Dielectric loss spectra are reported for $\alpha$-tocopherol acetate (an isomer of vitamin E) in the supercooled and glassy states. The $\alpha$-relaxation times, ${\tau }_{\alpha }$, measured over a 190° range of temperatures, $T$, at pressures, $P$, up to $400\mathrm{MPa}$ can be expressed as a single function of $T{V}^{3.9}$ ($V$ is specific volume, measured herein as a function of $T$ and $P$). At ambient pressure, there is no dynamic crossover over eight decades of measured ${\tau }_{\alpha }$. The relaxation spectra above the glass transition temperature $T_g$ show ionic conductivity and an excess wing on the high-frequency flank of the $\alpha$-relaxation loss peak. Temperature-pressure superpositioning is valid for the $\alpha$ process; moreover, the peak shape is constant (stretch exponent equal to 0.65). However, application of pressure changes the shape of the dielectric spectrum at higher frequencies due to the shift of the excess wing to form a resolved peak. Additionally, another relaxation process, absent at atmospheric pressure, emerges on the high-frequency side of the $\alpha$-process. We propose that this new peak reflects a more compact conformation of the $\alpha$-tocopherol acetate molecule. Drawing on the coupling model, the experimentally determined relaxation times, activation energy, and activation volume for the Johari-Goldstein process are compared to values calculated from the properties of the $\alpha$ relaxation. The agreement is generally satisfactory, at least for $T<T_g$.

The complementary strands of DNA molecules can be separated when stretched apart by a force; the unzipping signal is correlated to the base content of the sequence but is affected by thermal and instrumental noise. We consider here the ideal case where opening events are known to a very good time resolution (very large bandwidth), and study how the sequence can be reconstructed from the unzipping data. Our approach relies on the use of statistical Bayesian inference and of Viterbi decoding algorithm. Performances are studied numerically on Monte Carlo generated data, and analytically. We show how multiple unzippings of the same molecule may be exploited to improve the quality of the prediction, and calculate analytically the number of required unzippings as a function of the bandwidth, the sequence content, and the elasticity parameters of the unzipped strands.

Universal laws in the force-induced unbinding of receptor-ligand complexes are established for a general functional dependence of the dissociation rate constant on the applied force and are detailed with the two-pathway model that describes the recently discovered biological catch bond. The relationships link the data obtained with constant and time-dependent forces in different regimes, provide common representation for the previously unrelated data sets, and, thereby, greatly facilitate analysis and interpretation of experiments. The universal laws are demonstrated with the monomeric and dimeric catch-slip bonds between P-selectins and P-selectin glycoprotein ligands-1, and the slip bond between E-selectin and sialyl ${\text{Lewis}}^{\mathrm{x}}$ antigen.

We study the motion of a sphere falling through soft viscoelastic materials when the time scale of the motion is short compared to the elastic relaxation time of the material. We observe shocks generated by the passage of the sphere at Mach numbers greater than 1. The sphere can undergo oscillations before reaching a steady terminal speed, and we show that these oscillations have the same frequency as the shear wave associated with the shock.

We derived semianalytically the transient solution of a delayed differential equation that had been shown to be a simple but good model of the sensory-motor system. In the present Brief Report, we applied this transient solution for studying the global nature of the transient tracking motion when visual target information is changed suddenly. The results clarified that the dynamic error minimization principle in hand motion observed experimentally is robust over a wide range of the parameter space of the delay time, the time constant, and the feedforward parameter.

Transmembrane ion flow through channel proteins undergoing density fluctuations may cause lateral gradients of the electrical potential across the membrane giving rise to electrophoresis of charged channels. A model for the dynamics of the channel density and the voltage drop across the membrane (cable equation) coupled to a binding-release reaction with the cell skeleton [P. Fromherz and W. Zimmerman, Phys. Rev. E 51, R1659 (1995)] is analyzed in one and two spatial dimensions. Due to the binding release reaction spatially periodic modulations of the channel density with a finite wave number are favored at the onset of pattern formation, whereby the wave number decreases with the kinetic rate of the binding-release reaction. In a two-dimensional extended membrane hexagonal modulations of the ion channel density are preferred in a large range of parameters. The stability diagrams of the periodic patterns near threshold are calculated and in addition the equations of motion in the limit of a slow binding-release kinetics are derived.

In this study of catalytic microfluidic reactors we show that, when optimally structured, these reactors share underlying scaling properties. The scaling is predicted theoretically and verified numerically. Furthermore, we show how to increase the reaction rate significantly by distributing the active porous material within the reactor using a high-level implementation of topology optimization.

