We present new Nusselt-number (Nu) measurements for slowly rotating turbulent thermal convection in cylindrical samples with aspect ratio $\mathrm{\Gamma }=1.00$ and provide a comprehensive correlation of all available data for that $\mathrm{\Gamma }$. In the experiment compressed gasses (nitrogen and sulfur hexafluride) as well as the fluorocarbon ${\mathrm{C}}_6{\mathrm{F}}_{14}$ (3M Fluorinert FC72) and isopropanol were used as the convecting fluids. The data span the Prandtl-number (Pr) range $0.74<\mathrm{Pr}<35.5$ and are for Rayleigh numbers (Ra) from $3\times {10}^8$ to $4\times {10}^{11}$. The relative heat transport ${\mathrm{Nu}}_r(1/\mathrm{Ro})\equiv \mathrm{Nu}(1/\mathrm{Ro})/\mathrm{Nu}\left(0\right)$ as a function of the dimensionless inverse Rossby number $1/\mathrm{Ro}$ at constant Ra is reported. For $\mathrm{Pr}\approx 0.74$ and the smallest $\mathrm{Ra}=3.6\times {10}^8$ the maximum enhancement ${\mathrm{Nu}}_{\mathrm{r},\max }-1$ due to rotation is about 0.02. With increasing Ra, ${\mathrm{Nu}}_{\mathrm{r},\max }-1$ decreased further, and for $\mathrm{Ra}\gtrsim 2\times {10}^9$ heat-transport enhancement was no longer observed. For larger Pr the dependence of ${\mathrm{Nu}}_r$ on 1/Ro is qualitatively similar for all Pr. As noted before, there is a very small increase of ${\mathrm{Nu}}_r$ for small 1/Ro, followed by a decrease by a percent or so, before, at a critical value $1/{\mathrm{Ro}}_c$, a sharp transition to enhancement by Ekman pumping takes place. While the data revealed no dependence of $1/{\mathrm{Ro}}_c$ on Ra, $1/{\mathrm{Ro}}_c$ decreased with increasing Pr. This dependence could be described by a power law with an exponent $\alpha \simeq -0.41$. Power-law dependencies on Pr and Ra could be used to describe the slope $S_{\mathrm{Ro}}^{+}=\partial {\mathrm{Nu}}_r/\partial (1/\mathrm{Ro})$ just above $1/{\mathrm{Ro}}_c$. The Pr and Ra exponents were ${\beta }_1=-0.16\pm 0.08$ and ${\beta }_2=-0.04\pm 0.06$, respectively. Further increase of 1/Ro led to further increase of ${\mathrm{Nu}}_r$ until it reached a maximum value ${\mathrm{Nu}}_{r,\max }$. Beyond the maximum, the Taylor-Proudman (TP) effect, which is expected to lead to reduced vertical fluid transport in the bulk region, lowered ${\mathrm{Nu}}_r$. ${\mathrm{Nu}}_{r,\max }$ was largest for the largest Pr. For $\mathrm{Pr}=28.9$, for example, we measured an increase of the heat transport by up to 40% (${\mathrm{Nu}}_r-1=0.40$) for the smallest $\mathrm{Ra}=2.2\times {10}^9$, even though we were unable to reach ${\mathrm{Nu}}_{r,\max }$ over the accessible $1/\mathrm{Ro}$ range. Both ${\mathrm{Nu}}_{\mathrm{r},\max }(\mathrm{Pr},\mathrm{Ra})$ and its location $1/{\mathrm{Ro}}_{\max }(\mathrm{Pr},\mathrm{Ra})$ along the $1/\mathrm{Ro}$ axis increased with Pr and decreased with Ra. Although both could be given by power-law representations, the uncertainties of the exponents are relatively large.

