We show, using a model coupling mass transport and liquid theory calculations for a charge-stabilized colloidal dispersion, that diffusion significantly limits measurement times of its equation of state (EOS), osmotic pressure vs composition, using the osmotic compression technique. Following this result, we present a microfluidic chip allowing one to measure the entire EOS of a charged dispersion at the nanoliter scale in a few hours. We also show that time-resolved analyses of relaxation to equilibrium in this microfluidic experiment lead to direct estimates of the collective diffusion coefficient of the dispersion in Donnan equilibrium with a salt reservoir.

Using the Wehrl entropy, we study the delocalization in phase space of energy eigenstates in the vicinity of avoided crossings in the Lipkin-Meshkov-Glick model. These avoided crossings, appearing at intermediate energies in a certain parameter region of the model, originate classically from pairs of trajectories lying in different phase-space regions which, contrary to the low-energy regime, are not connected by the discrete parity symmetry of the model. As coupling parameters are varied, a sudden increase of the Wehrl entropy is observed for eigenstates participating in avoided crossings that are close to the critical energy of the excited-state quantum phase transition. This allows us to detect when an avoided crossing is accompanied by a superposition of the pair of classical trajectories in the Husimi function of eigenstates. This superposition yields an enhancement of dynamical tunneling, which is observed by considering initial Bloch states that evolve partially into the partner region of the paired classical trajectories, thus breaking the quantum-classical correspondence in the evolution of observables.

The differing ability of polypeptide conformations to act as the native state of proteins has long been rationalized in terms of differing kinetic accessibility or thermodynamic stability. Building on the successful applications of physical concepts and sampling algorithms recently introduced in the study of disordered systems, in particular artificial neural networks, we quantitatively explore how well a quantity known as the local entropy describes the native state of model proteins. In lattice models and all-atom representations of proteins, we are able to efficiently sample high local entropy states and to provide a proof of concept of enhanced stability and folding rate. Our methods are based on simple and general statistical-mechanics arguments, and thus we expect that they are of very general use.

There is a long-time quest for understanding physical mechanisms of weak magnetic field interaction with biological matter. Two factors impeded the development of such mechanisms: first, a high (room) temperature of a cellular environment, where a weak, static magnetic field induces a (classically) zero equilibrium response. Second, the friction in the cellular environment is large, preventing a weak field to alter nonequilibrium processes such as a free diffusion of charges. Here we study a class of nonequilibrium steady states of a cellular ion in a confining potential, where the response to a (weak, homogeneous, static) magnetic field survives strong friction and thermal fluctuations. The magnetic field induces a rotational motion of the ion that proceeds with the cyclotron frequency. Such nonequilibrium states are generated by a white noise acting on the ion additionally to the nonlocal (memory-containing) friction and noise generated by an equilibrium thermal bath. The intensity of this white noise can be weak, i.e., much smaller than the thermal noise intensity.

Two-dimensional liquid crystal (LC) models of interacting V-shaped bent-core molecules with two rigid rodlike identical segments connected at a fixed angle ($\theta ={112}^{\circ }$) are investigated. The model assigns equal biquadratic tensor coupling among constituents of the interacting neighboring molecules on a square lattice, allowing for reorientations in three dimensions ($d=2, n=3$). We find evidence of two temperature-driven topological transitions mediated by point disclinations associated with the three ordering directors, condensing the LC medium successively into uniaxial and biaxial phases. With Monte Carlo simulations, temperature dependencies of the system energy, specific heat, orientational order parameters, topological order parameters, and densities of unbound topological defects of the different ordering directors are computed. The high-temperature transition results in topological ordering of disclinations of the primary director, imparting uniaxial symmetry to the phase. The low-temperature transition precipitates simultaneous topological ordering of defects of the remaining directors, resulting in biaxial symmetry. The correlation functions, quantifying spatial variations of the orientational correlations of the molecular axes show exponential decays in the high-temperature (disordered) phase, and power-law decays in the low-temperature (biaxial) phase. Differing temperature dependencies of the topological parameters point to a significant degree of cross coupling among the uniaxial and biaxial tensors of interacting molecules. This simplified Hamiltonian leaves $\theta$ as the only free model parameter, and the system traces a $\theta$-dependent trajectory in a plane of the phenomenological parameter space.

