Random Fluctuations Research Articles

All-optical polarization scrambler based on polarization beam splitting with an amplified fiber ring

Optical-fiber-based polarization scramblers can reduce the impact of polarization sensitive performance of various optical fiber systems. Here, we propose a simple and efficient polarization scrambler based on an all-optical Mach-Zehnder structure by combining a polarization beam splitter and an amplified fiber ring. To totally decoherence one polarization split beam, a fiber ring together with an amplifier is incorporated. The ratio of two orthogonal beams can be controlled by varying the amplification factor, and we observe different evolution trajectories of the output state of polarizations on the Poincaré sphere. When the amplification factor exceeds a certain threshold, the scrambler system exhibits nearly ideal polarization scrambling behavior. A commercial single wavelength laser with a linewidth of 3 MHz is utilized to characterize the scrambling performance. We found that when the sampling rate is 1.6 MSa/s, a scrambling speed up to 2000krad/s can be obtained for the average degree of polarization being less than 0.1. We also exploit these random polarization fluctuations to generate random binary numbers, indicating that the proposed technique is a good candidate for a random bit generator.

Reliability of Hypersonic Airfoil with Freeplay and Stochasticity via Nonlinear Energy Sink

The reliability of a pitch-plunge hypersonic airfoil in random fluctuating flow with both cubic and freeplay nonlinearity is examined. The Hopf bifurcation and dynamic responses of the hypersonic airfoil are performed. To analyze the reliability, the effects of stochasticity on the dynamic behaviors of the hypersonic airfoil model are discussed in detail. Several unwanted phenomena that result in the failure of the airfoil structure are induced by random fluctuations. Subsequently, the reliability of the airfoil model is defined and analyzed according to the first passage failure criteria. The effects of different parameters on the reliability are investigated. Furthermore, a nonlinear energy sink is introduced to suppress the vibration of the airfoil and enhance the reliability. Two-dimensional reliability regions of the airfoil model are given to provide the safety parameter region. The results show that the reliability of the airfoil model is significantly improved with the nonlinear energy sink. This work will provide new insights into the safety design of hypersonic aircraft.

Output uncertainty mitigation in competitive markets

Output uncertainty is a major concern for industries prone to exogenous, persistent and large fluctuations in output, such as agriculture, wind and solar power generation, while technology adoption aimed at mitigating output uncertainty can improve social welfare. This paper constructs a competitive market model with random output fluctuations to examine the scale of technology adoption at the long-term equilibrium and its comparison with the social optimum. We show that the First Welfare Theorem no longer holds in general, and depending on the characteristics of the demand function, the scale of technology adoption in the competitive market may be greater or less than the socially optimal scale.

Spatial-temporal modeling of oil condition monitoring: A review

Lubricating oil plays a vital role as the information carrier for equipment tribological performance. Therefore, oil condition monitoring (OCM) serves as a crucial technology for assessing and predicting state degradation, providing the first-line defense against functional failure. However, limited by random fluctuation and insufficient knowledge, the modeling of OCM has suffered from uncertainty problems, leading to poor applicability and insufficient generalizability. The existing reviews are less elaborated on the information uncertainty for description, characterization, and treatment, which expresses the essence of modeling constraints. To bridge this gap, the paper provides a comprehensive review of the oil state modeling in terms of uncertainty. The existing methods and metrics are reviewed from the perspective of the spatial oil state assessment (OCA) and temporal remaining useful life (RUL) prediction modeling. Further, the existing methods are analyzed to solve the uncertainty problem, and then the solutions in oil state modeling considering uncertainty are discussed. Finally, targeting the challenges of the monitoring technology, the future trends of OCM are presented.

A novel approach for the lifetime prediction and structural health monitoring of concrete sewer systems exposed to biogenic sulphide corrosion

