We study the Lehmann rotation of the cholesteric helix in droplets of the liquid crystal N-($p$-methoxybenzilidene)-$p$-butylaniline doped with a small amount of the chiral molecule R811 when they are subjected to a temperature gradient. We show that the helix rotates much faster when it is parallel to the temperature gradient than when it is perpendicular to it. The first configuration is obtained by submitting the droplets to an ac electric field parallel to the temperature gradient, whereas the second one is observed at zero field. We show that the rotation velocity of the helix strongly depends on the droplet radius, even when the helix is parallel to the temperature gradient. This observation supports the idea that the Leslie thermomechanical coupling cannot explain alone the Lehmann effect.

The structure of a single alanine-based ACE-AEAAAKEAAAKA-NH2 peptide in explicit aqueous solutions with mixed inorganic salts (NaCl and KCl) is investigated by using molecular simulations. The concentration of Na${}^{+}$, $c_{{\mathrm{Na}}^{+}}$, varies from 0.0$M$ to 1.0$M$, whereas the concentration of K${}^{+}$ is $1-c_{{\mathrm{Na}}^{+}}$. The simulated peptide is very sensitive to the change of concentration ratio between Na${}^{+}$ and K${}^{+}$. When the concentration ratio between Na${}^{+}$ and K${}^{+}$ is changed from 0.5/0.5, the structure of the peptide becomes loose or disordered. This specific phenomenon is confirmed via checking the changes of helix parameters and mapping the free energy along different coordinates. The higher normalized probability of forming direct and indirect salt bridges between residues Glu$7^{-}$ and Lys11${}^{+}$ and the smallest probability of forming ringlike structures should be responsible for the stabilized helix structure in the 0.5 Na${}^{+}$/0.5 K${}^{+}$ solution. Furthermore, a noticeable conformational transition from an extended helix to an $\alpha$ helix is found in the 0.5 Na${}^{+}$/0.5 K${}^{+}$ solution, where a local ion cloud shows that some Na${}^{+}$ ions in the inner shells are still directly binding with the peptide, while K${}^{+}$ in the outer shells are moving into the inner shells, keeping the peptide in the collapsed state.

Aquaporins (AQPs), which transport water molecules across cell membranes, are involved in many physiological processes. Recently, it is reported that the water-water interactions within the channel are broken at the aromatic/arginine selectivity filter (ar/R region), which prevents proton transportation [U. K. Eriksson et al., Science 340, 1346 (2013)]. However, the effects of the conformational fluctuations of amino acids on water transportation remain unclear. Using all-atom molecular dynamics simulations, we analyze water transportation and fluctuations of amino acids within AQP1. The amino acids exhibit $1/f$ fluctuations, indicating possession of long-term memory. Moreover, we find that water molecules crossing the ar/R region obey a non-Poisson process. To investigate the effect of $1/f$ fluctuations on water transportation, we perform restrained molecular dynamics simulations of AQP1 and simple Langevin stochastic simulations. As a result, we confirm that $1/f$ fluctuations of amino acids contribute to water transportation in AQP1. These findings appreciably enhance our understanding of AQPs and suggest possibilities for developing biomimetic nanopores.

We propose a network of excitable systems that spontaneously initiates and completes loop searching against the removal and attachment of connection links. Network nodes are excitable systems of the FitzHugh-Nagumo type that have three equilibrium states depending on input from other nodes. The attractors of this network are stationary solutions that form loops, except in the case of an acyclic network. Thus, the system is regarded as a loop searching system. To design a system capable of self-recovery (the ability to find a loop when one of the connections in an existing loop is suddenly removed), we have investigated regulatory rules for the interaction between nodes and have used two characteristic properties of nonlinear dynamical systems to provide a solution: postinhibitory rebound phenomena and saddle-node bifurcation.

In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we model rare event occurrences due to large fluctuations probabilistically and employ a WKB ansatz to approximate their rate of occurrence. This results in the generation of a two-point boundary value problem that models the interaction of the state variables and the most likely noise force required to induce a rare event. The resulting equations of motion of describing the phenomenon are shown to be singularly perturbed. Vastly different time scales among the variables are leveraged to reduce the dimension and predict the dynamics on the slow manifold in a deterministic setting. The resulting constrained equations of motion may be used to directly compute an exponent that determines the probability of rare events. To verify the theory, a stochastic damped Duffing oscillator with three equilibrium points (two sinks separated by a saddle) is analyzed. The predicted switching time between states is computed using the optimal path that resides in an expanded phase space. We show that the exponential scaling of the switching rate as a function of system parameters agrees well with numerical simulations. Moreover, the dynamics of the original system and the reduced system via center manifolds are shown to agree in an exponentially scaling sense.

