Brownian Motion Research Articles

Fractional modeling of unsteady flow of Jeffrey fluid using active and passive control strategies

The current work is focused on the analysis of heat and mass transfer in a magnetohydrodynamics Jeffrey nanofluid flows across a vertical plate because of these possible uses. Free convection, magnetic effect, and thermo-diffusion properties are all applied to the flow considered here. The modeling also takes into account the passive and active control of the Jeffrey nanofluid. The constant proportional Caputo fractional operator which was recently introduced is used in this work together with generalized Fick’s and Fourier’s law. Using suitable nondimensional variables, ordinary differential equations are obtained from the modeling equations, and the Laplace transform method is used to solve these modeled equations. The concentration and temperature profiles are rising functions of the fractional and thermophoresis parameters, and they drop more quickly as the values of the Schmidt, Prandtl, and Nb (Brownian motion parameters) rise. The constant proportional Caputo (CPC) fractional derivative is the best choice for achieving more stable concentration, temperature, and velocity than conventional fields. Raising the values of α will increase the rate of heat transfer and skin friction coefficient. Additionally, as compared to the classical model, the constant proportional Caputo derivative model shows more decay nature. Consequently, compared to the classical model, the constant proportional Caputo differential model has a superior memory function.

Activation energy and angular momentum in electromagnetic radiation micropolar nanofluids: Focus on microbial eukaryotic species

Microbial eukaryotic species play a crucial role in biomedical research, aiding in the study of bacterial impurities, microorganism pathogenesis, and development of tactics to combat antimicrobial struggle. These species represent a complex and diverse aspect of bacteriological life, influencing ecosystems, human health, and technological progress. This study aims to create a comprehensive computational model to analyze the magnetohydrodynamics of a non-Newtonian micropolar nanofluid over an exponentially stretchable surface. It incorporates the Buongiorno model, which considers thermophoretic diffusion and Brownian motion effects to study the thermal behavior of micropolar nanofluids. It is also investigated how thermal radiation affects the current model. The classical Navier's stokes equations of motions of the current model are transform into a system of ordinary differential equation by employing similarity approach. The classical Navier-Stokes equations of motion are transformed into ordinary differential equations using similarity transformations, and MATLAB is used to solve them numerically. Here we considered three different cases, (i)-injection fw>0, (ii)-impermeable wall fw=0, (iii)-suction fw<0 which are illustrated visually. The consequence of various flow parameters effects on velocity, temperature, concentration, motile microorganism, and angular profiles are illustrated graphically. The high concordance between the model's results and the available data validates its originality. Present results indicate that while a larger porosity and Hartman number decrease velocity, increasing the mass and thermal convective factors raises the velocity profile. Raising the thermophoretic and magnetic parameters causes the temperature profile to climb; however, raising the temperature exponent and Prandtl number causes it to fall. The behavior of micropolar nanofluids is better understood thanks to this research, which could have applications in a variety of industries including manufacturing, energy, electronics, and healthcare. The novelty of the current model is verified using data that has already been published, and a great agreement is observed. When the values of the parameter K lies between the ranges 0.2<K< 0.3, and 0.3<K< 0.4, percentage increment noted in heat transfer enhancement is about 2.3 % and 6.3 % Until now, no such investigation has been performed to examine the implications of three-dimensional bio-convection micropolar based Casson fluid flow under the activation energy and suction/injection. From the outcomes, it was established that nanofluids are more fruitful for heat transfer enhancement.

Multiple serial correlations in global air temperature anomaly time series.

Serial correlations within temperature time series serve as indicators of the temporal consistency of climate events. This study delves into the serial correlations embedded in global surface air temperature (SAT) data. Initially, we preprocess the SAT time series to eradicate seasonal patterns and linear trends, resulting in the SAT anomaly time series, which encapsulates the inherent variability of Earth's climate system. Employing diverse statistical techniques, we identify three distinct types of serial correlations: short-term, long-term, and nonlinear. To identify short-term correlations, we utilize the first-order autoregressive model, AR(1), revealing a global pattern that can be partially attributed to atmospheric Rossby waves in extratropical regions and the Eastern Pacific warm pool. For long-term correlations, we adopt the standard detrended fluctuation analysis, finding that the global pattern aligns with long-term climate variability, such as the El Niño-Southern Oscillation (ENSO) over the Eastern Pacific. Furthermore, we apply the horizontal visibility graph (HVG) algorithm to transform the SAT anomaly time series into complex networks. The topological parameters of these networks aptly capture the long-term correlations present in the data. Additionally, we introduce a novel topological parameter, Δσ, to detect nonlinear correlations. The statistical significance of this parameter is rigorously tested using the Monte Carlo method, simulating fractional Brownian motion and fractional Gaussian noise processes with a predefined DFA exponent to estimate confidence intervals. In conclusion, serial correlations are universal in global SAT time series and the presence of these serial correlations should be considered carefully in climate sciences.

