A large number of eukaryotic cells are able to directly detect external chemical gradients with great accuracy and the ultimate limit to their sensitivity has been a topic of debate for many years. Previous work has been done to understand many aspects of this process but little attention has been paid to the possibility of emergent sensing states. Here we examine how cooperation between sensors existing in a two-dimensional network, as they do on the cell's surface, can both enhance and fundamentally alter the response of the cell to a spatially varying signal. We show that weakly interacting sensors linearly amplify the cell's response to an external gradient while a network of strongly interacting sensors form a collective nonlinear response with two separate domains of active and inactive sensors forming what have called a “1/2-state.” In our analysis we examine the cell's ability to sense the direction of a signal and pay special attention to the substantially different behavior realized in the strongly interacting regime.

We study the occurrence of events, subject to threshold, in a representative self-organized criticality (SOC) sandpile model and in high-resolution rainfall data. The predictability in both systems is analyzed by means of a decision variable sensitive to event clustering, and the quality of the predictions is evaluated by the receiver operating characteristic (ROC) method. In the case of the SOC sandpile model, the scaling of quiet-time distributions with increasing threshold leads to increased predictability of extreme events. A scaling theory allows us to understand all the details of the prediction procedure and to extrapolate the shape of the ROC curves for the most extreme events. For rainfall data, the quiet-time distributions do not scale for high thresholds, which means that the corresponding ROC curves cannot be straightforwardly related to those for lower thresholds. In this way, ROC curves are useful for highlighting differences in predictability of extreme events between toy models and real-world phenomena.

We present a quantum localization phenomenon that exists in periodically kicked three-dimensional rotors, but is absent in the commonly studied two-dimensional ones: edge localization. We show that under the condition of a fractional quantum resonance there are states of the kicked rotor that are strongly localized near the edge of the angular momentum space at $J=0$. These states are analogs of surface states in crystalline solids, and they significantly affect resonant excitation of molecular rotation by laser pulse trains.

We present an investigation of spiral waves pinned to circular and rectangular obstacles with different circumferences in both thin layers of the Belousov-Zhabotinsky reaction and numerical simulations with the Oregonator model. For circular objects, the area always increases with the circumference. In contrast, we varied the circumference of rectangles with equal areas by adjusting their width $w$ and height $h$. For both obstacle forms, the propagating parameters (i.e., wavelength, wave period, and velocity of pinned spiral waves) increase with the circumference, regardless of the obstacle area. Despite these common features of the parameters, the forms of pinned spiral waves depend on the obstacle shapes. The structures of spiral waves pinned to circles as well as rectangles with the ratio $w/h\sim 1$ are similar to Archimedean spirals. When $w/h$ increases, deformations of the spiral shapes are observed. For extremely thin rectangles with $w/h\gg 1$, these shapes can be constructed by employing semicircles with different radii which relate to the obstacle width and the core diameter of free spirals.

In this paper we consider the motion of point particles in a particular type of one-degree-of-freedom, slowly changing, temporally periodic Hamiltonian. Through most of the time cycle, the particles conserve their action, but when a separatrix is approached and crossed, the conservation of action breaks down, as shown in previous theoretical studies. These crossings have the effect that the numerical solution shows an apparent contradiction. Specifically we consider two initial constant energy phase space curves $H=E_A$ and $H=E_B$ at time $t=0$, where $H$ is the Hamiltonian and $E_A$ and $E_B$ are the two initial energies. The curve $H=E_A$ encircles the curve $H=E_B$. We then sprinkle many initial conditions (particles) on these curves and numerically follow their orbits from $t=0$ forward in time by one cycle period. At the end of the cycle the vast majority of points initially on the curves $H=E_A$ and $H=E_B$ now appear to lie on two new constant energy curves $H=E_A^{\prime }$ and $H=E_B^{\prime }$, where the $B^{\prime }$ curve now encircles the $A^{\prime }$ curve (as opposed to the initial case where the $A$ curve encircles the $B$ curve). Due to the uniqueness of Hamilton dynamics, curves evolved under the dynamics cannot cross each other. Thus the apparent curves $H=E_A^{\prime }$ and $H=E_B^{\prime }$ must be only approximate representations of the true situation that respects the topological exclusion of curve crossing. In this paper we resolve this apparent paradox and study its consequences. For this purpose we introduce a “robust” numerical simulation technique for studying the complex time evolution of a phase space curve in a Hamiltonian system. We also consider how a very tiny amount of friction can have a major consequence, as well as what happens when a very large number of cycles is followed. We also discuss how this phenomenon might extend to chaotic motion in higher dimensional Hamiltonian systems.