A novel, combined experimental-modelling approach is presented for the estimation of the corrosion depth, load bearing capacity and lifetime of unreinforced concrete sewer pipes exposed to prolonged biogenic sulphide corrosion. The biogenic sulphide corrosion process is mimicked through two types of representative chemical experiments, namely: (i) long-term experiments performed under moderately controlled pH conditions, where dry-cast concrete cube samples are exposed to monthly refreshed sulphuric acid solutions with initial pH values of 3, 2 and 1 for a period of 12 months, and (ii) short-term experiments carried out under highly controlled pH conditions, in which dry-cast concrete disk samples are subjected to sulphuric acid solutions with almost constant pH values of 2, 1 and 0.5 for a period of two months. By applying X-ray diffraction, optical microscopy, scanning electron microscopy and energy dispersive X-ray spectroscopy analyses, insight into the micro-scale morphology and elemental composition of the corrosion profile is obtained. In addition, the corrosion front and depth characteristics are measured by conducting phenolphthalein tests and analyses of surface colour and texture of macro-scale samples. From the experimental results, the time course of the corrosion depth is calibrated with a model for sulphate attack under a constant pH level. The model formulation is combined with detailed finite element method results from the literature to predict the long-term load bearing capacity of a concrete sewer pipe. The model is subsequently generalised for sulphate corrosion under a varying pH level. When combined with the installation of pH measuring devices on the inside of sewer pipes, the current engineering model may serve as an excellent practical tool for continuously monitoring the structural health and predicting the lifetime of in-situ sewer systems subject to sulphate attack under random acidity fluctuations.

Statistical methods for the computation and parameter estimation of a fractional SIRC model with Salmonella infection

This study analyzes the fractional order SIRC epidemic model under stochastic fractional differential equations in the Caputo sense. This article describes Salmonella infection in animal herds. For the deterministic system, we explain solution positivity and boundness. We also prove that the fractional stochastic solution exists and is unique. Other criteria considered include non-negativity of solutions, local and global stability analyses, Hyers-Ulam stability analysis, and sensitivity analysis for the deterministic system. Furthermore, according to the truncated Ito-Taylor expansion, we apply a numerical method to solve the stochastic fractional SIRC epidemic model, namely the Milstein method, to solve the stochastic fractional SIRC epidemic model. A comparison of the approximation solution and the corresponding deterministic model for different sample paths shows the efficiency of the numerical method. In addition, graphs and error tables provide insight into numerical experiments' results. The stochastic nature of the model allows random fluctuations in Salmonella infection spread. By incorporating uncertainty into the model, we gain a more realistic understanding of the epidemic dynamics and can better evaluate the effectiveness of control measures. Additionally, the numerical method used to solve the stochastic fractional SIRC epidemic model provides valuable insights into the variability of the results. This enhances our ability to make informed decisions about managing and preventing bacterial infections in animal herds.

A metaheuristic algorithm for regulating virtual inertia of a standalone microgrid incorporating electric vehicles

AbstractModern electrical networks, particularly microgrids, have seen a sharp rise in acquiring non‐conventional sources. The inertia of the microgrid decreases drastically because RESs have been used in place of traditional synchronous generators. The reduced inertia negatively impacts the dynamics and performance of the microgrid with RESs, which decreases the microgrid's stability, especially in operation on an island. The primary purpose of this research study is to enhance the dynamic security of an island microgrid by merging an electric vehicle with a frequency control technique based on virtual inertia control. A Proportional Integral Derivative Filter Constant (PIDFN) controller optimally created using the Modified Differential Evolution (MDE) method served as the foundation for control in the virtual inertia control loop. The effectiveness of the MDE‐based PIDFN controller was examined considering the diverse operational scenarios are compared and contrasted with those of traditional methods Differential Evolution (DE) and Teaching Learning Based Optimization (TLBO)‐based PIDFN controllers. Real‐time wind and solar power statistics and random load fluctuations were incorporated to provide realistic simulation settings. The outcomes demonstrate that the MDE‐based PIDFN controller performs better in reference frequency tracking and reducing frequency disturbances than the other optimization strategies.

Sample entropy-based quantitative assessment of the arc magnetic field spectrum for improved arc welding quality

Arc magnetic field analysis is a valuable approach for assessing the stability of the arc welding process, yet existing methods lack the ability to effectively quantify the disorder within the process. Through an investigation into the characteristics of the arc magnetic field signal, it was observed that the occurrence of low-frequency random fluctuations in arc magnetic field power, induced by unstable factors such as bubbles or short circuits, contributed to increased complexity and randomness in the arc magnetic field signals. To visualise the arc magnetic field signals in a time-frequency domain, a spectrogram was employed, revealing a strong correlation between the distribution of maximum power spectral density (PSD) in the spectrogram and the stability of the arc welding process. Furthermore, a novel method based on sample entropy was introduced to provide a quantitative measure of this relationship. A comprehensive quantitative assessment indicator called arc magnetic field sample entropy (AMFSE) was proposed. This indicator effectively mitigates the influence of varying parameters on the quantitative results, enabling a more accurate and consistent representation of the stability of the arc welding process. The proposed method was validated through testing, yielding an accuracy rate exceeding 90%.

