Hamiltonian daemons have recently been defined classically as small, closed Hamiltonian systems which can exhibit secular energy transfer from high-frequency to low-frequency degrees of freedom (steady downconversion), analogous to the steady transfer of energy in a combustion engine from the high terahertz frequencies of molecular excitations to the low kilohertz frequencies of piston motion [L. Gilz, E. P. Thesing, and J. R. Anglin, Phys. Rev. E 94, 042127 (2016)]. Classical daemons achieve downconversion within a small, closed system by exploiting nonlinear resonances; the adiabatic theorem permits their operation but imposes nontrivial limitations on their efficiency. Here we investigate a simple example of a quantum mechanical daemon. In the correspondence regime it obeys similar efficiency limits to its classical counterparts, but in the strongly quantum mechanical regime the daemon operates in an entirely different manner. It maintains an engine-like behavior in a distinctly quantum mechanical form: a weight is lifted at a steady average speed through a long sequence of quantum jumps in momentum, at each of which a quantum of fuel is consumed. The quantum daemon can cease downconversion at any time through nonadiabatic Landau-Zener transitions, and continuing operation of the quantum daemon is associated with steadily growing entanglement between fast and slow degrees of freedom.

There is recent evidence that the $XY$ spin model on complex networks can display three different macroscopic states in response to the topology of the network underpinning the interactions of the spins. In this work we present a way to characterize the macroscopic states of the $XY$ spin model based on the spectral decomposition of time series using topological information about the underlying networks. We use three different classes of networks to generate time series of the spins for the three possible macroscopic states. We then use the temporal Graph Signal Transform technique to decompose the time series of the spins on the eigenbasis of the Laplacian. From this decomposition, we produce spatial power spectra, which summarize the activation of structural modes by the nonlinear dynamics, and thus coherent patterns of activity of the spins. These signatures of the macroscopic states are independent of the underlying network class and can thus be used as robust signatures for the macroscopic states. This work opens avenues to analyze and characterize dynamics on complex networks using temporal Graph Signal Analysis.

We investigate nonlinear optical propagation of continuous-wave (CW) beams in bulk nematic liquid crystals. We thoroughly analyze the competing roles of reorientational and thermal nonlinearity with reference to self-focusing/defocusing and, eventually, the formation of nonlinear diffraction-free wavepackets, the so-called spatial optical solitons. To this extent we refer to dye-doped nematic liquid crystals in planar cells excited by a single CW beam in the highly nonlocal limit. To adjust the relative weight between the two nonlinear responses, we employ two distinct wavelengths, inside and outside the absorption band of the dye, respectively. Different concentrations of the dye are considered in order to enhance the thermal effect. The theoretical analysis is complemented by numerical simulations in the highly nonlocal approximation based on a semi-analytic approach. Theoretical results are finally compared to experimental results in the Nematic Liquid Crystals (NLC) 4-trans-4'-n-hexylcyclohexylisothiocyanatobenzene (6CHBT) doped with Sudan Blue dye.

A numerical method was recently proposed in Herdeiro and Doyon [Phys. Rev. E 94, 043322 (2016)] showing a precise sampling of the infinite plane two-dimensional critical Ising model for finite lattice subsections. The present note extends the method to a larger class of models, namely the O(n) loop gas models for $n\in (1,2]$. We argue that even though the Gibbs measure is nonlocal, it is factorizable on finite subsections when sufficient information on the loops touching the boundaries is stored. Our results attempt to show that provided an efficient Markov chain mixing algorithm and an improved discrete lattice dilation procedure the planar limit of the O(n) models can be numerically studied with efficiency similar to the Ising case. This confirms that scale invariance is the only requirement for the present numerical method to work.

The main objective of this paper is to extend an isothermal incompressible two-phase lattice Boltzmann equation method to model liquid-vapor phase change problems using a sharp-interface energy solver. Two discrete particle distribution functions, one for the continuity equation and the other for the pressure evolution and momentum equations, are considered in the current model. The sharp-interface macroscopic internal energy equation is discretized with an isotropic finite difference method to find temperature distribution in the system. The mass flow generated at liquid-vapor phase interface is embedded in the pressure evolution equation. The sharp-interface treatment of internal energy equation helps to find the interfacial mass flow rate accurately where no free parameter is needed in the calculations. The proposed model is verified against available theoretical solutions of the two-phase Stefan problem and the two-phase sucking interface problem, with which our simulation results are in good agreement. The liquid droplet evaporation in a superheated vapor, the vapor bubble growth in a superheated liquid, and the vapor bubble rising in a superheated liquid are analyzed and underlying physical characteristics are discussed in detail. The model is successfully tested for the liquid-vapor phase change with large density ratio up to 1000.

