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Biased and accelerated molecular simulations (BAMS) are widely used tools to observe relevant molecular phenomena occurring on time scales inaccessible to standard molecular dynamics, but evaluation of the physical time scales involved in the processes is not directly possible from them. For this reason, the problem of recovering dynamics from such kinds of simulations is the object of very active research due to the relevant theoretical and practical implications of dynamics on the properties of both natural and synthetic molecular systems. In a recent paper [A. Rapallo et al., J. Comput. Chem. 42, 586–599 (2021)], it has been shown how the coupling of BAMS (which destroys the dynamics but allows to calculate average properties) with Extended Diffusion Theory (EDT) (which requires input appropriate equilibrium averages calculated over the BAMS trajectories) allows to effectively use the Smoluchowski equation to calculate the orientational time correlation function of the head–tail unit vector defined over a peptide in water solution. Orientational relaxation of this vector is the result of the coupling of internal molecular motions with overall molecular rotation, and it was very well described by correlation functions expressed in terms of weighted sums of suitable time-exponentially decaying functions, in agreement with a Brownian diffusive regime. However, situations occur where exponentially decaying functions are no longer appropriate to capture the actual dynamical behavior, which exhibits persistent long time correlations, compatible with the so called subdiffusive regimes. In this paper, a generalization of EDT will be given, exploiting a fractional Smoluchowski equation (FEDT) to capture the non-exponential character observed in the relaxation of intramolecular distances and molecular radius of gyration, whose dynamics depend on internal molecular motions only. The calculation methods, proper to EDT, are adapted to implement the generalization of the theory, and the resulting algorithm confirms FEDT as a tool of practical value in recovering dynamics from BAMS, to be used in general situations, involving both regular and anomalous diffusion regimes. [ABSTRACT FROM AUTHOR]

We propose a Brownian ratchet for the unidirectional transport of stimuli-responsive molecules confined in a series of asymmetric geometries. It relies on repetitive cycles of aggregation and dispersion, which cause significant changes in molecular distribution within the confining geometry and enable the Brownian motion of the molecules to be ratcheted in a specific direction. To demonstrate the feasibility of the proposed Brownian ratchet, we conducted Brownian dynamics simulations where stimuli-responsive molecules were repeatedly aggregated and dispersed in a series of truncated conical tubes by altering intermolecular interactions. These simulations demonstrated the unidirectional transport of the molecules, indicating the efficacy of the proposed Brownian ratchet. Furthermore, we found that it becomes more effective with higher concentrations of molecules. This study suggests that, through the deliberate control of molecular assembly and disassembly by stimuli-responsive intermolecular interactions, it is possible to achieve directional and controlled molecular transport in various nanoscale applications. [ABSTRACT FROM AUTHOR]

As the physicochemical properties of ultrafine bubble systems are governed by their size, it is crucial to determine the size and distribution of such bubble systems. At present, the size or size distribution of nanometer-sized bubbles in suspension is often measured by either dynamic light scattering or the nanoparticle tracking analysis. Both techniques determine the bubble size via the Einstein–Stokes equation based on the theory of the Brownian motion. However, it is not yet clear to which extent the Einstein–Stokes equation is applicable for such ultrafine bubbles. In this work, using atomic molecular dynamics simulation, we evaluate the applicability of the Einstein–Stokes equation for gas nanobubbles with a diameter less than 10 nm, and for a comparative analysis, both vacuum nanobubbles and copper nanoparticles are also considered. The simulation results demonstrate that the diffusion coefficient for rigid nanoparticles in water is found to be highly consistent with the Einstein–Stokes equation, with slight deviation only found for nanoparticle with a radius less than 1 nm. For nanobubbles, including both methane and vacuum nanobubbles, however, large deviation from the Einstein–Stokes equation is found for the bubble radius larger than 3 nm. The deviation is attributed to the deformability of large nanobubbles that leads to a cushioning effect for collision-induced bubble diffusion. [ABSTRACT FROM AUTHOR]

Beyond well-documented confinement and surface effects arising from the large internal surface and severely confining porosity of nanoporous hosts, the transport of nanoconfined fluids remains puzzling in many aspects. With striking examples such as memory, i.e., non-viscous effects, intermittent dynamics, and surface barriers, the dynamics of fluids in nanoconfinement challenge classical formalisms (e.g., random walk, viscous/advective transport)—especially for molecular pore sizes. In this context, while molecular frameworks such as intermittent Brownian motion, free volume theory, and surface diffusion are available to describe the self-diffusion of a molecularly confined fluid, a microscopic theory for collective diffusion (i.e., permeability), which characterizes the flow induced by a thermodynamic gradient, is lacking. Here, to fill this knowledge gap, we invoke the concept of "De Gennes narrowing," which relates the wavevector-dependent collective diffusivity D0(q) to the fluid structure factor S(q). First, using molecular simulation for a simple yet representative fluid confined in a prototypical solid (zeolite), we unravel an essential coupling between the wavevector-dependent collective diffusivity and the structural ordering imposed on the fluid by the crystalline nanoporous host. Second, despite this complex interplay with marked Bragg peaks in the fluid structure, the fluid collective dynamics is shown to be accurately described through De Gennes narrowing. Moreover, in contrast to the bulk fluid, the departure from De Gennes narrowing for the confined fluid in the macroscopic limit remains small as the fluid/solid interactions in severe confinement screen collective effects and, hence, weaken the wavevector dependence of collective transport. [ABSTRACT FROM AUTHOR]

