A first-passage algorithm for the hydrodynamic friction and diffusion-limited reaction rate of macromolecules

Given, James A.; Hubbard, John H.; Douglas, Jack F.

doi:10.1063/1.473428

Cited by 64 publications

(49 citation statements)

References 36 publications

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“…However, as shown by Veshchunov (2010), in the continuum limit, analysis via the steady-state flux approach (the diffusion regime) and of dilute, homogenously distributed systems (the kinetic regime) lead to matching functional forms of the continuum regime collision kernel. For this reason, mean first passage time calculations and related Brownian Dynamics algorithms can and have been successfully employed to determine diffusion-limited reaction rates in the continuum regime (Klein 1952;Northrup et al 1984Northrup et al , 1986Douglas et al 1994;Given et al 1997) and are employed here for rate determination in the continuum, transition, and free molecular regimes.…”

Section: Simulation Proceduresmentioning

confidence: 99%

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Determination of the Transition Regime Collision Kernel from Mean First Passage Times

Gopalakrishnan

Hogan

2011

Aerosol Science and Technology

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Particle-vapor molecule (condensation) and particle-particle (coagulation) collision kernels are critically important parameters for the description of particle size distribution evolution in aerosols. We use mean first passage time calculations to find a dimensionless form of the collision kernel that applies in the limit where the ratio of the masses of colliding entities (aerosol particles or vapor molecules) to gas molecule mass, Z, approaches infinity, and the colliding entities are dilute in concentration. In these calculations, the motion of colliding entities is monitored with Langevin dynamics, and the collision kernel is inferred from the time required for collision. The presented analysis reveals that the dimensionless collisional kernel (H) is a function solely of the diffusive Knudsen number (Kn D , the square root of the product of kT and the reduced mass divided by the product of the reduced friction factor and collision radius), and a number of commonly used expressions for the collision kernel also collapse to the functional form H(Kn D ), irrespective of whether they were derived for Z → ∞ or Z → 0 conditions. The examined collision kernel expressions are further found to agree within 10% of our calculations as well as with each other across the entire Kn D range. This result suggests that a single collision kernel can be used to describe all transition regime collision rates, i.e., both condensation and coagulation rates, with reasonable accuracy, and establishes that Langevin-equationbased mean first passage time calculations can serve as a simple approach to examine transition regime collision phenomena.

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Section: Simulation Proceduresmentioning

confidence: 99%

“…Accurate calculation of collision rates thus requires accurate calculation of β. When the radius of at least one object is large relative to the mean persistence distance of the colliding entities (Rader 1985), the continuum approximation is satisfied and Smoluchowski's β applies (Chandrasekhar 1943;Given et al 1997):…”

Section: Introductionmentioning

confidence: 99%

Determination of the Transition Regime Collision Kernel from Mean First Passage Times

Gopalakrishnan

Hogan

2011

Aerosol Science and Technology

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“…This problem has no analytic solution, and has long been regarded as a benchmark in the electrostatic theory [3]. Different computational methods were used to solve it: boundary element [21,23,4], finite-difference [22], and stochastic algorithms [24,9,7] as well. The results (in units of 4π 0 ) and their published errors (in different senses) are given in Table 1.…”

Section: Computational Results For the Unit Cubementioning

confidence: 99%

“…Recently, it has been found that in computing the capacitance, the diffusion limited reaction rate, and other related properties of arbitrary shaped bodies, stochastic simulation algorithms can be competitive with boundary element and other conventional deterministic computational methods [7]. In many cases, simple Brownian dynamics simulations can be substantially refined, making it possible to use the walk on spheres (WOS) [8] and the Green's function first passage (GFFP) Monte Carlo methods [9]. Elimination of the WOS bias due to the boundary with GFFP, the simulation-tabulation technique [10], and last passage variants of these Monte Carlo algorithms [11] further extend the capabilities of stochastic computational methods when applied to electrostatics problems.…”

Section: Introductionmentioning

confidence: 99%

The random walk on the boundary method for calculating capacitance

Mascagni

Simonov

2004

Journal of Computational Physics

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“…The 'walk on spheres' (WOS) method (described in [20]) is based on such an approach. The Green's function first passage (GFFP) Monte Carlo method [9] is the natural extension of WOS [12]. The simulation-tabulation technique [14], and last passage variants of the GFFP algorithm [10], further extended the capabilities of stochastic computational methods when applied to solving electrostatics and similar problems.…”

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confidence: 99%

Monte Carlo Methods for Calculating Some Physical Properties of Large Molecules

Mascagni¹,

Simonov²

2004

SIAM J. Sci. Comput.

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Abstract. In this paper we describe Monte Carlo methods for solving some boundary-value problems for elliptic partial differential equations arising in the computation of physical properties of large molecules. The constructed algorithms are based on walk on spheres, Green's function first passage, walk in subdomains techniques, and finite-difference approximations of the boundary condition. The methods are applied to calculating the diffusion-limited reaction rate, the electrostatic energy of a molecule, and point values of an electrostatic field.Key words. Monte Carlo method, random walk, diffusion, reaction rate, electrostatic energy, molecule AMS subject classifications. 65C05, 65N99, 78M25, 92C451. Introduction. Elliptic partial differential equations such as the Laplace, Poisson, Poisson-Boltzmann, etc. are effectively used as mathematical models in different branches of computational biophysics and chemistry. Calculation of the diffusionlimited reaction rate, the electrostatic potential and field, the internal energy -are all problems that can be reduced to the solution of a diffusion equation with some conditions on the boundary and at the infinity. The intrinsic analogy between diffusion and electrostatics makes it possible to apply the same computational techniques to solve problems coming from these different fields. It is worth noting that the solution domain in this class of problems is usually infinite. So, it is natural that since the days of Maxwell, the boundary-element method has been used as an effective tool for solving such problems. In particular, one can calculate the capacitance and the diffusionlimited reaction rate as a surface integral [18]. The boundary-element method, as well as finite-difference and finite-element methods, are still commonly used for solving electrostatics and diffusion problems arising in biophysics. Review of these and other techniques used in the computation of molecular electrostatic properties is given in [2].Another possible way of computationally treating these problems comes from the probabilistic representation of solutions to elliptic and parabolic partial differential equations as functionals of diffusion process trajectories [15,7,8]. Direct computational simulation of physical diffusion in this case coincides with the approximation of Brownian motion as the solution to a stochastic differential equation via a firstorder Euler scheme [19,16]. This approach was applied [4] to simulation studies of diffusion-limited reactions. Though computationally far from being optimal, it allows one to include different physical phenomena (hydrodynamic, electrostatic, etc.) into the computational scheme, and, what is essential, it is efficient enough to be competitive with deterministic methods. Later, this algorithm was modified [30] by incorporating different boundary conditions [28,26]. In addition, other variants of the algorithm were suggested. In [31], in particular, the Brownian dynamics simulation method was compared to the algorithms based on survival probab...

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A first-passage algorithm for the hydrodynamic friction and diffusion-limited reaction rate of macromolecules

Cited by 64 publications

References 36 publications

Determination of the Transition Regime Collision Kernel from Mean First Passage Times

Determination of the Transition Regime Collision Kernel from Mean First Passage Times

The random walk on the boundary method for calculating capacitance

Monte Carlo Methods for Calculating Some Physical Properties of Large Molecules

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