Brownian Motion Research Articles

Playing with active matter

In the past 20 years, active matter has been a very successful research field, bridging the fundamental physics of nonequilibrium thermodynamics with applications in robotics, biology, and medicine. Active particles, contrary to Brownian particles, can harness energy to generate complex motions and emerging behaviors. Most active-matter experiments are performed with microscopic particles and require advanced microfabrication and microscopy techniques. Here, we propose some macroscopic experiments with active matter employing commercially available toy robots (the Hexbugs). We show how they can be easily modified to perform regular and chiral active Brownian motion and demonstrate through experiments fundamental signatures of active systems such as how energy and momentum are harvested from an active bath, how obstacles can sort active particles by chirality, and how active fluctuations induce attraction between planar objects (a Casimir-like effect). These demonstrations enable hands-on experimentation with active matter and showcase widely used analysis methods.

Current advancements in fluid-flow Problems: A brief review

This specific article is a compilation of a few current studies on fluid flow issues. This article provides an overview of current research on the experimental and theoretical analysis of various nanofluids' thermal conductivity. The current study examines a number of variables that have a significant impact on a nanofluid's ability to transfer heat, including temperature, solid volume fraction, type, size, shape, magnetic field, pH, ultrasonic time, and surfactant. In addition, some plausible and appealing theories that enhance the thermal conductivity of nanofluids are mentioned. The final important heat transmission mechanisms that play a significant part in improving thermal conductivity are Brownian motion, thermophoresis, nanoclustering, interfacial nano-layer, and osmophoresis. Thus, consideration is given to the heat transmission properties of nanofluids. And also discussed some Numerical method to solve fluid flow problems.

Reaction-diffusion for fish populations with realistic mobility

Nonlinear reaction-diffusion equations, with Fisher logistic growth and constant diffusion coefficient, have been used in fisheries research to estimate sustainable harvesting rates and critical domain sizes of no-take areas. However, constant diffusivity in a population density corresponds to standard Brownian motion of individuals, with a normal distribution for displacement over a fixed time interval. For available good data sets on mobile fish populations, the distribution is certainly not normal. The data can be fitted with a long-tailed stable Lévy distribution that results from diffusion by fractional Laplacian. Exact multidimensional solutions are developed here for realistic Fisher–Kolmogorov–Petrovski-Piscounov models with diffusion by fractional Laplacian. These can also account for a delay in the reaction term. It is then shown how to modify critical domain sizes of protected areas with Dirichlet and Robin boundary conditions for populations.

Stochastic harmonies: navigating Brownian paths through magnetic fields with Langevin approach

Stochastic harmonies: navigating Brownian paths through magnetic fields with Langevin approach

Finite Horizon Stochastic H2/H∞ Control for Continuous‐Time Systems Driven by G‐Brownian Motion

ABSTRACTIn this article, we consider a stochastic control problem under volatility ambiguity. In this framework, the state function is described by a stochastic differential equation driven by ‐Brownian motion. Different from the classical approach, the volatility ambiguity is characterized by a family of non‐dominated probability measures. control can be modeled as a “inf‐sup problem” and control can be modeled as a “sup‐sup problem.” With the help of stochastic maximum principle and dynamic programming principle, we derive the stochastic bounded real lemma and two sets of cross coupled generalized differential Riccati equations, which is associated with the solvability of control.

Reversible esterification process in Casson nanofluids: A numerical analysis of non-newtonian hydromagnetic flow

