Presence Of Random Fluctuations Research Articles

Features of spectral vibration diagnostics of traction power transformers in high-speed motion

This paper uses spectral analysis methods to develop a mathematical model and algorithms for evaluating the diagnosed signals corresponding to certain defects of windings and magnetic circuits of traction power transformers. A distinctive feature of the study is at certain frequencies of spectral dependences, taking into account the effects associated with defect formation that have a different cause of their manifestation, for example, wide-field fluctuations and changes in the shape and width of spectral peaks. The presence of random fluctuations caused the application of the normal Gaussian distribution law of the measured values of the spectra. To solve the problem of identifying the diagnosed spectra corresponding to certain defects of the power transformer, algorithms for identifying the vector of diagnostic features based on the method of statistical recognition theory for large amounts of information are proposed.

Transitions in stochastic non-equilibrium systems: Efficient reduction and analysis

A central challenge in physics is to describe non-equilibrium systems driven by randomness, such as a randomly growing interface, or fluids subject to random fluctuations that account e.g. for local stresses and heat fluxes in the fluid which are not related to the velocity and temperature gradients. For deterministic systems with infinitely many degrees of freedom, normal form and center manifold theory have shown a prodigious efficiency to often completely characterize how the onset of linear instability translates into the emergence of nonlinear patterns, associated with genuine physical regimes. However, in presence of random fluctuations, the underlying reduction principle to the center manifold is seriously challenged due to large excursions caused by the noise, and the approach needs to be revisited.In this study, we present an alternative framework to cope with these difficulties exploiting the approximation theory of stochastic invariant manifolds, on one hand, and energy estimates measuring the defect of parameterization of the high-modes, on the other. To operate for fluid problems subject to stochastic stirring forces, these error estimates are derived under assumptions regarding dissipation effects brought by the high-modes in order to suitably counterbalance the loss of regularity due to the nonlinear terms. As a result, the approach enables us to predict, from reduced equations of the stochastic fluid problem, the occurrence in large probability of a stochastic analogue to the pitchfork bifurcation, as long as the noise's intensity and the eigenvalue's magnitude of the mildly unstable mode scale accordingly.In the case of SPDEs forced by a multiplicative noise in the orthogonal subspace of e.g. its mildly unstable mode, our parameterization formulas show that the noise gets transmitted to this mode via non-Markovian coefficients, and that the reduced equation is only stochastically driven by the latter. These coefficients depend explicitly on the noise path's history, and their memory content is self-consistently determined by the intensity of the random force and its interaction through the SPDE's nonlinear terms. Applications to a stochastic Rayleigh-Bénard problem are detailed, for which conditions for a stochastic pitchfork bifurcation (in large probability) to occur, are clarified.

Solar Irradiance Forecasting Using Dynamic Ensemble Selection

Solar irradiance forecasting has been an essential topic in renewable energy generation. Forecasting is an important task because it can improve the planning and operation of photovoltaic systems, resulting in economic advantages. Traditionally, single models are employed in this task. However, issues regarding the selection of an inappropriate model, misspecification, or the presence of random fluctuations in the solar irradiance series can result in this approach underperforming. This paper proposes a heterogeneous ensemble dynamic selection model, named HetDS, to forecast solar irradiance. For each unseen test pattern, HetDS chooses the most suitable forecasting model based on a pool of seven well-known literature methods: ARIMA, support vector regression (SVR), multilayer perceptron neural network (MLP), extreme learning machine (ELM), deep belief network (DBN), random forest (RF), and gradient boosting (GB). The experimental evaluation was performed with four data sets of hourly solar irradiance measurements in Brazil. The proposed model attained an overall accuracy that is superior to the single models in terms of five well-known error metrics.

Diagenetic Self-Organization and Stochastic Resonance in a Model of Limestone-Marl Sequences

Banded patterns in limestone-marl sequences (“rhythmites”) form widespread sediments typical of shallow marine environments. They are characterized by alternations of limestone-rich layers and softer calcareous-clayey material (marl) extending over hundreds of meters with a thickness of a few tens of meters. The banded sequences are usually thought to result from systematic variations in the external environment, but the pattern may be distorted by diagenetic nonlinear processes. Here, we present a reactive-transport model for the formation of banded patterns in such a system. The model exhibits interesting features typical of nonlinear dynamical systems: (i) the existence of self-organized oscillating patterns between a calcite-rich mode (“limestone”) and a calcite-poor one (“marl”) for fixed environmental conditions and (ii) bistability between these two modes. We then illustrate the phenomena of stochastic resonance, whereby the multistable system is driven by a small external periodic signal (the 100,000 years’ Milankovitch cycle comes to mind) that is too weak to generate oscillations between the states on its own. In the presence of random fluctuations, however, the system generates transitions between the calcite-rich and calcite-poor states in statistical synchrony with the external forcing. The signal-to-noise ratio exhibits many maxima as the noise strength is varied. Hence, this amplification effect is maximized for specific values of the noise strength.

