Brownian Motion Research Articles

A numerical study of the effect of graphene nanoparticle size on brownian displacement, thermophoresis, and thermal performance of graphene/water nanofluid by molecular dynamics simulation

Brownian motion, often known as BM, is an inherent characteristic of minute particles suspended in a fluid. It plays an important role in several physical and chemical processes. Thermophoresis refers to the process where particles in a fluid are carried along with a gradient in temperature (Temp). This feature has significant importance in several applications, including microfluidics, thermal control, and energy conversion. Through the examination of the thermophoresis phenomenon in water/graphene nanofluid (NF), researchers might get valuable knowledge on the potential uses of these materials. The current study examined the effect of various sizes of graphene nanoparticles (NPs) (5, 6, 9, and 10 Å) on the thermal behavior (TB), BM, and thermophoresis of water/graphene NF using molecular dynamics (MD) simulation. This study reported the changes in heat flux (HF), thermal conductivity (TC), average Brownian displacement (BD), and thermophoresis. It is concluded that by increasing the size of graphene NPs from 5 to 10 Å, the average BD and thermophoresis increased from 3.06 Å and 23.88 Å to 4.16 Å and 31.46 Å, respectively. Due to their higher kinetic energy (KE) and momentum, larger graphene NPs experienced more BM, enabling them to withstand random thermal fluctuations more effectively than smaller particles. In addition, as the size of graphene NPs increased, the HF and TC values ​​increased from 39.54 W/m2 and 0.36 W/(m.K) to 47.19 W/m2 and 0.51 W/(m.K) after 10 ns. Therefore, the size-dependent changes in BD and thermophoretic effects led to a simultaneous increase in HF and TC of the NF, which was attributed to the larger heat transfer (HT) surface area, improved HT properties, and synergistic effects of larger graphene NPs. The maximum (Max) temperature increases from 1415 K to 1504 K. These findings were useful in a variety of industries, particularly for improving TB in different NFs.

Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension

AbstractFor large classes of even‐dimensional Riemannian manifolds , we construct and analyze conformally invariant random fields. These centered Gaussian fields , called co‐polyharmonic Gaussian fields, are characterized by their covariance kernels k which exhibit a precise logarithmic divergence: . They share a fundamental quasi‐invariance property under conformal transformations. In terms of the co‐polyharmonic Gaussian field , we define the Liouville Quantum Gravity measure, a random measure on , heuristically given as and rigorously obtained as almost sure weak limit of the right‐hand side with replaced by suitable regular approximations . In terms on the Liouville Quantum Gravity measure, we define the Liouville Brownian motion on and the random GJMS operators. Finally, we present an approach to a conformal field theory in arbitrary even dimension with an ansatz based on Branson's ‐curvature: we give a rigorous meaning to the Polyakov–Liouville measure and we derive the corresponding conformal anomaly. The set of admissible manifolds is conformally invariant. It includes all compact 2‐dimensional Riemannian manifolds, all compact non‐negatively curved Einstein manifolds of even dimension, and large classes of compact hyperbolic manifolds of even dimension. However, not every compact even‐dimensional Riemannian manifold is admissible. Our results concerning the logarithmic divergence of the kernel rely on new sharp estimates for heat kernels and higher order Green kernels on arbitrary closed manifolds.

Time-dependent flow of Reiner–Rivlin nanofluid over a stretching sheet with Arrhenius activation energy and binary chemical reaction

PurposeThe main purpose here is to explore the unsteadiness characteristics in magnetized flow of Reiner–Rivlin nanofluid. Energy and concentration expressions are modeled by utilizing Buongiorno model for nanoscale particles. Additionally, Joule heating and activation energy are also deliberated.Design/methodology/approachThe bvp4c solver in MATLAB is employed for graphical and numerical outcomes.FindingsA similar trend of temperature field is seen against thermophoresis and Brownian movement parameters. Thermal transport rate decreases via Prandtl number. Augmentation in mass transport rate is noted through unsteadiness parameter.Originality/valueTo the best of author’s knowledge, no such consideration has been given in the literature yet.

