Person:

Brenner, Michael

Young's law predicts that a colloidal sphere in equilibrium with a liquid interface will straddle the two fluids, its height above the interface defined by an equilibrium contact angle. This equilibrium analysis has been used to explain why colloids often bind to liquid interfaces, an effect first observed a century ago by Ramsden and Pickering and later exploited in a wide range of material processes, including emulsification, water purification, mineral recovery, encapsulation, and the making of nanostructured materials. But little is known about the dynamics of binding. Here we show that the adsorption of polystyrene microspheres to a water-oil interface is characterized by a sudden breach and an unexpectedly slow relaxation. Particles do not reach equilibrium even after 100 seconds, and the relaxation appears logarithmic in time, suggesting that complete equilibration may take months. Surprisingly, viscous dissipation appears to play little role. Instead, the observed dynamics, which bear strong resemblance to aging in glassy systems, agree well with a model describing activated hopping of the contact line over nanoscale surface heterogeneities. These results may provide clues to longstanding questions on colloidal interactions at an interface.

We show that time-oscillating electric fields applied to plasmas present in flames create steady flows of gas. Ions generated within the flame move in the field and migrate a distance δ before recombining; the net flow of ions away from the flame creates a time-averaged force that drives the steady flows observed experimentally. A quantitative model describes the response of the flame and reveals how δ decreases as the frequency of the applied field increases. Interestingly, above a critical frequency, ac fields can be used to manipulate flames at a distance without the need for proximal electrodes.

Particles interacting with short-ranged potentials have attracted increasing interest, partly for their ability to model mesoscale systems such as colloids interacting via DNA or depletion. We consider the free-energy landscape of such systems as the range of the potential goes to zero. In this limit, the landscape is entirely defined by geometrical manifolds, plus a single control parameter. These manifolds are fundamental objects that do not depend on the details of the interaction potential and provide the starting point from which any quantity characterizing the system—equilibrium or nonequilibrium—can be computed for arbitrary potentials. To consider dynamical quantities we compute the asymptotic limit of the Fokker–Planck equation and show that it becomes restricted to the low-dimensional manifolds connected by “sticky” boundary conditions. To illustrate our theory, we compute the low-dimensional manifolds for Graphic identical particles, providing a complete description of the lowest-energy parts of the landscape including floppy modes with up to 2 internal degrees of freedom. The results can be directly tested on colloidal clusters. This limit is a unique approach for understanding energy landscapes, and our hope is that it can also provide insight into finite-range potentials.

Previous work has demonstrated that combining mechanical vibration with magnetic interactions can result in the self-assembly of complex structures, albeit at low yield. Here we introduce a system where the yield of self-assembled structures is quantitatively predicted by a theoretical analysis. Millimeter-sized magnetic blocks, designed to form chains as their minimal energy state, are placed in a turbulent fluid flow. The distribution of chain lengths that form is quantitatively consistent with predictions, showing that the chain length distribution coincides with that of monomers or polymers in a thermal bath, with the turbulence strength parametrizing the effective temperature.

The explosive growth in the number of protein sequences gives rise to the possibility of using the natural variation in sequences of homologous proteins to find residues that control different protein phenotypes. Because in many cases different phenotypes are each controlled by a group of residues, the mutations that separate one version of a phenotype from another will be correlated. Here we incorporate biological knowledge about protein phenotypes and their variability in the sequence alignment of interest into algorithms that detect correlated mutations, improving their ability to detect the residues that control those phenotypes. We demonstrate the power of this approach using simulations and recent experimental data. Applying these principles to the protein families encoded by Dscam and Protocadherin allows us to make testable predictions about the residues that dictate the specificity of molecular interactions.

