The formulation of Taylor on the self-similar propagation of an expanding spherical piston with constant velocity was extended to an instability-wrinkled deflagration front undergoing acceleration with $R_F\propto t^{\alpha }$, where $R_F$ is the instantaneous flame radius, $t$ the time, and $\alpha$ a constant exponent. The formulation describes radial compression waves pushed by the front, trajectories of gas particles, and the explosion condition in the gas upstream of the front. The instant and position of explosion are determined for a given reaction mechanism. For a step-function induction time, analytic formulas for the explosion time and position are derived, showing their dependence on the reaction and flow parameters including thermal expansion, specific heat ratio, and acceleration of the front.

We represent the free energy functional by a diagrammatic series with tensorial coefficients indexed by powers of the length scale. For hard cores, we obtain Percus’s exact functional in one dimension and the Kierlik-Rosinberg form of fundamental measures theory in three dimensions. In five dimensions, the functional describes bulk fluids better than does the Percus-Yevick theory. At planar walls, density profiles oscillate with smaller periods than in lower dimensions. Our findings open up avenues for treating both more general high-dimensional systems and three-dimensional mixtures via dimensional reduction.

A general Landau’s free energy functional is used to study the dynamics of crystallization during liquid-solid spinodal decomposition (SD). The strong length scale selectivity imposed during the early stage of SD induces the appearance of small precursors for crystallization with icosahedral order. These precursors grow in densely packed clusters of tetrahedra through the addition of new particles. As the average size of the amorphous nuclei becomes large enough to reduce geometric frustration, crystalline particles with a body-centered cubic symmetry heterogeneously nucleate on the growing clusters. The volume fraction of the crystalline phase is strongly dependent on the depth of quench. At deep quenches, the SD mechanism produces amorphous structures arranged in dense polytetrahedral aggregates.

The dependence of the contact angles of nanodrops of Lennard-Jones type fluids in nanocavities on their sizes are calculated using a nonlocal density functional theory in a canonical ensemble. Cavities of various radii and depths, various temperatures, as well as various values of the energy parameter of the fluid-solid interactions were considered. It is argued that this dependence might affect strongly, for instance, the rate of heterogeneous nucleation on rough surfaces, which is usually calculated under the assumption of constant contact angle.

We find a parametric resonance in the gigahertz range of DNA dynamics, generated by pumping hypersound. The resonance may be accompanied by the formation of localized phonon modes due to the random structure of elastic modulii of DNA.

We have derived here an exact kinetic equation for the time evolution of the probability distribution for a general reaction coordinate space, starting from a multidimensional Liouville equation based on first-principles theory. To make the equation tractable we use two standard approximations, which reduce the exact equation into a Fokker-Planck-type equation with a sink term. As illustrative examples, we consider its application to two important classes of reactions, viz., the electron transfer and diffusion-controlled reactions. The kinetic equations for the reaction coordinates corresponding to these reactions become one dimensional. We also provide a scheme to find the critical value of the reaction coordinate at which the reaction takes place, and also to obtain the initial distribution function in the same space for different experimental situations. In the case of photoinduced electron transfer, we introduce the effect of excitation frequency through the use of suitable initial distribution functions.

The 0-1 test for chaos is a recently developed time series characterization algorithm that can determine whether a system is chaotic or nonchaotic. While the 0-1 test was designed for deterministic series, in real-world measurement situations, noise levels may not be known and the 0-1 test may have difficulty distinguishing between chaos and randomness. In this paper, we couple the 0-1 test for chaos with a test for determinism and apply these tests to noisy symbolic series generated from various model systems. We find that the pairing of the 0-1 test with a test for determinism improves the ability to correctly distinguish between chaos and randomness from a noisy series. Furthermore, we explore the modes of failure for the 0-1 test and the test for determinism so that we can better understand the effectiveness of the two tests to handle various levels of noise. We find that while the tests can handle low noise and high noise situations, moderate levels of noise can lead to inconclusive results from the two tests.