Although time-dependent random media with short-range correlations lead to (possibly biased) normal tracer diffusion, anomalous fluctuations occur away from the most probable direction. This was pointed out recently in one-dimensional (1D) lattice random walks, where statistics related to the 1D Kardar-Parisi-Zhang (KPZ) universality class, i.e., the Gaussian unitary ensemble Tracy-Widom distribution, were shown to arise. Here, we provide a simple picture for this correspondence, directly in the continuum, which allows one to study arbitrary space dimensions and to predict a variety of universal distributions. In $d=1$, we predict and verify numerically the emergence of the Gaussian orthogonal ensemble Tracy-Widom distribution for fluctuations of the transition probability. In $d=3$, we predict a phase transition from Gaussian fluctuations to three-dimensional KPZ-type fluctuations as the bias is increased. We predict KPZ universal distributions for the arrival time of a first particle from a cloud diffusing in such media.

Viewing the ways a living cell can organize its metabolism as the phase space of a physical system, regulation can be seen as the ability to reduce the entropy of that space by selecting specific cellular configurations that are, in some sense, optimal. Here we quantify the amount of regulation required to control a cell's growth rate by a maximum-entropy approach to the space of underlying metabolic phenotypes, where a configuration corresponds to a metabolic flux pattern as described by genome-scale models. We link the mean growth rate achieved by a population of cells to the minimal amount of metabolic regulation needed to achieve it through a phase diagram that highlights how growth suppression can be as costly (in regulatory terms) as growth enhancement. Moreover, we provide an interpretation of the inverse temperature $\beta$ controlling maximum-entropy distributions based on the underlying growth dynamics. Specifically, we show that the asymptotic value of $\beta$ for a cell population can be expected to depend on (i) the carrying capacity of the environment, (ii) the initial size of the colony, and (iii) the probability distribution from which the inoculum was sampled. Results obtained for E. coli and human cells are found to be remarkably consistent with empirical evidence.

We analyze an open quantum system under the influence of more than one environment: a dephasing bath and a probability-absorbing bath that represents a decay channel, as encountered in many models of quantum networks. In our case, dephasing is modeled by random fluctuations of the site energies, while the absorbing bath is modeled with an external lead attached to the system. We analyze under which conditions the effects of the two baths can enter additively the quantum master equation. When such additivity is legitimate, the reduced master equation corresponds to the evolution generated by an effective non-Hermitian Hamiltonian and a Haken-Strobl dephasing super-operator. We find that the additive decomposition is a good approximation when the strength of dephasing is small compared to the bandwidth of the probability-absorbing bath.

The present work is devoted to an analytical investigation of the thermal rectification mechanism. More specifically, we attempt to find the requisite ingredients for such a phenomenon to occur. Starting from the linearization of the time evolution equations of anharmonic chains of oscillators, we propose some effective harmonic toy models with a potential that is dependent on temperature, and we investigate their steady heat currents. This unusual temperature-dependent potential is the footprint of nonlinearity in the final effective linear model. The approach is not restricted to any particular regime of heat transport. Our results show that thermal rectification holds in a system if it has asymmetric parameters related to its own structure, e.g., a graded particle mass distribution and some other parameters or features dependent on the inner temperatures that change as we invert the baths at the boundaries. The description of rectification in these simplified models, with minimal ingredients, shows that it is a ubiquitous phenomenon, and it may serve as a guide for further research.

We present high statistics simulation data for the average time $\langle T_{\mathrm{cover}}\left(L\right)\rangle$ that a random walk needs to cover completely a two-dimensional torus of size $L\times L$. They confirm the mathematical prediction that $\langle T_{\mathrm{cover}}\left(L\right)\rangle \sim {(LlnL)}^2$ for large $L$, but the prefactor seems to deviate significantly from the supposedly exact result $4/\pi$ derived by Dembo et al. [Ann. Math. 160, 433 (2004)], if the most straightforward extrapolation is used. On the other hand, we find that this scaling does hold for the time $T_{N\left(t\right)=1}\left(L\right)$ at which the average number of yet unvisited sites is 1, as also predicted previously. This might suggest (wrongly) that $\langle T_{\mathrm{cover}}\left(L\right)\rangle$ and $T_{N\left(t\right)=1}\left(L\right)$ scale differently, although the distribution of rescaled cover times becomes sharp in the limit $L\to \infty$. But our results can be reconciled with those of Dembo et al. by a very slow and nonmonotonic convergence of $\langle T_{\mathrm{cover}}\left(L\right)\rangle /{(LlnL)}^2$, as had been indeed proven by Belius et al. [Probab. Theory Relat. Fields 167, 461 (2017)] for Brownian walks, and was conjectured by them to hold also for lattice walks.

