We propose a model that accounts for the budding transition of asymmetric two-component lipid domains, where the two monolayers (leaflets) have different average compositions controlled by independent chemical potentials. Assuming a coupling between the local curvature and local lipid composition in each of the leaflets, we discuss the morphology and thermodynamic behavior of asymmetric lipid domains. The membrane free-energy contains three contributions: the bending energy, the line tension, and a Landau free-energy for a lateral phase separation. Within a mean-field treatment, we obtain various phase diagrams containing fully budded, dimpled, and flat states as a function of the two leaflet compositions. The global phase behavior is analyzed, and depending on system parameters, the phase diagrams include one-phase, two-phase, and three-phase regions. In particular, we predict various phase coexistence regions between different morphologies of domains, which may be observed in multicomponent membranes or vesicles.

We characterize the fluctuation properties of a polymer chain under external tension and the fluctuation-induced forces between two ring molecules threaded around the chain. The problem is relevant in the context of fluctuation-induced forces in soft-matter systems, features of liquid interfaces, and to describe the properties of polyrotaxanes and slide-ring materials. We perform molecular-dynamics simulations of the Kremer-Grest bead-spring model for the polymer and a simple ring-molecule model in the canonical ensemble. We study transverse fluctuations of the stretched chain as a function of chain stretching and in the presence of ring-shaped threaded molecules. The fluctuation spectra of the chains are analyzed in equilibrium at constant temperature, and the differences in the presence of two-ring molecules are compared. For the rings located at fixed distances, we find an attractive fluctuation-induced force between the rings, proportional to the temperature and decaying with the ring distance. We characterize this force as a function of ring distance, chain stretching, and ring radius, and we measure the differences between the free chain spectrum and the fluctuations of the chain constrained by the rings. We also compare the dependence and range of the force found in the simulations with theoretical models coming from different fields.

We propose a natural model to probe in a controlled fashion the instability of interacting vortex rings shed from the edge of an oblate spheroid disk of major diameter $c$, undergoing oscillations of frequency $f_0$ and amplitude $A$. We perform a Floquet stability analysis to determine the characteristics of the instability modes, which depend strongly on the azimuthal (integer) wave number $m$. We vary two key control parameters, the Keulegan-Carpenter number $K_C=2\pi A/c$ and the Stokes number $\beta =f_0{c}^2/\nu$, where $\nu$ is the kinematic viscosity of the fluid. We observe two distinct flow regimes. First, for sufficiently small $\beta$, and hence low frequency of oscillation corresponding to relatively weak interaction between sequentially shedding vortex rings, symmetry breaking occurs directly to a single unstable mode with $m=1$. Second, for sufficiently large yet fixed values of $\beta$, corresponding to a higher oscillation frequency and hence stronger ring-ring interaction, the onset of asymmetry is predicted to occur due to two branches of high $m$ instabilities as the amplitude is increased, with $m=1$ structures being dominant only for sufficiently large values of $K_C$. These two branches can be distinguished by the phase properties of the vortical structures above and below the disk. The region in ($K_C,\beta$) parameter space where these two high $m$ instability branches arise can be described accurately in terms of naturally defined Reynolds numbers, using appropriately chosen characteristic length scales. We subsequently carry out direct numerical simulations of the fully three-dimensional flow to verify the principal characteristics of the Floquet analysis, in particular demonstrating that high wave-number symmetry-breaking generically occurs when vortex rings sequentially interact sufficiently strongly.

The shock wave structure of a binary mixture with very different molecular weights is analyzed using a two-fluid theory in the limit of small Prandtl ($\text{Pr}$) number of the light gas. In particular, the case in which both the density ratio and $\mathrm{\Lambda }=\text{Pr}/\delta \text{Sc}$ are order unity or below is considered, where $\delta \ll 1$ is the molecular mass ratio and $\text{Sc}$ is the Schmidt number. Approximate analytical solutions are given for weak, and for moderately strong, shock waves. In the former case the solution is continuous, while in the latter case the light gas shock exhibits a discontinuity and the heavy gas relaxes towards the final equilibrium state.

A theoretical model is developed for acoustic streaming generated by a cylindrical bubble confined in a fluid channel between two planar elastic walls. The bubble is assumed to undergo volume and translational oscillations. The volume oscillation is caused by an imposed acoustic pressure field and generates the bulk scattered wave in the fluid gap and Lamb-type surface waves propagating along the fluid-wall interfaces. The translational oscillation is induced by the velocity field of an external sound source such as another bubble or an oscillatory fluid flow. The acoustic streaming is assumed to result from the interaction of the volume and the translational modes of the bubble oscillations. The general solutions for the linear equations of fluid motion and the equations of acoustic streaming are calculated with no restrictions on the ratio between the viscous penetration depth and the bubble size. Approximate solutions for the limit of low viscosity are provided as well. Simulations of streamline patterns show that the geometry of the streaming resembles flows generated by a source dipole, while the vortex orientation is governed by the driving frequency, bubble size, and the distance of the bubble from the source of translational excitation. Experimental verification of the developed theory is performed using data for streaming generated by bubble pairs.

