Colloidal particles interacting via a long-range repulsion can, in contrast to hard-sphere systems, exhibit crystalline ordering at low volume fraction. Here we experimentally investigate the structure and properties of such “colloidal Wigner crystals.” We find a body-centered-cubic crystalline phase at volume fractions of $\varphi \gtrsim 15\%$, which exhibits large fluctuations of individual particles from their average positions. We determine the three independent crystalline elastic constants and find that these crystals are very compliant and highly anisotropic.

We analyze the free induction decay of nuclear spins under the influence of restricted diffusion in a magnetic dipole field around cylindrical objects. In contrast to previous publications no restrictions or simplifications concerning the diffusion process are made. By directly solving the Bloch-Torrey equation, analytical expressions for the magnetization are given in terms of an eigenfunction expansion. The field strength-dependent complex nature of the eigenvalue spectrum significantly influences the shape of the free induction decay. As the dipole field is the lowest order of the multipole expansion, the obtained results are important for understanding fundamental mechanisms of spin dephasing in many other applied fields of nuclear magnetic resonance such as biophysics or material science. The analytical methods are applied to interpret the spin dephasing in the free induction decay in cardiac muscle and skeletal muscle. A simple expression for the relevant transverse relaxation time is found in terms of the underlying microscopic parameters of the muscle tissue. The analytical results are in agreement with experimental data. These findings are important for the correct interpretation of magnetic resonance images for clinical diagnosis at all magnetic field strengths and therapy of cardiovascular diseases.

We study a mathematical model of social diffusion on a symmetric weighted network where individual nodes' states gradually assimilate to local social norms made by their neighbors' average states. Unlike physical diffusion, this process is not state conservational and thus the global state of the network (i.e., sum of node states) will drift. The asymptotic average node state will be the average of initial node states weighted by their strengths. Here we show that, while the global state is not conserved in this process, the inner product of strength and state vectors is conserved instead, and perfect positive correlation between node states and local averages of their self-neighbor strength ratios always results in upward (or at least neutral) global drift. We also show that the strength assortativity negatively affects the speed of homogenization. Based on these findings, we propose an adaptive link weight adjustment method to achieve the highest upward global drift by increasing the strength-state correlation. The effectiveness of the method was confirmed through numerical simulations and implications for real-world social applications are discussed.

The uniform electron gas (UEG) at finite temperature has recently attracted substantial interest due to the experimental progress in the field of warm dense matter. To explain the experimental data, accurate theoretical models for high-density plasmas are needed that depend crucially on the quality of the thermodynamic properties of the quantum degenerate nonideal electrons and of the treatment of their interaction with the positive background. Recent fixed-node path-integral Monte Carlo (RPIMC) data are believed to be the most accurate for the UEG at finite temperature, but they become questionable at high degeneracy when the Brueckner parameter $r_s=a/a_B$—the ratio of the mean interparticle distance to the Bohr radius—approaches 1. The validity range of these simulations and their predictive capabilities for the UEG are presently unknown. This is due to the unknown quality of the used fixed nodes and of the finite-size scaling from $N=33$ simulated particles (per spin projection) to the macroscopic limit. To analyze these questions, we present alternative direct fermionic path integral Monte Carlo (DPIMC) simulations that are independent from RPIMC. Our simulations take into account quantum effects not only in the electron system but also in their interaction with the uniform positive background. Also, we use substantially larger particle numbers (up to three times more) and perform an extrapolation to the macroscopic limit. We observe very good agreement with RPIMC, for the polarized electron gas, up to moderate densities around $r_s=4$, and larger deviations for the unpolarized case, for low temperatures. For higher densities (high electron degeneracy), $r_s\lesssim 1.5$, both RPIMC and DPIMC are problematic due to the increased fermion sign problem.

We investigate the completely packed $\mathrm{O}\left(n\right)$ loop model on the square lattice, and its generalization to an Eulerian graph model, which follows by including cubic vertices which connect the four incoming loop segments. This model includes crossing bonds as well. Our study was inspired by existing exact solutions of the so-called coloring model due to Schultz and Perk [Phys. Rev. Lett. 46, 629 (1981)], which is shown to be equivalent with our generalized loop model. We explore the physical properties and the phase diagram of this model by means of transfer-matrix calculations and finite-size scaling. The exact results, which include seven one-dimensional branches in the parameter space of our generalized loop model, are compared to our numerical results. The results for the phase behavior also extend to parts of the parameter space beyond the exactly solved subspaces. One of the exactly solved branches describes the case of nonintersecting loops and was already known to correspond with the ordering transition of the Potts model. Another exactly solved branch, describing a model with nonintersecting loops and cubic vertices, corresponds with a first-order, Ising-like phase transition for $n>2$. For $1<n<2$, this branch is interpreted in terms of a low-temperature $\mathrm{O}\left(n\right)$ phase with corner-cubic anisotropy. For $n>2$ this branch is the locus of a first-order phase boundary between a phase with a hard-square, lattice-gas-like ordering and a phase dominated by cubic vertices. A mean-field argument explains the first-order nature of this transition.