A computational mechanism has been formulated to scientifically analyze the phenomenon of combined convection in the occurrence of magnetohydrodynamic flow behavior of Casson nanofluid. This study emphasizes the trajectory of the nanofluid along a stretching sheet with nonlinear permeability, while considering additional physical effects such as reversible chemical reaction, thermal radiation, energy source/sink, suction and viscous dissipation. In this study, we have additionally integrated the nanofluid paradigm proposed by Buongiorno, which encompasses the repercussion of thermophoresis along with Brownian motion. The utilization of appropriate similarity renovations serves the purpose of recasting the dominant multivariate differential equations to a collection of nonlinear differential equations in single variable. The Runge–Kutta shooting mechanism is implemented for the intention of numerically determining the unknown boundary conditions. The solution to the dominant equations was obtained by employing the fourth-order Runge–Kutta technique and to ensure the dependability of the outcomes, the bvp4c method was employed. The graphical and tabulated observations are presented herein to facilitate a comprehensive analysis of the underlying physical characteristics inherent in the problem at hand. The utilization of the Casson parameter has been found to be advantageous in the reduction of shear stress rate, along with the enhancement of mass and energy transfer rates. Additionally, the application of suction has been observed to be beneficial in the enhancement of Sherwood number and energy transfer rate. Within the scope of the context of the esterification process, the purpose of this proposal is to evaluate the impact that numerous arithmetical values exert on the temperature field, the velocity profile and the volumetric concentration. An in-depth graphical analysis that takes into account the relevant physical consequences is used to evaluate the most important factors that relate to the physical quantities that describe the contours of temperature, velocity and concentration. In addition to being accompanied by their respective explanations, the tabular portrayal of the local Sherwood number, shear stress rate along with local Nusselt number all feature in this paper. There is a clear distinction that can be made between irreversible and reversible flows in the evaluation of the local Sherwood number, rate of shear stress and local Nusselt number. This differentiation is brought about by taking into analysis thermophoresis parameter, Brownian motion parameter and suction parameter. The results that were produced from the theoretical simulations have significant repercussions for a variety of fields that are related to energy engineering. The findings derived from the analysis indicate a negative correlation between the Brownian motion parameter and both irreversible and reversible flow in terms of rate of energy transfer and shear stress rate. It is imperative to highlight that reversible flow holds greater significance in comparison to irreversible flow.

Electroosmotic Flow-Driven DNA-CNT Nanomotor via Tunable Surface-Charged Nanopore Array.

Nanomotors are usually designed to work in liquid media and carry cargo; they exhibit excellent potential for biosensing and disease treatment applications due to their small size. Graphene and carbon nanotubes (CNTs) are crucial components of rotary nanomotors because of excellent mechanical properties and adaptability to the human body. Herein, we introduce a DNA-CNT-based nanomotor that achieves its rotational control through an array of nanopores with tunable surface charges. The findings demonstrate that by adjusting the surface charge density of the nanopores and the direction of electric field, a DNA strand can be sequentially captured by the nanopores, thereby rotating the connected CNT. The transition from a four-nanopore array to a six-nanopore array reveals that reducing the step angle to 60° significantly enhances the rotational stability of the nanomotor and reduces random fluctuations caused by Brownian motion. This method improves the control stability of the nanomotor, providing robust support for future applications in nanoscale manipulation.

Entropy generation in radiative motion of tangent hyperbolic nanofluid in the presence of gyrotactic microorganisms and activation energy

In this work, entropy generation is optimized through the application of the second law of thermodynamics. The slip mechanisms, Brownian diffusions, and thermophoresis are elaborated using the tangent hyperbolic nanomaterial model. Magnetohydrodynamic (MHD) fluid is taken into consideration. To characterize the impact of activation energy, a unique model involving the binary chemical reaction is deployed. The effects of mixed convection that is nonlinear in nature, bioconvection, and Joule effect are all taken into consideration. The key partial differential equations (PDEs) are reduced into ordinary differential equations (ODEs) by utilizing appropriate similarity transformations and then solved numerically with the help of a built-in ‘bvp4c’ technique of MATLAB software. Varied flow parameters’ impacts on the nanoparticle volume concentration, entropy number, microorganism concentration, temperature, and velocity fields are analyzed using graphs. Various flow variables are taken into consideration to calculate the total rate of entropy generation. The obtained results show that concentration irreversibility, Joule effect irreversibility, viscous dissipation, and heat irreversibility all influence the entropy. The numerical outcomes were observed by fixing the physical parameters as 0.1<α<4.0, 0.1<M<1.2, 0.1<Nr<2.2, 0.1<Le<2.2, 0.1<Nb<0.4, 0.1<Nt<1.0, 2.0<⁡Pr⁡<5.0, and 0.1<Lb<2.0, as well as their impact on the momentum, thermal, concentration, and microorganism density profiles. From results, an increasing estimate of the variable representing chemical reaction indicates a decline in the concentration. The higher the chemical reaction variable, Hartmann number, and Weissenberg number, the higher the entropy number, while the Bejan number has a contrary behavior. Subsequently, all the outcomes are plotted in graphs and discussed in detail, when subjected to the involving physical quantities.