Analytical spiral wave solutions for reaction-diffusion equations play an important role in studying spiral wave dynamics. In this paper, we focus on such analytical solutions in the case of highly excitable media. We present numerical evidence that, for rigidly rotating spiral waves in highly excitable media, the species values in the spiral core region do harmonic oscillations but not relaxation ones, and their amplitudes grow linearly with the distance from the rotation center. An analytical solution is proposed to describe such spiral wave dynamics, and the quantitative comparisons between the numerical results and the analytical solutions show that the proposed spiral core solution works well in highly excitable media.

We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density $\rho$ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, $D\left(\rho \right)=D_0{\rho }^2$. An explicit expression for $D_0$ is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.

To apply spectroscopy as a diagnostic tool for dense plasmas, a theoretical approach to pressure broadening is indispensable. Here, a quantum-statistical theory is used to calculate spectral line shapes of few-electron atoms. Ionic perturbers are treated quasistatically as well as dynamically via a frequency fluctuation model. Electronic perturbers are treated in the impact approximation. Strong electron-emitter collisions are consistently taken into account with an effective two-particle T-matrix approach. Convergent close-coupling calculations give scattering amplitudes including Debye screening for neutral emitters. For charged emitters, the effect of plasma screening is estimated. The electron densities considered reach up to $n_e={10}^{27}$ m${}^{-3}$. Temperatures are between $T={10}^4$ and ${10}^5$ K. The results are compared with a dynamically screened Born approximation for Lyman lines of H and H-like Li as well as for the He 3889 Å line. For the last, a comprehensive comparison to simulations and experiments is given. For the H Lyman-$\alpha$ line, the width and shift are drastically reduced by the Debye screening. In the T-matrix approach, the line shape is notably changed due to the dependence on the magnetic quantum number of the emitter, whereas the difference between spin-scattering channels is negligible.

Collective excitations of electron spins in a ferromagnetic sample dominated by the magnetic dipole-dipole interaction strongly influence the field structure of microwave radiation. A small quasi-two-dimensional ferrite disk with magnetic-dipolar-mode (MDM) oscillation spectra can behave as a source of specific fields in vacuum, termed magnetoelectric (ME) fields. A coupling between the time-varying electric and magnetic fields in the ME-field structures is different from such a coupling in regular electromagnetic fields. The ME fields are characterized by strong energy confinement at a subwavelength region of microwave radiation, topologically distinctive power-flow vortices, and helicity parameters [E. O. Kamenetskii, R. Joffe, and R. Shavit, Phys. Rev. E 87, 023201 (2013)]. We study topological properties of microwave ME fields by loading a MDM ferrite particle with different dielectric samples. We establish a close connection between the permittivity parameters of dielectric environment and the topology of ME fields. We show that the topology of ME fields is strongly correlated with the Fano-resonance spectra observed at terminals of a microwave structure. We reveal specific thresholds in the Fano-resonance spectra appearing at certain permittivity parameters of dielectric samples. We show that ME fields originated from MDM ferrite disks can be distinguished by topological portraits of the helicity parameters and can have a torsion degree of freedom. Importantly, the ME-field phenomena can be viewed as implementations of space-time coordinate transformations on waves.

We propose an algorithm, multifractal cross-correlation analysis (MFCCA), which constitutes a consistent extension of the detrended cross-correlation analysis and is able to properly identify and quantify subtle characteristics of multifractal cross-correlations between two time series. Our motivation for introducing this algorithm is that the already existing methods, like multifractal extension, have at best serious limitations for most of the signals describing complex natural processes and often indicate multifractal cross-correlations when there are none. The principal component of the present extension is proper incorporation of the sign of fluctuations to their generalized moments. Furthermore, we present a broad analysis of the model fractal stochastic processes as well as of the real-world signals and show that MFCCA is a robust and selective tool at the same time and therefore allows for a reliable quantification of the cross-correlative structure of analyzed processes. In particular, it allows one to identify the boundaries of the multifractal scaling and to analyze a relation between the generalized Hurst exponent and the multifractal scaling parameter ${\lambda }_q$. This relation provides information about the character of potential multifractality in cross-correlations and thus enables a deeper insight into dynamics of the analyzed processes than allowed by any other related method available so far. By using examples of time series from the stock market, we show that financial fluctuations typically cross-correlate multifractally only for relatively large fluctuations, whereas small fluctuations remain mutually independent even at maximum of such cross-correlations. Finally, we indicate possible utility of MFCCA to study effects of the time-lagged cross-correlations.

