Brownian Motion - Science topic

The current investigation considers the unsteady two-dimensional MHD flow along with heat and mass transfer of Williamson nanofluid over a moving cylinder of a porous medium. The influence of chemical reactions, thermal radiation, and Joule heating are also considered. This article will use the Buongiorno model to explore the Brownian motion heat t...

In this paper, the natural convection of a complex fluid that contains both nanoparticles and gyrotactic microorganisms in a heated square cavity is considered. The Buongiorno model is applied to describe the nanofluid behaviors. Both the top and bottom horizontal walls of the cavity are adiabatic, and there is a temperature difference between the...

In this study, natural convection heat transfer of a water based nanofluid inside a square cavity is numerically investigated for two different orientations of a wall-heated cavity. The enclosure is heated by applying a constant heat flux while cooled at ambient conditions. Lattice Boltzmann method (LBM) is used to simulate nanofluid natural convec...

Microplastics (MPs) and nanoplastics (NPs) are ubiquitous and intractable in urban waters. Compared with MPs, the smaller NPs have shown distinct physicochemical features, such as Brownian motion, higher specific surface area, and stronger interaction with other pollutants. Therefore, the qualitative and quantitative analysis of NPs is more challen...

In current analysis, A numerical approach for magnetohydrodynamics Stagnation point flow of Micropolar fluid due to a vertical stretching Surface is reported. The impact of buoyancy forces is considered. In additions the effects of the thermal radiation and thermal conductivity with non-zero mass flux have been analyzed. we implement the dimensionl...

The addition of gyrotactic microbes in the nanoparticles is essential to embellish the thermal efficiency of many systems such as microbial fuel cells, bacteria-powered micro-mixers, micro-volumes like microfluidics devices, enzyme biosensor, and chip-shaped microdevices like bio-microsystems. This analysis investigates the second law analysis in t...

Dissipation of quantum vortex motion is fundamental to superfluid dynamics and quantum turbulence, yet there is currently a large gap between theory and experiments with ultracold atoms. Here we present a microscopic open quantum systems theory of thermally damped vortex motion in oblate atomic superfluids that includes previously neglected energy-...

In this paper, we consider three models of non-linear Schrödinger’s equations (NLSEs) via It\^{o} sense. Specifically, we study these equations forced by multiplicative noise via the Brownian motion process. There are numerous approaches for converting non-linear partial differential equations (NPDEs) into ordinary differential equations (ODEs) to...

We model a quantum system coupled to an environment of damped harmonic oscillators by following the approach of Caldeira-Leggett and adopting the Caldirola-Kanai Lagrangian for the bath oscillators. In deriving the master equation of the quantum system of interest (a particle in a general potential), we show that the potential is modified non-trivi...

Monte Carlo (MC) simulations are widely used in financial risk management, from estimating value-at-risk (VaR) to pricing over-the-counter derivatives. However, they come at a significant computational cost due to the number of scenarios required for convergence. Quantum MC (QMC) algorithms are a promising alternative: they provide a quadratic spee...

The Pearson family of ergodic diffusions with a quadratic diffusion coefficient and a linear force are characterized by explicit dynamics of their integer moments and by explicit relaxation spectral properties towards their steady state. Besides the Ornstein-Uhlenbeck process with a Gaussian steady state, the other representative examples of the Pe...

A framework to study the eigenvalue probability density function for products of unitary random matrices with an invariance property is developed. This involves isolating a class of invariant unitary matrices, to be referred to as cyclic Pólya ensembles, and examining their properties with respect to the spherical transform on U(N)\documentclass[12...

Many composite manufacturing processes employ the consolidation of pre-impregnated preforms. However, in order to obtain adequate performance of the formed part, intimate contact and molecular diffusion across the different composites’ preform layers must be ensured. The latter takes place as soon as the intimate contact occurs and the temperature...

In engineering and manufacturing industries, stretching flow phenomena have numerous real-world implementations. Real-world applications related to stretched flow models are metalworking, crystal growth processes, cooling of fibers, and plastics sheets . Therefore, in this work, the mechanical characteristics of the magnetohydrodynamics of the non-...

