We revisit classical nucleation theory (CNT) for the homogeneous bubble nucleation rate and improve the classical formula using a correct prefactor in the nucleation rate. Most of the previous theoretical studies have used the constant prefactor determined by the bubble growth due to the evaporation process from the bubble surface. However, the growth of bubbles is also regulated by the thermal conduction, the viscosity, and the inertia of liquid motion. These effects can decrease the prefactor significantly, especially when the liquid pressure is much smaller than the equilibrium one. The deviation in the nucleation rate between the improved formula and the CNT can be as large as several orders of magnitude. Our improved, accurate prefactor and recent advances in molecular dynamics simulations and laboratory experiments for argon bubble nucleation enable us to precisely constrain the free energy barrier for bubble nucleation. Assuming the correction to the CNT free energy is of the functional form suggested by Tolman, the precise evaluations of the free energy barriers suggest the Tolman length is $\simeq 0.3\sigma$ independently of the temperature for argon bubble nucleation, where $\sigma$ is the unit length of the Lennard-Jones potential. With this Tolman correction and our prefactor one gets accurate bubble nucleation rate predictions in the parameter range probed by current experiments and molecular dynamics simulations.

For a quantum dot system of fixed geometry, in the presence of random impurities the average conductance over an appropriate range of the Fermi energy decreases as the impurity strength is increased. Can the nature of the corresponding classical dynamics in the dot region affect the rate of decrease? Utilizing graphene quantum dots with two semi-infinite, single-mode leads as a prototypical model, we address the device stability issue by investigating the combined effects of classical dynamics and impurities on the average conductance over the energy range of the first transverse mode. We find that, for chaotic dot systems, the rate of decrease in the average conductance with the impurity strength is in general characteristically smaller than that for integrable dots. We develop a semiclassical analysis for the phenomenon and also obtain an understanding based on the random matrix theory. Our results demonstrate that classical chaos can generally lead to a stronger stability in the device performance, strongly advocating exploiting chaos in the development of nanoscale quantum transport devices.

Phase reduction is an invaluable technique for investigating the dynamics of nonlinear limit cycle oscillators. Central to the implementation of phase reduction is the ability to calculate phase response curves (PRCs), which describe an oscillator's response to an external perturbation. Current experimental techniques for inferring PRCs require data from individual oscillators, which can be impractical to obtain when the oscillator is part of a much larger population. Here we present a simple methodology to calculate PRCs of individual oscillators using an aggregate signal from a large homogeneous population. This methodology is shown to be accurate in the presence of interoscillator coupling and noise and can also provide a good estimate of an average PRC of a heterogeneous population. We also find that standard experimental techniques for PRC measurement can produce misleading results when applied to aggregate population data.

Hierarchical porous media are multiscale systems, where different characteristic pore sizes and structures are encountered at each scale. Focusing the analysis to three pore scales, an upscaling procedure based on the volume-averaging method is applied twice, in order to obtain a macroscopic model for momentum and diffusion-dispersion. The effective transport properties at the macroscopic scale (permeability and dispersion tensors) are found to be explicitly dependent on the mesoscopic ones. Closure problems associated to these averaged properties are numerically solved at the different scales for two types of bidisperse porous media. Results show a strong influence of the lower-scale porous structures and flow intensity on the macroscopic effective transport properties.

A composite metallic foil (Al/Mg/Al) has been exposed to intense sub-100 fs free electron laser (FEL) pulses and driven to ultrafast massive photoionization. The resulting nonequilibrium state of matter has been monitored through absorption spectroscopy across the $L_{2,3}$ edge of Mg as a function of the FEL fluence. The raw spectroscopic data indicate that at about $100\mathrm{J}/{\mathrm{cm}}^2$ the main absorption channels of the sample, i.e., Mg $\left(2p\to \text{free}\right)$ and oxidized Al $\left(\text{valence}\to \text{free}\right)$, are almost saturated. The spectral behavior of the induced transparency has been interpreted with an analytical approach based on an effective ionization potential of the generated solid-density plasma.

Small quantum absorption refrigerators have recently attracted renewed attention. Here we present a missing design of a two-qubit fridge, the main feature of which is that one of the two machine qubits is itself maintained at a temperature colder than the cold bath. This is achieved by “reversing” the couplings to the baths compared to previous designs, where only a transition is maintained cold. We characterize the working regime and the efficiency of the fridge. We demonstrate the soundness of the model by deriving and solving a master equation. Finally, we discuss the performance of the fridge, in particular the heat current extracted from the cold bath. We show that our model performs comparably to the standard three-level quantum fridge and thus appears appealing for possible implementations of nanoscale thermal machines.

