Surfactancy in a tadpole model of proteins.

We model the environment of eukaryotic nuclei by representing macromolecules by only their entropic properties, with globular molecules represented by spherical colloids and flexible molecules by polymers. We put particular focus on proteins with both globular and intrinsically disordered regions, which we represent with 'tadpole' constructed by grafting single polymers and colloids together. In Monte Carlo simulations, we find these tadpoles support phase separation via depletion flocculation, and demonstrate several surfactant behaviours, including being found preferentially at interfaces and forming micelles in single phase solution.

Generalized Langevin equation formulation for anomalous diffusion in the Ising model at the critical temperature.

We consider the two- (2D) and three-dimensional (3D) Ising models on a square lattice at the critical temperature T_{c}, under Monte Carlo spin flip dynamics. The bulk magnetization and the magnetization of a tagged line in the 2D Ising model, and the bulk magnetization and the magnetization of a tagged plane in the 3D Ising model, exhibit anomalous diffusion. Specifically, their mean-square displacements increase as power laws in time, collectively denoted as ∼t^{c}, where c is the anomalous exponent.

Why Clothes Don't Fall Apart: Tension Transmission in Staple Yarns.

The problem of how staple yarns transmit tension is addressed within abstract models in which the Amontons-Coulomb friction laws yield a linear programing (LP) problem for the tensions in the fiber elements. We find there is a percolation transition such that above the percolation threshold the transmitted tension is in principle unbounded. We determine that the mean slack in the LP constraints is a suitable order parameter to characterize this supercritical state.

Wavelet Monte Carlo dynamics: A new algorithm for simulating the hydrodynamics of interacting Brownian particles.

We develop a new algorithm for the Brownian dynamics of soft matter systems that evolves time by spatially correlated Monte Carlo moves. The algorithm uses vector wavelets as its basic moves and produces hydrodynamics in the low Reynolds number regime propagated according to the Oseen tensor. When small moves are removed, the correlations closely approximate the Rotne-Prager tensor, itself widely used to correct for deficiencies in Oseen.

Nonlinear least-squares method for the inverse droplet coagulation problem.

If the rates, K(x,y), at which particles of size x coalesce with particles of size y is known, then the mean-field evolution of the particle size distribution of an ensemble of irreversibly coalescing particles is described by the Smoluchowski equation. We study the corresponding inverse problem which aims to determine the coalescence rates K(x,y) from measurements of the particle size distribution. We assume that K(x,y) is a homogeneous function of its arguments, a case which occurs commonly in practice.

Scale-invariant growth processes in expanding space.

Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting particles, and their large scale behavior depends on the overall growth geometry. We establish an exact relation between statistical properties of structures in uniformly expanding and fixed geometries, which preserves the local scale invariance and is independent of other properties such as the dimensionality.

Collective oscillations in irreversible coagulation driven by monomer inputs and large-cluster outputs.

We describe collective oscillatory behavior in the kinetics of irreversible coagulation with a constant input of monomers and removal of large clusters. For a broad class of collision rates, this system reaches a nonequilibrium stationary state at large times and the cluster size distribution tends to a universal form characterized by a constant flux of mass through the space of cluster sizes. Universality, in this context, means that the stationary state becomes independent of the cutoff as the cutoff grows.

Shape of a ponytail and the statistical physics of hair fiber bundles.

A general continuum theory for the distribution of hairs in a bundle is developed, treating individual fibers as elastic filaments with random intrinsic curvatures. Applying this formalism to the iconic problem of the ponytail, the combined effects of bending elasticity, gravity, and orientational disorder are recast as a differential equation for the envelope of the bundle, in which the compressibility enters through an "equation of state." From this, we identify the balance of forces in various regions of the ponytail, extract a remarkably simple equation of state from laboratory measurements of human ponytails, and relate the pressure to the measured random curvatures of individual hairs.

Instantaneous gelation in Smoluchowski's coagulation equation revisited.

We study the solutions of the Smoluchowski coagulation equation with a regularization term which removes clusters from the system when their mass exceeds a specified cutoff size, M. We focus primarily on collision kernels which would exhibit an instantaneous gelation transition in the absence of any regularization. Numerical simulations demonstrate that for such kernels with monodisperse initial data, the regularized gelation time decreases as M increases, consistent with the expectation that the gelation time is zero in the unregularized system.

Stochastic transitions and jamming in granular pipe flow.

We study a model granular suspension driven down a channel by an embedding fluid via computer simulations. We characterize the different system flow regimes and the stochastic nature of the transitions between them. For packing fractions below a threshold ϕ{m}, granular flow is disordered and exhibits an Ostwald-de Waele-type power-law shear-stress constitutive relation.

Reply to the comment on 'Anomalous dynamics of unbiased polymer translocation through a narrow pore' and other recent papers by D Panja, G Barkema and R Ball.

We reply to the comment made by Dubbeldam et al (2009 J. Phys.: Condens.

Identifying critical residues in protein folding: Insights from phi-value and P(fold) analysis.

