A recent paper of B. Naundorf et al. described an intriguing negative correlation between variability of the onset potential at which an action potential occurs (the onset span) and the rapidity of action potential initiation (the onset rapidity). This correlation was demonstrated in numerical simulations of the Hodgkin-Huxley model. Due to this antagonism, it is argued that Hodgkin-Huxley-type models are unable to explain action potential initiation observed in cortical neurons in vivo or in vitro. Here we apply a method from theoretical physics to derive an analytical characterization of this problem. We analytically compute the probability distribution of onset potentials and analytically derive the inverse relationship between onset span and onset rapidity. We find that the relationship between onset span and onset rapidity depends on the level of synaptic background activity. Hence we are able to elucidate the regions of parameter space for which the Hodgkin-Huxley model is able to accurately describe the behavior of this system.

The bacterium Bacillus subtilis produces the molecule surfactin, which is known to enhance the spreading of multicellular colonies on nutrient substrates by lowering the surface tension of the surrounding fluid, and to aid in the formation of aerial structures. Here we present experiments and a mathematical model that demonstrate how the differential accumulation rates induced by the geometry of the bacterial film give rise to surfactant waves. The spreading flux increases with increasing biofilm viscosity. Community associations are known to protect bacterial populations from environmental challenges such as predation, heat, or chemical stresses, and enable digestion of a broader range of nutritive sources. This study provides evidence of enhanced dispersal through cooperative motility, and points to nonintuitive methods for controlling the spread of biofilms.

Recent work has developed a beautiful model system for studying the energy focusing and heating power of collapsing bubbles. The bubble is effectively one-dimensional and the collapse and heating can be quantitatively measured. Thermal effects are shown to play an essential role in the time-dependent dynamics.

We develop a methodology for deriving continuum partial differential equations for the evolution of large-scale surface morphology directly from molecular dynamics simulations of the craters formed from individual ion impacts. Our formalism relies on the separation between the length scale of ion impact and the characteristic scale of pattern formation, and expresses the surface evolution in terms of the moments of the crater function. We demonstrate that the formalism reproduces the classical Bradley-Harper results, as well as ballistic atomic drift, under the appropriate simplifying assumptions. Given an actual set of converged molecular dynamics moments and their derivatives with respect to the incidence angle, our approach can be applied directly to predict the presence and absence of surface morphological instabilities. This analysis represents the first work systematically connecting molecular dynamics simulations of ion bombardment to partial differential equations that govern topographic pattern-forming instabilities.

The linear dynamics of ion sputtered solids is essential to understanding the evolution of ordered and disordered surface patterns. We review the existing models of linear dynamics and point out qualitative discrepancies between theory and experimental observations that characterize the linear regime. In particular, we emphasize the importance of experimental and theoretical analysis of bifurcation points: certain values of control parameters such as ion beam angle or energy, where flat surfaces undergo a transition from stability to instability.

We calculate the ground states of hard-sphere clusters, in which n identical hard spherical particles bind by isotropic short-ranged attraction. Combining graph theoretic enumeration with basic geometry, we analytically solve for clusters of n <= 10 particles satisfying minimal rigidity constraints. For n <= 9 the ground state degeneracy increases exponentially with n, but for n > 9 the degeneracy decreases due to the formation of structures with >3n - 6 contacts. Interestingly, for n = 10 and possibly at n = 11 and n = 12, the ground states of this system are subsets of hexagonal close-packed crystals. The ground states are not icosahedra at n = 12 and n = 13. We relate our results to the structure and thermodynamics of suspensions of colloidal particles with short-ranged attractions.

The nonlinearity of the Navier-Stokes equations makes predicting the flow of fluid around rapidly moving small bodies highly resistant to all approaches save careful experiments or brute force computation. Here, we show how a linearization of the Navier-Stokes equations captures the drag-determining features of the flow and allows simplified or analytical computation of the drag on bodies up to Reynolds number of order 100. We illustrate the utility of this linearization in 2 practical problems that normally can only be tackled with sophisticated numerical methods: understanding flow separation in the flow around a bluff body and finding drag-minimizing shapes.

