Computational Investigation of Brownian Motion and Thermophoresis Effect on Blood-Based Casson Nanofluid on a Non-linearly Stretching Sheet with Ohmic and Viscous Dissipation Effects

Motivated by the widespread applications of nanofluids,a nanofluid model is proposed which focuses on uniform magnetohydrodynamic(MHD)boundary layer flow over a non-linear stretching sheet,incorporating the Casson model for blood-based nanofluid while accounting for viscous and Ohmic dissipation effects under the cases of Constant Surface Temperature(CST)and Prescribed Surface Temperature(PST).The study employs a twophase model for the nanofluid,coupled with thermophoresis and Brownian motion,to analyze the effects of key fluid parameters such as thermophoresis,Brownian motion,slip velocity,Schmidt number,Eckert number,magnetic parameter,and non-linear stretching parameter on the velocity,concentration,and temperature profiles of the nanofluid.The proposed model is novel as it simultaneously considers the impact of thermophoresis and Brownian motion,along with Ohmic and viscous dissipation effects,in both CST and PST scenarios for blood-based Casson nanofluid.The numerical technique built into MATLAB’s bvp4c module is utilized to solve the governing system of coupled differential equations,revealing that the concentration of nanoparticles decreases with increasing thermophoresis and Brownian motion parameters while the temperature of the nanofluid increases.Additionally,a higher Eckert number is found to reduce the nanofluid temperature.A comparative analysis between CST and PST scenarios is also undertaken,which highlights the significant influence of these factors on the fluid’s characteristics.The findings have potential applications in biomedical processes to enhance fluid velocity and heat transfer rates,ultimately improving patient outcomes.

Influence of Brownian Motion, Thermophoresis and Magnetic Effects on a Fluid Containing Nanoparticles Flowing over a Stretchable Cylinder

The influence of Brownian motion and thermophoresis on a fluid containing nanoparticles flowing over a stretchable cylinder is examined.The classical Navier-Stokes equations are considered in a porous frame.In addition,the Lorentz force is taken into account.The controlling coupled nonlinear partial differential equations are transformed into a system of first order ordinary differential equations by means of a similarity transformation.The resulting system of equations is solved by employing a shooting approach properly implemented in MATLAB.The evolution of the boundary layer and the growing velocity is shown graphically together with the related profiles of concentration and temperature.The magnetic field has a different influence(in terms of trends)on velocity and concentration.

Nonparametric Estimation of the Trend Function for Stochastic Processes Driven by Fractional Brownian Motion of the Second Kind

The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of convergence,and the asymptotic normality of the kernel-type estimator are discussed.Besides,we prove that the rate of convergence of the kernel-type estimator depends on the smoothness of the trend of the nonperturbed system.

On a Compound Poisson Risk Model Perturbed by Brownian Motion with Variable Premium and Tail Dependence between Claims Amounts and Inter-Claim Time

This paper considers the compound Poisson risk model perturbed by Brownian motion with variable premium and dependence between claims amounts and inter-claim times via Spearman copula. It is assumed that the insurance company’s portfolio is governed by two classes of policyholders. On the one hand, the first class where the amount of claims is high, and on the other hand, the second class where the amount of claims is low, this difference in claim amounts has significant implications for the insurance company’s pricing and risk management strategies. When policyholders are in the first class, they pay an insurance premium of a constant amount c1 and when they are in the second class, the premium paid is a constant amount c2 such that c1 > c2. The nature of claims (low or high) is measured via random thresholds . The study in this work will focus on the determination of the integro-differential equations satisfied by Gerber-Shiu functions and their Laplace transforms in the risk model perturbed by Brownian motion with variable premium and dependence between claims amounts and inter-claim times via Spearman copula. .

HARNACK TYPE INEQUALITIES FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH MARKOVIAN SWITCHING

In this paper, by constructing a coupling equation, we establish the Harnack type inequalities for stochastic differential equations driven by fractional Brownian motion with Markovian switching. The Hurst parameter H is supposed to be in(1/2, 1). As a direct application, the strong Feller property is presented.

Some It Formulas with Respect to Mixed Fractional Brownian Motion and Brownian Motion

Some It formulas with respect to mixed Fractional Brownian motion and Brownian motion were given in this paper.These extended the It formula for the fractional Wick It Skorohod integral with respect to Fractional Brownian motion,meanwhile extended the It formula for It Skorohod integral with respect to Brownian motion.Taylor's formula is applied to prove our conclusion in this article.

Polar Functions for Fractional Brownian Motion

Let X (t)(t∈R^N) be a d-dimensional fractional Brownian motion. A contiunous function f:R^N→R^d is called a polar function of X(t)(t∈R^N) if P{ t∈R^N\{0},X(t)=t(t)}=0. In this paper, the characteristies of the class of polar functions are studied. Our theorem 1 improves the previous results of Graversen and Legall. Theorem2 solves a problem of Legall (1987) on Brownian motion.

SOME PATH PROPERTIES OF BROWNIAN MOTION AND SUPER-BROWNIAN MOTION ON THE SIERPINSKI GASKET

We study in this paper the path properties of the Brownian motion and super-Brownian motion on the fractal structure-the Sierpinski gasket. At first some results about the limiting behaviour of its increments are obtained and a kind of law of iterated logarithm is proved. Then A Lower bound of the spreading speed of its corresponding super-Brownian motion is obtained.

从x出发的漂移Brownian Motion的极值分布

该文研究了从x出发的正漂移Brownian Motion的极值问题,给出了关于这种随机过程的两种极大值的定义,并主要利用Brownian Motion的一些重要性质,比如正交不变性、时空齐次性及在有限停时上的强Markov性等,获得了两种极大值的分布函数的精确表达式.

