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. We argue that the anomalous diffusion in all these quantities for the Ising model stems from time-dependent restoring forces, decaying as power laws in time-also with exponent c -in striking similarity to anomalous diffusion in polymeric systems. Prompted by our previous work that has established a memory-kernel based generalized Langevin equation (GLE) formulation for polymeric systems, we show that a closely analogous GLE formulation holds for the Ising model as well. We obtain the memory kernels from spin-spin correlation functions, and the formulation allows us to consistently explain anomalous diffusion as well as anomalous response of the Ising model to an externally applied magnetic field in a consistent manner.

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. We argue the mechanism is generic, and in practical terms, it corresponds to a switch from a ductile to a brittle failure mode accompanied by a significant increase in mechanical strength.

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. We also include plane wave moves to provide the longest range correlations, which we detail for both infinite and periodic systems. The computational cost of the algorithm scales competitively with the number of particles simulated, N, scaling as N In N in homogeneous systems and as N in dilute systems. In comparisons to established lattice Boltzmann and Brownian dynamics algorithms, the wavelet method was found to be only a factor of order 1 times more expensive than the cheaper lattice Boltzmann algorithm in marginally semi-dilute simulations, while it is significantly faster than both algorithms at large N in dilute simulations. We also validate the algorithm by checking that it reproduces the correct dynamics and equilibrium properties of simple single polymer systems, as well as verifying the effect of periodicity on the mobility tensor.

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. The problem of determining K(x,y), a function to two variables, then reduces to the simpler problem of determining a function of a single variable plus two exponents, µ and ν, which characterize the scaling properties of K(x,y). The price of this simplification is that the resulting least-squares problem is nonlinear in the exponents µ and ν. We demonstrate the effectiveness of the method on a selection of coalescence problems arising in polymer physics, cloud science, and astrophysics. The applications include examples in which the particle size distribution is stationary owing to the presence of sources and sinks of particles and examples in which the particle size distribution is undergoing self-similar relaxation in time.

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. This relation generalizes standard conformal transformations as the natural symmetry of self-affine growth processes. We illustrate our main result numerically for various structures of coalescing Lévy flights and fractional Brownian motions, including also branching and finite particle sizes. One of the main benefits of this approach is a full, explicit description of the asymptotic statistics in expanding domains, which are often nontrivial and random due to amplification of initial fluctuations.

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. This universality is lost, however, if the aggregation rate between large and small clusters increases sufficiently steeply as a function of cluster sizes. We identify a transition to a regime in which the stationary state vanishes as the cutoff grows. This nonuniversal stationary state becomes unstable as the cutoff is increased. It undergoes a Hopf bifurcation after which the stationary state is replaced by persistent and periodic collective oscillations. These oscillations, which bear some similarities to relaxation oscillations in excitable media, carry pulses of mass through the space of cluster sizes such that the average mass flux through any cluster size remains constant. Universality is partially restored in the sense that the scaling of the period and amplitude of oscillation is inherited from the dynamical scaling exponents of the universal regime.

Social networks--the future for health care delivery.

With the rapid growth of online social networking for health, health care systems are experiencing an inescapable increase in complexity. This is not necessarily a drawback; self-organising, adaptive networks could become central to future health care delivery. This paper considers whether social networks composed of patients and their social circles can compete with, or complement, professional networks in assembling health-related information of value for improving health and health care. Using the framework of analysis of a two-sided network--patients and providers--with multiple platforms for interaction, we argue that the structure and dynamics of such a network has implications for future health care. Patients are using social networking to access and contribute health information. Among those living with chronic illness and disability and engaging with social networks, there is considerable expertise in assessing, combining and exploiting information. Social networking is providing a new landscape for patients to assemble health information, relatively free from the constraints of traditional health care. However, health information from social networks currently complements traditional sources rather than substituting for them. Networking among health care provider organisations is enabling greater exploitation of health information for health care planning. The platforms of interaction are also changing. Patient-doctor encounters are now more permeable to influence from social networks and professional networks. Diffuse and temporary platforms of interaction enable discourse between patients and professionals, and include platforms controlled by patients. We argue that social networking has the potential to change patterns of health inequalities and access to health care, alter the stability of health care provision and lead to a reformulation of the role of health professionals. Further research is needed to understand how network structure combined with its dynamics will affect the flow of information and potentially the allocation of health care resources.

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. This decrease appears to be a logarithmically slow function of M, indicating that instantaneously gelling kernels may still be justifiable as physical models despite the fact that they are highly singular in the absence of a cutoff. We also study the case when a source of monomers is introduced in the regularized system. In this case a stationary state is reached. We present a complete analytic description of this regularized stationary state for the model kernel, K(m(1),m(2)) = max{m(1),m(2)}(ν), which gels instantaneously when M → ∞ if ν>1. The stationary cluster size distribution decays as a stretched exponential for small cluster sizes and crosses over to a power law decay with exponent ν for large cluster sizes. The total particle density in the stationary state slowly vanishes as [(ν-1)log M](-1/2) when M → ∞. The approach to the stationary state is nontrivial: Oscillations about the stationary state emerge from the interplay between the monomer injection and the cutoff, M, which decay very slowly when M is large. A quantitative analysis of these oscillations is provided for the addition model which describes the situation in which clusters can only grow by absorbing monomers.

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. Above ϕ{m}, two asymptotic states exist; disordered flow can persist indefinitely, yet, in a fraction of samples, the system self-organizes in an ordered form of flow where grains move in parallel ordered layers. In the latter regime, the Ostwald-de Waele relationship breaks down and a nearly solid plug appears in the center, with linear shear regions at the boundaries. Above a higher threshold ϕ{g}, an abrupt jamming transition is observed if ordering is avoided.