In this paper, we formulate and study the quantum counterpart of the energy equipartition theorem for a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a passive quantum heat bath through coordinate variables. The bath is modeled as a collection of independent quantum harmonic oscillators. We derive closed form expressions for the mean kinetic and potential energies of the charged dissipative magneto-oscillator in the forms $E_k=\langle {\mathcal{E}}_k\rangle$ and $E_p=\langle {\mathcal{E}}_p\rangle$, respectively, where ${\mathcal{E}}_k$ and ${\mathcal{E}}_p$ denote the average kinetic and potential energies of individual thermostat oscillators. The net averaging is twofold; the first one is over the Gibbs canonical state for the thermostat, giving ${\mathcal{E}}_k$ and ${\mathcal{E}}_p$, and the second one, denoted by $\langle ·\rangle$, is over the frequencies $\omega$ of the bath oscillators which contribute to $E_k$ and $E_p$ according to probability distributions ${\mathcal{P}}_k\left(\omega \right)$ and ${\mathcal{P}}_p\left(\omega \right)$, respectively. The relationship of the present quantum version of the equipartition theorem with that of the fluctuation-dissipation theorem (within the linear-response theory framework) is also explored. Further, we investigate the influence of the external magnetic field and the effect of different dissipation processes through Gaussian decay and Drude and radiation bath spectral density functions on the typical properties of ${\mathcal{P}}_k\left(\omega \right)$ and ${\mathcal{P}}_p\left(\omega \right)$. Finally, the role of system-bath coupling strength and the memory effect is analyzed in the context of average kinetic and potential energies of the dissipative charged magneto-oscillator.

The narrow escape problem is a first-passage problem that concerns the calculation of the time needed for a Brownian particle to leave a domain with localized absorbing boundary traps, such that the measure of these traps is asymptotically small compared to the domain size. A common model for the mean first-passage time (MFPT) as a function of particle's starting location in a given domain with constant diffusivity is given by a Poisson partial differential equation subject to mixed Dirichlet-Neumann boundary conditions. The primary objective of this work is to perform direct numerical simulations of multiple particles undergoing Brownian motion in a three-dimensional spherical domain with boundary traps, compute MFPT values by averaging Brownian escape times, and compare these with explicit asymptotic results obtained previously by approximate solution of the Poisson problem. A close agreement of MFPT values is observed already at ${10}^4$ particle runs from a single starting point, providing a computational validation of the Poisson equation-based continuum model. Direct Brownian dynamics simulations are also used to study additional features of particle dynamics in narrow escape problems that cannot be captured in a continuum approach, such as average times spent by particles in a thin layer near the domain boundary, and effects of isotropic vs anisotropic near-boundary diffusion.

We study quantum Maxwell's demon in a discrete space-time setup. We consider a collection of particles hopping on a one-dimensional chain and a semipermeable barrier that allows the particles to hop in only one direction. Our main result is a formulation of a local unitary dynamics describing the action of this barrier. Such dynamics utilizes an auxiliary system $\mathcal{A}$ and we study how properties of $\mathcal{A}$ influence the behavior of particles. An immediate consequence of unitarity is the fact that particles cannot be trapped on one side of the barrier forever, unless $\mathcal{A}$ is infinite. In addition, coherent superpositions and quantum correlations are affected once particles enter the confinement region. Finally, we show that initial superposition of $\mathcal{A}$ allows the barrier to act as a beam splitter.

We consider a particle diffusing in a two-dimensional (2D) channel of varying width $h\left(x\right)$. It is driven by a force of constant magnitude $f$ but random orientation there or back along the channel. We derive the effective generalized Fick-Jacobs equation for this system, which describes the dynamics of such a particle in the longitudinal coordinate $x$. Aside from the effective diffusion coefficient $D\left(x\right)$, our mapping also generates an additional effective potential $-\gamma \left(x\right)$ added to the entropic potential $-log\left[h\right(x\left)\right]$. It acquires an increasing or decreasing component in asymmetric periodic channels, and thus it explains appearance of the ratchet current. We study this effect on a trial example and compare the results of our true 2D theory with a commonly used effective one-dimensional description; the data are verified by the numerical solution of the full 2D problem.

We consider a globally coupled Winfree model comprised of a phase-dependent influence function and sensitive function, and unravel the impact of offset and integer parameters, characterizing the shape of the influence function, on the phase diagram of the Winfree model. The decreasing value of the offset parameter decreases the degree of positive phase shift among the oscillators by promoting the negative phase shift, which indeed favors the onset of multistability among the synchronous oscillatory state and asynchronous stable steady states in a large region of the phase diagram. Further, large integer parameters lead to brief pulses of the influence function, which again enhances the effect of the offset parameter. There is an explosive transition to a synchronous oscillatory state from an asynchronous steady state via a Hopf bifurcation. Dynamical transitions and multistability emerge through saddle-node, pitchfork, and homoclinic bifurcations in the phase diagram. We deduce two ordinary differential equations corresponding to the two macroscopic variables from the population of globally coupled Winfree oscillators using the Ott-Antonsen ansatz. We also deduce various bifurcation curves analytically from the reduced low-dimensional macroscopic variables for the exactly solvable case. The analytical curves exactly match the simulation boundaries in the phase diagram.

