We analyze the effects of particle shape angularity on the macroscopic shear behavior and texture of granular packings simulated by means of the contact dynamics method. The particles are regular polygons with an increasing number of sides ranging from 3 (triangles) to 60. The packings are analyzed in the steady shear state in terms of their shear strength, packing fraction, connectivity, and fabric and force anisotropies, as functions of the angularity. An interesting finding is that the shear strength increases with angularity up to a maximum value and saturates as the particles become more angular (below six sides). In contrast, the packing fraction declines towards a constant value, so that the packings of more angular particles are looser but have higher shear strength. We show that the increase of the shear strength at low angularity is due to an increase of both contact and force anisotropies and the saturation of the shear strength for higher angularities is a consequence of a rapid falloff of the contact and normal force anisotropies compensated for by an increase of the tangential force anisotropy. This transition reflects clearly the rather special geometrical properties of these highly angular shapes, implying that the stability of the packing relies strongly on the side-side contacts and the mobilization of friction forces.

The aging-time dependence of the segmental relaxation time of poly(vinyl acetate) (PVAc) in the glassy state is investigated in the bulk polymer and its nanocomposites with silica (SiO${}_2$). These systems present identical segmental dynamics, when this is probed in the equilibrium supercooled liquid by broadband dielectric spectroscopy. An acceleration of the physical aging process of PVAc with SiO${}_2$ was detected by monitoring the enthalpy recovery through differential scanning calorimetry. The segmental relaxation time during physical aging, followed by means of BDS, has been shown to increase more rapidly the higher the SiO${}_2$ concentration in PVAc is. Thermally stimulated depolarization current experiments show that this is the case over the whole probed glassy state. This means that nanocomposites displaying a relatively slow segmental mobility evolve toward equilibrium more rapidly than the bulk. Furthermore, despite the faster increase in the relaxation time with aging time, so-called self-retardation, the nanocomposites and their bulk counterpart reach the same values of equilibrium relaxation time. These findings not only confirm the assumption of identical equilibrium dynamics even in the aging regime for all nanocomposites and bulk polymers, proposed in previous works, but also highlight the fact that the physical aging rate is not determined solely by the polymer segmental dynamics, the amount of interface being an additional relevant parameter.

The dynamics of coupled intermittent maps is used to model the correlated structure of genomic sequences. The use of intermittent maps, as opposed to other simple chaotic maps, is particularly suited for the production of long-range correlation features which are observed in the genomic sequences of higher eucaryotes. A weighted network approach to symbolic sequences is introduced, and it is shown that coupled intermittent polynomial maps produce degree and link size distributions with power-law exponents similar to the ones observed in real genomes. The proposed network approach to symbolic sequences is generic and can be applied to any symbol sequence (artificial or natural).

A vertically draining thin ferrofilm under the influence of gravity and a nonuniform magnetic field is considered. It is observed experimentally that the presence of the magnetic field greatly alters the drainage of the film. A mathematical model is developed to describe the behavior. Experiments are conducted for multiple magnetic field configurations. The model is solved for two different sets of boundary conditions and results are compared to experiments. It is shown that the magnetic field structure, the concentration of magnetite in the solution, and the boundary conditions all have noticeable affects on the evolution of the thinning film. Good qualitative agreement between the model and the experiments is observed.

Using top-end high fidelity computer simulations we demonstrate the existence of a mechanism present in turbulent flows generated by multiscale or fractal objects and which has its origin in the multiscale or fractal space-scale structure of such turbulent flow generators. As a result of this space-scale unfolding mechanism, fractal grids can enhance scalar transfer and turbulent diffusion by one order of magnitude while at the same time reduce pressure drop by half. This mechanism must be playing a decisive role in environmental, atmospheric, ocean, and river transport processes wherever turbulence originates from multiscale or fractal objects such as trees, forests, mountains, rocky riverbeds, and coral reefs. It also ushers in the concept of fractal design of turbulence which may hold the power of setting entirely new mixing and cooling industrial standards.

As an interesting example of how geometry affects the formation of defects, we study the defect structures of a hybrid nematic liquid-crystal film in a wedge-shaped cell made up of sinusoidal microwrinkles and an elastomer sheet. When the cell thickness is larger than a threshold value $h_c$, $+$1/2 and $-$1/2 disclinations are simultaneously stabilized along concave grooves and convex crests, respectively. A simple theoretical analysis gives a good estimate of $h_c$. The disclinations also show alternating optical rotations resulting from the curved boundary and liquid-crystal elastic anisotropy.

We study coalescence of topological defects in nematic liquid crystals confined to spherical shells using both experiments and computer simulations. We observe that the four $s=+\frac{1}{2}$ defects that are present due to topological constraints imposed by the spherical geometry coalesce by pairs after changing the molecular orientation at the outer surface from tangential to perpendicular; the result is the formation of two single $s=+1$ defects. It is noteworthy that the speed of the coalescence process is peaked when the defects are at opposite points on the equator of the shell; this maximum results from the thickness inhomogeneity of the shells.

