfections. We show that the synchronization error across space can be visualized as a rough surface governed by the Kardar-Parisi-Zhang equation with both upper and lower bounding walls corresponding to nonlinearities and model discrepancies, respectively. Two types of model imperfections are considered: parameter mismatch and unresolved fast scales, finding in both cases the same qualitative results. The consistency between different setups and systems indicates that the results are generic for a wide family of spatially extended systems.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Structure analysis of turbulent liquid phase by POD and LSE techniques
In this paper, vortical structures and turbulence characteristics of liquid phase in both single liquid phase and two-phase slug flow in pipes were studied. Two dimensional velocity vector fields of liquid phase were obtained by Particle image velocimetry (PIV). Two cases were considered one single phase liquid flow at 80 l/m and second slug flow by introducing gas at 60 l/m while keeping liquid flow rate same. Proper orthogonal decomposition (POD) and Linear stochastic estimation techniques were used for the extraction of coherent structures and analysis of turbulence in liquid phase for both cases. POD has successfully revealed large energy containing structures. The time dependent POD spatial mode coefficients oscillate with high frequency for high mode numbers. The energy distribution of spatial modes was also achieved. LSE has pointed out the coherent structured for both cases and the reconstructed velocity fields are in well agreement with the instantaneous velocity fields.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Financial derivative pricing under probability operator via Esscher transfomation
The problem of pricing contingent claims has been extensively studied for non-Gaussian models, and in particular, Black- Scholes formula has been derived for the NIG asset pricing model. This approach was first developed in insurance pricing{sup 9} where the original distortion function was defined in terms of the normal distribution. This approach was later studied6 where they compared the standard Black-Scholes contingent pricing and distortion based contingent pricing. So, in this paper, we aim at using distortion operators by Cauchy distribution under a simple transformation to price contingent claim. We also show that we can recuperate the Black-Sholes formula using the distribution. Similarly, in a financial market in which the asset price represented by a stochastic differential equation with respect to Brownian Motion, the price mechanism based on characteristic Esscher measure can generate approximate arbitrage free financial derivative prices. The price representation derived involves probability Esscher measure and Esscher Martingale measure and under a new complex valued measure φ (u) evaluated at the characteristic exponents φ{sub x}(u) of X{sub t} we recuperate the Black-Scholes formula for financial derivative prices.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Numerical and experimental study of the weld joints formation in welding foam materials
A numerical analysis of fusion welding of steel- and aluminum-based foam materials is carried out. The schemes of the structured and stochastic pore distribution are considered. The research results were used to conduct the experiments which confirmed the reliability of the numerical calculations.
36 MATERIALS SCIENCE↗
Numerical simulation of effective mechanical properties of stochastic composites with consideration for structural evolution under intensive dynamic loading
Mechanical behavior of stochastic metal-ceramic composites with the aluminum matrix under high-rate deformation at shock-wave loading is numerically simulated with consideration for structural evolution. Effective values of mechanical parameters of metal-ceramic composites Al B{sub 4}C, Al SiC, and Al Al{sub 2}O{sub 3} are evaluated depending on different concentration of ceramic inclusions.
36 MATERIALS SCIENCE↗
Full-dispersion Monte Carlo simulation of phonon transport in micron-sized graphene nanoribbons
We simulate phonon transport in suspended graphene nanoribbons (GNRs) with real-space edges and experimentally relevant widths and lengths (from submicron to hundreds of microns). The full-dispersion phonon Monte Carlo simulation technique, which we describe in detail, involves a stochastic solution to the phonon Boltzmann transport equation with the relevant scattering mechanisms (edge, three-phonon, isotope, and grain boundary scattering) while accounting for the dispersion of all three acoustic phonon branches, calculated from the fourth-nearest-neighbor dynamical matrix. We accurately reproduce the results of several experimental measurements on pure and isotopically modified samples [S. Chen et al., ACS Nano 5, 321 (2011);S. Chen et al., Nature Mater. 11, 203 (2012); X. Xu et al., Nat. Commun. 5, 3689 (2014)]. We capture the ballistic-to-diffusive crossover in wide GNRs: room-temperature thermal conductivity increases with increasing length up to roughly 100 μm, where it saturates at a value of 5800 W/m K. This finding indicates that most experiments are carried out in the quasiballistic rather than the diffusive regime, and we calculate the diffusive upper-limit thermal conductivities up to 600 K. Furthermore, we demonstrate that calculations with isotropic dispersions overestimate the GNR thermal conductivity. Zigzag GNRs have higher thermal conductivity than same-size armchair GNRs, in agreement with atomistic calculations.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Thermodynamically self-consistent non-stochastic micromagnetic model for the ferromagnetic state
In this work, a self-consistent thermodynamic approach to micromagnetism is presented. The magnetic degrees of freedom are modeled using the Landau-Lifshitz-Baryakhtar theory, which separates the different contributions to the magnetic damping, and thereby allows them to be coupled to the electron and phonon systems in a self-consistent way. We show that this model can quantitatively reproduce ultrafast magnetization dynamics in Nickel suggesting that in ferromagnetic metals the ultrafast angular momentum transfer happens via the relativistic spin-electron scattering.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
The stochastic dynamics of tethered microcantilevers in a viscous fluid
