We study relativistic hydrodynamics in the linear regime, based on Mori's projection operator method. In relativistic hydrodynamics, it is considered that an ambiguity about the fluid velocity occurs from the choice of a local rest frame: the Landau and Eckart frames. We find that the difference of the frames is not the choice of the local rest frame, but rather that of dynamic variables in the linear regime. We derive hydrodynamic equations in both frames by the projection operator method. We show that the natural derivation gives the linearized Landau equation. Also we find that, even for the Eckart frame, the slow dynamics is actually described by the dynamic variables for the Landau frame.

The dynamics and morphology of outwardly propagating, accelerating turbulent premixed flames and the effect of flame acceleration on explosion triggering are analyzed. Guided by recent theoretical results and substantiated by experiments, we find that an expanding flame front in an externally forced, near-isotropic turbulent environment exhibits accelerative propagation given by a well-defined power law based on the average global flame radius. In this context the limits of the power-law exponent and the effective turbulence intensity experienced by the flame are derived. The power-law exponent is found to be substantially larger than that for the hydrodynamically unstable cellular laminar flames, hence facilitating the possibility of detonation triggering in turbulent environments. For large length scales, hydrodynamic instability is expected to provide additional acceleration, thus further favoring the attainment of detonation triggering.

An experimental and numerical study has been conducted on the electrohydrodynamic flow around coplanar electrodes with a dielectric liquid: dodecane mixed with the surfactant Span 80. It is shown that the flow is asymmetric, although the electrode is symmetrically arranged, and numerically, we have shown that a difference in the ionic size can reproduce such asymmetric patterns. It is also found that the dissociation layer effect becomes more important in determining the flow pattern than is predicted from the conventional theory where the Langevin formula is used for the recombination constant. In numerical simulations, reducing the recombination constant to 0.035–0.055 times the Langevin value turned out to produce good comparisons between the experimental and the numerical results for the electrode pairs with 1 and 0.2 mm gaps.

Spatially resolved $K$-shell spectroscopy is used here to investigate the interaction of an ultrashort laser pulse ($\lambda =800$ nm, $\tau =40$ fs) with a Ti foil under intense irradiation ($I{\lambda }^2=2\times {10}^{18}\mathrm{W}\mu {\mathrm{m}}^2{\mathrm{cm}}^{-2}$) and the following fast electron generation and transport into the target. The effect of laser pulse polarization ($p$, $s$, and circular) on the $K\alpha$ yield and line shape is probed. The radial structure of intensity and width of the lines, obtained by a discretized Abel deconvolution algorithm, suggests an annular distribution of both the hot electron propagation into the target and the target temperature. An accurate modeling of $K\alpha$ line shapes was performed, revealing temperature gradients, going from a few eV up to 15–20 eV, depending on the pulse polarization. Results are discussed in terms of mechanisms of hot electron generation and of their transport through the preplasma in front of the target.

We have performed a systematic study of lithium hydride (LiH), using orbital-free molecular dynamics, with a focus on mass transport properties such as diffusion and viscosity by extending our previous studies at the lower end of the warm, dense matter regime to cover a span of densities from ambient to 10-fold compressed and temperatures from 10 eV to 10 keV. We determine analytic formulas for self- and mutual-diffusion coefficients, and viscosity, which are in excellent agreement with our molecular dynamics results, and interpolate smoothly between liquid and dense plasma regimes. In addition, we find the orbital-free calculations begin to agree with the Brinzinskii-Landau formula above about 250 eV at which point the medium becomes fully ionized. A binary-ion model based on a bare Coulomb interaction within a neutralizing background with the effective charges determined from a regularization prescription shows good agreement above about 100 eV with the orbital-free results. Finally, we demonstrate the validity of a pressure-based mixing rule in determining the transport properties from the pure-species quantities.

Numerical transfer-matrix methods are used to discuss the shape of the phase diagram, in field-temperature parameter space, of two-dimensional honeycomb-lattice Ising spin-$\frac{1}{2}$ magnets, with antiferromagnetic couplings along at least one lattice axis, in a uniform external field. Both the order and universality class of the underlying phase transition are examined as well. Our results indicate that in one particular case, the critical line has, at least to a very good approximation, a horizontal section (i.e., at constant field) of finite length, starting at the zero-temperature end of the phase boundary. Other than that, we find no evidence of unusual behavior, at variance with the re-entrant features predicted in earlier studies.

Ginzburg-Landau–de Gennes-type covariant theories are extensively used in connection with twist grain boundary phases of chiral smectogens. We analyze the stability conditions for the linear, covariant elasticity theory of smectic-$C$ liquid crystals in the context of achiral materials, and predict an equilibrium modulated structure with an oblique wave vector. We suggest that a previous experimental observation of stripes in smectic-$C$ is consistent with the predicted structure.

A nonlinear optical medium with nonlocal feedback is shown to have all the necessary ingredients to simulate a growthlike process that generates golden spirals and phyllotactic patterns. Elementary droplets of light are generated by the optical nonlinearity whereas the combination of rotation and translation in the feedback loop geometrically distributes them on spiraling patterns. The symmetry of the geometrical arrangements is described with the help of a simple replication algorithm.

