Ice Ih, ordinary ice at atmospheric pressure, is a proton-disordered crystal that when cooled under special conditions is believed to transform to ferroelectric proton-ordered ice XI, but this transformation is still subject to controversy. Ice VII, also proton disordered throughout its region of stability, transforms to proton-ordered ice VIII upon cooling. In contrast to the ice Ih/XI transition, the VII/VIII transition and the crystal structure of ice VIII are well characterized. In order to shed some light on the ice Ih proton ordering transition, we present the results of periodic electronic density functional theory calculations and statistical simulations. We are able to describe the small energy differences among the innumerable H-bond configurations possible in a large simulation cell by using an analytic theory to extrapolate from electronic DFT calculations on small unit cells to cells large enough to approximate the thermodynamic limit. We first validate our methods by comparing our predictions to the well-characterized ice VII/VIII proton ordering transition, finding agreement with respect to both the transition temperature and structure of the low-temperature phase. For ice Ih, our results indicate that a proton-ordered phase is attainable at low temperatures, the structure of which is in agreement with the experimentally proposed ferroelectric $Cmc{2}_1$ structure. The predicted transition temperature of $98\mathrm{K}$ is in qualitative agreement with the observed transition at $72\mathrm{K}$ on KOH-doped ice samples.

We set up an analytical framework that allows one to describe and compute streaming effects and electro-osmosis on an equal footing. This framework relies on the thin double layer approximation commonly used for description of electroosmotic flows, but rarely used for streaming problems. Using this framework we quantitatively assess the induction of bulk streaming current patterns by topographic or charge heterogeneities on surfaces. This too also permits analytical computation of all linear electrokinetic effects in complex microfluidic geometries, and we discuss a few immediate applications.

Equation of state data and electrical resistivity of warm dense gold were measured in the internal energy range $8–12\mathrm{MJ}∕\mathrm{kg}$. Experimental results were compared with quantum molecular dynamics simulations. The theoretical results match well the experimental data, allowing a detailed interpretation of the theoretical thermodynamic properties and frequency-dependent conductivities.

We derive an expression for the Minkowski momentum under conditions of dispersive susceptibility and permeability, and compare it to the Abraham momentum in order to test the principle of conservation of linear momentum when matter is present. We investigate cases when an incident pulse interacts with a variety of structures, including thick substrates, resonant, free-standing, micron-sized multilayer stacks, and negative index materials. In general, we find that for media only a few wavelengths thick the Minkowski and Abraham momentum densities yield similar results. For more extended media, including substrates and Bragg mirrors embedded inside thick dielectric substrates, our calculations show dramatic differences between the Minkowski and Abraham momenta. Without exception, in all cases investigated the instantaneous Lorentz force exerted on the medium is consistent only with the rate of change of the Abraham momentum. As a practical example, we use our model to predict that electromagnetic momentum and energy buildup inside a multilayer stack can lead to widely tunable accelerations that may easily reach and exceed ${10}^{10}\mathrm{m}∕{\mathrm{s}}^2$ for a mass of ${10}^{-5}\mathrm{g}$. Our results suggest that the physics of the photonic band edge and other similar finite structures may be used as a testing ground for basic electromagnetic phenomena such as momentum transfer to macroscopic media.

We analyze the effect of microscopic disorder on the macroscopic properties of composite metamaterials and study how weak statistically independent fluctuations of the parameters of the structure elements can modify their collective magnetic response and left-handed properties. We demonstrate that even a weak microscopic disorder may lead to a substantial modification of the metamaterial magnetic properties, and a 10% deviation in the parameters of the microscopic resonant elements may lead to a substantial suppression of the wave propagation in a wide frequency range. A noticeable suppression occurs also if more than 10% of the resonant magnetic elements possess strongly different properties, and in the latter case the defects can create an additional weak resonant line. These results are of a key importance for characterizing and optimizing novel composite metamaterials with the left-handed properties at terahertz and optical frequencies.

A quantum Monte Carlo method with a nonlocal update scheme is presented. The method is based on a path-integral decomposition and a worm operator which is local in imaginary time. It generates states with a fixed number of particles and respects other exact symmetries. Observables like the equal-time Green’s function can be evaluated in an efficient way. To demonstrate the versatility of the method, results for the one-dimensional Bose-Hubbard model and a nuclear pairing model are presented. Within the context of the Bose-Hubbard model the efficiency of the algorithm is discussed.

A complex dielectric constant for double-strand DNA molecules with a length of not greater than 120 base pairs in an aqueous solution containing $30\mathrm{mM}$ $\mathrm{NaCl}$ was systematically measured as a function of chain length in such a way that experimental uncertainties associated with the molecular-weight distribution of specimens were virtually excluded. In contrast to the past experimental and theoretical studies for much longer DNA molecules, both the molar specific dielectric increment and the relaxation time are proportional to the chain length. These scaling rules cannot be accounted for by any theory so far proposed that gives analytical expressions for those two quantities in the long-chain limit.