In various polymeric/molecular glass-formers, crossover from a non-Gaussian to Gaussian subdiffusion has been observed ubiquitously. We have developed a framework which generalizes the fractional Brownian motion (fBm) model to incorporate non-Gaussian features by introducing a jump kernel. We illustrate that the non-Gaussian fBm (nGfBm) model accur...

The generalized inverse Gaussian-Poisson (GIGP) distribution proposed by Sichel in the 1970s has proved to be a flexible fitting tool for diverse frequency data, collectively described using the item production model. In this paper, we identify the limit shape (specified as an incomplete gamma function) of the properly scaled diagrammatic represent...

Stochastic processes play a fundamental role in physics, mathematics, engineering and finance. One potential application of quantum computation is to better approximate properties of stochastic processes. For example, quantum algorithms for Monte Carlo estimation combine a quantum simulation of a stochastic process with amplitude estimation to impr...

This work focuses on the slow-fast system perturbed by the mixed fractional Brownian motion with Hurst parameter H\in(1/2,1). The integral with respect to fractional Brownian motion is the generalized Riemann-Stieltjes integral and the integral with respect to Brownian motion is standard Ito integral. We establish large deviation principles with a...

In this note we deduce well known modular identities for Jacobi theta functions using the spectral representations associated with the real valued Brownian motion taking values on $[-1,+1]$. We consider two cases: (i) reflection at $-1$ and $+1$, (ii) killing at $-1$ and $+1$. It is seen that these two representations give, in a sense, most compact...

In this study we analyzed the flow, heat and mass transfer behavior of Casson nanofluid past an exponentially stretching surface under the impact of activation energy, Hall current, thermal radiation, heat source/sink, Brownian motion and thermophoresis. Transverse magnetic field with the assumption of small Reynolds number is implemented verticall...

We study a particle system without branching but with selection at timepoints depending on a given probability distribution on the positive real line. The hydrodynamic limit of the particle system is identified as the distribution of a Brownian motion conditioned to not having passed the solution of the so-called inverse first-passage time problem....

Wavelet-type random series representations of the well-known Fractional Brownian Motion (FBM) and many other related stochastic processes and fields have started to be introduced since more than two decades. Such representations provide natural frameworks for approximating almost surely and uniformly rough sample paths at different scales and for s...

The stochastic shallow water wave equation (SSWWE) in the sense of the beta-derivative is considered in this study. The solutions of the SSWWE are obtained using the F-expansion technique with the Riccati equation and He’s semi-inverse method. Since the shallow water equation has many uses in ocean engineering, including river irrigation flows, tid...

In the last decades, the production of fuel ethanol from corn has spread as a valid renewable alternative to pursue sustainability goals. However the uncertain nature of both input (corn) and output (gasoline) prices, together with price dependent operational decisions, combine to make this difficult plant valuation require a real options approach....

Motivated from the increasing need to develop a science-based, predictive understanding of the dynamics and response of cities when subjected to natural hazards, in this paper, we apply concepts from statistical mechanics and microrheology to develop mechanical analogues for cities with predictive capabilities. We envision a city to be a matrix whe...

It is known that obstacles can hydrodynamically trap bacteria and synthetic microswimmers in orbits, where the trapping time heavily depends on the swimmer flow field and noise is needed to escape the trap. Here, we use experiments and simulations to investigate the trapping of microrollers by obstacles. Microrollers are rotating particles close to...

We define multifractional Hermite processes which generalize and extend both multifractional Brownian motion and Hermite processes. It is done by substituting the Hurst parameter in the definition of Hermite processes as a multiple Wiener-It\^o integral by a Hurst function. Then, we study the pointwise regularity of these processes, their local asy...

In this paper we aim at generalizing the results of A. K. Zvonkin (That removes the drift, 22, 129, 41) and A. Y. Veretennikov (Theory Probab. Appl., 24, 354, 39) on the construction of unique strong solutions of stochastic differential equations with singular drift vector field and additive noise in the Euclidean space to the case of infinite-dime...