During the past decade, there has been a hot debate about the physical mechanisms that determine when a colloidal dispersion approaches the gel transition. However, there is still no consensus on a possible unique route that leads to the conditions for the formation of a gel-like state. Based on gel states identified in experiments, Valadez-Pérez et al. [Phys. Rev. E 88, 060302(R) (2013)] proposed rigidity percolation as the precursor of colloidal gelation in adhesive hard-sphere dispersions with coordination number $\langle n_b\rangle$ equal to 2.4. Although this criterion was originally established to describe mechanical transitions in network-forming molecular materials with highly directional interactions, it worked well to explain gel formation in colloidal suspensions with isotropic short-range attractive forces. Recently, this idea has also been used to account for the dynamical arrest experimentally observed in attractive spherocylinders. Then, by assuming that rigidity percolation also drives gelation in spherical colloids interacting with short-ranged and highly directional potentials, we locate the thermodynamic states where gelation seems to occur in dispersions made up of patchy colloids. To check whether the criterion $\langle n_b\rangle =2.4$ also holds in patchy colloidal systems, we apply the so-called bond-bending analysis to determine the fraction of floppy modes at some percolating clusters. This analysis confirms that the condition $\langle n_b\rangle =2.4$ is a good approximation to determine those percolating clusters that are either mechanically stable or rigid. Furthermore, our results point out that not all combinations of patches and coverages lead to a gel-like state. Additionally, we systematically study the structure and the cluster size distribution along those thermodynamic states identified as gels. We show that for high coverage values, the structure is very similar for systems that have the same coverage regardless the number or the position of the patches on the particle surface. Finally, by using dynamic Monte Carlo computer simulations, we calculate both the mean-square displacement and the intermediate scattering function at and in the neighborhood of the gel-like states.

Physical properties of liquids and glasses are controlled not only by the short-range order (SRO) in the nearest-neighbor atoms but also by the medium-range order (MRO) observed for atoms beyond the nearest neighbors. In this article the nature of the MRO as the descriptor of point-to-set atomic correlation is discussed focusing on simple liquids, such as metallic liquids. Through the results of x-ray diffraction and simulation with classical potentials we show that the third peak of the pair-distribution function, which describes the MRO, shows a distinct change in temperature dependence at the glass transition, whereas the first peak, which represents the SRO, changes smoothly through the glass transition. The result suggests that the glass transition is induced by the freezing of the MRO rather than that of the SRO, implying a major role of the MRO on the viscosity of supercooled liquid.

The spatial atomic correlations in liquids and glasses extend often significantly beyond the nearest neighbors. Such correlations, called the medium-range order (MRO), affect many physical properties, but their nature is not well understood. In this article the variation of the MRO with temperature is calculated based upon the concept of the atomic-level pressure, focusing on simple liquids, such as metallic liquids. It is shown that the structural coherence length that characterizes MRO follows the Curie-Weiss law with a negative Curie temperature as observed by experiment and simulation. It is also shown that the glass transition is induced by freezing of the MRO, rather than the freezing of the nearest-neighbor shell. The implications of these results are discussed.

We consider three-dimensional lattice $\mathrm{SU}(N_c$) gauge theories with degenerate multicomponent ($N_f>1$) complex scalar fields that transform under the fundamental representation of the gauge $\mathrm{SU}(N_c$) group and of the global $\mathrm{U}(N_f$) invariance group, interacting with the most general quartic potential compatible with the global (flavor) and gauge (color) symmetries. We investigate the phase diagrams, identifying the low-temperature Higgs phases and their global and gauge symmetries, and the critical behaviors along the different transition lines. In particular, we address the role of the quartic scalar potential, which determines the Higgs phases and the corresponding symmetry-breaking patterns. Our study is based on the analysis of the minimum-energy configurations and on numerical Monte Carlo simulations. Moreover, we investigate whether some of the transitions observed in the lattice model can be related to the behavior of the renormalization-group flow of the continuum field theory with the same symmetries and field content around its stable charged fixed points. For $N_c=2$, numerical results are consistent with the existence of charged critical behaviors for $N_f>N_f^{★}$, with $20<N_f^{★}<40$.