The elastic fingering phenomenon occurs when two confined fluids are brought into contact, and due to a chemical reaction, the interface separating them becomes elastic. We study elastic fingering pattern formation in Newtonian fluids flowing in a lifting (time-dependent gap) Hele-Shaw cell. Using a mode-coupling approach, nonlinear effects induced by the interplay between viscous and elastic forces are investigated and the weakly nonlinear behavior of the fluid-fluid interfacial patterns is analyzed. Our results indicate that the existence of the elastic interface allows the development of unexpected morphological behaviors in such Newtonian fluid flow systems. More specifically, we show that depending on the values of the governing physical parameters, the observed elastic fingering structures are characterized by the occurrence of either finger tip splitting or side branching. The impact of the elastic interface on finger-competition events is also discussed.

Translationally diffusive behavior arising from the combination of orientational diffusion and powered motion at microscopic scales is a known phenomenon, but the peculiarities of the evolution of expected position conditioned on initial position and orientation have been neglected. A theory is given of the spiral motion of the mean trajectory depending upon propulsion speed, angular velocity, orientational diffusion, and rate of random chirality reversal. We demonstrate the experimental accessibility of this effect using both tadpole-like and Janus sphere dimer rotating motors. Sensitivity of the mean trajectory to the kinematic parameters suggest that it may be a useful way to determine those parameters.

Three different tensor network (TN) optimization algorithms are employed to accurately determine the ground state and thermodynamic properties of the spin-3/2 kagome Heisenberg antiferromagnet. We found that the $\sqrt{3}\times \sqrt{3}$ state (i.e., the state with ${120}^{\circ }$ spin configuration within a unit cell containing 9 sites) is the ground state of this system, and such an ordered state is melted at any finite temperature, thereby clarifying the existing experimental controversies. Three magnetization plateaus ($m/m_s=1/3,23/27$, and 25/27) were obtained, where the 1/3-magnetization plateau has been observed experimentally. The absence of a zero-magnetization plateau indicates a gapless spin excitation that is further supported by the thermodynamic asymptotic behaviors of the susceptibility and specific heat. At low temperatures, the specific heat is shown to exhibit a $T^2$ behavior, and the susceptibility approaches a finite constant as $T\to 0$. Our TN results of thermodynamic properties are compared with those from high-temperature series expansion. In addition, we disclose a quantum phase transition between $q=0$ state (i.e., the state with ${120}^{\circ }$ spin configuration within a unit cell containing three sites) and $\sqrt{3}\times \sqrt{3}$ state in a spin-3/2 kagome XXZ model at the critical point ${\mathrm{\Delta }}_c=0.54$. This study provides reliable and useful information for further explorations on high-spin kagome physics.

Let ${\mathcal{P}}_{\beta }^{\left(V\right)}\left(N_{\mathcal{I}}\right)$ be the probability that a $N\times N\beta$-ensemble of random matrices with confining potential $V\left(x\right)$ has $N_{\mathcal{I}}$ eigenvalues inside an interval $\mathcal{I}=[a,b]$ on the real line. We introduce a general formalism, based on the Coulomb gas technique and the resolvent method, to compute analytically ${\mathcal{P}}_{\beta }^{\left(V\right)}\left(N_{\mathcal{I}}\right)$ for large $N$. We show that this probability scales for large $N$ as ${\mathcal{P}}_{\beta }^{\left(V\right)}\left(N_{\mathcal{I}}\right)\approx exp\left[-\beta N^2{\psi }^{\left(V\right)}(N_{\mathcal{I}}/N)\right]$, where $\beta$ is the Dyson index of the ensemble. The rate function ${\psi }^{\left(V\right)}\left(k_{\mathcal{I}}\right)$, independent of $\beta$, is computed in terms of single integrals that can be easily evaluated numerically. The general formalism is then applied to the classical $\beta$-Gaussian ($\mathcal{I}=[-L,L]$), $\beta$-Wishart ($\mathcal{I}=[1,L]$), and $\beta$-Cauchy ($\mathcal{I}=[-L,L]$) ensembles. Expanding the rate function around its minimum, we find that generically the number variance $var\left(N_{\mathcal{I}}\right)$ exhibits a nonmonotonic behavior as a function of the size of the interval, with a maximum that can be precisely characterized. These analytical results, corroborated by numerical simulations, provide the full counting statistics of many systems where random matrix models apply. In particular, we present results for the full counting statistics of zero-temperature one-dimensional spinless fermions in a harmonic trap.