The Drosophila miR-310 cluster negatively regulates synaptic strength at the neuromuscular junction.

Emerging data implicate microRNAs (miRNAs) in the regulation of synaptic structure and function, but we know little about their role in the regulation of neurotransmission in presynaptic neurons. Here, we demonstrate that the miR-310-313 cluster is required for normal synaptic transmission at the Drosophila larval neuromuscular junction. Loss of miR-310-313 cluster leads to a significant enhancement of neurotransmitter release, which can be rescued with temporally restricted expression of mir-310-313 in larval presynaptic neurons. Kinesin family member, Khc-73 is a functional target for miR-310-313 as its expression is increased in mir-310-313 mutants and reducing it restores normal synaptic function. Cluster mutants show an increase in the active zone protein Bruchpilot accompanied by an increase in electron dense T bars. Finally, we show that repression of Khc-73 by miR-310-313 cluster influences the establishment of normal synaptic homeostasis. Our findings establish a role for miRNAs in the regulation of neurotransmitter release.

Retrograde BMP signaling controls synaptic growth at the NMJ by regulating trio expression in motor neurons.

Retrograde signaling is essential for coordinating the growth of synaptic structures; however, it is not clear how it can lead to modulation of cytoskeletal dynamics and structural changes at presynaptic terminals. We show that loss of retrograde bone morphogenic protein (BMP) signaling at the Drosophila larval neuromuscular junction (NMJ) leads to a significant reduction in levels of Rac GEF Trio and a diminution of transcription at the trio locus. We further find that Trio is required in motor neurons for normal structural growth. Finally, we show that transgenic expression of Trio in motor neurons can partially restore NMJ defects in larvae mutant for BMP signaling. Based on our findings, we propose a model in which a retrograde BMP signal from the muscle modulates GTPase activity through transcriptional regulation of Rac GEF trio, thereby regulating the homeostasis of synaptic growth at the NMJ.

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. Matter 21 098001) on our paper 'Anomalous dynamics of unbiased polymer translocation through a narrow pore' and our other recent papers.

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. For growth on an fcc lattice, our data suggest at least two stable fixed points of anisotropy, one matching the bcc case. Hexagonal growths, favoring six planar and two polar directions, appear to approach a line of asymptotic states with continuously tunable polar anisotropy. The more planar of these growths visually resembles real snowflake morphologies. Our simulations use a new and dimension-independent implementation of the DLA model. The algorithm maintains a hierarchy of sphere coverings of the growth, supporting efficient random walks onto the growth by spherical moves. Anisotropy was introduced by restricting growth to certain preferred directions.

Heterogeneity in synaptic transmission along a Drosophila larval motor axon.

At the Drosophila melanogaster larval neuromuscular junction (NMJ), a motor neuron releases glutamate from 30-100 boutons onto the muscle it innervates. How transmission strength is distributed among the boutons of the NMJ is unknown. To address this, we created synapcam, a version of the Ca2+ reporter Cameleon. Synapcam localizes to the postsynaptic terminal and selectively reports Ca2+ influx through glutamate receptors (GluRs) with single-impulse and single-bouton resolution. GluR-based Ca2+ signals were uniform within a given connection (that is, a given bouton/postsynaptic terminal pair) but differed considerably among connections of an NMJ. A steep gradient of transmission strength was observed along axonal branches, from weak proximal connections to strong distal ones. Presynaptic imaging showed a matching axonal gradient, with higher Ca2+ influx and exocytosis at distal boutons. The results suggest that transmission strength is mainly determined presynaptically at the level of individual boutons, possibly by one or more factors existing in a gradient.

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+/-0.01 , in agreement with earlier studies, and the asymptotic value of the relative penetration depth is xi/ R(dep) =0.122+/-0.002 . The multipole powers of the growth measure also exhibit universal asymptotes. The fixed point noise reduction is estimated to be epsilon(f) approximately 0.0035 , meaning that large clusters can be identified with a low noise regime. The slowest correction to scaling exponents are measured for a number of properties of the clusters, and the exponent for the relative penetration depth and quadrupole moment are found to be significantly different from each other. The relative penetration depth exhibits the slowest correction to scaling of all quantities, which is consistent with a theoretical result derived in two dimensions. We also note fast corrections to scaling, whose limited relevance is consistent with the requirement that clusters grow far enough in radius to support sufficient scales of ramification.

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. For the dielectric breakdown model our technique grows large clusters efficiently and we are led to significantly revise earlier exponent estimates. Previous results by two conformal mapping techniques were less converged than expected, and in particular a recent theoretical suggestion of superuniversality is firmly refuted.

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](0.872-0.105p)f(np), where p is the probability of a city needing to be visited, and f(np)-->1 as np--> infinity. The average length of the a priori tour (before omitting any cities) is found to follow E(L(a priori))=sqrt[n/p]beta(p), where beta(p)=1/[1.25-0.82 ln(p)] is measured for 0.05< or =p< or =0.6. Scaling arguments and indirect measurements suggest that beta(p) tends towards a constant for p<0.03. Our stochastic annealing algorithm is based on limited sampling of the pruned tour lengths, exploiting the sampling error to provide the analog of thermal fluctuations in simulated (thermal) annealing. The method has general application to the optimization of functions whose cost to evaluate rises with the precision required.

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+/-0.002 and its leading correction to scaling are the same as in the radial case. The average cluster, defined as the average conformal map, is similar but not identical to Saffman-Taylor fingers.

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.