Boost heat transfer efficiency through thermal radiation and electrical conductivity in nanofluids

AbstractThermal radiation and electrical conductivity in nanofluids are crucial for their heat transfer characteristics, especially in applications with elevated temperatures or significant radiative heat transfer. The suspension of nanoparticles in suspension contributes to the fluid's electrical conductivity, which is essential for efficient heat dissipation in electronic cooling systems. Understanding the behavior of electroconductive nanofluids is particularly important in electronic cooling applications, where effective heat dissipation is crucial to prevent overheating. A study using a similarity parameter transformed a system of coupled PDEs into a set of nonlinear ordinary differential equations, revealing significant changes in key physical characteristics, such as temperature distribution, cubic concentration field, and velocity field. The study also examined the effects of parameters like Brownian motion, Rayleigh number, Peclet number, thermophoresis parameter, and buoyancy ratio parameter. The research provides valuable insights into the complex dynamics of magnetized non‐Newtonian nanofluids and offers practical implications for applications like microbial fuel cells and heat transmission equipment.

Irreversibility analysis of radiative TiO2+Al2O3+Cu/H2O ternary nanofluid flow over a bidirectional stretching sheet with cattaneo-christov heat flux: nanotechnology applications

Ternary nanofluids demonstrate better heat transfer characteristics in contrast to conventional liquids and typical hybrid nanofluids. These are applied in sophisticated cooling systems for electronics, heat exchangers, and automotive engines, along with renewable energy systems such as solar collectors, where efficient heat transfer plays a crucial role. The aim of this research is to investigate the movement of a Casson ternary nanofluid passing through a bidirectional exponential sheet by employing the innovative Cattaneo-Christov heat flux concept. The utilization of the energy equation considers thermal radiation, viscous dissipation, and heat source/sink effects, with the integration of chemical reaction effects into the concentration equation. An analysis of entropy generation is utilized to evaluate the thermodynamic irreversibility within the system. The conversion of transport equations involves a transformation from partial to ordinary differential equations, followed by a numerical solution utilizing the BVP4C solver embedded in the MATLAB package R2022b. The impacts of developed factors on thermal, concentration, and velocity behavior, as well as engineering quantities, are thoroughly explored graphically. The outcome reveals that the velocity gradients diminish as magnetic fields intensify, while it amplified by the Hall factor. The rise in temperature of ternary nanofluid correlates with elevated levels of radiation, and Brownian motion. Concentration intensifies with the rapid development of thermophoresis influences. Heightened values of the Reynolds and Brinkman numbers give rise to amplified entropy production but a decrease in the Bejan number. The ternary nanofluid displays a remarkable 8.92% increase in skin friction on the x-axis and y-axis, influenced by the potent Darcy-Forchheimer factor. The rates of mass and heat transfer in nanofluids undergo a decrease of 8.58% and 12.52%, respectively, due to the heightened influence of Brownian motion and Eckert number. The results could provide valuable insights into the performance of ternary nanofluids in various industrial environments under specific conditions.

Bioconvective magnetohydrodynamic flow of tangent hyperbolic nanofluid across a stretched surface, with Arrhenius activation and convective heat and slip conditions

The current study investigates mixed convective flow of an unsteady MHD tangent hyperbolic nanofluid due to a stretching surface with motile microorganisms via convective heat transfer and slip conditions. The flow analysis's governing equations were converted into a nondimensional relation by using the proper alteration. The pertinent similarity transformations are utilized in the main equations, and the solutions are obtained using the integrated bvp4c software. A good agreement with previously published data indicates the efficacy of the numerical technique. The following are the main findings: increasing the magnitude of the radiation and mixed convection parameters improves the velocity profile, whereas the Weissenberg number and magnetic field demonstrate the opposite influence; improvements in heat transfer occur due to the thermal radiation parameter, Brownian movement, and thermophoretic effects; activation energy improves concentration profile, whereas Lewis number shows opposite effect; bioconvection Lewis number and Peclet number declines the Motile microorganism density. Additionally, a tabular analysis of the skin friction, motile microorganism density, Nusselt number, and Sherwood number is also provided.