The dynamics of a soft particle suspended in a viscous fluid can be changed by the presence of an elastic boundary. Understanding the mechanisms and dynamics of soft–soft surface interactions can provide valuable insights into many important research fields, including biomedical engineering, soft robotics development, and materials science. This work investigates the anomalous transport properties of a soft nanoparticle near a visco-elastic interface, where the particle consists of a polymer assembly in the form of a micelle and the interface is represented by a lipid bilayer membrane. Mesoscopic simulations using a dissipative particle dynamics model are performed to examine the impact of micelle's proximity to the membrane on its Brownian motion. Two different sizes are considered, which correspond to ≈ 10 − 20 n m in physical units. The wavelengths typically seen by the largest micelle fall within the range of wavenumbers where the Helfrich model captures fairly well the bilayer mechanical properties. Several independent simulations allowed us to compute the micelle trajectories during an observation time smaller than the diffusive time scale (whose order of magnitude is similar to the membrane relaxation time of the largest wavelengths), this time scale being hardly accessible by experiments. From the probability density function of the micelle normal position with respect to the membrane, it is observed that the position remains close to the starting position during ≈ 0.05 τ d (where τd corresponds to the diffusion time), which allowed us to compare the negative excess of mean-square displacement (MSD) to existing theories. In that time range, the MSD exhibits different behaviors along parallel and perpendicular directions. When the micelle is sufficiently close to the bilayer (its initial distance from the bilayer equals approximately twice its gyration radius), the micelle motion becomes quickly subdiffusive in the normal direction. Moreover, the temporal evolution of the micelle MSD excess in the perpendicular direction follows that of a nanoparticle near an elastic membrane. However, in the parallel direction, the MSD excess is rather similar to that of a nanoparticle near a liquid interface. [ABSTRACT FROM AUTHOR]

Single-file transport occurs in various scientific fields, including diffusion through nanopores, nanofluidic devices, and cellular processes. We here investigate the impact of polydispersity on particle currents for single-file Brownian motion of hard spheres when they are driven through periodic potentials by a constant drag force. Through theoretical analysis and extensive Brownian dynamics simulations, we unveil the behavior of particle currents for random binary mixtures. The particle currents show a recurring pattern in dependence of the hard-sphere diameters and mixing ratio. We explain this recurrent behavior by showing that a basic unit cell exists in the space of the two hard-sphere diameters. Once the behavior of an observable inside the unit cell is determined, it can be inferred for any diameter. The overall variation of particle currents with the mixing ratio and hard-sphere diameters is reflected by their variation in the limit where the system is fully covered by hard spheres. In this limit, the currents can be predicted analytically. Our analysis explains the occurrence of pronounced maxima and minima of the currents by changes in the effective potential barrier for the center-of-mass motion. [ABSTRACT FROM AUTHOR]

We propose a generalization of the stochastic resetting mechanism for a Brownian particle diffusing in a one-dimensional periodic potential: randomly in time, the particle gets reset at the bottom of the potential well it was in. Numerical simulations show that in mirror asymmetric potentials, stochastic resetting rectifies the particle's dynamics, with a maximum drift speed for an optimal average resetting time. Accordingly, an unbiased Brownian tracer diffusing on an asymmetric substrate can rectify its motion by adopting an adaptive stop-and-go strategy. Our proposed ratchet mechanism can model the directed autonomous motion of molecular motors and micro-organisms. [ABSTRACT FROM AUTHOR]

We propose a stochastic Schrödinger equation in which the momentum is coupled to a white Gaussian noise. In the stochastic representation, the kinetic energy representing the self-interaction of momentum is reduced to a linear term of momentum. As such, the quantum evolution operator factorizes into two contributions due to the momentum and the potential, respectively. The exact quantum propagator thereby becomes an expectation of the stochastic one in which the amplitude results from the potential with a fluctuating position: The particle moves with a constant velocity, subjected to a complex Brownian motion. We demonstrate that the stochastic Schrödinger equation can be feasibly used to derive the quantum propagators for the linear potential and the harmonic oscillator system. Novel semiclassical and other approximations may be developed from the new representation of quantum mechanics. [ABSTRACT FROM AUTHOR]

We consider the problem of detecting a shift in the mean of a multivariate time-series process with general marginal distributions and general cross- and auto-correlation structures. We propose a distribution-free monitoring procedure that does not need model fitting or trial-and-error calibration for control limits, which makes the procedure convenient to be implemented when a facility consists of many processes to be monitored. The main idea is to convert each observation vector into a one-dimensional T 2 quantity that captures cross-correlation. The T 2 quantities form a univariate auto-correlated process, and CUSUM statistics are constructed on the T 2 quantities. Then using the fact that the CUSUM statistics on the auto-correlated process behave as a reflected Brownian motion asymptotically under some conditions, the control limits of the CUSUM procedure are analytically determined by setting the first-passage time of the Brownian motion equal to a target in-control average run length. We compare the performance of our procedure with three competing procedures on simulated data with various cross- and auto-correlation and real data from a wafer etching process. The proposed procedure delivers actual in-control average run lengths close to the target and shows comparable or better performance in detecting a shift in mean than the competitors. [ABSTRACT FROM AUTHOR]

This study investigates the intricate interplay among various factors, including melting heat, Brownian motion, activation energy, and thermophoresis in the Maxwell fluid along a stretching sheet. To model these complex phenomena, we have formulated mathematical equations that are subsequently transformed into a set of partial differential equations. Through a similarity renovation, these equations are transformed into ordinary differential equations, and we solve the resulting boundary value problem using numerical techniques, specifically the BVP4C method, known for its fourth-order accuracy. Utilizing the numerical capabilities of BVP4C, we delve into the influence of different parameters, including thermophoresis, melting effect, Brownian motion, and activation energy, on critical flow characteristics. These characteristics encompass the concentration profile and the Sherwood number profile. Our work has been validated against previously published research, showing good matching. The primary objective of this work is to provide plots depicting Nusselt number, skin friction, and Sherwood number profiles for different parameters. This examination aims to shed light on the interconnected effects of these complex phenomena, which have direct relevance across numerous industrial and engineering applications, spanning areas such as metallurgy, nanotechnology, and chemical processing. The primary finding from this research underscores that both the melting heat effect and activation energy contribute to an increase in the concentration profile.

