A partially wetting plate withdrawn from a liquid reservoir causes the deposition of a liquid film that is characterized by inclined contact lines. It has been experimentally indicated that the normal component of the contact-line velocity relative to the plate remains constant and is independent of the inclination angles, a fact that has never theoretically been justified. We demonstrate, in the framework of lubrication theory, that the speed-angle independence is only approximate and the normal velocity actually exhibits a weak decrease with the inclination angle of the contact line. This correlation is attributed to the variation of the effective separation of microscopic and macroscopic length scales. In addition, the inclination of the contact line results in a tangential flux of the liquid, which is confined in the vicinity of the contact line. Simple scaling relations are provided for both the normal velocity and the tangential flux.

The pseudopotential lattice Boltzmann method has been widely used to simulate many multiphase flow applications. However, there still exist problems with reproducing realistic values of density ratio and surface tension. In this study, a higher-order analysis of a general forcing term is derived. A forcing scheme is then constructed for the pseudopotential method that is able to accurately reproduce the full range of coexistence curves. As a result, multiphase flow of arbitrarily high density ratios independent of the surface tension can be simulated. Furthermore, the interface width can be tuned to allow for grid refinement and systematic error reduction. Numerical results confirm that the proposed scheme enables independent control of density ratio, surface tension, and interface width simultaneously.

We show that underdamped molecular vibrations fuel the efficient excitation energy transfer in the Fenna-Matthews-Olson molecular aggregate under realistic physiological conditions. By employing an environmental fluctuation spectral function derived from experiments, we obtain numerically exact results for the exciton quantum dynamics in the presence of underdamped vibrationally coherent quantum states. Assuming the prominent $180-{\mathrm{cm}}^{-1}$ vibrational mode to be underdamped, additional coherent transport channels for the excitation energy transfer open up and we observe an increase of the transfer speed towards the reaction center by up to $24\%$.

We propose a network metric, edge proximity, ${\mathcal{P}}_e$, which demonstrates the importance of specific edges in a network, hitherto not captured by existing network metrics. The effects of removing edges with high ${\mathcal{P}}_e$ might initially seem inconspicuous but are eventually shown to be very harmful for networks. Compared to existing strategies, the removal of edges by ${\mathcal{P}}_e$ leads to a remarkable increase in the diameter and average shortest path length in undirected real and random networks till the first disconnection and well beyond. ${\mathcal{P}}_e$ can be consistently used to rupture the network into two nearly equal parts, thus presenting a very potent strategy to greatly harm a network. Targeting by ${\mathcal{P}}_e$ causes notable efficiency loss in U.S. and European power grid networks. ${\mathcal{P}}_e$ identifies proteins with essential cellular functions in protein-protein interaction networks. It pinpoints regulatory neural connections and important portions of the neural and brain networks, respectively. Energy flow interactions identified by ${\mathcal{P}}_e$ form the backbone of long food web chains. Finally, we scrutinize the potential of ${\mathcal{P}}_e$ in edge controllability dynamics of directed networks.

We report different types of chimera states in the Kuramoto model with inertia. They arise on the route from coherence, via so-called solitary states, to the rotating waves. We identify the wide region in parameter space, in which a different type of chimera state, i.e., the imperfect chimera state, which is characterized by a certain number of oscillators that have escaped from the synchronized chimera's cluster, appears. We describe a mechanism for the creation of chimera states via the appearance of the solitary states. Our findings reveal that imperfect chimera states represent characteristic spatiotemporal patterns at the transition from coherence to incoherence.