Brownian colloids in optothermal field: An experimental perspective

Colloidal matter undergoing Brownian motion serves as a model system to study various physical phenomena. Understanding the effect of external perturbation on the assembly and dynamics of “Brownian colloids” has emerged as a relevant research issue in soft matter and biological physics. Optical perturbation in the form of photonic forces and torques has added impetus to this exploration. In recent years, optothermal effects arising due to optical excitation of mesoscale matter have expanded the toolbox of light–colloidal matter interactions. In this perspective, we present an experimental viewpoint on some of the developments related to the assembly and dynamics of Brownian colloids driven by the optothermal field. Furthermore, we discuss some interesting prospects on driven colloidal matter that can have implications on soft matter physics and soft photonics.

An exactly solvable model for non-Fickian transport in dynamically heterogeneous media

Abstract Diffusion, observed in various condensed phases, finds its theoretical background in Einstein’s theory of Brownian motion, characterized by the linear time-dependence of mean square displacement (MSD) denoting Fickian behavior and the Gaussian distribution of particle displacement. Nevertheless, diverse systems exhibit either non-linear, non-Fickian time-dependence of the MSD or non-Gaussian displacement distribution. Montroll and Weiss’s continuous-time random walk (CTRW) model and the stochastic diffusivity (SD) model have provided insights into anomalous diffusion phenomena and Fickian-yet-non-Gaussian transport in dynamically heterogeneous environments, respectively. Building upon these approaches, Song et al developed a generalized transport equation with an environment-dependent diffusion kernel, providing a quantitative explanation for non-Fickian MSD and non-Gaussian displacement distribution. Based on the generalized transport equation, this study introduces an exactly solvable model for a non-Gaussian displacement distribution, accommodating arbitrary time profiles in its MSD, including both Fickian and non-Fickian behaviors. Our findings confirm the model’s capability in describing such transport processes. Furthermore, the proposed model unifies the CTRW model under fast environmental fluctuations and the SD model under Fickian time dependencies, making it suitable for understanding tracer particle motion within explicit solvent or complex media.

Numerical heat transfer analysis of Carreau nanofluid flow over curved stretched surface with nonlinear effects and viscous dissipation

The article presents a comprehensive study that thoroughly assesses the effects of Carreau fluid flow over a curved stretch surface. The study meticulously considers various factors, including nonlinear thermal radiation, convective boundary conditions, viscous dissipation, thermophoresis, Brownian motion, and nonlinear mixed convection. By using similarity variables, the problem's governing equations are transformed from nonlinear partial differential equations to nonlinear ordinary differential equations, and then the shooting method is applied to obtain the results. The study also rigorously examines the effect of modifying flow factors on velocity, temperature, and concentration in shear-thickening situations through graphical assessment. Furthermore, according to the corresponding values, a table is provided with data on skin friction, Nusselt, and Sherwood numbers. This study offers new perspectives on the complex mechanisms of Carreau fluids flowing over curved surfaces, with potential applications in materials engineering and fluid mechanics.

Heat and mass transfer analysis of s-PTT nanofluid in microchannels under combined electroosmotic and pressure-driven flows with wall slip using the homotopy perturbation method

The heat and mass transfer of the electroosmotic flow in microchannel transporting viscoelastic nanofluid is investigated considering Brownian motion of nanoparticles and slip boundary conditions. The simplified Phan-Thien-Tanner model is employed to describe the rheological behavior of fluid and the nonlinear Navier model with non-zero slip critical shear stress is considered at walls. The governing nonlinear momentum, mass, and heat transfer equations are solved using the Homotopy Perturbation Method. The study reveals that increasing the fluid elasticity, nanoparticle concentration, and size significantly enhances the flow rate, heat and mass transfer. Additionally, elasticity and Reynolds number decrease the friction factor. Reducing the double-layer thickness and increasing the Reynolds number lead to higher flow rates and fluid velocities. Notably, the findings emphasize the critical role of the slip conditions on the Sherwood and Nusselt numbers.

