Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional (2D) defocusing nonlinear Schrödinger (NLS) equation. This problem is of fundamental importance as a dispersive analog of the corresponding classical gas-dynamics problem. Assuming the oncoming flow speed is sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched $x$ coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear “ship-wave” pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles.

The author’s nonequilibrium probability distribution is tested for time-varying mechanical work. Nonequilibrium Monte Carlo (NEMC) is used to simulate a Brownian particle in a soft-sphere solvent, driven by a moving external potential. Results are obtained for the phase lag and amplitude for drive frequencies ranging from the steady state to the transient regime. This now extends the application of the NEMC algorithm to a time-varying nonequilibrium system. The results are shown to agree with those obtained by nonequilibrium stochastic molecular dynamics and by Nosé-Hoover molecular dynamics, from which it is concluded that the nonequilibrium probability distribution correctly describes time-varying mechanical work and that it provides a fundamental basis for nonequilibrium statistical mechanics.

A system-reservoir nonlinear coupling model has been proposed to the situation when the system is driven externally by a random force and the associated bath is kept in thermal equilibrium, in an attempt to put forth a microscopic approach to quantum state-dependent diffusion and multiplicative noises in terms of a quantum Langevin equation in the overdamped limit (quantum Smoluchowski equation). We then obtain the analytical expression for phase induced quantum current in a periodic potential when the external noise has finite correlation time and explore the dependence of the current on various parameters related to the external noise, for example, the noise strength.

Here, we outline the theoretical fundamentals of a promising growth kinetics of films from the vapor phase, in which pulsed fluxes are combined with temperature transients to enable short-range surface relaxations (e.g., species rearrangements) and to inhibit long-range relaxations (atomic exchange between species). A group of physical techniques (fully pulsed thermal and/or laser depositions) based on this kinetics is developed that can be used to prepare films with roughnesses even lower than those obtained with pulsed-laser deposition, which is the physical vapor-phase deposition technique that has produced the flattest films reported so far.

The ternary system consisting of cholesterol, a saturated lipid, and an unsaturated one exhibits a rich phase behavior with multiple phase coexistence regimes. Remarkably, phase separation even occurs when each of the three binary systems consisting of two of these components is a uniform mixture. We use a Flory-Huggins like model in which the phase separation of the ternary system is a consequence of an interaction between all three components to describe the system. From the associated Gibbs free energy we calculate phase diagrams, spinodals, and critical points. Moreover, we use a Van der Waals/Cahn-Hilliard like construction to derive an expression for the line tension between coexisting phases. We show how the line tension depends on the position in the phase diagram, and give an explicit expression for the concentration profile at the phase boundary.

Recent experiments measuring the electrical conductivity of DNA molecules highlight the need for a theoretical model of ion transport along a charged surface. Here we present a simple theory based on the idea of unbinding of ion pairs. The strong humidity dependence of conductivity is explained by the decrease in the electrostatic self-energy of a separated pair when a layer of water (with high dielectric constant) is adsorbed to the surface. We compare our prediction for conductivity to experiment and discuss the limits of its applicability.

We study a simplified model of the RNA molecule proposed by Vernizzi et al. in the regime of strong concentration of positive ions in solution. The model considers a flexible chain of equal bases that can pairwise interact with any other one along the chain while preserving the property of saturation of the interactions. In the regime considered, we observe the emergence of a critical temperature $T_c$ separating two phases that can be characterized by the topology of the predominant configurations: in the large temperature regime, the dominant configurations of the molecule have very large genera (on the order of the size of the molecule), corresponding to a complex topology, whereas in the opposite regime of low temperatures the dominant configurations are simple and have the topology of a sphere. We determine that this topological phase transition is of first order and provide an analytical expression for $T_c$. The regime studied for this model exhibits analogies with the dense polymer systems studied by de Gennes.

The Hilbert phase $\varphi \left(t\right)$ of a signal $x\left(t\right)$ exhibits slips when the magnitude of their successive phase difference $\left|\varphi \left(t_{i+1}\right)-\varphi \left(t_i\right)\right|$ exceeds $\pi$. By applying this approach to periodic, uncorrelated, and long-range correlated data, we show that the standard deviation of the time difference between the successive phase slips $\Delta \tau$ normalized by the percentage of slips in the data is characteristic of the correlation in the data. We consider a $50\times 50$ square lattice and model each lattice point by a second-order autoregressive (AR2) process. Further, we model a subregion of the lattice using a different set of AR2 parameters compared to the rest. By applying the proposed approach to the lattice model, we show that the two distinct parameter regions introduced in the lattice are clearly distinguishable. Finally, we demonstrate the application of this approach to spatiotemporal neonatal and fetal magnetoencephalography signals recorded using 151 superconducting quantum interference device sensors to identify the sensors containing the neonatal and fetal brain signals and discuss the improved performance of this approach over the traditionally used spectral approach.

Stable chaos refers to the long irregular transients, with a negative largest Lyapunov exponent, which is usually observed in certain high-dimensional dynamical systems. The mechanism underlying this phenomenon has not been well studied so far. In this paper, we investigate the dynamical formation of stable irregular transients in coupled discontinuous map systems. Interestingly, it is found that the transient dynamics has a hidden pattern in the phase space: it repeatedly approaches a basin boundary and then jumps from the boundary to a remote region in the phase space. This pattern can be clearly visualized by measuring the distance sequences between the trajectory and the basin boundary. The dynamical formation of stable chaos originates from the intersection points of the discontinuous boundaries and their images. We carry out numerical experiments to verify this mechanism.

