Brownian Motion Research Articles

Convergence analysis of a fully discrete scheme for diffusion-wave equation forced by tempered fractional Brownian motion

In this paper, we investigate a fully discrete approximation of stochastic diffusion-wave equation driven by additive tempered fractional Gaussian noise. This additive noise exhibits semi-long range dependence. The model involves two nonlocal terms in time, i.e., a Caputo fractional derivative and a tempered fractional Brownian motion. The space discretization is achieved via the spectral Galerkin method. The Caputo fractional derivative of order α∈(1,2) is approximated by using the Grünwald–Letnikov formula. Combining Mittag-Leffler function, Laplace transform and z-transform, we establish the error estimates of the full discretization in the sense of mean-squared L2-norm. Numerical experiments are presented to confirm the strong convergence rates.

Buongiorno’s radiative Prandtl-Eyring nanofluid flow through porous medium over a stretching surface with cross-diffusion effects

The main focus of the current analysis is to describe the thermo-magnetic flow, heat and mass transport features of two-dimensional dissipative Prandtl-Eyring nanofluid (PE-NF) flow over a stretching sheet under the influence of porous medium and magnetic Ohmic dissipation numerically. An innovative Buongiorno’s nanofluid model in terms of Brownian motion and thermophoresis is deployed to accurately simulate the nano behavior in Prandtl-Eyring within the boundary layer regime. The thermal radiation and heat source/sink effects are also included to describe the thermal transport process. In addition to this, the thermo-diffusion and diffusion-thermo effect are included to demonstrate the temperature and concentration diffusion mechanism under the presence of chemical reaction process. The emerged coupled nonlinear two-dimensional time-independent partial differential equations are rendered to their dimensionless form through appropriate similarity transformations and solved by deploying Matlab-based BVP4C technique. The graphical visualization showed that, the increasing magnetic number diminished the flow field and enhanced the temperature and concentration profiles in the flow regime. Rising porous parameter decayed the Prandtl-Eyring nanofluid velocity. Increasing radiation and Eckert numbers enhance the temperature field in the flow regime. Magnifying Prandtl-Eyring parameter suppressed the velocity diffusion. Increasing Brownian motion and thermophoresis parameters increases the temperature profile. Amplifying Soret parameter upsurges the concentration profile. Skin-friction coefficient amplified with enhanced magnetic and porous numbers. Heat transfer rate acts as increasing function of thermophoresis and Brownian motion parameters. The main objective of this study is the addition of magnetic Ohmic dissipation, radiation, porous medium, thermal source/sink, Soret and Dufour effects and Buongiorno nanofluid model and this consideration generalizes former studies and gives a new re-defined mathematical formulation of heat and mass transport features of Prandtl-Eyring nanofluid flow over a stretching sheet. Finally, the numerical accuracy of the current similarity results is validated with available solutions and noticed a good agreement.

Multi-level Reflecting Brownian Motion on the Half Line and Its Stationary Distribution

Multi-level Reflecting Brownian Motion on the Half Line and Its Stationary Distribution

Probability of entering an orthant by correlated fractional Brownian motion with drift: exact asymptotics

Probability of entering an orthant by correlated fractional Brownian motion with drift: exact asymptotics

Prediction of dynamic behaviors of vibrational-powered electromagnetic generators: Synergies between analytical and artificial intelligence modelling

