We experiment the interaction between a liquid puddle and a spherical probe by Atomic Force Microscopy (AFM) for a probe radius $R$ ranging from 10 nm to 30 $\mu \mathrm{m}$. We have developed a new experimental setup by coupling an AFM with a high-speed camera and an inverted optical microscope. Interaction force-distance curves (in contact mode) and frequency shift–distance curves (in frequency modulation mode) are measured for different bulk model liquids for which the probe-liquid Hamaker constant $H_{pl}$ is known. The experimental results, analyzed in the frame of the theoretical model developed in Phys. Rev. Lett. 108, 106104 (2012) and Phys. Rev. E 85, 061602 (2012), allow to determine the “jump-to-contact” critical distance $d_{\min }$ below which the liquid jumps and wets the probe. Comparison between theory and experiments shows that the probe-liquid interaction at nanoscale is controlled by the liquid interface deformation. This work shows a very good agreement between the theoretical model and the experiments and paves the way to experimental studies of liquids at the nanoscale.

A theory is developed for the modeling of acoustic streaming in a microfluidic channel confined between an elastic solid wall and a rigid reflector. A situation is studied where the acoustic streaming is produced by two leaky surface waves that propagate towards each other in the solid wall and thus form a combined standing wave in the fluid. Full analytical solutions are found for both the linear acoustic field and the field of the acoustic streaming. A dispersion equation is derived that allows one to calculate the wave speed in the system under study. The obtained solutions are used to consider particular numerical examples and to reveal the structure of the acoustic streaming. It is shown that two systems of vortices are established along the boundaries of the microfluidic channel.

The Richtmyer-Meshkov instability for the case of a reflected rarefaction is studied in detail following the growth of the contact surface in the linear regime and providing explicit analytical expressions for the asymptotic velocities in different physical limits. This work is a continuation of the similar problem when a shock is reflected [Phys. Rev. E 93, 053111 (2016)]. Explicit analytical expressions for the asymptotic normal velocity of the rippled surface ($\delta v_i^{\infty }$) are shown. The known analytical solution of the perturbations growing inside the rarefaction fan is coupled to the pressure perturbations between the transmitted shock front and the rarefaction trailing edge. The surface ripple growth (${\psi }_i$) is followed from $t=0+$ up to the asymptotic stage inside the linear regime. As in the shock reflected case, an asymptotic behavior of the form ${\psi }_i\left(t\right)\cong {\psi }_{\infty }+\delta v_i^{\infty }t$ is observed, where ${\psi }_{\infty }$ is an asymptotic ordinate to the origin. Approximate expressions for the asymptotic velocities are given for arbitrary values of the shock Mach number. The asymptotic velocity field is calculated at both sides of the contact surface. The kinetic energy content of the velocity field is explicitly calculated. It is seen that a significant part of the motion occurs inside a fluid layer very near the material surface in good qualitative agreement with recent simulations. The important physical limits of weak and strong shocks and high and low preshock density ratio are also discussed and exact Taylor expansions are given. The results of the linear theory are compared to simulations and experimental work [R. L. Holmes et al., J. Fluid Mech. 389, 55 (1999); C. Mariani et al., Phys. Rev. Lett. 100, 254503 (2008)]. The theoretical predictions of $\delta v_i^{\infty }$ and ${\psi }_{\infty }$ show good agreement with the experimental and numerical reported values.

We investigate how next-generation laser pulses at $10\text{–}200\mathrm{PW}$ interact with a solid target in the presence of a relativistically underdense preplasma produced by amplified spontaneous emission (ASE). Laser hole boring and relativistic transparency are strongly restrained due to the generation of electron-positron pairs and $\gamma$-ray photons via quantum electrodynamics (QED) processes. A pair plasma with a density above the initial preplasma density is formed, counteracting the electron-free channel produced by hole boring. This pair-dominated plasma can block laser transport and trigger an avalanchelike QED cascade, efficiently transferring the laser energy to the photons. This renders a $1\text{−}\mu \mathrm{m}$ scale-length, underdense preplasma completely opaque to laser pulses at this power level. The QED-induced opacity therefore sets much higher contrast requirements for such a pulse in solid-target experiments than expected by classical plasma physics. Our simulations show, for example, that proton acceleration from the rear of a solid with a preplasma would be strongly impaired.