We investigate the transition to synchronization in the Kuramoto model with bimodal distributions of the natural frequencies. Previous studies have concluded that the model exhibits a hysteretic phase transition if the bimodal distribution is close to a unimodal one due to the shallowness of the central dip. Here we show that proximity to the unimodal-bimodal border does not necessarily imply hysteresis when the width, but not the depth, of the central dip tends to zero. We draw this conclusion from a detailed study of the Kuramoto model with a suitable family of bimodal distributions.

Alternating laminar and turbulent helical bands appearing in shear flows between counterrotating cylinders are accurately computed and the near-wall instability phenomena responsible for their generation identified. The computations show that this intermittent regime can only exist within large domains and that its spiral coherence is not dictated by endwall boundary conditions. A supercritical transition route, consisting of a progressive helical alignment of localized turbulent spots, is carefully studied. Subcritical routes disconnected from secondary laminar flows have also been identified.

The onset of convection in two superimposed fluid layers of the same height is considered. It is found that the neutral curve for $R\left(a\right)$ for the onset Rayleigh number $R$ in dependence on the wave number $a$ is an invariant of a multidimensional parameter space of property ratios of the system even though the corresponding convection solutions may vary strongly with these property ratios. For each neutral curve $R\left(a\right)$ two manifolds of solutions are found one of which can be understood on the basis of symmetry properties of the system, while the other does not exhibit simple symmetry features. In particular the neutral curves $R\left(a\right)$ for various single Rayleigh-Bénard convection layers are shown to correspond to two two-dimensional manifolds of solutions. Analytical expressions for the latter are derived in the case of outer stress-free boundary conditions.

Osborne et al. [Phys. Rev. E 74, 036309 (2006)] suggested that our conclusions on the ability of kinematic simulation to represent the $t^3$ Richardson law [Thomson and Devenish, J. Fluid Mech. 526, 277 (2005)] were an artifact of our choice of time step. Here we repeat some of the simulations with a small fixed time step, enabling us to confirm that our previous study was not compromised by the variable time step used.

Monte Carlo simulations have been carried out for a system of monomers on square lattices that, by decreasing temperature or increasing density, polymerize reversibly into chains with two allowed directions and, at the same time, undergo a continuous isotropic-nematic (IN) transition. The results show that the self-assembly process affects the nature of the transition. Thus, the calculation of the critical exponents and the behavior of Binder cumulants indicate that the universality class of the IN transition changes from two-dimensional Ising-type for monodisperse rods without self-assembly to $q=1$ Potts-type for self-assembled rods.

An important limitation of nonequilibrium pulling experiments/simulations in recovering free energy differences is the poor convergence of path-ensemble averages. Therefore, a large number of fast-switching trajectories needs to achieve free energy estimates with acceptable accuracy. We propose a method to improve free energy estimates by drastically lowering the computational cost of steered molecular dynamics simulations employed to realize such trajectories. This is accomplished by generating trajectories where the particles not directly involved in the driven process are dynamically frozen. Such a freezing is dynamical rather than thermal because it is reached by a synchronous scaling of atomic masses and velocities keeping the kinetic energy of each particle unchanged. The forces between dynamically frozen particles can then be calculated rarely. Thus, it is possible to generate realizations of a process whose computational cost is not correlated with the size of the whole system, but only with that of the reaction site. The method is illustrated on a simple model system and its general applicability is discussed.

Transfer-matrix methods are used, in conjunction with finite-size scaling and conformal invariance concepts, to generate an accurate phase diagram for a two-dimensional square-lattice Ising spin-1/2 magnet, with couplings which are positive along one coordinate axis and negative along the other, in a uniform external field. Our results indicate that the critical line starts horizontally at the zero-temperature end of the phase boundary, at variance with the re-entrant behavior predicted in some earlier studies. Estimates of the thermal scaling exponent are very close to the Ising value $y_T=1$ along the critical line, except near $T=0$, where strong crossover effects prevent a reliable analysis.

We derive the effective viscosity of dilute suspensions of swimming bacteria from the microscopic details of the interaction of an elongated body with the background flow. An individual bacterium propels itself forward by rotating its flagella and reorients itself randomly by tumbling. Due to the bacterium’s asymmetric shape, interactions with a prescribed generic (such as planar shear or straining) background flow cause the bacteria to preferentially align in directions in which self-propulsion produces a significant reduction in the effective viscosity, in agreement with recent experiments on suspensions of Bacillus subtilis.

A transition rate model of cargo transport by $N$ molecular motors is proposed. Under the assumption of steady state, the force-velocity curve of multimotor system can be derived from the force-velocity curve of a single motor. Our work shows, in the case of low load, that the velocity of multimotor system can decrease or increase with increasing motor number, which is dependent on the single motor force-velocity curve; and most commonly, the velocity decreases. This gives a possible explanation to some recent experimental observations.

The energy transport in cone-guided low-$Z$ targets has been studied for laser intensities on target of $2.5\times {10}^{20}\text{W}{\text{cm}}^{-2}$. Extreme ultraviolet (XUV) imaging and transverse optical shadowgraphy of the rear surfaces of slab and cone-slab targets show that the cone geometry strongly influences the observed transport patterns. The XUV intensity showed an average spot size of $65\pm 10\mu \text{m}$ for slab targets. The cone slabs showed a reduced spot size of $44\pm 10\mu \text{m}$. The shadowgraphy for the aforementioned shots demonstrate the same behavior. The transverse size of the expansion pattern was $357\pm 32\mu \text{m}$ for the slabs and reduced to $210\pm 30\mu \text{m}$. A transport model was constructed which showed that the change in transport pattern is due to suppression of refluxing electrons in the material surrounding the cone.