We show that the director-density coupling theory gives rise to a singular behavior for the mass density. To overcome this drawback, we propose to supplement the theory with a term that can be derived by regarding liquid crystals as anisotropic Korteweg fluids. We thus show that the static bevahior of the resulting theory predicts a Fréedericksz transition accompanied by a modulation in the mass density.

We consider a prisoner's dilemma model where the interaction neighborhood is defined by a square lattice. Players are equipped with basic cognitive abilities such as being able to distinguish their partners, remember their actions, and react to their strategy. By means of their short-term memory, they can remember not only the last action of their partner but the way they reacted to it themselves. This additional accuracy in the memory enables the handling of different interaction patterns in a more appropriate way and this results in a cooperative community with a strikingly high cooperation level for any temptation value. However, the more developed cognitive abilities can only be effective if the copying process of the strategies is accurate enough. The excessive extent of faulty decisions can deal a fatal blow to the possibility of stable cooperative relations.

Though biological and artificial complex systems having inhibitory connections exhibit a high degree of clustering in their interaction pattern, the evolutionary origin of clustering in such systems remains a challenging problem. Using genetic algorithm we demonstrate that inhibition is required in the evolution of clique structure from primary random architecture, in which the fitness function is assigned based on the largest eigenvalue. Further, the distribution of triads over nodes of the network evolved from mixed connections reveals a negative correlation with its degree providing insight into origin of this trend observed in real networks.

The quasicontinuum method was previously extended to the nonzero temperature conditions by implementing a free-energy correction on non-nodal atoms in coarse-grained solid systems to avoid the dynamical constraint, [Diestler, Wu, and Zeng, J. Chem. Phys. 121, 9279 (2004)]. In this paper, we combine the extended quasicontinuum method and an atomistic simulation to treat the monolayer film lubrication with elastic (nonrigid) substrates. It is shown that the multiscale method with the coarse-graining local elements in the merging regions between the atomistic and continuous descriptions of the substrates can reasonably predict the shear stress profile, the mean separation curve, and the transverse stress profile in the fully atomistic simulation for the tribological system. Moreover, when the nonlocal elements are placed in the merging regions, the inhomogeneous solid atoms in the near regions covered by the cut-off circles of the nonlocal elements replace the homogeneous ones at the equilibrium configuration for the free-energy correction on the non-nodal atoms. The treatment can cause an unphysical sliding between the near and far regions of the upper substrate. It is shown that if the free-energy correction on the non-nodal atoms in the coarse-grained merging regions is removed, the multiscale method can still well reproduce the shear stress profile, the mean separation curve, and the transverse stress profile obtained from the fully atomistic simulation for the system.

Droplets and bubbles protected by armors of particles have found vast applications in encapsulation, stabilization of emulsions and foams, or flotation processes. The liquid phase stores capillary energy, while concurrently the solid contacts of the granular network induce friction and energy dissipation, leading to hybrid interfaces of combined properties. By means of nonintrusive tensiometric methods and structural measurements, we distinguish three surface phases of increasing rigidity during the evaporation of armored droplets. The emergence of surface rigidity is reminiscent of jamming of granular matter, but it occurs differently since it is marked by a step by step hardening under surface compression. These results show that the concept of the effective surface tension remains useful only below the first jamming transition. Beyond this point, the surface stresses become anisotropic.

In this work we study the transport properties of non-interacting overdamped particles, moving on tilted disordered potentials, subjected to Gaussian white noise. We give exact formulas for the drift and diffusion coefficients for the case of random potentials resulting from the interaction of a particle with a “random polymer”. In our model the polymer is made up, by means of some stochastic process, of monomers that can be taken from a finite or countable infinite set of possible monomer types. For the case of uncorrelated random polymers we found that the diffusion coefficient exhibits a non-monotonous behavior as a function of the noise intensity. Particularly interesting is the fact that the relative diffusivity becomes optimal at a finite temperature, a behavior which is reminiscent of stochastic resonance. We explain this effect as an interplay between the deterministic and noisy dynamics of the system. We also show that this behavior of the diffusion coefficient at a finite temperature is more pronounced for the case of weakly disordered potentials. We test our findings by means of numerical simulations of the corresponding Langevin dynamics of an ensemble of noninteracting overdamped particles diffusing on uncorrelated random potentials.