The linear stability analysis of a plane Couette flow of an Oldroyd-B viscoelastic fluid past a flexible solid medium is carried out to investigate the role of polymer addition in the stability behavior. The system consists of a viscoelastic fluid layer of thickness $R$, density $\rho$, viscosity $\eta$, relaxation time $\lambda$, and retardation time $\beta \lambda$ flowing past a linear elastic solid medium of thickness $HR$, density $\rho$, and shear modulus $G$. The emphasis is on the high-Reynolds-number wall-mode instability, which has recently been shown in experiments to destabilize the laminar flow of Newtonian fluids in soft-walled tubes and channels at a significantly lower Reynolds number than that for flows in rigid conduits. For Newtonian fluids, the linear stability studies have shown that the wall modes become unstable when flow Reynolds number exceeds a certain critical value ${\mathrm{Re}}_c$ which scales as ${\Sigma }^{3/4}$, where Reynolds number $\mathrm{Re}=\rho VR/\eta ,V$ is the top-plate velocity, and dimensionless parameter $\Sigma =\rho G{R}^2/{\eta }^2$ characterizes the fluid-solid system. For high-Reynolds-number flow, the addition of polymer tends to decrease the critical Reynolds number in comparison to that for the Newtonian fluid, indicating a destabilizing role for fluid viscoelasticity. Numerical calculations show that the critical Reynolds number could be decreased by up to a factor of 10 by the addition of small amount of polymer. The critical Reynolds number follows the same scaling ${\mathrm{Re}}_c\sim {\Sigma }^{3/4}$ as the wall modes for a Newtonian fluid for very high Reynolds number. However, for moderate Reynolds number, there exists a narrow region in $\beta \text{−}H$ parametric space, corresponding to very dilute polymer solution $(0.9\lesssim \beta <1)$ and thin solids $(H\lesssim 1.1)$, in which the addition of polymer tends to increase the critical Reynolds number in comparison to the Newtonian fluid. Thus, Reynolds number and polymer properties can be tailored to either increase or decrease the critical Reynolds number for unstable modes, thus providing an additional degree of control over the laminar-turbulent transition.

We investigate the effects of smooth inhomogeneities at first-order quantum transitions (FOQTs), such as those arising in the presence of a space-dependent external field, which smooths out the discontinuities of the low-energy properties at the transition. We argue that a universal scaling behavior emerges in the space transition region close to the point in which the external field takes the value for which the homogeneous system undergoes the FOQT. We verify the general theory in two model systems. We consider the quantum Ising chain in the ferromagnetic phase and the $q$-state Potts chain for $q=10$, investigating the scaling behavior which arises in the presence of an additional inhomogeneous parallel and transverse magnetic field, respectively. Numerical results are in full agreement with the general theory.

Active particles may happen to be confined in channels so narrow that they cannot overtake each other (single-file conditions). This interesting situation reveals nontrivial physical features as a consequence of the strong interparticle correlations developed in collective rearrangements. We consider a minimal two-dimensional model for active Brownian particles with the aim of studying the modifications introduced by activity with respect to the classical (passive) single-file picture. Depending on whether their motion is dominated by translational or rotational diffusion, we find that active Brownian particles in single file may arrange into clusters that are continuously merging and splitting (active clusters) or merely reproduce passive-motion paradigms, respectively. We show that activity conveys to self-propelled particles a strategic advantage for trespassing narrow channels against external biases (e.g., the gravitational field).

We study the thermodynamic Casimir force for films with various types of boundary conditions and the bulk universality class of the three-dimensional Ising model. To this end, we perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. In particular, we employ the exchange or geometric cluster cluster algorithm [Heringa and Blöte, Phys. Rev. E 57, 4976 (1998)]. In a previous work, we demonstrated that this algorithm allows us to compute the thermodynamic Casimir force for the plate-sphere geometry efficiently. It turns out that also for the film geometry a substantial reduction of the statistical error can achieved. Concerning physics, we focus on $(O,O)$ boundary conditions, where $O$ denotes the ordinary surface transition. These are implemented by free boundary conditions on both sides of the film. Films with such boundary conditions undergo a phase transition in the universality class of the two-dimensional Ising model. We determine the inverse transition temperature for a large range of thicknesses $L_0$ of the film and study the scaling of this temperature with $L_0$. In the neighborhood of the transition, the thermodynamic Casimir force is affected by finite size effects, where finite size refers to a finite transversal extension $L$ of the film. We demonstrate that these finite size effects can be computed by using the universal finite size scaling function of the free energy of the two-dimensional Ising model.