Mathematically, it takes an infinite amount of time for the transient solution of a diffusion equation to transition from initial to steady state. Calculating a finite transition time, defined as the time required for the transient solution to transition to within a small prescribed tolerance of the steady-state solution, is much more useful in practice. In this paper, we study estimates of finite transition times that avoid explicit calculation of the transient solution by using the property that the transition to steady state defines a cumulative distribution function when time is treated as a random variable. In total, three approaches are studied: (i) mean action time, (ii) mean plus one standard deviation of action time, and (iii) an approach we derive by approximating the large time asymptotic behavior of the cumulative distribution function. Our approach leads to a simple formula for calculating the finite transition time that depends on the prescribed tolerance $\delta$ and the $(k-1)\mathrm{th}$ and $k\mathrm{th}$ moments ($k\ge 1$) of the distribution. Results comparing exact and approximate finite transition times lead to two key findings. First, although the first two approaches are useful at characterizing the time scale of the transition, they do not provide accurate estimates for diffusion processes. Second, the new approach allows one to calculate finite transition times accurate to effectively any number of significant digits using only the moments with the accuracy increasing as the index $k$ is increased.

We investigate a family of urn models that correspond to one-dimensional random walks with quadratic transition probabilities that have highly diverse applications. Well-known instances of these two-urn models are the Ehrenfest model of molecular diffusion, the voter model of social influence, and the Moran model of population genetics. We also provide a generating function method for diagonalizing the corresponding transition matrix that is valid if and only if the underlying mean density satisfies a linear differential equation and express the eigenvector components as terms of ordinary hypergeometric functions. The nature of the models lead to a natural extension to interaction between agents in a general network topology. We analyze the dynamics on uncorrelated heterogeneous degree sequence networks and relate the convergence times to the moments of the degree sequences for various pairwise interaction mechanisms.

In a conventional liquid crystal (LC) cell, polyimide layers are used to align the LC homogeneously in the cell, and transmissive indium tin oxide (ITO) electrodes are used to apply the electric field to reorient the LC along the field. It is experimentally presented here that monolayer graphene films on the two glass substrates can function concurrently as the LC aligning layers and the transparent electrodes to fabricate an LC cell, without using the conventional polyimide and ITO substrates. This replacement can effectively decrease the thickness of all the alignment layers and electrodes from about 100 nm to less than 1 nm. The interaction between LC and graphene through $\pi -\pi$ electron stacking imposes a planar alignment on the LC in the graphene-based cell—which is verified using a crossed polarized microscope. The graphene-based LC cell exhibits an excellent nematic director reorientation process from planar to homeotropic configuration through the application of an electric field—which is probed by dielectric and electro-optic measurements. Finally, it is shown that the electro-optic switching is significantly faster in the graphene-based LC cell than in a conventional ITO-polyimide LC cell.

We study the relationship between the granular contact angle distribution and local particle friction on the macroscopic friction and bulk modulus in noncohesive disk packings. Molecular dynamics in two dimensions are used to simulate uniaxial loading-unloading cycles imposed on the granular packings. While macroscopic Mohr friction depends on the granular pack geometric details, it reaches a stationary limit after a finite number of loading-unloading cycles that render well-defined values for bulk modulus, grain coordination, porosity, and friction. For random packings and for all polydispersities analyzed, we found that as interparticle friction increases, the bulk modulus for the limit cycle decreases linearly, while the mean coordination number is reduced and the porosity increased, also as approximately linear functions. On the other hand, the macroscopic Mohr friction increases in a monotonous trend with interparticle friction. The latter result is compared to a theoretical model that assumes the existence of sliding planes corresponding to definite Mohr-friction values. The simulation results for macroscopic friction are well described by the theoretical model that incorporates the local neighbor angle distribution that can be quantified through the contact angle entropy. As local friction is increased, the limit entropy of the neighbor angle distribution is reduced, thus introducing the geometric component to granular friction. Surprisingly, once the limit cycle is reached, the Mohr friction seems to be insensitive to polydispersity as has been recently reported.

Two-dimensional crystalline membranes have recently been realized experimentally in systems such as graphene and molybdenum disulfide, sparking a resurgence in interest in their statistical properties. Thermal fluctuations can significantly affect the effective mechanical properties of properly thermalized membranes, renormalizing both bending rigidity and elastic moduli so that in particular they become stiffer to bending than their bare bending rigidity would suggest. We use molecular dynamics simulations to examine how the mechanical behavior of thermalized two-dimensional clamped ribbons (cantilevers) depends on their precise topology and geometry. We find that a simple slit smooths roughness as measured by the variance of height fluctuations. This counterintuitive effect may be due to the counterposed coupling of the lips of the slit to twist in the intact regions of the ribbon.

