Stochastic Theory Research Articles

Tensile performance and cracking characteristics of sustainable textile-reinforced cementitious composites utilizing expanded glass aggregate and fly ash replacement

In this study, sustainable textile-reinforced cementitious composites (TRC) were developed using lightweight expanded glass (EG) aggregates combined with fly ash (FA) as a partial cement replacement. Recycled nylon fibers were incorporated to enhance the cementitious matrix. The tensile performances and cracking characteristics of the developed TRC materials were comprehensively investigated. The key parameters investigated included the lightweight aggregate size, FA replacement content, fabric reinforcement ratio, and volume fraction of additional nylon fibers. The experimental results revealed that utilizing FA replacement content within the range of 20–30% and employing maximum EG aggregate sizes of 0.5 mm and 1.0 mm had a negligible influence on cracking characteristics and the tensile performance of TRC. Conversely, an adverse effect was observed with a 50% FA replacement content and a maximum EG size of 2.0 mm. Moreover, employing a higher fabric reinforcement ratio and an increased volume fraction of dispersed nylon fibers in the matrix endowed the TRC with favorable tensile performance and cracking characteristics. Eventually, an analytical model simulating the tensile stress-strain responses of TRC composites based on the cracking characteristics and stochastic matrix theory was proposed. The proposed model exhibits a reasonable correlation with the experimental results.

Finite dimensional approximation to fractional stochastic integro-differential equations with non-instantaneous impulses

This manuscript proposes a class of fractional stochastic integro-differential equations (FSIDEs) with non-instantaneous impulses in an arbitrary separable Hilbert space. We use a projection scheme of increasing sequence of finite dimensional subspaces and projection operators to define approximations. In order to demonstrate the existence and convergence of approximate solutions, we utilize stochastic analysis theory, fractional calculus, theory of fractional cosine family of linear operators, and fixed point approach. Furthermore, we examine the convergence of the Faedo–Galerkin (F–G) approximate solutions to the mild solution of our given problem. Finally, a concrete example involving a partial differential equation is provided to validate the main abstract results.

Controllability of semilinear noninstantaneous impulsive neutral stochastic differential equations via Atangana-Baleanu Caputo fractional derivative

This study mainly concerns the controllability of semilinear noninstantaneous impulsive neutral stochastic differential equations via the Atangana-Baleanu (AB) Caputo fractional derivative (FD). The essential findings are created using methods and concepts from semigroup theory, stochastic theory, fractional calculus, K-set contraction, and measure of noncompactness. Finally, an example is provided to demonstrate the applications of the key findings.

Fixed‐time Synchronization of Stochastic Kuramoto‐Oscillator Networks With Switching Topology Under Dynamic Event‐triggered Scheme

AbstractThis paper proposes a dynamic event‐triggered fixed‐time control scheme for the phase synchronization of Kuramoto networks with switching topology and stochastic coupling noise. To deal with the problems of switching topology and stochastic coupling noise, a multilayered control structure with a specially designed noise reduction layer is developed. The effectiveness is proved based on stochastic differential theory. To save communication resources and reduce control frequency, a dynamic event‐triggered mechanism is proposed. By introducing a dynamic variable into the triggering condition, the triggered instants are further reduced compared to the traditional static event‐triggered method. The synchronizing criteria and parameter conditions are established with stochastic Lyapunov stability theory. The analysis of Zeno behavior is also given. Finally, numerical simulation experiments are conducted to demonstrate the effectiveness of the proposed dynamic event‐triggered control scheme.

Narrowband Internet of Things via Low Earth Orbit Satellite Networks: An Efficient Coverage Enhancement Mechanism Based on Stochastic Geometry Approach.

