An exact relationship for the local skin friction is derived for the compressible turbulent wall-bounded flow (channel, pipe, flat plate). This expression is an extension of the compressible case of that derived by Fukagata et al. [Phys. Fluids 14, L73 (2002)] in the case of incompressible wall-bounded flows. This decomposition shows that the skin friction can be interpreted as the contribution of four physical processes, i.e., laminar, turbulent, compressible, and a fourth coming from the interaction between turbulence and compressibility. Compressible numerical simulations show that, even at Mach number $M=2$, the main contribution comes from the turbulence, i.e., the Reynolds stress term.

Phase separation under directional quenching has been studied in a Cahn-Hilliard model. In distinct contrast to the disordered patterns which develop under a homogeneous quench, periodic stripe patterns are generated behind the quench front. Their wavelength is uniquely defined by the velocity of the quench interface in a wide range. Numerical simulations match perfectly analytical results obtained in the limit of small and large velocities of the quench interface. Additional periodic modulation of the quench interface may lead to cellular patterns. The quenching protocols analyzed are expected to be an effective tool in technological applications to design nanostructured materials.

We investigate the ratchet dynamics of solitons of a sine-Gordon system with additive inhomogeneities. We show by means of a collective coordinate approach that the soliton moves like a particle in an effective potential which is a result of the inhomogeneities. Different degrees of freedom of the soliton are used as collective coordinates in order to study their influence on the motion of the soliton. The collective coordinates considered are the soliton position, its width and offset, and the height of the spikes that appear on the soliton. The results of the theory are compared with numerical simulations of the full system.

This paper experimentally investigates the clustering conditions for compartmentalized monodisperse granular gases, determining the critical particle number and condensation granular temperature at the gas-clustering transition. When one heavier intruding particle is added to a monodisperse gas, it is found that the condensation temperature decreases with the ratio of the mass of the intruding particle to that of the background particle. This phenomenon can be mathematically characterized by a proposed linear relation, which is reminiscent of a relation between the freezing point depression for a solvent and the concentration of an added solute. Finally we perform various tests by changing the numbers of two types of particles in bidisperse granular mixtures to construct the phase diagrams, which present the range of the five different states, namely, homogeneous gas, unstable-gas, one-clustering, two-clustering, and granular oscillation states.

Vibrational spectra and normal modes of mechanically stable particle packings in three dimensions are analyzed over a range of compressions, from near the jamming transition, where the packings lose their rigidity, to far above it. At high frequency, the normal modes are localized at all compressions. At low frequency, the nature of the modes depends somewhat on compression. At large compressions, far from the transition, the lowest-frequency normal modes have some plane-wave character, though less than one would expect for a crystalline or isotropic solid. At low compressions near the jamming transition, the lowest-frequency modes are neither plane-wave-like nor localized. We characterize these differences, highlighting the unusual dispersion behavior that emerges for marginally jammed solids.

We have evaluated a universal ratio between diffusion constants of the ring polymer with a given knot $K$ and a linear polymer with the same molecular weight in solution through the Brownian dynamics under hydrodynamic interaction. The ratio is found to be constant with respect to the number of monomers, $N$, and hence the estimate at some $N$ should be valid practically over a wide range of $N$ for various polymer models. Interestingly, the ratio is determined by the average crossing number $\left(N_{\text{AC}}\right)$ of an ideal conformation of knotted curve $K$, i.e., that of the ideal knot. The $N_{\text{AC}}$ of ideal knots should therefore be fundamental in the dynamics of knots.

We study the quantum-to-classical transition in a chaotic system surrounded by a diffusive environment. First, we analyze the emergence of classicality when it is monitored by the Renyi entropy, a measure of the entanglement of a system with its environment. We show that the Renyi entropy has a transition from quantum to classical behavior that scales with ${\hslash }_{\mathrm{eff}}^2∕D$, where ${\hslash }_{\mathrm{eff}}$ is the effective Planck constant and $D$ is the strength of the noise. However, it was recently shown that a different scaling law controls the quantum-to-classical transition when it is measured comparing the corresponding phase-space distributions. Then, we discuss the meaning of both scalings in the precise definition of a frontier between the classical and quantum behaviors. Finally, we show that there are quantum coherences that the Renyi entropy is unable to detect, which questions its use in studies of decoherence.

In particle-based algorithms, the effect of binary collisions is commonly described in a statistical way, using Monte Carlo techniques. It is shown that, in the relativistic regime, stringent constraints should be considered on the sampling of particle pairs for collision, which are critical to ensure physically meaningful results, and that nonrelativistic sampling criteria (e.g., uniform random pairing) yield qualitatively wrong results, including equilibrium distributions that differ from the theoretical Jüttner distribution. A general procedure for relativistically consistent algorithms is provided, and verified with three-dimensional Monte Carlo simulations, thus opening the way to the numerical exploration of the statistical properties of collisional relativistic systems.

This paper is motivated by the following two related problems in complex networks: (i) control of cascading failures and (ii) mitigation of traffic congestion. Both problems are of significant recent interest as they address, respectively, the security of and efficient information transmission on complex networks. Taking into account typical features of load distribution and weights in real-world networks, we have discovered an optimal solution to both problems. In particular, we shall provide numerical evidence and theoretical analysis that, by choosing a proper weighting parameter, a maximum level of robustness against cascades and traffic congestion can be achieved, which practically rids the network of occurrences of the catastrophic dynamics.