We present the analytic expression of the stress correlation (SC) function for the ubiquitous hydration water layer (HWL) using the Green-Kubo equation and the shear modulus of HWL. The SC function is then experimentally obtained by measuring the viscoelastic properties of HWL using shear-mode dynamic force spectroscopy. Interestingly, the SC changes sign from positive to negative as the HWL thickness increases, where the shear stresses acting on the HWLs bound to two nearby surfaces are out of phase. We also suggest that the repulsive hydration force originates from the SC of HWL. Our results provide the first demonstration of the microscopic understanding of the HWL viscoelasticity and may allow a deeper insight on the HWL dynamics as well as the complex liquids.

Using confocal microscopy we investigate binary colloidal mixtures with large size asymmetry, in particular the formation of dynamically arrested states of the large spheres. The volume fraction of the system is kept constant, and as the concentration of small spheres is increased we observe a series of transitions of the large spheres to different arrested states: an attractive glass, a gel, and an asymmetric glass. These states are distinguished by the degree of dynamical arrest and the amount of structural and dynamical heterogeneity. The transitions between two different arrested states occur through melting and the formation of a fluid state. While a space-spanning network of bonded particles is found in both arrested and fluid states, only arrested states are characterized by the presence of a space-spanning network of dynamically arrested particles.

We carried out Monte Carlo simulations in the $N,\Pi ,T$ ensemble of a Langmuir monolayer coarse-grained molecular model. Considering that the hydrophilic groups can be ionized by modulating acid-base interactions, here we study the phase behavior of a model that incorporates the short-range steric and long-range ionic interactions. The simulations were carried out in the reduced temperature range $0.1\le T^{*}<4.0$, where there is a competition of these interactions. Different order parameters were calculated and analyzed for several values of the reduced surface pressure in the interval, $1\le {\Pi }^{*}\le 40$. For most of the surface pressures two directions of molecular tilt were found: (i) towards the nearest neighbor (NN) at low temperatures, $T^{*}<0.7$, and most of the values of ${\Pi }^{*}$ and (ii) towards next-nearest neighbors (NNN) in the temperature interval $0.7\le T^{*}<1.1$ for ${\Pi }^{*}<25$. We also found the coexistence of the NN and NNN at intermediate temperatures and ${\Pi }^{*}>25$. A low-temperature reentrant disorder-order-disorder transition in the positions of the molecular heads and in the collective tilt of the tails was found for all the surface pressure values. It was also found that the molecular tails arranged forming “rotating patterns” in the temperature interval, $0.5<T^{*}<1.5$, at intermediate surface pressures. We estimated the monolayer's surface pressure versus temperature and the temperature versus area per molecule phase diagrams. It was found that the $\mathrm{LE}\leftrightarrow \mathrm{LC}$ phase transition shifts to smaller temperatures when the molecular heads carry an ion in qualitative agreement with experimental observations of fatty acid monolayers with ionic head groups. Two surface pressure versus area per molecule isotherms were also calculated. At low temperatures near the LC-NN $\leftrightarrow$ LC-NNN transitions and at higher temperatures close to the LE $\leftrightarrow$ LC transitions. From these isotherms the monolayer's area compression modulus was obtained and its variation ranges in the LE and LC phases were found to be consistent with the experimental values.

The hard-sphere crystal-liquid interfacial free energy ${\gamma }_{\mathrm{cl}}$ is determined from molecular dynamics simulations using a thermodynamic integration (TI) scheme. The advantage of this TI scheme compared to previous methods is to successfully circumvent hysteresis effects due to the movement of the crystal-liquid interface. This is accomplished by the use of extremely-short-range and impenetrable Gaussian flat walls that prevent the drift of the interface while imposing a negligible free-energy penalty. We find that it is crucial to analyze finite-size effects in order to obtain reliable estimates of ${\gamma }_{\mathrm{cl}}$ in the thermodynamic limit.

