Brownian Motion Research Articles

On the pointwise regularity of the Multifractional Brownian Motion and some extensions

We study the pointwise regularity of the Multifractional Brownian Motion and, in particular, we obtain the existence of so-called slow points of the process, that is points which exhibit a slow oscillation instead of the a.e. regularity. This result entails that a non self-similar process can also exhibit such a behavior. We also consider various extensions with the aim of imposing weaker regularity assumptions on the Hurst function without altering the regularity of the process.

Simultaneous Model Change Detection in Multivariate Linear Regression With Application to Indonesian Economic Growth Data

In this paper, we study asymptotic model change detection in multivariate linear regression by using the Kolmogorov–Smirnov function of the partial sum process of recursive residuals. We approximate the rejection region and also the power function of the test by establishing a functional central limit theorem for the sequence of the partial sum processes of the recursive residuals of the observations. When the assumed model is true, the limit process is given by the standard multivariate Brownian motion which does not depend on the regression functions. However, when the assumed model is not true (some models change), the limit process is represented by a vector of deterministic trend plus the standard multivariate Brownian motion. The finite sample size rejection region and the power of the test are investigated by means of Monte Carlo simulation. The simulation study shows evidence that the proposed test is consistent in the sense that it attains the power larger than the size of the test when the hypothesis is not true. We also demonstrate the application of the proposed test method to Indonesian economic growth data in which we test the adequacy of three-variate low-order polynomial model. The test result shows that the growth of the Indonesian economy is neither simultaneously constant nor linear. The test has successfully detect the appearance of a change in the model which is mainly caused by the COVID-19 pandemic in 2020.

Parisian times for linear diffusions

We compute the joint distribution of the first times a linear diffusion makes an excursion longer than some given duration above (resp. below) some fixed level. In the literature, such stopping times have been introduced and studied in the framework of Parisian barrier options, mainly in the case of Brownian motion with drift. We also exhibit several independence properties, and provide some formulae for the associated ruin probabilities.

Enzymatic Reaction Enhanced Diffusion Accelerates Cargo Transport through Micro/Nano-Channels.

Energy conversion and transfer of enzyme-catalyzed reactions at molecular level are an interesting and challenging scientific topic that helps understanding biological processes in nature. In this study, it is demonstrated that enzyme-catalyzed reactions can enhance diffusion of surrounding molecules and thus accelerate cargo transport within 1D micro/nanochannels. Specifically, urease is immobilized on the inner walls of silica micro/nano-tubes to construct bio-catalytically active micro/nanochannels. The catalytic reaction inside the channels drives a variety of cargoes, including small dye molecules, polymers, and rigid nanoparticles (e.g., quantum dots, QDs), to pass through these micro/nanochannels much faster than they will by free diffusion. The enhanced diffusion of molecular species inside the channels is validated by direct observation of the Brownian motion of tracer particles, and further confirmed by significantly enhanced Raman intensity of reporter molecules. Finite element and Brownian dynamics simulations provide a theoretical understanding of these experimental observations. Furthermore, the effect of the channels' size on the diffusion enhancement is examined. The acceleration effect of the cargo transport through these enzymatically active micro/nanochannels can be turned on or off via chemical activators or inhibitors. This study provides valuable insights on the design of biomimetic channels capable of controlled and efficient transmembrane transport.

Anomalous diffusion of synaptic vesicles and its influences on spontaneous and evoked neurotransmission.

Neurons in the central nervous system communicate with each other by activating billions of tiny synaptic boutons distributed along their fine axons. These presynaptic varicosities are very crowded environments, comprising hundreds of synaptic vesicles. Only a fraction of these vesicles can be recruited in a single release episode, either spontaneous or evoked by action potentials. Since the seminal work by Fatt and Katz, spontaneous release has been modelled as a memoryless process. Nevertheless, at central synapses, experimental evidence indicates more complex features, including non-exponential distributions of release intervals and power-law behaviour in their rate. To describe these features, we developed a probabilistic model of spontaneous release based on Brownian motion of synaptic vesicles in the presynaptic environment. To account for different diffusion regimes, we based our simulations on fractional Brownian motion. We show that this model can predict both deviation from the Poisson hypothesis and power-law features in experimental quantal release series, thus suggesting that the vesicular motion by diffusion could per se explain the emergence of these properties. We demonstrate the efficacy of our modelling approach using electrophysiological recordings at single synaptic boutons and ultrastructural data. When this approach was used to simulate evoked responses, we found that the replenishment of the readily releasable pool driven by Brownian motion of vesicles can reproduce the characteristic binomial release distributions seen experimentally. We believe that our modelling approach supports the idea that vesicle diffusion and readily releasable pool dynamics are crucial factors for the physiological functioning of neuronal communication. KEY POINTS: We developed a new probabilistic model of spontaneous and evoked vesicle fusion based on simple biophysical assumptions, including the motion of vesicles before they dock to the release site. We provide closed-form equations for the interval distribution of spontaneous releases in the special case of Brownian diffusion of vesicles, showing that a power-law heavy tail is generated. Fractional Brownian motion (fBm) was exploited to simulate anomalous vesicle diffusion, including directed and non-directed motion, by varying the Hurst exponent. We show that our model predicts non-linear features observed in experimental spontaneous quantal release series as well as ultrastructural data of synaptic vesicles spatial distribution. Evoked exocytosis based on a diffusion-replenished readily releasable pool might explain the emergence of power-law behaviour in neuronal activity.

