Effects Of Stochastic Fluctuations Research Articles

Hydrodynamic fluctuations and long-time tails in a fluid on an anisotropic background

The effective low-energy late-time description of many body systems near thermal equilibrium provided by classical hydrodynamics in terms of dissipative transport phenomena receives important corrections once the effects of stochastic fluctuations are taken into account. One such physical effect is the occurrence of long-time power law tails in correlation functions of conserved currents. In the hydrodynamic regime k→0 this amounts to non-analytic dependence of the correlation functions on the frequency ω. In this article, we consider a relativistic fluid with a conserved global U(1) charge in the presence of a strong background magnetic field, and compute the long-time tails in correlation functions of the stress tensor. The presence of the magnetic field renders the system anisotropic. In the absence of the magnetic field, there are three out-of-equilibrium transport parameters that arise at the first order in the hydrodynamic derivative expansion, all of which are dissipative. In the presence of a background magnetic field, there are ten independent out-of-equilibrium transport parameters at the first order, three of which are non-dissipative and the rest are dissipative. We provide the most general linearized equations about a given state of thermal equilibrium involving the various transport parameters in the presence of a magnetic field, and use them to compute the long-time tails for the fluid.

Stochastic dynamic analysis of a Kaplan turbine system considering synergistic regulation

A stochastic dynamic model of a Kaplan turbine is established in this paper during the transient process. When the Kaplan turbine operates with fluctuating load, the synergistic relationship between the guide vanes and blades experiences random fluctuation resulting from the mechanical, hydraulic and signal factors. To study the effect of stochastic fluctuations of the synergistic relationship, Chebyshev polynomial approximation method is adopted to analyze the stochastic dynamic characteristics of the Kaplan turbine during the transient process. Using Chebyshev polynomial approximation, the stochastic model of the Kaplan turbine is simplified to its equivalent deterministic model, and the stochastic dynamic characteristics of the model are investigated in the transient process. The effects of stochastic intensity on the dynamic behaviors of the Kaplan turbine are analyzed by means of numerical simulation. Moreover, the influences of PID parameters on the stochastic dynamic characteristics of the Kaplan turbine are studied through bifurcation diagrams. Analysis of stochastic characteristics and dynamic behaviors suggests that transient performance improvement can be obtained by controlling the synergistic stochastic intensity and PID parameters.

Stochastic Differential Game-Based Malware Propagation in Edge Computing-Based IoT

Internet of Things (IoT) has played an important role in our daily life since its emergence. The applications of IoT cover from the traditional devices to intelligent equipment. With the great potential of IoT, there comes various kinds of security problems. In this paper, we study the malware propagation under the dynamic interaction between the attackers and defenders in edge computing-based IoT and propose an infinite-horizon stochastic differential game model to discuss the optimal strategies for the attackers and defenders. Considering the effect of stochastic fluctuations in the edge network on the malware propagation, we construct the Itô stochastic differential equations to describe the propagation of the malware in edge computing-based IoT. Subsequently, we analyze the feedback Nash equilibrium solutions for our proposed game model, which can be considered as the optimal strategies for the defenders and attackers. Finally, numerical simulations show the effectiveness of our proposed game model.

Deterministic Sudden Changes and Stochastic Fluctuation Effects on Stability and Persistence Dynamics of Two-Predator One-Prey Model

In this paper, we present new results on deterministic sudden changes and stochastic fluctuations’ effects on the dynamics of a two-predator one-prey model. We purpose to study the dynamics of the model with some impacting factors as the problem statement. The methodology depends on investigating the seasonality and stochastic terms which make the predator-prey interactions more realistic. A theoretical analysis is introduced for studying the effects of sudden deterministic changes, using three different cases of sudden changes. We show that the system in a good situation presents persistence dynamics only as a stable dynamical behavior. However, the system in a bad situation leads to three main outcomes as follows: first, constancy at the initial conditions of the prey and predators; second, extinction of the whole system; third, extinction of both predators, resulting in the growth of the prey population until it reaches a peak carrying capacity. We perform numerical simulations to study effects of stochastic fluctuations, which show that noise strength leads to an increase in the oscillations in the dynamical behavior and became more complex and finally leads to extinction when the strength of the noise is high. The random noises transfer the dynamical behavior from the equilibrium case to the oscillation case, which describes some unstable environments.