Resolvent decomposition with applications to semigroups and cosine functions

AbstractFor an operator whose domain is the kernel of a functional that is a finite sum of simpler functionals, we show that the resolvent of the operator can be decomposed as an affine combination of resolvents associated with these simpler functionals. Specifically, given an operator A and a finite number of functionals $$\phi $$ ϕ defined on the domain of A, we prove that the resolvent $$(\lambda - A_{|\ker \sum \phi })^{-1}$$ ( λ - A | ker ∑ ϕ ) - 1 is an affine combination of resolvents $$(\lambda - A_{|\ker \phi })^{-1}$$ ( λ - A | ker ϕ ) - 1 , provided that the sum of the functionals is nontrivial on the kernel of $$\lambda - A$$ λ - A . We use this result to derive generation theorems for semigroups and cosine functions.As applications, we prove that there are cosine functions associated with skew and snapping out Brownian motions on star graphs, and that skew Brownian motion can be approximated by snapping out Brownian motion.

Analysis of thermophoretic and Brownian diffusions in hydromagnetic curvilinear flow of Carreau nanofluid with activation energy and heat generation

This study presents a theoretical analysis of the thermophoretic and Brownian diffusion effects on the magnetized flow of Carreau nanofluid over a stretchable curved surface. The investigation includes the impact of heat generation and activation energy, which are incorporated into the energy and concentration equations, respectively. The mathematical model of the boundary layer flow is formulated as a set of nonlinear partial differential equations using curvilinear coordinates. These equations are transformed into ordinary differential equations through the application of appropriate similarity variables. The resulting system is solved numerically by using the shooting method along with the Runge-Kutta technique. The accuracy of the numerical results is further verified by the Keller-box method, a finite difference technique. The obtained results are also checked by giving a comparison table with the published data in the literature. Furthermore, the convergence of the solutions is also checked by a convergent series method known as the homotopy analysis method (HAM). The study examines the influence of several key parameters, including the radius of curvature, Weissenberg number, Prandtl number, Lewis number, Brownian and thermophoretic diffusions parameters, Hartmann number, heat generation parameter, activation energy parameter, temperature difference parameter, chemical reaction parameter, and power law index. The effects of these parameters on momentum, temperature, concentration distributions, mass and heat transfer rates, and as well as the skin friction coefficient are examined through graphs and tables. Graphical observations declare that the velocity field diminishes against the rising values of the Hartmann number and Weissenberg number. However, the velocity profile rises with improved values of the radius of curvature parameter and power law index parameter. It is also noticed that the magnitude of the concentration field rises with growing values of the Brownian parameter, activation energy parameter and Lewis number, whereas it shows a decreasing manner against the enhanced values of the thermophoresis parameter and temperature difference parameter.

The Upshots of Dufour and Soret in Stretching Porous Flow of Convective Maxwell Nanofluid with Nonlinear Thermal Emission

In this paper, the combined upshot of Soret and Dufoue of a convective Maxwell nanofluid on a porous perpendicular surface with nonlinear thermal emission was investigated. In the present work, the impact of permeable stretching sheet, nonlinear thermal emission, heat sour sink, Dufour and Soret effect, chemical reaction, Brownian motion and thermophoresis in a convective Maxwell nanofluid flow is widely discussed. The governing equations derived for the problem are highly nonlinear coupled partial differential equations. The governing equations were transformed into ordinary differential equations using Lie symmetry group alterations. The BVP4C MATLAB solver was employed to solve the ordinary differential equations numerically after validating the convergence of the method with existing results in the literature. The numerical results were established and discussed using tables and graphs. It was found that variations in porosity parameter (K), Dufour (Du) and Soret (Sr) improves velocity, temperature and concentration profiles respectively and the present of nonlinear thermal radiation and heat source emit more heat for the flow. Also, it is exciting to report that both porosity (K) and Dufour (Du) parameters has a strong impact on the flow of skin frictions, Nusselt number and Sherwood number. However, the current results may present applications in the areas of petroleum reservoir, heat exchangers, steel industries, cooling applications, nuclear waste disposal and so on.

