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1

Second law analysis of mhd forced convective nanoliquid flow through a two-dimensional channel

Miri Rached, Abbassi Mohamed A., Ferhi Mokhtar, Djebali Ridha

Acta Mechanica et Automatica

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2022

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Vol. 16, no. 4

417--431

EN

The present study deals with fluid flow, heat transfer and entropy generation in a two-dimensional channel filled with Cu–water nanoliquid and containing a hot block. The nanoliquid flow is driven along the channel by a constant velocity and a cold temperature at the inlet, and the partially heated horizontal walls. The aim of this work is to study the influence of the most important parameters such as nanoparticle volume fraction (0%≤ϕ≤4%), nanoparticle diameter (5 nm≤dp≤55 nm), Reynolds number (50≤Re≤200), Hartmann number (0≤Ha≤90), magnetic field inclination angle (0≤γ≤π) and Brownian motion on the hydrodynamic and thermal characteristics and entropy generation. We used the lattice Boltzmann method (LBM: SRT-BGK model) to solve the continuity, momentum and energy equations. The obtained results show that the maximum value of the average Nusselt number is found for case (3) when the hot block is placed between the two hot walls. The minimum value is calculated for case (2) when the hot block is placed between the two insulated walls. The increase in Reynolds and Hartmann numbers enhances the heat transfer and the total entropy generation. In addition, the nanoparticle diameter increase reduces the heat transfer and the irreversibility, the impact of the magnetic field inclination angle on the heat transfer and the total entropy generation is investigated, and the Brownian motion enhances the heat transfer and the total entropy generation.

2

On the Exact Asymptotics of Exit Time From a Cone of an Isotropic α-Self-Similar Markov Process with a Skew-Product Structure

Palmowski Zbigniew, Wang Longmin

Probability and Mathematical Statistics

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2021

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Vol. 41, Fasc. 1

25--38

EN

In this paper we identify the asymptotic tail of the distribution of the exit time τC from a cone C of an isotropic α-self-similar Markov process Xt with a skew-product structure, that is, Xt is a product of its radial process and an independent time changed angular component θt. Under some additional regularity assumptions, the angular process θt killed on exiting the cone C has a transition density that can be expressed in terms of a complete set of orthogonal eigenfunctions with corresponding eigenvalues of an appropriate generator. Using this fact and some asymptotic properties of the exponential functional of a killed Lévy process related to the Lamperti representation of the radial process, we prove that Px(τC> t) ~h(x)t-k1 as t→∞ for h and k1 identified explicitly. The result extends the work of De Blassie (1988) and Bañuelos and Smits (1997) concerning the Brownian motion.

3

Heat and mass transfer flow of nanofluids in presence of chemical reaction with partial slip conditions

Narender G., Govardhan K., Sreedhar-Sarma G.

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 3

71-84

EN

A mathematical model is presented for analyzing the convective fluid over a stretching surface in the presence of nanoparticles. The analysis of heat and mass transfer of converted fluid with slip boundary condition is investigated. To convert the governing Partial Differential Equations (PDEs) into a system of nonlinear Ordinary Differential Equations (ODEs) we use similarity transformations. The shooting method is used to solve the system of ODEs numerically, and obtained numerical results are compared with the published results and found that both are in excellent agreement. The numerical values obtained for the velocity, temperature and concentration profiles are presented through graphs and tables. A discussion on the effects of various physical parameters and heat transfer characteristics is also included.

4

Mathematical modeling of convective heat and mass transfer of a rotating nano-fluid bounded by stretching and stationary walls in a vertical conduit

Haritha B., Umadevi C., Dhange M. Y.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 4

69--83

EN

The influence of thermal emission and unvarying magnetic field of convective heat and mass transfer of a rotating nano-liquid in an upright conduit constrained by a stretching and motionless wall is studied. The temperature, concentration profile, primary and secondary velocities have been computed through similarity transformation and fourth-order Runge-Kutta shooting technique. The objective of this article is to measure the impact of emission constraint, Brownian movement constraint and Eckert number, thermophoresis constraint, Prandtl number, space, and temperature-dependent heat source constraint on velocity. The results are presented in tables and graphs. Further, various constraint impacts on the skin friction coefficient, heat and mass transfer rates are also explored. This work is pertinent to biotechnological and engineering uses, like mass and heat transfer enhancement of microfluids and design of bioconjugates.

5

Influence of chemical reaction on the heat and mass transfer of nanofluid flow over a nonlinear stretching sheet: a numerical study

Misra Santoshi, Govardhan K.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 2

103--121

EN

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.

6

Melting heat transfer and MHD boundary layer flow of Eyring-Powell nanofluid over a nonlinear stretching sheet with slip

Reddy N. V. B., Kishan N., Reddy C. S.