Supercritical fluids are widely used in a number of important technological applications, yet the theoretical progress in the field has been rather moderate. Fairly recently, a new understanding of the liquidlike and gaslike properties of supercritical fluids has come to the fore, particularly with the advent of the Widom and Frenkel lines that aim to demarcate different physical properties on the phase diagram. Here, we report the results of a computational study of supercritical carbon dioxide, one of the most important fluids in the chemical industry. We study the response functions of ${\mathrm{CO}}_2$ in the supercritical state and calculate the locations of their maxima (Widom lines). We also report the preliminary calculations of the Frenkel line, the line of crossover of microscopic dynamics of particles. Our insights are relevant to physical processes in the atmosphere of Venus and its evolution.

We present experimental measurements of penetration depths for the impact of spheres into wetted granular media. We observe that the penetration depth in the liquid saturated case scales with projectile density, size, and drop height in a fashion consistent with the scaling observed in the dry case, but with smaller penetrations. Neither viscous drag nor density effects can explain the enhancement to the stopping force. The penetration depth exhibits a complicated dependence on liquid fraction, accompanied by a change in the drop-height dependence, that must be the consequence of accompanying changes in the conformation of the liquid phase in the interstices.

I investigate the possibility that electrically neutral porous spheres electrophorese in electrolyte solutions with asymmetric affinity of ions to spheres on the basis of electrohydrodynamics and the Poisson–Boltzmann and Debye–Bueche–Brinkman theories. Assuming a weak electric field and ignoring the double-layer polarization, I obtain analytical expressions for electrostatic potential, electrophoretic mobility, and flow field. In the equilibrium state, the Galvani potential forms across the interface of the spheres. Under a weak electric field, the spheres show finite mobility with the same sign as the Galvani potential. When the radius of the spheres is significantly larger than the Debye and hydrodynamic screening length, the mobility monotonically increases with increasing salinity.

X-ray free-electron lasers have enabled femtosecond protein nanocrystallography, a novel method to determine the structure of proteins. It allows time-resolved imaging of nanocrystals that are too small for conventional crystallography. The short pulse duration helps in overcoming the detrimental effects of radiation damage because x rays are scattered before the sample has been significantly altered. It has been suggested that, fortuitously, the diffraction process self-terminates abruptly once radiation damage destroys the crystalline order. Our calculations show that high-intensity x-ray pulses indeed trigger a cascade of damage processes in ferredoxin crystals, a particular metalloprotein of interest. However, we found that the damage process is initially not completely random. Correlations exist among the protein monomers, so that Bragg diffraction still occurs in the damaged crystals, despite significant atomic displacements. Our results show that the damage process is reproducible to a certain degree, which is potentially beneficial for the orientation step in single-molecule imaging.

Recently large-scale cascading failures in complex systems have garnered substantial attention. Such extreme events have been treated as an integral part of self-organized criticality (SOC). Recent empirical work has suggested that some extreme events systematically deviate from the SOC paradigm, requiring a different theoretical framework. We shed additional theoretical light on this possibility by studying financial crisis. We build our model of financial crisis on the well-known forest fire model in scale-free networks. Our analysis shows a nontrivial scaling feature indicating supercritical behavior, which is independent of system size. Extreme events in the supercritical state result from bursting of a fat bubble, seeds of which are sown by a protracted period of a benign financial environment with few shocks. Our findings suggest that policymakers can control the magnitude of financial meltdowns by keeping the economy operating within reasonable duration of a benign environment.

