We found a subphase with a six-layer periodicity which appears between the ferroelectric Sm$C^{*}$ and the antiferroelectric Sm$C_A$${}^{*}$($q_T$ $=$ 0) phases. The six-layer periodic structure is directly determined by the microbeam resonant x-ray scattering measurement. Furthermore, considering the dielectric constants, this phase was found to be ferrielectric, assigned as Sm$C_A$${}^{*}$($q_T$ $=$ 2/3). This subphase indicates the importance of the competition between the ferro- and the antiferroelectric phases and, in that point, it is essentially different from the previously observed six-layer phase. The relation between current theories and our present experimental results has been studied and discussed.

We show experimentally that a stable wave propagating into a region characterized by an opposite current may become modulationally unstable. Experiments have been performed in two independent wave tank facilities; both of them are equipped with a wavemaker and a pump for generating a current propagating in the opposite direction with respect to the waves. The experimental results support a recent conjecture based on a current-modified nonlinear Schrödinger equation which establishes that rogue waves can be triggered by a nonhomogeneous current characterized by a negative horizontal velocity gradient.

The chemical potentials of multicomponent fluids are derived in terms of the pair correlation functions for arbitrary number of components, interaction potentials, and dimensionality. The formally exact result is particularized to hard-sphere mixtures with zero or positive nonadditivity. As a simple application, the chemical potentials of three-dimensional additive hard-sphere mixtures are derived from the Percus-Yevick theory and the associated equation of state is obtained. This Percus-Yevick chemical-route equation of state is shown to be more accurate than the virial equation of state. An interpolation between the chemical-potential and compressibility routes exhibits a better performance than the well-known Boublík-Mansoori-Carnahan-Starling-Leland equation of state.

The description of subdiffusive transport in complex media by fractional equations with a constant anomalous exponent is not robust where the stationary distribution is concerned. The Gibbs-Boltzmann distribution is radically changed by even small spatial perturbations to the anomalous exponent [S. Fedotov and S. Falconer, Phys. Rev. E 85, 031132 (2012)]. To rectify this problem we propose the inclusion of the random death process in the random walk scheme, which is quite natural for biological applications including morphogen gradient formation. From this, we arrive at the modified fractional master equation and analyze its asymptotic behavior, both analytically and by Monte Carlo simulation. We show that this equation is structurally stable against spatial variations of the anomalous exponent. We find that the stationary flux of the particles has a Markovian form with rate functions depending on the anomalous rate functions, the death rate, and the anomalous exponent. Additionally, in the continuous limit we arrive at an advection-diffusion equation where advection and diffusion coefficients depend on both the death rate and anomalous exponent.

Impact dynamics is measured for spherical and cylindrical projectiles of many different densities dropped onto a variety non-cohesive granular media. The results are analyzed in terms of the material-dependent scaling of the inertial and frictional drag contributions to the total stopping force. The inertial drag force scales similar to that in fluids, except that it depends on the internal friction coefficient. The frictional drag force scales as the square-root of the density of granular medium and projectile, and hence cannot be explained by the combination of granular hydrostatic pressure and Coulomb friction law. The combined results provide an explanation for the previously observed penetration depth scaling.

A set of four confocal laser beams of 1064-nm wavelength is used to prepare optically induced crystals of submicron particles in aqueous solution. Thousands of polystyrene spheres of about 200 nm in diameter are trapped in three dimensions. Bragg scattering patterns obtained with a probe beam of 532-nm wavelength are in agreement with the calculated lattice structure and its polarization dependence. The decay and rise of the Bragg scattering intensity upon switching the lattice off and on reveal the Brownian motion dynamics of the particles in the periodic optical trapping potential. Experimental results agree well with results from trajectory simulations based on the Langevin equation. The results exhibit the interplay between Brownian motion and deterministic forces in an inhomogeneous (near-)periodic optical trapping potential.

Many eukaryotic cells are able to perform directional mechanosensing by directly measuring minute spatial differences in the mechanical stress on their membranes. Here, we explore the limits of a single mechanosensitive channel activation using a two-state double-well model for the gating mechanism. We then focus on the physical limits of directional mechanosensing by a single cell having multiple mechanosensors and subjected to a shear flow inducing a nonuniform membrane tension. Our results demonstrate that the accuracy in sensing the mechanostimulus direction not only increases with cell size and exposure to a signal, but also grows for cells with a near-critical membrane prestress. Finally, the existence of a nonlinear threshold effect, fundamentally limiting the cell's ability to effectively perform directional mechanosensing at a low signal-to-noise ratio, is uncovered.

Time perception in the suprasecond range is crucial for fundamental cognitive processes such as decision making, rate calculation, and planning. In the vast majority of species, behavioral manipulations, and neurophysiological manipulations, interval timing is scale invariant: the time-estimation errors are proportional to the estimated duration. The origin and mechanisms of this fundamental property are unknown. We discuss the computational properties of a circuit consisting of a large number of (input) neural oscillators projecting on a small number of (output) coincidence detector neurons, which allows time to be coded by the pattern of coincidental activation of its inputs. We show that time-scale invariance emerges from the neural noise, such as small fluctuations in the firing patterns of its input neurons and in the errors with which information is encoded and retrieved by its output neurons. In this architecture, time-scale invariance is resistant to manipulations as it depends neither on the details of the input population nor on the distribution probability of noise.

