We show that the number of harmonics of the Wigner function, recently proposed as a measure of quantum complexity, can also be used to characterize quantum phase transitions. The nonanalytic behavior of this quantity in the neighborhood of a quantum phase transition is illustrated by means of the Dicke model and is compared to two well-known measures of the (in)stability of quantum motion: the quantum Loschmidt echo and fidelity.

Gelation in a two component disperse system wherein binary coagulation governs the temporal changes of particle composition spectra is studied for the crossproduct coagulation kernel proportional to $m_1{n}_2+m_2{n}_1$, with $m,n$ being the numbers of monomers of the first and the second component in the coalescing pair of particles. This model reveals the sol-gel transition, i.e., after a finite interval of time the conservation of the total particle mass concentration violates because of the formation of giant particles (the gel). This paper reports on the exact solution of this model for arbitrary initial particle composition spectra. Exact expressions for the particle composition spectrum, the gel mass, and the second moments of the composition distribution are derived. Two scenarios of gelation, where the gel is either active or passive, are considered.

In this work I derive analytic expressions for the curvature-dependent fluid-substrate surface tension of a hard-sphere fluid on a hard curved wall. In the first step, the curvature thermodynamic properties are found as truncated power series in the activity in terms of the exactly known second- and third-order cluster integrals of the hard-sphere fluid near spherical and cylindrical walls. These results are then expressed as packing fraction power series and transformed to different reference regions, which is equivalent to considering different positions of the dividing surface. Based on the truncated series it is shown that the bending rigidity of the system is non-null and that higher-order terms in the curvature also exist. In the second step, approximate analytic expressions for the surface tension, the Tolman length, the bending rigidity, and the Gaussian rigidity as functions of the packing fraction are found by considering the known terms of the series expansion complemented with a simple fitting approach. It is found that the obtained formulas accurately describe the curvature thermodynamic properties of the system; further, they are more accurate than any previously published expressions.

A free-energy-based phase-field lattice Boltzmann method is proposed in this work to simulate multiphase flows with density contrast. The present method is to improve the Zheng-Shu-Chew (ZSC) model [Zheng, Shu, and Chew, J. Comput. Phys. 218, 353 (2006)] for correct consideration of density contrast in the momentum equation. The original ZSC model uses the particle distribution function in the lattice Boltzmann equation (LBE) for the mean density and momentum, which cannot properly consider the effect of local density variation in the momentum equation. To correctly consider it, the particle distribution function in the LBE must be for the local density and momentum. However, when the LBE of such distribution function is solved, it will encounter a severe numerical instability. To overcome this difficulty, a transformation, which is similar to the one used in the Lee-Lin (LL) model [Lee and Lin, J. Comput. Phys. 206, 16 (2005)] is introduced in this work to change the particle distribution function for the local density and momentum into that for the mean density and momentum. As a result, the present model still uses the particle distribution function for the mean density and momentum, and in the meantime, considers the effect of local density variation in the LBE as a forcing term. Numerical examples demonstrate that both the present model and the LL model can correctly simulate multiphase flows with density contrast, and the present model has an obvious improvement over the ZSC model in terms of solution accuracy. In terms of computational time, the present model is less efficient than the ZSC model, but is much more efficient than the LL model.

An adaptive-mesh-refinement (AMR) algorithm for the finite-difference lattice Boltzmann method (FDLBM) is presented in this study. The idea behind the proposed AMR is to remove the need for a tree-type data structure. Instead, pointer attributes are used to determine the neighbors of a certain block via appropriate adjustment of its children identifications. As a result, the memory and time required for tree traversal are completely eliminated, leaving us with an efficient algorithm that is easier to implement and use on parallel machines. To allow different mesh sizes at separate parts of the computational domain, the Eulerian formulation of the streaming process is invoked. As a result, there is no need for rescaling the distribution functions or using a temporal interpolation at the fine-coarse grid boundaries. The accuracy and efficiency of the proposed FDLBM AMR are extensively assessed by investigating a variety of vorticity-dominated flow fields, including Taylor-Green vortex flow, lid-driven cavity flow, thin shear layer flow, and the flow past a square cylinder.

We have developed a Green-Kubo relation that enables accurate calculations of friction at solid-liquid interfaces directly from equilibrium molecular dynamics (MD) simulations and that provides a pathway to bypass the time-scale limitations of typical nonequilibrium MD simulations. The theory has been validated for a number of different interfaces and it is demonstrated that the liquid-solid slip is an intrinsic property of an interface. Because of the high numerical efficiency of our method, it can be used in the design of interfaces for applications in aqueous environments, such as nano- and microfluidics.

