Although a small point ultrasound transducer has a wide acceptance angle, its small active area leads to a high thermal-noise-induced electric voltage in the transducer, thus the sensitivity is low. By contrast, a finite-size flat transducer has high sensitivity, but the acceptance angle is small, which limits its application in reconstruction-based photoacoustic tomography (PAT). Here, we propose a negative lens concept to increase the acceptance angle of a flat transducer without losing sensitivity. Phantom experiments demonstrate that use of this concept greatly increases the detection region for PAT with high sensitivity.

The effects of hidden nodes can lead to erroneous identification of connections among measured nodes in a network. For example, common input from a hidden node may cause correlations among a pair of measured nodes that could be misinterpreted as arising from a direct connection between the measured nodes. We present an approach to control for effects of hidden nodes in networks driven by a repeated stimulus. We demonstrate the promise of this approach via simulations of small networks of neurons driven by a visual stimulus.

We have investigated how the interface width between two thin polymer films approaches its equilibrium state. Neutron reflection for different polyolefin bilayers of various degrees of incompatibility as a function of the annealing time was measured. By tuning the interaction parameter, we have probed both an immiscible polymer couple and systems approaching criticality where the interface is wider. Since polymer chains have slow dynamics, we have observed the slow broadening of the interface connected to the growth at long times of the wavelength capillary-wave modes, which involve large-scale hydrodynamic flows.

It is possible to compare results for the classical tests for embeddings of chaotic data with the results of a recently proposed test. The classical tests, which depend on real numbers (fractal dimensions, Lyapunov exponents) averaged over an attractor, are compared with a topological test that depends on integers. The comparison can only be done for mappings into three dimensions. We find that the classical tests fail to predict when a mapping is an embedding and when it is not. We point out the reasons for this failure, which are not restricted to three dimensions.

A major challenge in turbulence research is to understand from first principles the origin of the anomalous scaling of velocity fluctuations in high-Reynolds-number turbulent flows. One important idea was proposed by Kolmogorov [J. Fluid Mech. 13, 82 (1962)], which attributes the anomaly to variations of the locally averaged energy dissipation rate. Kraichnan later pointed out [J. Fluid Mech. 62, 305 (1973)] that the locally averaged energy dissipation rate is not an inertial-range quantity and a proper inertial-range quantity would be the local energy transfer rate. As a result, Kraichnan’s idea attributes the anomaly to variations of the local energy transfer rate. These ideas, generally known as refined similarity hypotheses, can also be extended to study the anomalous scaling of fluctuations of an active scalar, such as the temperature in turbulent convection. We examine the validity of these refined similarity hypotheses and their extensions to an active scalar in shell models of homogeneous turbulence and turbulent convection. We find that Kraichnan’s refined similarity hypothesis and its extension are valid.

A nonlinear relaxation process is considered for a macroscopic thermodynamic quantity, generalizing recent work by Taniguchi and Cohen [J. Stat. Phys. 126, 1 (2006)] that was based on the Onsager-Machlup theory. It is found that the fluctuation theorem holds in the nonlinear nonequilibrium regime if the change of entropy characterized by local equilibria is appropriately renormalized. The fluctuation theorem for the ordinary entropy change is recovered in the linear near-equilibrium case.

The Boltzmann–Gibbs–von Neumann entropy of a large part (of linear size $L$) of some (much larger) $d$-dimensional quantum systems follows the so-called area law (as for black holes), i.e., it is proportional to $L^{d-1}$. Here we show, for $d=1,2$, that the (nonadditive) entropy $S_q$ satisfies, for a special value of $q\ne 1$, the classical thermodynamical prescription for the entropy to be extensive, i.e., $S_q\propto L^d$. Therefore, we reconcile with classical thermodynamics the area law widespread in quantum systems. Recently, a similar behavior was exhibited in mathematical models with scale-invariant correlations [C. Tsallis, M. Gell-Mann, and Y. Sato, Proc. Natl. Acad. Sci. U.S.A.102 15377 (2005)]. Finally, we find that the system critical features are marked by a maximum of the special entropic index $q$.

We analyze the generalized Fick-Jacobs equation, obtained by a rigorous mapping of the diffusion equation in a quasi-one-dimensional (quasi-1D) (narrow 2D or 3D) channel with varying cross section $A\left(x\right)$ onto the longitudinal coordinate $x$. We show that for constructing approximations and understanding their applicability in practice, it is crucial to study the 2D (3D) density inside the channel in the regime of stationary flow. We present algorithms enabling us to derive approximate formulas for the effective diffusion coefficient involving derivatives of $A\left(x\right)$ higher than $A^{\prime }\left(x\right)$ and give examples for 2D channels. Effects of the boundary conditions at the ends of a finite channel and the case of nonsmooth $A\left(x\right)$ are also discussed.