We present an experimental analysis of the effects of gravity level on the formation and rise dynamics of bubbles. Experiments were carried out with millimeter-diameter bubbles in the hypergravity environment provided by the large-diameter centrifuge of the European Space Agency. Bubble detachment from a nozzle is determined by buoyancy and surface tension forces regardless of the gravity level. Immediately after detachment, bubble trajectory is deviated by the Coriolis force. Subsequent bubble rise is dominated by inertial forces and follows a zig-zag trajectory with amplitude and frequency dependent on the gravity level. Vorticity production is enhanced as gravity increases, which destabilizes the flow and therefore the bubble path.

We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of quasistationary states of free interface in fluid dynamical systems subject to vibrations, revealed the existence of standing periodic waves and solitons in this system. However, this approach does not provide regular means for dealing with evolutionary problems: neither stability problems nor ones associated with propagating waves. In this work, we rigorously derive the evolution equations for long waves in the system, which turn out to be identical to the plus (or good) Boussinesq equation. With these equations one can find all the time-independent-profile solitary waves (standing solitons are a specific case of these propagating waves), which exist below the linear instability threshold; the standing and slow solitons are always unstable while fast solitons are stable. Depending on initial perturbations, unstable solitons either grow in an explosive manner, which means layer rupture in a finite time, or falls apart into stable solitons. The results are derived within the long-wave approximation as the linear stability analysis for the flat-interface state [D.V. Lyubimov and A.A. Cherepanov, Fluid Dynamics 21, 849 (1986)] reveals the instabilities of thin layers to be long wavelength.

We present numerical simulations of the flow confined in a wide gap Taylor-Couette system, with a rotating inner cylinder and variable length-to-gap aspect ratio. A complex experimental bifurcation scenario differing from the classical Ruelle-Takens route to chaos has been experimentally reported in this geometry. The wavy vortex flow becomes quasiperiodic due to an axisymmetric very low frequency mode. This mode plays a key role in the dynamics of the system, leading to the occurrence of chaos via a period-doubling scenario. Further increasing the rotation of the inner cylinder results in the appearance of a new flow pattern which is characterized by large amplitude oscillations localized in some of the vortex pairs. The purpose of this paper is to study numerically the dynamics of these axially localized states, paying special attention to the transition to chaos. Frequency analysis from time series simultaneously recorded at several points has been applied in order to identify the flow transitions taking place. It has been found that the very low frequency mode is essential to explain the behavior associated with the different transitions towards chaos including localized states.

A recent model for radiative transfer that accounts for spatial coherence is extended in such a way as to retain temporal coherence. The method employs Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy techniques. Both spatial and temporal coherence are shown to affect the formation of atomic line spectra. Calculations of Lyman $\alpha$ radiation transport in optically thick divertor plasma conditions are reported as an illustration of the model. A possible extension of the formalism to dense media involving correlations between atoms is discussed in an appendix. A link to partial frequency redistribution modeling is also discussed.

Based on Santos' general solution for the scaled-particle differential equation [Phys. Rev. E 86, 040102(R) (2012)], we construct a free-energy functional for the hard-sphere system. The functional is obtained by a suitable generalization and extension of the set of scaled-particle variables using the weighted densities from Rosenfeld's fundamental measure theory for the hard-sphere mixture [Phys. Rev. Lett. 63, 980 (1989)]. While our general result applies to the hard-sphere mixture, we specify remaining degrees of freedom by requiring the functional to comply with known properties of the pure hard-sphere system. Both for mixtures and pure systems, the functional can be systematically extended following the lines of our derivation. We test the resulting functionals regarding their behavior upon dimensional reduction of the fluid as well as their ability to accurately describe the hard-sphere crystal and the liquid-solid transition.