We demonstrate that epitaxy can be used to obtain a wide range of ordered to disordered granular packings by simply changing the deposition flux. We show that a defect-free face-centered-cubic (fcc) monocrystal can be obtained by depositing athermal granular spheres randomly into a container with a templated surface in a gravitational field without direct manipulation. This packing corresponds to the maximum sphere packing fraction and is obtained when the substrate is templated corresponding to the (100) plane of a fcc crystal and the container side is an integer multiple of the sphere diameter. We find that the maximum sphere packing is obtained when the deposited grains come to rest, one at a time, without damaging the substrate. A transition to a disordered packing is observed when the flux is increased. Using micro x-ray computed tomography, we find that defects nucleate at the boundaries of the container in which the packing is grown as grains cooperatively come to rest above their local potential minimum. This leads to a transition from ordered to disordered loose packings that grow in the form of an inverted cone, with the apex located at the defect nucleation site. We capture the observed decrease in order using a minimal model in which a defect leads to growth of further defects in the neighboring sites in the layer above with a probability that increases with the deposition flux.

A nanoslit is a long narrow opening between two parallel plates that are nanometers apart from each other. When an electrolyte solution is present inside a nanoslit, an overlapped electrical double layer (EDL) is formed and there exist distributions of the osmotic pressure and the Maxwell stress across the nanoslit. It is well known that the total normal stress (osmotic pressure contribution + Maxwell stress contribution) in the direction normal to the nanoslit surface is uniform and the value is the same as the osmotic pressure at the centerline. On the other hand, it is not well known that the total normal stress in the direction parallel to the slit surface is not uniform. When there is an electrolyte-gas interface inside a nanoslit, this total normal stress in the direction parallel to the slit surface generates the electrocapillarity effect. In the present work, the electromechanical approach is adopted to estimate the electrocapillarity effect in terms of the slit surface potential (or the surface charge density), the gap size, and the bulk ion concentrations. In order to handle the problem analyically, it is assumed that the nanoslit problem is in the continuum range and the interface is initially flat. The deformation of the interface due to the nonuniform total normal stress along the interface is also obtained by using the first order perturbation method. The significance of the present work can be manifested by the fact that external voltage is frequently used in nanoscaled systems and the electrocapillarity effect should be considered in addition to the intrinsic capillarity due to surface tension.

Nonequilibrium interface phenomena play a key role in crystallization, hydrate formation, pipeline depressurization, and a multitude of other examples. Square gradient theory extended to the nonequilibrium domain is a powerful tool for understanding these processes. The theory gives an accurate prediction of surface tension at equilibrium, only with temperature-dependent influence parameters. We extend in this work the nonequilibrium square gradient model to have temperature-dependent influence parameters. The extension leads to thermodynamic quantities which depend on temperature gradients. Remarkably the Gibbs relation proposed in earlier work is still valid. Also for the extended framework, the “Gibbs surface” described by excess variables is found to be in local equilibrium. The temperature-dependent influence parameters give significantly different interface resistivities ($\sim 9\%–50\%$), due to changed density gradients and additional terms in the enthalpy. The presented framework facilitates a more accurate description of transport across interfaces with square gradient theory.

In the new digital age, information is available in large quantities. Since information consumes primarily the attention of its recipients, the scarcity of attention is becoming the main limiting factor. In this study, we investigate the impact of advertisement pressure on a cultural market where consumers have a limited attention capacity. A model of competition for attention is developed and investigated analytically and by simulation. Advertisement is found to be much more effective when the attention capacity of agents is extremely scarce. We have observed that the market share of the advertised item improves if dummy items are introduced to the market while the strength of the advertisement is kept constant.

