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Fluctuations due to Brownian Motion of Domain Walls, arXiv:0910.063v1 [cond-mat.mes-hall] (2009), submitted to "Special issue: Caloritronics in Solid State Communications. MAZO, R. M.: Brownian Motion. Fluctuations, Dynamics, and Applications, Oxford University Press, New York, 2009. DUINE, R. A.: Spin Pumping by a Field-Driven Domain Wall, arXiv:0706.3160v3 [cond-mat.mes-hall], Phys. Rev. B 77 (2008), 01440. DUINE, R. A.: Effects of Non-Adiabaticity on the Voltage Generated by a Moving Domain Wall, arXiv:0809.2201v1 [cond-mat.mes.-hall], Phys. Rev. B 79 (2009), 14407

References [1] X. Bardina, K. Es-Sebaiy, An extension of bifractional Brownian motion, Communications on Stochastic Analysis , 5 (2) (2011), 333–340. [2] K. Es-Sebaiy and C. A. Tudor, Multidimensional bifractional Brownian motion: Itô and Tanaka formulas, Stoch. Dyn ., 7 (3) (2007), 365–388. [3] C. Houdré and J. Villa, An example of infinite dimensional quasi-helix, Stochastic models (Mexico City, 2002), C ontemp. Math ., 336 (2003), 195–201. [4] J. P. Kahane, Hélices et quasi-hélices, Adv. Math ., 7B (1981), 417–433. [5] A. N. Kolmogorov, Wienersche

, Bernis, G. and Scotti, S. (2017). Alternative to beta coefficients in the context of diffusions, Quantitative Finance 17(2): 275-288. Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities, The Journal of Political Economy 81(3): 637-654. Bonollo, M., Di Persio, L., Oliva, I. and Semmoloni, A. (2015). A quantization approach to the counterparty credit exposure estimation, Borodin, A. and Salminen, P. (2002). Handbook of Brownian Motion: Facts and Formulae, 2nd Edn

References TANG, K. T.: Vector Analysis, Ordinary Differential Equations and Laplace Transforms. Mathematical Methods for Engineers and Scientists, Part II, Springer-Verlag, Berlin, Heidelberg, 2007. NIEUWENHUIZEN, T. M.—ALLAHVERDYAN, A. E.: Statistical Thermodynamics of Quantum Brownian Motion: Construction of Perpetuum Mobile of the Second Kind, Phys. Rev. E 66 (2002), 036102. ALLAHVERDYAN, A. E.—NIEUWENHUIZEN, T. M.: On Testing the Violation of the Clausius Inequality in Nanoscale Electric Circuits, arXiv:cond-mat/0205156v1, Phys. Rev. B 66 (2002), 115309


A numerical study on a steady, laminar, boundary layer flow of a nanofluid with the influence of chemical reaction resulting in the heat and mass transfer variation is made. The non-linear governing equations with related boundary conditions are solved using Adam’s predictor corrector method with the effect of a Brownian motion and thermophoresis being incorporated as a model for the nanofluid, using similarity transformations. Validation of the current numerical results has been made in comparison to the existing results in the absence of chemical reaction on MHD flows. The numerical solutions obtained for the velocity, temperature and concentration profiles for the choice of various parameters are represented graphically. Variations of heat and mass transfer across a Brownian motion and thermophoresis are studied and analyzed.

-18. [21] Falana A., Ojewale O.A., Adeboje T.B. (2016): Effect of Brownian motion and thermophoresis on a nonlinearly stretching permeable sheet in a nanofluid. – Advances in Nanoparticles, vol.5, pp.123-134. [22] Nield D.A. and Kuznetsov A.V. (2014): Thermal instability in a porous medium layer Saturated by a nanofluid: A revised model. – Int. J. Heat Mass Transfer, vol.68, pp.211-214. [23] Rosseland S. (1936): Theoretical Astrophysics. – Oxford: Clarendon Press. [24] Anjali Devi S.P. and Mekala S. (2015): Thermal radiation effects on hydromagnetic flow of


The study of radiative heat transfer in a nanofluid with the influence of magnetic field over a stretching surface is investigated numerically. Physical mechanisms responsible for magnetic parameter, radiation parameter between the nanoparticles and the base fluid, such as Brownian motion and thermophoresis, are accounted for in the model. The parameters for Prandtl number Pr, Eckert number Ec, Lewis number Le, stretching parameter b/a and constant parameter m are examined. The governing partial differential equations were converted into nonlinear ordinary differential equations by using a suitable similarity transformation, which are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six order iteration scheme. The accuracy of the numerical method is tested by performing various comparisons with previously published work and the results are found to be in excellent agreement. Numerical results for velocity, temperature and concentration distributions as well as skin-friction coefficient, Nusselt number and Sherwood number are discussed at the sheet for various values of physical parameters.

REFERENCES [1] Cai J. and Xu C. (2006). On the decomposition of the ruin probability for a jump-diffusion surplus process compounded by a geometric Brownian motion. North American Actuarial Journal 10, 120-132. [2] Gerber H. and Yang H. (2007). Absolute ruin probabilities in a jump diffusion risk model with investment. North American Actuarial Journal 11, 159-169. [3] Gihman I. I. and Skorohod A. V. (1972). Stochastic Differential Equations . New York-Heidelberg, Springer. [4] Jiang T. and Yan H-F. (2006). The finite-time ruin probability for the jump

= v α , L e = v D B , N b = ( ρ c ) p D B ( C w − C ∞ ) ( ρ c ) f v , N t = ( ρ c ) p D T ( T w − T ∞ ) ( ρ c ) f v T ∞ . $$\begin{array}{} \displaystyle Pr=\frac{v}{\alpha},\quad Le=\frac{v}{D_B}, \quad Nb=\frac{(\rho c)_pD_B(C_w-C_{\infty})}{(\rho c)_fv}, \quad Nt=\frac{(\rho c)_pD_T(T_w-T_{\infty})}{(\rho c)_fvT_{\infty}}. \end{array}$$ (15) Here Pr , Le , Nb , and Nt denote the Prandtl number, the lewis number, the Brownian motion parameter and the thermophoresis parameter respectively. In the present paper, we study the nonliner system analyticaly through

Controllability of nonlinear impulsive Ito type stochastic systems

In this article, we consider finite dimensional dynamical control systems described by nonlinear impulsive Ito type stochastic integrodifferential equations. Necessary and sufficient conditions for complete controllability of nonlinear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable. A fixed point approach is employed for achieving the required result.