Critical properties of a liquid film between two planar walls are investigated in the canonical ensemble, within which the total number of fluid particles, rather than their chemical potential, is kept constant. The effect of this constraint is analyzed within mean-field theory (MFT) based on a Ginzburg-Landau free-energy functional as well as via Monte Carlo simulations of the three-dimensional Ising model with fixed total magnetization. Within MFT and for finite adsorption strengths at the walls, the thermodynamic properties of the film in the canonical ensemble can be mapped exactly onto a grand canonical ensemble in which the corresponding chemical potential plays the role of the Lagrange multiplier associated with the constraint. However, due to a nonintegrable divergence of the mean-field order parameter profile near a wall, the limit of infinitely strong adsorption turns out to be not well-defined within MFT, because it would necessarily violate the constraint. The critical Casimir force (CCF) acting on the two planar walls of the film is generally found to behave differently in the canonical and grand canonical ensembles. For instance, the canonical CCF in the presence of equal preferential adsorption at the two walls is found to have the opposite sign and a slower decay behavior as a function of the film thickness compared to its grand canonical counterpart. We derive the stress tensor in the canonical ensemble and find that it has the same expression as in the grand canonical case, but with the chemical potential playing the role of the Lagrange multiplier associated with the constraint. The different behavior of the CCF in the two ensembles is rationalized within MFT by showing that, for a prescribed value of the thermodynamic control parameter of the film, i.e., density or chemical potential, the film pressures are identical in the two ensembles, while the corresponding bulk pressures are not.

Locally thermal quantum systems may contradict traditional thermodynamics: heat can flow from a cold body to a hotter one, if the two are highly entangled. We show that to recover thermodynamic laws, we must use a stronger notion of thermalization: a system $S$ is thermal relative to a reference $R$ if $S$ is both locally thermal and uncorrelated with $R$. Considering a general quantum reference is particularly relevant for a thermodynamic treatment of nanoscale quantum systems. We derive a technical condition for relative thermalization in terms of conditional entropies. Established results on local thermalization, which implicitly assume a classical reference, follow as special cases.

A majority of studied models for scale-free networks have degree distributions with exponents greater than two. Real networks, however, can demonstrate essentially more heavy-tailed degree distributions. We explore two models of scale-free equilibrium networks that have the degree distribution exponent $\gamma =1, P\left(q\right)\sim q^{-\gamma }$. Such degree distributions can be identified in empirical data only if the mean degree of a network is sufficiently high. Our models exploit a rewiring mechanism. They are local in the sense that no knowledge of the network structure, apart from the immediate neighborhood of the vertices, is required. These models generate uncorrelated networks in the infinite size limit, where they are solved explicitly. We investigate finite size effects by the use of simulations. We find that both models exhibit disassortative degree-degree correlations for finite network sizes. In addition, we observe a markedly degree-dependent clustering in the finite networks. We indicate a real-world network with a similar degree distribution.

The incubation times for the eggs of 21 dinosaurs are determined from an estimate of their embyronic metabolic rate and the mass of the hatchlings via a mass growth model based on conservation of energy. Embryos in extant birds and crocodiles are studied in order to determine the best model for embryonic metabolism and growth. These results are used to develop a theoretical model that predicts the incubation times of an egg. This model is applied to dinosaur eggs and provides a unique window into dinosaur reproduction. The dinosaurs studied come from both Saurischia and Ornithischia. The incubation times vary from about 28 days for Archaeopteryx lithographica to about 76 days for Alamosaurus sanjuanensis.

Coherent emergent structures have been observed in a high-energy-density supersonic mixing layer experiment. A millimeter-scale shock tube uses lasers to drive Mbar shocks into the tube volume. The shocks are driven into initially solid foam (60 $\mathrm{mg}/{\mathrm{cm}}^3$) hemicylinders separated by an Al or Ti metal tracer strip; the components are vaporized by the drive. Before the experiment disassembles, the shocks cross at the tube center, creating a very fast ($\mathrm{\Delta }U>$ 200 km/s) shear-unstable zone. After several nanoseconds, an expanding mixing layer is measured, and after 10+ ns we observe the appearance of streamwise-periodic, spanwise-aligned rollers associated with the primary Kelvin-Helmholtz instability of mixing layers. We additionally image roller pairing and spanwise-periodic streamwise-aligned filaments associated with secondary instabilities. New closures are derived to connect length scales of these structures to estimates of fluctuating velocity data otherwise unobtainable in the high-energy-density environment. This analysis indicates shear-induced specific turbulent energies ${10}^3–{10}^4$ times higher than the nearest conventional experiments. Because of difficulties in continuously driving systems under these conditions and the harshness of the experimental environment limiting the usable diagnostics, clear evidence of these developing structures has never before been observed in this regime.

We describe how a single-particle tracking experiment should be designed in order for its recorded trajectories to contain the most information about a tracked particle's diffusion coefficient. The precision of estimators for the diffusion coefficient is affected by motion blur, limited photon statistics, and the length of recorded time series. We demonstrate for a particle undergoing free diffusion that precision is negligibly affected by motion blur in typical experiments, while optimizing photon counts and the number of recorded frames is the key to precision. Building on these results, we describe for a wide range of experimental scenarios how to choose experimental parameters in order to optimize the precision. Generally, one should choose quantity over quality: experiments should be designed to maximize the number of frames recorded in a time series, even if this means lower information content in individual frames.