International Journal of Applied Mechanics and Engineering

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2019

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Vol. 24, no. 1

161--178

EN

The steady laminar incompressible viscous magneto hydrodynamic boundary layer flow of an Eyring- Powell fluid over a nonlinear stretching flat surface in a nanofluid with slip condition and heat transfer through melting effect has been investigated numerically. The resulting nonlinear governing partial differential equations with associated boundary conditions of the problem have been formulated and transformed into a non-similar form. The resultant equations are then solved numerically using the Runge-Kutta fourth order method along with the shooting technique. The physical significance of different parameters on the velocity, temperature and nanoparticle volume fraction profiles is discussed through graphical illustrations. The impact of physical parameters on the local skin friction coefficient and rate of heat transfer is shown in tabulated form.

7

Minimizing the time spent in an interval by a Wiener process with uniform jumps

Lefebvre Mario

Control and Cybernetics

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2019

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Vol. 48, No. 3

407--415

EN

Let Xu(t) be a controlled Wiener process with jumps that are uniformly distributed over the interval [−c, c]. The aim is to minimize the time spent by Xu(t) in the interval [a, b]. The integro- differential equation, satisfied by the value function, is transformed into an ordinary differential equation and is solved explicitly for a particular case. The approximate solution obtained is precise when c is small.

8

The LQG homing problem for a Wiener process with random infinitesimal parameters

Lefebvre Mario, Moutassim Abderrazak

Archives of Control Sciences

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2019

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Vol. 29, No. 3

413--422

EN

The problem of optimally controlling a Wiener process until it leaves an interval (a, b) for the first time is considered in the case when the infinitesimal parameters of the process are random. When a = -∞, the exact optimal control is derived by solving the appropriate system of differential equations, whereas a very precise approximate solution in the form of a polynomial is obtained in the two-barrier case.

9

Translational and rotational Brownian displacements of colloidal particles of complex shapes

Cichocki B., Ekiel-Jeżewska M. L., Wajnryb E.

Archives of Mechanics

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2017

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Vol. 69, nr 3

257--267

EN

The exact analytical expressions for the time-dependent cross-correlations of the translational and rotational Brownian displacements of a particle with arbitrary shape were derived by us in [3, 4]. They are in this work applied to construct a method to analyze the Brownian motion of a particle of an arbitrary shape, and to extract accurately the self-diffusion matrix from the measurements of the crosscorrelations, which in turn allows to gain some information on the particle structure. As an example, we apply our new method to analyze the experimental results of D. J. Kraft et al. for the micrometer-sized aggregates of the beads [8]. We explicitly demonstrate that our procedure, based on the measurements of the time-dependent cross-correlations in the whole range of times, allows to determine the self-diffusion (or alternatively the friction matrix) with a much higher precision than the method based only on their initial slopes. Therefore, the analytical time-dependence of the cross-correlations serves as a useful tool to extract information about particle structure from trajectory measurements.

10

Nano-particles transport in a concentric annulus: a lattice Boltzmann approach

Pourmirzaagha H., Hassanzadeh A. H., Abouei M. A.

Journal of Theoretical and Applied Mechanics

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2015

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Vol. 53 nr 3

683--695

EN

A combination of the lattice Boltzmann method and lagrangian Runge-Kutta procedure is used to study dispersion and removal of nano-particles in a concentric annulus. The effect of aspect ratio, Rayleigh number and particles diameter are examined on particles removal and their dispersion characteristics. Simulations are performed for the Rayleigh number ranges from 103 to 105 and aspect ratio of 2, 3 and 4. Higher aspect ratios have led to weaker recirculation strength. The finest particles move on stochastic path due to the effect of Brownian motion. The Brownian motion has a greater effect on the removal of nano-particles with respect to thermophoresis.

11

U źródeł geologicznych zainteresowań Mariana Smoluchowskiego

Miecznik J. B.

Przegląd Geologiczny

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2013

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Vol. 61, nr 5

286--289

EN

Marian Smoluchowski (1872-1917) was an eminent physicist of international renown. His research in the field of the Kinetic Theory of Matter (e.g. the Brownian motion) contributed to strengthen the nuclear science. He is considered a pioneer of the statistical physics. Childhood and the years of study he spent in Vienna. From an early age, he was associated with mountains and was a prominent mountaineer. Along with his brother, Tadeusz, he climbed many unclimbed peaks in the Eastern Alps: Dolomites, Ortler group and Hohe Tauern. Those achievements passed into the history of Alpine mountaineering. In addition to sports and aesthetic aspects (he painted mountain landscapes), Smoluchowski found his scientific inspirations in the mountains. He was interested in the mechanics of tectonic movements and joined the discussion on the concepts concerning the nappe structure of orogens at the beginning of the 20th century (1909). Research on the physicalfoundations of tectonic movements in the Tatra Mountains, that he planned to undertake, was thwarted by the outbreak of World War I in 1914, and his premature death in 1917.

