The final stages of pinchoff and breakup of dripping droplets of near-inviscid Newtonian fluids are studied experimentally for pure water and ethanol. High-speed imaging and image analysis are used to determine the angle and the minimum neck size of the cone-shaped extrema of the ligaments attached to dripping droplets in the final microseconds before pinchoff. The angle is shown to steadily approach the value of 18.0 $\pm {0.4}^{\circ }$, independently of the initial flow conditions or the type of breakup. The filament thins and necks following a ${\tau }^{2/3}$ law in terms of the time remaining until pinchoff, regardless of the initial conditions. The observed behavior confirms theoretical predictions.

We consider two coupled particles moving along a periodic substrate potential with negligible inertia effects (overdamped limit). Even when the particles are identical and the substrate spatially symmetric, a sinusoidal external driving of appropriate amplitude and frequency may lead to spontaneous symmetry breaking in the form of a permanent directed motion of the dimer. Thermal noise restores ergodicity and thus zero net velocity, but entails arbitrarily fast diffusion of the dimer for sufficiently weak noise. Moreover, upon application of a static bias force, the dimer exhibits a motion opposite to that force (absolute negative mobility). The key requirement for all these effects is a nonconvex interaction potential of the two particles.

We argue that thermal machines can be understood from the perspective of “virtual qubits” at “virtual temperatures”: The relevant way to view the two heat baths which drive a thermal machine is as a composite system. Virtual qubits are two-level subsystems of this composite, and their virtual temperatures can take on any value, positive or negative. Thermal machines act upon an external system by placing it in thermal contact with a well-selected range of virtual qubits and temperatures. We demonstrate these claims by studying the smallest thermal machines. We show further that this perspective provides a powerful way to view thermodynamics, by analyzing a number of phenomena. This includes approaching Carnot efficiency (where we find that all machines do so essentially by becoming equivalent to the smallest thermal machines), entropy production in irreversible machines, and a way to view work in terms of negative temperature and population inversion. Moreover we introduce the idea of “genuine” thermal machines and are led to considering the concept of “strength” of work.

We develop and investigate a particle-based model for ski slope traffic. Skiers are modeled as particles with a mass that are exposed to social and physical forces, which define the riding behavior of skiers during their descents on ski slopes. We also report position and speed data of 21 skiers recorded with GPS-equipped cell phones on two ski slopes. A comparison of these data with the trajectories resulting from computer simulations of our model shows a good correspondence. A study of the relationship among the density, speed, and flow of skiers reveals that congestion does not occur even with arrival rates of skiers exceeding the maximum ski lift capacity. In a sensitivity analysis, we identify the kinetic friction coefficient of skis on snow, the skier mass, the range of repelling social forces, and the arrival rate of skiers as the crucial parameters influencing the simulation results. Our model allows for the prediction of speed zones and skier densities on ski slopes, which is important in the prevention of skiing accidents.

In our busy lives, almost all of us have to walk with a cup of coffee. While often we spill the drink, this familiar phenomenon has never been explored systematically. Here we report on the results of an experimental study of the conditions under which coffee spills for various walking speeds and initial liquid levels in the cup. These observations are analyzed from the dynamical systems and fluid mechanics viewpoints as well as with the help of a model developed here. Particularities of the common cup sizes, the coffee properties, and the biomechanics of walking proved to be responsible for the spilling phenomenon. The studied problem represents an example of the interplay between the complex motion of a cup, due to the biomechanics of a walking individual, and the low-viscosity-liquid dynamics in it.

Recent work by Teifel and Mahler [Eur. Phys. J. B 75, 275 (2010)] raises legitimate concerns regarding the validity of quantum nonequilibrium work relations in processes involving moving hard walls. We study this issue in the context of the rapidly expanding one-dimensional quantum piston. Utilizing exact solutions of the time-dependent Schrödinger equation, we find that the evolution of the wave function can be decomposed into static and dynamic components, which have simple semiclassical interpretations in terms of particle-piston collisions. We show that nonequilibrium work relations remain valid at any finite piston speed, provided both components are included, and we study explicitly the work distribution for this model system.