We study the model of a supercooled liquid for which the equation of motion for the coarse-grained density $\rho (\mathbf{x},t)$ is the nonlinear diffusion equation originally proposed by Dean and Kawasaki, respectively, for Brownian and Newtonian dynamics of fluid particles. Using a Martin-Siggia-Rose (MSR) field theory we study the renormalization of the dynamics in a self-consistent form in terms of the so-called self-energy matrix $\mathrm{\Sigma }$. The appropriate model for the renormalized dynamics involves an extended set of field variables $\{\rho ,\theta \}$, linked through a nonlinear constraint. The latter incorporates, in a nonperturbative manner, the effects of an infinite number of density nonlinearities in the dynamics. We show that the contributing element of $\mathrm{\Sigma }$ which renormalizes the bare diffusion constant $D_0$ to $D_R$ is same as that proposed by Kawasaki and Miyazima [Z. Phys. B Condens. Matter 103, 423 (1997)]. $D_R$ sharply decreases with increasing density. We consider the likelihood of a ergodic-nonergodic (ENE) transition in the model beyond a critical point. The transition is characterized by the long-time limit of the density correlation freezing at a nonzero value. From our analysis we identify an element of $\mathrm{\Sigma }$ which arises from the above-mentioned nonlinear constraint and is key to the viability of the ENE transition. If this self-energy would be zero, then the model supports a sharp ENE transition with $D_R=0$ as predicted by Kawasaki and Miyazima. With the full model having nonzero value for this self-energy, the density autocorrelation function decays to zero in the long-time limit. Hence the ENE transition is not supported in the model.

Recently, the similarity of the functional network of the brain and the Ising model was investigated by Chialvo [Nat. Phys. 6, 744 (2010)]. This similarity supports the idea that the brain is a self-organized critical system. In this study we derive a functional network of the two-dimensional Bak-Tang-Wiesenfeld sandpile model as a self-organized critical model, and compare its characteristics with those of the functional network of the brain, obtained from functional magnetic resonance imaging.

Incomplete mixing of reactive solutes is well known to slow down reaction rates relative to what would be expected from assuming perfect mixing. In purely diffusive systems, for example, it is known that small initial fluctuations in reactant concentrations can lead to reactant segregation, which in the long run can reduce global reaction rates due to poor mixing. In contrast, nonuniform flows can enhance mixing between interacting solutes. Thus, a natural question arises: Can nonuniform flows sufficiently enhance mixing to restrain incomplete mixing effects and, if so, under what conditions? We address this question by considering a specific and simple case, namely, a laminar pure shear reactive flow. Two solution approaches are developed: a Lagrangian random walk method and a semianalytical solution. The results consistently highlight that if shear effects in the system are not sufficiently strong, incomplete mixing effects initially similar to purely diffusive systems will occur, slowing down the overall reaction rate. Then, at some later time, dependent on the strength of the shear, the system will return to behaving as if it were well mixed, but represented by a reduced effective reaction rate.

The propagation of an electromagnetic wave in a uniaxial ferromagnetic nanowire under the spin transfer torque effect is widely investigated in the soliton frame. The magnetization dynamics of the ferromagnetic nanowire is governed by the Landau-Lifshitz-Gilbert (LLG) equation coupled to the Maxwell equation for the electromagnetic wave propagation. A nonuniform multiscale analysis is invoked for the coupled LLG-Maxwell equations and obtains the extended derivative nonlinear Schrödinger (DNLS) equation for the magnetization and external magnetic field. The effect of electric current is explored by constructing multisoliton solutions to the extended DNLS equation and the possibility of the soliton collision is exploited using the Hirota bilinearization procedure.