We study the probability distribution and the escape rate in systems with delayed dissipation that comes from the coupling to a thermal bath. To logarithmic accuracy in the fluctuation intensity, the problem is reduced to a variational problem. It describes the most probable fluctuational paths, which are given by acausal equations due to the delay. In thermal equilibrium, the most probable path passing through a remote state has time-reversal symmetry, even though one cannot uniquely define a path that starts from a state with given system coordinate and momentum. The corrections to the distribution and the escape activation energy for small delay and small noise correlation time are obtained in explicit form.

The effect of resource usage on economic growth has been studied in multiple models. However, the generic effect of improving resource usage efficacy through improved technical skills has not been studied in detail. We here analyze a model incorporating resource usage by capital and the parallel production of technical skill in order to study the effect of improving the efficacy of resources usage with advanced technologies. We show that a practically inevitable result of such a model is that improving the resource usage efficacy leads to a lower steady-state level of resources. A surprising conclusion from ordinary differential equations realization of the model is an extreme sensitivity to parameters, where a small parameter change can lead to an irreversible state through a hysteresis mechanism between a scenario of a collapse of the economy and a scenario of sustainable economy. This sensitivity is lost when spatial stochastic simulations are performed. In the stochastic regime the two scenarios coexist, with different fractions of the lattice residing in each state. Changing parameters smoothly changes the fraction of lattice sites in each state. The transition between the collapsed economy and the sustainable one is not symmetrical. Escape from the collapsed situation can only occur through diffusion from neighboring sustained lattice sites. On the other hand, the collapse can occur even in the absence of diffusion. This difference leads to diffusion dependent capital growth, where an optimal capital is obtained for middiffusion values. Such a transition may actually be generic phenomena in ecological and economic systems.

By means of extensive contact dynamics simulations, we investigate the mechanical equilibrium and deformation of a granular material composed of irregular polyhedral particles confined between two horizontal frictional planes. We show that, as a consequence of mobilized wall-particle friction forces at the top and bottom boundaries, the transient deformation induced by a constant vertical load is controlled by the aspect ratio (thickness over width) of the packing as well as the stress ratio. The transient deformation declines considerably for increasingly smaller aspect ratios and grows with the stress ratio. From the simulation data for a large number of independent configurations, we find that sample-to-sample fluctuations of the deformation have a broad distribution and they scale with the average deformation. We also analyze the evolution of particle connectivity during settlement and with the applied force. The face-face and edge-face contacts between polyhedral particles concentrate strong force chains with a growing proportion as a function of the applied force.

We investigate the response of a dense monodisperse quasi-two-dimensional colloid suspension when a particle is dragged by a constant velocity optical trap. Consistent with microrheological studies of other geometries, the perturbation induces a leading density wave and trailing wake. We also use a hybrid version of Stokesian dynamics simulations to parse direct colloid-colloid and hydrodynamic interactions. We go on to analyze the underlying individual particle-particle collisions in the experimental images. The displacements of particles occur in chains reminiscent of stress propagation in sheared granular materials. From these data, we can reconstruct steady-state dipolar-like flow patterns that were predicted for dilute suspensions and previously observed in granular analogs to our system. The decay of this field differs, however, from point Stokeslet calculations, indicating that the nonzero size of the colloids is important. Moreover, there is a pronounced angular dependence that corresponds to the surrounding colloid structure, which develops in response to the perturbation. Put together, our results show that the response of the complex fluid is highly anisotropic owing to the fact that the effects of the perturbation propagate through the structured medium via chains of colloid-colloid collisions.

Laser probe diagnostics: shadowgraphy, interferometry, and polarimetry were used for a comprehensive characterization of ionization wave dynamics inside a glass target induced by a laser-driven, relativistic electron beam. Experiments were done using the 50-TW Leopard laser at the University of Nevada, Reno. We show that for a laser flux of ∼2 × 10${}^{18}$ W/cm${}^2$ a hemispherical ionization wave propagates at c/3 for 10 ps and has a smooth electron-density distribution. The maximum free-electron density inside the glass target is ∼2 × 10${}^{19}$ cm${}^{-3}$, which corresponds to an ionization level of ∼0.1$\%$. Magnetic fields and electric fields do not exceed ∼15 kG and ∼1 MV/cm, respectively. The electron temperature has a hot, ringlike structure with a maximum of ∼0.7 eV. The topology of the interference phase shift shows the signature of the “fountain effect”, a narrow electron beam that fans out from the propagation axis and heads back to the target surface. Two-dimensional particle-in-cell (PIC) computer simulations demonstrate radial spreading of fast electrons by self-consistent electrostatic fields driven by laser. The very low ionization observed after the laser heating pulse suggests a fast recombination on the sub-ps time scale.