GENERALIZED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY TWO MUTUALLY INDEPENDENT FRACTIONAL BROWNIAN MOTIONS

This paper deals with a class of generalized backward stochastic differential equations driven by two mutually independent fractional Brownian motions (FGBSDEs in short). The existence and uniqueness of solutions for FGBSDE as well as a comparison theorem are obtained.

Small Deviations for the Mutual Intersection Local Time of Brownian Motions

Small Deviations for the Mutual Intersection Local Time of Brownian Motions

Random Walks and Lorentz Processes

Random walks and Lorentz processes serve as fundamental models for Brownian motion. The study of random walks is a favorite object of probability theory, whereas that of Lorentz processes belongs to the theory of hyperbolic dynamical systems. Here we first present an example where the method based on the probabilistic approach led to new results for the Lorentz process: concretely, the recurrence of the planar periodic Lorentz process with a finite horizon. Afterwards, an unsolved problem—related to a 1981 question of Sinai on locally perturbed periodic Lorentz processes—is formulated as an analogous problem in the language of random walks.

Synthesis of Nanoparticles for Drug Delivery in Korea

Purpose: The aim of the study was to assess the synthesis of nanoparticles for drug delivery in Korea. Methodology: This study adopted a desk methodology. A desk study research design is commonly known as secondary data collection. This is basically collecting data from existing resources preferably because of its low cost advantage as compared to a field research. Our current study looked into already published studies and reports as the data was easily accessed through online journals and libraries. Findings: The study indicated that the synthesis of nanoparticles for drug delivery has emerged as a promising strategy to enhance the efficacy and precision of therapeutic interventions. Nanoparticles offer several advantages, such as improved bioavailability, targeted delivery, and controlled release of drugs. Various methods are employed in their synthesis, including chemical reduction, sol-gel processes, and biological methods using natural organisms. These nanoparticles can be engineered to carry a wide range of drugs, including chemotherapeutics, antibiotics, and vaccines. Their small size allows them to navigate biological barriers and deliver drugs directly to specific tissues or cells, reducing side effects and improving treatment outcomes. However, challenges such as scalability, toxicity, and regulatory hurdles remain, necessitating further research to optimize their clinical applications. Implications to Theory, Practice and Policy: Brownian motion theory, nanoscale phenomena theory, thermodynamic theory of nanoparticle stability may be used to anchor future studies on the synthesis of nanoparticles for drug delivery in Korea. Practitioners in the field should prioritize the enhancement of synthesis techniques and the focus on biocompatibility and safety to improve the practical applications of nanoparticle drug delivery systems. To ensure the safe and effective use of nanoparticles in drug delivery, policymakers must establish clear guidelines and regulations governing their application.

Fragility Analysis of Masonry Structures Subjected to Random Sequential Ground Motions

In this study, a fragility analysis of masonry structures is conducted using a random sequential ground motion model. Initially, the relationship between a mainshock and its aftershocks is clarified based on the physical mechanism of “source-path-local site”. Building on this, the random sequential ground motion model is developed by integrating a point-source model with a homogeneous isotropic medium model. A five-story masonry structure model is then constructed in ABAQUS (6.14), and its accuracy is validated through experimental testing. Following this, 21 sets of random sequential ground motions are generated. Using the Incremental Dynamic Analysis (IDA) method, 1260 nonlinear response samples of the structure under varying sequential ground motions are obtained, providing an insight into the fragility of the masonry structure subjected to these ground motions.

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) Temp increased 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.