Calculation of Temperature Action of Flat Steel Box Girder of Long-Span Bridges Using a Joint Model of ARMA Mean and GARCH Variance

Using the monitoring temperature field data from the flat steel box girder, the time histories of temperature data and temperature difference data are investigated using the extreme value analysis method. Because the calculation of standard values of temperature action needs massive temperature field data, the simulation of daily extreme values of temperature data and temperature difference data is carried out by virtual of Probability Statistical Method. The seasonal and nonstationary trend terms are described using the weighted sum of a series of basic elementary functions. The random fluctuation term is represented by a joint model of ARMA mean and GARCH variance. Moreover, the yearly extreme values of temperature data and temperature difference data are considered as statistical variables, and their standard values of temperature action with 50-year return period are calculated by means of the general extreme value (GEV) distributive function. The research results can supply references for temperature action of flat steel box girder.

Research on Prediction of Illegal Wildlife Trade Based on PCA and Multiple Linear Regression

Illegal wildlife trade is a long-standing issue, exerting negative impacts over national economies, regional security, and even global ecosystems. Governments worldwide and numerous environmental and animal protection organizations have been deeply engaged in addressing this issue for many years. Historically, there has been a lack of a quantifiable model to analyze the impact of implementing wildlife monitoring and conservation projects using drones on illegal wildlife trade.In this paper, we primarily propose an Illegal Wildlife Trade Prediction Model. By integrating four secondary indicators related to wildlife trade with the aforementioned 16 indicators, we reduced them to four primary indicators. The methodological tests confirmed their strong correlation, and multiple regression analysis was used to predict illegal wildlife trade, thereby verifying the project's effectiveness. Innovatively, we established a model to measure the probability of project completion, combining data from model predictions, resulting in an approximate completion probability of 60%. In conducting a project sensitivity analysis, we also developed a new model to perturb the three primary indicators, predicting the project's final outcome under random fluctuation of indicators, with variation rates as low as 0.34%, 0.98%, and 1.22%, indicating the project's stability.

Parametric resonance in Abelian and non-Abelian gauge fields via spacetime oscillations

We study the evolution of Abelian U(1) electromagnetic as well as non-Abelian SU(2) gauge fields, in the presence of spacetime oscillations. Analysis of the time evolution of Abelian gauge fields shows the presence of parametric resonance in spatial modes. A similar analysis in the case of non-Abelian gauge fields, in the linear approximation, shows the presence of the same resonant spatial modes. The resonant modes induce large fluctuations in physical observables including those that break the CP symmetry. We also carry out time evolution of small random fluctuations of the gauge fields, using numerical simulations in 2+1 and 3+1 dimensions. These simulations help to study nonlinear effects in the case of non-Abelian gauge theories. Our results show that there is an increase in energy density with the coupling, at late times. These results suggest that gravitational waves may excite non-Abelian gauge fields more efficiently than electromagnetic fields. Also, gravitational waves in the early Universe and from the merger of neutron stars, black holes, etc., may enhance CP violation and generate an imbalance in chiral charge distributions, magnetic fields, etc. Published by the American Physical Society 2024

Modeling and FDTD discretization of stochastic Maxwell's equations with Drude dispersion

We develop the stochastic Maxwell's equations with Drude model under both additive and multiplicative noises. The additive noises characterize the random fluctuations in the electric current and magnetic current densities in Maxwell's equations, while the multiplicative noise describes the external fluctuation of electric field in the Drude dispersion equation of motion. For the stochastic models with Drude dispersion, we derive the averaged global energy law considering both types of noises. The CN-FDTD and Yee-FDTD discretization schemes are developed for solving the stochastic system over staggered grids. We establish the discrete averaged global energy laws for the CN-FDTD and Yee-FDTD schemes. Numerical experiments show the discrete averaged global energy evolutions and the convergence rates of the schemes for the stochastic Maxwell's equations with Drude model. We numerically simulate and analyze the stochastic electromagnetic propagation within Drude materials under various sinusoidal sources, initial wave conditions and additive and multiplicative noises.