Synoptic-scale pollution plumes in the free troposphere can preserve their identity as well-defined structures for a week or more while traveling around the globe. Eulerian chemical transport models (CTMs) have difficulty reproducing these layered structures due to numerical plume dissipation. We show that this dissipation is much faster than would be expected from the order of the advection scheme because of interaction between numerical diffusion and the nonuniformity of the atmospheric flow. The nonuniform flow stretches out the plume, enhancing the effect of numerical diffusion. For sufficiently strong stretching, the numerical decay of the plume is independent of the model grid resolution and is set instead by the flow Lyapunov exponent l. In this regime, conventional numerical methods are not convergent: upon increasing grid resolution, the plume still decays with the same decay rate. The critical plume size below which the numerical scheme does not converge is set by the geometric mean of the grid spacing and the characteristic length scale l = v/l over which the flow varies, where v is the wind speed. Above this critical plume size the numerically induced decay rate of the plume scales like the square root of the grid spacing. Application to an intercontinental pollution plume in a global CTM with realistic atmospheric flow shows that proper simulation of such a plume would require an impractical increase in grid resolution. Novel methods such as adaptive grids or embedded Lagrangian plumes are needed.

We present a computationally efficient adaptive method for calculating the time evolution of the concentrations of chemical species in global 3-D models of atmospheric chemistry. Our strategy consists of partitioning the computational domain into fast and slow regions for each chemical species at every time step. In each grid box, we group the fast species and solve for their concentration in a coupled fashion. Concentrations of the slow species are calculated using a simple semi-implicit formula. Separation of species between fast and slow is done on the fly based on their local production and loss rates. This allows for example to exclude short-lived volatile organic compounds (VOCs) and their oxidation products from chemical calculations in the remote troposphere where their concentrations are negligible, letting the simulation determine the exclusion domain and allowing species to drop out individually from the coupled chemical calculation as their production/loss rates decline. We applied our method to a 1-year simulation of global tropospheric ozone-NOx-VOC-aerosol chemistry using the GEOS-Chem model. Results show a 50% improvement in computational performance for the chemical solver, with no significant added error.

Sphere packing problems have a rich history in both mathematics and physics; yet, relatively few analytical analyses of sphere packings exist, and answers to seemingly simple questions are unknown. Here, we present an analytical method for deriving all packings of n spheres in R3 satisfying minimal rigidity constraints (≥ 3 contacts per sphere and ≥ 3n − 6 total contacts). We derive such packings for n ≤ 10 and provide a preliminary set of maximum contact packings for 10 < n ≤ 20. The resultant set of packings has some striking features; among them are the following: (i) all minimally rigid packings for n ≤ 9 have exactly 3n−6 contacts; (ii) nonrigid packings satisfying minimal rigidity constraints arise for n ≥ 9; (iii) the number of ground states (i.e., packings with the maximum number of contacts) oscillates with respect to n; (iv) for 10 ≤ n ≤ 20 there are only a small number of packings with the maximum number of contacts, and for 10 ≤ n < 13 these are all commensurate with the hexagonal close-packed lattice. The general method presented here may have applications to other related problems in mathematics, such as the Erdos repeated distance problem and Euclidean distance matrix completion problems.

The study of clusters has provided the most tangible link between local geometry and bulk condensed matter. But experiments have not yet systematically explored the thermodynamics of even the smallest clusters. Here we present experimental measurements of the structures and free energies of colloidal clusters in which the particles act as hard spheres with short-range attractions. We find that highly symmetric clusters are strongly suppressed by rotational entropy, while the most stable clusters have anharmonic vibrational modes or extra bonds. Many of these are subsets of close-packed lattices. As the number of particles increases from 6 to 10 we observe the emergence of a complex free energy landscape with a small number of ground states and many local minima.

Cyanobacteria are photosynthetic bacteria with a unique CO2 concentrating mechanism (CCM), enhancing carbon fixation. Understanding the CCM requires a systems level perspective of how molecular components work together to enhance CO2 fixation. We present a mathematical model of the cyanobacterial CCM, giving the parameter regime (expression levels, catalytic rates, permeability of carboxysome shell) for efficient carbon fixation. Efficiency requires saturating the RuBisCO reaction, staying below saturation for carbonic anhydrase, and avoiding wasteful oxygenation reactions. We find selectivity at the carboxysome shell is not necessary; there is an optimal non-specific carboxysome shell permeability. We compare the efficacy of facilitated CO2 uptake, CO2 scavenging, and HCO3− transport with varying external pH. At the optimal carboxysome permeability, contributions from CO2 scavenging at the cell membrane are small. We examine the cumulative benefits of CCM spatial organization strategies: enzyme co-localization and compartmentalization. DOI: http://dx.doi.org/10.7554/eLife.02043.001