Abstract We record and analyze the movement patterns of the marsupial Didelphis aurita at different temporal scales. Animals trajectories are collected at a daily scale by using spool-and-line techniques and, with the help of radio-tracking devices, animals traveled distances are estimated at intervals of weeks. Small-scale movements are well described by truncated Lévy flight, while large-scale movements produce a distribution of distances which is compatible with a Brownian motion. A model of the movement behavior of these animals, based on a truncated Lévy flight calibrated on the small scale data, converges towards a Brownian behavior after a short time interval of the order of 1 week. These results show that whether Lévy flight or Brownian motion behaviors apply, will depend on the scale of aggregation of the animals paths. In this specific case, as the effect of the rude truncation present in the daily data generates a fast convergence towards Brownian behaviors, Lévy flights become of scarce interest for describing the local dispersion properties of these animals, which result well approximated by a normal diffusion process and not a fast, anomalous one. Interestingly, we are able to describe two movement phases as the consequence of a statistical effect generated by aggregation, without the necessity of introducing ecological constraints or mechanisms operating at different spatio-temporal scales. This result is of general interest, as it can be a key element for describing movement phenomenology at distinct spatio-temporal scales across different taxa and in a variety of systems.

Abstract Phylogenies are viewed as potentially powerful resources to predict missing values in trait datasets, but they are often misused. Critically, many of the imputed values that completely or partially rely on phylogenetic information are trusted without convincingly demonstrating that the data meet the requirements for the predictions to be at least minimally valuable. I discuss that phylogenetic signal, which is the mainstay of phylogenetic imputation, is often interpreted as ‘strong’ because the outcome of randomization tests has prevailed over the actual strength of the signal in determining whether it is strong or not. This circumstance has led many researchers to infer conclusions based on ‘strong’ signals that are actually way more labile than a phylogenetic random walk (i.e. Brownian motion). Although trait evolutionary trajectories that nearly fit Brownian motion are typically considered as strongly conserved, the Brownian process is subject to high levels of stochasticity that may render spurious predictions under some circumstances. To my knowledge, very few studies (if any) that rely on phylogenetically imputed information have rigorously evaluated the expected accuracy of individual predictions, despite among‐lineage variability in prediction accuracy can be dramatic even for strongly conserved traits. Here, I advocate for a Monte‐Carlo approach that is based on trait simulations to assess the prediction accuracy that is expected for each missing value in the traits of interest, which can be continuous or discrete. The framework is presented in a detailed step‐by‐step R tutorial that was conceived for non‐specialized researchers to identify highly likely spurious predictions without the need for advanced technical and statistical skills. Although phylogenetic imputation has important limitations, I suggest that leveraging advances in our understanding of such hindrances and using the technique with caution and restraint will allow trait‐based research to progress further while sampling efforts continue replacing imputed data.

Relativistic ratcheting of Dirac fermions on the surface of topological insulator Bi 2 Se 3 attached to a spiral multiferroic oxide is investigated. We find that the Dirac fermions on the surface of topological insulator Bi 2 Se 3 exhibit pronounced Brownian motion, tuned by the strength of exchange field established by the interaction of spin degrees of Dirac fermions and multiferroic oxide. The surface Dirac fermions show ratchet effect as a net current under the influence of orthogonal, commensurate ac drives in the presence of a symmetric periodic potential set by the exchange field. [ABSTRACT FROM AUTHOR]

A vast array of phenomena, ranging from chemical reactions to phase transformations, are analyzed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used, especially in the presence of large free energy barriers, to estimate free energies using biasing protocols and sampling of transition paths. Kinetic reconstructions of free energy barriers of intermediate height have been performed, with respect to a single order parameter, employing the steady state properties of unconstrained simulation trajectories when barrier crossing is achievable with reasonable computational effort. Considering such cases, we describe a method to estimate free energy surfaces with respect to multiple order parameters from a steady state ensemble of trajectories. The approach applies to cases where the transition rates between pairs of order parameter values considered is not affected by the presence of an absorbing boundary, whereas the macroscopic fluxes and sampling probabilities are. We demonstrate the applicability of our prescription on different test cases of random walkers executing Brownian motion in order parameter space with an underlying (free) energy landscape and discuss strategies to improve numerical estimates of the fluxes and sampling. We next use this approach to reconstruct the free energy surface for supercooled liquid silicon with respect to the degree of crystallinity and density, from unconstrained molecular dynamics simulations, and obtain results quantitatively consistent with earlier results from umbrella sampling. [ABSTRACT FROM AUTHOR]

Understanding the motion of nanoparticles in liquid is of practical importance for drug delivery and fluid flow in nanofluidic systems. In this work, we use a nanoparticle tracking analyzer to investigate the Brownian motion of polydivinylbenzene (PDVB) nanoparticles in water and a video camera to record the aggregation of PDVB aggregates on the water surface. Using water as the liquid medium precludes the possible complex interaction between the liquid medium and the PDVB nanoparticles, which can possibly alter the random characteristics of the motion of the PDVB nanoparticles. The diffusivity of the PDVB nanoparticles determined from the mean square displacements of the PDVB nanoparticles has the same activation energy as that for the intrinsic viscosity of the corresponding aqueous suspension of the PDVB nanoparticles. The correlation between the diffusivity for the motion of the PDVB nanoparticles in water and the intrinsic viscosity of the corresponding aqueous suspension follows the Stokes–Einstein relation. The capillary effect and the interaction between PDVB aggregates and the liquid media enable the aggregation of the PDVB aggregates on the water surface, which follows the first-order reaction with activation energy larger than that for the random motion of the PDVB nanoparticles in water. [ABSTRACT FROM AUTHOR]