Randomized matrix games in a finite population: Effect of stochastic fluctuations in the payoffs on the evolution of cooperation

A diffusion approximation for a randomized 2 × 2-matrix game in a large finite population is ascertained in the case of random payoffs whose expected values, variances and covariances are of order given by the inverse of the population size N. Applying the approximation to a Randomized Prisoner’s Dilemma (RPD) with independent payoffs for cooperation and defection in random pairwise interactions, conditions on the variances of the payoffs for selection to favor the evolution of cooperation, favor more the evolution of cooperation than the evolution of defection, and disfavor the evolution of defection are deduced. All these are obtained from probabilities of ultimate fixation of a single mutant. It is shown that the conditions are lessened with an increase in the variances of the payoffs for defection against cooperation and defection and a decrease in the variances of the payoffs for cooperation against cooperation and defection. A RPD game with independent payoffs whose expected values are additive is studied in detail to support the conclusions. Randomized matrix games with non-independent payoffs, namely the RPD game with additive payoffs for cooperation and defection based on random cost and benefit for cooperation and the repeated RPD game with Tit-for-Tat and Always-Defect as strategies in pairwise interactions with a random number of rounds, are studied under the assumption that the population-scaled expected values, variances and covariances of the payoffs are all of the same small enough order. In the first model, the conditions in favor of the evolution of cooperation hold only if the covariance between the cost and the benefit is large enough, while the analysis of the second model extends the results on the effects of the variances of the payoffs for cooperation and defection found for the one-round RPD game.

Modeling low mass stellar populations

AbstractModeling low mass stellar populations, like clusters and dwarf galaxies, with population synthesis models requires that we evaluate the role played by stochastic fluctuations in the sampling of the IMF on the spectro-photometric properties of these sparse populations. Interacting binaries may also modify the integrated spectra of these systems depending on the final product of the binary interaction and on the frequency of binary stars. In this work we compare the relative importance of stochastic fluctuations and binary evolution on low mass galaxy properties as a function of the population age and total mass. In most cases the effects of stochastic fluctuations dominate those produced by binary interactions. We explore and quantify the relative importance of these effects through cosmic times.

Stability of Ring-Type MEMS Gyroscopes Subjected to Stochastic Angular Speed Fluctuation

Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of largest Lyapunov exponents (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.

Response dynamics of a freely oscillating cylinder under the effect of noise

The present work revisits free vibration of a circular cylinder undergoing Vortex Induced Vibrations situations in terms of a two dimensional CFD framework, under the effect of a random input flow. Randomness in the oncoming fluid and its effect on the overall dynamical behaviour of the system is a likely scenario that has not received its due attention in the community. The analytical models, prove to be good enough in capturing the qualitative behaviour of the responses, with appropriate tuning of parameters. The effect of stochastic fluctuations in the oncoming flow is analyzed on the structural amplitude. Noise seems to have major effects on the structural amplitude, the onset and range of lock-in. A stability analysis of the structure for both deterministic and stochastic cases is complete only when the spatial and temporal evolution of the wake pattern is also considered. In this context, a Navier Stokes high fidelity solver is used, to determine the bifurcation behavior of the system for deterministic and stochastic cases. Effects of a few relevant system parameters such as Reynolds number, structural stiffness have been studied to resolve the qualitative and quantitative changes in the response dynamics. The intensity of noise seems to have major effects in determining the quality and quantity of the response.

Variability in primary productivity determines metapopulation dynamics.