Local linear estimator for fractional diffusions

In this paper, we investigate the nonparametric local linear estimator for the drift function of stochastic differential equations (SDEs) driven by fractional Brownian motion with Hurst parameter [Formula: see text]. The drift function is one-sided dissipative Lipschitz that ensures the ergodic property of the SDE. We derive the strong consistency of the proposed estimator with proper bandwidth selectors associated with the determined Hurst parameter [Formula: see text]. The main tools are the ergodic theorem, Malliavin calculus, and a maximum inequality for It[Formula: see text]–Skorohod integrals.

A sine cosine algorithm guided by elite pool strategy for global optimization

When handling global optimization problems by metaheuristic algorithms (MAs), an important yet difficult assignment is to keep a tradeoff between the swarm’s diversity and convergence. Hence, this paper develops an enhanced sine cosine algorithm called EPSCA to achieve the above target. In EPSCA, to balance diversity and convergence, the elite pool strategy and Brownian motion are introduced to modify the position updating formula of the original SCA. Then the pattern search method serves as a local search tool to reinforce the quality of the current best solution. Additionally, an efficient mutation operator is devised to discourage premature convergence. The comparative analysis between the developed EPSCA and other state-of-the-art techniques is conducted on 30 CEC2017 benchmarks. Besides, EPSCA is employed to identify the core parameters of photovoltaic (PV) systems. The experimental evidence based on 30 independent runs demonstrated that EPSCA can perform better than four state-of-the-art SCA variants and five other well-known methodologies. The source code of EPSCA is publicly available at https://github.com/denglingyun123/EPSCA.

Intelligent computing for the electro-osmotically modulated peristaltic pumping of blood-based nanofluid

The study delves into a novel application of artificial neural networks within the biomedical realm, specifically focusing on the peristaltic pumping of ionized blood-infused nanofluid using the Casson model. The investigation takes into account the impacts of electrokinetic forces, chemical reaction, thermal radiation and variable thermal conductivity. The endorsed nanofluid model encompasses both thermophoretic and Brownian diffusions. The Nernst-Planck and Poisson equations are used to characterize electroosmotic process. The mathematical model is then numerically solved using NDSolve in Mathematica. The variation in relevant hemodynamic characteristics concerning key flow parameters is explored through numerous graphical representations. Two distinct artificial neural networks have been developed to estimate values for rates of mass and heat transfer. The Levenberg-Marquardt algorithm is used as the training algorithm in network models with multi-layer perceptron architecture. Graphical inspection of the results demonstrates a decrease in blood flow with an elevated Helmholtz-Smoluchowski velocity. A lower pressure gradient is recorded with a higher electroosmotic parameter. Furthermore, an augmentation in the thermal conductivity parameter leads to a reduction in heat transfer rate at the wall. The concentration profile demonstrates an increase with a rise in the chemical reaction parameter. The results obtained from the neural network models exhibit an ideal harmony with the target values. The developed neural network models demonstrated the ability to predict rates of heat and mass transfer values with average deviations of −0.01% and 0.004%, respectively.

Moderate Deviations for Two-Time Scale Systems with Mixed Fractional Brownian Motion

Moderate Deviations for Two-Time Scale Systems with Mixed Fractional Brownian Motion

Electrothermosolutal convection in nanofluid

This article employs linear stability theory to investigate the thermosolutal instability phenomenon within a horizontal layer of nanofluid subjected to a vertical alternating current (AC) electric field while being heated from below. The model integrates the impacts of Brownian diffusion, thermophoresis, and electrophoresis into the nanofluid dynamics. Free-free boundary conditions are assumed at the upper and lower boundaries of the fluid layer. Employing the normal mode technique, the set of coupled differential equations is solved analytically for stress-free boundaries. The computed numerical values of the stationary thermal Rayleigh number are illustrated graphically. The conditions for nonexistence of overstability are also derived. The study focuses on stationary convection, examining the analytical and graphical implications of modified diffusivity ratio, AC electric Rayleigh number, solutal Lewis number, nanofluid Lewis number, solutal Rayleigh number, and nanoparticle Rayleigh number on the system dynamics. The analysis demonstrates that the nanofluid Lewis number and modified diffusivity ratio produce a stabilizing effect on the initiation of convection, notably delaying its onset. AC electric field and solutal Rayleigh number exhibit a destabilizing influence, notably accelerating the onset of convection.