Many biological systems possess hierarchical and fractal-like interfaces and joint structures that bear and transmit loads, absorb energy, and accommodate growth, respiration, and/or locomotion. In this paper, an elastic deterministic fractal composite mechanical model was formulated to quantitatively investigate the role of structural hierarchy on the stiffness, strength, and failure of suture joints. From this model, it was revealed that the number of hierarchies ($N$) can be used to tailor and to amplify mechanical properties nonlinearly and with high sensitivity over a wide range of values (orders of magnitude) for a given volume and weight. Additionally, increasing hierarchy was found to result in mechanical interlocking of higher-order teeth, which creates additional load resistance capability, thereby preventing catastrophic failure in major teeth and providing flaw tolerance. Hence, this paper shows that the diversity of hierarchical and fractal-like interfaces and joints found in nature have definitive functional consequences and is an effective geometric-structural strategy to achieve different properties with limited material options in nature when other structural geometries and parameters are biologically challenging or inaccessible. This paper also indicates the use of hierarchy as a design strategy to increase design space and provides predictive capabilities to guide the mechanical design of synthetic flaw-tolerant bioinspired interfaces and joints.

Motivated by the problem of efficiently separating nanoparticles of different character held in solution, we investigate trajectory deflection and particle trapping in flows of nanoparticle suspensions past patterned surfaces. We consider rigid atomistic particles suspended in a viscous liquid solvent and driven by a pressure gradient through a channel, one side of which has a pattern of alternating stripes which attract or repel the particles. We first consider van der Waals forces alone, where the wall interaction is obtained by summing over semi-infinite slabs of material having a Lennard-Jones interaction with or without an attractive term, yielding a force field with nontrivial three-dimensional spatial variation. This wall interaction can either trap particles on the attractive stripes or deflect the trajectories of mobile particles away from the direction of mean flow. Using molecular dynamics simulations we determine the motion of particles of different sizes in this potential, and observe distinct but modest deflections of several degrees from the direction of the imposed fluid flow. The effects of electrostatic interactions are considered by decorating the particles and walls with opposite charges, resulting in significantly more trapping and larger deflection angles. We use Langevin simulations to treat the motion of larger particles in the van der Waals case, and again observe particle trapping and deflection, although the numerical details of the results differ from the molecular dynamics simulations. In the Langevin case we are furthermore able to obtain bounds on the deflection angle from an analysis of the associated Fokker-Planck equation. We conclude that patterned surfaces deflect particle trajectories to a degree depending on their size, and may be used as a vector chromatography separation technique.

A simple model for the boarding of an airplane is studied. Passengers have reserved seats but enter the airplane in arbitrary order. Queues are formed along the aisle, as some passengers have to wait to reach the seats for which they have reservation. We label a passenger by the number of his or her reserved seat. In most cases the boarding process is much slower than for the optimal situation, where passenger and seat orders are identical. We study this dynamical system by calculating the average boarding time when all permutations of $N$ passengers are given equal weight. To first order, the boarding time for a given permutation (ordering) of the passengers is given by the number $s$ of sequences of monotonically increasing values in the permutation. We show that the distribution of $s$ is symmetric on $[1,N]$, which leads to an average boarding time $(N+1)/2$. We have found an exact expression for $s$ and have shown that the full distribution of $s$ approaches a normal distribution as $N$ increases. However, there are significant corrections to the first-order results, due to certain correlations between passenger ordering and the substrate (seat ordering). This occurs for some cases in which the sequence of the seats is partially mirrored in the passenger ordering. These cases with correlations have a boarding time that is lower than predicted by the first-order results. The large number of cases with reduced boarding times have been classified. We also give some indicative results on the geometry of the correlations, with sorting into geometry groups. With increasing $N$, both the number of correlation types and the number of cases belonging to each type increase rapidly. Using enumeration we find that as a result of these correlations the average boarding time behaves like $N^{\alpha }$, with $\alpha \simeq 0.69$, as compared with $\alpha =1.0$ for the first-order approximation.

We determine the complexity of several constraint satisfaction problems using the quantum adiabatic algorithm in its simplest implementation. We do so by studying the size dependence of the gap to the first excited state of “typical” instances. We find that, at large sizes $N$, the complexity increases exponentially for all models that we study. We also compare our results against the complexity of the analogous classical algorithm WalkSAT and show that the harder the problem is for the classical algorithm, the harder it is also for the quantum adiabatic algorithm.