Temporal variability in primary productivity can change habitat quality for consumer species by affecting the energy levels available as food resources. However, it remains unclear how habitat-quality fluctuations may determine the dynamics of spatially structured populations, where the effects of habitat size, quality and isolation have been customarily assessed assuming static habitats. We present the first empirical evaluation on the effects of stochastic fluctuations in primary productivity—a major outcome of ecosystem functions—on the metapopulation dynamics of a primary consumer. A unique 13-year dataset from an herbivore rodent was used to test the hypothesis that inter-annual variations in primary productivity determine spatiotemporal habitat occupancy patterns and colonization and extinction processes. Inter-annual variability in productivity and in the growing season phenology significantly influenced habitat colonization patterns and occupancy dynamics. These effects lead to changes in connectivity to other potentially occupied habitat patches, which then feed back into occupancy dynamics. According to the results, the dynamics of primary productivity accounted for more than 50% of the variation in occupancy probability, depending on patch size and landscape configuration. Evidence connecting primary productivity dynamics and spatiotemporal population processes has broad implications for metapopulation persistence in fluctuating and changing environments.

Hitting Time Analysis of OneMax Problem in Genetic Algorithm

Genetic algorithms (GAs) are stochastic optimization techniques, and we have studied the effects of stochastic fluctuation in the process of GA evolution. A mathematical study was carried out for GA on OneMax function within the framework of Markov chain model. We treated the task of estimating convergence time of the Markov chain for OneMax problem. Then, in order to study hitting time, we study the state after convergence.

Comparison of adaptation motifs: temporal, stochastic and spatial responses.

The cells' ability to adapt to changes in the external environment is crucial for the survival of many organisms. There are two broad classes of signalling networks that achieve perfect adaptation. Both rely on complementary regulation of the response by an external signal and an inhibitory process. In one class of systems, inhibition comes about from the response itself, closing a negative feedback (NFB) loop. In the other, the inhibition comes directly from the external signal in what is referred to as an incoherent feedforward (IFF) loop. Although both systems show adaptive behaviour to constant changes in the level of the stimulus, their response to other forms of stimuli can differ. Here the authors consider the respective response to various such disturbances, including ramp increases, removal of the stimulus and pulses. The authors also consider the effect of stochastic fluctuations in signalling that come about from the interaction of the signalling elements. Finally, the authors consider the possible effect of spatially varying signals. The authors show that both the NFB and the IFF motifs can be used to sense static spatial gradients, under a local excitation, global inhibition assumption. The results may help experimentalists develop protocols that can discriminate between the two adaptation motifs.

The effect of stochastic fluctuation in radiation dose-rate on cell survival following fractionated radiation therapy

In radiobiological models, it is often assumed that the radiation dose rate remains constant during the course of radiation delivery. However, instantaneous radiation dose rate undergoes random (stochastic) temporal fluctuation. The effect of stochastic dose rate in fractionated radiation therapy is unknown and there has been no analytical formulation of stochastic dose-rate fluctuation effect in fractionated radiation therapy which we endeavor to pursue here. We have obtained the quantitative expression of cellular survival fraction considering stochastic temporal fluctuation or noise in dose rate. We have shown that the constant dose-rate approximation overestimates the survival fraction compared to that under stochastic dose rate in a fractionated radiation therapy situation and this overestimation effect increases appreciably with the increase in the fluctuation level in dose rate. However, for a given level of fluctuation in dose rate, overestimation of survival fraction also depends on the value of cellular radiation sensitivity parameter β and the repair rate of DNA lesion. This overestimation effect is higher for the cells which have a higher value of β parameter or have a lower repair rate. Our study draws attention to stochastic temporal fluctuation in the radiation dose rate and its potential contribution to cell survival following fractionated radiotherapy.