Understanding drop evaporation mechanisms is important for many industrial, biological, and other applications. Drops of organic solvents undergoing evaporation have been found to display distinct thermal patterns, which in turn depend on the physical properties of the liquid, the substrate, and ambient conditions. These patterns have been reported previously to be bulk patterns from the solid-liquid to the liquid-gas drop interface. In the present work the effect of ambient temperature and humidity during the first stage of evaporation, i.e., pinned contact line, is studied paying special attention to the thermal information retrieved at the liquid-gas interface through IR thermography. This is coupled with drop profile monitoring to experimentally investigate the effect of ambient temperature and relative humidity on the drop interfacial thermal patterns and the evaporation rate. Results indicate that self-generated thermal patterns are enhanced by an increase in ambient temperature and/or a decrease in humidity. The more active thermal patterns observed at high ambient temperatures are explained in light of a greater temperature difference generated between the apex and the edge of the drop due to greater evaporative cooling. On the other hand, the presence of water humidity in the atmosphere is found to decrease the temperature difference along the drop interface due to the heat of adsorption, absorption and/or that of condensation of water onto the ethanol drops. The control, i.e., enhancement or suppression, of these thermal patterns at the drop interface by means of ambient temperature and relative humidity is quantified and reported.

We put forward a simpler and improved variation of a recently proposed method to overcome the signal-to-noise problem found in Monte Carlo calculations of the entanglement entropy of interacting fermions. The present method takes advantage of the approximate log-normal distributions that characterize the signal-to-noise properties of other approaches. In addition, we show that a simple rewriting of the formalism allows circumvention of the inversion of the restricted one-body density matrix in the calculation of the $n\text{th}$ Rényi entanglement entropy for $n>2$. We test our technique by implementing it in combination with the hybrid Monte Carlo algorithm and calculating the $n=2,3,4,\cdots ,10$ Rényi entropies of the one-dimensional attractive Hubbard model. We use that data to extrapolate to the von Neumann $(n=1)$ and $n\to \infty$ cases.

The free surface lattice Boltzmann method (FSLBM) is a combination of the hydrodynamic lattice Boltzmann method with a volume-of-fluid (VOF) interface capturing technique for the simulation of incompressible free surface flows. Capillary effects are modeled by extracting the curvature of the interface from the VOF indicator function and imposing a pressure jump at the free boundary. However, obtaining accurate curvature estimates from a VOF description can introduce significant errors. This article reports numerical results for three different surface tension models in standard test cases and compares the according errors in the velocity field (spurious currents). Furthermore, the FSLBM is shown to be suited to simulate wetting effects at solid boundaries. To this end, a new method is developed to represent wetting boundary conditions in a least-squares curvature reconstruction technique. The main limitations of the current FSLBM are analyzed and are found to be caused by its simplified advection scheme. Possible improvements are suggested.

In a recent paper [S. Behnia and S. Fathizadeh, Phys. Rev. E 91, 022719 (2015)] an analytical approach is proposed for the investigation of the conductivity properties of DNA. The authors use mean Lyapunov exponent methods as the backbone of their approach and try to interpret properties of the system based on its behavior. Their interpretation regarding the change in nature of the mean Lyapunov exponent at the denaturation temperatures and discussions of stability and instability based on the mean Lyapunov exponent method are questioned. Moreover there is misunderstanding between mean Lyapunov exponent and Lyapunov exponent.

Functionals of Brownian and non-Brownian motions have diverse applications and attracted a lot of interest among scientists. This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of the functionals of the space and time-tempered anomalous diffusion, belonging to the continuous time random walk class. Several examples of the functionals are explicitly treated, including the occupation time in half-space, the first passage time, the maximal displacement, the fluctuations of the occupation fraction, and the fluctuations of the time-averaged position.

We calculate the efficiency at the unified trade-off optimization criterion (the so-called maximum $\mathrm{\Omega }$ criterion) representing a compromise between the useful energy and the lost energy of heat engines operating between two reservoirs at different temperatures and chemical potentials, and demonstrate that the linear coefficient 3/4 and quadratic coefficient 1/32 of the efficiency at maximum $\mathrm{\Omega }$ are universal for heat engines under strong coupling and symmetry conditions. It is further proved that the conclusions obtained here also apply to the ecological optimization criterion.

We investigate the influence that adding a new coupling has on the linear stability of the synchronous state in coupled-oscillator networks. Using a simple model, we show that, depending on its location, the new coupling can lead to enhanced or reduced stability. We extend these results to electric power grids where a new line can lead to four different scenarios corresponding to enhanced or reduced grid stability as well as increased or decreased power flows. Our analysis shows that the Braess paradox may occur in any complex coupled system, where the synchronous state may be weakened and sometimes even destroyed by additional couplings.