12

Szacowanie czasu uszkodzeń parametrycznych zaworów regulacyjnych modelami stochastycznymi

Kopka R.

Pomiary Automatyka Kontrola

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2012

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R. 58, nr 2

168-171

PL

Artykuł przedstawia wyniki badań związanych z możliwością wykorzystania modeli stochastycznych do szacowania czasu do powstania uszkodzeń obiektów technicznych. Na podstawie obserwacji początkowego procesu degradacji szacowane są parametry modelu, a następnie przy ich pomocy symuluje się jego kontynuację. Osiągnięcie przez modelowany proces przyjętego poziomu granicznego, traktowane jest jako uszkodzenie urządzenia. Przedstawione rozwiązania teoretyczne wykorzystano do opisu degradacji zaworu regulacyjnego, modelowanego procesem opisanym arytmetycznym i geometrycznym ruchem Browna.

EN

Use of technical devices always leads to degradation of their operating properties. Crossing a threshold level by the progressive degradation process is regarded as the so called 'soft failure' of a device (Fig. 1). When achieving such a state, there is need of repair or replacement of the device [7, 8]. Observing the first symptom of degradation, we can estimate the time in which the progressive degradation process reaches the limit value (Fig. 2).This allows us to predict the downtime and repair. The paper presents results of the work associated with use of stochastic models for description of the progressive degradation processes taking places in control valves. Use of the model describing arithmetic (3) or geometric (6) Brownian motion is proposed. The presented theoretical solutions are used to describe the control valve degradation process. On a basis of the recorded measurements of the valve control signal (Fig. 4) there were determined the model parameters (6). Then the time to the critical state was predicted (Fig. 5). A similar procedure for the flow residue signal was also carried out (Figs. 6 and 7). In this better fitting was achieved when assuming the model (3). The degradation processes contain important information about both current reliability level of a device and properties needed by the control algorithm. The possibility of their measuring and analysing can specify the time of soft turning the device off and can influence the procedures of its control. A significant problem is accuracy assessment. Using stochastic models it is possible based only on quantile lines received by multiple simulations of the considered process.

13

Conditional version of the Donati-Martin and Yor formula and its applications

Jakubowski J., Wiśniewolski M.

Demonstratio Mathematica

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2012

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Vol. 45, nr 2

257-263

EN

We present a new elementary and elegant probabilistic proof of conditional version of the Donati-Martin and Yor formula, more precisely, the conditional version of the Laplace transform of (…), where B is a Brownian motion. Next, using our form of conditional formula, we obtain the new results concerning Laplace transforms of some processes and a kind of reflection principle.

14

Upper and lower class separating sequences for brownian motion with random argument

Aistleitner C., Hörmann S.

Probability and Mathematical Statistics

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2011

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Vol. 31, Fasc. 2

183--202

EN

Let X = X1,X2, . . . be a sequence of random variables, let W be a Brownian motion independent of X and let Zk = W(Xk). A numerical sequence (tk) will be called an upper (lower) class sequence for {Zk} if P(Zk > tk for infinitely many k) = 0 (or 1, respectively). At a first look one might be tempted to believe that a “separating line” (t0k), say, between the upper and lower class sequences for {Zk} is directly related to the corresponding counterpart (s0k) for the process {Xk}. For example, by using the law of the iterated logarithm for the Wiener process a functional relationship t0k = √2s0k log log s0k seems to be natural. If Xk = |W2(k)| for a second Brownian motion W2 then we are dealing with an iterated Brownian motion, and it is known that the multiplicative constant √2 in (0.1) needs to be replaced by 2 · 3−3/4, contradicting this simple argument. We will study this phenomenon from a different angle by letting {Xk} be an i.i.d. sequence. It turns out that the relationship between the separating sequences (s0k) and (t0k) in the above sense depends in an interesting way on the extreme value behavior of {Xk}.

15

Przyspieszone badania degradacji przy stałym naprężeniu w analizie diod superelektroluminescencyjnych i wrażliwości parametrycznej

Li X., Jiang T., Sun F., Ma J.

