We use the angular deficit scheme [V. Borrelli, F. Cazals, and J.-M. Morvan, Comput. Aided Geom. Des. 20, 319 (2003)] to determine the distribution of Gaussian curvature in developable cones (d-cones) [E. Cerda, S. Chaieb, F. Melo, and L. Mahadevan, Nature (London) 401, 46 (1999)] numerically. These d-cones are formed by pushing a thin elastic sheet into a circular container. Negative Gaussian curvatures are identified at the rim where the sheet touches the container. Around the rim there are two narrow bands with positive Gaussian curvatures. The integral of the (negative) Gaussian curvature near the rim is almost completely compensated by that of the two adjacent bands. This suggests that the Gauss-Bonnet theorem which constrains the integral of Gaussian curvature globally does not explain the spontaneous curvature cancellation phenomenon [T. Liang and T. A. Witten, Phys. Rev. E 73, 046604 (2006)]. The locality of the compensation seems to increase for decreasing d-cone thickness. The angular deficit scheme also provides a way to confirm the curvature cancellation phenomenon.

Pulses of synchronization in chaotic coupled map lattices are discussed in the context of transmission of information. Synchronization and desynchronization propagate along the chain with different velocities which are calculated analytically from the spectrum of convective Lyapunov exponents. Since the front of synchronization travels slower than the front of desynchronization, the maximal possible chain length for which information can be transmitted by modulating the first unit of the chain is bounded.

This work provides a generalization of Evans’ homogeneous nonequilibrium method for estimating thermal conductivity to molecular systems that are described by general multibody potentials. A perturbed form of the usual Nose-Hoover equations of motion is formally constructed and is shown to satisfy the requirements of Evans’ original method. These include adiabatic incompressibility of phase space, equivalence of the dissipative and heat fluxes, and momentum preservation.

We revisit the line-shape theory of a single molecule with anomalous stochastic spectral diffusion. Waiting time profiles for bath induced spectral jumps in the ground and excited states become different when a molecule, probed by continuous-wave laser field, reaches the steady state. This effect is studied for the stationary dichotomic continuous-time-random-walk spectral diffusion of a single two-level chromophore with power-law distributions of waiting times. Correlated waiting time distributions, line shapes, two-point fluorescence correlation function, and Mandel $Q$ parameter are calculated for arbitrary magnitude of laser field. We extended previous weak field results and examined the breakdown of the central limit theorem in photon statistics, indicated by asymptotic power-law growth of Mandel $Q$ parameter. Frequency profile of the Mandel $Q$ parameter identifies the peaks of spectrum, which are related to anomalous spectral diffusion dynamics.

We study the traffic of two types of molecular motors using the two-species asymmetric simple exclusion process (ASEP) with periodic boundary conditions and with attachment and detachment of particles. We determine characteristic properties such as motor densities and currents by simulations and analytical calculations. For motors with different unbinding probabilities, mean-field theory gives the correct bound density and total current of the motors, as shown by numerical simulations. For motors differing in their stepping probabilities, the particle-hole symmetry of the current-density relationship is broken and mean-field theory fails drastically. The total motor current exhibits exponential finite-size scaling, which we use to extrapolate the total current to the thermodynamic limit. Finally, we also study the motion of a single motor in the background of many nonmoving motors.

Specular and off-specular neutron scattering are used to study the influence of molecular chemistry (mutation) on the intermembrane interactions and mechanical properties of the outer membrane of Gram-negative bacteria consisting of lipopolysaccharides (LPSs). For this purpose, solid-supported multilayers of mutant LPS membranes are deposited on silicon wafers and hydrated either at defined humidity or in bulk buffers. The planar sample geometry allows to identify out-of-plane and in-plane scattering vector components. The measured two-dimensional reciprocal space maps are simulated with membrane displacement correlation functions determined by two mechanical parameters (vertical compression modulus and bending rigidity) and an effective cutoff radius for the membrane fluctuation wavelength. Experiments at controlled humidity enable one to examine the influence of the disjoining pressure on the saccharide-mediated intermembrane interactions, while experiments in bulk buffers (i.e., in the absence of an external osmotic stress) reveal the effect of divalent cations on LPS membranes, highlighting the role of divalent cations in the survival mechanism of bacteria in the presence of antimicrobial molecules.