We report the capillary flow enhancement in rectangular polymer microchannels, when one of the channel walls is a deformable polymer membrane. We provide detailed insight into the physics of elastocapillary interaction between the capillary flow and elastic membrane, which leads to significant improvements in capillary flow performance. As liquid flows by capillary action in such channels, the deformable wall deflects inwards due to the Young-Laplace pressure drop across the liquid meniscus. This, in turn, decreases the radius of curvature of the meniscus and increases the driving capillary pressure. A theoretical model is proposed to predict the resultant increase in filling speed and rise height, respectively, in deformable horizontal and vertical microchannels having large aspect ratios. A non-dimensional parameter $J$, which represents the ratio of the capillary force to the mechanical restoring force, is identified to quantify the elastocapillary effects in terms of the improvement in filling speed (for $J>0.238$) and the condition for channel collapse ($J>1$). The theoretical predictions show good agreement with experimental data obtained using deformable rectangular poly(dimethylsiloxane) microchannels. Both model predictions and experimental data show that over 15% improvement in the Washburn coefficient in horizontal channels, and over 30% improvement in capillary rise height in vertical channels, are possible prior to channel collapse. The proposed technique of using deformable membranes as channel walls is a viable method for capillary flow enhancement in microfluidic devices.

A lattice Boltzmann method (LBM) of multicomponent diffusion is developed to examine multicomponent, noncontinuum mass diffusion in porous media. An additional collision interaction is proposed to mimic the Knudsen diffusion caused by the collision interaction between gas molecules and solid pore walls. Using the improved LBM model, the ternary mixtures diffusion is simulated in fractal porous structures which are reconstructed by the random midpoint displacement algorithm. The effects of fractal characteristics and Knudsen diffusion resistance on the multicomponent diffusion in porous structures are investigated and discussed. The results indicate that the smaller fractal dimension enhances the diffusion rate of gas mixtures in fractal porous structures. When the dimensionless Knudsen diffusion coefficient is less than 20, the presence of Knudsen diffusion resistance reduces the rate of mass diffusion in porous structures obviously, especially for the species with larger molecular weight.

We model both the photostationary state and dynamics of an illuminated, photosensitive, glassy liquid crystalline sheet. To illustrate the interplay between local tilt $\theta$ of the sheet, effective incident intensity, curvature, and dynamics, we adopt the simplest variation of local incident light intensity with angle, that is, $cos\theta$. The tilt in the stationary state never overshoots the vertical, but maximum curvature could be seen in the middle of the sheet for intense light. In dynamics, overshoot and self-eclipsing arise, revealing how important moving fronts of light penetration are. Eclipsing is qualitatively as in the experiments of Yu et al. [Y. Yu, M. Nakano, and T. Ikeda, Nature (London) 425, 145 (2003)].

We examine experimentally the deformation of flexible, microscale helical ribbons with nanoscale thickness subject to viscous flow in a microfluidic channel. Two aspects of flexible microhelices are quantified: the overall shape of the helix and the viscous frictional properties. The frictional coefficients determined by our experiments are consistent with calculated values in the context of resistive-force theory. The deformation of helices by viscous flow is well described by nonlinear finite extensibility. Under distributed loading, the pitch distribution is nonuniform, and from this we identify both linear and nonlinear behavior along the contour length of a single helix. Moreover, flexible helices are found to display reversible global to local helical transitions at a high flow rate.

It is intriguing how multiple molecular motors can perform coordinated and synchronous functions, which is essential in various cellular processes. Recent studies on skeletal muscle might have shed light on this issue, where rather precise motor force regulation was partly attributed to the specific stochastic features of a single attached myosin motor. Though attached motors can randomly detach from actin filaments either through an adenosine triphosphate (ATP) hydrolysis cycle or through “catch-slip bond” breaking, their respective contribution in motor force regulation has not been clarified. Here, through simulating a mechanical model of sarcomere with a coupled Monte Carlo method and finite element method, we find that the stochastic features of an ATP hydrolysis cycle can be sufficient while those of catch-slip bonds can be dispensable for motor force regulation.

We introduce a single-channel opening in a random Hamiltonian and a quantized chaotic map: localization on the opening occurs as a sensible deviation of the wave-function statistics from the predictions of random matrix theory, even in the semiclassical limit. Increasing the coupling to the open channel in the quantum model, we observe a similar picture to resonance trapping, made of a few fast-decaying states, whose left (right) eigenfunctions are entirely localized on the (preimage of the) opening, and plentiful long-lived states, whose probability density is instead suppressed at the opening. For the latter, we derive and test a linear relation between the wave-function intensities and the decay rates, similar to the Breit-Wigner law. We then analyze the statistics of the eigenfunctions of the corresponding (discretized) classical propagator, finding a similar behavior to the quantum system only in the weak-coupling regime.