Demonstrating Brownian motion and estimating Avogadro’s number using simple tools: a practical guide for students

Abstract Brownian motion provides crucial observational evidence for the kinetic molecular theory by demonstrating the random perpetual movement of small particles. This phenomenon underscores the existence and behaviour of atoms and molecules, fundamentally supporting our current understanding of molecular kinetic theory. Remarkably, in 1905 Albert Einstein was able to predict this motion exactly purely from a theoretical point of view and in 1908 Jean Perrin provided experimental proof. This provided experimental proof of the existence of atoms and molecules. This paper outlines a method to demonstrate and record Brownian motion using a drop of homogenised low fat milk, a microscope and a mobile phone. The captured video files can be analysed with Physics Tracker software, allowing for the estimation of Avogadro’s number.

Direct observation of the neural computations underlying a single decision

Neurobiological investigations of perceptual decision-making have furnished the first glimpse of a flexible cognitive process at the level of single neurons. Neurons in the parietal and prefrontal cortex are thought to represent the accumulation of noisy evidence, acquired over time, leading to a decision. Neural recordings averaged over many decisions have provided support for the deterministic rise in activity to a termination bound. Critically, it is the unobserved stochastic component that is thought to confer variability in both choice and decision time. Here, we elucidate this drift-diffusion signal on individual decisions. We recorded simultaneously from hundreds of neurons in the lateral intraparietal cortex of monkeys while they made decisions about the direction of random dot motion. We show that a single scalar quantity, derived from the weighted sum of the population activity, represents a combination of deterministic drift and stochastic diffusion. Moreover, we provide direct support for the hypothesis that this drift-diffusion signal approximates the quantity responsible for the variability in choice and reaction times. The population-derived signals rely on a small subset of neurons with response fields that overlap the choice targets. These neurons represent the integral of noisy evidence. Another subset of direction-selective neurons with response fields that overlap the motion stimulus appear to represent the integrand. This parsimonious architecture would escape detection by state-space analyses, absent a clear hypothesis.

Direct observation of the neural computations underlying a single decision.

Neurobiological investigations of perceptual decision-making have furnished the first glimpse of a flexible cognitive process at the level of single neurons. Neurons in the parietal and prefrontal cortex are thought to represent the accumulation of noisy evidence, acquired over time, leading to a decision. Neural recordings averaged over many decisions have provided support for the deterministic rise in activity to a termination bound. Critically, it is the unobserved stochastic component that is thought to confer variability in both choice and decision time. Here, we elucidate this drift-diffusion signal on individual decisions. We recorded simultaneously from hundreds of neurons in the lateral intraparietal cortex of monkeys while they made decisions about the direction of random dot motion. We show that a single scalar quantity, derived from the weighted sum of the population activity, represents a combination of deterministic drift and stochastic diffusion. Moreover, we provide direct support for the hypothesis that this drift-diffusion signal approximates the quantity responsible for the variability in choice and reaction times. The population-derived signals rely on a small subset of neurons with response fields that overlap the choice targets. These neurons represent the integral of noisy evidence. Another subset of direction-selective neurons with response fields that overlap the motion stimulus appear to represent the integrand. This parsimonious architecture would escape detection by state-space analyses, absent a clear hypothesis.