The electric efficiency of vibrational electromagnetic generators is highly dependent on their ability to ensure effective adaptability to uncertain and irregular dynamics of mechanical energy sources. Such adaptive ability demands a planning operation considering future information of the highly nonlinear dynamics of these generators and mechanical excitations patterns. High accurate energy predictions are then mandatory for high energy generation efficiencies. However, on the one hand, high prediction accuracy by analytical modelling from first principles requires high modelling complexity; on the other hand, artificial intelligence models ensuring high prediction accuracy have not yet been explored to enhance the performance of these generators, even though their pre-training holds potential to significantly reduce the energy production costs. We here provide a multifaceted study highlighting the synergies between analytical and artificial intelligence modelling for optimizing the efficiency of vibrational-powered electromagnetic generators. Two main innovations are introduced: (1) development and experimental validation of a time-series forecasting artificial intelligence model based on the deep deterministic policy gradient method; (2) validation of a pre-training scenario by analytical modelling ⟶ artificial intelligence modelling synergy. Both the analytical and artificial intelligence models were able to provide high prediction accuracies to periodic and random 3D motions combining translations and rotations. Moreover, the pre-training scenario, using simulation training data sets, ensures prediction accuracies within the ±20% absolute error surfaces, profiling approximately normal distributions centered at approximately null error. These are impacting results in the scope of vibrational electromagnetic generation, holding potential to be extended to innovative self-adaptive electromagnetic generators, including those with ability to absorb complex 6 DOF external mechanical excitations. Besides, it can support the implementation of high-performance AI modelling⟶analytical modelling synergies, aiming to re-parameterize the high complex analytical models throughout the EMG operation, such that a superior controllability of the adaptive systems can be achieved.

Effect of chemical reactions and melting heat on the dynamics of maxwell nanofluid flow

AbstractThis study investigates the electrically conducting Maxwell fluid flow over a stretching sheet with the effects of homogeneous‐heterogeneous chemical reactions, thermal radiation, and melting heat. The nanomaterial characteristics are analyzed considering Brownian motion and thermophoresis (Buongiorno's model). Irreversibility analysis is conducted to assess entropy generation. The governing equations of the problem are transformed into dimensionless equations through appropriate similarity transformations. The graphical and tabular numerical solutions are attained through NDSolve via Mathematica. The study examines how various parameters affect the velocity, concentration, temperature, and entropy generation within the flow. This study provides insights into isothermal chemical processes which contribute to the optimization of industrial and engineering applications. It is seen that heterogeneous diffusion parameter increases molecular disorder and rate of irreversible processes, whereas homogeneous diffusion parameter shows opposite trend.

Viability for impulsive stochastic differential inclusions driven by fractional Brownian motion

In this paper, we prove necessary and sufficient conditions for the viability for an impulsive stochastic functional differential inclusion driven by a fractional Brownian motion. The viable property is of interest since it reflects the stability of the model under consideration. The fractional Brownian motion provides a memory effect to the model. Whereas, the appearance of the impulsive factor introduces jumps to the solutions and is new to the analysis of this type. Hence our results are new even in the special case of stochastic differential equation setting.

Evaluation of hydrodynamic coefficients and sensitivity analysis of a work-class remotely operated vehicle using planar motion mechanism tests

This paper presents a comprehensive analysis of the hydrodynamic forces and moments relating to the drag on an open-frame work-class remotely operated vehicle (ROV) AUTO-1000. We describe the results of planar motion mechanism experiments conducted with the aim of modeling and simplifying the mathematical maneuverability model for such an ROV. The scale of the model is 1:4. Various experiments are performed in a nonlinear wave channel. The flow speeds in the static drag tests range from ±0.2–±0.5 m/s and the angle in the drift tests is less than 10°. The motion frequencies of the dynamic tests range from 0.25 to 3.14 rad/s. The amplitude of the translation motions is 0.03 m and the largest angular amplitude in the rolling tests is 5°. The viscous and inertial hydrodynamic coefficients are estimated. Normalized sensitivity coefficients are used to investigate the sensitivity of both the viscous and inertial hydrodynamic coefficients considering the multi-degree-of-freedom motion and velocity effect. The drag, drift, and stationary random motions are used to examine the sensitivity. A comparison of the motion simulation results given by simplified and complete models shows that a threshold normalized sensitivity coefficient value of 0.01 is suitable for filtering the ROV coefficients.