A neural network sensitivity analysis in the presence of random fluctuations

In this work we investigate the sensitivity analysis of the noise applied to a neural network. The goal of this study is to try to understand the network's behavior and the outputs sensitivity from the perturbation of weights during the training process. From an engineering point of view, noise is perceived as detrimental to the system and the quality of the output, but in biological neural systems, we can observe noise fluctuations, which possess certain abilities to improve information processing. By means of sensitivity analysis tools we show quantitatively the acceptable level of noise which provides optimal solution to the random fluctuations without sacrificing the behavior of the network. The three different indicators utilized in this endeavor allow us to observe whether the noise variance is detrimental or beneficial, and whether it acts as a source of fluctuation.

Stochastic theory of an optical vortex in nonlinear media

A stochastic theory is given of an optical vortex occurring in nonlinear Kerr media. This is carried out by starting from the nonlinear Schrödinger type equation which accommodates vortex solution. By using the action functional method, the evolution equation of vortex center is derived. Then the Langevin equation is introduced in the presence of random fluctuations, which leads to the Fokker-Planck equation for the distribution function of the vortex center coordinate by using a functional integral. The Fokker-Planck equation is analyzed for a specific form of pinning potential by taking into account an interplay between the strength of the pinning potential and the random parameters, diffusion and dissipation constants. This procedure is performed by several approximate schemes.

Influence of Imperfect Internal Waves on Long-Range Underwater Acoustic Propagation

This work presents a numerical analysis of the effect of random fluctuations of internal waves on the chaotic dynamics of ray trajectories in ocean acoustics. The Eikonal equation is considered in a form of the second order, nonlinear ordinary differential equation. Random phase modulations in the form of zero mean Gaussian white noise are considered for modeling an imperfectly periodic single mode internal wave. It is shown that in the presence of random fluctuations the intersection of acoustic rays with the ocean surface occurs sooner and becomes more frequent than predicted by deterministic ocean models.

The Impact of Random Device Variation on SRAM Cell Stability in Sub-90-nm CMOS Technologies

The impact of process variation on SRAM yield has become a serious concern in scaled technologies. In this paper, we propose a methodology to analyze the stability of an SRAM cell in the presence of random fluctuations in the device parameters. First, we develop a theoretical framework for characterizing the dc noise margin of a memory cell. The framework is based on the concept that an SRAM cell is on the verge of instability when the gain across the loop formed by the cross-coupled inverters in the cell is unity. The noise margin criteria developed in this manner can be used to verify a cell stability in the presence of arbitrary DC noise offsets at the two storage nodes in the cell. We also develop metrics for estimating the cell stability during read and write operations and verify these models by extensive Monte Carlo simulations in a 65-nm CMOS process. Our results show that the proposed robustness metrics can be used to estimate cell failure probabilities in an efficient and accurate manner.

Perfect quantum state transfer with randomly coupled quantum chains

We suggest a scheme that allows arbitrarily perfect state transfer even in the presence of random fluctuations in the couplings of a quantum chain. The scheme performs well for both spatially correlated and uncorrelated fluctuations if they are relatively weak (say 5%). Furthermore, we show that given a quite arbitrary pair of quantum chains, one can check whether it is capable of perfect transfer by only local operations at the ends of the chains, and the system in the middle being a ‘black box’. We argue that unless some specific symmetries are present in the system, it will be capable of perfect transfer when used with dual-rail encoding. Therefore our scheme puts minimal demand not only on the control of the chains when using them, but also on the design when building them.

Skeletons, noise and population growth: the end of an old debate?

Population dynamics models remain largely deterministic, although the presence of random fluctuations in nature is well recognized. This deterministic approach is based on the implicit assumption that systems can be separated into a deterministic part that captures the essential features of the system and a random part that can be neglected. But is it possible, in general, to understand population dynamics without the explicit consideration of random fluctuations? Here, we suggest perhaps not, and argue that the dynamics of many systems are a result of interactions between the deterministic nonlinear skeleton and noise.