Effects of stochastic fluctuations at molecule–electrode contacts in transition voltage spectroscopy

The influence of the stochastic fluctuations at contacts on the electron transport through molecular junctions based on alkanedithiols is investigated theoretically. Results are presented, which demonstrate that the transition voltage Vt is insensitive to fluctuations in the electrode–molecule hopping integrals. By contrast, reasonably large fluctuations (δJ∼2eV) in the Coulomb contact interaction J, included via an extended Newns–Anderson model, lead to fluctuations in the molecular orbital energetic alignment ε0, which are consistent with the fluctuations in Vt observed experimentally. The impact of these J- (or ε0-) fluctuations on the conductance G is considerably stronger than on Vt. The G-fluctuations driven by δJ represent a substantial fraction of the fluctuations displayed by experimental conductance histograms. The electron system for J≠0 is correlated, i.e., it cannot be described within a single-particle (Landauer-based) picture. However, in the J-range of interest, the ratio Vt/ε0 turns out to be only weakly dependent on J. The weak impact of J on the ratio Vt/ε0 is important because it suggests that, even in the presence of realistically strong electron correlations, transition voltage spectroscopy can be a useful tool of investigation.

Research Note: Long-Lasting Effects and Welfare Costs of Fluctuations

The tourism industry is growing rapidly but is also highly fluctuating. Using China's inbound tourism market as the object and based on the B–N data decomposition theory, this paper adopts the statistics of variance ratio to measure the long-lasting effects of stochastic fluctuations on China's inbound tourism industry. It also discusses the influences of stochastic fluctuations and the decreasing growth rate on the welfare of China's inbound tourism. The conclusion is that undoubtedly China's inbound tourism industry will continue to grow, but the impact of stochastic shocks will endure for a relatively long time. Twenty-four per cent of the long-term fluctuation of China's inbound tourism industry is the result of stochastic shocks, whose effect, in the short term, will continue to be reinforced. Though the elimination of fluctuations will increase welfare by 0.40%, lowering the growth rate will decrease welfare by a larger percentage. If the monthly growth rate decreases by 0.1%, welfare will fall by about 19.37%, 48 times the amount of welfare loss without fluctuation. Therefore, China's inbound tourism business should stick to the long-term policy of facilitating growth, while some administrative and legislative measures should be taken to address the negative impact of stochastic fluctuation appropriately.

ASSOCIATIONS BETWEEN PATCH AREA AND VITAL RATES: CONSEQUENCES FOR LOCAL AND REGIONAL POPULATIONS

The negative association between patch area and extinction risk is one of the most ubiquitous observations in ecology. This association is often attributed to the disproportionate effects of stochastic fluctuations on small populations, but it also may be explained by deterministic relationships between patch area and vital rates (i.e., fecundity and survival). We explored the consequences of including deterministic relationships between patch area and vital rates in metapopulation models. Field studies have revealed that fecundity and monthly survivorship were positively associated with patch size for the Florida scrub lizard (Sceloporus woodi). Using simulation techniques, we compared metapopulation models of artificial landscapes that included vital rates for this species (scaled for patch area) to models that used averaged estimates of vital rates for all patches. These two types of metapopulation models produced dramatically different results with respect to the proportion of occupied patches and the extinction probability of the regional population. Including deterministic relationships between patch area and vital rates often resulted in either all patches being occupied or all patches going extinct, depending on the size of the local patches. Few artificial landscapes resulted in a dynamic colonization–extinction equilibrium characteristic of a “classic metapopulation.” In contrast, model simulations with demographic parameters equal for all patch sizes produced a more linear decline in extinction probability with patch size. Our results highlight considerations for application of metapopulation theory in conservation.

Mathematical models of the balance between apoptosis and proliferation.