This paper is concerned with quantum stochastic differential equations driven by the fermion field in noncommutative space Lp(풞) for 2≤p<∞$$ 2\le p<\infty $$. First, we investigate the existence and uniqueness of Lp$$ {L}&#x0005E;p $$‐solutions of quantum stochastic differential equations in an infinite time horizon by using the noncommutative Burkholder–Gundy inequality given by Pisier and Xu and the noncommutative generalized Minkowski inequality. Then, we investigate the stability, self‐adjointness, and Markov properties of Lp$$ {L}&#x0005E;p $$‐solutions and analyze the error of numerical schemes of quantum stochastic differential equations. The results of this paper can be utilized for investigating the optimal control of quantum stochastic systems with infinite dimensions. [ABSTRACT FROM AUTHOR]

This study aims to obtain the optical soliton solutions of the stochastic perturbed Radhakrishnan–Kundu–Lakshmanan equation which models the optical solitons in optical waveguides such as silica fibers with Kerr law in the presence of chromatic and third-order dispersions by multiplicative white noise in Itô calculus. The study constitutes one of the works aimed at adapting the model in accordance with the importance of the noise effect in nonlinear optics. In the first step, the nonlinear ordinary differential form of the investigated problem has been obtained by using an appropriate complex wave transformation. The enhanced Kudryashov technique, which is the combination of Kudryashov and the new Kudryashov methods, is applied to the nonlinear ordinary differential form. As the result, bright, dark and singular stochastic soliton solutions of the analyzed problem have been carried out by assigning appropriate parameter values and the impact of noise effect on the soliton behavior has been investigated. Lastly, the graphical representations and required comments have been presented in the related sections. [ABSTRACT FROM AUTHOR]

Nanofluids are a relatively new class of materials that have gained attention in recent years due to their unique physical and thermal properties. They are used as contrast agents in biomedicine, including for magnetic resonance imaging (MRI) and computed tomography (CT). Keeping the above applications in mind, this theoretical study intended to explore the consequence of transient magnetized Casson nanoliquid driven by a permeable bi-direction time-dependent stretching platform positioned inclined subject to nonlinear heat source/sink. The Brownian movement, thermophoretic force, chemical reaction, and variable internal heating impacts are incorporated into the proposed flow problem. The leading constitutive PDEs are diminished into coupled nonlinear self-similar dimensionless ODEs through pertinent non-dimensional quantities. The resulting problems are addressed utilizing "Particle Swarm Optimization (PSO)" and a hybrid shooting methodology inspired by the Runge–Kutta four (RK4) method. The novelty of this work is the investigation of the numerical solution of magnetized Casson nanoliquid enclosing thermal radiation and chemical reaction via PSO along with hybrid shooting technique over time-dependent stretching sheet, which has not been elaborated on to date. The physical appearance of relevant physical factors on different flow phenomena are evaluated via graphs. For the stability purpose of the numerical method Average Square Residue Error (ASRE) and Total Average Square Residue Error (TASRE) are computed. For the validation purpose the present work is associated with the available work and great correlation is found. [ABSTRACT FROM AUTHOR]

The role of variable viscosity and variable thermal conductivity in nanofluid flows is significant, as they can strongly influence the flow behavior and heat transfer performance of nanofluids. Keeping in mind the importance of these effects of variable characteristics, our motivation in this study is to investigate the role of nonlinear radiative heat flux on unsteady Casson nanofluid flow across two concentric stretched cylinders in the presence of temperature-dependent viscosity and thermal conductivity. A convective condition on the inner cylinder wall is also considered. In addition, the nanofluid is immersed with microorganisms that can swim and move independently. The addition of microorganisms has a significant role in the stability of the nanofluid flow. The influence of thermophoresis and Brownian motion on the flow, heat, mass, and microorganisms are scrutinized by employing the Buongiorno model. The governing flow equations are converted into a system of differential equations engaging similarity transformations, and the bvp4c method is employed to solve it numerically. Engineering parameters are computed and tabulated numerically. The findings demonstrate that as the unsteadiness parameter upsurges, the radial profile intensifies while the axial profile diminishes near the outer cylinder surface. It is also comprehended that both Lewis and bioconvective Lewis numbers reduce the motile density profiles. The accuracy of the presented model is also given in a graphical illustration by comparing it with a published result in a limiting case. [ABSTRACT FROM AUTHOR]

AbstractThe unsteady simulation of hydromagnetic radiative polar fluid, including thermophoresis, Brownian motion, and higher-order chemical reactions across a perpendicular permeable plate with heat radiation, is performed numerically. The nonlinear PDEs are solved by the explicit finite difference technique and studio developer FORTRAN. The stability and convergence of the present model and a comparison are done to obtain accuracy. The effects of various parameters such as Brownian motion, thermophoresis, radiative heat transfer, and higher-order chemical reactions on the velocity, temperature, and concentration fields are investigated. It is found that the parameters have a significant influence on velocity and temperature profiles, angular velocity, concentration, shear stress, angular momentum density, and Nusselt and Sherwood numbers. In addition, the local share stress rises with the chemical reaction, Eckert number, and thermophoresis, whereas it decreases with the magnetic field and porous medium. In addition, the Nu (local) intensifies with higher order chemical reactions and porous mediums, whereas it falls with Eckert number, Brownian effects, micro-rotation, and thermophoresis. The concentration profile decreases with higher radiation, and the Lewis number whereas it augments with higher radiation. With an Eckert number and thermophoresis, the temperature and velocity increase. Additionally, the higher order of chemical reaction and Brownian motion augment the Sherwood number, whereas the chemical reaction, magnetic field, and porous medium reduce it. Moreover, the study may help to understand the dynamics of flow and heat transfer for the design and optimization of various engineering applications such as heat exchangers, pollutant dispersion models, energy systems, biomedical, and so on. [ABSTRACT FROM AUTHOR]