With the development of IoT technology and 5G massive machine-type communication, the 3GPP standardization body considered as viable the integration of Narrowband Internet of Things (NB-IoT) in low Earth orbit (LEO) satellite-based architectures. However, the presence of the LEO satellite channel comes up with new challenges for the NB-IoT random access procedures and coverage enhancement mechanism. In this paper, an Adaptive Coverage Enhancement (ACE) method is proposed to meet the requirement of random access parameter configurations for diverse applications. Based on stochastic geometry theory, an expression of random access channel (RACH) success probability is derived for LEO satellite-based NB-IoT networks. On the basis of a power consumption model of the NB-IoT terminal, a multi-objective optimization problem is formulated to trade-off RACH success probability and power consumption. To solve this multi-objective optimization problem, we employ the Non-dominated Sorting Genetic Algorithms-II (NSGA-II) method to obtain the Pareto-front solution set. According to different application requirements, we also design a random access parameter configuration method to minimize the power consumption under the constraints of RACH success probability requirements. Simulation results show that the maximum number of repetitions and back-off window size have a great influence on the system performance and their value ranges should be set within [4, 18] and [0, 2048]. The power consumption of coverage enhancement with ACE is about 58% lower than that of the 3GPP proposed model. All this research together provides good reference for the scale deployment of NB-IoT in LEO satellite networks.

Stochastic kinetic theory applied to coarse-grained polymer model.

A stochastic field theory approach is applied to a coarse-grained polymer model that will enable studies of polymer behavior under non-equilibrium conditions. This article is focused on the validation of the new model in comparison with explicit Langevin equation simulations under conditions with analytical solutions. The polymers are modeled as Hookean dumbbells in one dimension, without including hydrodynamic interactions and polymer-polymer interactions. Stochastic moment equations are derived from full field theory. The accuracy of the field theory and moment equations is quantified using autocorrelation functions. The full field theory is only accurate for a large number of polymers due to keeping track of rare occurrences of polymers with a large stretch. The moment equations do not have this error because they do not explicitly track these configurations. The accuracy of both methods depends on the spatial degree of discretization. The timescale of decorrelation over length scales bigger than the spatial discretization is accurate, while there is an error over the scale of single mesh points.

Stochastic thermodynamics of Brownian motion in temperature gradient

We study stochastic thermodynamics of a Brownian particle which is subjected to a temperature gradient and is confined by an external potential. We first formulate an over-damped Ito-Langevin theory in terms of local temperature, friction coefficient, and steady state distribution, all of which are experimentally measurable. We then study the associated stochastic thermodynamics theory. We analyze the excess entropy production both at trajectory level and at ensemble level, and derive the Clausius inequality as well as the transient fluctuation theorem (FT). We also use molecular dynamics to simulate a Brownian particle inside a Lennard-Jones fluid and verify the FT. Remarkably we find that the FT remains valid even in the under-damped regime. We explain the possible mechanism underlying this surprising result.

Derivation of Dirac equation from the stochastic optimal control principles of quantum mechanics.

In this paper, we present a stochastic approach to relativistic quantum mechanics. We formulate the three fundamental principles of this theory and derive the Dirac equations based on them. This approach enables us to bring more insight into the nature of Dirac's spinors. Furthermore, we provide a physical interpretation of the stochastic optimal control theory of quantum mechanics.

Pth Moment Exponential Stability of Impulsive Stochastic Differential Equations with Unbounded Delays

Stochastic impulsive differential equations with Markovian switching have been applied extensively in various areas including ecology systems, neural networks, and control systems, and stability analysis is one fundamental premise of their applications. For two categories of Markovian switched impulsive stochastic differential functional equations with unbounded delays, this paper investigates the pth moment exponential stability by adopting stochastic Lyapunov stability theory and stochastic analysis approach. Several criteria on pth moment exponential stability have been acquired. In the proposed model, the time-varying coefficients and the hybrid impulsive effects are considered simultaneously. It can be seen that the criteria derived in this paper are more concise and the conditions are easier to verify compared with those existing results based on Razumikhin theory. Finally, two examples are illustrated to show the effectiveness of the theoretical findings.