The unsteady (nonautonomous) analog of a hyperbolic fixed point is a hyperbolic trajectory, whose importance is underscored by its attached stable and unstable manifolds, which have relevance in fluid flow barriers, chaotic basin boundaries, and the long-term behavior of the system. We develop a method for obtaining the unsteady control velocity which forces a hyperbolic trajectory to follow a user-prescribed variation with time. Our method is applicable in any dimension, and accuracy to any order is achievable. We demonstrate and validate our method by (1) controlling the fixed point at the origin of the Lorenz system, for example, obtaining a user-defined nonautonomous attractor, and (2) the saddle points in a droplet flow, using localized control which generates global transport.

Electrons are weakly coupled in hot, dense matter that is created in high-energy-density experiments. They are also mildly quantum mechanical and the ions associated with them are classical and may be strongly coupled. In addition, the dynamical evolution of plasmas under these hot, dense matter conditions involve a variety of transport and energy exchange processes. Quantum kinetic theory is an ideal tool for treating the electrons but it is not adequate for treating the ions. Molecular dynamics is perfectly suited to describe the classical, strongly coupled ions but not the electrons. We develop a method that combines a Wigner kinetic treatment of the electrons with classical molecular dynamics for the ions. We refer to this hybrid method as “kinetic theory molecular dynamics,” or KTMD. The purpose of this paper is to derive KTMD from first principles and place it on a firm theoretical foundation. The framework that KTMD provides for simulating plasmas in the hot, dense regime is particularly useful since current computational methods are generally limited by their inability to treat the dynamical quantum evolution of the electronic component. Using the $N$-body von Neumann equation for the electron-proton plasma, three variations of KTMD are obtained. Each variant is determined by the physical state of the plasma (e.g., collisional versus collisionless). The first variant of KTMD yields a closed set of equations consisting of a mean-field quantum kinetic equation for the electron one-particle distribution function coupled to a classical Liouville equation for the protons. The latter equation includes both proton-proton Coulombic interactions and an effective electron-proton interaction that involves the convolution of the electron density with the electron-proton Coulomb potential. The mean-field approach is then extended to incorporate equilibrium electron-proton correlations through the Singwi-Tosi-Land-Sjolander (STLS) ansatz. This is the second variant of KTMD. The STLS contribution produces an effective electron-proton interaction that involves the electron-proton structure factor, thereby extending the usual mean-field theory to correlated but near equilibrium systems. Finally, a third variant of KTMD is derived. It includes dynamical electrons and their correlations coupled to a MD description for the ions. A set of coupled equations for the one-particle electron Wigner function and the electron-electron and electron-proton correlation functions are coupled to a classical Liouville equation for the protons. This latter variation has both time and momentum dependent correlations.

When elastic metamaterials are subjected to tension they may respond by undergoing contraction instead of expansion as an ordinary material would (and vice versa). This negative compressibility behavior can only occur if the system moves from one stable state to a different stable state as the force is applied, i.e., displays bistability. With a simple model potential, we demonstrate that this negative behavior leading to a pinched hysteresis on the stress cycle diagram is a solid-to-solid condensation-type phase transformation. In addition, we show that the negative compressibility may disappear in realistic dynamical systems, unless coupling with an external heat sink is strong enough to stabilize the newly formed phase. Such a material is an open thermodynamical system where the condensation process is accompanied by a fast return of the released heat into the ambient. Molecular dynamics with Verlet integration is used to study the dynamics of this behavior.