As our understanding of cellular behaviour grows, and we identify more and more genes involved in the control of such basic processes as cell division and programmed cell death, it becomes increasingly difficult to integrate such detailed knowledge into a meaningful whole. This is an area where mathematical modelling can complement experimental approaches, and even simple mathematical models can yield useful biological insights. This review presents examples of this in the context of understanding the combined effects of different levels of cell death and cell division in a number of biological systems including tumour growth, the homeostasis of immune memory and pre-implantation embryo development. The models we describe, although simplistic, yield insight into several phenomena that are difficult to understand using a purely experimental approach. This includes the different roles played by the apoptosis of stem cells and differentiated cells in determining whether or not a tumour can grow; the way in which a density dependent rate of apoptosis (for instance mediated by cell-cell contact or cytokine signalling) can lead to homeostasis; and the effect of stochastic fluctuations when the number of cells involved is small. We also highlight how models can maximize the amount of information that can be extracted from limited experimental data. The review concludes by summarizing the various mathematical frameworks that can be used to develop new models and the type of biological information that is required to do this.

RENORMALIZATION OF BLACK-SCHOLES EQUATION FOR STOCHASTICALLY FLUCTUATING INTEREST RATE

We investigate the effect of stochastic fluctuations of an interest rate on the value of a derivative. We derive the modified Black-Scholes equation that describes evolution of the value of a derivative averaged over an ensemble of stochastic fluctuations of the rate of interest and depends on the "renormalized" values of volatility and rate of interest. We present the explicit expressions for the renormalized volatility and interest rate that incorporate the corrections owing to the short-term stochastic variations of the interest rate. The stochastic component of the interest rate tends to enhance the effective volatility and reduce the effective interest rate that determine an evolution of the option pricing "smoothed out" over the stochastic variations. The results of numerical solution of the modified Black-Scholes equation with the renormalized coefficients are illustrated for an American put option on non-dividend-paying stock.

Meridional Localization of Planetary Waves in Stochastic Zonal Flows

The effect of stochastic fluctuations in the zonal-mean velocity field on the energy dispersion of planetary stationary waves is considered, using the nondivergent, barotropic vorticity equation. It is found that for small noise levels, the oscillatory structure of the solutions is not altered. However, for noise levels comparable to or larger than those observed in the circulation at 500 mb, the marginal density functions of the solution process in the subpolar region cluster near zero. This indicates that fluctuations in the velocity field inhibit the poleward dispersion of stationary wave energy. This localization phenomenon appears whether the ensemble average of the mean zonal flow is superrotation or has a simple two-jet structure.

Statistical and Stochastic Description of Microvoid Evolution Observed in Dynamic Failure of Ductile Materials

A brief review is presented of statistical approaches on microdamage evolution. An experimental study of statistical microdamage evolution in two ductile materials under dynamic loading is carried out. The observation indicates that there are large differences in size and distribution of microvoids between these two materials. With this phenomenon in mind, kinetic equations governing the nucleation and growth of microvoids in nonlinear rate-dependent materials are combined with the balance law of void number to establish statistical differential equations that describe the evolution of microvoids' number density. The theoretical solution provides a reasonable explanation of the experimentally observed phenomenon. The effects of stochastic fluctuation which is influenced by the inhomogeneous microscopic structure of materials are subsequently examined (i.e. stochastic growth model). Based on the stochastic differential equation, a Fokker-Planck equation which governs the evolution of the transition probability is derived. The analytical solution for the transition probability is then obtained and the effects of stochastic fluctuation is discussed. The statistical and stochastic analyses may provide effective approaches to reveal the physics of damage evolution and dynamic failure process in ductile materials.

On the Effect of Stochastic Fluctuations in the Dynamics of the Lifshitz–Slyozov–Wagner Model

In this paper the dynamics of a system of spherical particles that fill a small volume fraction of the space and that evolves in a concentration field is discussed. Corrections to the Lifshitz–Slyozov–Wagner (LSW) model that take into account the stochastic character of the problem are computed. It is proved, under suitable smallness assumptions for the volume fraction filled by the particles, that the effect of these corrections does not modify much the dynamics of the self-similar solutions of the LSW system of equations.