Brownian Motion Research Articles

Ti3C2T x MXene Additives for Enhanced Pool Boiling Regime.

This study investigates the potential applications of MXenes as an additive in heat-exchanging fluids under atmospheric pressure conditions. A low concentration of 0.1 wt % titanium carbide (Ti3C2T x ) MXene-enhanced deionized water altered the boiling regime by demonstrating high critical heat flux (CHF) of 2110.1 kW/m2 and heat transfer coefficient (HTC) 163.6 kW/m2 °C, representing a 70.1% increase in CHF and a 213.5% increase in HTC compared to deionized water. Rheological studies were conducted to determine the optimal MXene concentration for long-term stability in the base fluid, ensuring suitability for large-scale industrial applications. Notably, Ti3C2T x MXene dispersion demonstrated an 11% enhancement in CHF and a 45% enhancement in HTC compared to the highest reported values for Ag/ZnO-enhanced fluids on plain copper substrates in the literature. This shift in boiling regime is attributed to a combined mechanisms involving thermophoretic and Brownian motion that facilitated the circulation of the Ti3C2T x MXene flakes before their stratification on the copper heater surface, which further led to improved interfacial properties such as surface roughness, wettability, and conductivity. This study provides insights on rheological property modulation and Ti3C2T x MXene enhanced heat transfer fluid-surface interactions in pool boiling efficiency.

Barrier option pricing and hedging model under stochastic conditions

The application of barrier options is wide and diverse. This article formulates a pricing and hedging framework for barrier options within a stochastic environment, where the dynamics of interest rates are captured through the application of the Vasicek model. We further utilize the Dubins-Schwarz theorem and Girsanov theorem to transform the measure. Using the joint distribution of Brownian motion, the analytical solutions of the model are obtained. Finally, this article provides explicit solutions for barrier option price, delta and gamma under random interest rate conditions. A comparative analysis between the PDE method and our method validates our solution. In the numerical analysis, we take the up-and-out call option as an example to analyse the sensitivities of barrier level and volatility of the barrier asset, then discuss the impact of the relativity of the barrier asset and no-default zero-coupon on the price. This conclusion gives different inspirations for hedging.

Polar Coordinates for the 3/2 Stochastic Volatility Model

ABSTRACTThe 3/2 stochastic volatility model is a continuous positive process s with a correlated infinitesimal variance process . The exact definition is provided in the Introduction immediately below. By inspecting the geometry associated with this model, we discover an explicit smooth map from to the punctured plane for which the process satisfies an SDE of a simpler form, with independent Brownian motions and the identity matrix as diffusion coefficient. Moreover, is recoverable from the path by a map that depends only on the distance of from the origin and the winding angle around the origin of . We call the process together with its map to the polar coordinate system for the 3/2 model. We demonstrate the utility of the polar coordinate system by using it to write this model's asymptotic smile for all strikes at t = 0. We also state a general theorem on obstructions to the existence of a map that trivializes the infinitesimal covariance matrix of a stochastic volatility model.

Large deviation principle for a 2D liquid crystal model with multiplicative noise

In this paper, we consider a stochastic 2D liquid crystal system with a small multiplicative noise of Gaussian type, which models the dynamic of nematic liquid crystals under the influence of stochastic external forces. We derive a large deviation principle for the model. The proof relies on the weak convergence method that was introduced in [A. Budhiraja, P. Dupuis and V. Maroulas, Variational representations for continuous time processes, Ann. Inst. Henri Poincaré Probab. Stat. 47(3) (2011) 725–747] and based on a variational representation on infinite-dimensional Brownian motion.