Spectral quasi-linearization approach for the swimming of motile microorganisms on the bio-convection Casson nanofluid flow over a rotating circular disk

The ability of motile microorganisms is used to design of biomedical nanofluidic devices that utilize for targeted drug delivery, to influence heat transfer in nanofluids that are applied to the optimization of cooling system, in biotechnological processes where precise control over fluid flow, etc. However, based upon the several facts, the current investigation lead to propose the heat transfer characteristic of motile microorganisms swimming in a flow of bio-convection nanofluid over a rotating circular disk. The proposed study explores the impacts of dissipative heat generated by the movement of microorganisms, thermal radiation, and chemical reactions. The impact of cross-diffusive property organized by the implementation of Brownian motion and thermophorsis energies the flow phenomena of bio-convection. The set of coupled nonlinear system of non-dimensional equations is obtained by the implementation of similarity rules and further quasi-linearization method is utilized for the solution of this system. The characteristics of diversified parameters are presented through graphs with the variation of the proposed factors within their certain limitations and thee discuss briefly. Further, the important outcomes of the study are presented as; the fluid velocity decelerates due to the enhanced non-Newtonian Casson parameter, whereas the radiating heat for the inclusion of thermal radiation and coupling parameter, that is, Eckert number boosts up the heat transport phenomena.

Continuous psychophysics shows millisecond-scale visual processing delays are faithfully preserved in movement dynamics.

Image differences between the eyes can cause interocular discrepancies in the speed of visual processing. Millisecond-scale differences in visual processing speed can cause dramatic misperceptions of the depth and three-dimensional direction of moving objects. Here, we develop a monocular and binocular continuous target-tracking psychophysics paradigm that can quantify such tiny differences in visual processing speed. Human observers continuously tracked a target undergoing Brownian motion with a range of luminance levels in each eye. Suitable analyses recover the time course of the visuomotor response in each condition, the dependence of visual processing speed on luminance level, and the temporal evolution of processing differences between the eyes. Importantly, using a direct within-observer comparison, we show that continuous target-tracking and traditional forced-choice psychophysical methods provide estimates of interocular delays that agree on average to within a fraction of a millisecond. Thus, visual processing delays are preserved in the movement dynamics of the hand. Finally, we show analytically, and partially confirm experimentally, that differences between the temporal impulse response functions in the two eyes predict how lateral target motion causes misperceptions of motion in depth and associated tracking responses. Because continuous target tracking can accurately recover millisecond-scale differences in visual processing speed and has multiple advantages over traditional psychophysics, it should facilitate the study of temporal processing in the future.

Soliton solutions of nonlinear stochastic Fitz-Hugh Nagumo equation

This study deals with the stochastic Fitz-Hugh Nagumo (FHN) equation and its multiple soliton solutions. The underlying model has numerous applications in neuroscience that express the pulse behavior of neurons. In general, different kinds of noise affect neurons, e.g., oscillations in the opening and closing of ion stations within cell membranes and the fluctuations of the different conductivities in the system. This fluctuation creates a sequence of stochastic excitation. Various applications are branching Brownian motion process, flame propagation, nuclear reactor theory, autocatalytic chemical reaction, mobility in neurons, population growth in the open environment, and liquid environment. So, need of the hour to consider the FHN equation under the impact of noise. The ϕ6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi ^6$$\\end{document}-model expansion method is used to extract the analytical solutions that give a dynamic attitude of the transmission for the nerve impulses of a nervous system. The different constraint conditions for the existence of these solutions are also discussed. The solutions of this model are represented in hyperbolic, trigonometric, and rational forms. The 2 and 3-dimensional behavior of these solutions are depicted by choosing the different values of parameters. The impact of noise on the physical system is analyzed and its real-world applications are discussed. The spikes in the solutions are controlled through the Borel function. These important results will open a new horizon of research for the young researchers.

