Rayleigh-Bénard convection is a canonical example of spontaneous pattern formation in a nonequilibrium system. It has been the subject of considerable theoretical and experimental study, primarily for systems with constant (temperature or heat flux) boundary conditions. In this investigation, we have explored the behavior of a convecting fluid system with negative feedback boundary conditions. At the upper and lower system boundaries, the inward heat flux is defined such that it is a decreasing function of the boundary temperature. Thus the system's heat transport is not constrained in the same manner that it is in the constant temperature or constant flux cases. It has been suggested that the entropy production rate (which has a characteristic peak at intermediate heat flux values) might apply as a selection rule for such a system. In this work, we demonstrate with Lattice Boltzmann simulations that entropy production maximization does not dictate the steady state of this system, despite its success in other, somewhat similar scenarios. Instead, we will show that the same scaling law of dimensionless variables found for constant boundary conditions also applies to this system.

We report on the proton acceleration studies from thin metallic foils of varying atomic number ($Z$) and thicknesses, investigated using a 45 fs, 10 TW Ti:sapphire laser system. An optimum foil thickness was observed for efficient proton acceleration for our laser conditions, dictated by the laser ASE prepulse and hot electron propagation behavior inside the material. The hydrodynamic simulations for ASE prepulse support the experimental observation. The observed maximum proton energy at different thicknesses for a given element is in good agreement with the reported scaling laws. The results with foils of different atomic number $Z$ suggest that a judicious choice of the foil material can enhance the proton acceleration efficiency, resulting into higher proton energy.

In this paper we present molecular dynamics (MD) calculations of the interdiffusion coefficient for asymmetric mixed plasma for thermodynamic conditions relevant to astrophysical and inertial confinement fusion plasmas. Specifically, we consider mixtures of deuterium and argon at temperatures of 100–500 eV and a number density $\sim {10}^{25} \mathrm{ions}/{\mathrm{cm}}^3$. The motion of 30 000–120 000 ions is simulated in which the ions interact via the Yukawa (screened Coulomb) potential. The electric field of the electrons is included in this effective interaction; the electrons are not simulated explicitly. The species diffusivity is then calculated using the Green-Kubo approach using an integral of the interdiffusion current autocorrelation function, a quantity calculated in the equilibrium MD simulations. Our MD simulation results show that a widely used expression relating the interdiffusion coefficient with the concentration-weighted sum of self-diffusion coefficients overestimates the interdiffusion coefficient. We argue that this effect due to cross-correlation terms in velocities is characteristic of asymmetric mixed plasmas. Comparison of the MD results with predictions of kinetic theories also shows a discrepancy with MD giving effectively a larger Coulomb logarithm.

We show that the flow of granular material inside a two-dimensional flat bottomed hopper is altered significantly by having more than one exit orifice. For hoppers with small orifice widths, intermittent flow through one orifice enables the resumption of flow through the adjacent jammed orifice, thus displaying a sequence of jamming and unjamming events. Using discrete element simulations, we show that the total amount of granular material (i.e., avalanche size) emanating from all the orifices combined can be enhanced by about an order of magnitude difference by simply adjusting the interorifice distance. The unjamming is driven primarily by fluctuations alone when the interorifice distance is large, but when the orifices are brought close enough, the fluctuations along with the mean flow cause the flow to unjam.

In statistical mechanics, any quantum system in equilibrium with its weakly coupled reservoir is described by a canonical state at the same temperature as the reservoir. Here, by studying the equilibration dynamics of a harmonic oscillator interacting with a reservoir, we evaluate microscopically the condition under which the equilibration to a canonical state is valid. It is revealed that the non-Markovian effect and the availability of a stationary state of the total system play a profound role in the equilibration. In the Markovian limit, the conventional canonical state can be recovered. In the non-Markovian regime, when the stationary state is absent, the system equilibrates to a generalized canonical state at an effective temperature; whenever the stationary state is present, the equilibrium state of the system cannot be described by any canonical state anymore. Our finding of the physical condition on such noncanonical equilibration might have significant impact on statistical physics. A physical scheme based on circuit QED is proposed to test our results.

