Several model fluids in contact with planar, spherical, and cylindrical walls are investigated for small number densities within density functional theory. The dependence of the solid-fluid interfacial tension on the curvature of spherical and cylindrical walls is examined and compared with the corresponding expression derived within the framework of morphometric thermodynamics. Particular attention is paid to the implications of the choice of the interface location, which underlies the definition of the interfacial tension. We find that morphometric thermodynamics is never exact for the considered systems and that its quality as an approximation depends sensitively on the choice of the interface location.

The morphology of solution-cast, phase-separated polymers becomes finer with increasing solvent evaporation rate. We address this observation theoretically for a model polymer where demixing is induced by steady solvent evaporation. In contrast to what is the case for a classical, thermal quench involving immiscible blends, the spinodal instability initially develops slowly and the associated length scale is not time invariant but decreases with time as $t^{-1/2}$. After a time lag, phase separation accelerates. Time lag and characteristic length exhibit power-law behavior as a function of the evaporation rate with exponents of $-2/3$ and $-1/6$. Interestingly, at later stages the spinodal structure disappears completely while a second length scale develops. The associated structure coarsens but does not follow the usual Lifshitz-Slyozov-Wagner kinetics.

Biofilms are antibiotic-resistant bacterial aggregates that grow on moist surfaces and can trigger hospital-acquired infections. They provide a classical example in biology where the dynamics of cellular communities may be observed and studied. Gene expression regulates cell division and differentiation, which affect the biofilm architecture. Mechanical and chemical processes shape the resulting structure. We gain insight into the interplay between cellular and mechanical processes during biofilm development on air-agar interfaces by means of a hybrid model. Cellular behavior is governed by stochastic rules informed by a cascade of concentration fields for nutrients, waste, and autoinducers. Cellular differentiation and death alter the structure and the mechanical properties of the biofilm, which is deformed according to Föppl–Von Kármán equations informed by cellular processes and the interaction with the substratum. Stiffness gradients due to growth and swelling produce wrinkle branching. We are able to reproduce wrinkled structures often formed by biofilms on air-agar interfaces, as well as spatial distributions of differentiated cells commonly observed with B. subtilis.

Most of the work on opinion dynamics models focuses on the case of two or three opinion types. We consider the case of an arbitrary number of opinions in the mean field case of the naming game model in which it is assumed the population is infinite and all individuals are neighbors. A particular challenge of the naming game model is that the number of variables, which corresponds to the number of possible sets of opinions, grows exponentially with the number of possible opinions. We present a method for generating mean field dynamical equations for the general case of $k$ opinions. We calculate the steady states in two important special cases in arbitrarily high dimension: the case in which there exist zealots of only one type, and the case in which there are an equal number of zealots for each opinion. We show that in these special cases a phase transition occurs at critical values $p_c$ of the parameter $p$ describing the fraction of zealots. In the former case, the critical value determines the threshold value beyond which it is not possible for the opinion with no zealots to be held by more nodes than the opinion with zealots, and this point remains fixed regardless of dimension. In the latter case, the critical point $p_c$ is the threshold value beyond which a stalemate between all $k$ opinions is guaranteed, and we show that it decays precisely as a lognormal curve in $k$.

The self-propulsion of a sphere immersed in a polar liquid or ferrofluid is studied on the basis of ferrohydrodynamics. In the electrical case an oscillating charge density located inside the sphere generates an electrical field that polarizes the fluid. The lag of polarization with respect to the electrical field due to relaxation generates a time-independent electrical torque density acting on the fluid, causing it to move. The resulting propulsion velocity of the sphere is calculated in perturbation theory to second order in powers of the charge density.

We present closed-form expressions of the effective conductivity of composites made of matrix and impenetrable polydispersed particles. The approach developed in a recent work has been generalized to treat periodic multiphase composite materials. Particular cases including orthorhombic arrangements of spherical or spheroidal inclusions and random distributions of spheres are considered where simple closed-form expressions are obtained. The case of random distributions allows us to recover Mori-Tanaka estimation after introducing partial structure factors as a statistical information on the microstructure.

We propose a new method of detecting radiation reaction effects in the motion of particles subjected to laser pulses of moderate intensity and long duration. The effect becomes sizable for particles that gain almost no energy through the interaction with the laser pulse. Hence, there are regions of parameter space in which radiation reaction is actually the dominant influence on charged particle motion.

In the referred paper, the authors use a numerical method for solving ordinary differential equations and a softened Coulomb potential $-1/\sqrt{x^2+{\beta }^2}$ to study the one-dimensional Coulomb problem by approaching the parameter $\beta$ to zero. We note that even though their numerical findings in the soft potential scenario are correct, their conclusions do not extend to the one-dimensional Coulomb problem ($\beta =0$). Their claims regarding the possible existence of an even ground state with energy $-\infty$ with a Dirac-$\delta$ eigenfunction and of well-defined parity eigenfunctions in the one-dimensional hydrogen atom are questioned.