We study Brownian motion on the space of distinct landmarks in Rd$\mathbb {R}^d$, considered as a homogeneous space with a Riemannian metric inherited from a right‐invariant metric on the diffeomorphism group. As of yet, there is no proof of long‐time existence of this process, despite its fundamental importance in statistical shape analysis, where it is used to model stochastic shape evolutions. We make some first progress in this direction by providing a full classification of long‐time existence for configurations of exactly two landmarks, governed by a radial kernel. For low‐order Sobolev kernels, we show that the landmarks collide with positive probability in finite time, whilst for higher‐order Sobolev and Gaussian kernels, the landmark Brownian motion exists for all times. We illustrate our theoretical results by numerical simulations. [ABSTRACT FROM AUTHOR]

In recent scenario world is facing the problem of energy consumption. Researchers are keen on developing less energy consuming devices; in this regard, heat transfer using nanofluid has got the attention of current researchers for application in heat exchangers. In present study, an experiment was performed on double pipe heat exchanger using CuO-water nanofluids and sodium lauryl sulphate as the surfactant to examine the thermal performance factor (TPF) and pressure drop. The studies were conducted for a single phase fully developed flow with volume fractions of 0.005%, 0.02%, 0.04%, and 0.07% in the turbulent range between Reynolds numbers 5500 and 15,000. Along with thermal conductivity, Brownian motion and thickness of interfacial layer are also responsible for heat transfer enhancement in heat exchangers. For a volume fraction of 0.07% at Reynolds number 5500, the maximum enhancement in Nusselt number was observed 67.9% with the penalty of 189.47% increase in friction factor. The highest TPF recorded during the experiment is 1.18 for a volume fraction of 0.07% at 5500 Reynolds number. In present study a novel correlation was also developed for Nusselt number and friction factor. For better understanding the characterization of CuO nanoparticle, XRD, FeSEM, and EDS testing were conducted in the laboratory. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has caused severe global disasters, highlighting the importance of understanding the details and trends of epidemic transmission in order to introduce efficient intervention measures. While the widely used deterministic compartmental models have qualitatively presented continuous "analytical" insight and captured some transmission features, their treatment usually lacks spatiotemporal variation. Here, we propose a stochastic individual dynamical (SID) model to mimic the random and heterogeneous nature of epidemic propagation. The SID model provides a unifying framework for representing the spatiotemporal variations of epidemic development by tracking the movements of each individual. Using this model, we reproduce the infection curves for COVID-19 cases in different areas globally and find the local dynamics and heterogeneity at the individual level that affect the disease outbreak. The macroscopic trend of virus spreading is clearly illustrated from the microscopic perspective, enabling a quantitative assessment of different interventions. Seemingly, this model is also applicable to studying stochastic processes at the "meter scale", e.g., human society's collective dynamics. [ABSTRACT FROM AUTHOR]

The aim of the paper is to construct an analog of local time for the standard Wiener process multiplied by complex constant. [ABSTRACT FROM AUTHOR]

Brownian motion with linear drift on positive half-line and killed elastically at zero is considered. A goal is to get a result that allows us to calculate the distributions of integral functionals with respect to spatial variable of local time of such a process. The explicit form of the distribution of the supremum with respect to spatial variable of local time is calculated for Brownian motion with linear drift reflecting at zero. [ABSTRACT FROM AUTHOR]

Numerous systems and phenomena that appear to fluctuate randomly are mathematically modeled using stochastic processes. In this paper stochastic Phi-4 equation is considered with the multiplicative Wiener process that represents the temporal change of fluctuations. In particle and nuclear physics, the stochastic Phi-4 equation appears to be crucial. Stochastic phenomena represent the microscopic randomness of the nuclear particle. The extended sinh-Gordon expansion approach is used to study the stochastic model in terms of Itô formulation. With the use of this method, variety of solutions from important physical prospectives, such as dark, bright, singular, and periodic solitons has been examined, Furthermore, based on the Itô, the impact of the noise term on Brownian motion is examined. Both 2D and 3D graphs are used to show the impact of the noise term on the obtained soliton solutions. The computations and outcomes demonstrate the method's importance, precision, and effectiveness. Numerous robust nonlinear stochastic differential equations from mathematics, physics, and other relevant domains can be resolved using this method. [ABSTRACT FROM AUTHOR]

In this paper, we mainly explore the averaging principle of Caputo-type fractional delay stochastic differential equations with Brownian motion. Firstly, the solutions of this considered system are derived with the aid of the Picard iteration technique along with the Laplace transformation and its inverse. Secondly, we obtain the unique result by using the contradiction method. In addition, the averaging principle is discussed by means of the Burkholder-Davis-Gundy inequality, Jensen inequality, Hölder inequality and Grönwall-Bellman inequality under some hypotheses. Finally, an example with numerical simulations is carried out to prove the relevant theories. [ABSTRACT FROM AUTHOR]

In the general setting of long‐memory multivariate time series, the long‐memory characteristics are defined by two components. The long‐memory parameters describe the autocorrelation of each time series. And the long‐run covariance measures the coupling between time series, with general phase parameters. It is of interest to estimate the long‐memory, long‐run covariance and general phase parameters of time series generated by this wide class of models although they are not necessarily Gaussian nor stationary. This estimation is thus not directly possible using real wavelets decomposition or Fourier analysis. Our purpose is to define an inference approach based on a representation using quasi‐analytic wavelets. We first show that the covariance of the wavelet coefficients provides an adequate estimator of the covariance structure including the phase term. Consistent estimators based on a local Whittle approximation are then proposed. Simulations highlight a satisfactory behavior of the estimation on finite samples on multivariate fractional Brownian motions. An application on a real neuroscience dataset is presented, where long‐memory and brain connectivity are inferred. [ABSTRACT FROM AUTHOR]