In recent years, many efforts have been addressed on collision avoidance of collectively moving agents. In this paper, we propose a modified version of the Vicsek model with adaptive speed, which can guarantee the absence of collisions. However, this strategy leads to an aggregated state with slowly moving agents. We therefore further add a certain repulsion, which results in both faster consensus and longer safe distance among agents, and thus provides a powerful mechanism for collective motions in biological and technological multiagent systems.

In cellular automata models a glider gun is an oscillating pattern of nonquiescent states that periodically emits traveling localizations (gliders). The glider streams can be combined to construct functionally complete systems of logical gates and thus realize universal computation. The glider gun is the only means of ensuring the negation operation without additional external input and therefore is an essential component of a collision-based computing circuit. We demonstrate the existence of glider-gun-like structures in both experimental and numerical studies of an excitable chemical system—the light-sensitive Belousov-Zhabotinsky reaction. These discoveries could provide the basis for future designs of collision-based reaction-diffusion computers.

Coagulation of nanoparticles in a low-pressure radio frequency plasma was studied by means of a detailed numerical model for the spatiotemporal evolution of the nanoparticle-plasma system. Simulation results indicate that the occurrence of coagulation to any significant degree in such systems requires the existence of two effects: first, gas-phase nucleation is not limited to a brief burst, but rather continues in regions that are sufficiently free of nanoparticles; and second, coagulation coefficients for collisions between neutral and negatively charged nanoparticles are enhanced by the image potential induced in the neutral particle. Accounting for these effects, coagulation is predicted to be dominated by coagulation between very small ($\sim 1$ or $2\mathrm{nm}$ in diameter) neutral particles and larger negatively charged particles that are trapped in the plasma. Coagulation ceases when the spreading of the nanoparticle cloud across the plasma quenches gas-phase nucleation.

We study the wave scattering in an one-dimensional discrete system with two side-coupled defects. Each of the defects exhibits the Fano resonance as a resonant suppression of transmission, i.e., resonant reflection. We demonstrate that the interaction between two Fano resonances may give rise to a birth of a very narrow resonance. This effect may be understood in terms of the overlapping resonances, as suggested by Feshbach [Ann. Phys. 5, 357 (1958)]. We consider two cases, when the defects are coupled either locally or nonlocally to the discrete array. In the latter case, a sharp asymmetric resonance appears with a large quality factor. We demonstrate that by introducing a nonlinearity at side-coupled defects a closed loop in the nonlinear transmission coefficient may appear, which results in bistable response.

In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.

We revisit here the effect of quantum dissipation on the much studied problem of Landau diamagnetism and analyze the results in the light of the third law of thermodynamics. The case of an additional parabolic potential is separately assessed. We find that dissipation arising from strong coupling of the system to its environment qualitatively alters the low-temperature thermodynamic attributes such as the entropy and the specific heat.

The inconsistent temperature dependence of nucleation rates, disagreement of theoretical critical or onset supersaturations with experimental data, and insufficiently accurate predictions of nucleation rates are fundamental problems of the classical nucleation theory (CNT) of water vapors, which is a foundation of various multicomponent nucleation models widely used in the aerosol microphysics, physical chemistry, and chemical technology. In the present study, a correction to the CNT obtained from “first principles” has been derived and significant progress has been made in solving the fundamental problem of predicting nucleation rates of water vapors. The modified model with the quantum-mechanical correction incorporated is in very good agreement with experiments over the full range of temperatures $(T=210–290\mathrm{K})$, saturation ratios $(S=2–100)$, and nucleation rates $(J=\sim {10}^1–{10}^{17}{\mathrm{cm}}^{-3})$.

The $n\text{OHFBBB}1\text{M}7$ $\left(n=10\right)$ compound, 10OHF, shows a reversed $\text{Sm}{C}_{FI2}^{\ast }\text{-Sm}{C}^{\ast }$ phase sequence, unique among all known antiferroelectric liquid crystals. This reversed phase sequence is stabilized when 10OHF is doped with 9OTBBB1M7(C9) or 11OTBBB1M7(C11). In contrast, doping of the homologous members ($n=9$, 11, or 12) eliminates the $\text{Sm}{C}_{FI2}^{\ast }$ phase. One 10OHF/11OHF mixture without the $\text{Sm}{C}_{FI2}^{\ast }$ phase was selected for further studies. By adding C9 into this particular mixture, the reversed phase sequence is revived. To our surprise, even though 11OHF destabilizes the $\text{Sm}{C}_{FI2}^{\ast }$ phase in binary mixtures with 10OHF, it significantly increases the $\text{Sm}{C}_{FI2}^{\ast }$ temperature range in the 10OHF/11OHF/C9 ternary mixtures.

We investigate how defects in bipolar shells of liquid crystal evolve when the boundary conditions for the nematic director $\mathit{n}$ at the outer surface of the shell are changed from tangential to homeotropic. When the boundary conditions for $\mathit{n}$ are tangential, these bipolar shells are characterized by the presence of two pairs of boojums, one pair on each spherical surface. However, when $\mathit{n}$ is tangential at the inner surface and perpendicular at the outer surface, only the innermost pair of defects remains. Interestingly, there are two possible routes from one shell to the other and both involve the generation of a disclination ring that shrinks with time, eventually disappearing. Although the process is reminiscent of that encountered in bulk nematic droplets, in the case of nematic shells the two defects on the inner surface play a relevant role in the overall evolution process.