We study the role of the sample thickness $d$ and of the concentration $C$ of chiral molecules during the Lehmann rotation of cholesteric droplets of radius $R$ subjected to a temperature gradient $\vec{G}$. Two configurations are studied depending on how the helix is oriented with respect to $\vec{G}$. The first result is that, at fixed $C$ and $R$, the rotation velocity $\omega$ increases with $d$ when the helix is parallel to $\vec{G}$, whereas it is independent of $d$ when the helix is perpendicular to $\vec{G}$. The second result is that, for a given $C,{\omega }_0={lim}_{R\to 0}\omega \left(R\right)$ is the same for the two types of droplets independently of $d$. This suggests that the, as yet unknown, physical mechanism responsible for the droplet rotation is the same in the two types of droplets. The third result is that the Lehmann coefficient $\overline{\nu }$ defined from the Leslie-like relation ${\omega }_0=-\overline{\nu }G/{\gamma }_1$ (with ${\gamma }_1$ the rotational viscosity) is proportional to the equilibrium twist $q$. Last, but not least, the ratio $\overline{R}=\overline{\nu }/q$ depends on the liquid crystal chosen but is independent of the chiral molecule used to dope the liquid crystal.

We report many different nanostructures which are formed when model nanoparticles of different sizes (diameter ${\sigma }_n$) are allowed to aggregate in a background matrix of semiflexible self-assembled polymeric wormlike micellar chains. The different nanostructures are formed by the dynamical arrest of phase-separating mixtures of micellar monomers and nanoparticles. The different morphologies obtained are the result of an interplay of the available free volume, the elastic energy of deformation of polymers, the density (chemical potential) of the nanoparticles in the polymer matrix, and, of course, the ratio of the size of self-assembling nanoparticles and self-avoidance diameter of polymeric chains. We have used a hybrid semi-grand-canonical Monte Carlo simulation scheme to obtain the (nonequilibrium) phase diagram of the self-assembled nanostructures. We observe rodlike structures of nanoparticles which get self-assembled in the gaps between the nematically ordered chains, as well as percolating gel-like network of conjoined nanotubes. We also find a totally unexpected interlocked crystalline phase of nanoparticles and monomers, in which each crystal plane of nanoparticles is separated by planes of perfectly organized polymer chains. We identified the condition which leads to such interlocked crystal structure. We suggest experimental possibilities of how the results presented in this paper could be used to obtain different nanostructures in the laboratory.

Reversible cross-linking is a method of enhancing the mechanical properties of polymeric materials. The inspiration for this kind of cross-linking comes from nature, which uses this strategy in a large variety of biological materials to dramatically increase their toughness. Recently, first attempts were made to transfer this principle to technological applications. In this study, Monte Carlo simulations are used to investigate the effect of the number and the topology of reversible cross-links on the mechanical performance of a simple model system. Computational cyclic loading tests are performed, and the work to fracture and the energy dissipation per cycle are determined, which both increase when the density of cross-links is increased. Furthermore, a different topology of the bonds may increase the work to fracture by a factor of more than 2 for the same density. This dependence of the mechanical properties on the topology of the bonds has important implications on the self-healing properties of such systems, because only a fast return of the system to its unloaded state after release of the load ensures that the optimal topology may form.

The dynamic-equilibrium model for stabilization of a nanobubble on a hydrophobic surface by Brenner and Lohse [M. P. Brenner and D. Lohse, Phys. Rev. Lett. 101, 214505 (2008)] has been modified taking into account the van der Waals attractive force between gas molecules inside a nanobubble and solid surface. The present model is also applicable to a nanobubble on a hydrophilic surface. According to the model, the pressure inside a nanobubble is not spatially uniform and is relatively higher near the solid surface. As a result, there is gas outflux near a hydrophilic surface, while near a hydrophobic surface there is gas influx which has been already suggested. In the present model, the radius of curvature for a nanobubble depends on the distance from the solid surface because the pressure depends on it. The shape of the micropancake, which is a nearly-two-dimensional bubble, is reproduced by the present model due to the strong dependence of the radius of curvature on the distance from the solid surface. The effect of temperature on the stability of a nanobubble or micropancake is also discussed.

Cyclic, nonhierarchical interactions among biological species represent a general mechanism by which ecosystems are able to maintain high levels of biodiversity. However, species coexistence is often possible only in spatially extended systems with a limited range of dispersal, whereas in well-mixed environments models for cyclic competition often lead to a loss of biodiversity. Here we consider the dispersal of biological species in a fluid environment, where mixing is achieved by a combination of advection and diffusion. In particular, we perform a detailed numerical analysis of a model composed of turbulent advection, diffusive transport, and cyclic interactions among biological species in two spatial dimensions and discuss the circumstances under which biodiversity is maintained when external environmental conditions, such as resource supply, are uniform in space. Cyclic interactions are represented by a model with three competitors, resembling the children's game of rock-paper-scissors, whereas the flow field is obtained from a direct numerical simulation of two-dimensional turbulence with hyperviscosity. It is shown that the space-averaged dynamics undergoes bifurcations as the relative strengths of advection and diffusion compared to biological interactions are varied.