Unsteady MHD flow of tangent hyperbolic ternary hybrid nanofluid in a darcy-forchheimer porous medium over a permeable stretching sheet with variable thermal conductivity

Background This research investigates the unsteady magnetohydrodynamic (MHD) flow, heat, and mass transfer of tangent hyperbolic ternary hybrid nanofluids over a permeable stretching sheet. The study considers three types of nanoparticles—aluminum oxide (Al₂O₃), copper (Cu), and titanium oxide (TiO₂)—dispersed in a base fluid of ethylene glycol (C₂H₆O₂). This ternary hybrid nanofluid (Al₂O₃–Cu–TiO₂/C₂H₆O₂) has potential applications in cooling systems, biomedical uses for targeted drug delivery and hyperthermia treatments, heat exchangers, and polymer processing techniques like extrusion and casting. Methods The study examines the effects of various parameters, including the Weissenberg number, power law index, nanoparticle volume fraction, viscous dissipation, magnetic field, heat generation, nonlinear thermal radiation, temperature ratio, Joule heating, Brownian motion, thermophoresis, porous permeability, variable thermal conductivity, Eckert number, Prandtl number, Schmidt number, chemical reaction, velocity ratio, Forchheimer number, and unsteady parameters. The governing equations are transformed into similarity equations using appropriate transformations and solved numerically with the MATLAB BVP5C package. The results are validated against data from published articles to ensure reproducibility. Results The findings reveal that an increase in the Weissenberg and Forchheimer numbers reduces the velocity profile, while the temperature distribution increases. The variable thermal conductivity parameter (Γ) leads to a higher temperature profile, indicating improved heat transfer. Higher nanoparticle concentrations in the nanofluids and hybrid nanofluids result in enhanced skin friction, Nusselt number, and Sherwood number. Ternary hybrid nanofluids show the most significant improvement in heat transfer and thermal conductivity. Conclusions Ternary hybrid nanofluids significantly enhance heat and mass transfer, showing potential for applications in cooling systems, drug delivery, and polymer processing. The numerical results are consistent with previous research, confirming the reliability and reproducibility of the findings

Universality in the dynamical phase transitions of Brownian motion

We study the dynamical phase transitions (DPTs) appearing for a single Brownian particle without drift. We first explore how first-order DPTs in large deviations can be found even for a single Brownian particle without any force upon raising the dimension to higher than 4. The DPTs accompany temporal phase separations in their dynamical paths, which we numerically confirm by fitting to scaling functions. We next investigate how second-order DPTs can appear in one-dimensional free Brownian motion by choosing the observable, which essentially captures the localization transition of the trajectories. We discuss and confirm that the DPTs predicted for high dimensions can also be found when considering many Brownian particles at lower dimensions. Published by the American Physical Society 2025

Nanofluids for Advanced Applications: A Comprehensive Review on Preparation Methods, Properties, and Environmental Impact.

Nanofluids, an advanced class of heat transfer fluids, have gained significant attention due to their superior thermophysical properties, making them highly effective for various engineering applications. This review explores the impact of nanoparticle integration on the thermal conductivity, viscosity, and overall heat transfer performance of base fluids, highlighting improvements in systems, such as heat exchangers, electronics cooling, PV/T systems, CSP technologies, and geothermal heat recovery. Key mechanisms such as nanolayer formation, Brownian motion, and nanoparticle aggregation are discussed, with a focus on hybrid nanofluids that show enhanced thermal conductivity. The increase in viscosity poses a trade-off, necessitating careful control of the nanoparticle properties to optimize heat transfer while reducing energy consumption. Empirical data show up to a 123% increase in the convective heat transfer coefficients, demonstrating the tangible benefits of nanofluids in energy efficiency and system miniaturization. The review also considers the environmental impacts of nanofluid use, such as potential toxicity and the challenges of sustainable production and disposal. Future research directions include developing hybrid nanofluids with specific properties, integrating nanofluids with phase change materials, and exploring new nanomaterials such as metal chalcogenides to enhance the efficiency and sustainability of thermal management systems.

On the Curvature of the Bachelier Implied Volatility

Our aim in this paper is to analytically compute the at-the-money second derivative of the Bachelier implied volatility curve as a function of the strike price for correlated stochastic volatility models. We also obtain an expression for the short-term limit of this second derivative in terms of the first and second Malliavin derivatives of the volatility process and the correlation parameter. Our analysis does not need the volatility to be Markovian and can be applied to the case of fractional volatility models, both with H<1/2 and H>1/2. More precisely, we start our analysis with an adequate decomposition formula of the curvature as the curvature in the uncorrelated case (where the Brownian motions describing asset price and volatility dynamics are uncorrelated) plus a term due to the correlation. Then, we compute the curvature in the uncorrelated case via Malliavin calculus. Finally, we add the corresponding correlation correction and we take limits as the time to maturity tends to zero. The presented results can be an interesting tool in financial modeling and in the computation of the corresponding Greeks. Moreover, they allow us to obtain general formulas that can be applied to a wide class of models. Finally, they provide us with a precise interpretation of the impact of the Hurst parameter H on this curvature.