Pricing of geometric average Asian option under the sub-diffusion Merton interest rate model

. Asian option is an essentially new type of option. In existing option pricing models, the Brownian motion is generally the stochastic driving source of changes in the underlying asset price. This article explores the pricing problem of geometric average Asian option under the sub-diffusive Merton interest rate model. The results obtained the partial differential equations satisfied by the geometric average Asian option via constructing portfolios and utilizing the delta hedging technique. Finally, the findings provide display expressions for the geometric average Asian option under the sub-diffusive Merton interest rate model, combined with boundary conditions and variable substitutions.

Forward Starting Option Pricing under Double Fractional Stochastic Volatilities and Jumps

This paper aims to provide an effective method for pricing forward starting options under the double fractional stochastic volatilities mixed-exponential jump-diffusion model. The value of a forward starting option is expressed in terms of the expectation of the forward characteristic function of log return. To obtain the forward characteristic function, we approximate the pricing model with a semimartingale by introducing two small perturbed parameters. Then, we rewrite the forward characteristic function as a conditional expectation of the proportion characteristic function which is expressed in terms of the solution to a classic PDE. With the affine structure of the approximate model, we obtain the solution to the PDE. Based on the derived forward characteristic function and the Fourier transform technique, we develop a pricing algorithm for forward starting options. For comparison, we also develop a simulation scheme for evaluating forward starting options. The numerical results demonstrate that the proposed pricing algorithm is effective. Exhaustive comparative experiments on eight models show that the effects of fractional Brownian motion, mixed-exponential jump, and the second volatility component on forward starting option prices are significant, and especially, the second fractional volatility is necessary to price accurately forward starting options under the framework of fractional Brownian motion.

Numerical simulation of natural convection in a rectangular enclosure filled with porous medium saturated with magnetic nanofluid using Buongiorno's two‐component model

AbstractMotivated by studying emerging nanofluid‐based magnetic fuel cells and hybrid direct absorber solar collectors, a numerical study is presented for buoyancy‐driven flow in a vertical enclosure containing a porous medium saturated with magnetized nanofluid flow under a transverse static magnetic field. The enclosure features adiabatic side walls and vertical heat slits, ensuring consistent cold temperatures on the lower and upper bounded walls. The side walls of the regime are insulated, and the hot slits are centrally located on these walls. The finite difference method (FDM) is applied to employ the transformed dimensionless vorticity–stream function (VSF) formulation of the transport equations. The impact of pertinent parameters on isotherm, streamline, iso‐concentration, and average Nusselt and Sherwood numbers are visualized with contour plots and graphs. Increasing Darcy number values tend to amplify the isotherm magnitudes. Higher Hartmann (magnetic) number values, on the other hand, lead to a reduction in local Nusselt number profiles but do not significantly modify the local Sherwood number. The porous medium permeability, as simulated via the Darcy number, has a strong impact on streamlines, thermal contours, and iso‐concentrations. A reduction in Darcy's number suppresses local Nusselt and Sherwood numbers, whereas an elevation in Rayleigh's number enhances them. Increasing the Buongiorno nanoscale Brownian motion parameter enhances local Nusselt and Sherwood numbers at both cold walls of the enclosure. The simulations provide a deeper insight into enclosure flows involving electrically conducting nanofluids in advanced processing systems for nanomaterials and hybrid fuel cells utilizing electromagnetic and liquid fuel technologies.

Annihilating Branching Brownian Motion

Abstract We study an interacting system of competing particles on the real line. Two populations of positive and negative particles evolve according to branching Brownian motion. When opposing particles meet, their charges neutralize and the particles annihilate, as in an inert chemical reaction. We show that, with positive probability, the two populations coexist and that, on this event, the interface is asymptotically linear with a random slope. A variety of generalizations and open problems are discussed.