A secure steganographic communication algorithm based on patterns evolving in a Beddington-de Angelis-type predator-prey model with self- and cross-diffusion is proposed in this paper. Small perturbations of initial states of the system around the state of equilibrium result in the evolution of self-organizing patterns. Small differences between initial perturbations result in slight differences also in the evolving patterns. It is shown that the generation of interpretable target patterns cannot be considered as a secure mean of communication because contours of the secret image can be retrieved from the cover image using statistical techniques if only it represents small perturbations of the initial states of the system. An alternative approach when the cover image represents the self-organizing pattern that has evolved from initial states perturbed using the dot-skeleton representation of the secret image can be considered as a safe visual communication technique protecting both the secret image and communicating parties.

In seasonally ice-covered seas and along the margins of perennial ice pack, i.e., in regions with medium ice concentrations, the ice cover typically consists of separate floes interacting with each other by inelastic collisions. In this paper, hitherto unexplored analogies between this type of ice cover and two-dimensional granular gases are used to formulate a model of ice dynamics at the floe level. The model consists of (i) momentum equations for floe motion between collisions, formulated in the form of a Stokes-flow problem, with floe-size-dependent time constant and equilibrium velocity, and (ii) a hard-disk collision model. The numerical algorithm developed is suitable for simulating particle-laden flow of $N$ disk-shaped floes with arbitrary size distributions. The model is applied to study clustering phenomena in sea ice with power-law floe-size distribution. In particular, the influence of the average ice concentration $\overline{A}$ on the formation and characteristics of clusters is analyzed in detail. The results show the existence of two regimes, at low and high ice concentrations, differing in terms of the exponents of the cluster-size distribution and of the size of the largest cluster.

We present a physically intuitive model of ice-lens formation and growth during the freezing of soils and other dense, particulate suspensions. Motivated by experimental evidence, we consider the growth of an ice-filled crack in a freezing soil. At low temperatures, ice in the crack exerts large pressures on the crack walls that will eventually cause the crack to split open. We show that the crack will then propagate across the soil to form a new lens. The process is controlled by two factors: the cohesion of the soil and the geometrical supercooling of the water in the soil, a new concept introduced to measure the energy available to form a new ice lens. When the supercooling exceeds a critical amount (proportional to the cohesive strength of the soil) a new ice lens forms. This condition for ice-lens formation and growth does not appeal to any ad hoc, empirical assumptions, and explains how periodic ice lenses can form with or without the presence of a frozen fringe. The proposed mechanism is in good agreement with experiments, in particular explaining ice-lens pattern formation and surges in heave rate associated with the growth of new lenses. Importantly for systems with no frozen fringe, ice-lens formation and frost heave can be predicted given only the unfrozen properties of the soil. We use our theory to estimate ice-lens growth temperatures obtaining quantitative agreement with the limited experimental data that are currently available. Finally we suggest experiments that might be performed in order to verify this theory in more detail. The theory is generalizable to complex natural-soil scenarios and should therefore be useful in the prediction of macroscopic frost-heave rates.

For a class of nonequilibrium systems, called driven lattice gases, we study what happens when two systems are kept in contact and allowed to exchange particles with the total number of particles conserved. For both attractive and repulsive nearest-neighbor interactions among particles and for a wide range of parameter values, we find that, to a good approximation, one could define an intensive thermodynamic variable, such as the equilibrium chemical potential, that determines the final steady state for two initially separated driven lattice gases brought into contact. However, due to nontrivial contact dynamics, there are also observable deviations from this simple thermodynamic law. To illustrate the role of the contact dynamics, we study a variant of the zero-range process and discuss how the deviations could be explained by a modified large-deviation principle. We identify an additional contribution to the large-deviation function, which we call the excess chemical potential, for the variant of the zero-range process as well as the driven lattice gases. The excess chemical potential depends on the specifics of the contact dynamics and is in general a priori unknown. A contact dependence implies that, even though an intensive variable may equalize, the zeroth law could still be violated.

Ignition of exothermic chemical reactions in small volumes is considered as difficult or impossible due to the large surface-to-volume ratio. Here observation of the spontaneous reaction is reported between hydrogen and oxygen in bubbles whose diameter is smaller than a threshold value around 150 nm. The effect is attributed to high Laplace pressure and to fast dynamics in nanobubbles and is the first indication on combustion in the nanoscale. In this study the bubbles were produced by water electrolysis using successive generation of H${}_2$ and O${}_2$ above the same electrode with short voltage pulses in the microsecond range. The process was observed in a microsystem at current densities $>1000$ A/cm${}^2$ and relative supersaturations $>1000$.