In this paper, a class of second-order neutral impulsive stochastic evolution equations with infinite delay driven by fractional Brownian motion and Poisson jumps is considered. We utilise the Carathéodory approximation technique, the Burkhölder–Davies–Gundy inequality and the Gronwall inequality to present the existence and uniqueness of mild solutions for the addressed system under Carathéodory conditions. Furthermore, we derive an averaging principle for the proposed system which is approximated by the simplified equation in the sense of mean square. Finally, an application is used to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

We consider the optimal risk transfer from an insurance company to a reinsurer. The problem formulation considered in this paper is closely connected to the optimal portfolio problem in finance, with some crucial distinctions. In particular, the insurance company's surplus is here (as is routinely the case) approximated by a Brownian motion, as opposed to the geometric Brownian motion used to model assets in finance. Furthermore, risk exposure is dialled 'down' via reinsurance, rather than 'up' via risky investments. This leads to interesting qualitative differences in the optimal designs. In this paper, using the martingale method, we derive the optimal design as a function of proportional, non-cheap reinsurance design that maximises the quadratic utility of the terminal value of the insurance surplus. We also consider several realistic constraints on the terminal value: a strict lower boundary, the probability (Value at Risk) constraint, and the expected shortfall (conditional Value at Risk) constraints under the $ \mathbb {P} $ P and $ \mathbb {Q} $ Q measures, respectively. In all cases, the optimal reinsurance designs boil down to a combination of proportional protection and option-like protection (stop-loss) of the residual proportion with various deductibles. Proportions and deductibles are set such that the initial capital is fully allocated. Comparison of the optimal designs with the optimal portfolios in finance is particularly interesting. Results are illustrated. [ABSTRACT FROM AUTHOR]

The purpose of the current study is to evaluate the mass and energy transmission of a blood-based Casson Ferrofluid flow across a stretching cylinder. The consequences of the Casson parameter, cylinder curvature, thermal radiation, chemical reaction, and non-Newtonian viscous dissipation are also considered. The nanofluid flow phenomena are mathematically designed in the form of a system of nonlinear PDEs which are degraded and non-dimensionalized to the set of ODEs by using suitable similarity transformations. The homotopy analysis method has been applied to find out a semi-analytical solution for the nonlinear set of ODEs. The significance and physical behavior of flow parameters are graphically characterized versus the velocity, energy, and mass profiles. The numerical outcomes for Sherwood number, drag force and Nusselt number are also presented through Tables. A comparative evaluation has been done for validation purposes to authorize and justify the present results. From the tabular and graphical results, it has been noticed that the velocity profile lowers while the energy profile develops versus the variation of magnetic factor. The impact of curvature factor boosts the velocity and mass transfer rate of the Casson nanofluid while reducing the temperature curve. Furthermore, the consequences of the thermophoresis effect raise the temperature profile of the Casson Ferrofluid flow. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic SIS epidemic infectious diseases model with double stochastic perturbations is proposed. First, the existence and uniqueness of the positive global solution of the model are proved. Second, the controlling conditions for the extinction and persistence of the disease are obtained. Besides, the effects of the intensity of volatility ξ 1 and the speed of reversion 1 on the dynamical behaviors of the model are discussed. Finally, some numerical examples are given to support the theoretical results. The results show that if the basic reproduction number ℛ 0 s < 1 , the disease will be extinct, that is to say that we can control the threshold ℛ 0 s to suppress the disease outbreak. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of stability of linear time-varying stochastic perturbed systems. We present sufficient conditions ensuring the global practical uniform exponential stability of a different class of stochastic perturbed systems based on generalized integral inequalities of Gronwall type. Finally, we provide numerical examples to prove the usefulness of the main results of this paper. [ABSTRACT FROM AUTHOR]

The origin of fast radio bursts (FRBs), the brightest cosmic explosion in radio bands, remains unknown. We introduce here a novel method for a comprehensive analysis of active FRBs' behaviors in the time-energy domain. Using "Pincus Index" and "Maximum Lyapunov Exponent", we were able to quantify the randomness and chaoticity, respectively, of the bursting events and put FRBs in the context of common transient physical phenomena, such as pulsar, earthquakes, and solar flares. In the bivariate time-energy domain, repeated FRB bursts' behaviors deviate significantly (more random, less chaotic) from pulsars, earthquakes, and solar flares. The waiting times between FRB bursts and the corresponding energy changes exhibit no correlation and remain unpredictable, suggesting that the emission of FRBs does not exhibit the time and energy clustering observed in seismic events. The pronounced stochasticity may arise from a singular source with high entropy or the combination of diverse emission mechanisms/sites. Consequently, our methodology serves as a pragmatic tool for illustrating the congruities and distinctions among diverse physical processes. [ABSTRACT FROM AUTHOR]

The thermal radiation and Fourier flux have drawn the attention of scientists and experts due to their extensive applications in the fields of medicine, manufacturing modern airplanes, water distillation, more efficient electronic devices, more efficient batteries, radiating treatment, and the textile industry. Through careful consideration of this, the mathematical investigation of natural convection and Fourier flux on the flow of energy and diffusion transmission of a body of cone and cylinder revolution, located in a saturated medium, has been described for the dual situations (flow over a cone and a cylinder). After then, the Runge–Kutta technique was used to explain the leading mechanism. Possessions of governing physical measures of local Nusselt and Sherwood numbers as well as velocity, thermal and diffusion figures are provided with support of tables and diagrams. It is motivating to declare that mass transfer rate is advanced in cone kind of revolution matched to cylinder kind of revolution with rising N R , N t , Q S . Also, the heat transmission rate is upper in cylinder revolution equated to cone revolution. [ABSTRACT FROM AUTHOR]