To understand the dependence of phase-transition natures in explosive percolations on space dimensions, the number $n_{\text{cut}}$ of cutting bonds (sites) and the fractal dimension $d_{\text{CSC}}$ of the critical spanning cluster (CSC) for the six different models introduced in Phys. Rev. E 86, 051126 (2012) are studied on two- and three-dimensional lattices. It is found that $n_{\text{cut}}(L\to \infty )=1$ for the intrabond-enhanced models and the site models on the two-dimensional square lattice with lattice size $L$. In contrast, $n_{\text{cut}}$ for the intrabond-suppressed models scales as $n_{\text{cut}}\simeq L^{d_{\text{cut}}}$ with $d_{\text{cut}}=1$. $d_{\text{CSC}}=2.00\left(1\right)$ is obtained for the intrabond-enhanced models and the site models, while $d_{\text{CSC}}=1.96\left(1\right)(<2)$ is obtained for the intrabond-suppressed models in two dimensions (2D). These results strongly support that the intrabond-enhanced models and the site models undergo the discontinuous transition in 2D, while the intrabond-suppressed models do the continuous transition in 2D. On the three-dimensional cubic lattice, we find that $d_{\text{cut}}>0$ and $d_{\text{CSC}}=2.8\left(1\right)(<3)$ for all six models, which indicates that the models undergo the continuous transition. Based on the finite-size scaling analyses of mean cluster size and order parameter, all six models in 3D show nearly the same critical phenomena within numerical errors.

We compute the shear modulus of amorphous hard and soft spheres, using the exact solution in infinite spatial dimensions that has been developed recently. We characterize the behavior of this observable in the whole phase diagram, and in particular around the glass and jamming transitions. Our results are consistent with other theoretical approaches, which are unified within this general picture, and they are also consistent with numerical and experimental results. Furthermore, we discuss some properties of the out-of-equilibrium dynamics after a deep quench close to the jamming transition, and we show that a combined measure of the shear modulus and of the mean square displacement allows one to probe experimentally the complex structure of phase space predicted by the full replica-symmetry-breaking solution.

We developed a Bayesian method to extract macromolecular structure information from sparse single-molecule x-ray free-electron laser diffraction images. The method addresses two possible scenarios. First, using a “seed” structural model, the molecular orientation is determined for each of the provided diffraction images, which are then averaged in three-dimensional reciprocal space. Subsequently, the real space electron density is determined using a relaxed averaged alternating reflections algorithm. In the second approach, the probability that the “seed” model fits to the given set of diffraction images as a whole is determined and used to distinguish between proposed structures. We show that for a given x-ray intensity, unexpectedly, the achievable resolution increases with molecular mass such that structure determination should be more challenging for small molecules than for larger ones. For a sufficiently large number of recorded photons $(>200)$ per diffraction image an $M^{1/6}$ scaling is seen. Using synthetic diffraction data for a small glutathione molecule as a challenging test case, successful determination of electron density was demonstrated for $20000$ diffraction patterns with random orientations and an average of 82 elastically scattered and recorded photons per image, also in the presence of up to 50% background noise. The second scenario is exemplified and assessed for three biomolecules of different sizes. In all cases, determining the probability of a structure given set of diffraction patterns allowed successful discrimination between different conformations of the test molecules. A structure model of the glutathione tripeptide was refined in a Monte Carlo simulation from a random starting conformation. Further, effective distinguishing between three differently arranged immunoglobulin domains of a titin molecule and also different states of a ribosome in a tRNA translocation process was demonstrated. These results show that the proposed method is robust and enables structure determination from sparse and noisy x-ray diffraction images of single molecules spanning a wide range of molecular masses.

