scholarly journals Anomalous Stochastic Transport of Particles with Self-Reinforcement and Mittag–Leffler Distributed Rest Times

2021 ◽  
Vol 5 (4) ◽  
pp. 221
Author(s):  
Daniel Han ◽  
Dmitri V. Alexandrov ◽  
Anna Gavrilova ◽  
Sergei Fedotov
Keyword(s):  
Monte Carlo ◽  
Hyperbolic Partial Differential Equations ◽  
Residence Times ◽  
Biological Transport ◽  
Rest State ◽  
Persistent Random Walk ◽  
Stochastic Transport ◽  
Liouville Derivative ◽  
Long Time ◽  
Non Local

We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag–Leffler distributed residence times. The model involves a system of hyperbolic partial differential equations with a non-local switching term described by the Riemann–Liouville derivative. From Monte Carlo simulations, we found that this model generates superdiffusion at intermediate times but reverts to subdiffusion in the long time asymptotic limit. To confirm this result, we derived the equation for the second moment and find that it is subdiffusive in the long time limit. Analyses of two simpler models are also included, which demonstrate the dominance of the Mittag–Leffler rest state leading to subdiffusion. The observation that transient superdiffusion occurs in an eventually subdiffusive system is a useful feature for applications in stochastic biological transport.

Renewed thinking on groundwater age

2021 ◽  
Author(s):  
Grant Ferguson ◽  
Mark Cuthbert ◽  
Kevin Befus ◽  
Tom Gleeson ◽  
Chandler Noyes ◽  
...  
Keyword(s):  
Environmental Flows ◽  
Numerical Models ◽  
Groundwater Age ◽  
Holistic Approach ◽  
Water Levels ◽  
Residence Times ◽  
Groundwater Sustainability ◽  
Long Time ◽  
Mean Residence Times ◽  
Recharge Rates

<p>Groundwater age and mean residence times have been invoked as measures of groundwater sustainability, with the idea that old or "fossil" groundwater is non-renewable. This idea appears to come from the link between groundwater age and background recharge rates, which are also of questionable use in assessing the sustainability of groundwater withdrawals. The use of groundwater age to assess renewability is further complicated by its relationship with flow system geometry. Young groundwaters near recharge areas are not inherently more renewable than older groundwaters down gradient. Similarly, there is no reason to preferentially use groundwater from smaller aquifers, which will have smaller mean residence times than larger aquifers for the same recharge rate. In some cases, groundwater ages may provide some information where groundwater recharge rates were much higher in the past and systems are no longer being recharged. However, there are few examples where the relationship between depletion and changes in recharge over long time periods has been rigorously explored. Groundwater age measurements can provide insights into the functioning of groundwater flow systems and calibration targets for numerical models and we advocate for their continued use, but they are not a metric of sustainable development. Simple metrics to assess groundwater sustainability remain elusive and a more holistic approach is warranted to maintain water levels and environmental flows.</p>

Geometry entrapment in Walk-on-Subdomains

2019 ◽  
Vol 25 (4) ◽  
pp. 329-340 ◽  
Author(s):  
Preston Hamlin ◽  
W. John Thrasher ◽  
Walid Keyrouz ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Monte Carlo Method ◽  
Electrostatic Energy ◽  
Potential Solution ◽  
Long Time ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Monte Carlo Implementation

Abstract One method of computing the electrostatic energy of a biomolecule in a solution uses a continuum representation of the solution via the Poisson–Boltzmann equation. This can be solved in many ways, and we consider a Monte Carlo method of our design that combines the Walk-on-Spheres and Walk-on-Subdomains algorithms. In the course of examining the Monte Carlo implementation of this method, an issue was discovered in the Walk-on-Subdomains portion of the algorithm which caused the algorithm to sometimes take an abnormally long time to complete. As the problem occurs when a walker repeatedly oscillates between two subdomains, it is something that could cause a large increase in runtime for any method that used a similar algorithm. This issue is described in detail and a potential solution is examined.