This work is about the investigation of the flow of a micropolar nanoliquid over a stretching surface, taking into account the effects of thermal radiation, thermophoresis, and Brownian motion. The study focuses on the impact of these factors on heat and mass transfer rates, with the assumption that the Newtonian heat impact dominates. The homotropy approach is used to generate non-dimensional transformational parameters, which are then used to create a system of nonlinear differential equations. The study includes charts and tables that define transfer rates based on various parameters, and the results suggest that increased radiance levels and Nb parameters lead to improvements in heat and mass convection. The graphics used in the study are accurate and consistent with previous research in the field. Overall, this research provides insights into the complex dynamics of micropolar nanoliquid flow and the factors that impact heat and mass transfer in this system. [ABSTRACT FROM AUTHOR]

Compartmental models that describe infectious disease transmission across subpopulations are central for assessing the impact of non-pharmaceutical interventions, behavioral changes and seasonal effects on the spread of respiratory infections. We present a Bayesian workflow for such models, including four features: (1) an adjustment for incomplete case ascertainment, (2) an adequate sampling distribution of laboratory-confirmed cases, (3) a flexible, time-varying transmission rate, and (4) a stratification by age group. Within the workflow, we benchmarked the performance of various implementations of two of these features (2 and 3). For the second feature, we used SARS-CoV-2 data from the canton of Geneva (Switzerland) and found that a quasi-Poisson distribution is the most suitable sampling distribution for describing the overdispersion in the observed laboratory-confirmed cases. For the third feature, we implemented three methods: Brownian motion, B-splines, and approximate Gaussian processes (aGP). We compared their performance in terms of the number of effective samples per second, and the error and sharpness in estimating the time-varying transmission rate over a selection of ordinary differential equation solvers and tuning parameters, using simulated seroprevalence and laboratory-confirmed case data. Even though all methods could recover the time-varying dynamics in the transmission rate accurately, we found that B-splines perform up to four and ten times faster than Brownian motion and aGPs, respectively. We validated the B-spline model with simulated age-stratified data. We applied this model to 2020 laboratory-confirmed SARS-CoV-2 cases and two seroprevalence studies from the canton of Geneva. This resulted in detailed estimates of the transmission rate over time and the case ascertainment. Our results illustrate the potential of the presented workflow including stratified transmission to estimate age-specific epidemiological parameters. The workflow is freely available in the R package HETTMO, and can be easily adapted and applied to other infectious diseases. Author summary: Mathematical models are a central tool for understanding the spread of infectious diseases. These models can frequently be fitted to surveillance data such as the number of laboratory-confirmed cases and seroprevalence over time. We identified that in these situations, four crucial features are required for a model to provide insightful information for managing an epidemic. These features relate to the adjustment for incomplete case ascertainment, to the choice of sampling distribution, to the variation of transmission over time and to the stratification by age. For each feature, we identify and compare several implementation options on simulated data. This structural comparison of methods results in a Bayesian workflow that is optimized for modeling the transmission of SARS-CoV-2 over a short period. We highlight the advantages and limitations of our approach in a real situation, using real-world SARS-CoV-2 data from the canton of Geneva. In addition to providing validated solutions to important technical points, such a comprehensive workflow helps to improve the reliability and the transparency of epidemic models. [ABSTRACT FROM AUTHOR]

In recent years, nanotechnological research has introduced hybrid nanofluids, which are advanced fluids with augmented thermal properties that give better results than regular nanofluids. The thermal transfer characteristics of the Falkner-Skan flow of MgO-MoS2/Engine oil hybrid nanofluid induced by a wedge surface with thermophoresis and Brownian motion are numerically investigated. The main objective of this research is to examine the augmented thermal transport behavior of Casson and Carreau hybrid nanofluids. The equations that arise are solved by adopting the bvp5c scheme in MATLAB software. Plots and numerical values illustrate the stimulus of various pertinent parameters on the flow-determining factors such as velocity, thermal and concentration fields, wall friction, energy, and mass transports. The rate of energy transport in the Carreau hybrid nanofluid is significantly larger than that of the Casson hybrid nanofluid. The implication of 5% volume of MgO-MoS2 nanoparticles enhances the rate of thermal transport by 53% in the Carreau fluid and 47% in the Casson fluid, respectively. This research holds potential for applications in geothermal energy systems. [ABSTRACT FROM AUTHOR]