A fine analysis of the statistics of dry granular avalanches in a rotating drum setup reveals that, beyond the fluctuations, the angle at which an avalanche ends is correlated experimentally to the angle at which the avalanche starts. This correlation resulting from inertia defines an intermediate “neutral” angle that characterizes the corresponding granular pile. In addition, an intensive study of the dynamics of the avalanche shows that the time duration of the avalanche is correlated to its amplitude, being smaller for higher amplitude. The time relaxation of the pile slope during any avalanche, governed by the deviation of the starting angle from the neutral angle, follows a master curve. A simple model recovers most of the results and contributes to a better understanding of the physics of the avalanche flow.

This paper presents a quantitative theory of mixing via chaotic advection in near-integrable time-dependent volume-preserving flows for the case when the base (unperturbed) flow possesses two invariants (or actions). Using a model cellular flow introduced by Solomon and Mezic as an example, we construct a quantitative theory of mixing caused by the resonance-induced diffusion of an adiabatic invariant of the flow. We compute the fraction of the mixed volume as a function of the frequency of the perturbation and show that this function is strikingly nonmonotonic, with multiple peaks. In particular, essentially complete mixing inside a flow cell is achieved on experimentally accessible time scales for certain special frequencies.

Intermittency is usually identified in turbulent flows as non-Gaussian tails of the probability density functions (PDFs) of the turbulent field derivatives. Here we investigate the role of phase coherence among the Fourier modes in creating intermittency in magnetized space plasmas using the technique of surrogate data. We apply the technique to two examples: (i) synthetic data and (ii) magnetic field fluctuations recorded in the terrestrial magnetosheath by the Cluster spacecraft. We use a set of four series of data, one observed and three surrogate, and their PDFs and moments $(q⩽4)$ as discriminating statistics. We show that the technique allows for detecting coherent structures and estimating their scales. We show furthermore that the phases, but not the amplitudes, create the non-Gaussian tails of the PDFs. We show also that the surrogate data used cannot account for asymmetries of the PDFs of the observed data. This enables us to confirm a scenario of turbulent cascade of mirror structures proposed in previous publications, by showing the existence of an approximately constant energy flux in the inertial range.

The Lagrange-mesh method is an approximate variational calculation which resembles a mesh calculation because of the use of a Gauss quadrature. The hydrogen atom confined in a sphere is studied with Lagrange-Legendre basis functions vanishing at the center and surface of the sphere. For various confinement radii, accurate energies and mean radii are obtained with small numbers of mesh points, as well as dynamic dipole polarizabilities. The wave functions satisfy the cusp condition with 11-digit accuracy.

An approach for integration of motion in many-body systems of interacting polyatomic molecules is proposed. It is based on splitting time propagation of pseudovariables in a modified phase space, while the real translational and orientational coordinates are decoded by processing transformations. This allows one to overcome the barrier on the order of precision of the integration at a given number of force-torque evaluations per time step. Testing in dynamics of water versus previous methods shows that the algorithms obtained significantly improve the accuracy of the simulations without extra computational costs.

We study the rheological properties of colloidal microphases in two dimensions simulating a model of colloidal particles with competing interactions. Due to the competition between short-range attraction and long-range repulsion, as a function of the density the model exhibits a variety of microphases such as clusters, stripes, or crystals with bubbles. We prepare the system in a confined microphase employing Monte Carlo simulations and then shear the resulting configurations by applying a drag force profile. We integrate numerically the equation of motion for the particles and analyze the dynamics as a function of the density and the applied strain rate. We measure the stress-strain curves and characterize the yielding of the colloidal microphases. The results depend on the type of microphase. (i) Clusters are easily sheared along layers and the relative motion is assisted by rotations. (ii) Stripes shear easily when they are parallel to the flow and tend to jam when they are perpendicular to it. Under a sufficiently strong shear rate perpendicular stripes orient in the flow direction. (iii) Crystals with bubbles yield by fracturing along the bubbles and eventually forming stripes. We discuss the role of dislocations, emitted by the bubbles, in the yielding process. Finally, we analyze the effect of thermal fluctuations on the rheological properties.

The coupling between mechanical and thermal properties due to thermal expansion complicates the problem of measuring frequency-dependent thermoviscoelastic properties, in particular for highly viscous liquids. A simplification arises if there is spherical symmetry where—as detailed in the present paper—the thermoviscoelastic problem may be solved analytically in the inertia-free limit, i.e., the limit where the sample is much smaller than the wavelength of sound waves at the frequencies of interest. As for the one-dimensional thermoviscoelastic problem [Christensen et al., Phys. Rev. E 75, 041502 (2007)], the solution is conveniently formulated in terms of the so-called transfer matrix, which directly links to the boundary conditions that can be experimentally controlled. Once the transfer matrix has been calculated, it is fairly easy to deduce the equations describing various experimentally relevant special cases (boundary conditions that are adiabatic, isothermal, isochoric, etc.). In most situations the relevant frequency-dependent specific heat is the longitudinal specific heat, a quantity that is in between the isochoric and isobaric frequency-dependent specific heats.