Using a mixed-reality headset to elicit and track clinically relevant movement in the clinic.

21st century neurology will require scalable and quantitative tools that can improve neurologic evaluations over telehealth and expand access to care. Commercially available mixed-reality headsets allow for simultaneous presentation of stimuli via holograms projected into the real world and objective and quantitative measurement of hand movement, eye movement, and phonation. We created 6 tasks designed to mimic standard neurologic assessments and administered them to a single participant via the Microsoft HoloLens 2 mixed-reality headset. The tasks assessed postural hand tremor, finger tapping, pronation and supination of hands, hand and eye tracking of a center-out task, hand and eye tracking of a random motion task, and vocal assessment. We show the utility of the HoloLens for commonly used neurological exams. First, we demonstrate that headset-derived holograms can project hand movements and objects in 3D space, providing a method to accurately and reproducibly present test stimuli to reduce test-test variability. Second, we found that participant hand movements closely matched holographic stimuli using a variety of metrics calculated on recorded movement data. Third, we showed that the HoloLens can record and playback exam tasks for visual inspection, sharing with other medical providers, and future analysis. Fourth, we showed that vocal recordings and analysis could be used to profile vocal characteristics over time. Together, this demonstrates the versatility of mixed reality headsets and possible applications for neurological assessment. Administering components of the neurologic exam via a self-contained and commercially available mixed-reality headset has numerous benefits including detailed kinematic quantification, reproducible stimuli presentation from test to test, and can be self-administered expanding access to neurological care and saving hospital time and money. This work was supported by grants from the National Institutes of Health (NIH) (F30AG063468) (E.L.), (F31NS113395) (D.J.C), and the Pilot Grant Award from the University of Colorado Movement Disorders Center (D.J.C).

Optical Halo: A Proof of Concept for a New Broadband Microrheology Tool

Microrheology, the study of material flow at micron scales, has advanced significantly since Robert Brown’s discovery of Brownian motion in 1827. Mason and Weitz’s seminal work in 1995 established the foundation for microrheology techniques, enabling the measurement of viscoelastic properties of complex fluids using light-scattering particles. However, existing techniques face limitations in exploring very slow dynamics, crucial for understanding biological systems. Here, we present a proof of concept for a novel microrheology technique called “Optical Halo”, which utilises a ring-shaped Bessel beam created by optical tweezers to overcome existing limitations. Through numerical simulations and theoretical analysis, we demonstrate the efficacy of the Optical Halo in probing viscoelastic properties across a wide frequency range, including low-frequency regimes inaccessible to conventional methods. This innovative approach holds promise for elucidating the mechanical behaviour of complex biological fluids.

Optical Halo: A Proof of Concept for a New Broadband Microrheology Tool

Microrheology, the study of material flow at micron scales, has advanced significantly since Robert Brown’s discovery of Brownian motion in 1827. Mason and Weitz’s seminal work in 1995 established the foundation for microrheology techniques, enabling the measurement of viscoelastic properties of complex fluids using light-scattering particles. However, existing techniques face limitations in exploring very slow dynamics, crucial for understanding biological systems. Here, we present a proof of concept for a novel microrheology technique called “Optical Halo”, which utilises a ring-shaped Bessel beam created by optical tweezers to overcome existing limitations. Through numerical simulations and theoretical analysis, we demonstrate the efficacy of the Optical Halo in probing viscoelastic properties across a wide frequency range, including low-frequency regimes inaccessible to conventional methods. This innovative approach holds promise for elucidating the mechanical behaviour of complex biological fluids.

Deformations and q-Convolutions. Old and New Results

This paper is the survey of some of our results related to q-deformations of the Fock spaces and related to q-convolutions for probability measures on the real line R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}$$\\end{document}. The main idea is done by the combinatorics of moments of the measures and related q-cumulants of different types. The main and interesting q-convolutions are related to classical continuous (discrete) q-Hermite polynomial. Among them are classical (q=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q=1$$\\end{document}) convolutions, the case q=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q=0$$\\end{document}, gives the free and Boolean relations, and the new class of q-analogue of classical convolutions done by Carnovole, Koornwinder, Biane, Anshelovich, and Kula. The paper contains many questions and problems related to the positivity of that class of q-convolutions. The main result is the construction of Brownian motion related to q-Discrete Hermite polynomial of type I.