Boosting the HP filter for trending time series with long-range dependence

This article extends recent asymptotic theory developed for the Hodrick Prescott (HP) filter and boosted HP (bHP) filter to long-range dependent time series that have fractional Brownian motion (fBM) limit processes after suitable standardization. Under general conditions, it is shown that the asymptotic form of the HP filter is a smooth curve, analogous to the finding in Phillips and Jin for integrated time series and series with deterministic drifts. Boosting the filter using the iterative procedure suggested in Phillips and Shi leads under well-defined rate conditions to a consistent estimate of the fBM limit process or the fBM limit process with an accompanying deterministic drift when that is present. A stopping criterion is used to automate the boosting algorithm, giving a data-determined method for practical implementation. The theory is illustrated in simulations and two real data examples that highlight the differences between simple HP filtering and the use of boosting. The analysis is assisted by employing a uniformly and almost surely convergent trigonometric series representation of fBM.

Diffusion-thermo and thermo-diffusion impacts on MHD natural convection flow of maxwell nanofluids over a stretching sheet

The present study carried out significant importance in its magnetic field and crosswise diffusion influenced the Maxwell nanofluid flow past a nonlinear stretching sheet. This investigation aimed to shed light on the behavior of critical parameters, particularly in the presence of thermophoresis and Brownian motion. The primary aim is to investigate the impact of thermal diffusion, diffusion-thermo, and various influencing factors on a Maxwell nanofluid near a stretching sheet in the magnetic field, and the impact of three distinct slip conditions (velocity, thermal, and solutal). The partial differential equations by the nonlinear coefficients are utilized in obtaining the most important equations. These equations are distorting to beneficial nonlinear ordinary differential equations making use of the appropriate transformations variables and transformation coefficients. To investigating the computational solutions for the reducing sets of the nonlinear ordinary differential equations, these were developing and utilized the Keller box methodology. The simulations are carried out the nanofluids velocity, temperature, concentration, skin friction coefficients, the rate of temperature transport, in addition to the rate of mass transportation, amongst previous variables. The validations of this methodology are displayed via the comparison of the present outputs through the preceding judgments into the literatures. The major conclusions drawn from this study are the concentration profiles exhibited opposing behaviours as concentration slip parameter increased. However, the temperature profile increases for Brownian motion parameter and thermophoresis parameter parameters. Secondly, concentration displayed an increasing behavior as the Soret number increased.

Incorporating memory effect into a fractional stochastic diffusion particle tracking model for suspended sediment using Malliavin-Calculus-based fractional Brownian Motion

This study aims to develop a Fractional Stochastic Diffusion Particle Tracking Model (FSDPTM) to illustrate suspended sediment’s long-term dependence (LTD) trajectories immersed in fully developed turbulent flow. Carried by eddies in the open channel, individual suspended sediment behavior exhibits dependence on its past increments. The Fractional Brownian Motion (FBM) is incorporated into the FSDPTM to account for the randomness of turbulent flow and to include the time-dependent increments as a memory effect. Additionally, to enhance the capacity for differentiating FBM, this study introduces Malliavin Calculus, the stochastic calculus of variation, to construct the square -differentiable FBM. For the numerical realizations of square differentiable FBM, the integration of fractional Gaussian white noise and Wiener–Ito Chaos expansion with the Hermite sequence is employed. The FSDPTM offers probabilistic LTD trajectories as solutions to the Ito-type Langevin equation. It also provides particle velocity, acceleration, and ensemble statistics, collectively demonstrating the application of FBM to sediment transport modeling. In conclusion, the key feature of the FSDPTM is its ability to translate LTD derived from FBM into the trajectory of suspended sediment particles in fully developed turbulent flow. Additionally, it expands the solutions from non-differentiable to square-differentiable stochastic processes.