A Policy Gradient Algorithm for the Risk-Sensitive Exponential Cost MDP

We study the risk-sensitive exponential cost Markov decision process (MDP) formulation and develop a trajectory-based gradient algorithm to find the stationary point of the cost associated with a set of parameterized policies. We derive a formula that can be used to compute the policy gradient from (state, action, cost) information collected from sample paths of the MDP for each fixed parameterized policy. Unlike the traditional average cost problem, standard stochastic approximation theory cannot be used to exploit this formula. To address the issue, we introduce a truncated and smooth version of the risk-sensitive cost and show that this new cost criterion can be used to approximate the risk-sensitive cost and its gradient uniformly under some mild assumptions. We then develop a trajectory-based gradient algorithm to minimize the smooth truncated estimation of the risk-sensitive cost and derive conditions under which a sequence of truncations can be used to solve the original, untruncated cost problem. Funding: This work was supported by the Office of Naval Research Global [Grant N0001419-1-2566], the Division of Computer and Network Systems [Grant 21-06801], the Army Research Office [Grant W911NF-19-1-0379], and the Division of Computing and Communication Foundations [Grants 17-04970 and 19-34986].

Modeling COVID-19 spread and non-pharmaceutical interventions in South Africa: A stochastic approach

The COVID-19 pandemic has exerted a pervasive worldwide influence, including on South Africa, which stands out as one of the African nations most substantially impacted. As of March 20, 2021, the nation has encountered a multitude of obstacles in its efforts to contain the virus’s transmission. Conventional approaches to forecasting the transmission of contagious illnesses frequently prove inadequate when it comes to comprehending the intricate dynamics of COVID-19, specifically with regard to stochastic disruptions and the efficacy of non-pharmaceutical interventions. The deficiency in predictive modeling has impeded the capacity to effectively evaluate and execute measures to reduce the spread of the virus. The principal objective of this study is to construct a novel stochastic model, denoted as SEIHR, that can effectively forecast the transmission of COVID-19 in South Africa while also assessing the efficacy of diverse non-pharmacological interventions. By conducting an extensive data analysis spanning from April 17, 2020, to September 13, 2021, this research endeavors to provide a comprehensive and nuanced comprehension of the dynamics of the epidemic, with a particular focus on its early surges. Using the idea of stochastic Lyapunov function theory, this study aims to find out if there is and is not a solution in the given model. It also wants to find out what conditions must be met in order to get rid of diseases when there are random disturbances, such as white noise. Using this model, the efficacy of interventions such as lockdowns in preventing the spread of the virus during the epidemic will also be critically evaluated. The primary objective is to furnish policymakers and health authorities with invaluable insights and tools that will enable them to more effectively manage and alleviate the COVID-19 crisis in South Africa and comparable settings.

Thermodynamics and stochastic thermodynamics of strongly coupled systems.

We further develop the strong-coupling theory of thermodynamics and stochastic thermodynamics for continuous systems, constructed in the previous work [Phys. Rev. Res. 4, 013015 (2022)2643-156410.1103/PhysRevResearch.4.013015]. A small system strongly interacting with a its environment, the dynamics of the system is assumed to be much slower than that of the bath. The system Hamiltonian is defined to be the Hamiltonian of mean force, whereas the system entropy is defined as the Gibbs-Shannon entropy. Equilibrium ensemble theories and thermodynamic theories are established for the system. Variations of three types of parameters are considered: (i) the system parameter λ which couples to the system and to the interaction, (ii) the bath parameter λ^{'} which couples to the bath only, and (iii) the temperature T=1/β. The work done to the system consists of three parts, proportional to dλ,dλ^{'}, and dβ respectively. The part proportional to dβ can be understood as the work done by the bath. As long as λ^{'} and β are not fixed, the work is not the change of total energy of the joint system. The differences between our strong-coupling equilibrium thermodynamics and the classical thermodynamics are discussed. The thermodynamic theory is promoted to the nonequilibrium level. Both the first and second laws of thermodynamics, as well as fluctuation theorems, are established for nonequilibrium processes. For processes with varying temperatures, fluctuation theorems cannot be expressed in terms of integrated work alone. Regardless of various subtleties, however, the stochastic thermodynamic theory is formulated in terms of system variables only, and dS-βd[over ¯]Q is the change of total entropy. Thermodynamic quantities of the system are related to those of the joint system, and the equivalence of theories at two levels of coarse-graining is explicitly demonstrated. Finally we show that there are infinite numbers of equivalent strong-coupling theories, each determined by its definition of system Hamiltonian. Our theory is distinguished by its maximal similarity with the weak-coupling theory.