In contrast to the conventional continual case, discrete Poisson-Voronoi tessellations resulting from the growth to impingement of random nuclei differ from tessellations constructed from the nearest tile loci. Previously studied tessellations were based directly on the notion of locus [A. Korobov, Phys. Rev. E 79, 031607 (2009); A. Korobov, Phys. Rev. E 87, 014401 (2013)]. This paper presents results for tessellations constructed by the growth of random nuclei. Their boundaries have a different structure and scaling properties are comparably more robust. One more scalable characteristic may be introduced for them, the perimeter distribution function, which is well approximated by the normal distribution function with the unit mean and the standard deviation equal to 0.25.

We use Monte Carlo simulations to study the $XXZ$ Heisenberg antiferromagnet in a field in order to clearly determine the nature of the multicritical point. We use a hybrid sampling method with Metropolis and Wolff-cluster algorithms, along with histogram reweighting techniques. Staggered magnetization susceptibilities, Binder cumulants, and finite-size scaling are considered in an effort to detect a possible biconical phase. An analysis of the probability distribution of the magnetization allowed us to conclude that the multicritical point is bicritical and it is in the three-dimensional Heisenberg universality class.

The surface temperature can significantly affect the flow field of drying droplets. Most previous studies assumed a monotonic temperature variation along the droplet surface. However, the present analyses indicate that a nonmonotonic spatial distribution of the surface temperature should occur. Three different patterns of the surface temperature distribution may appear during the evaporation process of liquid droplets: (i) the surface temperature increases monotonically from the center to the edge of the droplet; (ii) the surface temperature exhibits a nonmonotonic spatial distribution along the droplet surface; (iii) the surface temperature decreases monotonically from the center to the edge of the droplet. These surface temperature distributions can be explained by combining the evaporative cooling at the droplet surface and the heat conduction across the substrate and the liquid. Furthermore, a “phase diagram” for the distribution of the surface temperature is introduced and the effect of the spatial temperature distribution along the droplet surface on the flow structure of the droplet is discussed. The results may provide a better understanding of the Marangoni effect of drying droplets and provide a potential way to control evaporation-driven deposition as well as the assembly of colloids and other materials.

The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation dependent on both short-run and long-run behaviors and allow the relationships between mutation, selection, and population size to be examined. Bounds for the entropy rate are given for the Moran process (independent of population size) and for the Wright-Fisher process (bounded for fixed population size). A generational Moran process is also presented for comparison to the Wright-Fisher Process. Results include analytic results and computational extensions.

Using a combination of ${}^2\mathrm{H}$ nuclear magnetic resonance (NMR) methods, we study internal rotational dynamics of the perdeuterated protein C-phycocyanin (CPC) in dry and hydrated states over broad temperature and dynamic ranges with high angular resolution. Separating ${}^2\mathrm{H}$ NMR signals from methyl deuterons, we show that basically all backbone deuterons exhibit highly restricted motion occurring on time scales faster than microseconds. The amplitude of this motion increases when a hydration shell exists, while it decreases upon cooling and vanishes near 175 K. We conclude that the vanishing of the highly restricted motion marks a dynamical transition, which is independent of the time window and of a fundamental importance. This conclusion is supported by results from experimental and computational studies of the proteins myoglobin and elastin. In particular, we argue based on findings in molecular dynamics simulations that the behavior of the highly restricted motion of proteins at the dynamical transition resembles that of a characteristic secondary relaxation of liquids at the glass transition, namely the nearly constant loss. Furthermore, ${}^2\mathrm{H}$ NMR studies on perdeuterated CPC reveal that, in addition to highly restricted motion, small fractions of backbone segments exhibit weakly restricted dynamics when temperature and hydration are sufficiently high.

