The centrifugally driven viscous fingering problem arises when two immiscible fluids of different densities flow in a rotating Hele-Shaw cell. In this conventional setting an interplay between capillary and centrifugal forces makes the fluid-fluid interface unstable, leading to the formation of fingered structures that compete dynamically and reach different lengths. In this context, it is known that finger competition is very sensitive to changes in the viscosity contrast between the fluids. We study a variant of such a rotating flow problem where the fluids react and produce a gellike phase at their separating boundary. This interface is assumed to be elastic, presenting a curvature-dependent bending rigidity. A perturbative weakly nonlinear approach is used to investigate how the elastic nature of the interface affects finger competition events. Our results unveil a very different dynamic scenario, in which finger length variability is not regulated by the viscosity contrast, but rather determined by two controlling quantities: a characteristic radius and a rigidity fraction parameter. By properly tuning these quantities one can describe a whole range of finger competition behaviors even if the viscosity contrast is kept unchanged.

Nanocomposites with high-aspect ratio fillers attract enormous attention because of the superior physical properties of the composite over the parent matrix. Nanocomposites with functionalized graphene as fillers did not produce the high thermal conductivity expected due to the high interfacial thermal resistance between the functional groups and graphene flakes. We report here a robust and efficient technique that identifies the configuration of the functionalities for improved thermal conductivity. The method combines linearization of the interatomic interactions, calculation, and optimization of the thermal conductivity using the globalized and bounded Nelder-Mead algorithm.

A reversible algorithm [enforced energy conservation (EEC)] that enforces total energy conservation for microcanonical simulations is presented. The key point is the introduction of the discrete-gradient method to define the forces from the conservative potentials, instead of the direct use of the force field at the actual position of the particle. We have studied the performance and accuracy of the EEC in two cases, namely Lennard-Jones fluid and a simple electrolyte model. Truncated potentials that usually induce inaccuracies in energy conservation are used. In particular, the reaction field approach is used in the latter. The EEC is able to preserve energy conservation for a long time, and, in addition, it performs better than the Verlet algorithm for these kinds of simulations.

We consider a model of an optical cavity with a nonequilibrium reservoir consisting of a beam of identical two-level atom pairs (TLAPs) in the general X state. We find that coherence of multiparticle nonequilibrium reservoir plays a central role on the potential work capability of the cavity. We show that no matter whether there are quantum correlations in each TLAP (including quantum entanglement and quantum discord) or not, the coherence of the TLAPs has an effect on the work capability of the cavity. Additionally, constructive and destructive interferences could be induced to influence the work capability of the cavity by adjusting only the relative phase, with which quantum correlations have nothing to do. In this paper, the coherence of the reservoir, rather than the quantum correlations, effectively reflecting the effects of the reservoir on the system's work capability is demonstrated clearly.

The Bose-Einstein condensation of noninteracting particles restricted to move on the sites of hierarchical diamond lattices is investigated. Using a tight-binding single-particle Hamiltonian with properly rescaled hopping amplitudes, we are able to employ an orthogonal basis transformation to exactly map it on a set of decoupled linear chains with sizes and degeneracies written in terms of the network branching parameter $q$ and generation number $n$. The integrated density of states is shown to have a fractal structure of gaps and degeneracies with a power-law decay at the band bottom. The spectral dimension $d_s$ coincides with the network topological dimension $d_f=ln\left(2q\right)/ln\left(2\right)$. We perform a finite-size scaling analysis of the fraction of condensed particles and specific heat to characterize the critical behavior of the BEC transition that occurs for $q>2$ ($d_s>2$). The critical exponents are shown to follow those for lattices with a pure power-law spectral density, with non-mean-field values for $q<8$ ($d_s<4$). The transition temperature is shown to grow monotonically with the branching parameter, obeying the relation $1/T_c=a+b/(q-2)$.

The Quincke effect—spontaneous rotation of dielectric particles in a liquid with low conductivity under the action of an electric field—is considered. The distribution functions for the orientation of particle rotation planes are introduced and a set of nonlinear kinetic equations is derived in the mean field approximation considering the dynamics of their orientation in the flow induced by rotating particles. As a result the nonequilibrium phase transition to the polar order, if the concentration of the particles is sufficiently high, is predicted and the condition of the synchronization of particle rotations is established. Two cases are considered: the layer of the Quincke suspension with one free boundary and the ensemble of the particles rolling on the solid wall under the action of a torque in an electric field. It is shown that in both cases the synchronization of particle rotations occurs due to the hydrodynamic interactions. In the limit of small spatial nonhomogeneity a set of nonlinear partial differential equations for the macroscopic variables—the concentration and the director of the polar order—is derived from the kinetic equation. Its properties are analyzed and compared with available recent experimental results.

