Study on the finiteness of the first meeting time between N-dimensional Gaussian jump and Brownian diffusion particles in the fluid

2019 ◽  
Vol 33 (28) ◽  
pp. 1950334 ◽  
Author(s):  
Alaa Awad Alzulaibani ◽  
Mohamed Abd Allah El-Hadidy
Keyword(s):  
Brownian Motion ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Expected Value ◽  
The Other ◽  
Brownian Diffusion ◽  
Modern Physics ◽  
Independent Brownian Motion

In this paper, we study the finiteness of the first meeting time between two different randomly moving particles in the fluid. The first particle moves with N-dimensional independent Gaussian jump and has a probability density function which is detailed in El-Hadidy (International Journal of Modern Physics B, Published Online with https://doi.org/10.1142/S0217979219502102 , 2019). The other target moves with N-dimensional independent Brownian motion. We present some analysis that proves the finiteness of the first meeting time expected value between the two particles in the fluid.

A nonlocal theory for stress in bound, Brownian suspensions of slender, rigid fibres

1995 ◽  
Vol 296 ◽  
pp. 271-324 ◽  
Author(s):  
Richard L. Schiek ◽  
Eric S. G. Shaqfeh
Keyword(s):  
Brownian Motion ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Fluid Velocity ◽  
Nonlocal Theory ◽  
Velocity Shear ◽  
Slender Body Theory ◽  
Nonlocal Stress ◽  
Fokker Planck

A nonlocal theory for stress in bound suspensions of rigid, slender fibres is developed and used to predict the rheology of dilute, rigid polymer suspensions when confined to capillaries or fine porous media. Because the theory is nonlocal, we describe transport in a fibre suspension where the velocity and concentration fields change rapidly on the fibre's characteristic length. Such rapid changes occur in a rigidly bound domain because suspended particles are sterically excluded from configurations near the boundaries. A rigorous no-flux condition resulting from the presence of solid boundaries around the suspension is included in our nonlocal stress theory and naturally gives rise to concentration gradients that scale on the length of the particle. Brownian motion of the rigid fibres is included within the nonlocal stress through a Fokker–Planck description of the fibres’ probability density function where gradients of this function are proportional to Brownian forces and torques exerted on the suspended fibres. This governing Fokker–Planck probability density equation couples the fluid flow and the nonlocal stress resulting in a nonlinear set of integral-differential equations for fluid stress, fluid velocity and fibre probability density. Using the method of averaged equations (Hinch 1977) and slender-body theory (Batchelor 1970), the system of equations is solved for a dilute suspension of rigid fibres experiencing flow and strong Brownian motion while confined to a gap of the same order in size as the fibre's intrinsic length. The full solution of this problem, as the fluid in the gap undergoes either simple shear or pressure-driven flow, is solved self-consistently yielding average fluid velocity, shear and normal stress profiles within the gap as well as the probability density function for the fibres’ position and orientation. From these results we calculate concentration profiles, effective viscosities and slip velocities and compare them to experimental data.

scholarly journals Two approaches to design of forward adaptive piecewise uniform scalar quantizers

2013 ◽  
Vol 26 (1) ◽  
pp. 61-68
Author(s):  
Jelena Nikolic ◽  
Zoran Peric
Keyword(s):  
High Resolution ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
The Other ◽  
Speech Signals ◽  
High Quality ◽  
Region Partition ◽  
The One ◽  
Scalar Quantizers

In this paper, two forward adaptive piecewise uniform scalar quantizers are proposed for high-quality quantization of speech signals modeled by the Laplacian probability density function. In designing both forward adaptive piecewise uniform scalar quantizers an equidistant support region partition is assumed and a distribution of the number of reproduction levels per segments is optimized. The proposed models differ in the approach of determining the reproduction levels. In particular, one model defines the reproduction levels as the cell centroids and the other one as the cell midpoints. We show that, in the high-resolution case, the proposed quantizers provide approximately the same performance being close to the one of the forward adaptive nonlinear scalar compandor with equal number of quantization levels.

scholarly journals Mathematical approach to human character

2020 ◽  
Author(s):  
Takuya Yabu
Keyword(s):  
Probability Density Function ◽  
Probability Distribution ◽  
Probability Density ◽  
Density Function ◽  
Negative Emotions ◽  
The Other ◽  
Mathematical Approach ◽  
Fixed Probability ◽  
To Receive

I thought about whether to receive positive or negative emotions from an event from the perspective of human character. Regarding the human character, I define it as a process of selecting one's emotion x so that the received emotion x becomes x=0 with respect to the event X and the reaction of the other party when one's thoughts and reactions occur as the accompanying reactions. Mathematically modeled it, the probability density function of how much to select an emotion has a fixed probability distribution. I also described how to deal with one's character as an application of this model.

scholarly journals The positive occupation time of Brownian motion with two-valued drift and asymptotic dynamics of sliding motion with noise

2014 ◽  
Vol 14 (04) ◽  
pp. 1450010 ◽  
Author(s):  
D. J. W. Simpson ◽  
R. Kuske
Keyword(s):  
Brownian Motion ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Planck Equation ◽  
Occupation Time ◽  
Dimensional System ◽  
Sliding Motion ◽  
Long Time ◽  
Long Time Asymptotics

We derive the probability density function of the positive occupation time of one-dimensional Brownian motion with two-valued drift. Long time asymptotics of the density are also computed. We use the result to describe the transitional probability density function of a general N-dimensional system of stochastic differential equations representing stochastically perturbed sliding motion of a discontinuous, piecewise-smooth vector field on short time frames. A description of the density at larger times is obtained via an asymptotic expansion of the Fokker-Planck equation.

scholarly journals Mathematical approach to human reaction

2020 ◽  
Author(s):  
Takuya Yabu
Keyword(s):  
Random Walk ◽  
Probability Density Function ◽  
Probability Distribution ◽  
Probability Density ◽  
Density Function ◽  
The Other ◽  
Mathematical Approach ◽  
One Dimensional ◽  
Human Reaction ◽  
Fixed Distribution

I thought about how to get the magnitude from the event and the reaction of the other party. Evaluating the values of events and opponents' reactions using a one-dimensional random walk shows that the probability density function of the values of events and opponents' reactions has a fixed probability distribution. Similarly, I have shown that the functions that determine the magnitude of events and reactions are also represented by a fixed distribution. Therefore, I also showed that when individuals gather to form a group, the functions that determine the magnitude of events and reactions as a group are also represented by a fixed distribution. Also, as an application example of this model, I described how to show my reaction and what to do when the magnitude of the event is large.

Sign in / Sign up

Export Citation Format

Share Document