Heat and mass transfer analysis of hybrid nanofluid flow over a rotating permeable cylinder: A modified Buongiorno model approach

Many external factors influence the properties of nanoparticles in the working fluid, which subsequently determines the efficacy attributes of the ensuing nanofluid. Incorporating these factors is essential for studying heat and mass transfer in hybrid nanofluids, as it provides a detailed representation of the mechanism. Such factors are porous medium, heat source, Thermophoresis, and Brownian motion. The rotation of a cylinder can alter the flow field and boundary layer around it, which could be used for flow management scenarios such as drag reduction or separation of boundary layers control, and the complex flow patterns generated through a rotating cylinder could be utilized for improved mixing and heat transfer in processes in industry. Thus, the current novel aspect of the study examines the impacts of thermophoresis and Brownian motion over a rotating cylinder in the presence of a porous media comprised of water-based TiO2 and Fe2O4. The physical circumstances are primarily represented as PDEs based on the considered flow conditions, which then get transformed into a system of ODEs using the relevant similarity variables. The numerical solution is obtained by using RKF-45th and the shooting procedure. The flow symmetry and the effects of the specific variables associated with the problem are examined and delivered graphically. The findings confirm that the drag coefficient improves with porous material, altering fluid dynamics. Heat transmission steadily drops as the thermophoretic parameter gets larger, but mass transfer displays a contrary trend for evolving Brownian motion parameters. Also, the current results are validated with existing past studies.

Measure pseudo S -asymptotically ω-periodic solution in distribution for some stochastic differential equations with Stepanov pseudo S -asymptotically ω-periodic coefficients

In this research paper, a mathematical concept known as the ω-periodic process is discussed, and a new type of processes called the doubly measure pseudo -asymptotically ω-periodic in distribution process is set forward. Additionally, the properties of these processes are identified and invested to tackle the solution of a stochastic differential equation guided by Brownian motion. The basic objective of the current work resides in corroborating the existence and uniqueness of the solution which is doubly measure pseudo -asymptotically ω-periodic in distribution.

Measure pseudo S -asymptotically ω-periodic solution in distribution for some stochastic differential equations with Stepanov pseudo S -asymptotically ω-periodic coefficients

In this research paper, a mathematical concept known as the ω-periodic process is discussed, and a new type of processes called the doubly measure pseudo -asymptotically ω-periodic in distribution process is set forward. Additionally, the properties of these processes are identified and invested to tackle the solution of a stochastic differential equation guided by Brownian motion. The basic objective of the current work resides in corroborating the existence and uniqueness of the solution which is doubly measure pseudo -asymptotically ω-periodic in distribution.

Bioconvective reversible (an esterification process) Casson nanofluid flow over a radiative spinning disc with microorganism

This study describes the Casson (a non-Newtonian fluid) nanofluid bioconvection flow across a spinning disc in the presence of gyrotactic microorganisms, many slips and thermal radiation. Also, the flow is considered as a reversible flow. The esterification process is taken into account. Using the proper variables, a system of extremely nonlinear PDEs is converted into a system of ODEs. To arrive to the solution of such equations, a numerical approach is used. Using the bvp4c approach, nonlinear flow equations can be numerically solved. Investigated are the effects of different numbers on the thermal field, volumetric concentration of nanoparticles and microbiological field. The key characteristics of the parameters in relation to the profiles of the velocity, temperature, concentration and microorganisms are graphically assessed with appropriate physical effects. A graphical explanation is provided for the wall shear stress, local Nusselt number, local Sherwood number and local motile density number. Rate of motile density number shows a prominent difference between reversible and irreversible flows for Brownian motion and Peclet number. The results of the theoretical simulations have dynamic applications in the fields of biotechnology and thermal engineering.

Influence of activation energy and variable thermal conductivity on magneto-convective nonlinear thermo-radiative Casson nanofluid containing motile microorganisms over a sinusoidal surface