Stochastic modeling of influenza transmission: Insights into disease dynamics and epidemic management

The stochastic SEIR model was employed to investigate the dynamics of influenza transmission. By incorporating transmission rates and prevalence ratios, this model provides the most comprehensive explanation of the virus’s unpredictable dissemination. To simulate the stochastic components of influenza transmission, we implemented conventional Brownian motions and stochastic differential equations. The investigation examines the uniqueness and presence of the solutions to demonstrate the conditions needed for eliminating the infection under random disturbances. The transmission rate coefficient (β) strongly impacts disease transmission speed. as demonstrated by the simulation results.Thus, the proper usage of safe transmission control methods is another decisive factor that determines the outcome of epidemics. Actual data of the Kingdom of Saudi Arabia was used. The results highlighted practicality of stochastic models and their usefulness to address and formulate and even execute the public health related policies. Regarding this, this study sets a high bar for other studies on modeling viral diseases on the grounds that stochastic and dynamic factors are also very important. These subsequent improvements in the model shall enable us to pinpoint the best strategies for the prevention and eradication of influenza and any other subsequent epidemic diseases, with reference to epidemic, epidemiology and public health.

Magnetohydrodynamics Marangoni boundary-layer copper/water nanofluid flow driven by surface temperature gradient over a rotating disk

Marangoni driving problem is very important in many practical science engineering, such as semiconductor industry, crystal growth, aerospace, material synthesis. Consider these applications, this work we investigate Marangoni boundary-layer Copper/Water nanofluid driven by the surface temperature gradient over a rotating disk in the presence of magnetic field. Buongiorno model of nanofluids, which contains two important terms, thermophoresis and Brownian motion, are taken into account. Rotating disk model is established, also a suitable Kármán transformation and the multi-shooting technique are applied. Graphical discussion include free stream concentration, rotating speed, magnetic field, Marangoni driving, thermophoresis, Brownian diffusion, Prandtl number, and Schmidt number. The results show that rotating speed inertia and Marangoni driving force tend to reduce temperature/concentration and thickness of thermal/mass boundary layer, while free stream concentration and magnetic field raise up. Meanwhile, Prandtl number tends to reduce temperature, while thermophoresis and Brownian diffusion raise up, and Schmidt number has little influence on temperature, and Schmidt number and Brownian diffusion tend to reduce concentration, while thermophoresis raises up, and Prandtl number has an important influence on concentration. For most selected values of physical parameters, as the nanofluid far away from the disk, the local temperature decreases directly, and the local concentration firstly increases to a peak and then decreases to zero.

Stochastic mortality model with respect to mixed fractional Poisson process: Calibration and empirical analysis of long-range dependence in actuarial valuation

Recently, many studies have adopted the fractional stochastic mortality process in characterising the long-range dependence (LRD) feature of mortality dynamics, while there are still fewer appropriate non-Gaussian fractional models to describe it. We propose a stochastic mortality process driven by a mixture of Brownian motion and modified fractional Poisson process to capture the LRD of mortality rates. The survival probability under this new stochastic mortality model keeps flexibility and consistency with existing affine-form mortality models, which makes the model convenient in evaluating mortality-linked products under the market-consistent method. The formula of survival probability also considers the historical information from survival data, which enables the model to capture historical health records of lives. The LRD feature is reflected by our proposed model in the empirical analysis, which includes the calibration and prediction of survival curves based on recent generation data in Japan and the UK. Finally, the consequent empirical analysis of annuity pricing illustrates the difference of whether this feature is involved in actuarial valuation.

Our brains sense the future through a new quantum-like implicit learning mechanism