We study viscoelastic subdiffusion in bistable and periodic potentials within the generalized Langevin equation approach. Our results justify the (ultra)slow fluctuating rate view of the corresponding bistable non-Markovian dynamics which displays bursting and anticorrelation of the residence times in two potential wells. The transition kinetics is asymptotically stretched exponential when the potential barrier $V_0$ several times exceeds thermal energy $k_{B}T$ $\left[V_0\sim \left(2–10\right)k_{B}T\right]$ and it cannot be described by the non-Markovian rate theory (NMRT). The well-known NMRT result approximates, however, ever better with the increasing barrier height, the most probable logarithm of the residence times. Moreover, the rate description is gradually restored when the barrier height exceeds a fuzzy borderline which depends on the power-law exponent of free subdiffusion $\alpha$. Such a potential-free subdiffusion is ergodic. Surprisingly, in periodic potentials it is not sensitive to the barrier height in the long time asymptotic limit. However, the transient to this asymptotic regime is extremally slow and it does profoundly depend on the barrier height. The time scale of such subdiffusion can exceed the mean residence time in a potential well or in a finite spatial domain by many orders of magnitude. All these features are in sharp contrast with an alternative subdiffusion mechanism involving jumps among traps with the divergent mean residence time in these traps.

With the numerical calculation of the spectrum of single bubble sonoluminescence, we find that when the maximum temperature inside a dimly luminescing bubble is relatively low, the spectral lines are prominent. As the maximum temperature of the bubble increases, the line spectrum from the bright bubble weakens or even fades away relative to the background continuum. The calculations in this paper effectively interpret the observed phenomena, indicating that the calculated results, which are closely related to the spectrum profile, such as temperature and pressure, should be reliable. The present calculation tends to negate the existence of a hot plasma core inside a sonoluminescing bubble.

Chagelishvili et al. [Phys. Rev. Lett. 79, 3178 (1997)] discovered a linear mechanism of acoustic wave emergence from vorticity fluctuations in shear flows. This paper illustrates how this “nonresonant” phenomenon is related to the non-normality of the operator governing the linear dynamics of disturbances in shear flows. The non-self-adjoint nature of the governing operator causes the emergent acoustic wave to interact strongly with the vorticity disturbance. Analytical expressions are obtained for the nondivergent vorticity perturbation. A discontinuity in the $x$ component of the velocity field corresponding to the vorticity disturbance was originally identified to be the cause of acoustic wave emergence. However, a different mechanism is proposed in this paper. The correct “acoustic source” is identified and the reason for the abrupt nature of wave emergence is explained. The impact of viscous damping is also discussed.

In this paper we present equilibrium molecular-dynamics results for the shear, rotational, and spin viscosities for fluids composed of linear molecules. The density dependence of the shear viscosity follows a stretched exponential function, whereas the rotational viscosity and the spin viscosities show approximately power-law dependencies. The frequency-dependent shear and spin viscosities are also studied. It is found that viscoelastic behavior is first manifested in the shear viscosity and that the real part of the spin viscosities features a maximum for nonzero frequency. The calculated transport coefficients are used together with the extended Navier-Stokes equations to investigate the effect of the coupling between the intrinsic angular momentum and linear momentum for highly confined fluids. Both steady and oscillatory flows are studied. It is shown, for example, that the fluid flow rate for Poiseuille flow is reduced by up to 10% in a 2 nm channel for a buta-triene fluid at density $236\text{kg}{\text{m}}^{-3}$ and temperature 306 K. The coupling effect may, therefore, become very important for nanofluidic applications.

In the present paper, a one-temperature model of transport properties in chemically nonequilibrium neutral gas-mixture flows with electronic excitation is developed. The closed set of governing equations for the macroscopic parameters taking into account electronic degrees of freedom of both molecules and atoms is derived using the generalized Chapman-Enskog method. The transport algorithms for the calculation of the thermal-conductivity, diffusion, and viscosity coefficients are proposed. The developed theoretical model is applied for the calculation of the transport coefficients in the electronically excited $\text{N}/{\text{N}}_2$ mixture. The specific heats and transport coefficients are calculated in the temperature range $50–50000\text{K}$. Two sets of data for the collision integrals are applied for the calculations. An important contribution of the excited electronic states to the heat transfer is shown. The Prandtl number of atomic species is found to be substantially nonconstant.

We extend former investigation to a partially degenerate electron fluid at any temperature of multiple slow ion scattering at $T=0$. We implement an analytic and mean-field interpolation of the target electron dielectric function between $T=0$ (Lindhard) and $T\to \infty$ (Fried-Conte). A specific attention is given to multiple scattering of proton projectiles in the keV energy range, stopped in a hot-electron plasma at solid density.

Trajectory of an optical vortex has been identified for its propagation in atmospheric turbulence using numerical simulations. An analytical expression has been found, relating the radial departure of the vortex in plane perpendicular to the direction of propagation, to the refractive index structure function parameter and the inner scale of turbulence. The angular orientation of the vortex in the same transverse plane is found to be related to the anisotropy of the medium. The obtained results provide an alternative way to find turbulent parameters with the help of optical vortices.