The state transition between the Peregrine rogue wave and W-shaped traveling wave induced by higher-order effects and background frequency is studied. We find that this intriguing transition, described by an exact explicit rational solution, is consistent with the modulation instability (MI) analysis that involves a MI region and a stability region in a low perturbation frequency region. In particular, the link between the MI growth rate and the transition characteristic analytically demonstrates that the localization characteristic of transition is positively associated with the reciprocal of the zero-frequency growth rate. Furthermore, we investigate the case for nonlinear interplay of multilocalized waves. It is interesting that the interaction of second-order waves in the stability region features a line structure rather than an elastic interaction between two W-shaped traveling waves.

Dynamical systems often contain oscillatory forces or depend on periodic potentials. Time or space periodicity is reflected in the properties of these systems through a dependence on the parameters of their periodic terms. In this paper we provide a general theoretical framework for dealing with these kinds of systems, regardless of whether they are classical or quantum, stochastic or deterministic, dissipative or nondissipative, linear or nonlinear, etc. In particular, we are able to show that simple symmetry considerations determine, to a large extent, how their properties depend functionally on some of the parameters of the periodic terms. For the sake of illustration, we apply this formalism to find the functional dependence of the expectation value of the momentum of a Bose-Einstein condensate, described by the Gross-Pitaewskii equation, when it is exposed to a sawtooth potential whose amplitude is periodically modulated in time. We show that, by using this formalism, a small set of measurements is enough to obtain the functional form for a wide range of parameters. This can be very helpful when characterizing experimentally the response of systems for which performing measurements is costly or difficult.

We investigate high-dimensional nonlinear dynamical systems exhibiting multiple resonances under adiabatic parameter variations. Our motivations come from experimental considerations where time-dependent sweeping of parameters is a practical approach to probing and characterizing the bifurcations of the system. The question is whether bifurcations so detected are faithful representations of the bifurcations intrinsic to the original stationary system. Utilizing a harmonically forced, closed fluid flow system that possesses multiple resonances and solving the Navier-Stokes equation under proper boundary conditions, we uncover the phenomenon of the early effect. Specifically, as a control parameter, e.g., the driving frequency, is adiabatically increased from an initial value, resonances emerge at frequency values that are lower than those in the corresponding stationary system. The phenomenon is established by numerical characterization of physical quantities through the resonances, which include the kinetic energy and the vorticity field, and a heuristic analysis based on the concept of instantaneous frequency. A simple formula is obtained which relates the resonance points in the time-dependent and time-independent systems. Our findings suggest that, in general, any true bifurcation of a nonlinear dynamical system can be unequivocally uncovered through adiabatic parameter sweeping, in spite of a shift in the bifurcation point, which is of value to experimental studies of nonlinear dynamical systems.

The laws of thermodynamics constrain the formulation of statistical mechanics at the microscopic level. The third law of thermodynamics states that the entropy must vanish at absolute zero temperature for systems with nondegenerate ground states in equilibrium. Conversely, the entropy can vanish only at absolute zero temperature. Here we ask whether or not generalized entropies satisfy this fundamental property. We propose a direct analytical procedure to test if a generalized entropy satisfies the third law, assuming only very general assumptions for the entropy $S$ and energy $U$ of an arbitrary $N$-level classical system. Mathematically, the method relies on exact calculation of $\beta =dS/dU$ in terms of the microstate probabilities $p_i$. To illustrate this approach, we present exact results for the two best known generalizations of statistical mechanics. Specifically, we study the Kaniadakis entropy $S_{\kappa }$, which is additive, and the Tsallis entropy $S_q$, which is nonadditive. We show that the Kaniadakis entropy correctly satisfies the third law only for $-1<\kappa <+1$, thereby shedding light on why $\kappa$ is conventionally restricted to this interval. Surprisingly, however, the Tsallis entropy violates the third law for $q<1$. Finally, we give a concrete example of the power of our proposed method by applying it to a paradigmatic system: the one-dimensional ferromagnetic Ising model with nearest-neighbor interactions.