BackgroundImagine if our brains could unconsciously predict future events. This study explores this concept, presenting evidence for an inherent 'foreseeing' ability, termed anomalous cognition (AC). We introduce a new experimentally verifiable approach to explain anomalous information anticipation (AIA), a type of AC, based on an innovative, quantum-like model of implicit learning, grounded in Nonlocal Plasticity Theory (NPT). MethodsOur research involved 203 participants using methods such as continuous flash suppression, random dot motion, and advanced 3D EEG neuroimaging, along with IBM quantum random event generators for precise measurements across 144 trials. These trials tested contingencies between undetectable sensory stimuli and dot movements, focusing on participants' prediction abilities. The design conditions were strictly experimental, violating fundamental classical learning principles, particularly reflex conditioning. If these principles were immutable, their violation would prevent any systematic behavioral changes, resulting in random responses. This violation was implemented through two quantum physics concepts: the mathematical principle of nonlocality and entanglement. ResultsDespite the sensory stimulus being inaccessible, our results showed a significant prediction between the contingencies and an increase in AIA accuracy, with explained variances between 25 % and 48 %. EEG findings supported this, showing a positive link between brain activity in specific regions and AIA success. Electrochemical activations were detected in the posterior occipital cortex, the intraparietal sulcus, and the medial temporal gyri. AIA hits exceeded the threshold value corresponding to one standard deviation above the expected mean, showing moderate effect sizes in the experimental group (Cohen’s d = 0.461). Analyzing the learning curve using the derivation technique, we identified the acceleration point of the wave function, indicating systematic implicit learning. This result showed that from repetition 63 onwards, AIA hits increased significantly. ConclusionsThe results suggest that, despite violating fundamental classical learning principles, cognitive processes produced changes in participants' responses susceptible to neuromodulation, considering quantum physics principles of nonlocality and entanglement (both present in NPT). We discuss (a) why the priming effect does not explain the significant results; (b) the potential discovery of a new form of quantum-like implicit learning, which could scientifically resolve phenomena associated with anomalous cognitions (e.g., AIA); and (c) future research directions, including potential applications and clinical impact.

Unsteady magnetohydrodynamic bioconvection Casson fluid flow in presence of gyrotactic microorganisms over a vertically stretched sheet

The free convective, unsteady, two-dimensional (2D) magnetohydrodynamic (MHD) Darcy–Forchheimer Casson fluid flow via a vertical stretching sheet containing gyrotactic microorganisms was the novel aspect of this investigation. We rewrote the collection of partial differential equations (PDEs) as nonlinear ordinary differential equations (ODEs) by considering an appropriate similarity variable. We solved the overhaul of nonlinear ODEs using MATLAB’s bvp4c approach. This study rigorously investigates the significance of gyrotactic microorganisms for Casson fluid motility. Additionally, this work investigates the impact of various parameters, including magnetic parameters, thermophoresis, Brownian motion, and radiation parameters, on temperature, motile microorganisms, velocity, and concentration profiles. We use graphs to illustrate the outcomes of various fluid flow parameters. Numerical tables display the effects of different parameters on skin friction, Sherwood number, Nusselt number, and the quantity of motile microorganisms. The unsteady parameter causes a drop in the velocity, temperature, concentration, and the density profile of microorganisms. Additionally, the Casson parameter leads to a decrease in the flow profile, while simultaneously increasing the heat, concentration, and microorganism density profiles. The microorganism density profile decreases as the bioconvection Schmidt number, Peclet number, and motile microbe parameter increase. We deem the new results extremely satisfactory when compared to earlier research. The fields of environmental remediation, biomedical sciences, and engineering may find this examination useful.

Compartmentalization in cardiomyocytes modulates creatine kinase and adenylate kinase activities.

Intracellular molecules are transported by motor proteins or move by diffusion resulting from random molecular motion. Cardiomyocytes are packed with structures that are crucial for function, but also confine the diffusional spaces, providing cells with a means to control diffusion. They form compartments in which local concentrations are different from the overall, average concentrations. For example, calcium and cyclic AMP are highly compartmentalized, allowing these versatile second messengers to send different signals depending on their location. In energetic compartmentalization, the ratios of AMP and ADP to ATP are different from the average ratios. This is important for the performance of ATPases fuelling cardiac excitation-contraction coupling and mechanical work. A recent study suggested that compartmentalization modulates the activity of creatine kinase and adenylate kinase in situ. This could have implications for energetic signaling through, for example, AMP-activated kinase. It highlights the importance of taking compartmentalization into account in our interpretation of cellular physiology and developing methods to assess local concentrations of AMP and ADP to enhance our understanding of compartmentalization in different cell types.