This is a response to the comment we received on our recent paper “Calculations for the one-dimensional soft Coulomb problem and the hard Coulomb limit.” In that paper, we introduced a computational algorithm that is appropriate for solving stiff initial value problems, and which we applied to the one-dimensional time-independent Schrödinger equation with a soft Coulomb potential. We solved for the eigenpairs using a shooting method and hence turned it into an initial value problem. In particular, we examined the behavior of the eigenpairs as the softening parameter approached zero (hard Coulomb limit). The commenters question the existence of the ground state of the hard Coulomb potential, which we inferred by extrapolation of the softening parameter to zero. A key distinction between the commenters' approach and ours is that they consider only the half-line while we considered the entire $x$ axis. Based on mathematical considerations, the commenters consider only a vanishing solution function at the origin, and they question our conclusion that the ground state of the hard Coulomb potential exists. The ground state we inferred resembles a $\delta \left(x\right)$, and hence it cannot even be addressed based on their argument. For the excited states, there is agreement with the fact that the particle is always excluded from the origin. Our discussion with regard to the symmetry of the excited states is an extrapolation of the soft Coulomb case and is further explained herein.

We introduce a model of interacting random walkers on a finite one-dimensional chain with absorbing boundaries or targets at the ends. Walkers are of two types: informed particles that move ballistically towards a given target and diffusing uninformed particles that are biased towards close informed individuals. This model mimics the dynamics of hierarchical groups of animals, where an informed individual tries to persuade and lead the movement of its conspecifics. We characterize the success of this persuasion by the first-passage probability of the uninformed particle to the target, and we interpret the speed of the informed particle as a strategic parameter that the particle can tune to maximize its success. We find that the success probability is nonmonotonic, reaching its maximum at an intermediate speed whose value increases with the diffusing rate of the uninformed particle. When two different groups of informed leaders traveling in opposite directions compete, usually the largest group is the most successful. However, the minority can reverse this situation and become the most probable winner by following two different strategies: increasing its attraction strength or adjusting its speed to an optimal value relative to the majority's speed.

For the random sequential adsorption model, we introduce the “availability” as a variable corresponding to the number of available locations in which an adsorbate can be accommodated. We investigate the relation of the availability to the coverage of the adsorbent surface over time. Power law scaling between the two is obtained both through numerical simulations and analytical techniques for both one- and two-dimensional random sequential adsorption, as well as in the case of competitive random sequential adsorption in one dimension.

An initially empty (no edges) graph of order $M$ evolves by randomly adding one edge at a time. This edge connects either two linked components and forms a new component of larger order (coalescence of graphs) or increases (by one) the number of edges in a given linked component (cycling). Assuming that the vertices of the graph have a finite valence (the number of edges connected with a given vertex is limited) the kinetic equation for the distribution of linked components of the graph over their orders and valences is formulated and solved by applying the generating function method. The evolution process is shown to reveal a phase transition: the emergence of a giant linked component whose order is comparable to the total order of the graph. The kinetics of growth of this component is studied for arbitrary initial conditions. Found are the time dependences of the average order and the valence of the giant component. The distribution over orders and valences of the linked components of the graph is derived for an initially empty graph comprising $M$ bare polyvalent vertices.

We use an exact transfer-matrix approach to compute the equilibrium properties of a system of hard disks of diameter $\sigma$ confined to a two-dimensional channel of width $1.95\sigma$ at constant longitudinal applied force. At this channel width, which is sufficient for next-nearest-neighbor disks to interact, the system is known to have a great many jammed states. Our calculations show that the longitudinal force (pressure) extrapolates to infinity at a well-defined packing fraction ${\varphi }_K$ that is less than the maximum possible ${\varphi }_{\max }$, the latter corresponding to a buckled crystal. In this quasi-one-dimensional problem there is no question of there being any real divergence of the pressure at ${\varphi }_K$. We give arguments that this avoided phase transition is a structural feature, the remnant in our narrow channel system of the hexatic to crystal transition, but that it has the phenomenology of the (avoided) ideal glass transition. We identify a length scale ${\tilde{\xi }}_3$ as our equivalent of the penetration length for amorphous order: In the channel system, it reaches a maximum value of around $15\sigma$ at ${\varphi }_K$, which is larger than the penetration lengths that have been reported for three-dimensional systems. It is argued that the $\alpha$-relaxation time would appear on extrapolation to diverge in a Vogel-Fulcher manner as the packing fraction approaches ${\varphi }_K$.

An open problem in evolutionary game dynamics is to understand the effect of peer pressure on cooperation in a quantitative manner. Peer pressure can be modeled by punishment, which has been proved to be an effective mechanism to sustain cooperation among selfish individuals. We investigate a symmetric punishment strategy, in which an individual will punish each neighbor if their strategies are different, and vice versa. Because of the symmetry in imposing the punishment, one might intuitively expect the strategy to have little effect on cooperation. Utilizing the prisoner's dilemma game as a prototypical model of interactions at the individual level, we find, through simulation and theoretical analysis, that proper punishment, when even symmetrically imposed on individuals, can enhance cooperation. Also, we find that the initial density of cooperators plays an important role in the evolution of cooperation driven by mutual punishment.

