In this paper, we present a numerical study on the deformation and breakup behavior of liquid droplet past a solid circular cylinder by using an improved interparticle-potential lattice Boltzmann method. The effects of the eccentric ratio $\beta$, viscosity ratio $\lambda$ between the droplet and the surrounding fluid, surface wettability, and Bond number (Bo) on the dynamic behavior of the liquid droplet are considered. The parameter $\beta$ represents the degree that the solid cylinder deviates from the center line, and Bo is the ratio between the inertial force and capillary force. Numerical results show that there are two typical patterns, i.e., breakup and no breakup, which are greatly influenced by the aforementioned parameters. When $\beta$ increases to a critical value ${\beta }_c$, the droplet can pass the circular cylinder without a breakup, otherwise, the breakup phenomenon occurs. The critical eccentric ratio ${\beta }_c$ increases significantly with increasing Bo for case with $\lambda >1$, while for the case with $\lambda <1$, the viscosity effects on the ${\beta }_c$ is not obvious when Bo is large. For the breakup case, the amount of deposited liquid on the tip of the circular cylinder is almost unaffected by $\beta$. In addition, the results also show that the viscosity ratio and wettability affect the deformation and breakup process of the droplet. For case with $\lambda <1$, the viscosity ratio plays a minor role in the thickness variations of the deposited liquid, which decreases to a nonzero constant eventually; while for $\lambda >1$, the increase of the viscosity ratio significantly accelerates the decrease of the deposited liquid, and finally no fluid deposits on the cylinder. In term of the wettability, there occurs continuous gas phase trapped by the wetting droplet, but this does not happen for nonwetting droplet. Besides, for $\lambda <1$, the time required to pass the cylinder $\left(t_p\right)$ decreases monotonically with decreasing contact angle, while a nonmonotonic decrease appears for $\lambda >1$. It is also found that $t_p$ decreases monotonically with increasing Bo and is less sensitive to $\lambda$ at a large Bo.

We present a numerical study of thermoviscous effects on the acoustic streaming flow generated by an ultrasound standing-wave resonance in a long straight microfluidic channel containing a Newtonian fluid. These effects enter primarily through the temperature and density dependence of the fluid viscosity. The resulting magnitude of the streaming flow is calculated and characterized numerically, and we find that even for thin acoustic boundary layers, the channel height affects the magnitude of the streaming flow. For the special case of a sufficiently large channel height, we have successfully validated our numerics with analytical results from 2011 by Rednikov and Sadhal for a single planar wall. We analyzed the time-averaged energy transport in the system and the time-averaged second-order temperature perturbation of the fluid. Finally, we have made three main changes in our previously published numerical scheme to improve the numerical performance: (i) The time-averaged products of first-order variables in the time-averaged second-order equations have been recast as flux densities instead of as body forces. (ii) The order of the finite-element basis functions has been increased in an optimal manner. (iii) Based on the International Association for the Properties of Water and Steam (IAPWS 1995, 2008, and 2011), we provide accurate polynomial fits in temperature for all relevant thermodynamic and transport parameters of water in the temperature range from 10 to $50 {}^{\circ }\text{C}$.

We show that the state of amide-I excitations in proteins is modeled by the discrete nonlinear Schrödinger equation with saturable nonlinearities. This is done by extending the Davydov model to take into account the competition between local compression and local dilatation of the lattice, thus leading to the interplay between self-focusing and defocusing saturable nonlinearities. Site-centered (sc) mode and/or bond-centered mode like discrete multihump soliton (DMHS) solutions are found numerically and their stability is analyzed. As a result, we obtained the existence and stability diagrams for all observed types of sc DMHS solutions. We also note that the stability of sc DMHS solutions depends not only on the value of the interpeak separation but also on the number of peaks, while their counterpart having at least one intersite soliton is instable. A study of mobility is achieved and it appears that, depending on the higher-order saturable nonlinearity, DMHS-like mechanism for vibrational energy transport along the protein chain is possible.

Using numerical simulations, the onset of Poiseuille flow in a confined soft glass is investigated. Starting from the quiescent state, steady flow sets in at a time scale which increases with a decrease in applied forcing. At this onset time scale, a rapid transition occurs via the simultaneous fluidization of regions having different local stresses. In the absence of steady flow at long times, creep is observed even in regions where the local stress is larger than the bulk yielding threshold. Finally, we show that the time scale to attain steady flow depends strongly on the history of the initial state.