European option pricing under a generalized fractional Brownian motion Heston exponential Hull–White model with transaction costs by the Deep Galerkin Method

European option pricing under a generalized fractional Brownian motion Heston exponential Hull–White model with transaction costs by the Deep Galerkin Method

Dynamical metastability and re-entrant localization of trapped active elements with speed and orientation fluctuations

We explore the dynamics of active elements performing persistent random motion with fluctuating active speed and in the presence of translational noise in a d-dimensional harmonic trap, modeling active speed generation through an Ornstein-Uhlenbeck process. Our approach employs an exact analytic method based on the Fokker-Planck equation to compute time-dependent moments of any dynamical variable of interest across arbitrary dimensions. We analyze dynamical crossovers in particle displacement before reaching the steady state, focusing on three key timescales: speed relaxation, persistence, and dynamical relaxation in the trap. Notably, for slow active speed relaxation, we observe an intermediate-time metastable saturation in the mean-squared displacement before reaching the final steady state. The steady-state distributions of particle positions exhibit two types of non-Gaussian departures based on control parameters: bimodal distributions with negative excess kurtosis and heavy-tailed unimodal distributions with positive excess kurtosis. We obtain detailed steady-state phase diagrams using the exact calculation of excess kurtosis, identifying Gaussian and non-Gaussian regions and potential re-entrant transitions. Published by the American Physical Society 2025

Carbon-contract-for-difference (CCfD) and green transition of coal power under dual price uncertainties in the Korean market—a real options approach

ABSTRACT Carbon pricing under the Korean Emission Trading System (K-ETS) is the most widely accepted policy for internalizing the externalities caused by greenhouse gas emissions to firms’ production decisions. However, the effect of K-ETS has been questioned because of two problems, namely low level and high volatility of carbon prices and time-inconsistent preferences of governments, which causes firms to hold their investment decisions. Carbon contract for difference (CCfD) can be an effective solution to these problems by serving as a credible commitment vehicle. This study analyzes the optimum investment trigger prices of carbon and subsidy for CACPs based on the Geometric Brownian Motion (GBM). As coal power generates about 80% of the power sector’s carbon emissions in Korea, CACPs are rising as an important alternative to reduce carbon emissions and mitigate the social cost of phasing out coal plants with remaining operational life expectancy. The uncertainty of both carbon prices and subsidy prices is considered. The results indicate that the investment trigger price under the current ETS is 95.0 USD/ton-CO2 and that under CCfD is 52.5 USD/ton-CO2. This paper shows that CCfD can reduce the burden that customers must eventually bear to meet Korea’s Nationally Determined Contribution (NDC) goal.

Temperature-Dependent Wax Precipitation Characteristics in Gas Condensates: Composition, Aggregation, and Crystallization Patterns.

This study investigates the characteristics of the wax precipitation activity in the condensates. The patterns of wax precipitation are elucidated by analyzing the composition and amount of precipitate produced at various temperatures, verifying the influence mechanism of factors such as condensate composition and temperature on wax separation. The findings reveal that a decrease in the temperature enhances the contact of wax molecules by reducing their thermal motion, leading to wax particle precipitation. This also weakens the Brownian motion of precipitated wax, further promoting their aggregation and subsequent deposition. Consequently, the amount of wax precipitate increased as the temperature drops. Moreover, an increase in asphaltenes and resins in the condensates raises the critical crystalline radius of wax, making wax precipitation more difficult. Therefore, the amount of wax precipitate decreases as the concentration of asphaltenes and resins in the condensates increases. Additionally, because the solubilities of different hydrocarbon components change at different rates with decreasing temperature, lower carbon number hydrocarbons precipitate more actively in the early stages, with their precipitation rate declining as their concentration in the system diminishes. This relatively increases the precipitation rate of higher carbon number hydrocarbons in the later stage, increasing the proportion of high carbon number components in the composition curve of the wax deposit as the temperature decreases. Finally, the four components of the system-saturated hydrocarbons, aromatic hydrocarbons, asphaltenes, and resins-exhibit different precipitation behaviors as the temperature decreases, and their precipitation proportions show different trends at various temperatures. This study provides data to enrich the theoretical understanding of wax precipitation mechanisms in condensates under well-bore environmental conditions. It can support the development of effective wax blockage prevention strategies in reservoir development.

