I study the spatial organization of retail commercial activities. These are organized in a network comprising “antilinks,” i.e., links of negative weight. From pure location data, network analysis leads to a community structure that closely follows the commercial classification of the U.S. Department of Labor. The interaction network allows one to build a “quality” index of optimal location niches for stores, which has been empirically tested.

We study the sedimentation of two identical but nonspherical particles sedimenting in a Stokesian fluid. Experiments and numerical simulations reveal periodic orbits wherein the bodies mutually induce an in-phase rotational motion accompanied by periodic modulations of sedimentation speed and separation distance. We term these “tumbling orbits” and find that they appear over a broad range of body shapes.

We explore the electromagnetic characterization of a planar artificial magnetic metamaterial. Because the composite structure is two- rather than three-dimensional, it does not form a medium with assignable bulk properties, such as the electric permittivity and magnetic permeability. However, we find that it is possible to characterize the expected bulk response of a structure composed of repeated layers of metamaterial planes, from a reflectance measurement of a single metamaterial surface made at an oblique angle. We present an analytical theory that relates the reflectance of a single plane to the expected bulk permeability and permeability of the composite, as well as supporting experiments and numerical simulations. Our results show that the recent use of reflectance measurements to characterize planar split ring resonator samples can reveal the presence of circulating currents in a sample—the precursor to artificial magnetism—but are insufficient to provide quantitative results unless the symmetry of the underlying metamaterial elements is carefully specified.

The coupled aggregation and sedimentation of colloidal particles with short-range attractions are investigated. Nonadsorbing polymer is used to induce depletion interactions between the hard-sphere particles. Gravitational forces, caused by a density mismatch between the particles and the suspending fluid, result in the sedimentation of particles and aggregates, as well as the compaction and rearrangement of the final sediment layer. At low polymer concentrations $C_{\mathrm{P}}$, or low initial volume fractions ${\varphi }_{\mathrm{o}}$, clusters formed during the period of fast sedimentation are small, and the structure of the final sediment is dense. Conversely, at high $C_{\mathrm{P}}$, or high ${\varphi }_{\mathrm{o}}$, large clusters form during sedimentation, and the resulting sediment structure is significantly less dense, with large void volumes. The size of the presediment aggregates depends on $C_{\mathrm{P}}$ and ${\varphi }_{\mathrm{o}}$ with a functional form that resembles other thermally activated barrier hopping processes in colloidal systems, such as the delayed sedimentation of colloidal gels. Finally, when the particles are weakly attractive, gravitational stresses are found to induce compaction of the sediment over long periods of time. However, sediments composed of particles that are strongly attractive resist rearrangements and compaction, even when the sediment layers have a relatively large amount of free volume.

Recent measurements have suggested that the antiplasticizing effect of glycerol on trehalose can significantly increase the preservation times of proteins stored in this type of preservative formulation. In order to better understand the physical origin of this phenomenon, we examine the nature of antiplasticization in trehalose-glycerol mixtures by dielectric spectroscopy. These measurements cover a broad frequency range between $40\mathrm{Hz}\text{to}18\mathrm{GHz}$ (covering the secondary relaxation range of the fragile glass-former trehalose and the primary relaxation range of the strong glass-former glycerol) and a temperature $\left(T\right)$ range bracketing room temperature $\left(220\mathrm{K}\text{to}350\mathrm{K}\right)$. The Havriliak-Negami function precisely fits our relaxation data and allows us to determine the temperature and composition dependence of the relaxation time $\tau$ describing a relative fast dielectric relaxation process appropriate to the characterization of antiplasticization. We observe that increasing the glycerol concentration at fixed $T$ increases $\tau$ (i.e., the extent of antiplasticization) until a temperature dependent critical “plasticization concentration” $x_{wp}$ is reached. At a fixed concentration, we find a temperature at which antiplasticization first occurs upon cooling and we designate this as the “antiplasticization temperature,” $T_{\mathit{ant}}$. The ratio of the $\tau$ values for the mixture and pure trehalose is found to provide a useful measure of the extent of antiplasticization, and we explore other potential measures of antiplasticization relating to the dielectric strength.

Boundary crisis is a mechanism for destroying a chaotic attractor when one parameter is varied. In a two-parameter setting the locus of the boundary crisis is associated with curves of homoclinic or heteroclinic bifurcations of periodic saddle points. It is known that this locus has nondifferentiable points. We show here that the locus of boundary crisis is far more complicated than previously reported. It actually contains infinitely many gaps, corresponding to regions (of positive measure) where attractors exist.