Field-theoretic approach to neutron noise in nuclear reactors.

An operating nuclear reactor is designed to maintain a sustained fission chain reaction in its core, which results from a delicate balance between neutron creations (i.e., fissions) and total absorptions. This balance is associated with random fluctuations that can have two, very different, origins. A distinction must thus be made between low-power noise, whose origin lies in the inherently stochastic nature of neutron interactions with matter, and high-power noise, whose origin lies in the particular thermomechanical constraints associated with the environment in which neutrons propagate. Modeling the behavior of this noisy neutron population with the help of stochastic differential equations, we first show how the Martin-Siggia-Rose-Janssen-De Dominicis (MSRJD) formalism, providing a field theoretical representation of the problem, reveals a convenient and adapted tool for the calculation of observable consequences of neutron noise. In particular, we show how the MSRJD approach is capable of encompassing both types of neutron noises in the same formalism. Emphasizing then on power noise, it is shown how the self-sustained chain reaction developing in a reactor core might be sensitive to noise-induced transitions. Establishing an unprecedented connection between the neutron population evolving in a reactor core and the celebrated Kardar-Parisi-Zhang (KPZ) equation, we indeed find evidence that a noisy reactor core power distribution might be subject to a process analogous to the roughening transition, well-known to occur in systems described by the KPZ equation.

From Brownian to Deterministic Motor Movement in a DNA-Based Molecular Rotor.

Molecular devices that have an anisotropic periodic potential landscape can be operated as Brownian motors. When the potential landscape is cyclically switched with an external force, such devices can harness random Brownian fluctuations to generate a directed motion. Recently, directed Brownian motor-like rotatory movement was demonstrated with an electrically switched DNA origami rotor with designed ratchet-like obstacles. Here, we demonstrate that the intrinsic anisotropy of DNA origami rotors is also sufficient to result in motor movement. We show that for low amplitudes of an external switching field, such devices operate as Brownian motors, while at higher amplitudes, they behave deterministically as overdamped electrical motors. We characterize the amplitude and frequency dependence of the movements, showing that after an initial steep rise, the angular speed peaks and drops for excessive driving amplitudes and frequencies. The rotor movement can be well described by a simple stochastic model of the system.

Experimental Validation of Comprehensive Calculation for High-Resolution Linear MALDI-TOF Mass Spectrometry.

This work discusses the effectiveness of the previously developed comprehensive calculation model to optimize linear MALDI-TOF mass spectrometers. The model couples space- and velocity-focusing to precisely analyze the flight-time distribution of ions and predict optimal experimental parameters for the highest mass resolving power. Experimental validation was conducted using a laboratory-made instrument to analyze CsI3 and angiotensin I ions in low to medium m/z range. The results indicate that the predicted optimal extraction voltage and delay were reasonably accurate and effective. In the low m/z range, the peak width obtained using optimal parameters reached the sub nanosecond range, corresponding to a mass resolving power of 10 000-17 000, or 20 000-34 000 if shot-to-shot random fluctuations were minimized by the dynamic data correction method. The observed optimal mass resolving power in the current experiment is 4.8-7.8 times that of commercial instruments. Practical limitations resulting in the gap between the observed and theoretical ultimate mass resolving power are discussed.

Optimizing Work Extraction in the Presence of an Entropic Potential: An Entropic Stochastic Resonance.

We study the nontrivial thermodynamic responses of an overdamped Brownian system driven by an unbiased driving force when the particle is confined inside a bilobal irregular structure. The spatial irregularity of the confinement results in an effective entropic bistable potential along the direction of transport. We calculate the thermodynamic response functions in terms of the averaged work done and the absorbed heat over a cycle of driving. We find that the thermodynamic responses are influenced by the nonlinearity of the effective entropic potential, the frequency of the external periodic driving force, and the random thermal fluctuations in a nontrivial way. In the presence of an optimal amount of thermal noise and a favoring driving frequency, the process exhibits a resonance-like precedent in terms of both output work and absorbed heat. We explore the conditions to get best synchronized work extraction (or absorbed heat), which can be utilized as a potential quantifier of an entropic stochastic resonance phenomenon. Finally, we identify a hallmark of entropy dominance over an analogous energy-driven scenario in terms of output work.