Two-dimensional Brownian motion with dependent components: Turning angle analysis.

Brownian motion in one or more dimensions is extensively used as a stochastic process to model natural and engineering signals, as well as financial data. Most works dealing with multidimensional Brownian motion consider the different dimensions as independent components. In this article, we investigate a model of correlated Brownian motion in R2, where the individual components are not necessarily independent. We explore various statistical properties of the process under consideration, going beyond the conventional analysis of the second moment. Our particular focus lies on investigating the distribution of turning angles. This distribution reveals particularly interesting characteristics for processes with dependent components that are relevant to applications in diverse physical systems. Theoretical considerations are supported by numerical simulations and analysis of two real-world datasets: the financial data of the Dow Jones Industrial Average and the Standard and Poor's 500, and trajectories of polystyrene beads in water. Finally, we show that the model can be readily extended to trajectories with correlations that change over time.

Brownian motion at various length scales with hydrodynamic and direct interactions

Brownian motion is essential for describing diffusion in systems ranging from simple to complex liquids. Unlike simple liquids, which consist of only a solvent, complex liquids, such as colloidal suspensions and the cytoplasm of a cell, are mixtures of various constituents with different shapes and sizes. Describing Brownian motion in such multiscale systems is extremely challenging because direct and many-body hydrodynamic interactions (and their interplay) play a pivotal role. Diffusion of small particles is mainly governed by a low viscous character of the solution, whereas large particles experience a highly viscous flow of the complex liquid on the macro scale. A quantity that encodes hydrodynamics on both length scales is the wavevector-dependent viscosity. Assuming this quantity to be known—in contrast to most studies in which the solvent shear viscosity is given—provides a new perspective on studying the diffusivity of a tracer, especially in situations where the tracer size can vary by several orders of magnitude. Here, we start systematic studies of exact formal microscopic expressions for the short- and long-time self-diffusion coefficients of a single probe particle in a complex liquid in terms of short-ranged hydrodynamic response kernels. We study Brownian motion as a function of the probe size, contrasting most theories that focus on self-diffusion as a function of the crowder volume fraction. We discuss the limits of small and large probe sizes for various levels of approximations in our theory and discuss the current successes and shortcomings of our approach.

A numerical simulation of electrically conducting Sisko fluid flow with melting heat transfer, nonlinear convection and variable thermal conductivity constraints over an inclined electromagnetic sheet

AbstractThe effects of suction, melting heat transfer, variable thermal conductivity, and viscous dissipation upon the convective flow of Sisko fluid over an electromagnetic inclined sheet are reported in the present study. The mechanisms of thermophoresis and Brownian motion are also taken into consideration. The 4th‐order R‐K method has been used to tackle reduced leading equations dedicated to the problem's relevant geometry. The key finding of the current investigation is that increased electromagnetic field strength, thermal and solutal mixed convection parameters, and Sisko fluid parameters are credited for enhanced fluid motion, whereas the increased melting parameter results in increased heat transmission rate from the electromagnetic sheet. The fluid suction, on the other hand, decreases the flow velocity and associated thickness of the momentum boundary layer.

