GPU-accelerated simulation of colloidal suspensions with direct hydrodynamic interactions

Solvent-mediated hydrodynamic interactions between colloidal particles can significantly alter their dynamics. We discuss the implementation of Stokesian dynamics in leading approximation for streaming processors as provided by the compute unified device architecture (CUDA) of recent graphics processors (GPUs). Thereby, the simulation of explicit solvent particles is avoided and hydrodynamic interactions can easily be accounted for in already available, highly accelerated molecular dynamics simulations. Special emphasis is put on efficient memory access and numerical stability. The algorithm is applied to the periodic sedimentation of a cluster of four suspended particles. Finally, we investigate the runtime performance of generic memory access patterns of complexity $O(N^2)$ for various GPU algorithms relying on either hardware cache or shared memory.Comment: to appear in a special issue of Eur. Phys. J. Special Topics on "Computer Simulations on GPUs

Tiling solutions for optimal biological sensing

Biological systems, from cells to organisms, must respond to the ever changing environment in order to survive and function. This is not a simple task given the often random nature of the signals they receive, as well as the intrinsically stochastic, many body and often self-organized nature of the processes that control their sensing and response and limited resources. Despite a wide range of scales and functions that can be observed in the living world, some common principles that govern the behavior of biological systems emerge. Here I review two examples of very different biological problems: information transmission in gene regulatory networks and diversity of adaptive immune receptor repertoires that protect us from pathogens. I discuss the trade-offs that physical laws impose on these systems and show that the optimal designs of both immune repertoires and gene regulatory networks display similar discrete tiling structures. These solutions rely on locally non-overlapping placements of the responding elements (genes and receptors) that, overall, cover space nearly uniformly.Comment: 11 page

Mathematics at the eve of a historic transition in biology

A century ago physicists and mathematicians worked in tandem and established quantum mechanism. Indeed, algebras, partial differential equations, group theory, and functional analysis underpin the foundation of quantum mechanism. Currently, biology is undergoing a historic transition from qualitative, phenomenological and descriptive to quantitative, analytical and predictive. Mathematics, again, becomes a driving force behind this new transition in biology.Comment: 5 pages, 2 figure

Towards quantifying uncertainty in predictions of Amazon 'dieback'.

This is the final version of the article. It first appeared from The Royal Society via http://dx.doi.org/10.1098/rstb.2007.0028Simulations with the Hadley Centre general circulation model (HadCM3), including carbon cycle model and forced by a 'business-as-usual' emissions scenario, predict a rapid loss of Amazonian rainforest from the middle of this century onwards. The robustness of this projection to both uncertainty in physical climate drivers and the formulation of the land surface scheme is investigated. We analyse how the modelled vegetation cover in Amazonia responds to (i) uncertainty in the parameters specified in the atmosphere component of HadCM3 and their associated influence on predicted surface climate. We then enhance the land surface description and (ii) implement a multilayer canopy light interception model and compare with the simple 'big-leaf' approach used in the original simulations. Finally, (iii) we investigate the effect of changing the method of simulating vegetation dynamics from an area-based model (TRIFFID) to a more complex size- and age-structured approximation of an individual-based model (ecosystem demography). We find that the loss of Amazonian rainforest is robust across the climate uncertainty explored by perturbed physics simulations covering a wide range of global climate sensitivity. The introduction of the refined light interception model leads to an increase in simulated gross plant carbon uptake for the present day, but, with altered respiration, the net effect is a decrease in net primary productivity. However, this does not significantly affect the carbon loss from vegetation and soil as a consequence of future simulated depletion in soil moisture; the Amazon forest is still lost. The introduction of the more sophisticated dynamic vegetation model reduces but does not halt the rate of forest dieback. The potential for human-induced climate change to trigger the loss of Amazon rainforest appears robust within the context of the uncertainties explored in this paper. Some further uncertainties should be explored, particularly with respect to the representation of rooting depth