A fundamental problem in the analysis of network data is the detection of network communities, groups of densely interconnected nodes, which may be overlapping or disjoint. Here we describe a method for finding overlapping communities based on a principled statistical approach using generative network models. We show how the method can be implemented using a fast, closed-form expectation-maximization algorithm that allows us to analyze networks of millions of nodes in reasonable running times. We test the method both on real-world networks and on synthetic benchmarks and find that it gives results competitive with previous methods. We also show that the same approach can be used to extract nonoverlapping community divisions via a relaxation method, and demonstrate that the algorithm is competitively fast and accurate for the nonoverlapping problem.

Glycolysis is one of the most essential intracellular networks, found in a wide range of organisms. Due to its importance and due to its wide industrial applications, many experimental studies on all details of this process have been performed. Until now, however, to the best of our knowledge, there has been no comprehensive investigation of the robustness of this important process with respect to internal and external noise. To close this gap, we applied two complementary and mutually supporting approaches to a full-scale model of glycolysis in yeast: (a) a linear stability analysis based on a generalized modeling that deals only with those effective parameters of the system that are relevant for its stability, and (b) a numerical integration of the rate equations in the presence of noise, which accounts for imperfect mixing. The results suggest that the occurrence of metabolite oscillations in part of the parameter space is a side effect of the optimization of the system for maintaining a constant adenosine triphosphate level in the face of a varying energy demand and of fluctuations in the parameters and metabolite concentrations.

The diffusion coefficient of an inclusion in a liquid membrane is investigated by taking into account the interaction between membranes and bulk solvents of arbitrary thickness. As illustrative examples, the diffusion coefficients of two types of inclusions, a circular domain composed of fluid with the same viscosity as the host membrane and that of a polymer chain embedded in the membrane, are studied. The diffusion coefficients are expressed in terms of the hydrodynamic screening lengths, which vary according to the solvent thickness. When the membrane fluid is dragged by the solvent of finite thickness, via stick boundary conditions, multiple hydrodynamic screening lengths together with the weight factors to the diffusion coefficients are obtained from the characteristic equation. The conditions for which the diffusion coefficients can be approximated by the expression including only a single hydrodynamic screening length are also shown.

Using numerical simulations of a simple sea-coast mechanical erosion model, we investigate the effect of spatial long-range correlations in the lithology of coastal landscapes on the fractal behavior of the corresponding coastlines. In the model, the resistance of a coast section to erosion depends on the local lithology configuration as well as on the number of neighboring sea sides. For weak sea forces, the sea is trapped by the coastline and the eroding process stops after some time. For strong sea forces erosion is perpetual. The transition between these two regimes takes place at a critical sea force, characterized by a fractal coastline front. For uncorrelated landscapes, we obtain, at the critical value, a fractal dimension $D=1.33$, which is consistent with the dimension of the accessible external perimeter of the spanning cluster in two-dimensional percolation. For sea forces above the critical value, our results indicate that the coastline is self-affine and belongs to the Kardar-Parisi-Zhang universality class. In the case of landscapes generated with power-law spatial long-range correlations, the coastline fractal dimension changes continuously with the Hurst exponent $H$, decreasing from $D=1.34$ to $1.04$, for $H=0$ and $1$, respectively. This nonuniversal behavior is compatible with the multitude of fractal dimensions found for real coastlines.

We study reversible polymerization of rings. In this stochastic process, two monomers bond and, as a consequence, two disjoint rings may merge into a compound ring or a single ring may split into two fragment rings. This aggregation-fragmentation process exhibits a percolation transition with a finite-ring phase in which all rings have microscopic length and a giant-ring phase where macroscopic rings account for a finite fraction of the entire mass. Interestingly, while the total mass of the giant rings is a deterministic quantity, their total number and their sizes are stochastic quantities. The size distribution of the macroscopic rings is universal, although the span of this distribution increases with time. Moreover, the average number of giant rings scales logarithmically with system size. We introduce a card-shuffling algorithm for efficient simulation of the ring formation process and we present numerical verification of the theoretical predictions.