Simple models for friction are typically one-dimensional, but real interfaces are two-dimensional. We investigate the effects of the second dimension on static and dynamic friction by using the Frenkel-Kontorova (FK) model. We study the two most straightforward extensions of the FK model to two dimensions and simulate both the static and dynamic properties. We show that the behavior of the static friction is robust and remains similar in two dimensions for physically reasonable parameter values. The dynamic friction, however, is strongly influenced by the second dimension and the accompanying additional dynamics and parameters introduced into the models. We discuss our results in terms of the thermal equilibration and phonon dispersion relations of the lattices, establishing a physically realistic and suitable two-dimensional extension of the FK model. We find that the presence of additional dissipation channels can increase the friction and produces significantly different temperature dependence when compared to the one-dimensional case. We also briefly study the anisotropy of the dynamic friction and show highly nontrivial effects, including that the friction anisotropy can lead to motion in different directions depending on the value of the initial velocity.

A paradigmatic microswimmer is the three-linked-spheres model, which follows a minimalist approach for propulsion by shape shifting. As such, it has been the subject of numerous analytical and numerical studies. In this Rapid Communication, an experimental three-linked-spheres swimmer is created by self-assembling ferromagnetic particles at an air-water interface. It is powered by a uniform oscillating magnetic field. A model, using two harmonic oscillators, reproduces the experimental findings. Because the model remains general, the same approach could be used to design a variety of efficient microswimmers.

We describe a generic scheme to extract critical exponents of quantum lattice models from sequences of numerical data, which is, for example, relevant for nonperturbative linked-cluster expansions or nonperturbative variants of continuous unitary transformations. The fundamental idea behind our approach is a reformulation of the numerical data sequences as a series expansion in a pseudoparameter. This allows us to utilize standard series expansion extrapolation techniques to extract critical properties such as critical points and critical exponents. The approach is illustrated for the deconfinement transition of the antiferromagnetic spin-1/2 Heisenberg chain.

We derive a generalization of the second law of thermodynamics that uses Bayesian updates to explicitly incorporate the effects of a measurement of a system at some point in its evolution. By allowing an experimenter's knowledge to be updated by the measurement process, this formulation resolves a tension between the fact that the entropy of a statistical system can sometimes fluctuate downward and the information-theoretic idea that knowledge of a stochastically evolving system degrades over time. The Bayesian second law can be written as $\mathrm{\Delta }H({\rho }_m,\rho )+{\langle \mathcal{Q}\rangle }_{F|m}\ge 0$, where $\mathrm{\Delta }H({\rho }_m,\rho )$ is the change in the cross entropy between the original phase-space probability distribution $\rho$ and the measurement-updated distribution ${\rho }_m$ and ${\langle \mathcal{Q}\rangle }_{F|m}$ is the expectation value of a generalized heat flow out of the system. We also derive refined versions of the second law that bound the entropy increase from below by a non-negative number, as well as Bayesian versions of integral fluctuation theorems. We demonstrate the formalism using simple analytical and numerical examples.

We propose a method for linear detection of weak forces using parametrically driven nonlinear resonators. The method is based on a peculiar feature in the response of the resonator to a near resonant periodic external force. This feature stems from a complex interplay among the parametric drive, external force, and nonlinearities. For weak parametric drive, the response exhibits the standard Duffing-like single jump hysteresis. For stronger drive amplitudes, we find a qualitatively new double jump hysteresis which arises from stable solutions generated by the cubic Duffing nonlinearity. The additional jump exists only if the external force is present and the frequency at which it occurs depends linearly on the amplitude of the external force, permitting a straightforward ultrasensitive detection of weak forces. With state-of-the-art nanomechanical resonators, our scheme should permit force detection in the attonewton range.

We study the influence of noise in a prototypical thermoacoustic system, which represents a nonlinear self-excited bistable oscillator. We analyze the time series of unsteady pressure obtained from a horizontal Rijke tube and a mathematical model to identify the effect of noise. We report the occurrence of stochastic bifurcations in a thermoacoustic system by tracking the changes in the stationary amplitude distribution. We observe a complete suppression of a bistable zone in the presence of high intensity noise. We find that the complete suppression of the bistable zone corresponds to the nonexistence of phenomenological (P) bifurcations. This is a study in thermoacoustics to identify the parameter regimes pertinent to P bifurcation using the stationary amplitude distribution obtained by solving the Fokker-Planck equation.

In this study we present an extension of the dynamics of diffusion in multiplex graphs, which makes the equations compatible with the replicator equation with mutations. We derive an exact formula for the diffusion term, which shows that, while diffusion is linear for numbers of agents, it is necessary to account for nonlinear terms when working with fractions of individuals. We also derive the transition probabilities that give rise to such macroscopic behavior, completing the bottom-up description. Finally, it is shown that the usual assumption of constant population sizes induces a hidden selective pressure due to the diffusive dynamics, which favors the increase of fast diffusing strategies.