Statistical Analysis of Ice Load on Icebreaker Ship Based on Stochastic Ice Fields

Accurately assessing ice loads is a fundamental issue in the field of structural design for ships in ice-covered regions. In this paper, we conducted research on extreme ice load estimation for icebreaking ships, combining stochastic theory with numerical simulation. Firstly, using sea ice data from the Arctic region of the United States National Snow and Ice Data Center, a stochastic ice field model was established under Arctic sea ice conditions using non-parametric estimation and the rejection sampling method, and ice field data were generated stochastically. Then, based on the stochastic ice field data, a three-dimensional numerical model of the interaction between the ice field and the ship hull was established, and the reliability of the numerical model was verified by experimental results. Finally, based on the numerical model of the interaction between the ice field and the ship hull, asymptotic methods were used to study the extreme ice load estimation in different parts of the ship hull, revealing the variation law of the extreme ice load in different parts of the ship hull. This study provides basic theory and technical support for the structural design of ships in polar regions and has engineering application value.

Study on the effect of tunneling and secondary grouting on the deformation of existing pipelines in bedrock raised strata

Shield crossing the bedrock raised strata easily leads to large deformation of the soil, resulting in deformation and damage of the upper pipelines. To investigate the law of pipeline deformation caused by shield underpassing in bedrock raised strata, the changes in the action range of the additional thrust of the cutter head (p1), the friction resistance of the shield shell (p2), and the additional grouting force (p3) were analysed. A convergence model of the excavation face suitable for bedrock raised strata was proposed. The calculation formula of soil displacement at the axis of the pipeline was derived by using Mindlin’s solution and stochastic medium theory. The solutions of the vertical displacement, bending moment and strain of the pipeline were obtained by the energy variational method and the principle of minimum potential energy. Pipeline deformation analysis and reliability verification were carried out by an engineering case in Hangzhou, China. The influence of bedrock distribution and secondary grouting behind the pipe wall on pipeline deformation was studied. The results show that the calculated results are similar to the measured data with a high degree of coincidence, and the degree of agreement is higher compared to the existing method. When the shield tunneling direction is well controlled, the settlement and bending moment of the pipeline caused by the shield crossing the raised bedrock stratum will be reduced, and the reduction increases with increasing bedrock length and intrusion depth. The secondary grouting behind the pipe wall can reduce the settlement of the pipe line, but it is necessary to reasonably control the three parameters of grouting amount per unit length (Vinj), grouting ring length (Lh), and grouting ring angle (δ). Lh should not be too long and can be controlled below 30 m, δ should be controlled within 60°, and Vinj can be adjusted according to the deformation size of the pipeline to prevent excessive or insufficient correction.

Probabilistic measures for biological adaptation and resilience.

This paper introduces an approach to quantifying ecological resilience in biological systems, particularly focusing on noisy systems responding to episodic disturbances with sudden adaptations. Incorporating concepts from nonequilibrium statistical mechanics, we propose a measure termed "ecological resilience through adaptation," specifically tailored to noisy, forced systems that undergo physiological adaptation in the face of stressful environmental changes. Randomness plays a key role, accounting for model uncertainty and the inherent variability in the dynamical response among components of biological systems. Our measure of resilience is rooted in the probabilistic description of states within these systems and is defined in terms of the dynamics of the ensemble average of a model-specific observable quantifying success or well-being. Our approach utilizes stochastic linear response theory to compute how the expected success of a system, originally in statistical equilibrium, dynamically changes in response to a environmental perturbation and a subsequent adaptation. The resulting mathematical derivations allow for the estimation of resilience in terms of ensemble averages of simulated or experimental data. Finally, through a simple but clear conceptual example, we illustrate how our resilience measure can be interpreted and compared to other existing frameworks in the literature. The methodology is general but inspired by applications in plant systems, with the potential for broader application to complex biological processes.