The effects of thermal coupling between two thin liquid layers separated by a gas layer are discussed. The liquid layers undergo long-wavelength instabilities driven by gravitational and thermocapillary stresses. To study the dynamics, both a linear stability analysis and a full numerical solution of the thin-film equations are performed. The results demonstrate that the stability properties of the combined system differs substantially from the case where both layers evolve independently from each other. Most prominently, oscillatory instabilities, not present in single-liquid layer configurations, may occur.

Reconstruction of complex structures is an inverse problem arising in virtually all areas of science and technology, from protein structure determination to bulk heterostructure solar cells and the structure of nanoparticles. We cast this problem as a complex network problem where the edges in a network have weights equal to the Euclidean distance between their endpoints. We present a method for reconstruction of the locations of the nodes of the network given only the edge weights of the Euclidean network. The theoretical foundations of the method are based on rigidity theory, which enables derivation of a polynomial bound on its efficiency. An efficient implementation of the method is discussed and timing results indicate that the run time of the algorithm is polynomial in the number of nodes in the network. We have reconstructed Euclidean networks of about 1000 nodes in approximately 24 h on a desktop computer using this implementation. We also reconstruct Euclidean networks corresponding to polymer chains in two dimensions and planar graphene nanoparticles. We have also modified our base algorithm so that it can successfully solve random point sets when the input data are less precise.

In this study, the immersed boundary–thermal lattice Boltzmann method has been used to simulate non-Newtonian fluid flow over a heated circular cylinder. The direct-forcing algorithm has been employed to couple the off-lattice obstacles and on-lattice fluid nodes. To investigate the effect of boundary sharpness, two different diffuse interface schemes are considered to interpolate the velocity and temperature between the boundary and computational grid points. The lattice Boltzmann equation with split-forcing term is applied to consider the effects of the discrete lattice and the body force to the momentum flux, simultaneously. A method for calculating the Nusselt number based on diffuse interface schemes is developed. The rheological and thermal properties of non-Newtonian fluids are investigated under the different power-law indices and Reynolds numbers. The effect of numerical parameters on the accuracy of the proposed method has been investigated in detail. Results show that the rheological and thermal properties of non-Newtonian fluids in the presence of a heated immersed body can be suitably captured using the immersed boundary thermal lattice Boltzmann method.

We study the Hamiltonian mean field (HMF) model of coupled Hamiltonian rotors with a heterogeneous distribution of moments of inertia and coupling strengths. We show that when the parameters of the rotors are heterogeneous, finite-size fluctuations can greatly modify the coupling strength at which the incoherent state loses stability by inducing correlations between the momenta and parameters of the rotors. When the distribution of initial frequencies of the oscillators is sufficiently narrow, an analytical expression for the modification in critical coupling strength is obtained that confirms numerical simulations. We find that heterogeneity in the moments of inertia tends to stabilize the incoherent state, while heterogeneity in the coupling strengths tends to destabilize the incoherent state. Numerical simulations show that these effects disappear for a wide, bimodal frequency distribution.

Negative differential thermal resistance (NDTR) can be generated for any one-dimensional heat flow with a temperature-dependent thermal conductivity. In a system-independent scaling analysis, the general condition for the occurrence of NDTR is found to be an inequality with three scaling exponents: $n_1{n}_2<-(1+n_3)$, where $n_1\in (-\infty ,+\infty )$ describes a particular way of varying the temperature difference, and $n_2$ and $n_3$ describe, respectively, the dependence of the thermal conductivity on an average temperature and on the temperature difference. For cases with a temperature-dependent thermal conductivity, i.e. $n_2\ne 0$, NDTR can always be generated with a suitable choice of $n_1$ such that this inequality is satisfied. The results explain the illusory absence of a NDTR regime in certain lattices and predict new ways of generating NDTR, where such predictions have been verified numerically. The analysis will provide insights for a designing of thermal devices, and for a manipulation of heat flow in experimental systems, such as nanotubes.