We study the percolation behavior of two interdependent scale-free (SF) networks under random failure of 1-$p$ fraction of nodes. Our results are based on numerical solutions of analytical expressions and simulations. We find that as the coupling strength between the two networks $q$ reduces from 1 (fully coupled) to 0 (no coupling), there exist two critical coupling strengths $q_1$ and $q_2$, which separate three different regions with different behavior of the giant component as a function of $p$. (i) For $q\ge q_1$, an abrupt collapse transition occurs at $p=p_c$. (ii) For $q_2<q<q_1$, the giant component has a hybrid transition combined of both, abrupt decrease at a certain $p=p_c^{\mathrm{jump}}$ followed by a smooth decrease to zero for $p<p_c^{\mathrm{jump}}$ as $p$ decreases to zero. (iii) For $q\le q_2$, the giant component has a continuous second-order transition (at $p=p_c$). We find that $\left(a\right)$ for $\lambda \le 3$, $q_1\equiv 1$; and for $\lambda >3$, $q_1$ decreases with increasing $\lambda$. Here, $\lambda$ is the scaling exponent of the degree distribution, $P\left(k\right)\propto k^{-\lambda }$. $\left(b\right)$ In the hybrid transition, at the $q_2<q<q_1$ region, the mutual giant component $P_{\infty }$ jumps discontinuously at $p=p_c^{\mathrm{jump}}$ to a very small but nonzero value, and when reducing $p$, $P_{\infty }$ continuously approaches to 0 at $p_c=0$ for $\lambda <3$ and at $p_c>0$ for $\lambda >3$. Thus, the known theoretical $p_c=0$ for a single network with $\lambda ⩽3$ is expected to be valid also for strictly partial interdependent networks.

We study the implications of unitarity for pseudo-orbit expansions of the spectral determinants of quantum maps and quantum graphs. In particular, we advocate to group pseudo-orbits into subdeterminants. We show explicitly that the cancellation of long orbits is elegantly described on this level and that unitarity can be built in using a simple subdeterminant identity which has a nontrivial interpretation in terms of pseudo-orbits. This identity yields much more detailed relations between pseudo-orbits of different lengths than was known previously. We reformulate Newton identities and the spectral density in terms of subdeterminant expansions and point out the implications of the subdeterminant identity for these expressions. We analyze furthermore the effect of the identity on spectral correlation functions such as the autocorrelation and parametric cross-correlation functions of the spectral determinant and the spectral form factor.

Falling parallelograms exhibit coupled motion of autogyration and tumbling, similar to the motion of falling tulip seeds, unlike maple seeds which autogyrate but do not tumble, or rectangular cards which tumble but do not gyrate. This coupled tumbling and autogyrating motion are robust, when card parameters, such as aspect ratio, internal angle, and mass density, are varied. We measure the three-dimensional (3D) falling kinematics of the parallelograms and quantify their descending speed, azimuthal rotation, tumbling rotation, and cone angle in each falling. The cone angle is insensitive to the variation of the card parameters, and the card tumbling axis does not overlap with but is close to the diagonal axis. In addition to this connection to the dynamics of falling seeds, these trajectories provide an ideal set of data to analyze 3D aerodynamic force and torque at an intermediate range of Reynolds numbers, and the results will be useful for constructing 3D aerodynamic force and torque models. Tracking these free falling trajectories gives us a nonintrusive method for deducing instantaneous aerodynamic forces. We determine the 3D aerodynamic forces and torques based on Newton-Euler equations. The dynamical analysis reveals that, although the angle of attack changes dramatically during tumbling, the aerodynamic forces have a weak dependence on the angle of attack. The aerodynamic lift is dominated by the coupling of translational and rotational velocities. The aerodynamic torque has an unexpectedly large component perpendicular to the card. The analysis of the Euler equation suggests that this large torque is related to the deviation of the tumbling axis from the principle axis of the card.

The agitation produced in a fluid by a suspension of microswimmers in the low Reynolds number limit is studied. In this limit, swimmers are modeled as force dipoles all with equal strength. The agitation is characterized by the active temperature defined, as in kinetic theory, as the mean square velocity, and by the equal-time spatial correlations. Considering the phase in which the swimmers are homogeneously and isotropically distributed in the fluid, it is shown that the active temperature and velocity correlations depend on a single scalar correlation function of the dipole-dipole correlation function. By making a simple medium-range order model, in which the dipole-dipole correlation function is characterized by a single correlation length $k_0^{-1}$ it is possible to make quantitative predictions. It is found that the active temperature depends on the system size, scaling as $L^{4-d}$ at large correlation lengths $L\ll k_0^{-1}$, while in the opposite limit it saturates in three dimensions and diverges logarithmically with the system size in two dimensions. In three dimensions the velocity correlations decay as $1/r$ for small correlation lengths, while at large correlation lengths the transverse correlation function becomes negative at maximum separation $r\sim L/2$, an effect that disappears as the system increases in size.