Thin shells are characterized by a high cost of stretching compared to bending. As a result isometries of the midsurface of a shell play a crucial role in their mechanics. In turn, curves on the midsurface with zero normal curvature play a critical role in determining the number and behavior of isometries. In this paper, we show how the presence of these curves results in a decrease in the number of linear isometries. Paradoxically, shells are also known to continuously fold more easily across these rigidifying curves than other curves on the surface. We show how including nonlinearities in the strain can explain these phenomena and demonstrate folding isometries with explicit solutions to the nonlinear isometry equations. In addition to explicit solutions, exact geometric arguments are given to validate and guide our analysis in a coordinate-free way.

The peculiarities of simple shear flow of shear thinning fluids over a superhydrophobic wall consisting of a set of parallel gas-filled grooves and solid stripes (domains with slip and stick boundary conditions) are studied numerically. The Carreau-Yasuda model is used to provide further insight into the problem of the slip behavior of non-Newtonian fluids having a decreasing viscosity with a shear rate increase. This feature is demonstrated to cause a nonlinear velocity profile leading to the apparent slip. The corresponding transverse and longitudinal apparent slip lengths of a striped texture are found to be noticeably larger than the respective effective slip lengths of Newtonian liquids in microchannels of various thicknesses and surface fractions of the slip domains. The viscosity distribution of the shear thinning fluid over the superhydrophobic wall is carefully investigated to describe the mechanism of the apparent slip. Nonmonotonic behavior of the apparent slip length as a function of the applied shear rate is revealed. This important property of shear thinning fluids is considered to be sensitive to the steepness of the viscosity flow curve, thus providing a way to decrease considerably the flow resistance in microchannels.

We use path integral Monte Carlo and density functional molecular dynamics to construct a coherent set of equations of state (EOS) for a series of hydrocarbon materials with various C:H ratios (2:1, 1:1, 2:3, 1:2, and 1:4) over the range of $0.07–22.4\mathrm{g}{\mathrm{cm}}^{-3}$ and $6.7\times {10}^3–1.29\times {10}^8\mathrm{K}$. The shock Hugoniot curve derived for each material displays a single compression maximum corresponding to $K$-shell ionization. For C:H = 1:1, the compression maximum occurs at 4.7-fold of the initial density and we show radiation effects significantly increase the shock compression ratio above 2 Gbar, surpassing relativistic effects. The single-peaked structure of the Hugoniot curves contrasts with previous work on higher-$Z$ plasmas, which exhibit a two-peak structure corresponding to both $K$- and $L$-shell ionization. Analysis of the electronic density of states reveals that the change in Hugoniot structure is due to merging of the $L$-shell eigenstates in carbon, while they remain distinct for higher-$Z$ elements. Finally, we show that the isobaric-isothermal linear mixing rule for carbon and hydrogen EOS is a reasonable approximation with errors better than 1% for stellar-core conditions.

The interaction between a tubular beam of charged particles and a dispersive metamaterial of cylindrical configuration has been investigated theoretically. This metamaterial may have negative permittivity and negative permeability simultaneously over a certain frequency range where it behaves like a left-handed metamaterial. The dispersion equation for the eigenmodes spectra of a metamaterial and the coupled modes spectra of the system have been derived and numerically analyzed. It has been found that the absolute beam instability of bulk-surface waves occurs because of peculiarities of the eigenmodes spectra of a left-handed metamaterial. Specifically, the resonant frequency behavior of the permeability causes the emergence of the sections of dispersion curves with anomalous dispersion. It has been demonstrated that the symmetric bulk-surface mode with two field variations along the cylinder radius possesses the maximum value of instability increment. The obtained results allow us to propose the left-handed metamaterial as the delaying medium in oscillators of electromagnetic radiation without a need to provide an additional feedback in the system just as in a backward-wave tube.

We present a graph-based methodology to reduce the computational cost of obtaining first passage times through sparse fracture networks. We derive graph representations of generic three-dimensional discrete fracture networks (DFNs) using the DFN topology and flow boundary conditions. Subgraphs corresponding to the union of the $k$ shortest paths between the inflow and outflow boundaries are identified and transport on their equivalent subnetworks is compared to transport through the full network. The number of paths included in the subgraphs is based on the scaling behavior of the number of edges in the graph with the number of shortest paths. First passage times through the subnetworks are in good agreement with those obtained in the full network, both for individual realizations and in distribution. Accurate estimates of first passage times are obtained with an order of magnitude reduction of CPU time and mesh size using the proposed method.