Numerical study of binary mixture and thermophoretic analysis near a solar radiative heat transfer

The main focus of the current article is to investigate the two-dimensional boundary layer flow of non-Newtonian fluid induced by a linear stretching surface in the streamwise direction. The flow features of non-Newtonian fluid (i.e. shear-thinning and thickening nature of the fluids) are explored with Carreau fluid model. In addition, thermophoresis, Brownian motion, thermal radiation (with Rosseland approximation), binary mixture and activation enthalpy are also incorporated in fluid model for better analysis of thermal and solutal properties. The mathematical modelling of under consider physical problem yields nonlinear partial differential system. The governing mathematical system is first simplified with scaling transformations for the high Reynolds number and then transformed into non-dimensional ordinary differential system by using the similarity variables. Since the governing mathematical system comprised on nonlinear boundary value problem, thus shooting method is utilized for the numerical solution of the fluid flow governing equations. The obtained results followed the qualitative manners of the previously reported data. The computed results for important physical quantities (i.e. velocity, temperature, and concentration) are presented through graphs and then interpreted physically. It is observed that the boundary layer thickness increased for shear thickening fluids (n>1) while it is reduced for shear thinning fluids (n<1). Also, the temperature of shear thinning fluid is higher than shear thickening fluid. In addition, heat generation and thermal radiations enhance the thermal boundary layer. Thermophoretic viscosity effect reduces the concentration profile significantly in the flow domain.

Female black bear home range and resource selection in relation to West Virginia mine lands

AbstractWildlife space use is a key component to consider when determining effective conservation and management practices. Home range size and resource selection can vary temporally and spatially depending on mortality risks in the area and access to food resources. Lands used for coal mining can contain unique mortality risks and food resources for American black bears (Ursus americanus) relative to surrounding landscapes due to hunting restrictions, vegetation planted as part of the reclamation process, and other anthropogenic food resources. We examined the influence of mining sites on resource selection of female black bears in southern West Virginia, USA, during 2007 and 2008. We estimated home range size with Brownian Bridge movement models and evaluated variation in home range size with mixed‐effects linear regression. We evaluated resource selection with mixed‐effects Poisson point process models. On mine sites, the mean 95% home range for female black bears was 1,996 ha (SD = 2,633) in the autumn and 544 ha (SD = 238) in the spring, and on non‐mine sites the mean 95% home range was 1,926 ha (SD = 1,292) in the autumn and 771 ha (SD = 480) in the spring. Our resource selection model indicated black bears used nonhunting zones associated with mine lands much greater than their availability, and that black bears in mine areas disproportionately used areas in close proximity to anthropogenic structures. Interannual variation in home range size was likely associated with mast conditions, because smaller home ranges were associated with high mast production. Our data suggest black bears may be using non‐hunting zones within mine lands as refugia from hunting and are using anthropogenic food sources available at refuse sites on mine lands, which may increase regional black bear populations in areas with high mining activity.

A computational analysis on two phase Eyring-Powell (non-Newtonian) dust particles flow for heat and mass transfer phenomenon with variable thermal features

In this instigation, the heat and mass transfer pattern on Eyring-Powell nanofluid with suspension of dust particles is focused. For heat transfer phenomenon, the Eyring-Powell nanofluid capturing the variable thermal conductivity. Furthermore, the variable and mass diffusivity assumptions are entertained for summarizing the observations chemical reaction phenomenon. The flow is endorsed to magnetic force impact. The additional impact of Brownian motion and thermophoresis consequences have been adopted. The numerical computations with shooting technique are performed. The physical aspects of parameters have been observed graphically. Based on depicted observations, it is examined that the fluid velocity reduces due to interaction velocity parameter which reverse trend is noted for dust particles velocity. The temperature profile for dusty fluid particles enhanced due to interaction parameter for temperature. Furthermore, the concentration profile reduces due to concentration interaction parameter. Current results present applications in solar energy, thermal processes, heat transform devices cooling systems, plasma, manufacturing processes, energy systems, etc.

P-adic Brownian motion is a scaling limit

A p-adic Brownian motion is a continuous time stochastic process in a p-adic state space that has a Vladimirov operator as its infinitesimal generator. The current work shows that any such process is the scaling limit of a discrete time random walk on a discrete group. Earlier work required the exponent of the Vladimirov operator to be in (1,∞) , and the convergence was the weak convergence of probability measures on the Skorohod space of paths on a compact time interval. The current approach simplifies the earlier approach, allows for any positive exponent, eliminates the restriction to compact time intervals, and establishes some moment estimates for the discrete time processes that are of independent interest.

External Electric Field Control of Exciton Motion in Porphyrin-Based Metal Organic Frameworks.