Due to the nonlinearity of Hertzian contacts, the speed of sound $c$ in granular matter is expected to increase with pressure as $P^{1∕6}$. A static layer of grains under gravity is thus stratified so that the bulk waves are refracted toward the surface. The reflection at the surface being total, there is a discrete number of modes (both in the sagittal plane and transverse to it) localized close to the free surface. The shape of these modes and the corresponding dispersion relation are investigated in the framework of an elastic description taking into account the main features of granular matter: Nonlinearity between stress and strain and the existence of a yield transition. We show in this context that the surface modes localized at the free surface exhibit a waveguide effect related to the nonlinear Hertz contact. Recent results about the song of dunes are reinterpreted in light of the theoretical results. The predicted propagation speed is compared with measurements performed in the field. Taking into account the finite depth effects, we show that the booming instability threshold can be explained quantitatively by a waveguide cutoff frequency below which no sound can propagate. Therefore, we propose another look at a recent controversy, confirming that the song of dunes can well originate from a coupling between avalanching grains and surface elastic waves once the specificity of surface waves (we baptized Rayleigh-Hertz) is correctly taken into account.

We present an analysis of second-order and third-order nonlinear susceptibilities and wave-mixing properties of negative refractive index materials. We show that the nonlinear susceptibilities for noncentrosymmetric and centrosymmetric media may be positive or negative and away from resonance depending on the frequency of interest relative to the resonant frequencies of the material. Manipulation of the signs of the nonlinear susceptibilities is important in the field of optics, particularly for solitons and compensation of nonlinear effects. We also show that three- and four-wave mixing can be naturally phase matched in the material.

Many important issues of colloidal physics can be expressed in the context of inhomogeneous fluid phenomena. When two large colloids approach one another in solvent, they interact at least partly by the response of the solvent to finding itself adsorbed in the annular wedge formed between the two colloids. At shortest range, this fluid mediated interaction is known as the depletion force/interaction because solvent is squeezed out of the wedge when the colloids approach closer than the diameter of a solvent molecule. An equivalent situation arises when a single colloid approaches a substrate/wall. Accurate treatment of this interaction is essential for any theory developed to model the phase diagrams of homogeneous and inhomogeneous colloidal systems. The aim of our paper is a test of whether or not we possess sufficient knowledge of statistical mechanics that can be trusted when applied to systems of large size asymmetry and the depletion force in particular. When the colloid particles are much larger than a solvent diameter, the depletion force is dominated by the effective two-body interaction experienced by a pair of solvated colloids. This low concentration limit of the depletion force has therefore received considerable attention. One route, which can be rigorously based on statistical mechanical sum rules, leads to an analytic result for the depletion force when evaluated by a key theoretical tool of colloidal science known as the Derjaguin approximation. A rival approach has been based on the assumption that modern density functional theories (DFT) can be trusted for systems of large size asymmetry. Unfortunately, these two theoretical predictions differ qualitatively for hard sphere models, as soon as the solvent density is higher than about $2∕3$ that at freezing. Recent theoretical attempts to understand this dramatic disagreement have led to the proposal that the Derjaguin and DFT routes represent opposite limiting behavior, for very large size asymmetry and molecular sized mixtures, respectively. This proposal implies that nanocolloidal systems lie in between the two limits, so that the depletion force no longer scales linearly with the colloid radius. That is, by decreasing the size ratio from mesoscopic to molecular sized solutes, one moves smoothly between the Derjaguin and the DFT predictions for the depletion force scaled by the colloid radius. We describe the results of a simulation study designed specifically as a test of compatibility with this complex scenario. Grand canonical simulation procedures applied to hard-sphere fluid adsorbed in a series of annular wedges, representing the depletion regime of hard-body colloidal physics, confirm that neither the Derjaguin approximation, nor advanced formulations of DFT, apply at moderate to high solvent density when the geometry is appropriate to nanosized colloids. Our simulations also allow us to report structural characteristics of hard-body solvent adsorbed in hard annular wedges. Both these aspects are key ingredients in the proposal that unifies the disparate predictions, via the introduction of new physics. Our data are consistent with this proposed physics, although as yet limited to a single colloidal size asymmetry.

The application of a sufficiently strong strain perpendicular to the pitch axis of a monodomain cholesteric elastomer unwinds the cholesteric helix. Previous theoretical analyses of this transition ignored the effects of Frank elasticity which we include here. We find that the strain needed to unwind the helix is reduced because of the Frank penalty and the cholesteric state becomes metastable above the transition. We consider in detail a previously proposed mechanism by which the topologically stable helical texture is removed in the metastable state: namely, by the nucleation of twist disclination loops in the plane perpendicular to the pitch axis. We present an approximate calculation of the barrier energy for this nucleation process which neglects possible spatial variation of the strain fields in the elastomer, as well as a more accurate calculation based on a finite-element modeling of the elastomer.