Localized nonlinear modes, or solitons, are obtained for the two-dimensional nonlinear Schrödinger equation with various external potentials that possess large variations from periodicity, i.e., vacancy defects, edge dislocations, and quasicrystal structure. The solitons are obtained by employing a spectral fixed-point computational scheme. Investigation of soliton evolution by direct numerical simulations shows that irregular-lattice solitons can be stable, unstable, or undergo collapse.

The phase-field-crystal model [K. R. Elder and M. Grant, Phys. Rev. E 70, 051605 (2004)] produces multigrain structures on atomistic length scale but on diffusive time scales. Since individual atoms are resolved but are treated identically it is difficult to distinguish the exact position of grain boundaries and defects within grains. In order to analyze and visualize the whole grains a two-dimensional wavelet transform has been developed, which is capable of extracting grain boundaries and the lattice orientation of a grain relative to a laboratory frame of reference. This transformation makes it possible not only to easily visualize the multigrain structure, but also to perform exact measurements on low- and high-angle boundaries, grain size distributions and boundary-angle distributions, which can then be compared to experimental data. The presented wavelet transform can also be applied to results of other atomistic simulations, e.g., molecular dynamics or granular materials.

Real collective density variables $C\left(\mathbf{k}\right)$ [cf. Eq. (1.3)] in many-particle systems arise from nonlinear transformations of particle positions, and determine the structure factor $S\left(\mathbf{k}\right)$, where $\mathbf{k}$ denotes the wave vector. Our objective is to prescribe $C\left(\mathbf{k}\right)$ and then to find many-particle configurations that correspond to such a target $C\left(\mathbf{k}\right)$ using a numerical optimization technique. Numerical results reported here extend earlier one- and two-dimensional studies to include three dimensions. In addition, they demonstrate the capacity to control $S\left(\mathbf{k}\right)$ in the neighborhood of $\mid \mathbf{k}\mid =0$. The optimization method employed generates multiparticle configurations for which $S\left(\mathbf{k}\right)\propto {\mid \mathbf{k}\mid }^{\alpha }$, $\mid \mathbf{k}\mid ⩽K$, and $\alpha =1$, 2, 4, 6, 8, and 10. The case $\alpha =1$ is relevant for the Harrison-Zeldovich model of the early universe, for superfluid ${}^4\mathrm{He}$, and for jammed amorphous sphere packings. The analysis also provides specific examples of interaction potentials whose classical ground states are configurationally degenerate and disordered.

We have used equilibrium and nonequilibrium molecular dynamics simulations to study the solute self-diffusion coefficient and the shear rate dependence of the solution viscosity in solutions of model nanocolloidal particles that range in mass ratio from $\mu =1$ up to $\mu =50$ and size ratio from $s=1$ up to $s=4.03$ at various concentrations. The zero shear rate viscosities and the initial rates of shear thinning were determined from data in the shear rate region in which the suspension is strongly shear thinning while the solvent remains Newtonian or is weakly shear thinning. The rate of shear thinning increased dramatically with solute volume fraction, regardless of whether the increase was due to increasing solute size or increasing the solute concentration. In a series of simulations in which the mass ratio was varied while keeping the size ratio fixed at $s=1$, we found that the approach of the viscosities and self-diffusion coefficients to their limiting mass ratio independent values was well described by a rather simple exponential dependence on mass ratio. The concentration dependence of the limiting infinite mass ratio values of the self-diffusion coefficients and zero shear rate viscosities were determined, and used to compute the hydrodynamic radius $R_H$ of the solute particles by various methods. The values of $R_H$ that were obtained by the different methods were reasonably consistent with each other, and indicated that the radius at which the slip boundary condition holds is slightly smaller than the cross-interaction radius between the solute and solvent particles.

We report on Monte Carlo studies of the elastic properties of the helix-coil wormlike chain model of $\alpha$-helical polypeptides. In this model the secondary structure enters as a scalar (Ising-like) variable that controls the local chain bending modulus. We characterize the nonlinear elastic properties of these molecules including their response to applied tensile forces and bending torques both individually and in combination. We find a pronounced effect of applied torque on the extensional compliance of the molecule and a similar effect of tension on the bending compliance. Finally we speculate that the strongly nonlinear response of $\alpha$-helical polypeptides to combinations of torque and force plays a role in allosteric transitions in proteins.