At a three-phase contact line, a liquid bulk phase is in contact with and coexists with a very thin layer of adsorbed molecules. This adsorbed film in the immediate vicinity of a liquid wedge modifies the balance of forces between the liquid and solid phases such that, when included in the balance of forces, a quantitative relationship emerges between the adsorbed film thickness and the static contact angle. This relationship permits the prediction of static contact angles from molecular forces and equilibrium adsorption data by means of quantities that are physically meaningful and measurable. For n-alkanes on polytetrafluoroethylene, for which there are experimental data available on adsorption and contact angles, our computations show remarkable agreement with the data. The results obtained are an improvement on previously published calculations—particularly for alkanes with a low number of carbon atoms, for which adsorption is significant.

Random sequential adsorption of linear and square particles with excluded volume interaction is studied numerically on planar lattices considering Gaussian distributions of lateral sizes of the incident particles, with several values of the average $\mu$ and of the width-to-average ratio $w$. When the coverage $\theta$ is plotted as function of the logarithm of time $t$, the maximum slope is attained at a time $t_M$ of the same order of the time $\tau$ of incidence of one monolayer, which is related to the molecular flux and/or sticking coefficients. For various $\mu$ and $w$, we obtain $1.5\tau <t_M<5\tau$ for linear particles and $0.3\tau <t_M<\tau$ for square particles. At $t_M$, the coverages with linear and square particles are near 0.3 and 0.2, respectively. Extrapolations show that coverages may vary with $\mu$ up to $20\%$ and $2\%$ for linear and square particles, respectively, for $\mu \ge 64$, fixed time, and constant $w$. All $\theta$ vs $logt$ plots have approximately the same shape, but other quantities measured at times of order $t_M$ help to distinguish narrow and broad incident distributions. The adsorbed particle-size distributions are close to the incident ones up to long times for small $w$, but appreciably change in time for larger $w$, acquiring a monotonically decreasing shape for $w=1/2$ at times of order $100\tau$. At $t_M$, incident and adsorbed distributions are approximately the same for $w\le 1/8$ and show significant differences for $w\ge 1/2$; this result may be used as a consistency test in applications of the model. The pair correlation function $g\left(r,t\right)$ for $w\le 1/8$ has a well defined oscillatory structure at $10t_M$, with a minimum at $r\approx \mu$ and maximum at $r\approx 1.5\mu$, but this structure is not observed for $w\ge 1/4$.

We report measurements of electron densities, $n_e$, and temperatures, $T_e$, in a magnetized expanding hydrogen plasma performed using Thomson scattering. The effects of applying an axial magnetic field and changing the background pressure in the plasma vessel on $n_e$ and $T_e$ along the expansion axis are reported. Magnetic field strengths ($B$ field) up to 170 mT were applied, which are one order of magnitude larger than previously reported. The main effect of the applied $B$ field is the plasma confinement, which leads to higher $n_e$. At $B$ fields larger than 88 mT the electron density along the expansion axis does not depend strongly on the magnetic field strength. However, $T_e$ is susceptible to the $B$ field and reaches at 170 mT a maximum of 2.5 eV at a distance of 1.5 cm from the exit of the cascaded arc. To determine also the effect of the arc current through the arc, measurements were performed with arc currents of 45, 60, and 75 A at background pressures of 9.7 and 88.3 Pa. At constant magnetic field $n_e$ decreases from the exit of the arc along the expansion axis when the arc current is decreased. At 88.3 Pa $n_e$ shows a higher value close to the exit of the arc, but a faster decay along the expansion axis with respect to the 9.7 Pa case. $T_e$ is overall higher at lower pressure reaching a maximum of 3.2 eV at the lower arc current of 45 A. The results of this study complement our understanding and the characterization of expanding hydrogen plasmas.

Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case of large but finite datasets. We first show how the steepest descent dynamics is not optimal as it is slowed down by the inhomogeneous curvature of the model parameters' space. We then provide a way for rectifying this space which relies only on dataset properties and does not require large computational efforts. We conclude by solving the long-time limit of the parameters' dynamics including the randomness generated by the systematic use of Gibbs sampling. In this stochastic framework, rather than converging to a fixed point, the dynamics reaches a stationary distribution, which for the rectified dynamics reproduces the posterior distribution of the parameters. We sum up all these insights in a “rectified” data-driven algorithm that is fast and by sampling from the parameters' posterior avoids both under- and overfitting along all the directions of the parameters' space. Through the learning of pairwise Ising models from the recording of a large population of retina neurons, we show how our algorithm outperforms the steepest descent method.

A critical analysis of several statements concerning experimental studies, molecular dynamics simulations, and the theoretical interpretation of bubble nucleation processes is performed. In particular, it is shown that the Tolman equation does not supply us, in general, with a satisfactory theoretically founded description of the curvature dependence of the surface tension and the dependence of the steady-state nucleation rate of bubbles and droplets on supersaturation in the framework of classical nucleation theory.