Differences in slow-release characteristics and release kinetics of three selenium nanoparticles from different synthesis strategies: Revealing the advantages synthesized by Lactiplantibacillus plantarum

The controlled release of selenium nanoparticles (SeNPs) is pivotal significance in improving bioavailability and mitigating potential side effects. Three types of SeNPs, Selenium nanoparticles synthesized by chemical method (CSeNPs), extracellular polysaccharide-encapsulated selenium nanoparticles (EPS-SeNP), and selenium nanoparticles synthesized by Lactiplantibacillus plantarum (LacSeNPs), were synthesized in this study using chemical reduction, polysaccharide-assisted, and microbial reduction methods, respectively. The selenium release kinetics of the nanoparticles were investigated in simulated gastrointestinal with five kinetics models. CSeNPs released 67.80% of selenium in simulated gastric fluids (SGF) and, depicting a Brownian motion fraction of 81.0. EPS-SeNPs released 77.38% of selenium in SGF while only releasing 16.28% in simulated intestinal fluids (SIF). The release process was primarily affected by changes in the nanoparticle structure after Super Case II Transport in SGF and the zero-order model in SIF. The zero-order model provided the best fit for releasing LacSeNP profiles in the SGF. In SIF, the release mechanism of LacSeNPs was regulated by combination of diffusion and carrier swelling or erosion, leading to non-Fickian diffusion. Therefore, synthetic nanoparticle methods determine their structures and compositions, leading to differences in their release kinetics and release mechanisms. Notably, the release of LacSeNPs in the SGF aligns with the absorption patterns of selenium within the human body. The current study elucidates the potential application advantages of SeNPs synthesized using microbial means as selenium-enriched supplements.

Dynamic X-ray Coherent Diffraction Analysis: Bridging the Time Scales between Imaging and Photon Correlation Spectroscopy.

The advent of diffraction limited sources and developments in detector technology opens up new possibilities for the study of materials in situ and operando. Coherent X-ray diffraction techniques such as coherent X-ray diffractive imaging (CXDI) and X-ray photon correlation spectroscopy (XPCS) are capable for this purpose and provide complementary information, although due to signal-to-noise requirements, their simultaneous demonstration has been limited. Here, we demonstrate a strategy for the simultaneous use of CXDI and XPCS to study in situ the Brownian motion of colloidal gold nanoparticles of 200 nm diameter suspended in a glycerol-water mixture. We visualize the process of agglomeration, examine the spatiotemporal space accessible with the combination of techniques, and demonstrate CXDI with 22 ms temporal resolution.

Equity-linked annuity valuation under fractional jump-diffusion financial and mortality models

The valuation of equity-linked annuity (EIA) has been extensively studied, while few papers consider the impact of long-range dependence (LRD) features on financial and mortality dynamics in EIAs' valuation. To characterise the LRD feature, we adopt the fractional Brownian motion (FBM) in modelling the dynamics of asset prices and mortality intensities, in which clustering jumps are captured by the compound Hawkes process. Besides, the interest rate dynamic is driven by the FBM and correlates to the asset price dynamic. Numerical analyses show that ignorance of the LRD feature and the jump component in the modelling framework could lead to a potential deficiency in the reserve and solvency capital of EIA policies.

Einstein–Perrin dilemma on the Brownian motion (Avogadro’s number) resolved?

The general recognition of the existence of atoms and molecules occurred only at the beginning of the twentieth century. Many researchers contributed to this, but the ultimate proof of the molecular nature of matter that convinced even the last sceptics was the confirmation of Albert Einstein’s statistical-fluctuation theory of Brownian motion, a part of his comprehension of interdisciplinary atomism, by Jean Perrin’s experiments on colloidal gamboge particles. Einstein noticed a difference between the values of Avogadro’s constant derived from Perrin’s experiments and Planck’s calculation from black-body radiation. Einstein assumed the incorrectly evaluated size of the gamboge spherules to be a culprit of the difference and asked Perrin to check the assumption with additional experiments and using the viscosity formula introduced in his own dissertation. The result was a discrepancy that neither Einstein nor Perrin settled any further. In this communication, based on the survey of developments in colloid and polymer science and their comparison with relevant experiments, an explanation of the dilemma is given that now, after more than a century, proves Einstein correct. The comparison was de facto possible during his lifetime.