A phenomenological approach to anomalous transport in complex or disordered media

We aim to derive a phenomenological approach to link the theories of anomalous transport governed by fractional calculus and stochastic theory with the conductivity behavior governed by the semi-empirical conductivity formalism involving Debye, Cole-Cole, Cole-Davidson, and Havriliak-Negami type conductivity equations. We want to determine the anomalous transport processes in the amorphous semiconductors and insulators by developing a theoretical approach over some mathematical instruments and methods. In this paper, we obtain an analytical expression for the average behavior of conductivity in complex or disordered media via using the fractional-stochastic differential equation, the Fourier-Laplace transform, some natural boundary-initial conditions, and familiar physical relations. We start with the stochastic equation of motion called the Langevin equation, develop its equivalent master equation called Klein-Kramers or Fokker-Planck equation, and consider the time-fractional generalization of the master equation. Once we derive the fractional master equation, then determine the expressions for the mean value of the variables or observables through some calculations and conditions. Finally, we use these expressions in the current density relation to obtain the average conductivity behavior.

Stochastic gravity and turbulence

We study the ensemble average of the thermal expectation value of an energy momentum tensor in the presence of a random external metric. In a holographic setup this quantity can be read off of the near boundary behavior of the metric in a stochastic theory of gravity. By numerically solving the associated Einstein equations and mapping the result to the dual boundary theory, we find that the non relativistic energy power spectrum exhibits a power law behavior as expected by the theory of Kolmogorov and Kraichnan.

Antidisturbance Control for Helicopter Stochastic Systems

In this paper, an antidisturbance controller is presented for helicopter stochastic systems under disturbances. To enhance the antidisturbance abilities, the nonlinear disturbance observer method is applied to reject the time-varying disturbances. Then, the antidisturbance nonlinear controller is designed by combining the backstepping control scheme. And the stochastic theory is used to guarantee that the closed-loop system is asymptotically bounded in mean square while the proposed control method is shown via some traditional nonlinear control techniques, which still show some common issues such as “dimension explosion” or others. The result of this paper can be regarded as a typical case of the nonlinear control method to help and promote the generation of advanced methods.

Stochastic Analysis of the Variability of Groundwater Flow Fields in Heterogeneous Confined Aquifers of Variable Thickness

The problem of flow through heterogeneous confined aquifers of variable thickness is analyzed from a stochastic point of view. The analysis is carried out on the basis of the integrated equations of the depth-averaged hydraulic head and integrated specific discharge, which are developed by integrating the continuity equation and equation for the specific discharge over the thickness, respectively. A spectrally based perturbation approach is used to arrive at the general results for the statistics of the flow fields in the Fourier domain, such as the variance of the depth-averaged head, and the mean and variance of integrated discharge. However, the closed-form expressions are obtained under the condition of steady unidirectional mean flow in the horizontal plane. In developing stochastic solutions, the input hydraulic conductivity parameter is viewed as a spatial random field characterized by the theoretical spatial covariance function. The evaluation of the closed-form solutions focuses on the influence of the controlling parameters, namely as a geometrical parameter defining the variation of the aquifer thickness and the correlation scale of log hydraulic conductivity, on the variability of the fluid fields. The application of the present stochastic theory to predict the total specific discharge under uncertainty using the field data is also provided.

Research on a modeling method of wing deformation under the influence of separation and compound multi-source disturbance

An aircraft wing is the carrier of imaging payload (interferometric synthetic aperture radar (SAR) or array SAR) of a high-resolution aerial remote sensing system, and high-precision estimation of wing deformation is the key. There are two main traditional modelling methods for wing deformation, namely stochastic theory modelling and material mechanics modelling only dealing with single disturbance, of which the model parameters are derived from empirical values. Aiming at the complex multi-source disturbance of an aircraft wing, this paper separately probes the influence of external disturbance (air disturbance) and internal disturbance (engine vibration) based on the real-time observation of sensors and classifies the wing deformation on the basis of auto-regressive (AR) modelling for parameter identification. With the authentic flight data of a certain types of aircraft, the experimental analysis shows that the wing deformation under the influence of engine vibration is the 14th-order AR model, and the wing deformation under the influence of turbulence is the fifth-order AR model. Meanwhile, this paper also provides an experimental verification idea for the wing deflection modelling built on the second- or third-order Markov model.

Features of Calculating the Characteristics of Energy Complexes Using Low-Grade Energy

The development of stationary energy seems to be an important aspect of introduction of energy-saving technologies in transportation sector. In Russia, it is conditioned by the main provisions of the Energy Strategy of the Russian Federation until 2030. In this regard, the problem of efficient use of low-grade heat based on the organic Rankine cycle (ORC) in stationary heat energy supply units in the transport industry is urgent. In particular, this task is typical for boiler houses converted from heavy fuel oil to gas fuel. In this case, the efficiency of ORC application will primarily be determined by the efficiency of the used heat exchangers (HE) with a phase transition, as a result of which, both technically and theoretically, the problem of designing and calculating the optimal characteristics of these HE will be of great interest.The article presents a theoretical and computational model of heat transfer during phase transitions in turbulent flows based on the relations obtained by the stochastic theory of hydrodynamics and heat transfer. The modelling of the effect of turbulence during the phase transition with undeveloped boiling of the bubble mode is considered. The comparison results show satisfactory conformity of the values obtained according to the formula based on stochastic equations with the values calculated according to the empirical formula for the flow in a pipe, used in the engineering method of designing heat exchangers. The results obtained open the prospect for studying the processes of heat transfer during phase transitions in turbulent flows of HE to reduce their overall and mass characteristics, as well as to increase the energy efficiency of both the devices themselves and the efficiency of the entire energy complex.

A Framework for Modelling Economic Regional Location Processes Under Uncertainty

This paper deals with the theoretical analysis of the spatial concentration and localization of firms and employees over a set of regions. In particular, it provides a simple site-selection theoretical model to describe the probabilistic framework of the location patterns. The adopted quantitative tool is the stochastic theory of urns. The model moves from the empirical evidence of the deviation of the spatial location of companies from the uniform distribution and of employees from the distribution of firms. Factors leading to such deviations are taken into consideration. Specifically, we formalize a decision problem grounded on the economic attributes of the regions and also on the distribution of the existing firms and employees in the territory. To our purpose, the site-selection model is presented as a stepwise process.