In the present study, we investigate the migration of DNA molecules through a microchannel using a series of electric traps controlled by an ac electric field. We describe the motion of DNA based on Brownian dynamics simulations of a bead-spring chain. The DNA chain captured by an electric field escapes due to thermal fluctuation. The mobility of the DNA chain was determined to depend on the chain length, the mobility of which sharply increases when the length of the chain exceeds a critical value that is strongly affected by the amplitude of the applied ac field. Thus we can optimize the separation selectivity of the channel for DNA molecules that is to be separated, without changing the structure of the channel. In addition, we present a phenomenological description for the relationship between the critical chain length and the strength of binding electric field.

We study the stability of quantum motion of classically regular systems in the presence of small perturbations. On the basis of a uniform semiclassical theory we derive the fidelity decay which displays a quite complex behavior, from Gaussian to power law decay $t^{-\alpha }$, with $1⩽\alpha ⩽2$. Semiclassical estimates are given for the time scales separating the different decaying regions, and numerical results are presented which confirm our theoretical predictions.

Based on the generating function of Laguerre polynomials, we propose a Laguerre polynomial expansion scheme in the calculation of the evolution of the time-dependent Schrödinger equation. Theoretical analysis and numerical tests show that the method is equally as good as the Chebyshev polynomial expansion method in efficiency and accuracy, with the additional merits that no scaling to the Hamiltonian is needed and it has wider suitability.

We consider decay of metastable states of forced vibrations of a quantum oscillator close to the bifurcation points where the states disappear. Decay occurs via quantum activation over a quasienergy barrier, a mechanism that differs from both tunneling and thermal activation. The decay probability $W$ scales with the distance $\eta$ to the bifurcation point as $\mid \ln W\mid \propto {\eta }^{\xi }$. The exponent $\xi$ is found for a resonantly driven oscillator and an oscillator modulated at nearly twice its eigenfrequency.

In a realistic three-dimensional setup, we simulate the slow deformation of idealized granular media composed of spheres undergoing an axisymmetric triaxial shear test. We follow the self-organization of the spontaneous strain localization process leading to a shear band and demonstrate the existence of a critical packing density inside this failure zone. The asymptotic criticality arising from the dynamic equilibrium of dilation and compaction is found to be restricted to the shear band, while the density outside of it keeps the memory of the initial packing. The critical density of the shear band depends on friction (and grain geometry) and in the limit of infinite friction it defines a specific packing state, namely the dynamic random loose packing.

Optical microscopy and atomic force microscopy were used to study a mechanically induced wrinkling instability in thin film poly(caprolactone)/polystyrene and poly(ethylene oxide)/poly(methyl methacrylate) bilayers. The instability in these samples was shown to be driven by changes in the interfacial area between a semicrystalline polymer underlayer and a glassy polymer capping layer that occurred when the underlayers were melted. The wrinkling instability resulted in the formation of one-dimensional corrugations at the surface of the bilayer samples that had a well-defined wavelength on the micrometer length scale. A linear stability analysis was used to derive a simple model of the wrinkling process in these samples. This model considered the flow and deformation of material in the molten underlayer as well as the balance of stresses in the glassy polymer capping layers. Rheological data were also obtained from polymers similar to those used to form the bilayers. These data were used to show that the model is capable of quantitatively predicting the capping layer and underlayer thickness dependencies of the characteristic wrinkling wavelengths, if the mechanical properties of the two layers and the strain in the capping layers can be determined.

We present results for Stark broadening of high principal quantum number (up to $n=15$) Balmer lines, using an analytical (the “standard theory”) approach and two independently developed computer simulation methods. The line shapes are calculated for several sets of plasma parameters, applicable to radio-frequency discharge $(N_e\approx {10}^{13}{\mathrm{cm}}^{-3})$ and magnetic fusion $(N_e\approx {10}^{15}{\mathrm{cm}}^{-3})$ experiments. Comparisons of the calculated line profiles to the experimental data show a very good agreement. Density and temperature dependences of the linewidths, as well as relative contributions of different Stark-broadening mechanisms, are analyzed. It is seen that the standard theory of line broadening is sufficiently accurate for the entire set of plasma conditions and spectral transitions considered here, while an alternative theory (“advanced generalized theory”) is shown to be inadequate for the higher-density region. A discussion of possible reasons for this disagreement is given.