We study the transverse instability and dynamics of bright soliton stripes in two-dimensional nonlocal nonlinear media. Using a multiscale perturbation method, we derive analytically the first-order correction to the soliton shape, which features an exponential growth in time—a signature of the transverse instability. The soliton's characteristic timescale associated with its exponential growth is found to depend on the square root of the nonlocality parameter. This, in turn, highlights the nonlocality-induced suppression of the transverse instability. Our analytical predictions are corroborated by direct numerical simulations, with the analytical results being in good agreement with the numerical ones.

Consider a multiplex network formed by two layers indicating social interactions: the first layer is a friendship network and the second layer is a network of business relations. In this duplex network each pair of individuals can be connected in different ways: they can be connected by a friendship but not connected by a business relation, they can be connected by a business relation without being friends, or they can be simultaneously friends and in a business relation. In the latter case we say that the links in different layers overlap. These three types of connections are called multilinks and the multidegree indicates the sum of multilinks of a given type that are incident to a given node. Previous opinion models on multilayer networks have mostly neglected the effect of link overlap. Here we show that link overlap can have important effects in the formation of a majority opinion. Indeed, the formation of a majority opinion can be significantly influenced by the statistical properties of multilinks, and in particular by the multidegree distribution. To quantitatively address this problem, we study a simple spin model, called the Ashkin-Teller model, including two-body and four-body interactions between nodes in different layers. Here we fully investigate the rich phase diagram of this model which includes a large variety of phase transitions. Indeed, the phase diagram or the model displays continuous, discontinuous, and hybrid phase transitions, and successive jumps of the order parameters within the Baxter phase.

We combine numerical and analytical methods to study two-dimensional active crystals formed by permanently linked swimmers and with two distinct alignment interactions. The system admits a stationary phase with quasi-long-range translational order, as well as a moving phase with quasi-long-range active force director and velocity order. The translational order in the moving phase is significantly influenced by alignment interaction. For Vicsek-like alignment, the translational order is short ranged, whereas the bond-orientational order is quasi-long ranged, implying a moving hexatic phase. For elasticity-based alignment, the translational order is quasi-long ranged parallel to the motion and short ranged in the perpendicular direction, whereas the bond orientational order is long ranged. We also generalize these results to higher dimensions.

We address questions that arose from studying gas and oil production from hydrofractured wells. Does past production predict the future? This depends on deducing from production as much as possible about the plausible geometries of the fracture network. We address the problem through a solvable model and use kinetic Monte Carlo and Green's function techniques to solve it. We have three main findings. First, at sufficiently long times, the production from all compact fracture networks is described by a universal function with two scaling parameters, one of which is the diffusivity of unbroken rock $\alpha$ and the second of which is a parameter ${\mathcal{V}}_{\mathrm{ext}}$ with units of volume. Second, for fracture networks where the power-law distribution of fracture spacings falls below a critical value (and this appears to be the case in practice), early-time production always scales as one over the square root of time. Third, the diffusivity $\alpha$ that sets the scale for late-time production is inherently difficult to estimate from production data, but the methods here provide the best hope of obtaining it and thus can determine the physics that will govern the decline of unconventional gas and oil wells.

Turbulence has been recognized as a factor of paramount importance for the survival or extinction of sinking phytoplankton species. However, dealing with its multiscale nature in models of coupled fluid and biological dynamics is a formidable challenge. Advection by coherent structures, such as those related to winter convection and Langmuir circulation, is also recognized to play a role in the survival and localization of phytoplankton. In this work we revisit a theoretically appealing model for phytoplankton vertical dynamics, and numerically investigate how large-scale fluid motions affect the survival conditions and the spatial distribution of the biological population. For this purpose, and to work with realistic parameter values, we adopt a kinematic flow field to account for the different spatial and temporal scales of turbulent motions. The dynamics of the population density are described by an advection-reaction-diffusion model with a spatially heterogeneous growth term proportional to sunlight availability. We explore the role of fluid transport by progressively increasing the complexity of the flow in terms of spatial and temporal scales. We find that, due to the large-scale circulation, phytoplankton accumulates in downwelling regions and its growth is reduced, confirming previous indications in slightly different conditions. We then explain the observed phenomenology in terms of a plankton filament model. Moreover, by contrasting the results in our different flow cases, we show that the large-scale coherent structures have an overwhelming importance. Indeed, we find that smaller-scale motions only quite weakly affect the dynamics, without altering the general mechanism identified. Such results are relevant for parametrizations in numerical models of phytoplankton life cycles in realistic oceanic flow conditions.