An optical illusion is an image of a real target perceived by the eye that is deceptive or misleading due to a physiological illusion or a specific visual trick. The recently developed metamaterials provide efficient approaches to generate a perfect optical illusion. However, all existing research on metamaterial illusions has been limited to theory and numerical simulations. Here, we propose the concept of a radar illusion, which can make the electromagnetic (EM) image of a target gathered by radar look like a different target, and we realize a radar illusion device experimentally to change the radar image of a metallic target into a dielectric target with predesigned size and material parameters. It is well known that the radar signatures of metallic and dielectric objects are significantly different. However, when a metallic target is enclosed by the proposed illusion device, its EM scattering characteristics will be identical to that of a predesigned dielectric object under the illumination of radar waves. Such an illusion device will confuse the radar, and hence the real EM properties of the metallic target cannot be perceived. We designed and fabricated the radar illusion device using artificial metamaterials in the microwave frequency, and good illusion performances are observed in the experimental results.

We model strong shock-wave propagation, both in the ideal gas and in the dense Lennard-Jones fluid, using a refinement of earlier work, which accounts for the cold compression in the early stages of the shock rise by a nonlinear, Burnett-like, strain-rate dependence of the thermal conductivity, and relaxation of kinetic-temperature components on the hot, compressed side of the shock front. The relaxation of the disequilibrium among the three components of the kinetic temperature, namely, the difference between the component in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, is accomplished at a much more quantitative level by a rigorous application of the Cattaneo-Maxwell relaxation equation to a reference solution, namely, the steady shock-wave solution of linear Navier-Stokes-Fourier theory, along with the nonlinear Burnett heat-flux term. Our new continuum theory is in nearly quantitative agreement with nonequilibrium molecular-dynamics simulations under strong shock-wave conditions, using relaxation parameters obtained from the reference solution.

A reentrant orthogonal smectic-$A$ (Sm$A$) phase below the tilted smectic-$C$ phase is established in a chiral liquid crystalline compound. The temperature evolution of the layer spacing confirms monolayer structure in both Sm$A$ phases, the upper Sm$A$ as well as the reentrant Sm$A$ phase. The reentrancy of the Sm$A$ phase is explained on the basis of the mean field free energy taking into account nonmonotoneous temperature dependence of the lowest term coefficient.

The Ising model with ferromagnetic couplings on the Hanoi networks is analyzed with an exact renormalization group. In particular, the fixed points are determined and the renormalization- flow for certain initial conditions is analyzed. Hanoi networks combine a one-dimensional lattice structure with a hierarchy of long-range bonds to create a mix of geometric and small-world properties. Generically, those small-world bonds result in nonuniversal behavior, i.e., fixed points and scaling exponents that depend on temperature and the initial choice of coupling strengths. It is shown that a diversity of different behaviors can be observed with seemingly small changes in the structure of the networks. Defining interpolating families of such networks, we find tunable transitions between regimes with power-law and certain essential singularities in the critical scaling of the correlation length. These are similar to the so-called inverted Berezinskii-Kosterlitz-Thouless transition previously observed only in scale-free or dense networks.

We introduce a general method to infer the directional information flow between populations whose elements are described by $n$-dimensional vectors of symbolic attributes. The method is based on the Jensen-Shannon divergence and on the Shannon entropy and has a wide range of application. We show here the results of two applications: first we extract the network of genetic flow between meadows of the seagrass Poseidonia oceanica, where the meadow elements are specified by sets of microsatellite markers, and then we extract the semantic flow network from a set of Wikipedia pages, showing the semantic channels between different areas of knowledge.

In a fully formed rivulet, the flow profile across the total cross section is downward, as would be intuitively expected. However, prior to this stage being reached, a strong backflow capable of carrying particles up to 125 mm up the incline back to the source is shown to occur. Two phases are described prior to a fully formed rivulet being established. First, a forming rivulet, in which a bulbous drop head slides down a slope with a flow occurring in the wetted trail behind it. In this stage, a linear increase in backflow height is observed over time. Subsequently, a transient rivulet occurs, with the transition happening once the end of the inclined solid surface is reached. The backflow decreases through this phase in a stepwise manner, coinciding with fluid dripping off the surface. The findings here strongly challenge common assumptions made regarding cleaning, whereby fluid will transport particulate matter downhill, and has significant implications on irrigation applied to remove bacterial biofilms in clinical medicine.

