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《Physics letters. A》2019,383(22):2594-2603
In this work, we address the systematic biases and random errors stemming from finite step sizes encountered in diffusion simulations. We introduce the Effective Geometry Monte Carlo (EG-MC) simulation algorithm which modifies the geometry of the receiver. We motivate our approach in a 1D toy model and then apply our findings to a spherical absorbing receiver in a 3D unbounded environment. We show that with minimal computational cost the impulse response of this receiver can be precisely simulated using EG-MC. Afterwards, we demonstrate the accuracy of our simulations and give tight constraints on the single free parameter in EG-MC. Finally, we comment on the range of applicability of our results. While we present the EG-MC algorithm for the specific case of molecular diffusion, we believe that analogous methods with effective geometry manipulations can be utilized to approach a variety of problems in other branches of physics such as condensed matter physics and cosmological large scale structure simulations. 相似文献
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Suppose that is a one-dimensional Brownian motion with negative drift . It is possible to make sense of conditioning this process to be in the state 0 at an independent exponential random time and if we kill the conditioned process at the exponential time the resulting process is Markov. If we let the rate parameter of the random time go to 0, then the limit of the killed Markov process evolves like conditioned to hit 0, after which time it behaves as killed at the last time visits 0. Equivalently, the limit process has the dynamics of the killed “bang–bang” Brownian motion that evolves like Brownian motion with positive drift when it is negative, like Brownian motion with negative drift when it is positive, and is killed according to the local time spent at 0.An extension of this result holds in great generality for a Borel right process conditioned to be in some state at an exponential random time, at which time it is killed. Our proofs involve understanding the Campbell measures associated with local times, the use of excursion theory, and the development of a suitable analogue of the “bang–bang” construction for a general Markov process.As examples, we consider the special case when the transient Borel right process is a one-dimensional diffusion. Characterizing the limiting conditioned and killed process via its infinitesimal generator leads to an investigation of the -transforms of transient one-dimensional diffusion processes that goes beyond what is known and is of independent interest. 相似文献
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The trench on a printed circuit board was reconstructed to fabricate a microfluidic framework that allows low-cost production for small quantities and integration with multifunctional elements. An on-chip electrolyte regulator was thus proposed on this platform to analyze diffusion properties in laminar flow. A numerical model was developed, highlighting the interplay between the electrolyte migration and hydrodynamic properties. Solutions with dissolved sodium chloride were simulated and experimentally tested for the regulation of electrical conductivity under the guidance of the normalized Nernst-Planck equation. The diffusion mechanism and the resulting concentration field were demonstrated in detail. This approach provides a satisfactory manufacturing method and a useful tool for integrated microfluidic systems. 相似文献
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Distinguishing and quantification of the human visual pathways using high-spatial-resolution diffusion tensor tractography 总被引:1,自引:0,他引:1
Arash Kamali Khader M. Hasan Pavani Adapa Azadeh Razmandi Zafer Keser John Lincoln Larry A. Kramer 《Magnetic resonance imaging》2014
Quantification of the living human visual system using MRI methods has been challenging, but several applications demand a reliable and time-efficient data acquisition protocol. In this study, we demonstrate the utility of high-spatial-resolution diffusion tensor fiber tractography (DTT) in reconstructing and quantifying the human visual pathways. Five healthy males, age range 24–37 years, were studied after approval of the institutional review board (IRB) at The University of Texas Health Science Center at Houston. We acquired diffusion tensor imaging (DTI) data with 1-mm slice thickness on a 3.0-Tesla clinical MRI scanner and analyzed the data using DTT with the fiber assignment by continuous tractography (FACT) algorithm. By utilizing the high-spatial-resolution DTI protocol with FACT algorithm, we were able to reconstruct and quantify bilateral optic pathways including the optic chiasm, optic tract, optic radiations free of contamination from neighboring white matter tracts. 相似文献
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《Applied and Computational Harmonic Analysis》2014,36(1):79-107
Graph Laplacians and related nonlinear mappings into low dimensional spaces have been shown to be powerful tools for organizing high dimensional data. Here we consider a data set X in which the graph associated with it changes depending on some set of parameters. We analyze this type of data in terms of the diffusion distance and the corresponding diffusion map. As the data changes over the parameter space, the low dimensional embedding changes as well. We give a way to go between these embeddings, and furthermore, map them all into a common space, allowing one to track the evolution of X in its intrinsic geometry. A global diffusion distance is also defined, which gives a measure of the global behavior of the data over the parameter space. Approximation theorems in terms of randomly sampled data are presented, as are potential applications. 相似文献