The long-time limit behavior of velocity correlation functions (VCFs) for an underdamped Brownian particle in an oscillatory viscoelastic shear flow is investigated using the generalized Langevin equation with a power-law memory kernel. The influence of a fluctuating environment is modeled by an additive external fractional Gaussian noise. The exact expressions of the correlation functions of the fluctuating components of velocity for the Brownian particle in the shear plane have been calculated. Also, the particle's angular momentum is found. It is shown that in a certain region of the system parameters an interplay of the shear flow, memory effects, and external noise can induce a bounded long-time behavior of the VCFs, even in the shear flow direction, where in the case of internal noise the velocity process is subdiffusive, i.e., unbounded in time. Moreover, we find resonant behavior of the VCFs and the angular momentum versus the shear oscillation frequency, implying that they can be efficiently excited by oscillatory shear. The role of the initial positional distribution of particles is also discussed.

We present an analytic expression for the heat current through a general harmonic network coupled with Ohmic reservoirs. We use a method that enables us to express the stationary state of the network in terms of the eigenvectors and eigenvalues of a generalized cubic eigenvalue problem. In this way, we obtain exact formulas for the heat current and the local temperature inside the network. Our method does not rely on the usual assumptions of weak coupling to the environments or on the existence of an infinite cutoff in the environmental spectral densities. We use this method to study nonequilibrium processes without the weak coupling and Markovian approximations. As a first application of our method, we revisit the problem of heat conduction in two- and three-dimensional crystals with binary mass disorder. We complement previous results showing that for small systems the scaling of the heat current with the system size greatly depends on the strength of the interaction between system and reservoirs. This somewhat counterintuitive result seems not to have been noticed before.

We experimentally measure the effects of fluid inertia on the diffusion of a Brownian particle at very long time scales. In previous experiments, the use of standard optical tweezers introduced a cutoff in the free diffusion of the particle, which limited the measurement of these effects to times comparable with the relaxation time of the fluid inertia, i.e., a few milliseconds. Here, by using blinking optical tweezers, we detect these inertial effects on time scales several orders longer up to a few seconds. The measured mean square displacement of a freely diffusing Brownian particle in a liquid shows a deviation from the Einstein-Smoluchowsky theory that diverges with time. These results are consistent with a generalized theory that takes into account not only the particle inertia but also the inertia of the surrounding fluid.

Koperwas et al. showed in a recent paper [Phys. Rev. Lett. 111, 125701 (2013)] that the dynamic susceptibility ${\chi }_4$ as estimated by dielectric measurements for certain glass-forming liquids decreases substantially with increasing pressure along a curve of constant relaxation time. This observation is at odds with other measures of dynamics being invariant and seems to pose a problem for theories of glass formation. We show that this variation is in fact consistent with predictions for liquids with hidden scale invariance: Measures of dynamics at constant volume are invariant along isochrones, called isomorphs in such liquids, but contributions to fluctuations from long-wavelength fluctuations can vary. This is related to the known noninvariance of the isothermal bulk modulus. Considering the version of ${\chi }_4$ defined for the NVT ensemble, data from simulations of a binary Lennard-Jones liquid show in fact a slight increase with increasing density. This is a true departure from the formal invariance expected for this quantity.

First return maps of interspike intervals for biological neurons that generate repetitive bursts of impulses can display stereotyped structures (neuronal signatures). Such structures have been linked to the possibility of multicoding and multifunctionality in neural networks that produce and control rhythmical motor patterns. In some cases, isolating the neurons from their synaptic network reveals irregular, complex signatures that have been regarded as evidence of intrinsic, chaotic behavior. We show that incorporation of dynamical noise into minimal neuron models of square-wave bursting (either conductance-based or abstract) produces signatures akin to those observed in biological examples, without the need for fine tuning of parameters or ad hoc constructions for inducing chaotic activity. The form of the stochastic term is not strongly constrained and can approximate several possible sources of noise, e.g., random channel gating or synaptic bombardment. The cornerstone of this signature generation mechanism is the rich, transient, but deterministic dynamics inherent in the square-wave (saddle-node and homoclinic) mode of neuronal bursting. We show that noise causes the dynamics to populate a complex transient scaffolding or skeleton in state space, even for models that (without added noise) generate only periodic activity (whether in bursting or tonic spiking mode).