On the sub-mixed fractional Brownian motion

Let {S t H, t ≥ 0） be a linear combination of a Brownian motion and an independent sub-fractional Brownian motion with Hurst index 0 〈 H 〈 1. Its main properties are studied. They suggest that SH lies between the sub-fractional Brownian motion and the mixed fractional Brownian motion. We also determine the values of H for which SH is not a semi-martingale.

Thermophoresis and Brownian motion effects on boundary layer flow of nanofluid in presence of thermal stratification due to solar energy

The problem of laminar fluid flow, which results from the stretching of a vertical surface with variable stream conditions in a nanofluid due to solar energy, is in- vestigated numerically. The model used for the nanofluid incorporates the effects of the Brownian motion and thermophoresis in the presence of thermal stratification. The sym- metry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations, namely, the scaling group of transfor- mations. An exact solution is obtained for the translation symmetrys, and the numerical solutions are obtained for the scaling symmetry. This solution depends on the Lewis number, the Brownian motion parameter, the thermal stratification parameter, and the thermophoretic parameter. The conclusion is drawn that the flow field, the temperature, and the nanoparticle volume fraction profiles are significantly influenced by these param- eters. Nanofluids have been shown to increase the thermal conductivity and convective heat transfer performance of base liquids. Nanoparticles in the base fluids also offer the potential in improving the radiative properties of the liquids, leading to an increase in the efficiency of direct absorption solar collectors.

EXACT MAXIMUM LIKELIHOOD ESTIMATOR FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION

This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.

On p-variation of bifractional Brownian motion

In this paper we study p-variation of bifractional Brownian motion. As an applica-tion, we introduce a class of estimators of the parameters of a bifractional Brownian motion andprove that both of them are strongly consistent; as another application, we investigate fractalnature related to the box dimension of the graph of bifractional Brownian motion.

POWER VARIATION OF SUBFRACTIONAL BROWNIAN MOTION AND APPLICATION

In this paper, we consider the power variation of subfractional Brownian mo- tion. As an application, we introduce a class of estimators for the index of a subfractional Brownian motion and show that they are strongly consistent.

LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION

In this article, we study a least squares estimator （LSE） of θ for the Ornstein- Uhlenbeck process X0=0,dXt=θXtdt＋dBt^ab, t ≥ 0 driven by weighted fractional Brownian motion B^a,b with parameters a, b. We obtain the consistency and the asymptotic distribution of the LSE based on the observation {Xs, s∈[0,t]} as t tends to infinity.

Dynamics of stochastic non-Newtonian fluids driven by fractional Brownian motion with Hurst parameter H∈(1/4,1/2)

A two-dimensional （2D） stochastic incompressible non-Newtonian fluid driven by the genuine cylindrical fractional Brownian motion （FBM） is studied with the Hurst parameter ∈ （1/4,1/2） under the Dirichlet boundary condition. The existence and regularity of the stochastic convolution corresponding to the stochastic non-Newtonian fluids are obtained by the estimate on the and the identity of the infinite double series spectrum of the spatial differential operator in the analytic number theory. The existence of the mild solution and the random attractor of a random dynamical system are then obtained for the stochastic non-Newtonian systems with ∈ （1/2,1） without any additional restriction on the parameter H.

AN ENLARGEMENT OF FILTRATION FOR BROWNIAN MOTION

Let Bt be an Ft Brownian motion and Gt be an enlargement of filtration of Ft from some Gaussian random variables. We obtain equations for ht such that Bt ht is a Gt-Brownian motion.

Asymptotic Behavior of Super Brownian Motion

Generally, super Brownian motion will not c on verge vaguely to 0 if the initial measure is sufficiet large, so it is very inte resting to get asymptotic estimation for super Brownian motion. In this paper, w e will prove two asymptotic for super Brownian motion with general critical bran ching mechanism.

SOME CENTRAL LIMIT THEOREMS FOR SUPER BROWNIAN MOTION

The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limiting field is the same aa that obtained by Dawson (1977). In the recurrent case it is a spatially uniform field. The author also give a central limit theorem for the weighted occupation time of the super Brownian motion with underlying dimension number d less than or equal to 3, completing the results of Iscoe (1986).

An image encryption scheme based on three-dimensional Brownian motion and chaotic system

At present, many chaos-based image encryption algorithms have proved to be unsafe, few encryption schemes permute the plain images as three-dimensional（3D） bit matrices, and thus bits cannot move to any position, the movement range of bits are limited, and based on them, in this paper we present a novel image encryption algorithm based on 3D Brownian motion and chaotic systems. The architecture of confusion and diffusion is adopted. Firstly, the plain image is converted into a 3D bit matrix and split into sub blocks. Secondly, block confusion based on 3D Brownian motion（BCB3DBM）is proposed to permute the position of the bits within the sub blocks, and the direction of particle movement is generated by logistic-tent system（LTS）. Furthermore, block confusion based on position sequence group（BCBPSG） is introduced, a four-order memristive chaotic system is utilized to give random chaotic sequences, and the chaotic sequences are sorted and a position sequence group is chosen based on the plain image, then the sub blocks are confused. The proposed confusion strategy can change the positions of the bits and modify their weights, and effectively improve the statistical performance of the algorithm. Finally, a pixel level confusion is employed to enhance the encryption effect. The initial values and parameters of chaotic systems are produced by the SHA 256 hash function of the plain image. Simulation results and security analyses illustrate that our algorithm has excellent encryption performance in terms of security and speed.