Extracting reliable indicators of chaos from a single experimental time series is a challenging task, in particular, for systems with many degrees of freedom. The techniques available for this purpose often require unachievably long time series. In this paper, we explore a method of discriminating chaotic from multi-periodic integrable motion in many-particle systems. The applicability of this method is supported by our numerical simulations of the dynamics of classical spin lattices at high temperatures. We compared chaotic and nonchaotic regimes of these lattices and investigated the transition between the two. The method is based on analyzing higher-order time derivatives of the time series of a macroscopic observable—the total magnetization of the spin lattice. We exploit the fact that power spectra of the magnetization time series generated by chaotic spin lattices exhibit exponential high-frequency tails, while, for the integrable spin lattices, the power spectra are terminated in a non-exponential way. We have also demonstrated the applicability limits of the above method by investigating the high-frequency tails of the power spectra generated by quantum spin lattices and by the classical Toda lattice.

We investigate thermocapillary-driven contact-line dynamics of two immiscible fluids in a narrow fluidic confinement comprising substrates with patterned wettability variations. Our study, based on phase field formalism, demonstrates that the velocity of the contact line is a strong function of the combined consequences of the applied thermal gradient and the substrate wetting characteristics. Finally, we evaluate different energy transfer rates and show that the dissipation due to fluid slip over the solid surface plays a dominating role in transferring energy into the contact-line motion. Our analysis, in effect, provides an elegant way of controlling the capillary filling rate in a narrow fluidic confinement by tailoring the applied temperature gradient and the substrate wettability in tandem.

In a recent paper we proposed a non-Markovian random walk model with memory of the maximum distance ever reached from the starting point (home). The behavior of the walker is different from the simple symmetric random walk only when she is at this maximum distance, where, having the choice to move either farther or closer, she decides with different probabilities. If the probability of a forward step is higher than the probability of a backward step, the walker is bold and her behavior turns out to be superdiffusive; otherwise she is timorous and her behavior turns out to be subdiffusive. The scaling behavior varies continuously from subdiffusive (timorous) to superdiffusive (bold) according to a single parameter $\gamma \in R$. We investigate here the asymptotic properties of the bold case in the nonballistic region $\gamma \in [0,1/2]$, a problem which was left partially unsolved previously. The exact results proved in this paper require new probabilistic tools which rely on the construction of appropriate martingales of the random walk and its hitting times.

Collective behavior of proteins on biomembranes is usually studied within the spontaneous curvature model. Here we consider an alternative phenomenological approach, which accounts consistently for partial ordering of proteins as well as the anchoring forces exerted on a membrane by layer of proteins. We show analytically that such anisotropic interactions can drive membrane bending, resulting in nontrivial equilibrium morphologies. The predicted instabilities can advance our conceptual understanding of physical mechanisms behind collective phenomena in biological systems, in particular those with inherent anisotropy.

The topic of finding an effective strategy to halt virus in a complex network is of current interest. We propose an immunization strategy for seasonal epidemics that occur periodically. Based on the local information of the infection status from the previous epidemic season, the selection of vaccinated nodes is optimized gradually. The evolution of vaccinated nodes during iterations demonstrates that the immunization tends to locate in both global hubs and local hubs. We analyze the epidemic prevalence using a heterogeneous mean-field method, and we present numerical simulations of our model. This immunization performs better than some other previously known strategies. Our work highlights an alternative direction in immunization for seasonal epidemics.

We study the macroscopic behavior of two-phase flow in porous media from a phase-field model. A dissipation law is first derived from the phase-field model by homogenization. For simple channel geometry in pore scale, the scaling relation of the averaged dissipation rate with the velocity of the two-phase flow can be explicitly obtained from the model which then gives the force-velocity relation. It is shown that, for the homogeneous channel surface, Dacry's law is still valid with a significantly modified permeability including the contribution from the contact line slip. For the chemically patterned surfaces, the dissipation rate has a non-Darcy linear scaling with the velocity, which is related to a depinning force for the patterned surface. Our result offers a theoretical understanding on the prior observation of non-Darcy behavior for the multiphase flow in either simulations or experiments.

