A lattice Boltzmann method for axisymmetric multiphase flows is presented and validated. The method is capable of accurately modeling flows with variable density. We develop the classic Shan-Chen multiphase model [Phys. Rev. E 47, 1815 (1993)] for axisymmetric flows. The model can be used to efficiently simulate single and multiphase flows. The convergence to the axisymmetric Navier-Stokes equations is demonstrated analytically by means of a Chapmann-Enskog expansion and numerically through several test cases. In particular, the model is benchmarked for its accuracy in reproducing the dynamics of the oscillations of an axially symmetric droplet and on the capillary breakup of a viscous liquid thread. Very good quantitative agreement between the numerical solutions and the analytical results is observed.

Long flexible polymers undergo a coil to stretch transition (CST) in an elongational flow. Near the CST, a peak can be observed in the fluctuations of the size of a molecule ($\left|R\right|$). Solvent effects on the fluctuations are studied using Brownian dynamics simulations of a nonlinear spring force relation that can represent real molecules. Ignoring the influence of hydrodynamic interactions, a linear region in the spring force relation is known to cause the peak in $\left|R\right|$ fluctuations. In contrast, we find that a peak in the fluctuations can be obtained even for the nonlinear spring force relation. We analyze the influence of hydrodynamic interactions on the fluctuations using a dumbbell model with a conformation-dependent drag coefficient.

This paper presents a model of network formation in repeated games where the players adapt their strategies and network ties simultaneously using a simple reinforcement-learning scheme. It is demonstrated that the coevolutionary dynamics of such systems can be described via coupled replicator equations. We provide a comprehensive analysis for three-player two-action games, which is the minimum system size with nontrivial structural dynamics. In particular, we characterize the Nash equilibria (NE) in such games and examine the local stability of the rest points corresponding to those equilibria. We also study general $n$-player networks via both simulations and analytical methods and find that, in the absence of exploration, the stable equilibria consist of star motifs as the main building blocks of the network. Furthermore, in all stable equilibria the agents play pure strategies, even when the game allows mixed NE. Finally, we study the impact of exploration on learning outcomes and observe that there is a critical exploration rate above which the symmetric and uniformly connected network topology becomes stable.

We study the signal propagation in a feed-forward motif consisting of three bistable neurons: Two input neurons receive input signals and the third output neuron generates the output. We find that a weak input signal can be propagated from the input neurons to the output neuron without amplitude attenuation. We further reveal that the initial states of the input neurons and the coupling strength act as signal gates and determine whether the propagation is enhanced or not. We also investigate the effect of the input signal frequency on enhanced signal propagation.

In this paper we study the generation of top-down vortices by thermoconvective mechanisms in a cylindrical annulus nonhomogeneously cooled on the top. Assuming axisymmetry we study the structure of the vortices, characterized by a spiral downward motion, similar to that observed in tornadoes generated in supercell storms.

We present a self-contained formalism modeled after the Brownian motion of a quantum harmonic oscillator for describing the performance of microscopic Brownian heat engines such as Carnot, Stirling, and Otto engines. Our theory, besides reproducing the standard thermodynamics results in the steady state, enables us to study the role dissipation plays in determining the efficiency of Brownian heat engines under actual laboratory conditions. In particular, we analyze in detail the dynamics associated with decoupling a system in equilibrium with one bath and recoupling it to another bath and obtain exact analytical results, which are shown to have significant ramifications on the efficiencies of engines involving such a step. We also develop a simple yet powerful technique for computing corrections to the steady state results arising from finite operation time and use it to arrive at the thermodynamic complementarity relations for various operating conditions and also to compute the efficiencies of the three engines cited above at maximum power. Some of the methods and exactly solvable models presented here are interesting in their own right and could find useful applications in other contexts as well.

The effects of thermal history on the enthalpy relaxation in polystyrene are studied by differential scanning calorimetry. The temperature dependence of the specific heat in the liquid and the glassy states, that of relaxation time, and the exponent of the Kohlrausch-Williams-Watts function are determined by measurements of the thermal response against sinusoidal temperature variation. A phenomenological model equation previously proposed to interpret the memory effect in the frozen state is applied to the enthalpy relaxation and the evolution of entropy under a given thermal history is calculated. The annealing below the glass transition temperature produces two effects on enthalpy relaxation: the decay of excess entropy with annealing time in the early stage of annealing and the increase in relaxation time due to physical aging in the later stage. The crossover of these effects is reflected in the variation of temperature of the maximum specific heat observed in the heating process after annealing and cooling.