Colloidal membranes are monolayer assemblies of rodlike particles that capture the long-wavelength properties of lipid bilayer membranes on the colloidal scale. Recent experiments on colloidal membranes formed by chiral rodlike viruses showed that introducing a second species of virus with different length and opposite chirality leads to the formation of rafts—micron-sized domains of one virus species floating in a background of the other viruses [Sharma et al., Nature (London) 513, 77 (2014)]. In this article we study the interaction of such rafts using liquid crystal elasticity theory. By numerically minimizing the director elastic free energy, we predict the tilt angle profile for both a single raft and two rafts in a background membrane, and the interaction between two rafts as a function of their separation. We find that the chiral penetration depth in the background membrane sets the scale for the range of the interaction. We compare our results with the experimental data and find good agreement for the strength and range of the interaction. Unlike the experiments, however, we do not observe a complete collapse of the data when rescaled by the tilt angle at the raft edge.

An accurate understanding of the interplay between random and deterministic processes in generating extreme events is of critical importance in many fields, from forecasting extreme meteorological events to the catastrophic failure of materials and in the Earth. Here we investigate the statistics of record-breaking events in the time series of crackling noise generated by local rupture events during the compressive failure of porous materials. The events are generated by computer simulations of the uniaxial compression of cylindrical samples in a discrete element model of sedimentary rocks that closely resemble those of real experiments. The number of records grows initially as a decelerating power law of the number of events, followed by an acceleration immediately prior to failure. The distribution of the size and lifetime of records are power laws with relatively low exponents. We demonstrate the existence of a characteristic record rank $k^{*}$, which separates the two regimes of the time evolution. Up to this rank deceleration occurs due to the effect of random disorder. Record breaking then accelerates towards macroscopic failure, when physical interactions leading to spatial and temporal correlations dominate the location and timing of local ruptures. The size distribution of records of different ranks has a universal form independent of the record rank. Subsequences of events that occur between consecutive records are characterized by a power-law size distribution, with an exponent which decreases as failure is approached. High-rank records are preceded by smaller events of increasing size and waiting time between consecutive events and they are followed by a relaxation process. As a reference, surrogate time series are generated by reshuffling the event times. The record statistics of the uncorrelated surrogates agrees very well with the corresponding predictions of independent identically distributed random variables, which confirms that temporal and spatial correlation in the crackling noise is responsible for the observed unique behavior. In principle the results could be used to improve forecasting of catastrophic failure events, if they can be observed reliably in real time.

Real-time prediction of signals is a task often encountered in control problems as well as by living systems. Here, a parsimonious prediction approach based on the coupling of a linear relaxation-delay system to a smooth, stationary signal is described. The resulting anticipatory relaxation dynamics (ARD) is a frequency-dependent predictor of future signal values. ARD not only approximately predicts signals on average but can anticipate the occurrence of signal peaks, too. This can be explained by recognizing ARD as an input-output system with negative group delay. It is characterized, including its prediction horizon, by its analytically given frequency response function.

We examine a rarefied gas with inter-molecular attraction. It is argued that the attraction force amplifies random density fluctuations by pulling molecules from lower-density regions into high-density regions and thus may give rise to an instability. To describe this effect, we use a kinetic equation where the attraction force is taken into account in a way similar to how electromagnetic forces in plasma are treated in the Vlasov model. It is demonstrated that the instability occurs when the temperature $T$ is lower than a certain threshold value $T_s$ depending on the gas density. It is further shown that, even if $T$ is only marginally lower than $T_s$, the instability generates clusters with density much higher than that of the gas. These results suggest that the instability should be interpreted as a gas-liquid phase transition, with $T_s$ being the temperature of saturated vapor and the high-density clusters representing liquid droplets.

This pedagogical comment highlights three misconceptions concerning the usefulness of the concept of negative temperature, being derived from the usual, often termed Boltzmann, definition of entropy. First, both the Boltzmann and Gibbs entropies must obey the same thermodynamic consistency relation. Second, the Boltzmann entropy does obey the second law of thermodynamics. Third, there exists an integrating factor of the heat differential with both definitions of entropy.

The classical theory of Brownian dynamics follows from coarse graining the underlying linearized fluctuating hydrodynamics of the solvent. We extend this procedure to globally nonisothermal conditions, requiring only a local thermal equilibration of the solvent. Starting from the conservation laws, we establish the stochastic equations of motion for the fluid momentum fluctuations in the presence of a suspended Brownian particle. These are then contracted to the nonisothermal generalized Langevin description of the suspended particle alone, for which the coupling to stochastic temperature fluctuations is found to be negligible under typical experimental conditions.