We present a multiresolution approach to compressing the degrees of freedom and potentials associated with molecular dynamics, such as the bond potentials. The approach suggests a systematic way to accelerate large-scale molecular simulations with more than two levels of coarse graining, particularly applications of polymeric materials. In particular, we derive explicit models for (arbitrarily large) linear (homo)polymers and iterative methods to compute large-scale wavelet decompositions from fragment solutions. This approach does not require explicit preparation of atomistic-to-coarse-grained mappings, but instead uses the theory of diffusion wavelets for graph Laplacians to develop system-specific mappings. Our methodology leads to a hierarchy of system-specific coarse-grained degrees of freedom that provides a conceptually clear and mathematically rigorous framework for modeling chemical systems at relevant model scales. The approach is capable of automatically generating as many coarse-grained model scales as necessary, that is, to go beyond the two scales in conventional coarse-grained strategies; furthermore, the wavelet-based coarse-grained models explicitly link time and length scales. Furthermore, a straightforward method for the reintroduction of omitted degrees of freedom is presented, which plays a major role in maintaining model fidelity in long-time simulations and in capturing emergent behaviors.

The immersed-boundary lattice-Boltzmann method (IB-LBM) is increasingly being used in simulations of dense suspensions. These systems are computationally very expensive and can strongly benefit from lower resolutions that still maintain the desired accuracy for the quantities of interest. IB-LBM has a number of free parameters that have to be defined, often without exact knowledge of the tradeoffs, since their behavior in low resolutions is not well understood. Such parameters are the lattice constant $\mathrm{\Delta }x$, the number of vertices $N_v$, the interpolation kernel $\varphi$, and the LBM relaxation time $\tau$. We investigate the effect of these IB-LBM parameters on a number of straightforward but challenging benchmarks. The systems considered are (a) the flow of a single sphere in shear flow, (b) the collision of two spheres in shear flow, and (c) the lubrication interaction of two spheres. All benchmarks are performed in three dimensions. The first two systems are used for determining two effective radii: the hydrodynamic radius $r_{\mathrm{hyd}}$ and the particle interaction radius $r_{\mathrm{inter}}$. The last system is used to establish the numerical robustness of the lubrication forces, used to probe the hydrodynamic interactions in the limit of small gaps. Our results show that lower spatial resolutions result in larger hydrodynamic and interaction radii, while surface densities should be chosen above two vertices per ${\mathrm{LU}}^2$ result to prevent fluid penetration in underresolved meshes. Underresolved meshes also failed to produce the migration of particles toward the center of the domain due to lift forces in Couette flow, mostly noticeable for IBM-kernel ${\varphi }_2$. Kernel ${\varphi }_4$, despite being more robust toward mesh resolution, produces a notable membrane thickness, leading to the breakdown of the lubrication forces in larger gaps, and its use in dense suspensions where the mean particle distances are small can result in undesired behavior. $r_{\mathrm{hyd}}$ is measured to be different from $r_{\mathrm{inter}}$, suggesting that there is no consistent measure to recalibrate the radius of the suspended particle.

We study edge fluctuations of a flat colloidal membrane comprised of a monolayer of aligned filamentous viruses. Experiments reveal that a peak in the spectrum of the in-plane edge fluctuations arises for sufficiently strong virus chirality. Accounting for internal liquid crystalline degrees of freedom by the length, curvature, and geodesic torsion of the edge, we calculate the spectrum of the edge fluctuations. The theory quantitatively describes the experimental data, demonstrating that chirality couples in-plane and out-of-plane edge fluctuations to produce the peak.

We consider diffusion-controlled evolution of a $d$-dimensional $A$-particle island in the $B$-particle sea at propagation of the sharp reaction front $A+B\to 0$ at equal species diffusivities. The $A$-particle island is formed by a localized (point) $A$-source with a strength $\lambda$ that acts for a finite time $T$. We reveal the conditions under which the island collapse time $t_c$ becomes much longer than the injection period $T$ (long-living island) and demonstrate that regardless of $d$ the evolution of the long-living island radius $r_f\left(t\right)$ is described by the universal law ${\zeta }_f=r_f/r_f^M=\sqrt{e\tau |ln\tau |}$, where $\tau =t/t_c$ and $r_f^M$ is the maximal island expansion radius at the front turning point $t_M=t_c/e$. We find that in the long-living island regime the ratio $t_c/T$ changes with the increase of the injection period $T$ by the law $\propto {\left({\lambda }^2{T}^{2-d}\right)}^{1/d}$, i.e., increases with the increase of $T$ in the one-dimensional (1D) case, does not change with the increase of $T$ in the 2D case and decreases with the increase of $T$ in the 3D case. We derive the scaling laws for particles death in the long-living island and determine the limits of their applicability. We demonstrate also that these laws describe asymptotically the evolution of the $d$-dimensional spherical island with a uniform initial particle distribution generalizing the results obtained earlier for the quasi-one-dimensional geometry. As striking results, we present a systematic analysis of the front relative width evolution for fluctuation, logarithmically modified, and mean-field regimes, and we demonstrate that in a wide range of parameters the front remains sharp up to a narrow vicinity of the collapse point.