The binodal of a boson square-well fluid is determined as a function of the particle mass through a quantum Gibbs ensemble Monte Carlo algorithm devised by R. Fantoni and S. Moroni [J. Chem. Phys. (to be published)]. In the infinite mass limit we recover the classical result. As the particle mass decreases, the gas-liquid critical point moves at lower temperatures. We explicitly study the case of a quantum delocalization de Boer parameter close to the one of ${}^4\mathrm{He}$. For comparison, we also determine the gas-liquid coexistence curve of ${}^4\mathrm{He}$ for which we are able to observe the binodal anomaly below the $\lambda$-transition temperature.

We demonstrate that a circular Bessel density function describes the electromagnetic field statistics in the Anderson localization regime using example numerical terahertz field data in strongly scattering media. This density function for localized fields provides a measure that allows identification and description in a manner akin to the Gaussian density function for weakly interacting scatterers, the mathematical framework to date for statistical optics. Our theory provides a framework for improved understanding of wave propagation in random media, random scattering media characterization, and imaging in and through randomly scattering media.

We present a study of the critical behavior of the Blume-Capel model with three spin states ($S=\pm 1,0$) confined between parallel walls separated by a distance $L$ where competitive surface magnetic fields act. By properly choosing the crystal field ($D$), which regulates the density of nonmagnetic species ($S=0$), such that those impurities are excluded from the bulk (where $D=-\infty$) except in the middle of the sample [where $D_M(L/2)\ne -\infty$], we are able to control the presence of a defect line in the middle of the sample and study its influence on the interface between domains of different spin orientations. So essentially we study an Ising model with a defect line but, unlike previous work where defect lines in Ising models were defined via weakened bonds, in the present case the defect line is due to mobile vacancies and hence involves additional entropy. In this way, by drawing phase diagrams, i.e., plots of the wetting critical temperature ($T_w$) versus the magnitude of the crystal field at the middle of the sample ($D_M$), we observe curves of (first-) second-order wetting transitions for (small) high values of $D_M$. Theses lines meet in tricritical wetting points, i.e., ($T_w^{\mathrm{tc}},D_M^{\mathrm{tc}}$), which also depend on the magnitude of the surface magnetic fields. It is found that second-order wetting transitions satisfy the scaling theory for short-range interactions, while first-order ones do not exhibit hysteresis, provided that small samples are used, since fluctuations wash out hysteretic effects. Since hysteresis is observed in large samples, we performed extensive thermodynamic integrations in order to accurately locate the first-order transition points, and a rather good agreement is found by comparing such results with those obtained just by observing the jump of the order parameter in small samples.

Multilayer graphene was deposited on indium tin oxide (ITO) -coated glass plates and characterized by suitable techniques. A liquid crystal sample cell was designed using graphene deposited ITO glass plates without any additional treatment for alignment. Ferroelectric liquid crystal (FLC) material was filled in the sample cell. The effect of multilayer graphene on the characteristics of FLC material was investigated. The extremely high relative permittivity of pristine graphene and charge transfer between graphene and FLC material were consequences of the enormous increase in relative permittivity for the graphene-FLC (GFLC) system as compared to pure FLC. The presence of multilayer graphene suppresses the ionic impurities, comprised in the FLC material at lower frequencies. The ionic charge annihilation mechanism might be responsible for the reduction of ionic impurities. The presence of graphene reduces the net ferroelectricity and results in a change in the spontaneous polarization of pure FLC. Rotational viscosity of the GFLC system also decreases due to the strong π-π interaction between the FLC molecule and multilayer graphene. The photoluminescence of the GFLC system is blueshifted as compared to pure FLC, which is due to the coupling of energy released in the process of charge annihilation and photon emission.