In this work we study the self-integral of a function-measure kernel and its importance on stochastic integration. A continuous-function measure kernel $K$ over $D \subset \mathbb{R}^{d}$ is a function of two variables which acts as a continuous function in the first variable and as a real Radon measure in the second. Some analytical properties of...

We propose both a probabilistic fractal model and fractal dimension estimator for multi-spectral images. The model is based on the widely known fractional Brownian motion fractal model, which is extended to the case of images with multiple spectral bands. The model is validated mathematically under the assumption of statistical independence of the...

We investigate the evolution dynamics of inhomogeneous discrete-time one-dimensional quantum walks displaying long-range correlations in both space and time. The associated quantum coin operators are built to exhibit a random inhomogeneity distribution of long-range correlations embedded in the time evolution protocol through a fractional Brownian...

We consider a model of Non-Brownian self-propelled particles with anti-alignment interactions where particles try to avoid each other by attempting to turn into opposite directions. The particles undergo apparent Brownian motion, even though the particle's equations are fully deterministic. We show that the deterministic interactions lead to intern...

Ring, or cyclic, polymers have unique properties compared to linear polymers, due to their topologically closed structure that has no beginning or end. Experimental measurements on the conformation and diffusion of molecular ring polymers simultaneously are challenging due to their inherently small size. Here, we study an experimental model system...

Complexity, defined as the number of parts and their degree of differentiation, is a poorly explored aspect of macroevolutionary dynamics. The maximum anatomical complexity of organisms has undoubtedly increased through evolutionary time. However, it is unclear whether this increase is a purely diffusive process or whether it is at least partly dri...

We perform extensive simulations and systematic statistical analyses of the structural dynamics of amorphous silicon. The simulations follow the dynamics introduced by Wooten, Winer and Weaire: the energy is obtained with the Keating potential, and the dynamics consists of bond transpositions proposed at random locations and accepted with the Metro...

Let F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {F}}$$\end{document} be a holomorphic foliation on a compact Kähler surface with hyperbolic singularities...

We propose a virtual bidding strategy by modeling the price differences between the day-ahead market and the real-time market as Brownian motion with drift, where the drift rate and volatility are functions of meteorological variables. We then transform the virtual bidding problem into a mean-variance portfolio management problem, where we approach...

In this paper we give easy-to-implement closed expressions for European and Asian Greeks for general L^{2}-payoff functions and underlying assets in an exponential Lévy process model with nonvanishing Brownian motion part. The results are based on Hilbert space valued Malliavin Calculus and extend previous results from the literature. Numerical exp...

The paper shows that the distribution of the normalized least squares estimator of the drift parameter in the fractional Ornstein-Uhlenbeck process observed over [0, T] converges to the standard normal distribution with an uniform optimal error bound of the order O(T −1/2) for 0.5 ≤ H ≤ 0.63 and of the order O(T4H-3) for 0.63 < H < 0.75 where H is...

The Nano non-Newtonian Reiner-Philippoff model is examined via the local non-similarity method. The local non-similarity method is applied to transform the governing equation of fluid flow. The transformed equations are solved by utilising the MATLAB bvp4c solver. The Reiner-Philippoff model behaviour of shear-thinning, Newtonian, and shear-thicken...

We propose a generalization of the widely used fractional Brownian motion (FBM), memory-multi-FBM (MMFBM), to describe viscoelastic or persistent anomalous diffusion with time-dependent memory exponent $\alpha(t)$ in a changing environment. In MMFBM the built-in, long-range memory is continuously modulated by $\alpha(t)$. We derive the essential st...

The enriched thermal mechanisms and progressive of nanomaterial has enthused scientists to give devotion to this area in current days. The versatile and synthesizing utilization of such particles embrace energy production, solar systems, heating and cooling monitoring processes, renewable energy systems, cancer treatments, hybrid-powered motors and...

Nanotechnology applications have occupied a wide range in engineering applications and achieved distinctive performance due to their potential as a working fluid instead of conventional liquids due to their outstanding performance. Sustaining stable performance nanofluids for a longer time retaining their properties without clustering and nanoparti...