Fast-electron generation and dynamics, including electron refluxing, is at the core of understanding high-intensity laser-plasma interactions. This field is itself of strong relevance to fast ignition fusion and the development of new short-pulse, intense, x-ray, $\gamma$-ray, and particle sources. In this paper, we describe experiments that explicitly link fast-electron refluxing and anisotropy in hard-x-ray emission. We find the anisotropy in x-ray emission to be strongly correlated to the suppression of refluxing. In contrast to some previous work, the peak of emission is directly along the rear normal to the target rather than along either the incident laser direction or the specular reflection direction.

We investigate the survival of circularly polarized light in random scattering media. The surprising persistence of this form of polarization has a known dependence on the size and refractive index of scattering particles, however a general description regarding polydisperse media is lacking. Through analysis of Mie theory, we present a means of calculating the magnitude of circular polarization memory in complex media, with total generality in the distribution of particle sizes and refractive indices. Quantification of this memory effect enables an alternate pathway toward recovering particle size distribution, based on measurements of diffusing circularly polarized light.

The isometric fluctuation relation (IFR) [P. I. Hurtado et al., Proc. Natl. Acad. Sci. USA 108, 7704 (2011)] relates the relative probability of current fluctuations of fixed magnitude in different spatial directions. We test its validity in an experiment on a tapered rod, rendered motile by vertical vibration and immersed in a sea of spherical beads. We analyze the statistics of the velocity vector of the rod and show that they depart significantly from the IFR of Hurtado et al. Aided by a Langevin-equation model we show that our measurements are largely described by an anisotropic generalization of the IFR [R. Villavicencio et al., Europhys. Lett. 105, 30009 (2014)], with no fitting parameters, but with a discrepancy in the prefactor whose origin may lie in the detailed statistics of the microscopic noise. The experimentally determined large-deviation function of the velocity vector has a kink on a curve in the plane.

Three-dimensional wave propagation simulations and experiments show that the gain exponent, an often used metric to assess the likelihood of stimulated Brillouin scatter, is insufficient and must be augmented with another parameter, $N_r$, the ratio of the resonance length, $L_{\text{res}}$, to the laser speckle length. The damping rate of ion acoustic waves, $\nu$, and thus $L_{\text{res}}$, which is proportional to $\nu$, are easily varied with plasma species composition, e.g., by varying the ratio of hydrogen and carbon ions. As $N_r$ decreases, stimulated Brillouin scattering increases despite the same gain exponent.

By the use of extensive numerical simulations, we show that the nearest-neighbor energy-level spacing distribution $P\left(s\right)$ and the entropic eigenfunction localization length of the adjacency matrices of Erdős-Rényi (ER) fully random networks are universal for fixed average degree $\xi \equiv \alpha N$ ($\alpha$ and $N$ being the average network connectivity and the network size, respectively). We also demonstrate that the Brody distribution characterizes well $P\left(s\right)$ in the transition from $\alpha =0$, when the vertices in the network are isolated, to $\alpha =1$, when the network is fully connected. Moreover, we explore the validity of our findings when relaxing the randomness of our network model and show that, in contrast to standard ER networks, ER networks with diagonal disorder also show universality. Finally, we also discuss the spectral and eigenfunction properties of small-world networks.

We study critical Casimir forces (CCFs) $f_{\mathrm{C}}$ for films of thickness $L$ which in the three-dimensional bulk belong to the Ising universality class and which are exposed to random surface fields (RSFs) on both surfaces. We consider the case in which, in the absence of RSFs, the surfaces of the film belong to the surface universality class of the so-called ordinary transition. We carry out a finite-size scaling analysis and show that for weak disorder, CCFs still exhibit scaling, acquiring a random field scaling variable $w$ that is zero for pure systems. We confirm these analytic predictions by Monte Carlo (MC) simulations. Moreover, our MC data show that $f_{\mathrm{C}}$ varies as $f_{\mathrm{C}}(w\to 0)-f_{\mathrm{C}}(w=0)\sim w^2$. Asymptotically, for large $L$, $w$ scales as $w\sim L^{-0.26}\to 0$, indicating that this type of disorder is an irrelevant perturbation of the ordinary surface universality class. However, for thin films such that $w\simeq 1$, we find that the presence of RSFs with vanishing mean value increases significantly the strength of CCFs, as compared to systems without them, and it shifts the extremum of the scaling function of $f_{\mathrm{C}}$ toward lower temperatures. But $f_{\mathrm{C}}$ remains attractive.