We examine the morphology of magnetic structures in thin plasma accretion disks, generalizing a stationary ideal magnetohydrodynamics model for the time-dependent viscoresistive case. Our analysis deals with small-scale perturbations to a central dipolelike magnetic field, which give rise—as in the ideal case—to the periodic modulation of magnetic flux surfaces along the radial direction, corresponding to the formation of a toroidal current channel's sequence. These microstructures suffer an exponential damping in time because of the nonzero resistivity coefficient, allowing us to define a configuration lifetime which mainly depends on the midplane temperature and on the length scale of the structure itself. By means of this lifetime, we show that the microstructures can exist within the inner regions of stellar disks in a defined range of temperatures, precisely for radii of $R\lesssim {10}^9\mathrm{cm}$ and temperatures of ${10}^4\mathrm{K}\lesssim T\lesssim {10}^5\mathrm{K}$. Their duration—minutes to hours—is shown to be consistent with local transient phenomena rather than with a steady equilibrium.

We present an algorithm for solving the self-consistency equations of the dynamical mean-field theory (DMFT) with high precision and efficiency at low temperatures. In each DMFT iteration, the impurity problem is mapped to an auxiliary Hamiltonian, for which the Green function is computed by combining determinantal quantum Monte Carlo (BSS-QMC) calculations with a multigrid extrapolation procedure. The method is numerically exact, i.e., yields results which are free of significant Trotter errors, but retains the BSS advantage, compared to direct QMC impurity solvers, of linear (instead of cubic) scaling with the inverse temperature. The new algorithm is applied to the half-filled Hubbard model close to the Mott transition; detailed comparisons with exact diagonalization, Hirsch-Fye QMC, and continuous-time QMC are provided.

We report on the dynamical behavior of defects of strength $s=\pm 1/2$ in a lyotropic liquid crystal during the annihilation process. By following their positions using time-resolved polarizing microscopy technique, we present statistically significant evidence that the relative velocity between defect pairs is Gaussian distributed, antipersistent, and long-range correlated. We further show that simulations of the Lebwohl-Lasher model reproduce quite well our experimental findings.

We explore the phase behavior of tilted hard rods as a model of de Vries smectic behavior and the first order smectic-$C$ (Sm-$C$) to smectic-$A$ (Sm-$A$) phase transition. The free energy cost of azimuthal rotation of a molecule away from the local tilt direction is calculated via umbrella sampling. This calculation is used to map the hard rod system onto a lattice spin system which shows a cross-over from a continuous to first-order phase transition as the tilt of the rods is increased. This analysis offers a natural explanation of the first-order Sm-$A$–Sm-$C$ phase transition common to de Vries smectics.

We derive an exact closed-form expression for fidelity susceptibility of the quantum Ising model in the transverse field. We also establish an exact one-to-one correspondence between fidelity susceptibility in the ferromagnetic and paramagnetic phases of this model. Elegant summation formulas are obtained as a by-product of these studies.

We present some exact results on the behavior of branching and annihilating random walks, both in the directed percolation and parity conserving universality classes. Contrary to usual perturbation theory, we perform an expansion in the branching rate around the nontrivial pure annihilation (PA) model, whose correlation and response function we compute exactly. With this, the nonuniversal threshold value for having a phase transition in the simplest system belonging to the directed percolation universality class is found to coincide with previous nonperturbative renormalization group (RG) approximate results. We also show that the parity conserving universality class has an unexpected RG fixed point structure, with a PA fixed point which is unstable in all dimensions of physical interest.

We aim at quantitatively determining transport parameters like conductivity, mean free path, etc., for simple models of spatially completely disordered quantum systems, comparable to the systems which are sometimes referred to as Lifshitz models. While some low-energy eigenstates in such models always show Anderson localization, we focus on models for which most states of the full spectrum are delocalized, i.e., on the metallic regime. For the latter we determine transport parameters in the limit of high temperatures and low fillings using linear response theory. The Einstein relation (proportionality of conductivity and diffusion coefficient) is addressed numerically and analytically and found to hold. Furthermore, we find the transport behavior for some models to be in accord with a Boltzmann equation, i.e., rather long mean free paths, exponentially decaying currents, while this does not apply to other models even though they are also almost completely delocalized.

We show that the derivative of the logarithm of the average characteristic polynomial of a diffusing Wishart matrix obeys an exact partial differential equation valid for an arbitrary value of $N$, the size of the matrix. In the large $N$ limit, this equation generalizes the simple inviscid Burgers equation that has been obtained earlier for Hermitian or unitary matrices. The solution, through the method of characteristics, presents singularities that we relate to the precursors of shock formation in the Burgers equation. The finite $N$ effects appear as a viscosity term in the Burgers equation. Using a scaling analysis of the complete equation for the characteristic polynomial, in the vicinity of the shocks, we recover in a simple way the universal Bessel oscillations (so-called hard-edge singularities) familiar in random-matrix theory.