On the log‐normal diffusion process

1989 ◽  
Vol 30 (4) ◽  
pp. 953-955 ◽  
Author(s):  
Siegfried H. Lehnigk
Keyword(s):  
Diffusion Process ◽  
Normal Diffusion ◽  
Log Normal

Fitting real data by means of non-homogeneous log-normal diffusion processes

2017 ◽  
Vol 10 (4) ◽  
pp. 585-600 ◽  
Author(s):  
Patricia Román-Román ◽  
Juan José Serrano-Pérez ◽  
Francisco Torres-Ruiz
Keyword(s):  
Diffusion Processes ◽  
Real Data ◽  
Normal Diffusion ◽  
Log Normal

On the quasi-Monte Carlo method with Halton points for elliptic PDEs with log-normal diffusion

2016 ◽  
Vol 86 (304) ◽  
pp. 771-797 ◽  
Author(s):  
Helmut Harbrecht ◽  
Michael Peters ◽  
Markus Siebenmorgen
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Elliptic Pdes ◽  
Quasi Monte Carlo ◽  
Normal Diffusion ◽  
Log Normal

scholarly journals Optimal consumption/portfolio choice with borrowing rate higher than deposit rate

1998 ◽  
Vol 39 (4) ◽  
pp. 449-462 ◽  
Author(s):  
Wensheng Xu ◽  
Shuping Chen
Keyword(s):  
Portfolio Choice ◽  
Optimal Strategies ◽  
Optimal Investment ◽  
Dynamic Programming Principle ◽  
Optimal Consumption ◽  
Bank Account ◽  
Normal Diffusion ◽  
Hamilton Jacobi Bellman ◽  
Log Normal ◽  
Optimal Consumption And Investment

AbstractIn this paper, optimal consumption and investment decisions are studied for an investor who has available a bank account and a stock whose price is a log normal diffusion. The bank pays at an interest rate r(t) for any deposit, and vice takes at a larger rate r′(t) for any loan. Optimal strategies are obtained via Hamilton-Jacobi-Bellman (HJB) equation which is derived from dynamic programming principle. For the specific HARA case, we get the optimal consumption and optimal investment explicitly, which coincides with the classical one under the condition r′(t) ≡ r(t)

An Eshelbian homogenization solution for a coupled stress-diffusion moving interface problem in composites

2016 ◽  
Vol 01 (03n04) ◽  
pp. 1640011 ◽  
Author(s):  
Yang Zhang ◽  
Xian-Cheng Zhang ◽  
Shan-Tung Tu ◽  
Shaofan Li
Keyword(s):  
Diffusion Process ◽  
Chemical Potential ◽  
Diffusion Processes ◽  
Homogenization Method ◽  
Interface Problem ◽  
Diffusion Treatment ◽  
Moving Interface ◽  
Normal Diffusion ◽  
The One ◽  
And Diffusion

In this work, we proposed a homogenization model to treat the coupled mechanical-diffusion moving interface problem. The Eshelbian homogenization method is applied to find the effective mechanical properties and diffusivity. On the one hand, the diffusion of solute elements would induce the formation of inclusion phases, affecting the mechanical equilibrium, properties and diffusivity. On the other hand, the stress condition will also have effects on the chemical potential and diffusion process. The coupling of the mechanical and diffusion processes were simulated using the present model, i.e., normal diffusion process and that with previous diffusion treatment. In the former case, thicknesses of outer and inner diffusion parts both increased with time. In the latter case, decomposition of the outer diffusion part might take place to maintain the growth of the inner part.

Electrokinetic Driven Micro-Mixing of Fluids in a Circular Electrode Pattern

2017 ◽  
Author(s):  
Rakesh Guduru ◽  
Nazmul Islam
Keyword(s):  
Diffusion Process ◽  
Flow Pattern ◽  
Small Volume ◽  
Lab On A Chip ◽  
Fluid Mixing ◽  
Research Groups ◽  
Buffer Solutions ◽  
Mixing Behavior ◽  
Normal Diffusion ◽  
Experimental Values

Manipulation of fluids in a small volume is often a challenge in the field of Microfluidics. While many research groups have addressed this issue with robust methodologies, manipulation of fluids remains a scope of study due to the ever-changing technology (Processing Tools) and increase in the demand for “Lab-On-a-Chip” devices. This research peruses the flow pattern and fluid mixing behavior in a metallic circular electrode, charged with AC voltage. In this study, micromixing in a circular electrode pattern device is demonstrated with numerical and experimental values. Experiments were performed using two buffer solutions with conductivities 1.62 S/m and 0.0732 S/m. The efficiency of mixing was found to be three to five times faster than the normal diffusion process. It was found that the increase in the conductivity of fluid increases the efficiency of mixing in the proposed device.

Heterogeneous diffusion with stochastic resetting

2022 ◽  
Author(s):  
Trifce Sandev ◽  
Viktor Domazetoski ◽  
Ljupco Kocarev ◽  
Ralf Metzler ◽  
Alexei Chechkin
Keyword(s):  
Steady State ◽  
Diffusion Process ◽  
Inner Core ◽  
Numerical Solutions ◽  
Diffusion Length ◽  
Large Deviation ◽  
Nonequilibrium Steady State ◽  
Length Scale ◽  
Normal Diffusion ◽  
Long Time

Abstract We study a heterogeneous diffusion process with position-dependent diffusion coefficient and Poissonian stochastic resetting. We find exact results for the mean squared displacement and the probability density function. The nonequilibrium steady state reached in the long time limit is studied. We also analyze the transition to the non-equilibrium steady state by finding the large deviation function. We found that similarly to the case of the normal diffusion process where the diffusion length grows like $t^{1⁄2}$ while the length scale ξ(t) of the inner core region of the nonequilibrium steady state grows linearly with time t, in the heterogeneous diffusion process with diffusion length increasing like $t^{p⁄2}$ the length scale ξ(t) grows like $t^{p}$. The obtained results are verified by numerical solutions of the corresponding Langevin equation.

scholarly journals Efficient recurrent neural network methods for anomalously diffusing single particle short and noisy trajectories

2021 ◽  
Author(s):  
Òscar Garibo i Orts ◽  
Alba Baeza-Bosca ◽  
Miguel A. García-March ◽  
J. Alberto Conejero
Keyword(s):  
Diffusion Process ◽  
Anomalous Diffusion ◽  
Good Accuracy ◽  
Biological Tissues ◽  
Cell Organelles ◽  
Atomic Systems ◽  
Artificial Materials ◽  
Network Methods ◽  
Normal Diffusion ◽  
And Diffusion

Abstract Anomalous diffusion occurs at very different scales in nature, from atomic systems to motions in cell organelles, biological tissues or ecology, and also in artificial materials, such as cement. Being able to accurately measure the anomalous exponent associated to a given particle trajectory, thus determining whether the particle subdiffuses, superdiffuses or performs normal diffusion, is of key importance to understand the diffusion process. Also it is often important to trustingly identify the model behind the trajectory, as it this gives a large amount of information on the system dynamics. Both aspects are particularly difficult when the input data are short and noisy trajectories. It is even more difficult if one cannot guarantee that the trajectories output in experiments are homogeneous, hindering the statistical methods based on ensembles of trajectories. We present a data-driven method able to infer the anomalous exponent and to identify the type of anomalous diffusion process behind single, noisy and short trajectories, with good accuracy. This model was used in our participation in the Anomalous Diffusion (AnDi) Challenge. A combination of convolutional and recurrent neural networks was used to achieve state-of-the-art results when compared to methods participating in the AnDi Challenge, ranking top 4 in both classification and diffusion exponent regression.

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