In this study we investigate the resilience of duplex networked layers $\alpha$ and $\beta$ coupled with antagonistic interlinks, each layer of which inhibits its counterpart at the microscopic level, changing the following factors: whether the influence of the initial failures in $\alpha$ remains [quenched (case $\mathrm{Q}$)] or not [free (case $\mathrm{F}$)]; the effect of intralayer degree-degree correlations in each layer and interlayer degree-degree correlations; and the type of the initial failures, such as random failures or targeted attacks (TAs). We illustrate that the percolation processes repeat in both cases $\mathrm{Q}$ and $\mathrm{F}$, although only in case $\mathrm{F}$ are nodes that initially failed reactivated. To analytically evaluate the resilience of each layer, we develop a methodology based on the cavity method for deriving the size of a giant component (GC). Strong hysteresis, which is ignored in the standard cavity analysis, is observed in the repetition of the percolation processes particularly in case $\mathrm{F}$. To handle this, we heuristically modify interlayer messages for macroscopic analysis, the utility of which is verified by numerical experiments. The percolation transition in each layer is continuous in both cases $\mathrm{Q}$ and $\mathrm{F}$. We also analyze the influences of degree-degree correlations on the robustness of layer $\alpha$, in particular for the case of TAs. The analysis indicates that the critical fraction of initial failures that makes the GC size in layer $\alpha$ vanish depends only on its intralayer degree-degree correlations. Although our model is defined in a somewhat abstract manner, it may have relevance to ecological systems that are composed of endangered species (layer $\alpha$) and invaders (layer $\beta$), the former of which are damaged by the latter whereas the latter are exterminated in the areas where the former are active.

We present an effective and simple multiscale method for equilibrating Kremer Grest model polymer melts of varying stiffness. In our approach, we progressively equilibrate the melt structure above the tube scale, inside the tube and finally at the monomeric scale. We make use of models designed to be computationally effective at each scale. Density fluctuations in the melt structure above the tube scale are minimized through a Monte Carlo simulated annealing of a lattice polymer model. Subsequently the melt structure below the tube scale is equilibrated via the Rouse dynamics of a force-capped Kremer-Grest model that allows chains to partially interpenetrate. Finally the Kremer-Grest force field is introduced to freeze the topological state and enforce correct monomer packing. We generate 15 melts of 500 chains of 10.000 beads for varying chain stiffness as well as a number of melts with 1.000 chains of 15.000 monomers. To validate the equilibration process we study the time evolution of bulk, collective, and single-chain observables at the monomeric, mesoscopic, and macroscopic length scales. Extension of the present method to longer, branched, or polydisperse chains, and/or larger system sizes is straightforward.

A detailed systematic derivation of a logarithmically discretized model for two-dimensional turbulence is given, starting from the basic fluid equations and proceeding with a particular form of discretization of the wave-number space. We show that it is possible to keep all or a subset of the interactions, either local or disparate scale, and recover various limiting forms of shell models used in plasma and geophysical turbulence studies. The method makes no use of the conservation laws even though it respects the underlying conservation properties of the fluid equations. It gives a family of models ranging from shell models with nonlocal interactions to anisotropic shell models depending on the way the shells are constructed. Numerical integration of the model shows that energy and enstrophy equipartition seem to dominate over the dual cascade, which is a common problem of two-dimensional shell models.

We revisit the problem of calculating the survival probability of Lévy flights in a finite interval with absorbing boundaries. Our approach is based on the master equation for discrete Lévy fliers, previously considered to treat the semi-infinite domain. We argue that, although the semi-infinite case can be treated exactly due to Wiener-Hopf factorization, the approximation involved in the problem with the finite interval is actually fairly good. We evidence the shift in the universal behavior of the long-term survival probability from the exponential decay in the presence of two absorbing barriers to the Sparre-Andersen power-law dependence in the single-barrier limit. In some cases, we also calculate the short- and intermediate-term behavior and present the explicit dependence of the survival probability on the Lévy flier's starting position. Our analytical results are confirmed by numerical simulations.

We show how two electrically coupled semiconductor lasers having optical feedback can present simultaneous antiphase correlated fast power fluctuations, and strong in-phase synchronized spikes of chaotic power drops. This quite counterintuitive phenomenon is demonstrated experimentally and confirmed by numerical solutions of a deterministic dynamical system of rate equations. The occurrence of negative and positive cross correlation between parts of a complex system according to time scales, as proved in our simple arrangement, is relevant for the understanding and characterization of collective properties in complex networks.