We develop a general recursion-transform (R-T) method for a two-dimensional resistor network with a zero resistor boundary. As applications of the R-T method, we consider a significant example to illuminate the usefulness for calculating resistance of a rectangular $m\times n$ resistor network with a null resistor and three arbitrary boundaries, a problem never solved before, since Green's function techniques and Laplacian matrix approaches are invalid in this case. Looking for the exact calculation of the resistance of a binary resistor network is important but difficult in the case of an arbitrary boundary since the boundary is like a wall or trap which affects the behavior of finite network. In this paper we obtain several general formulas of resistance between any two nodes in a nonregular $m\times n$ resistor network in both finite and infinite cases. In particular, 12 special cases are given by reducing one of the general formulas to understand its applications and meanings, and an integral identity is found when we compare the equivalent resistance of two different structures of the same problem in a resistor network.

The $J_1\text{−}{J}_2$ Ising model in the square lattice in the presence of an external field is studied by two approaches: the cluster variation method (CVM) and Monte Carlo simulations. The use of the CVM in the square approximation leads to the presence of a new equilibrium phase, not previously reported for this model: an Ising-nematic phase, which shows orientational order but not positional order, between the known stripes and disordered phases. Suitable order parameters are defined, and the phase diagram of the model is obtained. Monte Carlo simulations are in qualitative agreement with the CVM results, giving support to the presence of the new Ising-nematic phase. Phase diagrams in the temperature-external field plane are obtained for selected values of the parameter $\kappa =J_2/\left|J_1\right|$ which measures the relative strength of the competing interactions. From the CVM in the square approximation we obtain a line of second order transitions between the disordered and nematic phases, while the nematic-stripes phase transitions are found to be of first order. The Monte Carlo results suggest a line of second order nematic-disordered phase transitions in agreement with the CVM results. Regarding the stripes-nematic transitions, the present Monte Carlo results are not precise enough to reach definite conclusions about the nature of the transitions.

In this article we generalize the classical Edgeworth expansion for the probability density function (PDF) of sums of a finite number of symmetric independent identically distributed random variables with a finite variance to PDFs with a diverging variance, which converge to a Lévy $\alpha$-stable density function. Our correction may be written by means of a series of fractional derivatives of the Lévy and the conjugate Lévy PDFs. This series expansion is general and applies also to the Gaussian regime. To describe the terms in the series expansion, we introduce a new family of special functions and briefly discuss their properties. We implement our generalization to the distribution of the momentum for atoms undergoing Sisyphus cooling, and show the improvement of our leading order approximation compared to previous approximations. In vicinity of the transition between Lévy and Gauss behaviors, convergence to asymptotic results slows down.

Colloidal suspensions flowing through microchannels were studied for the effects of both the shear flow and the proximity of walls on the particles' self-diffusion. Use of hydrostatic pressure to pump micron-sized silica spheres dispersed in water-glycerol mixture through poly(dimethylsiloxane) channels with a cross section of $30\times 24\mu {\mathrm{m}}^2$, allowed variation in the local Peclet number (Pe) from 0.01 to 50. To obtain the diffusion coefficients, image-time series from a confocal scanning laser microscope were analyzed with a method that, after finding particle trajectories, subtracts the instantaneous advective displacements and subsequently measures the slopes of the mean squared displacement in the flow $\left(x\right)$ and shear $\left(y\right)$ directions. For dilute suspensions, the thus obtained diffusion coefficients $(D_x$ and $D_y)$ are close to the free diffusion coefficient at all shear rates. In concentrated suspensions, a clear increase with the Peclet number (for Pe > 10) is found, that is stronger for $D_x$ than for $D_y$. This effect of shear-induced collisions is counteracted by the contribution of walls, which cause a strong local reduction in $D_x$ and $D_y$.

The average mean-square displacement, $\langle r^2\rangle$, of $H$ atoms in a protein is frequently determined using incoherent neutron-scattering experiments. $\langle r^2\rangle$ is obtained from the observed elastic incoherent dynamic structure factor, $S_i(Q,\omega =0)$, assuming the form $S_i(Q,\omega =0) =exp(-Q^2\langle r^2\rangle /3)$. This is often referred to as the Gaussian approximation (GA) to $S_i(Q,\omega =0)$. $\langle r^2\rangle$ obtained in this way depends on the value of the wave vector, $Q$ considered. Equivalently, the observed $S_i(Q,\omega =0)$ deviates from the GA. We investigate the origin of the $Q$ dependence of $\langle r^2\rangle$ by evaluating the scattering functions in different approximations using molecular dynamics (MD) simulation of the protein lysozyme. We find that keeping only the Gaussian term in a cumulant expansion of $S(Q,\omega )$ is an accurate approximation and is not the origin of the $Q$ dependence of $\langle r^2\rangle$. This is demonstrated by showing that the term beyond the Gaussian is negligible and that the GA is valid for an individual atom in the protein. Rather, the $Q$ dependence (deviation from the GA) arises from the dynamical heterogeneity of the $H$ in the protein. Specifically it arises from representing, in the analysis of data, this diverse dynamics by a single average scattering center that has a single, average $\langle r^2\rangle$. The observed $Q$ dependence of $\langle r^2\rangle$ can be used to provide information on the dynamical heterogeneity in proteins.