We consider the transport of rigid objects with internal structure in a flashing ratchet potential by investigating the overdamped behavior of a rodlike chain of evenly spaced point particles. In one dimension, analytical arguments show that the velocity can reverse direction multiple times in response to changing the size of the chain or the temperature of the heat bath. The physical reason is that the effective potential experienced by the mechanically coupled objects can have a different symmetry than that of individual objects. All analytical predictions are confirmed by Brownian dynamics simulations. These results may provide a route to simple, coarse-grained models of molecular motor transport that incorporate an object’s size and rotational degrees of freedom into the mechanism of transport.

Using field theoretic renormalization, an MBE-type growth process with an obliquely incident influx of atoms is examined. The projection of the beam on the substrate plane selects a “parallel” direction, with rotational invariance restricted to the transverse directions. Depending on the behavior of an effective anisotropic surface tension, a line of second-order transitions is identified, as well as a line of potentially first-order transitions, joined by a multicritical point. Near the second-order transitions and the multicritical point, the surface roughness is strongly anisotropic. Four different roughness exponents are introduced and computed, describing the surface in different directions, in real or momentum space. The results presented challenge an earlier study of the multicritical point.

In the present paper we investigate the exact average number of attempts until saturation when a square lattice is ceaselessly bombarded with $\beta$-bell $(\beta ⩾1)$ particles, i.e., linear particles that require $\beta$ consecutive lattice sites to be adsorbed. When that average number is normalized with the corresponding single-particle average, a scale invariant behavior is revealed with a scaling exponent $\alpha =0.017\pm 0.001$, independent of $\beta$ $(\beta >1)$. The scale behavior is suggested by the branching characteristics governing the sequential random adsorption of $\beta$-bell $(\beta >1)$ particles, which is indeed a consequence of configurational correlations.

We report on and analyze the textural transformations in islands, thicker circular domains, floating in very thin free standing chiral Smectic-$C^{*}$ liquid crystal films. As an island is growing, an initial pure bend texture of the $c$ director changes into a reversing spiral at a critical size. Another distinct spiral texture is induced by changing the boundary condition at the central point defect in the island. To understand these transformations from a pure bend island, a linear stability analysis of the $c$-director free energy is developed, which predicts a state diagram for the island. Our observations are consistent with the theoretical phase diagram.

A navigation process is studied on a variant of the Watts-Strogatz small-world network model embedded on a square lattice. With probability $p$, each vertex sends out a long-range link, and the probability of the other end of this link falling on a vertex at lattice distance $r$ away decays as $r^{-\alpha }$. Vertices on the network have knowledge of only their nearest neighbors. In a navigation process, messages are forwarded to a designated target. For $\alpha <3$ and $\alpha \ne 2$, a scaling relation is found between the average actual path length and $pL$, where $L$ is the average length of the additional long range links. Given $pL>1$, a dynamic small world effect is observed, and the behavior of the scaling function at large enough $pL$ is obtained. At $\alpha =2$ and 3, this kind of scaling breaks down, and different functions of the average actual path length are obtained. For $\alpha >3$, the average actual path length is nearly linear with network size.

We performed extensive simulations accompanied by a detailed study of a two-segment size random sequential model on the line. We followed the kinetics towards the jamming state, but we paid particular attention to the characterization of the jamming state structure. In particular, we studied the effect of the size ratio on the mean-gap size, the gap-size dispersion, gap-size skewness, and gap-size kurtosis at the jamming state. We also analyzed the above quantities for the four possible segment-to-segment gap types. We ranged the values of the size ratio from one to twenty. In the limit of a size ratio of one, one recovers the classical car-parking problem. We observed that at low size ratios the jamming state is constituted by short streaks of small and large segments, while at high values of the size ratio the jamming state structure is formed by long streaks of small segments separated by a single large segment. This view of the jamming state structure as a function of the size ratio is supported by the various measured quantities. The present work can help provide insight, for example, on how to minimize the interparticle distance or minimize fluctuations around the mean particle-to-particle distance.

Interacting surface waves, parametrically excited by two commensurate frequencies (Faraday waves), yield a rich family of nonlinear states, which result from a variety of three-wave resonant interactions. By perturbing the system with a third frequency, we selectively favor different nonlinear wave interactions. Where quadratic nonlinearities are dominant, the only observed patterns correspond to “grid” states. Grid states are superlattices in which two corotated sets of critical wave vectors are spanned by a sublattice whose basis states are linearly stable modes. Specific driving phase combinations govern the selection of different grid states.