Hydromagnetic micropolar nanofluid heat and mass transfer in a porous channel with thermophoresis, brownian motion and non-uniform heat source

Hydromagnetic micropolar nanofluid heat and mass transfer in a porous channel with thermophoresis, brownian motion and non-uniform heat source

Nanoparticle sizing in the presence of large particles by oblique incident dynamic ultrasound scattering method

Abstract Dynamic ultrasound scattering methods are becoming established to allow measurements of the dynamics of microparticles in Brownian motion. Using a focused transducer, nanoparticles can be analyzed, but applying strong ultrasound to large submicron particles causes problems with excessive acoustic energy that interferes with the dynamics of the particles. Backscattering is an attractive setup that maximizes spatial resolution, but when the sample thickness is reduced to eliminate the acoustic flow effects, the reflected waves of two cell window that sandwich the suspension and the weak particle scattering signal interfere with each other. Therefore, a new technique was attempted to remove the reflected waves and extract only the scattered waves. After showing that the acoustic energy does not interfere with the analysis of nanoparticles even in the presence of large particles, we showed that these sizes can be extracted simultaneously, using a mixture of particles with diameters of 50 and 500 nm.

Two‐phase flow of dusty Carreau nanofluid with dual‐Cattaneo–Christov heat flux and non‐uniform heat source over a disk

AbstractThe main aim of the present work is to examine a mathematical model for the flow and heat transfer characteristics of a Carreau nanofluid with suspended dust particles over a rotating disk. It explores the influence of dual Cattaneo–Christov heat flux models, which combine relaxation and thermal retardation effects, on the temperature distribution in the fluid. By integrating theoretical models with real‐world engineering problems, this study advances our understanding of expertise in optimizing systems such as dusty flows and nanofluids. The BVP4C built‐in solver in MATrix LABoratory (MATLAB) software is used to solve the governing equations using the shooting technique. A graphic representation of the relationship between temperature, velocity, concentration, skin friction coefficients, heat, and mass transfer rates over the rotating disk is displayed for a range of values of the pertinent parameters, such as interaction parameter , Weissenberg number , mass concentration Hartmann number , Thermal radiation , Thermophoresis , Brownian motion , fluid temperature , Space‐dependent parameter , the specific heat ratio . The Graphs and tables illustrate the impacts of active parameters on the fluid's transport properties. An increase in Hartmann's number decelerates the radial and azimuthal velocities for fluid and dusty flow cases. For the radiation parameter (Rd = 0.5), the Nusselt number is 4.8. When the Radiation parameter increases to 1.5, the Nusselt number improves to 6.3, representing a 31.25% enhancement in heat transfer efficiency. Also, it was observed that the temperature profile increases as the Nusselt number rises, indicating better thermal transport due to thermophoretic forces.

Viscous dissipation effects on heat propagating MHD nanofluid flow induced by the Brownian motion and thermophoresis impacts in a vertical cone with convective surface conditions

Viscous dissipation effects on heat propagating MHD nanofluid flow induced by the Brownian motion and thermophoresis impacts in a vertical cone with convective surface conditions

A Population Representation of the Confidence in a Decision in the Parietal Cortex.

Confidence in a decision is the belief, prior to feedback, that one's choice is correct. In the brain, many decisions are implemented as a race between competing evidence-accumulation processes. We ask whether the neurons that represent evidence accumulation also carry information about whether the choice is correct (i.e., confidence). Monkeys performed a reaction time version of the random dot motion task. Neuropixels probes were used to record from neurons in the lateral intraparietal (LIP) area. LIP neurons with response fields that overlap the choice-target contralateral to the recording site ( neurons) represent the accumulation of evidence in favor of contralateral target selection. We demonstrate that shortly before a contralateral choice is reported, the population of neurons contains information about the accuracy of the choice (i.e., whether the choice is correct or incorrect). This finding is unexpected because, on average, neurons exhibit a level of activity before the report that is independent of reaction time and evidence strength-both strong predictors of accuracy. This apparent contradiction is resolved by examining the variability in neuronal responses across the population of neurons. While on average, neurons exhibit a stereotyped level of activity before a contralateral choice, many neurons depart from this average in a consistent manner. From these neurons, the accuracy of the choice can be predicted using a simple logistic decoder. The accuracy of the choice predicted from neural activity reproduces the hallmarks of confidence identified in human behavioral experiments. Therefore, neurons that represent evidence accumulation can also inform the monkey's confidence.