Analysis of the stochastic perturbed Schrödinger–Hirota equation with Kerr law in the presence of spatio-temporal dispersion with bifurcation and chaotic phenomena along with soliton solutions

The goal of this work is to use the complete discriminant system (CDS) of the polynomial method (CDSPM) to provide soliton solutions for the perturbed Schrödinger–Hirota equation (PSHE) with the Kerr law by taking the stochastic into consideration. We examine exact and analytical solutions, such as those for the hyperbolic function, trigonometric function, Jacobian elliptic function (JEF), and other solitary wave (SW) solutions. Moreover, we also analyze the qualitative analysis of the governing model by using the terms of chaos and bifurcation. The trajectories of chaotic behavior show exponential divergence, which indicates that small changes in the initial circumstances cause the trajectories to become widely separated and divergent over time. We also discuss the phase portraits, which are useful in figuring out if the system’s equilibrium points are stable. Finally, we examine our governing model’s sensitivity analysis under different initial conditions. Sensitivity analysis measures a system’s or model’s robustness or sensitivity to changes in its input variables. Furthermore, we have included a number of graphs that clearly show the impact of the white noise so that you can better comprehend our results. The white noise effect is a distinct pattern of random fluctuations that may be seen in a variety of systems and incidents. It is distinguished by a uniform distribution of frequencies throughout the spectrum, resulting in a continuous and uncorrelated signal.

Dynamics of a Stochastic SVEIR Epidemic Model with Nonlinear Incidence Rate

This paper delves into the analysis of a stochastic epidemic model known as the susceptible–vaccinated–exposed–infectious–recovered (SVEIR) model, where transmission dynamics are governed by a nonlinear function. In the theoretical analysis section, by suitable stochastic Lyapunov functions, we establish that when the threshold value, denoted as R0s, falls below 1, the epidemic is destined for extinction. Conversely, if the reproduction number R0 of the deterministic model surpasses 1, the model manifests an ergodic endemic stationary distribution. In the numerical simulations and data interpretation section, leveraging a graphical analysis with COVID-19 data, we illustrate that random fluctuations possess the capacity to quell disease outbreaks, underscoring the role of vaccines in curtailing the spread of diseases. This study not only contributes to the understanding of epidemic dynamics but also highlights the pivotal role of stochasticity and vaccination strategies in epidemic control and management. The inherent balance and patterns observed in epidemic spread and control strategies, reflect a symmetrical interplay between stochasticity, vaccination, and disease dynamics.

Emergence of a hexagonal pattern in shear-thickening suspensions under orbital oscillations

A dense particle suspension under shear may lose its uniform state to large local density and stress fluctuations, which challenge the mean-field description of the system. Here, we explore the novel dynamics of a non-Brownian suspension under orbital oscillations, where localized density waves along the flow direction appear beyond an excitation frequency threshold and self-organize into a hexagonal pattern across the system. The spontaneous occurrence of the inhomogeneity pattern arises from a coupling between particle advection and the shear-thickening nature of the suspension. Through linear stability analysis, we show that they overcome the stabilizing effects of particle pressure at sufficient particle volume fraction and oscillation frequency. In addition, the long-standing density waves degenerate into random fluctuations when replacing the free surface with rigid confinement. It indicates that the shear-thickened state is intrinsically heterogeneous, and the boundary conditions are crucial for developing local disturbance.

Dislike of general opinion makes for tight elections.

In modern democracies, the outcome of elections and referendums is often remarkably tight. The repetition of these divisive events are the hallmark of a split society; to the physicist, however, it is an astonishing feat for such large collections of diverse individuals. Many sociophysics models reproduce the emergence of collective human behavior with interacting agents, which respond to their environment according to simple rules, modulated by random fluctuations. A paragon of this class is the Ising model which, when interactions are strong, predicts that order can emerge from a chaotic initial state. In contrast with many elections, however, this model favors a strong majority. Here we introduce a new element to this classical theory, which accounts for the influence of opinion polls on the electorate. This brings about a new phase in which two groups divide the opinion equally. These political camps are spatially segregated, and the sharp boundary that separates them makes the system size dependent, even in the limit of a large electorate. Election data show that, since the early 1990s, countries with more than about a million voters often found themselves in this state, whereas elections in smaller countries yielded more consensual results. We suggest that this transition hinges on the electorate's awareness of the general opinion.