A high velocity impact between a liquid droplet and a solid surface produces a splash. Classical work traced the origin of the splash to a thin sheet of fluid ejected near the impact point. Mechanisms of sheet formation have heretofore relied on initial contact of the droplet and the surface. We demonstrate that, neglecting intermolecular forces between the liquid and the solid, the liquid does not contact the solid, and instead spreads on a very thin air film. The interface of the droplet develops a high curvature and emits capillary waves.

Recent experiments have convincingly demonstrated the existence of surface nanobubbles on submerged hydrophobic surfaces. However, classical theory dictates that small gaseous bubbles quickly dissolve because their large Laplace pressure causes a diffusive outflux of gas. Here we suggest that the bubbles are stabilized by a continuous influx of gas near the contact line, due to the gas attraction towards hydrophobic walls [Dammer and Lohse, Phys. Rev. Lett. 96, 206101 (2006); Zhang , Phys. Rev. Lett. 98, 136101 (2007); Mezger , J. Chem. Phys. 128, 244705 (2008)]. This influx balances the outflux and allows for a metastable equilibrium, which, however, vanishes in thermodynamic equilibrium. Our theory predicts the equilibrium radius of the surface nanobubbles, as well as the threshold for surface nanobubble formation as a function of hydrophobicity and gas concentration.

The forcibly launched spores of ascomycete fungi must eject through several millimeters of nearly still air surrounding fruiting bodies to reach dispersive air flows. Because of their microscopic size, spores experience great fluid drag, and although this drag can aid transport by slowing sedimentation out of dispersive air flows, it also causes spores to decelerate rapidly after launch. We hypothesize that spores are shaped to maximize their range in the nearly still air surrounding fruiting bodies. To test this hypothesis we numerically calculate optimal spore shapes-shapes of minimum drag for prescribed volumes-and compare these shapes with real spore shapes taken from a phylogeny of > 100 species. Our analysis shows that spores are constrained to remain within 1% of the minimum possible drag for their size. From the spore shapes we predict the speed of spore launch, and confirm this prediction through high-speed imaging of ejection in Neurospora tetrasperma. By reconstructing the evolutionary history of spore shapes within a single ascomycete family we measure the relative contributions of drag minimization and other shape determinants to spore shape evolution. Our study uses biomechanical optimization as an organizing principle for explaining shape in a mega-diverse group of species and provides a framework for future measurements of the forces of selection toward physical optima.

Wind tunnel experiments have shown that bumps on the leading edge of model humpback whale flippers cause them to ``stall'' (i.e., lose lift dramatically) more gradually and at a higher angle of attack. Here we develop an aerodynamic model which explains the observed increase in stall angle. The model predicts that as the amplitude of the bumps is increased, the lift curve flattens out, leading to potentially desirable control properties. We find that stall delay is insensitive to the wavelength of the bumps, in accordance with experimental observations.

We study the patterns formed on ion sputtered Si surfaces as a function of ion energy and incidence angle, and identify a region in parameter space where the flat surface is stable. The boundaries between the stable and pattern-forming regions represent mathematical bifurcations. Our data set exhibits at least two different bifurcation types. We discuss the constraints imposed by these observations on the correct model of long wavelength dynamics of ion sputtered surfaces.

We study the shapes of perfect projectiles: Bodies of prescribed volume that are designed to suffer minimum fluid drag in steady flight. Perfect projectiles have a surprising property: Although the flow of fluid around the body of the projectile is fore-aft asymmetric at moderate flow speeds, the shape of the body that minimizes drag is nonetheless highly symmetrical. We show that perfect projectiles are weakly asymmetric and that their asymmetry grows with the cube of the projectile size for sufficiently small projectiles. The persistence of apparent fore-aft symmetry is speculated to be a signature of the linearity and reciprocity of the drag-determining features of the flow around the projectile. (C) 2008 American Institute of Physics.

The velocity fluctuations of particles in a low-Reynolds-number fluidized bed have important similarities and differences with the velocity fluctuations in a low-Reynolds-number sedimenting suspension. We show that, like sedimentation, the velocity fluctuations in a fluidized bed are described well by the balance between density fluctuations due to Poisson statistics and Stokes drag. However, unlike sedimentation, the correlation length of the fluctuations in a fluidized bed increases with volume fraction. We argue that this difference arises because the relaxation time of density fluctuations is completely different in the two systems.