We explore and quantify the coupled dynamics of a pair of micron scale cantilevers immersed in a viscous fluid that are also directly tethered to one another at their tips by a spring force. The spring force, for example, could represent the molecular stiffness or elasticity of a biomolecule or material tethered between the cantilevers. We use deterministic numerical simulations with the fluctuation-dissipation theorem to compute the stochastic dynamics of the cantilever pair for the conditions of experiment when driven only by Brownian motion. We validate our approach by comparing directly with experimental measurements in the absence of the tether which shows excellent agreement. Using numerical simulations, we quantify the correlated dynamics of the cantilever pair over a range of tether stiffness. Our results quantify the sensitivity of the auto- and cross-correlations of equilibrium fluctuations in cantilever displacement to the stiffness of the tether. We show that the tether affects the magnitude of the correlations which can be used in a measurement to probe the properties of an attached tethering substance. For the configurations of current interest using micron scale cantilevers in water, we show that the magnitude of the fluid coupling between the cantilevers is sufficiently small such that the influence of the tether can be significant. Our results show that the cross-correlation is more sensitive to tether stiffness than the auto-correlation indicating that a two-cantilever measurement has improved sensitivity when compared with a measurement using a single cantilever.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Reduction of scattering using thin all-dielectric shells designed by stochastic optimizer
Adaptive differential evolution method has been used for optimization of all-dielectric multilayer coatings in order to reduce total scattering from spherical targets. The optimal refractive index profiles have been found for various sizes of targets and thicknesses of coatings. Few profile types that appear to be optimal for various geometrical parameters have been identified. Scattering of the target with diameter of 0.75 λ has been reduced by 85% using 0.16 λ thick coating formed by isotropic dielectric materials. For larger targets, scattering reduction becomes smaller, but it still reaches 50% for targets with the diameter of 1.5 λ. The obtained designs provide a route to implement cloaking without the use of magnetic and anisotropic metamaterials.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Biomanufacturing and self-propulsion dynamics of nanoscale bacteria-enabled autonomous delivery systems
Flagellated bacteria have superb self-propulsion capabilities and are able to effectively move through highly viscous fluid and semi-solid (porous) environments. This innate aptitude has been harvested for whole-cell actuation of bio-hybrid microrobotic systems with applications in directed transport and microassembly. In this work, we present the biomanufacturing of Nanoscale Bacteria-Enabled Autonomous Delivery Systems (NanoBEADS) by controlled self-assembly and investigate the role of nanoparticle load on the dynamics of their self-propulsion in aqueous environments. Each NanoBEADS agent is comprised of spherical polystyrene nanoparticles assembled onto the body of a flagellated Escherichia coli bacterium. We demonstrate that the NanoBEADS assembly configuration is strongly dependent upon the nanoparticles to bacteria ratio. Furthermore, we characterized the stochastic motion of the NanoBEADS as a function of the quantity and size of the nanoparticle load and computationally analyzed the effect of the nanoparticle load on the experienced drag force. We report that the average NanoBEADS swimming speed is reduced to 65% of the free-swimming bacteria speed (31 μm/s) at the highest possible load. NanoBEADS can be utilized as single agents or in a collaborative swarm in order to carry out specific tasks in a wide range of applications ranging from drug delivery to whole cell biosensing.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On noise induced Poincaré–Andronov–Hopf bifurcation
It has been numerically seen that noise introduces stable well-defined oscillatory state in a system with unstable limit cycles resulting from subcritical Poincaré–Andronov–Hopf (or simply Hopf) bifurcation. This phenomenon is analogous to the well known stochastic resonance in the sense that it effectively converts noise into useful energy. Herein, we clearly explain how noise induced imperfection in the bifurcation is a generic reason for such a phenomenon to occur and provide explicit analytical calculations in order to explain the typical square-root dependence of the oscillations' amplitude on the noise level below a certain threshold value. Also, we argue that the noise can bring forth oscillations in average sense even in the absence of a limit cycle. Thus, we bring forward the inherent general mechanism of the noise induced Hopf bifurcation naturally realisable across disciplines.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Statistical modelling of discharge behavior of atmospheric pressure dielectric barrier discharge
In this work, stochastic behavior of atmospheric pressure dielectric barrier discharge (DBD) has been investigated. The experiment is performed in a DBD reactor consisting of a pair of stainless steel parallel plate electrodes powered by a 50 Hz ac high voltage source. Current pulse amplitude distributions for different space gaps and the time separation between consecutive current pulses are studied. A probability distribution function is proposed to predict the experimental distribution function for the current pulse amplitudes and the occurrence of the transition regime of the pulse distribution. Breakdown voltage at different positions on the dielectric surface is suggested to be stochastic in nature. The simulated results based on the proposed distribution function agreed well with the experimental results and able to predict the regime of transition voltage. This model would be useful for the understanding of stochastic behaviors of DBD and the design of DBD device for effective operation and applications.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows
In this paper, we establish a set of criteria which are applied to discuss various formulations under which Lagrangian stochastic models can be found. These models are used for the simulation of fluid particles in single-phase turbulence as well as for the fluid seen by discrete particles in dispersed turbulent two-phase flows. The purpose of the present work is to provide guidelines, useful for experts and non-experts alike, which are shown to be helpful to clarify issues related to the form of Lagrangian stochastic models. A central issue is to put forward reliable requirements which must be met by Lagrangian stochastic models and a new element brought by the present analysis is to address the single- and two-phase flow situations from a unified point of view. For that purpose, we consider first the single-phase flow case and check whether models are fully consistent with the structure of the Reynolds-stress models. In the two-phase flow situation, coming up with clear-cut criteria is more difficult and the present choice is to require that the single-phase situation be well-retrieved in the fluid-limit case, elementary predictive abilities be respected and that some simple statistical features of homogeneous fluid turbulence be correctly reproduced. This analysis does not address the question of the relative predictive capacities of different models but concentrates on their formulation since advantages and disadvantages of different formulations are not always clear. Indeed, hidden in the changes from one structure to another are some possible pitfalls which can lead to flaws in the construction of practical models and to physically unsound numerical calculations. A first interest of the present approach is illustrated by considering some models proposed in the literature and by showing that these criteria help to assess whether these Lagrangian stochastic models can be regarded as acceptable descriptions. A second interest is to indicate how future developments can be safely built, which is also relevant for stochastic subgrid models for particle-laden flows in the context of Large Eddy Simulations.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Estimating the epidemic threshold on networks by deterministic connections
For many epidemic networks some connections between nodes are treated as deterministic, while the remainder are random and have different connection probabilities. By applying spectral analysis to several constructed models, we find that one can estimate the epidemic thresholds of these networks by investigating information from only the deterministic connections. Nonetheless, in these models, generic nonuniform stochastic connections and heterogeneous community structure are also considered. The estimation of epidemic thresholds is achieved via inequalities with upper and lower bounds, which are found to be in very good agreement with numerical simulations. Since these deterministic connections are easier to detect than those stochastic connections, this work provides a feasible and effective method to estimate the epidemic thresholds in real epidemic networks.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Smoothed particle hydrodynamics model for Landau-Lifshitz-Navier-Stokes and advection-diffusion equations
We propose a novel smoothed particle hydrodynamics (SPH) discretization of the fully coupled Landau-Lifshitz-Navier-Stokes (LLNS) and stochastic advection-diffusion equations. The accuracy of the SPH solution of the LLNS equations is demonstrated by comparing the scaling of velocity variance and the self-diffusion coefficient with kinetic temperature and particle mass obtained from the SPH simulations and analytical solutions. The spatial covariance of pressure and velocity fluctuations is found to be in a good agreement with theoretical models. To validate the accuracy of the SPH method for coupled LLNS and advection-diffusion equations, we simulate the interface between two miscible fluids. We study formation of the so-called “giant fluctuations” of the front between light and heavy fluids with and without gravity, where the light fluid lies on the top of the heavy fluid. We find that the power spectra of the simulated concentration field are in good agreement with the experiments and analytical solutions. In the absence of gravity, the power spectra decay as the power −4 of the wavenumber—except for small wavenumbers that diverge from this power law behavior due to the effect of finite domain size. Gravity suppresses the fluctuations, resulting in much weaker dependence of the power spectra on the wavenumber. Finally, the model is used to study the effect of thermal fluctuation on the Rayleigh-Taylor instability, an unstable dynamics of the front between a heavy fluid overlaying a light fluid. The front dynamics is shown to agree well with the analytical solutions.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Stochastic resonance in a generalized Von Foerster population growth model
The stochastic dynamics of a population growth model, similar to the Von Foerster model for human population, is studied. The influence of fluctuating environment on the carrying capacity is modeled as a multiplicative dichotomous noise. It is established that an interplay between nonlinearity and environmental fluctuations can cause single unidirectional discontinuous transitions of the mean population size versus the noise amplitude, i.e., an increase of noise amplitude can induce a jump from a state with a moderate number of individuals to that with a very large number, while by decreasing the noise amplitude an opposite transition cannot be effected. An analytical expression of the mean escape time for such transitions is found. Particularly, it is shown that the mean transition time exhibits a strong minimum at intermediate values of noise correlation time, i.e., the phenomenon of stochastic resonance occurs. Applications of the results in ecology are also discussed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Sensitive response of a model of symbiotic ecosystem to seasonal periodic drive
A symbiotic ecosysytem (metapopulation) is studied by means of the stochastic Lotka-Volterra model with generalized Verhulst self-regulation. The effect of variable environment on the carrying capacities of populations is taken into account as an asymmetric dichotomous noise and as a deterministic periodic stimulus. In the framework of the mean-field theory an explicit self-consistency equation for the system in the long-time limit is presented. Also, expressions for the probability distribution and for the moments of the population size are found. In certain cases the mean population size exhibits large oscillations in time, even if the amplitude of the seasonal environmental drive is small. Particularly, it is shown that the occurrence of large oscillations of the mean population size can be controlled by noise parameters (such as amplitude and correlation time) and by the coupling strength of the symbiotic interaction between species.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