Universal values of dimensional effective coupling constants $g_{2k}$ that determine nonlinear susceptibilities ${\chi }_{2k}$ and enter the scaling equation of state are calculated for $n$-vector field theory within the pseudo-$\epsilon$ expansion approach. Pseudo-$\epsilon$ expansions for $g_6$ and $g_8$ at criticality are derived for arbitrary $n$. Analogous series for ratios $R_6=g_6/g_4^2$ and $R_8=g_8/g_4^3$ that figure in the equation of state are also found, and the pseudo-$\epsilon$ expansion for Wilson fixed point location $g_4^{*}$ descending from the six-loop renormalization group (RG) expansion for the $\beta$ function is reported. Numerical results are presented for $0\le n\le 64$, with the most attention paid to the physically important cases $n=0,1,2,3$. Pseudo-$\epsilon$ expansions for quartic and sextic couplings have rapidly diminishing coefficients, so Padé resummation turns out to be sufficient to yield high-precision numerical estimates. Moreover, direct summation of these series with optimal truncation gives values of $g_4^{*}$ and $R_6^{*}$ that are almost as accurate as those provided by the Padé technique. Pseudo-$\epsilon$ expansion estimates for $g_8^{*}$ and $R_8^{*}$ are found to be much worse than those for lower-order couplings independently of the resummation method employed. The numerical effectiveness of the pseudo-$\epsilon$ expansion approach in two dimensions is also studied. Pseudo-$\epsilon$ expansion for $g_4^{*}$ originating from the five-loop RG series for the $\beta$ function of two-dimensional $\lambda {\varphi }^4$ field theory is used to get numerical estimates for $n$ ranging from 0 to 64. The approach discussed gives accurate enough values of $g_4^{*}$ down to $n=2$ and leads to fair estimates for Ising and polymer ($n=0$) models.

As quantum systems become more experimentally accessible, we are forced to reconsider the notions of control and work to fully account for quantum effects. To this end, we identify the work injected into a quantum system during a general quantum-mechanical driving protocol and quantify the relevant heat flows. The known results that are applicable in the limit of a classical drive are shown to emerge from our equations as a special case. Using the established framework, we show that the Bochkov-Kuzovlev identity for the exclusive work distribution is modified in a nontrivial way by the accumulation of system-drive correlations resulting from quantum back action. Our results accentuate the conceptual and discernible differences between a fully quantum-mechanical and classical driving protocols of quantum systems.

An infinitely wide plate, subject to an external force in its normal direction obeying Hooke's law, is placed in an infinite expanse of a rarefied gas. When the plate is displaced from its equilibrium position and released, it starts in general an oscillatory motion in its normal direction. This is the one-dimensional setting of a linear pendulum considered previously for a collisionless gas and a special Lorentz gas by the present authors [T. Tsuji and K. Aoki, J. Stat. Phys. 146, 620 (2012)]. The motion decays as time proceeds because of the drag force on the plate exerted by the surrounding gas. The long-time behavior of the unsteady motion of the gas caused by the motion of the plate is investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation with special interest in the rate of the decay of the oscillatory motion of the plate. The result provides numerical evidence that the displacement of the plate decays in proportion to an inverse power of time for large time.

The microscopic dynamics of an excess proton in water and in low-density amorphous ices has been studied by means of a series of molecular dynamics simulations. Interaction of water with the proton species was modelled using a multistate empirical valence bond Hamiltonian model. The analysis of the effects of low temperatures on proton diffusion and transfer rates has been considered for a temperature range between 100 and 298 K at the constant density of 1 g cm${}^{-3}$. We observed a marked slowdown of proton transfer rates at low temperatures, but some episodes are still seen at 100 K. In a similar fashion, mobility of the lone proton gets significantly reduced when temperature decreases below 273 K. The proton transfer in low-density amorphous ice is an activated process with energy barriers between 1–10 kJ/mol depending of the temperature range considered and eventually showing Arrhenius-like behavior. Spectroscopic data indicated the survival of both Zundel and Eigen structures along the whole temperature range, revealed by significant spectral frequency shifts.