Swarming behavior continues to be a subject of immense interest because of its centrality in many naturally occurring systems in physics and biology, as well as its importance in applications such as robotics. Here we examine the effects on swarm pattern formation from delayed communication and topological heterogeneity, and in particular, the inclusion of a relatively small number of highly connected nodes, or “motherships,” in a swarm's communication network. We find generalized forms of basic patterns for networks with general degree distributions, and a variety of dynamic behaviors including parameter regions with multistability and hybrid motions in bimodal networks. The latter is an interesting example of how heterogeneous networks can have dynamics that is a mix of different states in homogeneous networks, where high- and low-degree nodes have distinct behavior simultaneously.

Evolutionary forces resulted from competitions between different populations are common, which change the evolutionary behavior of a single population. In an isolated population of coordination games of two strategies (e.g., $s_1$ and $s_2$), the previous studies focused on determining the fixation probability that the system is occupied by only one strategy ($s_1$) and their expectation times, given an initial mixture of two strategies. In this work, we propose a model of two interdependent populations, disclosing the effects of the interaction strength on fixation probabilities. In the well-mixing limit, a detailed linear stability analysis is performed, which allows us to find and to classify the different equilibria, yielding a clear picture of the bifurcation patterns in phase space. We demonstrate that the interactions between populations crucially alter the dynamic behavior. More specifically, if the coupling strength is larger than some threshold value, the critical initial density of one strategy ($s_1$) that corresponds to fixation is significantly delayed. Instead, the two populations evolve to the opposite state of all ($s_2$) strategy, which are in favor of the red queen hypothesis. We delineate the extinction time of strategy ($s_1$) explicitly, which is an exponential form. These results are validated by systematic numerical simulations.

Various microstructures are obtained through the self-assembly of block copolymers on the basis of the compositional fractions and repulsive interactions among different types of beads. The inhomogeneity of block copolymers can be studied by molecular dynamics. However, preparing initial configurations of various self-assembled structures directly by molecular dynamics requires extensive computational time because of topological constraints. Furthermore, manual preparation often becomes a complicated and time-consuming procedure even for the simplest structures, such as a lamellar phase, not to mention three-dimensional bicontinuous cubic phases such as a gyroid phase. In this paper, this difficulty is overcome by using a soft potential, which allows the system to reach a self-assembled state quickly (within $3{\tau }_d$). Once a self-assembled microstructure is obtained, the normal potential is restored and equilibration steps are performed to enable the calculation of various properties of the microstructures. Various equilibrated phase structures—including $S$ (spherical), $H$ (hexagonal), $G$ (gyroid), and $L$ (lamellar) phases—are obtained by this approach. To verify our method, static and dynamic properties of the lamellar phase are examined and compared with previous results.

A mixture of 13X molecular sieve (13XMS) particles and glass particles with identical diameters is placed in a cylindrical container. Under vertical vibration, heavier glass particles tend to cluster and are wrapped inside the convection of 13XMS particles, resulting in the granular core phenomenon. The vibration frequency $f$ strongly influences particle convection and particle cluster modes. By contrast, the effect of the dimensionless acceleration amplitude Γ can be neglected. For different $f$ ranges, the granular core is classified as center-type and ring-type cores. For the center-type core, heavy particles are distributed as an approximate zeroth-order Bessel function of the first kind in the radial direction and an exponential function in the height direction. For the ring-type core, the concentration of heavy particles follows the power-series function in the radial direction. A granular transport model is then established based on heavy-particle movements under steady state to analyze the effect of vibration parameters and granular convection on density segregation.

This study presents a comprehensive procedure to calculate the exact dynamic Green's function of a harmonic semi-infinite solid and the time trajectories of the atoms, in the framework of the Green's function molecular dynamics. This Green's function properly describes the energy dissipation caused by excitations of the surface phonons, and the simulated atoms serve as well-defined thermo- and barostats for the nonequilibrium surface and interface systems. Moreover, the use of the exact dynamic Green's function coupled with a fast convolution algorithm significantly improves both the accuracy and the computing speed. The presented method is applied to a diamond (001) surface, and the results demonstrate that the properties of the nonreflecting boundary, the thermal fluctuations, and the energy dissipations involving long-wavelength phonons are correctly reproduced. These distinctive performances potentially allow us to reveal the nonequilibrium phenomena in a wide spectrum of applications such as catalysis, thermal transport, fracture mechanics, mechanochemistry, and tribology.