Porphyrins are excellent light-harvesting complexes. Presently they are unsuitable for photovoltaic applications, as their excellent light absorbance is compensated to a large extent by their poor transport properties, where most excitons are lost by recombination. Arranging porphyrins in regular, strongly bound, lattices of surface-anchored metal-organic frameworks (PP-SURMOFs) may facilitate charge carrier dissociation, but does not significantly enhance the conductive properties. In most cases, photogenerated excitons traverse undirected, Brownian motion through a hopping process, resulting in a substantial diffusion length to reach electrodes, leading to significant exciton loss through recombination. Here, we propose to guide exciton diffusion indirectly by an external electric field. We show that electric fields, even as strong as 1 V nm-1, do not affect the HOMO-LUMO gap of the porphyrins. However, fields of 0.1 V nm-1 and even less demonstrate a notable Stark effect, with slight band gap reductions, for some PP-SURMOFs. When applied as an electric field gradient, for instance, via the substrate, it creates a unidirectional hopping pathway for the excitons. Consequently, we expect a significant reduction of exciton diffusion length leading to increased utilization of photogenerated excitons as they reach the electrodes. This strategy holds promise for integrating photoactive molecules in photovoltaic and photocatalytic applications.

A Systematic Study on the Physicochemical Interactions Between Polymeric Micelles and Mucin: Toward the Development of Optimal Drug Delivery Nanocarriers

AbstractThe optimal performance of drug delivery formulations, including polymeric nanoparticles, relies on particle distribution throughout the body and the interactions with biological barriers, particularly mucosal layers, which often limit their potential. A systematic and comprehensive study is presented through a multidisciplinary approach combining conventional and novel techniques for in vitro studies to understand the key molecular interactions between polymeric micelles and mucin. The results shows that polymeric micelles are integrates within the mucin layer, mirroring its viscoelastic properties, evidenced as a dissipation difference of 0.1 ± 0.44, measured by quartz crystal microbalance with dissipation. Surface‐enhanced Raman scattering reveals predominant hydrogen bonding within the mucin's hydrophilic core, while the isothermal titration calorimetry method confirms multiple non‐specific binding sites on the protein backbone. By performing the periodic acid‐Schiff stain assay, a binding amount of 0.20 mg of mucin per milligram of nanoparticles is quantified. Furthermore, motility studies show the surface binding of mucin on the polymeric nanoparticles influencing their Brownian motion. This study sheds light toward the improvement for a better drug delivery formulation and fabrication of optimal nanoparticle colloidal systems, which can advance translational drug delivery technologies into clinical application while enriching the field of surface and colloidal chemistry.

Optical control and coherent coupling of spin diffusive modes in thermal gases

Quantum science and technology devices exploiting collective spins in thermal gases are extremely appealing due to their simplicity and robustness. This comes at the cost of dealing with the random thermal motion of the atoms which is usually an uncontrolled source of decoherence and noise. There are however conditions, for example, when diffusing in a buffer gas, where thermal atoms can occupy a discrete set of stable spatial modes. Diffusive modes can be extended or localized, have different magnetic properties depending on boundary conditions, and can react differently to external perturbations. Here, we selectively excite, manipulate, and interrogate the longest-lived of these modes by using laser light. In particular, we identify the conditions for the generation of modes that are exceptionally resilient to detrimental effects such as light induced frequency shifts and power-broadening, which are often the dominant sources of systematic errors in atomic magnetometers and comagnetometers. Moreover, we show that the presence of spatial inhomogeneities in the pump introduces a coupling that leads to a coherent exchange of excitation between the two longest-lived modes. Our results demonstrate that systematic engineering of the multi-mode nature of diffusive gases has great potential for improving the performance of quantum sensors based on alkali-metal thermal vapors, and opens new perspectives for quantum information applications. Published by the American Physical Society 2024

The new bond on the block — Designing a carbon-linked bond for sustainable investment projects

Over the last decade, the green bond market experienced strong growth rates fueled by the need to combat climate change. However, the discourse on enhancing the effectiveness of green bonds primarily revolves around regulatory measures, often overlooking the possibility of designing inherent incentives. We show that a green bond with a coupon structure positively related to the carbon price development stimulates (early) investment in an emission-reducing project and creates higher net present values (NPVs) when applied in project financing. In our simulation-based framework, we model carbon prices using a geometric Brownian motion, and create a general optimal stopping time problem regarding the start of the project. The green bond in our setting carries the risk of default, also mitigated by its carbon price-linked coupon structure.