We study how functional constraints bound and shape evolution through an analysis of mammalian voltage-gated sodium channels. The primary function of sodium channels is to allow the propagation of action potentials. Since Hodgkin and Huxley, mathematical models have suggested that sodium channel properties need to be tightly constrained for an action potential to propagate. There are nine mammalian genes encoding voltage-gated sodium channels, many of which are more than approximate to 90% identical by sequence. This sequence similarity presumably corresponds to similarity of function, consistent with the idea that these properties must be tightly constrained. However, the multiplicity of genes encoding sodium channels raises the question: why are there so many? We demonstrate that the simplest theoretical constraints bounding sodium channel diversity-the requirements of membrane excitability and the uniqueness of the resting potential-act directly on constraining sodium channel properties. We compare the predicted constraints with functional data on mammalian sodium channel properties collected from the literature, including 172 different sets of measurements from 40 publications, wild-type and mutant, under a variety of conditions. The data from all channel types, including mutants, obeys the excitability constraint; on the other hand, channels expressed in muscle tend to obey the constraint of a unique resting potential, while channels expressed in neuronal tissue do not. The excitability properties alone distinguish the nine sodium channels into four different groups that are consistent with phylogenetic analysis. Our calculations suggest interpretations for the functional differences between these groups.

Physiological and evolutionary adaptations operate at very different time scales. Nevertheless, there are reasons to believe there should be a strong relationship between the two, as together they modify the phenotype. Physiological adaptations change phenotype by altering certain microscopic parameters; evolutionary adaptation can either alter genetically these same parameters or others to achieve distinct or similar ends. Although qualitative discussions of this relationship abound, there has been very little quantitative analysis. Here, we use the hemoglobin molecule as a model system to quantify the relationship between physiological and evolutionary adaptations. We compare measurements of oxygen saturation curves of 25 mammals with those of human hemoglobin under a wide range of physiological conditions. We fit the data sets to the Monod-Wyman-Changeux model to extract microscopic parameters. Our analysis demonstrates that physiological and evolutionary change act on different parameters. The main parameter that changes in the physiology of hemoglobin is relatively constant in evolution, whereas the main parameter that changes in the evolution of hemoglobin is relatively constant in physiology. This orthogonality suggests continued selection for physiological adaptability and hints at a role for this adaptability in evolutionary change.

A recent experiment [Boncheva Proc. Natl. Acad. Sci. U.S.A. 102, 3924 (2005)] introduced the possibility of initiating the self-assembly of a three-dimensional structure from a flat elastic sheet. The ultimate utility of this method for assembly depends on whether it leads to incorrect, metastable structures. Here we examine how the number of metastable states depends on the sheet shape and thickness. Using simulations and theory, we identify out-of-plane buckling as the key event leading to metastability. The buckling strain that arises from joining edges of a planar sheet can be estimated using the theory of dislocations in elastic media. The number of metastable states increases rapidly with increasing variability in the boundary curvature and decreasing sheet thickness.

Numerical modeling of global atmospheric chemical dynamics presents an enormous challenge, associated with simulating hundreds of chemical species with time scales varying from milliseconds to years. Here we present an algorithm that provides a significant reduction in computational cost. Because most of the fast reactants and their quickly decomposing reaction products are localized near emission sources, we use a series of reduced chemical models of decreasing complexity with increasing distance from the source. The algorithm diagnoses the chemical dynamics on the-run, locally and separately for every species according to its characteristic reaction time. Unlike conventional time-scale separation methods, the spatial reduction algorithm speeds up not only the chemical solver but also advection-diffusion integration. Through several examples we demonstrate that the algorithm can reduce computational cost by at least an order of magnitude for typical atmospheric chemical kinetic mechanisms.

We demonstrate that a flowing liquid jet can be controllably split into two separate subfilaments through the application of a sufficiently strong tangential stress to the surface of the jet. In contrast, normal stresses can never split a liquid jet. We apply these results to observations of uncontrolled splitting of jets in electric fields. The experimental realization of controllable jet splitting would provide an entirely novel route for producing small polymeric fibers.