High-Performance Suspension Bead Sensor Based on Optical Tweezers and Immuno-Rolling Circle Amplification.

In recent years, optical tweezers have become an effective bioassay tool due to their unique advantages, especially in combination with suspension beads, which can be applied to develop a high-performance analysis platform capable of high-quality imaging and stable signal output. However, the optical tweezer-assisted bead analysis is still at the early stage, and further development of different favorable methods is in need. Herein, we have first developed the optical tweezer-assisted immuno-rolling circle amplification (immuno-RCA) on beads for protein detection. Prostate-specific antigen was selected as the model analyte, and the immunosandwich structure on beads was built by the high affinity of "antibody-antigen". The "protein-nucleic acid" signals were effectively converted through the covalent coupling procedure of antibodies and oligonucleotides, further initiating the RCA reaction to achieve signal amplification. The individual beads with the strong irregular Brownian motion in a fluid environment were eventually trapped by the optical tweezers to acquire the accurate and high-quality signal. Compared with the conventional immunoassay on beads, the sensitivity of the developed strategy was increased by 587 times with a limit of detection of 4.29 pg/mL (0.13 pM), as well as excellent specificity, stability, and reproducibility. This study developed the new optical tweezer-assisted beads imaging strategy for protein targets, which has great potential for being applied to clinical serology research and expands the application of optical tweezers in the bioassays.

Modelling the Chinese crude oil futures returns through a skew‐geometric Brownian motion correlated with the market volatility index process for pricing financial options

AbstractIn this paper we model the dynamics of the Chinese crude oil futures returns by using a skew‐geometric Brownian motion correlated with the market volatility, which is taken as a square‐root stochastic process. We use the OVX index data as proxy for market volatility. We validate the proposed model in terms of accuracy of its calibrations through an in‐sample simulation. Instead, out‐of‐sample simulations are used to show that a correlated skew‐geometric Brownian motion is more appropriate for modelling the Chinese returns compared to a single skew‐geometric Brownian motion in terms of forecasts. Furthermore, we price an American call option on the Chinese futures by using a recursively scheme based on a closed‐form formula, and an alternative Monte Carlo approach, for the related European call option. We show that our call price estimates are very close to market values and our model generally outperforms many benchmarks in literature, such as the Barone‐Adesi and Whaley formula and its generalizations.

Clinically established early Parkinson's disease patients do not show impaired use of priors in conditions of perceptual uncertainty

The ability to use past learned experiences to guide decisions is an important component of adaptive behavior, especially when decision-making is performed under time pressure or when perceptual information is unreliable. Previous studies using visual discrimination tasks have shown that this prior-informed decision-making ability is impaired in Parkinson's disease (PD), but the mechanisms underlying this deficit and the precise impact of dopaminergic denervation within cortico-basal circuits remain unclear. To shed light on this problem, we evaluated prior-informed decision-making under various conditions of perceptual uncertainty in a sample of 13 clinically established early PD patients, and compared behavioral performance with healthy control (HC) subjects matched in age, sex and education. PD patients and HC subjects performed a random dot motion task in which they had to decide the net direction (leftward vs. rightward) of a field of moving dots and communicate their choices through manual button presses. We manipulated prior knowledge by modulating the probability of occurrence of leftward vs. rightward motion stimuli between blocks of trials, and by explicitly giving these probabilities to subjects at the beginning of each block. We further manipulated stimulus discriminability by varying the proportion of dots moving coherently in the signal direction and speed-accuracy instructions. PD patients used choice probabilities to guide perceptual decisions in both speed and accuracy conditions, and their performance did not significantly differ from that of HC subjects. An additional analysis of the data with the diffusion decision model confirmed this conclusion. These results suggest that the impaired use of priors during visual discrimination observed at more advanced stages of PD is independent of dopaminergic denervation, though additional studies with larger sample sizes are needed to more firmly establish this conclusion.