Optical properties of fcc opals oriented along the [111] direction are calculated by means of a scattering-matrix approach based on approximating each sphere with cylindrical slices. The use of a plane-wave basis in each layer allows distinguishing zero-order reflection and transmission from higher-order (diffraction) spectra. Optical spectra at large values of the angle of incidence indicate the presence of diffraction effects and of polarization mixing along the $LW$ orientation. Reflectance and transmittance in the high-energy region show a rich spectral dependence and compare reasonably well with recent experimental observations on polystyrene opals. Diffraction spectra as a function of the number of layers display an oscillatory behavior, pointing to the existence of a Pendellösung phenomenon, related to the exchange of energy between two propagating modes in the investigated three-dimensional photonic crystal. This phenomenon could be observed in transmittance experiments on high-quality opals with controlled thickness.

Mechanical properties of lipidic membranes such as their bending rigidity are governing liposome morphology and play an important role in processes like membrane fusion and adhesion. Force versus deformation measurements are the most direct means to determine this, but so far experimental data is scarce and mainly stems from techniques that are limited to giant vesicles. We present atomic force microscope force spectroscopy as a method allowing force-deformation measurements of submicron vesicles. Bending rigidities of small unilamellar dipalmitoylphosphatidylcholine (DPPC) liposomes $(R<200\mathrm{nm})$ can be derived from the force-deformation data using analytical models based on shell theory and are in good agreement with independent measurements.

The classic Michaelis-Menten equation describes the catalytic activities for ensembles of enzyme molecules very well. But recent single-molecule experiments showed that the waiting time distribution and other properties of single enzyme molecules were not consistent with the prediction based on the ensemble viewpoint. They have contributed to the slow conformational changes of a single enzyme in the catalytic processes. In this work, we study the general dynamics of single enzymes in the presence of dynamic disorder. We find that, within the time separation regimes, i.e., the slow reaction and nondiffusion limits, the Michaelis-Menten equation holds exactly. In particular, by employing the decoupling approximation we demonstrate analytically that the classic Michaelis-Menten equation is still an excellent approximation in the presence of general dynamic disorder.

This paper investigates stochastic resonance in parallel arrays of uncoupled saturating devices. The Fisher information is used to demonstrate the possibility of noise improved parameter estimation for arbitrary parametric signals. Especially, it is shown that improvement by noise always occurs in these arrays, for any configuration of the input signal, even in optimal configuration. The results contribute to establish stochastic resonance in parallel uncoupled arrays as a general mechanism of enhancement by noise, which can occur in wide classes of nonlinearities and for various information processing tasks. It can supplement other mechanisms of stochastic resonance that take place in isolated nonlinearities but generally in restricted configurations of the input signal.

Biofilm structure plays an important role in biofilm function and control. It is thus important to determine the extent to which mechanics may determine structure in biofilms. We consider a generic qualitative constitutive description of biofilm incorporating as assumptions a small number of fundamental physical properties of biofilm viscoelasticity and cohesion. Implications of cohesive energy on biofilm structure are then explored. Steady solutions and energy minima are studied and it is demonstrated that cohesion energy leads naturally to a free surface film state. It is found that in many circumstances, biofilms could be subject to heterogeneity formation via spinodal decomposition. Such material heterogeneity may have important implications for structural stability in biofilms both on short and long time scales.

This paper presents a cellular automaton model without step back for pedestrian dynamics considering the human behaviors which can make judgments in some complex situations. This model can simulate pedestrian movement with different walk velocities through update at different time-step intervals. Two kinds of boundary conditions including periodic and open boundary for pedestrian counter flow are considered, and their dynamical characteristics are discussed. Simulation results show that for periodic boundary condition there are three phases of pedestrian patterns, i.e., freely moving phase, lane formation phase, and perfectly stopped phase at some certain total density ranges. In the stage of lane formation, the phenomenon that pedestrians exceed those with lower walk velocity through a narrow walkway can be found. For open boundary condition, at some certain entrance densities, there are two steady states of pedestrian patterns; but the first is metastable. Spontaneous fluctuations can break the first steady state, i.e., freely moving phase, and run into the second steady state, i.e., perfectly stopped phase.

We examine properties of a reaction front that forms in irreversible reaction-diffusion systems with concentration-dependent diffusivities. We study two different models of such systems and find that in the limit of a vanishingly small diffusivity of the reaction product, the reaction front dynamics enters a separate universality class, with the front width asymptotically tending to a constant value, and the reaction rate at the reaction front center diminishing with time $t$ as $t^{-1∕2}$. This behavior can be also observed in systems with nonvanishing (but small) diffusivity of the reaction product at intermediate times.