Intrinsically disordered regions (IDRs) are segments of proteins without stable three-dimensional structures. As this flexibility allows them to interact with diverse binding partners, IDRs play key roles in cell signaling and gene expression. Despite the prevalence and importance of IDRs in eukaryotic proteomes and various biological processes, associating them with specific molecular functions remains a significant challenge due to their high rates of sequence evolution. However, by comparing the observed values of various IDR-associated properties against those generated under a simulated model of evolution, a recent study found most IDRs across the entire yeast proteome contain conserved features. Furthermore, it showed clusters of IDRs with common "evolutionary signatures," i.e. patterns of conserved features, were associated with specific biological functions. To determine if similar patterns of conservation are found in the IDRs of other systems, in this work we applied a series of phylogenetic models to over 7,500 orthologous IDRs identified in the Drosophila genome to dissect the forces driving their evolution. By comparing models of constrained and unconstrained continuous trait evolution using the Brownian motion and Ornstein-Uhlenbeck models, respectively, we identified signals of widespread constraint, indicating conservation of distributed features is mechanism of IDR evolution common to multiple biological systems. In contrast to the previous study in yeast, however, we observed limited evidence of IDR clusters with specific biological functions, which suggests a more complex relationship between evolutionary constraints and function in the IDRs of multicellular organisms. Author summary: Proteins are the molecular machines that carry out many processes required for life at an atomic level. Though many proteins use fixed structures to perform their functions, proteins with flexible segments are widespread, especially in multicellular organisms. Furthermore, these intrinsically disordered regions (IDRs) are often involved in essential cellular functions. However, the sequences of IDRs evolve quickly, which challenges traditional bioinformatics methods that depend on sequence conservation to predict function. Several studies have demonstrated that distributed biophysical features of IDRs are constrained rather than their exact sequences, and a recent study in yeast found that IDRs with common patterns of conserved features were associated with specific functions. Therefore, in this work we ask if IDRs in fruit flies, another common laboratory organism, also have patterns of conservation with associated functions. We build on the previous study by integrating their approach into a fully statistical framework based on mathematical models of trait evolution. Though we identify widespread signals of conservation in the IDRs of fruit flies, we find less evidence of a simple relationship between features and function. These methods and results will provide a valuable resource that can guide future experimental analyses of IDRs in fruit flies and other organisms. [ABSTRACT FROM AUTHOR]

This manuscript focuses on a class of stochastic functional differential equations driven by time-changed Brownian motion. By utilizing the Lyapunov method, we capture some sufficient conditions to ensure that the solution for the considered equation is η-stable in the pth moment sense. Subsequently, we present some new criteria of the η-stability in mean square by using time-changed Itô formula and proof by contradiction. Finally, we provide some examples to demonstrate the effectiveness of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we examine the Carreau nanofluid flow past a nonlinearly stretchable surface accompanied by chemical reactions, thermal slip parameter and thermal radiation. A two-phase nanofluid criterion is considered to examine the behavior of flowing fluid and temperature profile. We used the similarity transition to change the basic equations into the set of ordinary differential equations in order to obtain the results. Shooting criteria are applied to calculate the solution of momentum, energy, and concentration fields using MATLAB. The effects of physical entities on the velocity, concentration, and temperature fields are analyzed by numeric tabular data. Furthermore, it is analyzed that the temperature field and concentration profile are diminished while velocity and thermal slip parameters are increased. The increasing nature of Brownian movement N b corresponds to a lower nanoparticle profile concentration is observed. The temperature profile is a growing function of magnetic parameter. As the Eckert number rises, so does the thermal pattern. [ABSTRACT FROM AUTHOR]

In this paper, the importance of mass and heat transfer characteristics of mixed convective conditions on nonlinear free convection flow embedded with non-Fourier flux and thermal radiation is numerically investigated. A partial Casson slip and mixed impact of thermophoresis and Brownian motion is considered at the elastic surface. To change the highly nonlinear partial differential equations into ordinary differential system, we used the similarity transformations and then the shooting method is employed to solve resulting equations. The significance of various physical parameters on the velocity, concentration and temperature profiles are investigated for both negative value of ferromagnetic interaction ( β 1 = − 0. 2) and positive value of ferromagnetic interaction ( β 1 = 0. 2). The governing physical aspects of coefficient of skin friction, the Sherwood and Nusselt numbers are obtained for various embedded parameters. Our findings concluded that the ferromagnetic interaction is positive and then more mass transfer rate is identified compared to the negative value of ferromagnetic interaction, but whereas in friction and heat transfer rate, it was completely mixed sense (i.e., different effects have different results). Brownian motion has less Nusselt number values in positive ferromagnetism compared to negative ferromagnetism and quite opposite behavior is observed in the presence of thermophoresis, this happened due to nonlinear flux and buoyancy. [ABSTRACT FROM AUTHOR]

Improvement of efficiency in drug release is of profound importance in biomedical engineering. The drift and diffusion of Brownian particles in a flexible and porous medium is a typical model for describing the directional drug release system. The tilted periodic potential, usually referred to as the washboard potential (WBP), is a well-known model for describing the motion of Brownian particles in a complex medium. Considering that the drug cargo, such as hydrogel, is flexible and thermally fluctuating, a soft matter potential (SMP), which allows Brownian particles to actively modify the structure of the soft medium, is proposed to describe the polymer networks. The giant acceleration of diffusion (GAD) and the thermodynamic uncertainty relation (TUR) of Brownian particles are investigated in the SMP and WBP, and it is found that the SMP leads to lower GAD and energy cost ⟨ q ⟩ for a given precision A of drug directional transport. Furthermore, the results indicate that a more deformable drug cargo can achieve a higher directional transport efficiency, that is, a lower Q = ⟨ q ⟩ / A. This is potentially applicable to improve the efficiency of controlled directional drug release. [ABSTRACT FROM AUTHOR]

This paper studies the optimal reinsurance and investment problem with multiple risky assets and correlation risk. The claim process is described by a Brownian motion with drift. The insurer is allowed to invest in a risk-free asset and multiple risky assets and the instantaneous return rate of each risky asset follows the Ornstein-Uhlenbeck (O-U) model. Moreover, the correlation between risk model and the risky assets' price is taken into account. We first consider the optimal investment problem for the insurer. Subsequently, we assume that the insurer can purchase proportional reinsurance and invest in the financial market. In both cases, the insurer's objective is to maximize the expected exponential utility of the terminal wealth. By applying stochastic control approach, we derive the optimal reinsurance and investment strategies and the corresponding value functions explicitly. Finally, numerical simulations are presented to illustrate the effects of model parameters on the optimal reinsurance and investment strategies. [ABSTRACT FROM AUTHOR]