Biomedical subjects

E A J F Peters

Publications and source records attributed to E A J F Peters.

3 recordsLinked to original sources

PubMed2004

Detailed fluctuation theorem for mesoscopic modeling.

The detailed fluctuation theorem is derived. The basic assumptions are phase space incompressibility (Liouville's theorem) and time reversibility on the microscopic level. The theorem relates the conditional probability to end up in a mesoscopic state Gamma(B) at time t(B) , starting from Gamma(A) at time t(A) , to the time-reversed process. The ratio of these two probability densities is related to the entropy difference of the two mesoscopic states. The fluctuation theorem remains valid even far from equilibrium as long as the local equilibrium condition is obeyed. It is shown that the theorem imposes constraints on the form mesoscopic equations can take. For stochastic differential equations a generalized kinetic form is derived. The fluctuation theorem can be used to derive thermodynamically consistent simulation techniques. At the end of this paper the relation with the GENERIC formalism is discussed.

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PubMed2002

Efficient Brownian dynamics simulation of particles near walls. I. Reflecting and absorbing walls.

In this paper a method of numerically handling boundary conditions within Brownian dynamics simulations is discussed. The usual naive treatment of identifying reflection or absorption processes by checking for boundary crossings yields O(sqrt[deltat]) discretization errors. The method we propose here yields O(deltat) errors, similar to the case of Brownian dynamics without wall interaction. The main idea is to ensure that the zeroth (in the case of absorption), first, and second moments of the particle's displacement steps are correct up to order deltat. To fulfill this requirement near a wall, one has to include nontrivial corrections, because the stochastic contribution does not average out when the distance to the wall is of the order of the step length. We demonstrate here that the method substantially reduces the discretization error for the simple cases of an absorbing and a reflecting wall. Our method comprises an improvement over earlier methods proposed by Lamm and Schulten [J. Chem. Phys. 78, 2713 (1983)] and Ottinger [J. Chem. Phys. 91, 6455 (1937)]. Their methods heavily depend on full, explicit, analytical expressions for solutions of the diffusion equation near a wall, which they use to make a correction after a stochastic step has been made. Our method only involves the, usually much simpler, lowest moments (up to the second) of the probability density distributions for the displacement of the particle in one time step. This means the method only uses the initial particle position to determine a valid step, and there is no need for corrections afterwards. Because much less information is needed (three moments instead of full probability densities), in many cases information can be stored simply in interpolation functions and there is no need to evaluate complicated analytical expressions at every time step. This makes the method more efficient and easy to generalize to other situations than the relatively simple case of a flat wall. Moreover, because analytic expressions are not needed, other methods to determine the needed moments can be used. This makes our method much more flexible.

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PubMed2002

Efficient Brownian dynamics simulation of particles near walls. II. Sticky walls.

In this paper we treat a boundary condition, the "sticky boundary," which appears to be quite useful in mesoscopic models. The sticky boundary is modeled as an infinitely deep, infinitely narrow, potential well adjacent to a reflecting boundary. The free energy corresponding to this boundary is finite. The boundary condition, which can be viewed as an intermediate between the absorbing and reflecting boundary condition, may have many applications, e.g., for the simulation of the partial adsorption of polymer molecules to walls and for the modeling of solvent quality. We will derive an efficient Brownian dynamics algorithm, capable of handling interactions of a diffusing particle with a sticky wall. Our approach avoids the large discretization errors that occur in the simulation of boundary interactions within the "standard" Brownian dynamics approach. The essence of our method was presented before [E. Peters and T. Barenbrug, Phys. Rev. E (to be published)]. The treatment of the wall as proposed here is quite general, and therefore not limited to the use within Brownian dynamics. In other simulation techniques which aim at treating the dynamics of mesoscopic particles near walls, we expect it to be of use as well.

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