We study numerically scattering and transport statistical properties of tight-binding random networks characterized by the number of nodes $N$ and the average connectivity $\alpha$. We use a scattering approach to electronic transport and concentrate on the case of a small number of single-channel attached leads. We observe a smooth crossover from insulating to metallic behavior in the average scattering matrix elements $\langle |S_{mn}{|}^2\rangle$, the conductance probability distribution $w\left(T\right)$, the average conductance $\langle T\rangle$, the shot noise power $P$, and the elastic enhancement factor $F$ by varying $\alpha$ from small ($\alpha \to 0$) to large ($\alpha \to 1$) values. We also show that all these quantities are invariant for fixed $\xi =\alpha N$. Moreover, we proposes a heuristic and universal relation between $\langle |S_{mn}{|}^2\rangle$, $\langle T\rangle$, and $P$ and the disorder parameter $\xi$.

Motivated by breakthroughs in the synthesis of faceted nano- and colloidal particles, as well as theoretical and computational studies of their packings, we investigate a family of truncated triangular bipyramids. We report dense periodic packings with small unit cells that were obtained via numerical and analytical optimization. The maximal packing fraction ${\varphi }_{\max }$ changes continuously with the truncation parameter $t$. Eight distinct packings are identified based on discontinuities in the first and second derivatives of ${\varphi }_{\max }\left(t\right)$. These packings differ in the number of particles in the fundamental domain (unit cell) and the type of contacts between the particles. In particular, we report two packings with four particles in the unit cell for which both ${\varphi }_{\max }\left(t\right)$ and ${\varphi }_{\max }^{\prime }\left(t\right)$ are continuous and the discontinuity occurs in the second derivative only. In the self-assembly simulations that we perform for larger boxes with 2048 particles, only one out of eight packings is found to assemble. In addition, the degenerate quasicrystal reported previously for triangular bipyramids without truncation [Haji-Akbari et al., Phys. Rev. Lett. 107, 215702 (2011)] assembles for truncations as high as $0.45$. The self-assembly propensities for the structures formed in the thermodynamic limit are explained using the isoperimetric quotient of the particles and the coordination number in the disordered fluid and in the assembled structure.

Modeling of thermal transport in practical nanostructures requires making tradeoffs between the size of the system and the completeness of the model. We study quantum heat transfer in a self-consistent thermal bath setup consisting of two lead regions connected by a center region. Atoms both in the leads and in the center region are coupled to quantum Langevin heat baths that mimic the damping and dephasing of phonon waves by anharmonic scattering. This approach treats the leads and the center region on the same footing and thereby allows for a simple and physically transparent thermalization of the system, enabling also perfect acoustic matching between the leads and the center region. Increasing the strength of the coupling reduces the mean-free path of phonons and gradually shifts phonon transport from ballistic regime to diffusive regime. In the center region, the bath temperatures are determined self-consistently from the requirement of zero net energy exchange between the local heat bath and each atom. By solving the stochastic equations of motion in frequency space and averaging over noise using the general fluctuation-dissipation relation derived by Dhar and Roy [J. Stat. Phys. 125, 801 (2006)], we derive the formula for thermal current, which contains the Caroli formula for phonon transmission function and reduces to the Landauer-Büttiker formula in the limit of vanishing coupling to local heat baths. We prove that the bath temperatures measure local kinetic energy and can, therefore, be interpreted as true atomic temperatures. In a setup where phonon reflections are eliminated, the Boltzmann transport equation under gray approximation with full phonon dispersion is shown to be equivalent to the self-consistent heat bath model. We also study thermal transport through two-dimensional constrictions in square lattice and graphene and discuss the differences between the exact solution and linear approximations.

The inner product between the ground-state eigenvectors with proximate interaction parameters, namely, the fidelity, plays a significant role in the quantum dynamics. In this paper, the critical behaviors of the transverse- and longitudinal-field fidelity susceptibilities for the $d=2$ quantum (transverse-field) Ising model are investigated by means of the numerical-diagonalization method; the former susceptibility has been investigated rather extensively. The critical exponents for these fidelity susceptibilities are estimated as ${\alpha }_F^{\left(t\right)}=0.752\left(24\right)$ and ${\alpha }_F^{\left(h\right)}=1.81\left(13\right)$, respectively. These indices are independent, and suffice for obtaining conventional critical indices such as $\nu =0.624\left(12\right)$ and $\gamma =1.19\left(13\right)$.