Virtual move Monte Carlo is a cluster algorithm which was originally developed for strongly attractive colloidal, molecular, or atomistic systems in order to both approximate the collective dynamics and avoid sampling of unphysical kinetic traps. In this paper, we present the algorithm in the form, which selects the moving cluster through a wider class of virtual states and which is applicable to general pairwise interactions, including hard-core repulsion. The newly proposed way of selecting the cluster increases the acceptance probability by up to several orders of magnitude, especially for rotational moves. The results have their applications in simulations of systems interacting via anisotropic potentials both to enhance the sampling of the phase space and to approximate the dynamics.

We use entanglement entropy and finite-size scaling methods to investigate the ground-state properties of a $\mathrm{spin}\text{−}1/2$ Ising chain with two-spin $\left(J_2\right)$ and four-spin $\left(J_4\right)$ interactions in a transverse magnetic field $\left(B\right)$. We concentrate our study on the unexplored critical region $B=1$ and obtain the phase diagram of the model in the $\left(J_4-J_2\right)$ plane. The phases found include ferromagnetic (F), antiferromagnetic (AF), as well as more complex phases involving spin configurations with multiple periodicity. The system presents both first- and second-order transitions separated by tricritical points. We find an unusual phase boundary on the semi-infinite segment $(J_4<-1,J_2=0)$ separating the F and AF phases.

We propose a four-level quantum heat engine in an Otto cycle with a working substance of two spins subject to an external magnetic field and coupled to each other by a one-axis twisting spin squeezing nonlinear interaction. We calculate the positive work and the efficiency of the engine for different parameter regimes. In particular, we investigate the effects of quantum correlations at the end of the two isochoric processes of the Otto cycle, as measured by the entanglement of formation and quantum discord, on the work extraction and efficiency. The regimes where the quantum correlations could enhance the efficiency and work extraction are characterized.

In this article we have studied Shannon entropic nonequilibrium temperature (NET) extensively for a system which is coupled to a thermal bath that may be Markovian or non-Markovian in nature. Using the phase-space distribution function, i.e., the solution of the generalized Fokker Planck equation, we have calculated the entropy production, NET, and their bounds. Other thermodynamic properties like internal energy of the system, heat, and work, etc. are also measured to study their relations with NET. The present study reveals that the heat flux is proportional to the difference between the temperature of the thermal bath and the nonequilibrium temperature of the system. It also reveals that heat capacity at nonequilibrium state is independent of both NET and time. Furthermore, we have demonstrated the time variations of the above-mentioned and related quantities to differentiate between the equilibration processes for the coupling of the system with the Markovian and the non-Markovian thermal baths, respectively. It implies that in contrast to the Markovian case, a certain time is required to develop maximum interaction between the system and the non-Markovian thermal bath (NMTB). It also implies that longer relaxation time is needed for a NMTB compared to a Markovian one. Quasidynamical behavior of the NMTB introduces an oscillation in the variation of properties with time. Finally, we have demonstrated how the nonequilibrium state is affected by the memory time of the thermal bath.

We study a noisy drive mechanism for efficiency enhancement of Brownian motors operating on the microscale domain. It was proven [J. Spiechowicz et al., J. Stat. Mech. (2013) P02044] that biased noise $\eta \left(t\right)$ can induce normal and anomalous transport processes similar to those generated by a static force $F$ acting on inertial Brownian particles in a reflection-symmetric periodic structure in the presence of symmetric unbiased time-periodic driving. Here, we show that within selected parameter regimes, noise $\eta \left(t\right)$ of the mean value $\langle \eta \left(t\right)\rangle =F$ can be significantly more effective than the deterministic force $F$: the motor can move much faster, its velocity fluctuations are much smaller, and the motor efficiency increases several times. These features hold true in both normal and absolute negative mobility regimes. We demonstrate this with detailed simulations by resource to generalized white Poissonian noise. Our theoretical results can be tested and corroborated experimentally by use of a setup that consists of a resistively and capacitively shunted Josephson junction. The suggested strategy to replace $F$ by $\eta \left(t\right)$ may provide a new operating principle in which micro- and nanomotors could be powered by biased noise.