Rogue waves in fluid dynamics and optical waveguides are unexpectedly large displacements from a background state, and occur in the nonlinear Schrödinger equation with positive linear dispersion in the regime of positive cubic nonlinearity. Rogue waves of a derivative nonlinear Schrödinger equation are calculated in this work as a long-wave limit of a breather (a pulsating mode), and can occur in the regime of negative cubic nonlinearity if a sufficiently strong self-steepening nonlinearity is also present. This critical magnitude is shown to be precisely the threshold for the onset of modulation instabilities of the background plane wave, providing a strong piece of evidence regarding the connection between a rogue wave and modulation instability. The maximum amplitude of the rogue wave is three times that of the background plane wave, a result identical to that of the Peregrine breather in the classical nonlinear Schrödinger equation model. This amplification ratio and the resulting spectral broadening arising from modulation instability correlate with recent experimental results of water waves. Numerical simulations in the regime of marginal stability are described.

Nanoparticles, with sizes ranging between 1 and $\sim$${10}^2$ nm, show dynamical properties distinctly different than those of bulk materials. Due to their large surface area to volume ratio, their properties often depend on length scales. We investigate the size and the collision velocity ($v_{\text{coll}}$) dependence of the coefficient of restitution (COR) for nanoparticles made of a face-centered cubic lattice of Lennard-Jones atoms via nonequilibrium molecular dynamics simulations. A sharp crossover between elastic collision and plastic collision occurs when $v_{\text{coll}}=v_Y$, where $v_Y$ is the size-dependent yield velocity. For high-collision velocities the COR $\sim v_{\text{coll}}^{-\alpha }$, $\alpha \sim 1$. This result is in agreement with recent small system simulations and with experiments and is distinct from the elasticity-theory-based result for COR for inelastic collisions which behaves as $v_{\text{coll}}^{-\alpha }$, with $\alpha =\frac{1}{4}$. We find that the size-dependent critical $v_Y$ approaches the theoretical constant value for macroscopic spheres as our particle sizes grow. Possible insights into the origins of $\alpha \sim 1$ and the size dependence of the yield velocity are suggested. The work also suggests that sufficiently fast moving nanoparticles traveling through vacuum could be sticky and hence could be of potential interest in many applications.

We investigate the dynamics of thermal Casimir interactions between plates described within a living conductor model, with embedded mobile anions and cations, whose density field obeys a stochastic partial differential equation which can be derived starting from the Langevin equations of the individual particles. This model describes the thermal Casimir interaction in the same way that the fluctuating dipole model describes van der Waals interactions. The model is analytically solved in a Debye-Hückel-like approximation. We identify several limiting dynamical regimes where the time dependence of the thermal Casimir interactions can be obtained explicitly. Most notably we find a regime with diffusive scaling, even though the charges are confined to the plates and do not diffuse into the intervening space, which makes the diffusive scaling difficult to anticipate and quite unexpected on physical grounds.

We derive expressions for the critical density for jamming in a hyper-rhomboid system of arbitrary shape in any dimension for the Kob-Andersen and Fredrickson-Andersen kinetically constrained models. We find that changing the system's shape without altering its total volume or particle density may induce jamming. We also find a transition between shapes in which the correlation length between jammed particles is infinite and shapes that have a finite correlation length.

Despite extensive investigation using hydrodynamic models and experiments over the past decades, there remain open questions regarding the origin of the initial rupture of thin liquid films. One of the reasons that makes it difficult to identify the rupture origin is the coexistence of two dewetting mechanisms, namely, thermal nucleation and spinodal instability, as observed in many experimental studies. Using a coarse-grained model and large-scale molecular dynamics simulations, we are able to characterize the very early stage of dewetting in nanometer-thick liquid-metal films wetting a solid substrate. We observe the features characteristic of both spinodal instability and thermal nucleation in the spontaneously dewetting films and show that these two macroscopic mechanisms share a common origin at molecular levels.

We propose a simple theoretical model which explains the formation of dipolar two- (2D) and three-dimensional (3D) colloidal structures in nematic liquid crystals. The colloidal particles are treated as effective hard spheres interacting via their elastic dipole, quadrupole, and octopole moments. It is shown that the octopole moment plays an important role in the formation of 2D and 3D nematic colloidal crystals. We generalize this assumption to the case of an external electric field and theoretically explain a giant electrostriction effect in 3D crystals observed recently.

Simple RNA viruses efficiently encapsulate their genome into a nano-sized protein shell: the capsid. Spontaneous coassembly of the genome and the capsid proteins is driven predominantly by electrostatic interactions between the negatively charged RNA and the positively charged inner capsid wall. Using field theoretic formulation we show that the inherently branched RNA secondary structure allows viruses to maximize the amount of encapsulated genome and make assembly more efficient, allowing viral RNAs to out-compete cellular RNAs during replication in infected host cells.