The numerical code VAAQP (variational average atom in quantum plasmas), which is based on a fully variational model of equilibrium dense plasmas, is applied to equation-of-state calculations for aluminum, iron, copper, and lead in the warm-dense-matter regime. VAAQP does not impose the neutrality of the Wigner-Seitz ion sphere; it provides the average-atom structure and the mean ionization self-consistently from the solution of the variational equations. The formula used for the electronic pressure is simple and does not require any numerical differentiation. In this paper, the virial theorem is derived in both nonrelativistic and relativistic versions of the model. This theorem allows one to express the electron pressure as a combination of the electron kinetic and interaction energies. It is shown that the model fulfills automatically the virial theorem in the case of local-density approximations to the exchange-correlation free-energy. Applications of the model to the equation-of-state and Hugoniot shock adiabat of aluminum, iron, copper, and lead in the warm-dense-matter regime are presented. Comparisons with other approaches, including the inferno model, and with available experimental data are given. This work allows one to understand the thermodynamic consistency issues in the existing average-atom models. Starting from the case of aluminum, a comparative study of the thermodynamic consistency of the models is proposed. A preliminary study of the validity domain of the inferno model is also included.

We developed a simulation scheme based on the coupling of the lattice-Boltzmann method with the smoothed-profile method (SPM) to predict the dynamic behavior of colloidal dispersions. The SPM provides a coupling scheme between continuum fluid dynamics and rigid-body dynamics through a smoothed profile of the fluid-particle interface. In this approach, the flow is computed on fixed Eulerian grids which are also used for the particles. Owing to the use of the same grids for simulation of fluid flow and particles, this method is highly efficient. Furthermore, an external boundary is used to impose the no-slip boundary condition at the fluid-particle interface. In addition, the operations in the present method are local; it can be easily programmed for parallel machines. The methodology is validated by comparing with previously published data.

Extensive kinetic Monte Carlo simulations are presented for ballistic deposition (BD) in $(1+1)$ dimensions. Asymptotic scaling is found only for lattice sizes $L\gtrsim 2^{12}$. Such a large system size for the onset of scaling explains the widespread discrepancies of previous reports for exponents of BD in one and likely higher dimensions. The exponents obtained from our simulations, $\alpha =0.499\pm 0.004$ and $\beta =0.336\pm 0.004$, are in excellent agreement with the exact values $\alpha =\frac{1}{2}$ and $\beta =\frac{1}{3}$ for the one-dimensional Kardar-Parisi-Zhang equation. Our findings make possible a more informed exploration of exponents for BD in higher dimensions, accurate estimates of which have proven to be elusive.

We present a theoretical study of the growth of a two-phase finger in eutectic systems. This pattern was observed experimentally by Akamatsu and Faivre [Phys. Rev. E 61, 3757 (2000)]. We study this two-phase finger using a boundary-integral formulation and we complement our investigation by a phase-field validation of the stability of the pattern. The deviations from the eutectic temperature and from the eutectic concentration provide two independent control parameters, leading to very different patterns depending on their relative importance. We propose scaling laws for the velocity and the different length scales of the pattern.

We performed neutron reflectivity measurements on multilayered polymer thin films consisting of alternatively stacked deuterated polystyrene ($d$-PS) and hydrogenated polystyrene ($h$-PS) layers ∼200 Å thick as a function of temperature covering the glass-transition temperature $T_g$, and we found a wide distribution of $T_g$ as well as a distribution of the thermal expansivity α within the thin films, implying the dynamic heterogeneity of the thin films along the depth direction. The reported anomalous film thickness dependences of $T_g$ and α were reasonably understood in terms of the distributions, showing that the surface mobile layer and the bottom hard interfacial layer are, respectively, responsible for the depressions of $T_g$ and α with decreasing film thickness. The molecular mobility in each layer is also discussed in relation to the distribution of $T_g$, based on the results on mutual diffusion at the layer interface.

The paper presents a simple dynamical model to systemically explain the rotation mechanism of the liquid film motor reported by experiments. The field-induced-plasticity effect of the liquid film is introduced into our model, in which the liquid film in crossed electric fields is considered as a Bingham plastic fluid with equivalent electric dipole moment. Several analytic results involving the torque of rotation, the scaling relation of the threshold fields, and the dynamics equation of a square film and its solution are obtained. We find that the rotation of the liquid film motor originates from the continuous competition between the destruction and the reestablishment of the polarization equilibrium maintained by the external electric field, which is free from the boundary effects. Most experimental phenomena observed in direct current electric fields are interpreted well.