In spatial evolutionary games the payoff matrices are used to describe pair interactions among neighboring players located on a lattice. Now we introduce a way how the payoff matrices can be built up as a sum of payoff components reflecting basic symmetries. For the two-strategy games this decomposition reproduces interactions characteristic to the Ising model. For the three-strategy symmetric games the Fourier components can be classified into four types representing games with self-dependent and cross-dependent payoffs, variants of three-strategy coordinations, and the rock-scissors-paper (RSP) game. In the absence of the RSP component the game is a potential game. The resultant potential matrix has been evaluated. The general features of these systems are analyzed when the game is expressed by the linear combinations of these components.

A method of averaging is applied to study the dynamics of a kink in the damped double sine-Gordon equation driven by both external (nonparametric) and parametric periodic forces at high frequencies. This theoretical approach leads to the study of a double sine-Gordon equation with an effective potential and an effective additive force. Direct numerical simulations show how the appearance of two connected $\pi$ kinks and of an individual $\pi$ kink can be controlled via the frequency. An anomalous negative mobility phenomenon is also predicted by theory and confirmed by simulations of the original equation.

We consider a general class of maps of the interval having Lyapunov subexponential instability $|\delta x_t|\sim |\delta x_0|exp\left[{\Lambda }_t\left(x_0\right)\zeta \left(t\right)\right]$, where $\zeta \left(t\right)$ grows sublinearly as $t\to \infty$. We outline here a scheme [J. Stat. Phys. 154, 988 (2014)] whereby the choice of a characteristic function automatically defines the map equation and corresponding growth rate $\zeta \left(t\right)$. This matching approach is based on the infinite measure property of such systems. We show that the average information that is necessary to record without ambiguity a trajectory of the system tends to $\langle \Lambda \rangle \zeta \left(t\right)$, suitably extending the Kolmogorov-Sinai entropy and Pesin's identity. For such systems, information behaves like a random variable for random initial conditions, its statistics obeying a universal Mittag-Leffler law. We show that, for individual trajectories, information can be accurately inferred by the number of first-passage times through a given turbulent phase-space cell. This enables us to calculate far more efficiently Lyapunov exponents for such systems. Lastly, we also show that the usual renewal description of jumps to the turbulent cell, usually employed in the literature, does not provide the real number of entrances there. Our results are supported by exhaustive numerical simulations.

Self-organized quasiperiodicity is one of the most puzzling dynamical phases observed in systems of nonlinear coupled oscillators. The single dynamical units are not locked to the periodic mean field they produce, but they still feature a coherent behavior, through an unexplained complex form of correlation. We consider a class of leaky integrate-and-fire oscillators on random sparse and massive networks with dynamical synapses, featuring self-organized quasiperiodicity, and we show how complex collective oscillations arise from constructive interference of microscopic dynamics. In particular, we find a simple quantitative relationship between two relevant microscopic dynamical time scales and the macroscopic time scale of the global signal. We show that the proposed relation is a general property of collective oscillations, common to all the partially synchronous dynamical phases analyzed. We argue that an analogous mechanism could be at the origin of similar network dynamics.

The widely used Nose-Hoover chain (NHC) thermostat in molecular dynamics simulations is generally believed to impart the canonical distribution as well as quasi- (i.e., space-filling) ergodicity on the thermostatted physical system (PS). Working with the standard single harmonic oscillator, we prove analytically that the two-chain Nose-Hoover thermostat with unequal thermostat masses approaches the standard Nose-Hoover dynamics, and hence the PS loses its canonical and quasiergodic nature. We also show through numerical simulations over substantially long times that for certain Poincaré sections, for both the equal and unequal thermostat mass cases, the bivariate distribution function of position and momentum $\left(x,p\right)$ and of reservoir degrees of freedom $\left(\xi ,\eta \right)$ lose their Gaussian nature. Further, the four-dimensional $x\text{−}p\text{−}\xi \text{−}\eta$ extended phase space exhibits two holes of nonzero measure. The NHC thermostat therefore does not generate the canonical distribution or preserve quasiergodicity for the PS.