The nonlinear stability of the asymptotic suction boundary layer is studied numerically, searching for finite-amplitude solutions that bifurcate from the laminar flow state. By changing the boundary conditions for disturbances at the plate from the classical no-slip condition to more physically sound ones, the stability characteristics of the flow may change radically, both for the linearized as well as the nonlinear problem. The wall boundary condition takes into account the permeability $\widehat{K}$ of the plate; for very low permeability, it is acceptable to impose the classical boundary condition ($\widehat{K}=0$). This leads to a Reynolds number of approximately ${\text{Re}}_c=54400$ for the onset of linearly unstable waves, and close to ${\text{Re}}_g=3200$ for the emergence of nonlinear solutions [F. A. Milinazzo and P. G. Saffman, J. Fluid Mech. 160, 281 (1985); J. H. M. Fransson, Ph.D. thesis, Royal Institute of Technology, KTH, Sweden, 2003]. However, for larger values of the plate's permeability, the lower limit for the existence of linear and nonlinear solutions shifts to significantly lower Reynolds numbers. For the largest permeability studied here, the limit values of the Reynolds numbers reduce down to ${\text{Re}}_c=796$ and ${\text{Re}}_g=294$. For all cases studied, the solutions bifurcate subcritically toward lower Re, and this leads to the conjecture that they may be involved in the very first stages of a transition scenario similar to the classical route of the Blasius boundary layer initiated by Tollmien-Schlichting (TS) waves. The stability of these nonlinear solutions is also investigated, showing a low-frequency main unstable mode whose growth rate decreases with increasing permeability and with the Reynolds number, following a power law ${\text{Re}}^{-\rho }$, where the value of $\rho$ depends on the permeability coefficient $\widehat{K}$. The nonlinear dynamics of the flow in the vicinity of the computed finite-amplitude solutions is finally investigated by direct numerical simulations, providing a viable scenario for subcritical transition due to TS waves.

The interaction of a small-wavelength multimodal perturbation with a large-wavelength inclined interface perturbation is investigated for the reshocked Richtmyer-Meshkov instability using three-dimensional simulations. The ares code, developed at Lawrence Livermore National Laboratory, was used for these simulations and a detailed comparison of simulation results and experiments performed at the Georgia Tech Shock Tube facility is presented first for code validation. Simulation results are presented for four cases that vary in large-wavelength perturbation amplitude and the presence of secondary small-wavelength multimode perturbations. Previously developed measures of mixing and turbulence quantities are presented that highlight the large variation in perturbation length scales created by the inclined interface and the multimode complex perturbation. Measures are developed for entrainment, and turbulence anisotropy that help to identify the effects of and competition between each perturbations type. It is shown through multiple measures that before reshock the flow processes a distinct memory of the initial conditions that is present in both large-scale-driven entrainment measures and small-scale-driven mixing measures. After reshock the flow develops to a turbulentlike state that retains a memory of high-amplitude but not low-amplitude large-wavelength perturbations. It is also shown that the high-amplitude large-wavelength perturbation is capable of producing small-scale mixing and turbulent features similar to the small-wavelength multimode perturbations.

Beginning with the exact equations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, we obtain the density, momentum, and stress tensor-moment equations. We close the moment equations with two closures, one that guarantees an equilibrium state given by density-functional theory and another that includes collisions in the relaxation of the stress tensor. The introduction of a density functional-theory closure ensures self-consistency in the equation-of-state properties of the plasma (ideal and excess pressure, electric fields, and correlations). The resulting generalized hydrodynamics thus includes all impacts of Coulomb coupling, viscous damping, and the high-frequency (viscoelastic) response. We compare our results with those of several known models, including generalized hydrodynamic theory and models obtained using the Singwi-Tosi-Land-Sjolander approximation and the quasilocalized charge approximation. We find that the viscoelastic response, including both the high-frequency elastic generalization and viscous wave damping, is important for correctly describing ion-acoustic waves. We illustrate this result by considering three very different systems: ultracold plasmas, dusty plasmas, and dense plasmas. The new model is validated by comparing its results with those of the current autocorrelation function obtained from molecular-dynamics simulations of Yukawa plasmas, and the agreement is excellent. Generalizations of this model to mixtures and quantum systems should be straightforward.