An important problem in statistical physics concerns the fascinating connections between partition functions of lattice models studied in equilibrium statistical mechanics on the one hand and graph theoretical enumeration problems on the other hand. We investigate the nature of the relationship between the number of spanning trees and the partition function of the Ising model on the square lattice. The spanning tree generating function $T\left(z\right)$ gives the spanning tree constant when evaluated at $z=1$, while giving the lattice green function when differentiated. It is known that for the infinite square lattice the partition function $Z\left(K\right)$ of the Ising model evaluated at the critical temperature $K=K_c$ is related to $T\left(1\right)$. Here we show that this idea in fact generalizes to all real temperatures. We prove that ${\left[Z\left(K\right)sech2K\right]}^2=kexp\left[T\left(k\right)\right]$ , where $k=2tanh\left(2K\right)sech\left(2K\right)$. The identical Mahler measure connects the two seemingly disparate quantities $T\left(z\right)$ and $Z\left(K\right)$. In turn, the Mahler measure is determined by the random walk structure function. Finally, we show that the the above correspondence does not generalize in a straightforward manner to nonplanar lattices.

We analyze the thermodynamic costs of the three main approaches to generating random numbers via the recently introduced Information Processing Second Law. Given access to a specified source of randomness, a random number generator (RNG) produces samples from a desired target probability distribution. This differs from pseudorandom number generators (PRNGs) that use wholly deterministic algorithms and from true random number generators (TRNGs) in which the randomness source is a physical system. For each class, we analyze the thermodynamics of generators based on algorithms implemented as finite-state machines, as these allow for direct bounds on the required physical resources. This establishes bounds on heat dissipation and work consumption during the operation of three main classes of RNG algorithms—including those of von Neumann, Knuth, and Yao and Roche and Hoshi—and for PRNG methods. We introduce a general TRNG and determine its thermodynamic costs exactly for arbitrary target distributions. The results highlight the significant differences between the three main approaches to random number generation: One is work producing, one is work consuming, and the other is potentially dissipation neutral. Notably, TRNGs can both generate random numbers and convert thermal energy to stored work. These thermodynamic costs on information creation complement Landauer's limit on the irreducible costs of information destruction.

We employ the heat perturbation correlation function to study thermal transport in the one-dimensional Fermi-Pasta-Ulam-$\beta$ lattice with both nearest-neighbor and next-nearest-neighbor couplings. We find that such a system bears a peculiar phonon dispersion relation, and thus there exists a competition between phonon dispersion and nonlinearity that can strongly affect the heat correlation function's shape and scaling property. Specifically, for small and large anharmoncities, the scaling laws are ballistic and superdiffusive types, respectively, which are in good agreement with the recent theoretical predictions; whereas in the intermediate range of the nonlinearity, we observe an unusual multiscaling property characterized by a nonmonotonic delocalization process of the central peak of the heat correlation function. To understand these multiscaling laws, we also examine the momentum perturbation correlation function and find a transition process with the same turning point of the anharmonicity as that shown in the heat correlation function. This suggests coupling between the momentum transport and the heat transport, in agreement with the theoretical arguments of mode cascade theory.

Canonical models for studying the unjamming scenario in systems of soft repulsive particles assume pairwise potentials with a sharp cutoff in the interaction range. The sharp cutoff renders the potential nonanalytic but makes it possible to describe many properties of the solid in terms of the coordination number $z$, which has an unambiguous definition in these cases. Pairwise potentials without a sharp cutoff in the interaction range have not been studied in this context, but should in fact be considered to understand the relevance of the unjamming phenomenology in systems where such a cutoff is not present. In this work we explore two systems with such interactions: an inverse power law and an exponentially decaying pairwise potential, with the control parameters being the exponent (of the inverse power law) for the former and the number density for the latter. Both systems are shown to exhibit the characteristic features of the unjamming transition, among which are the vanishing of the shear–to–bulk modulus ratio and the emergence of an excess of low-frequency vibrational modes. We establish a relation between the pressure–to–bulk modulus ratio and the distance to unjamming in each of our model systems. This allows us to predict the dependence of other key observables on the distance to unjamming. Our results provide the means for a quantitative estimation of the proximity of generic glass-forming models to the unjamming transition in the absence of a clear-cut definition of the coordination number and highlight the general irrelevance of nonaffine contributions to the bulk modulus.