Droplets in smectic free-standing films interact due to elastic distortion of the $\mathbf{c}$-director field and formation of topological defects. Our experiments show that chirality of the liquid-crystal medium plays a key role in the interaction between droplets. We find that the configuration of the $\mathbf{c}$-director field near the droplets and the position of the topological defects on the droplet boundary depend on droplet size and film polarity. An intermediate $\mathbf{c}$-director configuration between dipolar and quadrupolar is formed near droplets in smectic films due to the competition between elasticity and chirality. We observed that the distance between droplets in self-organized structures depends on the position of defects on the droplet boundary and significantly changes with respect to that for dipolar droplets. Our results open the way to modify the droplet interaction and the structures formed by droplets.

Large-scale hierarchies characterize complex networks in different domains. Elements at the top, usually the most central or influential, may show multipolarization or tend to club together, forming tightly interconnected communities. The rich-club phenomenon quantified this tendency based on unweighted network representations. Here, we define this metric for weighted networks and discuss the appropriate normalization which preserves the nodes’ strengths and discounts structural strength-strength correlations if present. We find that in some real networks the results given by the weighted rich-club coefficient can be in sharp contrast to the ones in the unweighted approach. We also discuss the ability of the scanning of weighted subgraphs formed by the high-strength hubs to unveil features in contrast to the average: the formation of local alliances in multipolarized environments, or a lack of cohesion even in the presence of rich-club ordering. Beyond structure, this analysis matters for correct understanding of functionalities and dynamical processes relying on hub interconnectedness.

In this paper we study nonlinear oscillatory systems consisting of two media, one supporting forward propagating waves and the other inwardly propagating waves, separated by an interface. We find that the interface can select the type of wave. Under certain well-defined parameter condition, these waves propagate in two different media with the same frequency and same wave number; the interface of the two media is transparent to these waves. The frequency and wave number of these interface-selected waves (ISWs) are predicted explicitly. When parameters are varied from this parameter set, the wave numbers of the two domains become different, and the difference increases from zero continuously as the distance between the given parameters and this parameter set increases from zero. It is found that ISWs can play crucial roles in practical problems of wave competition, e.g., ISWs can suppress spirals and antispirals.

Human red blood cells (RBCs) exhibit vibratory motions, referred to as “flickering.” Their dynamical properties, classically attributed to thermal mechanisms, have not been fully characterized. Using detrended fluctuation analysis and multiscale entropy methods, we show that the short-term flickering motions of RBCs, observed under phase contrast microscopy, have a fractal scaling exponent close to that of $1∕f$ noise and exhibit complex patterns over multiple time scales. Further, these dynamical properties degrade with in vivo aging such that older cells that have been in the circulation longer generate significantly $(p<0.003)$ less complex flickering patterns than newly formed cells. Quantitative assessment of multiscale flickering may provide a way of measuring RBC functionality. Membrane models need to account for the complex properties of these motions and their changes with in vivo senescence.

We investigate a class of granular materials characterized by the possibility of interlocking between the particles. The interlocking is modeled by its effect through rolling resistance depending on relative rotation and normal force at the contact points and involving a single parameter analogous to the sliding friction coefficient. The model, which is introduced in the framework of the contact dynamics method, is applied to simulate the simple shear of a large granular sample. We present a detailed analysis regarding the influence of rolling and sliding friction parameters on the macroscopic response in terms of shear strength, fabric properties, and force transmission. Interestingly, two distinct regimes can be distinguished in which the steady-state shear strength is controlled by either rolling resistance or sliding friction. The relative contributions of rolling and sliding contacts to the shear strength are consistent with the same two regimes. Interlocking strongly affects the force network by enhancing the arching effect and thus increasing the relative importance of weak contact forces and torques, which is reflected in a decreasing power-law probability distribution of the contact forces and torques below the mean. Due to the combined effect of friction and interlocking, the force-carrying backbone takes an increasingly columnar aspect involving a low fraction of particles. Our data suggest that the nature of the weak contact network is strongly affected by the formation of these columns of particles which do not need to be propped laterally. In particular, in the limit of high rolling resistance and sliding friction, the role of the weak network of contacts is no longer to prop the force chains, but, like the strong contact network, to actively sustain the deviatoric load imposed on the system.