We introduce network $L$-cloning, a technique for creating ensembles of random networks from any given real-world or artificial network. Each member of the ensemble is an $L$-cloned network constructed from $L$ copies of the original network. The degree distribution of an $L$-cloned network and, more importantly, the degree-degree correlation between and beyond nearest neighbors are identical to those of the original network. The density of triangles in an $L$-cloned network, and hence its clustering coefficient, is reduced by a factor of $L$ compared to those of the original network. Furthermore, the density of loops of any fixed length approaches zero for sufficiently large values of $L$. Other variants of $L$-cloning allow us to keep intact the short loops of certain lengths. As an application, we employ these network cloning methods to investigate the effect of short loops on dynamical processes running on networks and to inspect the accuracy of corresponding tree-based theories. We demonstrate that dynamics on $L$-cloned networks (with sufficiently large $L$) are accurately described by the so-called adjacency tree-based theories, examples of which include the message passing technique, some pair approximation methods, and the belief propagation algorithm used respectively to study bond percolation, SI epidemics, and the Ising model.

We present a structural phase-field crystal model [M. Greenwood et al., Phys. Rev. Lett. 105, 045702 (2010)] that yields a stable $dc$ structure. The stabilization of a $dc$ structure is accomplished by constructing a two-body direct correlation function (DCF) approximated by a combination of two Gaussian functions in Fourier space. A phase diagram containing a $dc$-liquid phase coexistence region is calculated for this model. We examine the energies of solid-liquid interfaces with normals along the [100], [110], and [111] directions. The dependence of the interfacial energy on a temperature parameter, which controls the heights of the peaks in the two-body DCF, is described by a Gaussian function. Furthermore, the dependence of the interfacial energy on the peak widths of the two-body DCF, which controls the excess energy associated with interfaces, defects, and strain, is described by an inverse power law. These relationships can be used to parametrize the phase-field crystal model for the $dc$ structure to match solid-liquid interfacial energies to those measured experimentally or calculated from atomistic simulations.

Based on two capacitively coupled quantum dots in the Coulomb-blockade regime, a model of three-terminal quantum-dot refrigerators is proposed. With the help of the master equation, the transport properties of steady-state charge current and energy flow between two quantum dots and thermal reservoirs are revealed. It is expounded that such a structure can be used to construct a refrigerator by controlling the voltage bias and temperature ratio. The thermodynamic performance characteristics of the refrigerator are analyzed, including the cooling power, coefficient of performance (COP), maximum cooling power, and maximum COP. Moreover, the optimal regions of main performance parameters are determined. The influence of dissipative tunnel processes on the optimal performance is discussed in detail. Finally, the performance characteristics of the refrigerators operated in two different cases are compared.

The random search problem is a challenging and interdisciplinary topic of research in statistical physics. Realistic searches usually take place in nonuniform heterogeneous distributions of targets, e.g., patchy environments and fragmented habitats in ecological systems. Here we present a comprehensive numerical study of search efficiency in arbitrarily fragmented landscapes with unlimited visits to targets that can only be found within patches. We assume a random walker selecting uniformly distributed turning angles and step lengths from an inverse power-law tailed distribution with exponent $\mu$. Our main finding is that for a large class of fragmented environments the optimal strategy corresponds approximately to the same value ${\mu }_{\mathrm{opt}}\approx 2$. Moreover, this exponent is indistinguishable from the well-known exact optimal value ${\mu }_{\mathrm{opt}}=2$ for the low-density limit of homogeneously distributed revisitable targets. Surprisingly, the best search strategies do not depend (or depend only weakly) on the specific details of the fragmentation. Finally, we discuss the mechanisms behind this observed robustness and comment on the relevance of our results to both the random search theory in general, as well as specifically to the foraging problem in the biological context.