A bosonic gas formed by two interacting species trapped in a double-well potential features macroscopic localization effects when the interspecies interaction becomes sufficiently strong. A repulsive interaction spatially separates the species into different wells while an attractive interaction confines both species in the same well. We perform a fully analytic study of the transitions from the weak- to the strong-interaction regime by exploiting the semiclassical method in which boson populations are represented in terms of continuous variables. We find an explicit description of low-energy eigenstates and spectrum in terms of the model parameters which includes the neighborhood of the transition point. To test the effectiveness of the continuous-variable method we compare its predictions with the exact results found numerically. Numerical calculations confirm the spectral collapse evidenced by this method when the space localization takes place.

We introduce a minimalistic quantum motor for coupled energy and particle transport. The system is composed of two spins, each coupled to a different bath and to a particle which can move on a ring consisting of three sites. We show that the energy flowing from the baths to the system can be partially converted to perform work against an external driving, even in the presence of moderate dissipation. We also analytically demonstrate the necessity of coupling between the spins. We suggest an experimental realization of our model using trapped ions or quantum dots.

When is keeping a memory of observations worthwhile? We use hidden Markov models to look at phase transitions that emerge when comparing state estimates in systems with discrete states and noisy observations. We infer the underlying state of the hidden Markov models from the observations in two ways: through naive observations, which take into account only the current observation, and through Bayesian filtering, which takes the history of observations into account. Defining a discord order parameter to distinguish between the different state estimates, we explore hidden Markov models with various numbers of states and symbols and varying transition-matrix symmetry. All behave similarly. We calculate analytically the critical point where keeping a memory of observations starts to pay off. A mapping between hidden Markov models and Ising models gives added insight into the associated phase transitions.

We study work extraction (defined as the difference between the initial and the final energy) in noninteracting and (effectively) weakly interacting isolated fermionic quantum lattice systems in one dimension, which undergo a sequence of quenches and equilibration. The systems are divided in two parts, which we identify as the subsystem of interest and the bath. We extract work by quenching the on-site potentials in the subsystem, letting the entire system equilibrate, and returning to the initial parameters in the subsystem using a quasistatic process (the bath is never acted upon). We select initial states that are direct products of thermal states of the subsystem and the bath, and consider equilibration to the generalized Gibbs ensemble (GGE, noninteracting case) and to the Gibbs ensemble (GE, weakly interacting case). We identify the class of quenches that, in the thermodynamic limit, results in GE and GGE entropies after the quench that are identical to the one in the initial state (quenches that do not produce entropy). Those quenches guarantee maximal work extraction when thermalization occurs. We show that the same remains true in the presence of integrable dynamics that results in equilibration to the GGE.

We investigate statistical properties of wave turbulence by monitoring the dynamics of ensembles of trajectories. The system under investigation is a simplified model for surface gravity waves in one and two dimensions with a square-root dispersion and a four-wave interaction term. The simulations of decaying turbulence confirm the Kolmogorov-Zakharov spectral power distribution of wave turbulence theory. Fourth-order correlations are computed numerically as ensemble averages of trajectories. The shape, scaling, and time evolution of the correlations agree with the predictions of wave turbulence theory.

We study the exact first-order soliton and breather solutions of the integrable nonlinear Schrödinger equations hierarchy up to fifth order. We reveal the underlying physical mechanism which transforms a breather into a soliton. Furthermore, we show how the dynamics of the Akhmediev breathers which exist on a constant background as a result of modulation instability, is connected with solitons on a zero background. We also demonstrate that, while a first-order rogue wave can be directly transformed into a soliton, higher-order rogue wave solutions become rational two-soliton solutions with complex collisional structure on a background. Our results will have practical implications in supercontinuum generation, turbulence, and similar other complex nonlinear scenarios.

A model of interdependent networks of networks (NONs) was introduced recently [Proc. Natl. Acad. Sci. (USA) 114, 3849 (2017)] in the context of brain activation to identify the neural collective influencers in the brain NON. Here we investigate the emergence of robustness in such a model, and we develop an approach to derive an exact expression for the random percolation transition in Erdös-Rényi NONs of this kind. Analytical calculations are in agreement with numerical simulations, and highlight the robustness of the NON against random node failures, which thus presents a new robust universality class of NONs. The key aspect of this robust NON model is that a node can be activated even if it does not belong to the giant mutually connected component, thus allowing the NON to be built from below the percolation threshold, which is not possible in previous models of interdependent networks. Interestingly, the phase diagram of the model unveils particular patterns of interconnectivity for which the NON is most vulnerable, thereby marking the boundary above which the robustness of the system improves with increasing dependency connections.