The current communication, manifest mathematical modelling and numerical computations of Sutterby nanofluids with radiant heat assessment subject to heat generation/absorption. The thermophoresis and Brownian motion effects are incorporated via the Buongiorno model in flow governing equations. Moreover, the present analysis reveals the impacts of t...

This study aims to investigate the magnetohydrodynamic flow induced by a moving surface in a nanofluid and the occurrence of suction and solar radiation effects using the Buongiorno model. The numerical findings are obtained using MATLAB software. The effects of various governing parameters on the rates of heat and mass transfer along with the nano...

Fluid flow through a porous media has many industrial applications such as water flowing through rocks and soil and purification of gas and oil mixed in rocks. Also, heat transfer enhancement has been introduced in various thermal and mechanical systems by improving the thermal conductance of base fluids. In this article, the flow of an electricall...

In this paper we solve a L\'evy driven linear stochastic first order partial differential equation (transport equation) understood in the canonical (Marcus) form. The solution can be obtained with the help of the method of stochastic characteristics. It has the same form as a solution of a deterministic PDE or a solution of a stochastic PDE driven...

In this analysis, the generalized Fourier and Fick's law for Second-grade fluid flow at a slendering vertical Riga sheet is examined along with thermophoresis and Brownian motion effects. Boundary layer approximations in terms of PDE's (Partial Differential Equations) are used to build the mathematical model. An appropriate transformation has been...

The artificial intelligence based neural networking with Back Propagated Levenberg-Marquardt method (NN-BPLMM) is developed to explore the modeling of double‐diffusive free convection nanofluid flow considering suction/injection, Brownian motion and thermophoresis effects past an inclined permeable sheet implanted in a porous medium. By applying su...

This study proposes a modified Geometric Brownian motion (GBM), to simulate stock price paths under normal and convoluted distributional assumptions. This study utilised four selected continuous probability distributions for the convolution because of shared properties, including normality, and parameters that have a standard distribution with a lo...

A bstract Popular comparative phylogenetic models such as Brownian Motion, Ornstein-Ulhenbeck, and their extensions, assume that, at speciation, a trait value is inherited identically by the two descendant species. This assumption contrasts with models of speciation at the micro-evolutionary scale where phenotypic distributions of the descendants a...

For the stochastic heat equation with multiplicative noise we consider the problem of estimating the diffusivity parameter in front of the Laplace operator. Based on local observations in space, we first study an estimator that was derived for additive noise. A stable central limit theorem shows that this estimator is consistent and asymptotically...

The general problem of tracer diffusion in non-equilibrium baths is important in a wide range of systems, from the cellular level to geographical lengthscales. In this paper, we revisit the archetypical example of such a system: a collection of small passive particles immersed in a dilute suspension of non-interacting dipolar microswimmers, represe...

The physiological systems and biological applications that have arisen during the past 15 years depend heavily on the microscale and nanoscale fluxes. Microchannels have been utilized to develop new diagnostic assays, examine cell adhesion and molecular transport, and replicate the fluid flow microenvironment of the circulatory system. The various use...

Non-ergodicity of neuronal dynamics from rapid ion channel gating through the membrane induces membrane displacement statistics that deviate from Brownian motion. The membrane dynamics from ion channel gating were imaged by phase-sensitive optical coherence microscopy. The distribution of optical displacements of the neuronal membrane showed a Lévy...

Microgels are soft microparticles that often exhibit thermoresponsiveness and feature a transformation at a critical temperature, referred to as the volume phase transition temperature. The question of whether this transformation occurs as a smooth or as a discontinuous one is still a matter of debate. This question can be addressed by studying ind...

The nonequilibrium dynamics of light in a coherently driven nonlinear cavity resembles the equilibrium dynamics of a Brownian particle in a scalar potential. This resemblance has been known for decades, but the correspondence between the two systems has never been properly assessed. Here we demonstrate that this correspondence can be exact, be appr...

This research studies three mathematical models, namely geometric Brownian motion (GBM), geometric fractional Brownian motion (GFBM) model which was developed by adding the Hurst parameter to GBM to characterize the long-memory phenomenon, and Merton jump-diffusion (MJD) model which captures shocks via GBM. This study sets out to forecast Malaysia...