We construct a quantum system of spherical spins with a continuous local symmetry. The model is exactly soluble in the thermodynamic limit and exhibits a number of interesting properties. We show that the local symmetry is spontaneously broken at finite as well as zero temperatures, implying the existence of classical and quantum phase transitions with a nontrivial critical behavior. The dynamical generation of gauge fields and the equivalence with the ${\text{CP}}^{(\mathcal{N}-1)}$ model in the limit $\mathcal{N}\to \infty$ are investigated. The dynamical generation of gauge fields is a consequence of the restoration of the local symmetry.

We analyze the statistics of work generated by a gradient flow to stretch a nonlinear polymer. We obtain the large deviation function (LDF) of the work in the full range of appropriate parameters by combining analytical and numerical tools. The LDF shows two distinct asymptotes: “near tails” are linear in work and dominated by coiled polymer configurations, while “far tails” are quadratic in work and correspond to preferentially fully stretched polymers. We find the extreme value statistics of work for several singular elastic potentials, as well as the mean and the dispersion of work near the coil-stretch transition. The dispersion shows a maximum at the transition.

When water molecules are confined to nanoscale spacings, such as in the nanometer-size pores of activated carbon fiber (ACF), their freezing point gets suppressed down to very low temperatures $(\sim 150\mathrm{K})$, leading to a metastable liquid state with remarkable physical properties. We have investigated the ambient pressure diffusive dynamics of water in microporous Kynol ACF-10 (average pore size $\sim 11.6\AA$, with primarily slit-like pores) from temperature $T=280$ K in its stable liquid state down to $T=230$ K into the metastable supercooled phase. The observed characteristic relaxation times and diffusion coefficients are found to be, respectively, higher and lower than those in bulk water, indicating a slowing down of the water mobility with decreasing temperature. The observed temperature-dependent average relaxation time $\langle \tau \rangle$ when compared to previous findings indicate that it is the width of the slit pores—not their curvature—that primarily affects the dynamics of water for pore sizes larger than 10 Å. The experimental observations are compared to complementary molecular dynamics simulations of a model system, in which we studied the diffusion of water within the 11.6 Å gap of two parallel graphene sheets. We find generally a reasonable agreement between the observed and calculated relaxation times at the low momentum transfer $Q(Q\le 0.9\AA {}^{-1})$. At high $Q$, however, where localized dynamics becomes relevant, this ideal system does not satisfactorily reproduce the measurements. Consequently, the simulations are compared to the experiments at low $Q$, where the two can be best reconciled. The best agreement is obtained for the diffusion parameter $D$ associated with the hydrogen-site when a representative stretched exponential function, rather than the standard bimodal exponential model, is used to parametrize the self-correlation function $I(Q,t)$.

The pulse broadening and decay of coherent sound waves propagating in disordered granular media are investigated. We find that the pulse width of these compressional waves is broadened when the disorder is increased by mixing the beads made of different materials. To identify the responsible mechanism for the pulse broadening, we also perform the acoustic attenuation measurement by spectral analysis and the numerical simulation of pulsed sound wave propagation along one-dimensional disordered elastic chains. The qualitative agreement between experiment and simulation reveals a dominant mechanism by scattering attenuation at the high-frequency range, which is consistent with theoretical models of sound wave scattering in strongly random media via a correlation length.

A model is derived for the elastic response of polyelectrolyte gels subjected to unconstrained and constrained swelling. A gel is treated as a three-phase medium consisting of a solid phase (polymer network), solvent (water), and solutes (mobile ions). Transport of solvent and solutes is modeled as their diffusion through the network accelerated by an electric field formed by ions and accompanied by chemical reactions (dissociation of functional groups attached to the chains). Constitutive equations (including the van't Hoff law for ionic pressure and the Henderson-Hasselbach equation for ionization of chains) are derived by means of the free energy imbalance inequality. Good agreement is demonstrated between equilibrium swelling diagrams on several pH-sensitive gels and results of simulation. It is revealed that swelling of polyelectrolyte gels is driven by electrostatic repulsion of bound charges, whereas the effect of ionic pressure is of secondary importance.

We show that coupling to curvature nontrivially affects collective motion in active systems, leading to motion patterns not observed in flat space. Using numerical simulations, we study a model of self-propelled particles with polar alignment and soft repulsion confined to move on the surface of a sphere. We observe a variety of motion patterns with the main hallmarks being polar vortex and circulating band states arising due to the incompatibility between spherical topology and uniform motion—a consequence of the “hairy ball” theorem. We provide a detailed analysis of density, velocity, pressure, and stress profiles in the circulating band state. In addition, we present analytical results for a simplified model of collective motion on the sphere showing that frustration due to curvature leads to stable elastic distortions storing energy in the band.