Nonlinear Optimal Control for Stochastic Dynamical Systems

This paper presents a comprehensive framework addressing optimal nonlinear analysis and feedback control synthesis for nonlinear stochastic dynamical systems. The focus lies on establishing connections between stochastic Lyapunov theory and stochastic Hamilton–Jacobi–Bellman theory within a unified perspective. We demonstrate that the closed-loop nonlinear system’s asymptotic stability in probability is ensured through a Lyapunov function, identified as the solution to the steady-state form of the stochastic Hamilton–Jacobi–Bellman equation. This dual assurance guarantees both stochastic stability and optimality. Additionally, optimal feedback controllers for affine nonlinear systems are developed using an inverse optimality framework tailored to the stochastic stabilization problem. Furthermore, the paper derives stability margins for optimal and inverse optimal stochastic feedback regulators. Gain, sector, and disk margin guarantees are established for nonlinear stochastic dynamical systems controlled by nonlinear optimal and inverse optimal Hamilton–Jacobi–Bellman controllers.

Correlation-induced viscous dissipation in concentrated electrolytes.

Electrostatic correlations between ions dissolved in water are known to impact their transport properties in numerous ways, from conductivity to ion selectivity. The effects of these correlations on the solvent itself remain, however, much less clear. In particular, the addition of salt has been consistently reported to affect the solution's viscosity, but most modeling attempts fail to reproduce experimental data even at moderate salt concentrations. Here, we use an approach based on stochastic density functional theory, which accurately captures charge fluctuations and correlations. We derive a simple analytical expression for the viscosity correction in concentrated electrolytes, by directly linking it to the liquid's structure factor. Our prediction compares quantitatively to experimental data at all temperatures and all salt concentrations up to the saturation limit. This universal link between the microscopic structure and viscosity allows us to shed light on the nanoscale dynamics of water and ions under highly concentrated and correlated conditions.

A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control

A stochastic discrete fractional Cournot duopoly game model with a unique interior Nash equilibrium is developed in this study. Some sufficient criteria of the Lyapunov stability in probability for the proposed model at the interior Nash equilibrium are derived using the Lyapunov theory. The proposed model’s finite time stability in probability is then investigated using a nonlinear feedback control approach at the interior Nash equilibrium. The stochastic Bellman theory is also used to explore the locally optimum control problem. Furthermore, bifurcation diagrams, time series, and the 0-1 test are used to investigate the chaotic dynamics of this model. Finally, numerical examples are given to illustrate the obtained results.

Optimal portfolio strategy of wealth process: a Lévy process model-based method

This paper is concerned with the optimal portfolio problem for a company that can invest in two risky assets, where a novel Lévy-process-driven model is constructed to describe the dynamics of the wealth process by using a constant elasticity of variance model and a jump-diffusion process. A delicately designed value function is proposed under the mean–variance criterion to reflect the optimal portfolio for the stochastic volatility model. By using the verification theorem, the desired optimal portfolio strategy is proposed by the solution to certain Hamilton–Jacobi–Bellman equations. Furthermore, the corresponding expressions are achieved by using the stochastic analysis theory. Finally, a numerical simulation example is provided to verify the effectiveness of the proposed optimal portfolio strategy.

Controllability of stochastic fractional systems involving state-dependent delay and impulsive effects

In this paper, the controllability concept of a nonlinear fractional stochastic system involving state-dependent delay and impulsive effects is addressed by employing Caputo derivatives and Mittag-Leffler (ML) functions. Based on stochastic analysis theory, novel sufficient conditions are derived for the considered nonlinear system by utilizing Krasnoselkii’s fixed point theorem. Correspondingly, the applicability of the derived theoretical results is indicated by an example.