Microscopic semiflexible filaments suspended in a viscous fluid are widely encountered in biophysical problems. The classic example is the flagella used by microorganisms to generate propulsion. Simulating the dynamics of these filaments numerically is complicated because of the coupling between the motion of the filament and that of the surrounding fluid. An attractive idea is to simplify this coupling by modeling the fluid motion by using Stokeslets distributed at equal intervals along the model filament. We show that, with an appropriate choice of the hydrodynamic radii, one can recover accurate hydrodynamic behavior of a filament with a finite cross section without requiring an explicit surface. This is true, however, only if the hydrodynamic radii take specific values and that they differ in the parallel and perpendicular directions leading to a caterpillarlike hydrodynamic shape. Having demonstrated this, we use the model to compare with analytic theory of filament deformation and rotation in the small deformation limit. Generalization of the methodology, including application to simulations using the Rotne-Prager tensor, is discussed.

Stochastic effects may cause “fade-out” of an infectious disease in a population immediately after an epidemic outbreak. We evaluate the epidemic fade-out probability by a WKB method and find that the most probable path to extinction of the disease comes from an instantonlike orbit in the phase space of an underlying Hamiltonian flow.

Previous works on the queuing model introduced by Barabási to account for the heavy tailed distributions of the temporal patterns found in many human activities mainly concentrate on the extremal dynamics case and on lists of only two items. Here we obtain exact results for the general case with arbitrary values of the list length $L$ and of the degree of randomness that interpolates between the deterministic and purely random limits. The statistically fundamental quantities are extracted from the solution of master equations. From this analysis, scaling features of the model are uncovered.

We introduce the Poisson-Boltzmann cell model for spherical colloidal particles with a heterogeneous surface charge distribution. This model is obtained by generalizing existing cell models for mixtures of homogeneously charged colloidal spheres. Our model has similar features as Onsager’s second-virial theory for liquid crystals, but it predicts no orientational ordering if there is no positional ordering. This implies that all phases of heterogeneously charged colloids that are liquidlike with respect to translational degrees of freedom are also isotropic with respect to particle orientation.

Homogeneous diethyl phthalate/phenylphthalein-dimethylether (DEP/PDE) mixtures have been investigated by means of broadband dielectric spectroscopy. Contrarily to the widespread view that homogenous binary mixtures should give rise to a single glass transition, the mixture displays two dynamics giving rise to two glass transitions. Such a finding can be rationalized invoking the self-concentration concept that relies on the localized nature of the glass transition phenomenon. In such a way, the analogy with miscible polymer blends, for which this concept has been introduced, is highlighted. A model based on the combination of the Adam-Gibbs (AG) theory of the glass transition and the self-concentration concept resulted to be fully predictive once the only unknown variable, namely, the glass-former specific parameter $\left(\alpha \right)$ connecting the characteristic length for the glass transition to the configurational entropy, is extracted applying the model itself to DEP/toluene and DEP/PDE solutions highly concentrated, respectively, in DEP and PDE. The $\alpha$ parameter obtained in such a way allows the precise determination of the most probable relaxation time even for those DEP/PDE mixtures displaying a strong overlap of the dielectric response. The model incorporating the self-concentration concept to the AG theory also provides the characteristic length scale for the glass transition for both DEP and PDE. Such a length scale was found to be on the order of 1–2 nm. This is comparable to that obtained for other glass formers.

The symmetry of the cholesteric uniform lying helix (ULH) structure, where the helix axis is aligned in a single direction parallel to the device substrates, is not compatible with a uniform surface alignment and an unwinding of the helical structure is expected at the interface. Fluorescence confocal polarizing microscopy experiments are performed on the interface between a bulk ULH and a uniform aligning surface (for both planar and homeotropic alignments). The results are analyzed in the framework of a finite difference numerical simulation based on the Frank elastic distortion, to determine relevant director structures. An optical model is introduced to predict three-dimensional fluorescence profiles for the structures. Comparison of experimental and theoretical results shows that the equilibrium structure of the system involves a continuous unwinding of the helix close to the surface.

We consider a prototypical nonlinear system which can be stabilized by multiplicative noise: an underdamped nonlinear pendulum with a stochastically vibrating pivot. A numerical solution of the pertinent Fokker-Planck equation shows that the upper equilibrium point of the pendulum can become stable even when the noise is white, and the “Kapitsa pendulum” effect is not at work. The stabilization occurs in a strong-noise regime where WKB approximation does not hold.