Spatially embedded networks are important in several disciplines. The prototypical spatial network we assume is the Random Geometric Graph, of which many properties are known. Here we present new results for the two-point degree correlation function in terms of the clustering coefficient of the graphs for two-dimensional space in particular, with extensions to arbitrary finite dimensions.

We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we obtain the probability $P\left(\omega \right)$ distribution of the random variable $\omega ={\tau }_1/({\tau }_1+{\tau }_2)$, which is a measure for how similar the first passage times ${\tau }_1$ and ${\tau }_2$ are of two independent realizations of a Brownian walk starting at the same location. We construct a chart for each domain, determining whether $P\left(\omega \right)$ represents a unimodal, bell-shaped form, or a bimodal, M-shaped behavior. While in the former case the mean first passage time (MFPT) is a valid characteristic of the first passage behavior, in the latter case it is an insufficient measure for the process. Strikingly we find a distinct turnover between the two modes of $P\left(\omega \right)$, characteristic for the domain shape and the respective location of absorbing and reflective boundaries. Our results demonstrate that large fluctuations of the first passage times may occur frequently in two-dimensional domains, rendering quite vague the general use of the MFPT as a robust measure of the actual behavior even in bounded domains, in which all moments of the first passage distribution exist.

We study the fluctuations of the directed polymer in 1+1 dimensions in a Gaussian random environment with a finite correlation length $\xi$ and at finite temperature. We address the correspondence between the geometrical transverse fluctuations of the directed polymer, described by its roughness, and the fluctuations of its free energy, characterized by its two-point correlator. Analytical arguments are provided in favor of a generic scaling law between those quantities, at finite time, nonvanishing $\xi$, and explicit temperature dependence. Numerical results are in good agreement both for simulations on the discrete directed polymer and on a continuous directed polymer (with short-range correlated disorder). Applications to recent experiments on liquid crystals are discussed.

Dielectric, calorimetric, and x-ray diffraction measurements were carried out on α-, β-, and γ-cyclodextrins, which are cyclic saccharides built by, respectively, six, seven, and eight glucose units connected via glycosidic linkage. Differential scanning calorimetry measurements indicated that each carbohydrate has a melting temperature located much above the temperature at which thermal decomposition begins. Moreover, calorimetric data revealed that it is possible to completely dehydrate each cyclodextrin by annealing them above 413 K. Unfortunately, it is impossible to obtain amorphous forms of cyclodextrin by simple cooling of the melt. Thus, a solid state amorphization method has been applied. X-ray diffraction studies demonstrated that by ball milling at room temperature we are able to obtain completely amorphous cyclodextrins. Finally, dielectric measurements were carried out to probe molecular dynamics in the amorphous state of cyclodextrins. It was found that there is only one relaxation process in amorphous hydrated cyclodextrins, while in dried samples two secondary relaxations are present. Moreover, we have shown that water has an enormous effect on the dynamics of both relaxation modes, i.e., with increasing content of water, the activation energy of the slow mode decreases, while that evaluated for the fast mode increases. We were not able to follow the dynamics of the structural relaxation process, because glass transition temperatures of amorphous cyclodextrins were found to lie above thermal degradation points.

Flexoelectric and piezoelectric effects in ferroelectric liquid crystals (FLCs) have been studied. It is shown that nonlinear electromechanical coupling is determined by a local flexoelectric effect. Dependence of the parameters of nonlinearity of the flexoelectric effect on the parameter of phase transition from a paraelectric phase to a polar phase has been studied. Dependencies of flexoelectric and piezoelectric coefficients on the frequency of the mechanical vibrations have been studied.

Theoretical models describing specific adhesion of membranes predict (for certain parameters) a macroscopic phase separation of bonds into adhesion domains. We show that this behavior is fundamentally altered if the membrane is pinned randomly due to, e.g., proteins that anchor the membrane to the cytoskeleton. Perturbations which locally restrict membrane height fluctuations induce quenched disorder of the random-field type. This rigorously prevents the formation of macroscopic adhesion domains following the Imry-Ma argument [Imry and Ma, Phys. Rev. Lett. 35, 1399 (1975)]. Our prediction of random-field disorder follows from analytical calculations and is strikingly confirmed in large-scale Monte Carlo simulations. These simulations are based on an efficient composite Monte Carlo move, whereby membrane height and bond degrees of freedom are updated simultaneously in a single move. The application of this move should prove rewarding for other systems also.

In appropriate situations, large populations of geese exhibit dynamical rearrangements by repeated mergers and splits among the groups. We describe the grouping process in terms of a mean-field model based on the Smoluchowski equation of coagulation with fragmentation and observationally plausible kernels. To verify our model, we conducted field observations on skeins of airborne geese, noting both the group-size distribution and the group-forming processes. We found that the group-size distribution we obtained in our field measurements could be represented by a fractional power function with an exponential cutoff. This function matches the asymptotic form of the steady-state solution of our model. Furthermore, we estimated the effective number of individuals involved in interactions by comparison of the model to our field data.