The driving mechanism and the swirl direction of the bathtub vortex are investigated by the linear stability analysis of the no-vortex flow as well as numerical simulations. We find that only systems having plane symmetries with respect to vertical planes deserve research for the swirl direction. The bathtub vortex appearing in a vessel with a rectangular cross section having a drain hole at the center of the bottom is proved to be induced by instability when the flow rate exceeds a threshold. The Coriolis force is capable of determining the swirl direction to be cyclonic.

Two-dimensional hybrid simulations of super-Alfvénic expanding debris plasma interacting with an inhomogeneous ambient plasma are presented. The simulations demonstrate improved collisionless coupling of energy to the ambient ions when encountering a density gradient. Simulations of an expanding cylinder running into a step function gradient are performed and compared to a simple analytical theory. Magnetic flux probe data from a laboratory shock experiment are compared to a simulation with a more realistic debris expansion and ambient ion density. The simulation confirms that a shock is formed and propagates within the high density region of ambient plasma.

We carefully reexamine the conditions of validity for the consistent derivation of the Lifshitz-Matsubara sum formula for the Casimir pressure between metallic plane mirrors. We recover the usual expression for the lossy Drude model but not for the lossless plasma model. We give an interpretation of this new result in terms of the modes associated with the Foucault currents, which play a role in the limit of vanishing losses, in contrast to common expectations.

We study the optimal exergy efficiency and power for thermodynamic systems with an Onsager-type “current-force” relationship describing the linear response to external influences. We derive, in analytic forms, the maximum efficiency and optimal efficiency for maximum power for a thermodynamic machine described by a $N\times N$ symmetric Onsager matrix with arbitrary integer $N$. The figure of merit is expressed in terms of the largest eigenvalue of the “coupling matrix” which is solely determined by the Onsager matrix. Some simple but general relationships between the power and efficiency at the conditions for (i) maximum efficiency and (ii) optimal efficiency for maximum power are obtained. We show how the second law of thermodynamics bounds the optimal efficiency and the Onsager matrix and relate those bounds together. The maximum power theorem (Jacobi's Law) is generalized to all thermodynamic machines with a symmetric Onsager matrix in the linear-response regime. We also discuss systems with an asymmetric Onsager matrix (such as systems under magnetic field) for a particular situation and we show that the reversible limit of efficiency can be reached at finite output power. Cooperative effects are found to improve the figure of merit significantly in systems with multiply cross-correlated responses. Application to example systems demonstrates that the theory is helpful in guiding the search for high performance materials and structures in energy researches.

Particle-stabilized emulsions are commonly used in various industrial applications. These emulsions can present in different forms, such as Pickering emulsions or bijels, which can be distinguished by their different topologies and rheology. We numerically investigate the effect of the volume fraction and the uniform wettability of the stabilizing spherical particles in mixtures of two fluids. For this, we use the well-established three-dimensional lattice Boltzmann method, extended to allow for the added colloidal particles with non-neutral wetting properties. We obtain data on the domain sizes in the emulsions by using both structure functions and the Hoshen-Kopelman (HK) algorithm, and we demonstrate that both methods have their own (dis)advantages. We confirm an inverse dependence between the concentration of particles and the average radius of the stabilized droplets. Furthermore, we demonstrate the effect of particles detaching from interfaces on the emulsion properties and domain-size measurements.

We investigate the segregation pattern formation of strongly and weakly fluctuating Brownian particle mixtures confined in a three-dimensional spherical container. We consider systems where the particle motion is restricted by the harmonic external trapping potential and the container edge wall. In such systems, two segregation patterns are observed. When the container radius is sufficiently large, more weakly fluctuating particles accumulate near the center of the container than strongly fluctuating particles. On the other hand, the distributions of the strongly and weakly fluctuating particles are inverted when the container radius is small. With no external trapping potentials, we find similar segregation and phase inversion if the particles construct a chain (heterofluctuating polymer) and are confined in a three-dimensional spherical container. We could apply these phenomena in the study of biopolymer behavior, such as chromosomes in the cell nucleus.