The activation energy of convective-radiative nanoliquids with sinusoidal walls has garnered significant academic interest in recent years. This focus arises due to the pivotal applications of nanoparticles in thermal engineering, industrial processes, and medical sciences. This article investigates the magnetohydrodynamic heat transfer characteristics of Casson nanofluids containing microorganisms influenced by an oscillatory surface. The study incorporates temperature-dependent viscosity and utilizes Buongiorno’s mathematical model to account for nonlinear thermal radiation, Brownian motion, and thermophoretic effects from using nanomaterials in Casson fluids. These effects enhance thermal conductivity, improving the heat transportation phenomenon while considering gyrotactic microorganism density distributions. The boundary layer flow problem is formulated using partial differential equations and associated boundary conditions, subsequently numerically simulated using the bvp4c function. The investigation explores the thermal behavior of nanoparticles in the presence of bioconvection phenomena, Lorentz force, chemical reactions, and activation energy. As a result, this model addresses variable thermal conductivity and bioconvection aspects in Casson nanofluids over a sinusoidal surface. Numerically computed results for the Nusselt number, motile density, and Sherwood number provide insights into several essential features. The findings reveal that an increase in the Casson fluid parameter correlates with a decreased velocity profile. The assumptions of variable thermal conductivity and temperature-dependent viscosity prove more effective in raising the temperature of nanoparticles. The nanoparticle concentration profile rises noticeably for smaller Schmidt number Sc values when the activation energy parameter is higher than larger Sc values. Additionally, the presence of microorganisms in Casson nanofluids leads to increased temperatures due to an elevation in the bioconvection Rayleigh number. Moreover, heightened oscillating frequency parameters decrease nanoparticle concentration and microorganism density. Including activation energy and oscillating frequency parameters further enhances the understanding of nanoparticle concentration and microorganism density dynamics, offering valuable contributions to theoretical research and practical applications across multiple interdisciplinary fields.

Thermal analysis of radiative Sutterby nanofluid flow over stretching curved surface

In this analysis, Sutterby fluid model over a curved surface is considered. The main mechanisms that contribute to the improvement of the convection characteristics of the nanofluid are categorized as Brownian motion and thermophoresis. The radiation and slip mechanism have been studied at curved stretchable surface. The suction/injection impacts also studied. The partial differential equations are converted into ordinary differential equations through transformations.The numerical solution of the specified mathematical model is obtained using the built-in bvp4c tool in MATLAB. The effects of various parameters related to the system of ordinary differential equations are illustrated in the graphs. The influence of some intended parameters through the physical quantities are presented through tabular form.

Natural convection of water-based nanofluids in three-dimensional enclosures

The single-phase approach, in which nanofluids are treated as pure fluids assuming that the solid and liquid phases are in local thermal and hydrodynamic equilibrium, has been used with good results to simulate forced convection flows. Conversely, its extension to natural convection has revealed to be more problematic, as the obtained numerical results are substantially different from the experimental data, mainly due to the effects of the slip motion occurring between the suspended nanoparticles and the base liquid, whose consequent nonuniform distribution of the solid phase concentration can significantly affect both heat and momentum transfer. In the present article, a two-phase model based on a double-diffusive approach is proposed to study the natural convection flows of water-based metal oxide nanofluids inside cylindrical and rectangular enclosures heated and cooled at their opposite sides with the scope to reproduce a number of experimental data-sets available in the literature. Given the assumption of local thermal equilibrium between nanoparticles and host liquid, and considering the Brownian and thermophoretic diffusion as responsible for causing significant relative velocity between the solid and liquid phases, the governing equations are solved by a control-volume numerical method implemented using the open-source platform OpenFOAM (Open Field Operation and Manipulation). It has been found that the nanoparticle diffusion gives the major contribution to the decrease of the heat transfer rate red usually observed experimentally in natural convection flows of nanofluids inside differentially-heated enclosures. This means that a two-phase model, in conjunction with proper correlations for the evaluation of the nanofluid effective physical properties, must be necessarily enforced to obtain reliable results for many engineering applications.

Natural convection of water-based nanofluids in three-dimensional enclosures

The single-phase approach, in which nanofluids are treated as pure fluids assuming that the solid and liquid phases are in local thermal and hydrodynamic equilibrium, has been used with good results to simulate forced convection flows. Conversely, its extension to natural convection has revealed to be more problematic, as the obtained numerical results are substantially different from the experimental data, mainly due to the effects of the slip motion occurring between the suspended nanoparticles and the base liquid, whose consequent nonuniform distribution of the solid phase concentration can significantly affect both heat and momentum transfer. In the present article, a two-phase model based on a double-diffusive approach is proposed to study the natural convection flows of water-based metal oxide nanofluids inside cylindrical and rectangular enclosures heated and cooled at their opposite sides with the scope to reproduce a number of experimental data-sets available in the literature. Given the assumption of local thermal equilibrium between nanoparticles and host liquid, and considering the Brownian and thermophoretic diffusion as responsible for causing significant relative velocity between the solid and liquid phases, the governing equations are solved by a control-volume numerical method implemented using the open-source platform OpenFOAM (Open Field Operation and Manipulation). It has been found that the nanoparticle diffusion gives the major contribution to the decrease of the heat transfer rate red usually observed experimentally in natural convection flows of nanofluids inside differentially-heated enclosures. This means that a two-phase model, in conjunction with proper correlations for the evaluation of the nanofluid effective physical properties, must be necessarily enforced to obtain reliable results for many engineering applications.