The article exhibited the impact of variable fluid possessions (temperature dependent viscosity) on nanofluid over a wedge in the presence of heat generation and absorption. We also incorporated the magnetic field, Buogirnio model and nonlinear chemical reaction in this study. It is accepted to take viscosity and thermal conductivity as a reverse c...

Natural rubber was a vital pillar of Malaysia's export-oriented economy throughout much of the twentieth century, according to the Economic History of Malaya (EHM) website, the worldwide demand for natural rubber is expected to expand at a CAGR of 4.8% in the future (2019–2023). Therefore, it could be concluded that rubber is one of the commodities...

In various fields of science and engineering, such as financial mathematics, mathematical physics models, and radiation transfer, stochastic integral equations are important and practical tools for modeling and describing problems. Due to the existence of random factors, we face a fundamental problem in solving stochastic integral equations, and th...

We consider stochastic differential equation $$ d X_t=b(X_t) dt +d W_t^H, $$ where the drift $b$ is either a measure or an integrable function, and $W^H$ is a $d$-dimensional fractional Brownian motion with Hurst parameter $H\in(0,1)$, $d\in\mathbb{N}$. For the case where $b\in L_p(\mathbb{R}^d)$, $p\in[1,\infty]$ we show weak existence of solution...

We introduce the conformable fractional (CF) noninstantaneous impulsive stochastic evolution equations with fractional Brownian motion (fBm) and Poisson jumps. The approximate controllability for the considered problem was investigated. Principles and concepts from fractional calculus, stochastic analysis, and the fixed-point theorem were used to s...

The fluctuation-dissipation theorem, in the Kubo original formulation, is based on the decomposition of the thermal agitation forces into a dissipative contribution and a stochastically fluctuating term. This decomposition can be avoided by introducing a stochastic velocity field, with correlation properties deriving from linear response theory. He...

Mathematical difficulty remains in many classical financial problems, especially for a closed-form expression of asset value. The European option evaluation problem based on a regime-switching has been formally modeled since early 2000, for which a recursive algorithm was developed to solve it. The key mathematical difficulty of this problem relies...

This paper aims to propose a generalized fractional Fokker–Planck equation based on a stable Lévy stochastic process. To develop the general fractional equation, we will use the Lévy process rather than the Brownian motion. Due to the Lévy process, this fractional equation can provide a better description of heavy tails and skewness. The analytical...

We prove that stochastic replicator dynamics can be interpreted as intrinsic Brownian motion on the simplex equipped with the Aitchison geometry. As an immediate consequence, we derive three approximation results in the spirit of Wong–Zakai approximation, Donsker’s invariance principle and a JKO-scheme. Using the Fokker–Planck equation andWasserste...

We consider an investor who is dynamically informed about the future evolution of one of the independent Brownian motions driving a stock's price fluctuations. With linear temporary price impact the resulting optimal investment problem with exponential utility turns out to be not only well posed, but it even allows for a closed-form solution. We de...

We analyze pros and cons of the recently introduced theoretical framework, within which the dynamics of nonequilibrium diffusion processes is related to the fully Euclidean version of the Schr\"{o}dinger quantum mechanics with a minimal electromagnetic coupling. The arising "magnetic" affinity is set against the standard theory of the Brownian moti...

We analyze pros and cons of the recently introduced theoretical framework, within which the dynamics of nonequilibrium diffusion processes is related to the fully Euclidean version of the Schrödinger quantum mechanics with a minimal electromagnetic coupling. The arising "magnetic" affinity is set against the standard theory of the Brownian motion i...

Research interest in nanotechnology is growing due to its diversified engineering and medical applications. Due to the importance of bioconvection in biotechnology and various biological systems, scientists have made significant contributions in the last ten years. The present study is focusing on the investigation of the magnetohydrodynamics (MHD)...

An electrically conducting nanofluid saturated with a uniform porous media has been tested to determine how rotation affects thermal convection. Utilizing the Oldroydian model, which incorporates the specific effects of the electric field, Brownian motion, thermophoresis, and rheological factors for the distribution of nanoparticles that are top- a...