Photodetachment dynamics of closed-shell anions: Effects of perturbation by a strong neighboring dipole

We have investigated the quantum dynamics of photodetachment of an electron from closed-shell anions by pulsed light in the presence of perturbation produced by a neighboring solvent dipole. The anion is modeled by a suitable one-dimensional potential and assumed to interact with the dipolar solvent molecule through ion-dipole and ion-induced dipole interactions. The dynamics is followed by invoking the time-dependent Fourier grid Hamiltonian method to solve the relevant Schrödinger equation. The detachment rates in the presence of random fluctuations in the binding energy of the anion-electron and orientation of the dipole (with respect to the anion) have been computed and compared with the rates observed for an anion with fixed binding energy and a fixed orientation of the dipole. The possibility of the detached electron being captured by the perturbing dipole is also considered. The capture probability and rate are studied as functions of important system parameters. The possibility of using the model to understand the evolution of the charge-transfer-to-solvent spectrum is explored. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 178–189, 2000

The Time Evolution of Bias

We study the evolution of the bias factor b and the mass-galaxy correlation coefficient r in a simple analytic model for galaxy formation and the gravitational growth of clustering. The model shows that b and r can be strongly time dependent but tend to approach unity even if galaxy formation never ends as the gravitational growth of clustering debiases the older galaxies. The presence of random fluctuations in the sites of galaxy formation relative to the mass distribution can cause large and rapidly falling bias values at high redshift.

Optimum control of deterministic and stochastic distributed populations with intra-species competition†

Abstract Most of the literature devoted to the study of dynamic populations with predators is focused on the use of the so-called ‘population law’ discovered by Verhulst in 1937, and generalized later by several authors. Basically this model deals with the total number of individuals in the population, irrespective of their distribution over the geographical space of definition. In contrast, the present paper suggests a distributed approach to populations with intra-species competitions, which explicitly takes into account the distributed parameter, for instance the age, of the individuals. Two models are given: a distributed version of the logistic law and a generalization of the transfer equation, and two frameworks are considered: the deterministic case and the stochastic one. The equations so obtained are mainly distributed differential integral equations; one considers The optimum control or such systems and necessary optimality conditions are given. The covariance of the deviation from a steady state in the presence of random fluctuations is derived. This model applies not only to biological populations, but also to social and economic systems, and it may be used as a basis for general studies on populations with intra-species competitions.

The stability of inviscid plane Couette flow in the presence of random fluctuations

The stability of a plane parallel flow which varies randomly across a channel is investigated. The mean velocity profile corresponds to plane Couette flow which is stable in the absence of fluctuations. The mean component of an infinitesimal disturbance in the flow is governed by an equation which is analogous to the Rayleigh equation arising in the classical stability analysis of an inviscid flow. The flow is found to be unstable when the correlation scale of the fluctuations in the basic flow is small compared with the channel width.

An optimal branching migration process

We consider a population distributed over two habitats as represented by two separate one-dimensional branching processes with random environments. The presence of random fluctuation in reproduction rates in both habitats implies the possibility that neither habitat is universally superior to the other for all times and that a maximal population size is to be achieved by having population members present in both habitats. We show that optimal population growth occurs when migration between habitats occurs at a fixed rate which can be found from the environmentally determined reproduction variables of the separate habitats. The optimal processes are themselves two-type branching processes with random environments.

An optimal branching migration process

We consider a population distributed over two habitats as represented by two separate one-dimensional branching processes with random environments. The presence of random fluctuation in reproduction rates in both habitats implies the possibility that neither habitat is universally superior to the other for all times and that a maximal population size is to be achieved by having population members present in both habitats. We show that optimal population growth occurs when migration between habitats occurs at a fixed rate which can be found from the environmentally determined reproduction variables of the separate habitats. The optimal processes are themselves two-type branching processes with random environments.

An industrial dynamics model for start-up management

Efficient start-up management can result in considerable productivity increases compared to improvements possible in `steady-state' activities. Provided adequate targets are set and updated in accordance with realistic productivity expectation, management can interact rapidly in order to achieve optimum performance. Such a management process is dependent on the availability of suitable methods of predicting future productivity and estimating present productivity in the presence of random fluctuation due to many causes. This paper develops a predictive start-up model which performs both these functions. At each observation time, observed productivity is compared with predicted productivity as estimated from previous data, the difference being used to update the model parameters in a manner analogous to exponential smoothing. The model is applied to a number of start-up problems and is shown to track the parameters in an acceptable fashion. Long- and short-term productivity predictions resulting from the model are shown to be a useful management aid.