For time-dependent states generated by an external operation, a generalized free energy may be introduced by the relative entropy with respect to an equilibrium state realized after sufficient relaxation from the time-dependent states. Recently, by studying overdamped systems, Sivak and Crooks presented a formula that relates the generalized free energy with measurable thermodynamic works. We rederive this relation with emphasizing a connection to an extended Clausius relation proposed in the framework of steady state thermodynamics. As a natural consequence, we generalize this relation to be valid for systems with momentum degrees of freedom, where the Shannon entropy in the generalized free energy is replaced by a symmetric one.

We analyze the contact network of simulated two-dimensional granular packings in different states of mechanical equilibrium obtained by tapping. We show that topological descriptors of the contact network allow one to distinguish steady states of the same mean density obtained with different tap intensities. These equal-density states were recently proven to be distinguishable through the mean force moment tensor. In contrast, geometrical descriptors, such as radial distribution functions, bond order parameters, and Voronoi cell distributions, can hardly discriminate among these states. We find that small-order loops of contacts—the polygons of the network—are especially sensitive probes for the contact structure.

The interactions among time series as individual components of complex systems can be quantified by measuring to what extent they exchange information among each other. In many applications, one focuses not on the original series but on its ordinal pattern. In such cases, trivial noises appear more likely to be filtered and the abrupt influence of extreme values can be weakened. Cross-sample entropy and inner composition alignment have been introduced as prominent methods to estimate the information interactions of complex systems. In this paper, we modify both methods to detect the interactions among the ordinal pattern of stock return and volatility series, and we try to uncover the information exchanges across sectors in Chinese stock markets.

Identifying changes in the parameters of a dynamical system can be vital in many diagnostic and sensing applications. Sensitivity vector fields (SVFs) are one way of identifying such parametric variations by quantifying their effects on the morphology of a dynamical system's attractor. In many cases, SVFs are a more effective means of identification than commonly employed modal methods. Previously, it has only been possible to construct SVFs for a given dynamical system when a full set of state variables is available. This severely restricts SVF applicability because it may be cost prohibitive, or even impossible, to measure the entire state in high-dimensional systems. Thus, the focus of this paper is constructing SVFs with only partial knowledge of the state by using time-delay coordinate embeddings. Local models are employed in which the embedded states of a neighborhood are weighted in a way referred to as embedded point cloud averaging. Application of the presented methodology to both simulated and experimental time series demonstrates its utility and reliability.

We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We represent each step of this dynamics as a combination of two processes. The first one is a linear energy-conserving evolution of the two-particle distribution, for which the entropy growth can be easily verified. The original nonlinear process is actually a result of a specific “coarse graining” of this linear evolution, when after the collision one variable is integrated away. This coarse graining is of the same type as the real space renormalization group transformation and leads to an additional entropy growth. The combination of these two factors produces the required result which is obtained only by means of information theory inequalities.

Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting particles, and their large scale behavior depends on the overall growth geometry. We establish an exact relation between statistical properties of structures in uniformly expanding and fixed geometries, which preserves the local scale invariance and is independent of other properties such as the dimensionality. This relation generalizes standard conformal transformations as the natural symmetry of self-affine growth processes. We illustrate our main result numerically for various structures of coalescing Lévy flights and fractional Brownian motions, including also branching and finite particle sizes. One of the main benefits of this approach is a full, explicit description of the asymptotic statistics in expanding domains, which are often nontrivial and random due to amplification of initial fluctuations.

Recent advances in quantum optics and atomic physics allow for an unprecedented level of control over light-matter interactions, which can be exploited to investigate new physical phenomena. In this work we are interested in the role played by the topology of quantum networks describing coupled optical cavities and local atomic degrees of freedom. In particular, using a mean-field approximation, we study the phase diagram of the Jaynes-Cummings-Hubbard model on complex networks topologies, and we characterize the transition between a Mott-like phase of localized polaritons and a superfluid phase. We found that, for complex topologies, the phase diagram is nontrivial and well defined in the thermodynamic limit only if the hopping coefficient scales like the inverse of the maximal eigenvalue of the adjacency matrix of the network. Furthermore we provide numerical evidences that, for some complex network topologies, this scaling implies an asymptotically vanishing hopping coefficient in the limit of large network sizes. The latter result suggests the interesting possibility of observing quantum phase transitions of light on complex quantum networks even with very small couplings between the optical cavities.

We study the motion of a particle in spatially periodic potentials with broken mirror symmetry under the influence of white $\alpha$-stable Lévy noises. We consider both time-independent and fluctuating potentials. We focus on cases in which the spatial asymmetry of the potential is due not to a difference between the distances from an absolute minimum to the absolute maximum on its left and to the absolute maximum on its right but only to the curvatures of the potential profiles. The analysis is performed using the fractional Fokker-Planck formalism. Consistent results from Langevin simulations are also presented. We analyze the influence of the symmetry properties of the potentials in combination with the fluctuating characteristics of the system in the determination of the current. We find different situations in which both the absolute value and the direction of the current depend not only on the properties of the potential but also on the parameters characterizing the $\alpha$-stable Lévy noise. Among other features, we analyze the case of supersymmetric potentials. In particular, we show that a static supersymmetric potential produces no current, and we analyze the conditions for observing a nonvanishing current when the potential fluctuates between different supersymmetric profiles.

The last half-century of research into the structure, dynamics, and thermodynamics of simple liquids has revealed a number of approximate universalities. This paper argues that simple liquids’ reduced-coordinate constant-potential-energy hypersurfaces constitute a quasiuniversal family of compact Riemannian manifolds parametrized by a single number; from this follows the quasiuniversalities.