Nonuniversal scale transformations of the physical fields are extended to pure quantum fluids and used to calculate the susceptibility, the specific heat, and the order parameter density along the critical isochore of ${\mathrm{He}}^3$ near its liquid-vapor critical point. Within the so-called preasymptotic domain, where the Wegner expansion restricted to the first term of confluent corrections to scaling is expected to be valid, the results are in agreement with the experimental measurements and recent predictions, either based on the minimal-substraction renormalization and the massive renormalization schemes within the ${\Phi }_{d=3}^4(n=1)$ model, or based on the crossover parametric equation of state for Ising-like systems.

Analytical and numerical studies of secondary electro-osmotic flow (EOF) and its mixing in microchannels with heterogeneous zeta potentials are carried out in the present work. The secondary EOFs are analyzed by solving the Stokes equation with heterogeneous slip velocity boundary conditions. The analytical results obtained are compared with the direct numerical simulation of the Navier-Stokes equations. The secondary EOFs could transport scalar in larger areas and increase the scalar gradients, which significantly improve the mixing rate of scalars. It is shown that the heterogeneous zeta potentials could generate complex flow patterns and be used to enhance scalar mixing.

We study the effects on the dynamics of kinks due to expansions and contractions of the space. We show that the propagation velocity of the kink can be adiabatically tuned through slow expansions and/or contractions, while its width is given as a function of the velocity. We also analyze the case of fast expansions and/or contractions, where we are no longer on the adiabatic regime. In this case the kink moves more slowly after an expansion-contraction cycle as a consequence of the loss of energy through radiation. All these effects are numerically studied in the nonlinear Klein-Gordon equations (both for the sine-Gordon and for the ${\varphi }^4$ potential), and they are also studied within the framework of the collective coordinate evolution equations for the width and the center of mass of the kink. These collective coordinate evolution equations are obtained with a procedure that allows us to consider even the case of large expansions and/or contractions.

Molecular rotational dynamics in $p,p^{\prime }$-di-$n$-heptyl-azoxybenzene was studied by means of quasielastic neutron scattering (QENS) and ${}^{13}\mathrm{C}$ cross-polarization magic-angle-spinning (CPMAS) NMR. Fast reorientation of the hydrogen nuclei was observed by QENS in the two liquid crystalline (LC) phases nematic and smectic $A$, as well as in the crystalline phase. The latter could not be restricted to the –$\mathrm{C}{\mathrm{H}}_3$ rotations alone, and a clear indication was found of some other reorientation motions persisting in the crystal. Two Lorentz-type components convoluted with the resolution function gave an excellent fit to the QENS spectra in both LC phases. The narrow (slow) component was attributed to the reorientation of the whole molecule around the long axis. The corresponding characteristic time of $\sim 130\mathrm{ps}$ agreed well with the values obtained in recent dielectric relaxation and ${}^2\mathrm{H}$ NMR studies. The full width at half maximum of the broader (fast) component shows a quadratic $Q$ dependence ($Q$ is the momentum transfer). Hence the corresponding motions could be described by a stretched exponential correlation function and were interpreted as various “crankshaft-type” motions within the alkyl tails. The ${}^{13}\mathrm{C}$ CPMAS experiments fully corroborated the QENS results, sometimes considered ambiguous in complex systems.

We present a detailed analysis and theoretical growth models to account for recent experimental data on the growth of cortical neuronal networks in vitro [Phys. Rev. Lett. 93, 088101 (2004)]. The experimentally observed synchronized firing frequency of a well-connected neuronal network is shown to be proportional to the mean network connectivity. The growth of the network is consistent with the model of an early enhanced growth of connection, but followed by a retarded growth once the synchronized cluster is formed. Microscopic models with dominant excluded volume interactions are consistent with the observed exponential decay of the mean connection probability as a function of the mean network connectivity. The biological implications of the growth model are also discussed.

Three remarkable features of the nervous system—complex spatiotemporal patterns, oscillations, and persistent activity—are fundamental to such diverse functions as stereotypical motor behavior, working memory, and awareness. Here we report that cultured cortical networks spontaneously generate a hierarchical structure of periodic activity with a strongly stereotyped population-wide spatiotemporal structure demonstrating all three fundamental properties in a recurring pattern. During these “superbursts,” the firing sequence of the culture periodically converges to a dynamic attractor orbit. Precursors of oscillations and persistent activity have previously been reported as intrinsic properties of the neurons. However, complex spatiotemporal patterns that are coordinated in a large population of neurons and persist over several hours—and thus are capable of representing and preserving information—cannot be explained by known oscillatory properties of isolated neurons. Instead, the complexity of the observed spatiotemporal patterns implies large-scale self-organization of neurons interacting in a precise temporal order even in vitro, in cultures usually considered to have random connectivity.