Eksploatacja i Niezawodność

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2010

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nr 2

21-26

PL

Ruchy Browna są jednym z najpotężniejszych procesów stochastycznych w ciągłym czasie i ciągłej przestrzeni, który ma też mocne podstawy fi zyczne. W analizie przyspieszonych badań degradacji (ADT), rozkład odwrotny gaussowski, będący rozkładem czasu pierwszego przejścia ruchu Browna z dryfem (drift Brownian motion), staje się bardzo popularnym modelem predykcji statystycznej życia i niezawodności produktów. Diody superelektroluminescencyjne (SLD) o długiej żywotności i wysokiej niezawodności mają wiele zalet fi zycznych, które sprawiają, że zastępują one diody laserowe (LD) oraz diody elektroluminescencyjne (świecące) (LED) i mają szerokie zastosowanie w czujnikach światłowodowych. W niniejszym artykule przeprowadzono badania ADT diody SLD przy stałym naprężeniu. Aby ocenić możliwość zastosowania rozkładu odwrotnego gaussowskiego do badań diod SLD, określono najpierw trwałość i niezawodność SLD na podstawie danych o spadku mocy optycznej uzyskanych z badania ADT prowadzonego przy stałym naprężeniu. Następnie przeprowadzono analizy wrażliwości parametrycznej w trzech wymiarach: niezawodności, czasu życia i parametru analitycznego. Wreszcie, kierując się wynikami analizy wrażliwościowej, przedstawiono niektóre zasady planowania i przeprowadzania testów ADT przy stałym naprężeniu.

EN

Brownian motion is one of the most powerful stochastic processes in continuous time and continuous space and has a good physics background. For the analysis of accelerated degradation testing (ADT), the inverse Gaussian (IG) distribution, which is the fi rst passage time distribution of the drift Brownian motion (DBM), becomes a very popular statistical prediction model of product life and reliability. Instead of laser diode (LD) and Light Emitting Diode (LED), long-life and high-reliability super-luminescent diode (SLD) has many physical advantages and has been widely used in optical fi ber sensors. In this paper, the constant stress ADT (CSADT) of SLD was conducted. In order to evaluate the applicability of IG distribution to SLD, we fi rst estimate the life and reliability of SLD based on the optical power degradation data collected in CSADT. Then parameter sensitivity analyses are conducted in the 3-dimensions of reliability, lifetime and the analytic parameter. Finally, according to the sensitive analysis results, some CASDT planning and testing principles are presented.

16

The Influence of Parameters on Stable Space-time “Pillar” in Optical Tweezer using Counter-propagating Pulsed Laser Beams

Quang Quy H., Dinh Hai H., Van Luu M.

Computational Methods in Science and Technology

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2010

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Vol. spec. iss. (2)

xx-xx

EN

In this article the stable process of the optical tweezer using the pulsed counter-propagating Gaussian beams is investigated using the Langevin equation with optical gradient force. The influence of parameters as the total energy, the beam waist, the radius of particle and the viscosity of fluid on the dimension of the stable space-time “pillar” is simulated and discussed.

17

Controllability of nonlinear impulsive Ito type stochastic systems

Sakthivel R.

International Journal of Applied Mathematics and Computer Science

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2009

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Vol. 19, no 4

589-595

EN

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.

18

Some remarks on the maximum of a one-dimensional diffusion process

Abundo M.

Probability and Mathematical Statistics

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2008

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Vol. 28, Fasc. 1

107--120

EN

For a certain class of one-dimensional diffusions X(t); we study the distribution of maxtЄ[0;T] X(t) and the distribution of the first instant at whichX(t) attains the maximum by reducingX(t) to Brownian motion. Moreover, for T fixed or random, we study the asymptotics of threshold crossing probability, i.e. the rate of decay of P(maxsЄ[0;T ] X(s) > z ) as z goes to infinity. Some examples are also reported.

19

On truncated variation of Brownian motion with drift

Łochowski R.

Bulletin of the Polish Academy of Sciences. Mathematics

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2008

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Vol. 56, no 3-4

267-281

EN

We introduce the concept of truncated variation of Brownian motion with drift, which differs from regular variation by neglecting small jumps (smaller than some c > 0). We estimate the expected value of the truncated variation. The behaviour resembling phase transition as c varies is revealed. Truncated variation appears in the formula for an upper bound for return from any trading based on a single asset with flat commission.

20

Ruchy Browna z kamerą wideo

Greczyło T., Dębowska E.

Aparatura Badawcza i Dydaktyczna

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2005

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T. 10, nr 3

172--177

PL

Artykuł opisuje wyniki wstępnych pomiarów, mających na celu sprawdzenie czy możliwym jest wykorzystanie metody pomiarów wideo do badania zjawiska ruchów Browna w II Pracowni Fizycznej Instytutu Fizyki Doświadczalnej Uniwersytetu Wrocławskiego. Autorzy prezentują proces przygotowywania stanowiska doświadczalnego oraz ilustrują przykładowymi wynikami eksperymentalnymi jego działanie. Przedstawiają również wady i zalety metody oraz propozycje rozszerzenia jej zastosowania.

EN

The paper presents preliminary results used to design and prepare an advanced physics experiment to be carried out in Physics Laboratory II at the Institute of Experimental Physics, University of Wrocław. The authors discuss the process of setting up the experiment and the results. Advantages and disadvantages of the apparatus are discussed along with descriptions of possible future uses.