The motion of the ribosome is modeled here, assuming that its two subunits are subject to stochastic rearrangements, thus producing different conformations constituting its deformation cycle, or swimming stroke. Using a general statistical mechanical formulation, the mean propulsion velocity of the ribosome is obtained as a function of the transition rates among the different conformations and of the relevant deformation variables. A calculation with reasonable parameter estimations shows that the ribosome can match the average protein synthesis speed with deformations of a size comparable to its radius.

Molecular spiders are synthetic catalytic DNA-based nanoscale walkers. We study the mean first-passage time for abstract models of spiders moving on a finite two-dimensional lattice with various boundary conditions and compare it with the mean first-passage time of spiders moving on a one-dimensional track. We evaluate by how much the slowdown on newly visited sites, owing to catalysis, can improve the mean first-passage time of spiders and show that in one dimension, when both ends of the track are an absorbing boundary, the performance gain is lower than in two dimensions, when the absorbing boundary is a circle; this persists even when the absorbing boundary is a single site.

A large number of published studies have examined the properties of either networks of citation among scientific papers or networks of coauthorship among scientists. Here we study an extensive data set covering more than a century of physics papers published in the Physical Review, which allows us to construct both citation and coauthorship networks for the same set of papers. We analyze these networks to gain insight into temporal changes in citation and collaboration over the long time period of the data, as well as correlations and interactions between the two. Among other things, we investigate the change over time in the number of publishing authors, the number of papers they publish, and the number of others with whom they collaborate, changes in the typical number of citations made and received, the extent to which individuals tend to cite themselves or their collaborators more than others, the extent to which they cite themselves or their collaborators more quickly after publication, and the extent to which they tend to return the favor of a citation from another scientist.

We present quantitative measurements of time-dependent flagellar waveforms for freely swimming biflagellated algal cells, for both synchronous and asynchronous beating. We use the waveforms in conjunction with resistive force theory as well as a singularity method to predict a cell's time-dependent velocity for comparison with experiments. While net propulsion is thought to arise from asymmetry between the power and recovery strokes, we show that hydrodynamic interactions between the flagella and cell body on the return stroke make an important contribution to enhance net forward motion.

As in most interfacial flow problems, the standard theoretical procedure to establish wavelength selection in the viscous fingering instability is to maximize the linear growth rate. However, there are important discrepancies between previous theoretical predictions and existing experimental data. In this work we perform a linear stability analysis of the radial Hele-Shaw flow system that takes into account the combined action of viscous normal stresses and wetting effects. Most importantly, we introduce an alternative selection criterion for which the selected wavelength is determined by the maximum of the interfacial perturbation amplitude. The effectiveness of such a criterion is substantiated by the significantly improved agreement between theory and experiments.

It is well known that there is an analogy between optics and mechanics that prompted much of the classical theory of mechanics and indeed extended it to the theory of quantum mechanics. We develop here an optical mechanical analogy for a prototypical nonholonomic mechanical system, a knife edge moving on a plane under the influence of a potential. We show that this approach is related to but different from the classical theory of Hamiltonization of nonholonomic systems.

An alternative derivation of Brownian motion is presented. Instead of supplementing the linearized Navier-Stokes equations with a fluctuating force, we directly assume a Gaussian action functional for solvent velocity fluctuations. Solvating a particle amounts to expelling the solvent and prescribing a boundary condition to the solvent on the interface that is shared with the solute. We study the dynamical effects of this boundary condition on the solvent and derive explicit expressions for the solvent mean flow and velocity correlations. Moreover, we show that the probability to observe solvent velocity fluctuations that are compatible with the boundary condition reproduces random Brownian motion of the solvated particle. We explicitly calculate the translational and rotational diffusion coefficients of a spherical particle using the presented formalism.

This Brief Report studies the linear stability of a thermoconvective problem in an annular domain for relatively low ($\sim$1) Prandtl (viscosity effects) and Biot (heat transfer) numbers. The four possible patterns for the instabilities, namely, hydrothermal waves of first and second class, longitudinal rolls, and corotating rolls, are present in a small region of the Biot-Prandtl plane. This region can be split in four zones, depending on the sort of instability found. The boundary of these four zones is composed of codimension-two points. Authors have also found two codimension-three points, where some of the former curves intersect. Results shown in this Brief Report clarify some reported experiments, predict new instabilities, and, by giving a deeper insight into how physical parameters affect bifurcations, open a gateway to control those instabilities.