We study analytically the effect of a small inertial correction on the properties of adiabatically driven flashing ratchets. Parrondo's lemma [J. M. R. Parrondo, Phys. Rev. E 57, 7297 (1998)] is generalized to include the inertial term so as to establish the symmetry conditions allowing directed motion (other than in the overdamped massless case) and to obtain a high-temperature expansion of the motion velocity for arbitrary potential profiles. The inertial correction is thus shown to enhance the ratchet effect at all temperatures for sawtooth potentials and at high temperatures for simple potentials described by the first two harmonics. With the special choice of potentials represented by at least the first three harmonics, the correction gives rise to the motion reversal in the high-temperature region. In the low-temperature region, inertia weakens the ratchet effect, with the exception of the on-off model, where diffusion is important. The directed motion adiabatically driven by potential sign fluctuations, though forbidden in the overdamped limit, becomes possible due to purely inertial effects in neither symmetric nor antisymmetric potentials, i.e., not for commonly used sawtooth and two-sinusoid profiles.

We study closed dense collections of freely cooling hard spheres that collide inelastically with constant coefficient of normal restitution. We find inhomogeneous states (ISs) where the density profile is spatially nonuniform but constant in time. The states are exact solutions of nonlinear partial differential equations that describe the coupled distributions of density and temperature valid when inelastic losses of energy per collision are small. The derivation is performed without modeling the equations' coefficients that are unknown in the dense limit (such as the equation of state) using only their scaling form specific for hard spheres. Thus the IS is the exact state of this dense many-body system. It captures a fundamental property of inelastic collections of particles: the possibility of preserving nonuniform temperature via the interplay of inelastic cooling and heat conduction that generalizes previous results. We perform numerical simulations to demonstrate that arbitrary initial state evolves to the IS in the limit of long times where the container has the geometry of the channel. The evolution is like a gas-liquid transition. The liquid condenses in a vanishing part of the total volume but takes most of the mass of the system. However, the gaseous phase, which mass grows only logarithmically with the system size, is relevant because its fast particles carry most of the energy of the system. Remarkably, the system self-organizes to dissipate no energy: The inelastic decay of energy is a power law ${[1+t/t_c]}^{-2}$, where $t_c$ diverges in the thermodynamic limit. This is reinforced by observing that for supercritical systems the IS coincide in most of the space with the steady states of granular systems heated at one of the walls. We discuss the relation of our results to the recently proposed finite-time singularity in other container's geometries.

We report experimental measurements of the surface fluctuations of micron-thick oil films spread onto a solid substrate. We use a recently developed optical technique based on the measurement of the deflection of a laser beam triggered by changes in the local surface slope. When the liquid is spread on a flat substrate, fluctuation dynamics slow down as the thickness is decreased, in quantitative agreement with previous predictions. In addition, we investigate the consequences on surface fluctuations of the patterning of the substrate with a rectangular grating. For liquid film thicknesses smaller than the typical wavelength probed, we demonstrate that surface fluctuations are modified by the underlying pattern: The shape of the fluctuation spectra varies periodically with the spatial position over the pattern and, in addition, the fluctuations become locally anisotropic. However, the spatially averaged spectrum is isotropic.

Comparing the entropies of hard spheres in the limit of close packing, for different stacking sequences of the hexagonal layers, has been a challenge because the differences are so small. Here we present a method based on a “sticky-sphere” model by which the system interpolates between hard spheres in one limit and a harmonic crystal in the other. For the fcc and hcp stackings we have calculated the entropy difference in the harmonic (sticky) limit, as well as the differences in the free energy change upon removing the stickiness in the model. The former, or phonon entropy, accounts for most of the entropy difference. Our value for the net entropy difference, $\Delta s=0.001164\left(8\right)k_{\mathrm{B}}$ per sphere, is in excellent agreement with the best previous estimate by Mau and Huse [Phys. Rev. E 59, 4396 (1999)].

The effect of superimposed ac and dc electric fields on the formation of electroconvection and flexoelectric patterns in nematic liquid crystals was studied. For selected ac frequencies, an extended standard model of the electrohydrodynamic instabilities was used to characterize the onset of pattern formation in the two-dimensional parameter space of the magnitudes of the ac and dc electric field components. Numerical as well as approximate analytical calculations demonstrate that depending on the type of patterns and on the ac frequency, the combined action of ac and dc fields may either enhance or suppress the formation of patterns. The theoretical predictions are qualitatively confirmed by experiments in most cases. Some discrepancies, however, seem to indicate the need to extend the theoretical description.