We study a susceptible-infected-removed (SIR) model with multiple seeds on a regular random graph. Many researchers have studied the epidemic threshold of epidemic models above which a global outbreak can occur, starting from an infinitesimal fraction of seeds. However, there have been few studies of epidemic models with finite fractions of seeds. The aim of this paper is to clarify what happens in phase transitions in such cases. The SIR model in networks exhibits two percolation transitions. We derive the percolation transition points for the SIR model with multiple seeds to show that as the infection rate increases epidemic clusters generated from each seed percolate before a single seed can induce a global outbreak.

A self-propelling semiflexible filament exhibits a variety of dynamical states depending on the flexibility and activity of the filament. Here we investigate the dynamics of such an active filament using a bead-spring model with the explicit hydrodynamic interactions. The activity in the filament is incorporated by inserting chemically active dimers at regular intervals along the chain. The chemical reactions at the catalytic bead of the dimer produces a self-generated concentration gradient and gives sufficient fuel to exhibit self-propulsion for the filament. Depending upon the rigidity and the configuration, the polymeric filament exhibits three distinct types of spontaneous motion, namely, rotational, snaking, and translational motion. The self-propulsion velocity of the filament for various rigidity and sizes has been calculated, and the factors affecting the propulsion are identified.

Polymer chains winding around each other or around other objects occur in many natural systems; the physical consequences of this winding are therefore of significant interest. A polymer chain could be surrounded by various bulky objects (referred as obstacles), such as other macromolecules or macromolecular aggregates. Here we show that for a long flexible polymer chain wound around a cylinder, the presence of obstacles could modify the winding-torque interdependence, in some cases leading to phase-transition-like behavior in which the winding occurs only when the torque exceeds some critical value. Possible implications of this effect are discussed in relation to the biophysics of nucleic acids.

We report on the collapse of bubble rafts under compression in a closed rectangular geometry. A bubble raft is a single layer of bubbles at the air-water interface. A collapse event occurs when bubbles submerge beneath the neighboring bubbles under compression, causing the structure of the bubble raft to go from single-layer to multilayer. We studied the collapse dynamics as a function of compression velocity. At higher compression velocity we observe a more uniform distribution of collapse events, whereas at lower compression velocities the collapse events accumulate at the system boundaries. We propose that this system can be understood in terms of a linear elastic sheet coupled to a local internal (Ising) degree of freedom. The two internal states, which represent one bubble layer versus two, couple to the elasticity of the sheet by locally changing the reference state of the material. By exploring the collapse dynamics of the bubble raft, one may address the basic nonlinear mechanics of a number of complex systems in which elastic stress is coupled to local internal variables.

We reveal the existence of slowly decaying dark solitons in the radiation build-up dynamics of bright pulses in all-normal dispersion mode-locked fiber lasers, numerically modeled in the framework of a generalized nonlinear Schrödinger equation. The evolution of noise perturbations to quasistationary dark solitons is examined, and the significance of background shape and soliton-soliton collisions on the eventual soliton decay is established. We demonstrate the role of a restoring force in extending soliton interactions in conservative systems to include the effects of dissipation, as encountered in laser cavities, and generalize our observations to other nonlinear systems.

For a limited set of impact conditions, a drop impacting onto a pool can entrap an air bubble as large as its own size. The subsequent rise and rupture of this large bubble plays an important role in aerosol formation and gas transport at the air-sea interface. The large bubble is formed when the impact crater closes up near the pool surface and is known to occur only for drops that are prolate at impact. Herein we use experiments and numerical simulations to show that a concentrated vortex ring, produced in the neck between the drop and the pool, controls the crater deformations and pinchoff. However, it is not the strongest vortex rings that are responsible for the large bubbles, as they interact too strongly with the pool surface and self-destruct. Rather, it is somewhat weaker vortices that can deform the deeper craters, which manage to pinch off the large bubbles. These observations also explain why the strongest and most penetrating vortex rings emerging from drop impacts are not produced by oblate drops but by more prolate drop shapes, as had been observed in previous experiments.