We apply a simulational proxy of the phi-value analysis and perform extensive mutagenesis experiments to identify the nucleating residues in the folding "reactions" of two small lattice Go polymers with different native geometries. Our findings show that for the more complex native fold (i.e.

Fermions without fermion fields.

It is shown that an arbitrary fermion hopping Hamiltonian can be mapped into a system with no fermion fields, generalizing an earlier model of Levin and Wen. All operators in the Hamiltonian of the resulting description commute (rather than anticommute) when acting at different sites, despite the system having excitations obeying Fermi statistics. While extra conserved degrees of freedom are introduced, they are all locally identified in the representation obtained.

Anisotropic diffusion limited aggregation in three dimensions: universality and nonuniversality.

We explore the macroscopic consequences of lattice anisotropy for diffusion limited aggregation (DLA) in three dimensions. Simple cubic and bcc lattice growths are shown to approach universal asymptotic states in a coherent fashion, and the approach is accelerated by the use of noise reduction. These states are strikingly anisotropic dendrites with a rich hierarchy of structure.

Off-lattice noise reduced diffusion-limited aggregation in three dimensions.

Using off-lattice noise reduction, it is possible to estimate the asymptotic properties of diffusion-limited aggregation clusters grown in three dimensions with greater accuracy than would otherwise be possible. The fractal dimension of these aggregates is found to be 2.50+/-0.

Growth by random walker sampling and scaling of the dielectric breakdown model.

Random walkers absorbing on a boundary sample the harmonic measure linearly and independently: we discuss how the recurrence times between impacts enable nonlinear moments of the measure to be estimated. From this we derive a technique to simulate dielectric breakdown model growth, which is governed nonlinearly by the harmonic measure. For diffusion-limited aggregation, recurrence times are shown to be accurate and effective in probing the multifractal growth measure in its active region.

Theory of growth by differential sedimentation, with application to snowflake formation.

A simple model of irreversible aggregation under differential sedimentation of particles in a fluid is presented. The structure of the aggregates produced by this process is found to feed back on the dynamics in such a way as to stabilize both the exponents controlling the growth rate, and the fractal dimension of the clusters produced at readily predictable values. The aggregation of ice crystals to form snowflakes is considered as a potential application of the model.

Folding and form: insights from lattice simulations.

Monte Carlo simulations of a Miyazawa-Jernigan lattice-polymer model indicate that, depending on the native structure's geometry, the model exhibits two broad classes of folding mechanisms for two-state folders. Folding to native structures of low contact order is driven by backbone distance and is characterized by a progressive accumulation of structure towards the native fold. By contrast, folding to high contact order targets is dominated by intermediate stage contacts not present in the native fold, yielding a more cooperative folding process.

Diffusion-limited aggregation in channel geometry.

We performed extensive numerical simulation of diffusion-limited aggregation in two-dimensional channel geometry. Contrary to earlier claims, the measured fractal dimension D=1.712+/-0.

Characterization of the probabilistic traveling salesman problem.

We show that stochastic annealing can be successfully applied to gain new results on the probabilistic traveling salesman problem. The probabilistic "traveling salesman" must decide on an a priori order in which to visit n cities (randomly distributed over a unit square) before learning that some cities can be omitted. We find the optimized average length of the pruned tour follows E(L(pruned))=sqrt[np](0.

Stochastic annealing.

We show how to simulate a system in thermal equilibrium when the energy cannot be evaluated exactly: the error distribution needs to be symmetric, but it does not need to be known. We also solve the Ceperley-Dewing version of this problem, where the error distribution is taken to be fully known. These underlying ideas give an effective optimization strategy for problems where the evaluation of each design can be sampled only statistically, including an application to protein folding.

From plasticity to a renormalization group.

The marginally rigid state is a candidate paradigm for what makes granular material a state of matter distinct from both liquid and solid. The coordination number is identified as a discriminating characteristic, and for rough-surfaced particles we show that the low values predicted are indeed approached in simple two-dimensional experiments. We show calculations of the stress transmission, suggesting that this is governed by local linear equations of constraint between the stress components.

Diffusion-controlled growth: theory and closure approximations.

We expand upon a new theoretical framework for diffusion-limited aggregation and associated dielectric breakdown models in two dimensions [R. C. Ball and E.

Protein design depends on the size of the amino acid alphabet.

We consider the design of proteins to be simultaneously thermodynamically stable in multiple independent and correlated conformations. We first show that a protein can be trained to fold to multiple independent conformations and calculate its capacity. The number of configurations that it can remember is proportional to the logarithm of the number of amino acid species A, independent of chain length.

Off-lattice noise reduction and the ultimate scaling of diffusion-limited aggregation in two dimensions.

Off-lattice diffusion-limited aggregation (DLA) clusters grown with different levels of noise reduction are found to be consistent with a simple fractal fixed point. Cluster shapes and their ensemble variation exhibit a dominant slowest correction to scaling, and this also accounts for the apparent "multiscaling" in the DLA mass distribution. We interpret the correction to scaling in terms of renormalized noise.