scholarly journals Probabilistic Analysis of the Hard Rock Disintegration Process

10.14311/1041 ◽  
2008 ◽  
Vol 48 (4) ◽  
Author(s):  
K. Frydrýšek
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Hard Rock ◽  
Assessment Method ◽  
Contact Forces ◽  
Disintegration Process ◽  
Long Time ◽  
Structural Nonlinearities ◽  
Reaction Forces ◽  
Mathcad Software

This paper focuses on a numerical analysis of the hard rock (ore) disintegration process. The bit moves and sinks into the hard rock (mechanical contact with friction between the ore and the cutting bit) and subsequently disintegrates it. The disintegration (i.e. the stress-strain relationship, contact forces, reaction forces and fracture of the ore) is solved via the FEM (MSC.Marc/Mentat software) and SBRA (Simulation-Based Reliability Assessment) method (Monte Carlo simulations, Anthill and Mathcad software). The ore is disintegrated by deactivating the finite elements which satisfy the fracture condition. The material of the ore (i.e. yield stress, fracture limit, Young’s modulus and Poisson’s ratio), is given by bounded histograms (i.e. stochastic inputs which better describe reality). The results (reaction forces in the cutting bit) are also of stochastic quantity and they are compared with experimental measurements. Application of the SBRA method in this area is a modern and innovative trend in mechanics. However, it takes a long time to solve this problem (due to material and structural nonlinearities, the large number of elements, many iteration steps and many Monte Carlo simulations). Parallel computers were therefore used to handle the large computational needs of this problem. 

scholarly journals Cancellation of vacuum diagrams and the long-time limit in out-of-equilibrium diagrammatic quantum Monte Carlo

2019 ◽  
Vol 100 (8) ◽  
Author(s):  
Alice Moutenet ◽  
Priyanka Seth ◽  
Michel Ferrero ◽  
Olivier Parcollet
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Time Limit ◽  
Long Time

scholarly journals Simulations of long time scale dynamics using the dimer method

2001 ◽  
Vol 677 ◽  
Author(s):  
Graeme Henkelman ◽  
Hannes Jónsson
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Transition State ◽  
Time Scale ◽  
Transition State Theory ◽  
Kinetic Monte Carlo ◽  
Chem Phys ◽  
State Theory ◽  
Kinetic Monte Carlo Method ◽  
Long Time

We have carried out long time scale simulations where the “dimer method” [G. Henkelman and H. Jónsson, J. Chem. Phys. 111, 7010 (1999)] is used to find the mechanism and estimate the rate of transitions within harmonic transition state theory and time is evolved by using the kinetic Monte Carlo method. Unlike traditional applications of kinetic Monte Carlo, the atoms are not assigned to lattice sites and a list of all possible transitions does not need to be specified beforehand. Rather, the relevant transitions are found on the y during the simulation. An application to the diffusion and island formation of Al adatoms on an Al(100) surface is presented.

scholarly journals Monte Carlo Simulation of Non-Local Transport Effects in Strained Si on Relaxed Si1 – xGex Heterostructures

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 253-256
Author(s):  
F. Gámiz ◽  
J. B. Roldán ◽  
J. A. López-Villanueva
Keyword(s):  
Monte Carlo ◽  
Performance Enhancement ◽  
Deep Submicron ◽  
Strained Si ◽  
Electron Transport Properties ◽  
Transport Effects ◽  
Non Local ◽  
Local Transport ◽  
Monte Carlo Simulator ◽  
The Impact

Electron transport properties of strained-Si on relaxed Si1 – xGex channel MOSFETs have been studied using a Monte Carlo simulator. The steady- and non-steady-state high-longitudinal field transport regimes have been described in detail. Electronvelocity- overshoot effects are studied in deep-submicron strained-Si MOSFETs, where they show an improvement over the performance of their normal silicon counterparts. The impact of the Si layer strain on the performance enhancement are described in depth in terms of microscopic magnitudes.

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