Peter R. Kramer

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Several simple mathematical models for the turbulent di!usion of a passive scalar "eld are developed here with an emphasis on the symbiotic interaction between rigorous mathematical theory (including exact solutions), physical intuition, and numerical simulations. The homogenization theory for periodic velocity "elds and random velocity "elds with(More)
In modeling many biological systems, it is important to take into account flexible structures which interact with a fluid. At the length scale of cells and cell organelles, thermal fluctuations of the aqueous environment become significant. In this work, it is shown how the immersed boundary method of [C.S. Peskin, The immersed boundary method, Acta Num. 11(More)
The phosphorus cycle in the ecosystem of the shallow, hypertrophic Loosdrecht lakes (The Netherlands) was simulated by means of the dynamic eutrophication model PCLOOS. The model comprises three algal groups, zooplankton, fish, detritus, zoobenthos, sediment detritus and some inorganic phosphorus fractions. All organic compartments are modelled in two(More)
We illustrate the stochastic mode reduction procedure as formulated recently by Majda, Timofeyev, and Vanden-Eijnden [Comm. Pure Appl. Math., 54 (2001), pp. 891–974] (MTV) on the equations of motion underlying various particle-based simulation approaches (such as Stokesian dynamics and Brownian dynamics) and the conceptually distinct dissipative particle(More)
We examine stochastic coarse-graining strategies for two biomolecular systems. First, we compute the large-scale transport properties of the basic flashing ratchet mathematical model for (Brownian) molecular motors and consider in this light whether the underlying continuous-space, continuous-time Markovian model can be coarse-grained as a discrete-state,(More)
We apply the formulation of a stochastic mode reduction method developed in a recent paper of Majda, Timofeyev, and Vanden-Eijnden [Comm. Pure Appl. Math., 54 (2001), pp. 891– 974] (MTV) to obtain simplified equations for the dynamics of structures immersed in a thermally fluctuating fluid at low Reynolds (or Kubo) number, as simulated by a recent extension(More)
The basic ingredient of osmotic pressure is a solvent fluid with a soluble molecular species which is restricted to a chamber by a boundary which is permeable to the solvent fluid but impermeable to the solute molecules. For macroscopic systems at equilibrium, the osmotic pressure is given by the classical van 't Hoff law, which states that the pressure is(More)