We present a nonequilibrium strong-coupling approach to inhomogeneous systems of ultracold atoms in optical lattices. We demonstrate its application to the Mott-insulating phase of a two-dimensional Fermi-Hubbard model in the presence of a trap potential. Since the theory is formulated self-consistently, the numerical implementation relies on a massively parallel evaluation of the self-energy and the Green's function at each lattice site, employing thousands of CPUs. While the computation of the self-energy is straightforward to parallelize, the evaluation of the Green's function requires the inversion of a large sparse ${10}^d\times {10}^d$ matrix, with $d>6$. As a crucial ingredient, our solution heavily relies on the smallness of the hopping as compared to the interaction strength and yields a widely scalable realization of a rapidly converging iterative algorithm which evaluates all elements of the Green's function. Results are validated by comparing with the homogeneous case via the local-density approximation. These calculations also show that the local-density approximation is valid in nonequilibrium setups without mass transport.

Highly engineered materials are arousing great interest because of their ability to manipulate heat, as described by the coordinate transformation approach. Based on recently developed analog gravity models, we present how a simple device based on nematic liquid crystals can achieve in principle either thermal concentration or expulsion. These outcomes are shown to stem from the topological properties of a disclination-like structure, induced in the nematic phase by anchoring conditions.

We study the statistical properties of orientation and rotation dynamics of elliptical tracer particles in two-dimensional, homogeneous, and isotropic turbulence by direct numerical simulations. We consider both the cases in which the turbulent flow is generated by forcing at large and intermediate length scales. We show that the two cases are qualitatively different. For large-scale forcing, the spatial distribution of particle orientations forms large-scale structures, which are absent for intermediate-scale forcing. The alignment with the local directions of the flow is much weaker in the latter case than in the former. For intermediate-scale forcing, the statistics of rotation rates depends weakly on the Reynolds number and on the aspect ratio of particles. In contrast with what is observed in three-dimensional turbulence, in two dimensions the mean-square rotation rate increases as the aspect ratio increases.

Strongly confined active liquids are subject to unique hydrodynamic interactions due to momentum screening and lubricated friction by the confining walls. Using numerical simulations, we demonstrate that two-dimensional dilute suspensions of fore-aft asymmetric polar swimmers in a Hele-Shaw geometry can exhibit a rich variety of novel phase behaviors depending on particle shape, including coherent polarized density waves with global alignment, persistent counterrotating vortices, density shocks and rarefaction waves. We also explain these phenomena using a linear stability analysis and a nonlinear traffic flow model, both derived from a mean-field kinetic theory.

The fluctuation theorem of the Crooks type is studied for thermodynamic nonlinear-multivariate systems. In particular, a bivariate system having a limit cycle is discussed in detail. It is explicitly shown how the time reversal operation has to be combined with the parity transformation in order to derive the fluctuation theorem for the change of the “renormalized entropy.” Furthermore, breakdown of the symmetry in a limit-cycle model due to the effect of fluctuations is also discussed.

We study the problem of the basis of an open quantum system, under a quantum chaotic environment, which is preferred in view of its stationary reduced density matrix (RDM), that is, the basis in which the stationary RDM is diagonal. It is shown that, under an initial condition composed of sufficiently many energy eigenstates of the total system, such a basis is given by the eigenbasis of a renormalized self-Hamiltonian of the system, in the limit of large Hilbert space of the environment. Here, the renormalized self-Hamiltonian is given by the unperturbed self-Hamiltonian plus a certain average of the interaction Hamiltonian over the environmental degrees of freedom. Numerical simulations performed in two models, both with the kicked rotor as the environment, give results consistent with the above analytical predictions.

Various biological sensory systems exhibit a response to a relative change of the stimulus, often referred to as fold-change detection. In the past few years, fold-change detecting mechanisms, based on transcriptional networks, have been proposed. Here we present a fold-change detecting mechanism, based on protein-protein interactions, consisting of two interacting proteins. This mechanism does not consume chemical energy and is not subject to transcriptional and translational noise, in contrast to previously proposed mechanisms. We show by analytical and numerical calculations that the mechanism is robust and can have a fast, precise, and efficient response for parameters that are relevant to eukaryotic cells.

We study diffusion coefficients of liquid domains by explicitly taking into account the two-layered structure called leaflets of the bilayer membrane. In general, the velocity fields associated with each leaflet are different and the layers sliding past each other cause frictional coupling. We obtain analytical results of diffusion coefficients for a circular liquid domain in a leaflet, and quantitatively study their dependence on the interleaflet friction. We also show that the diffusion coefficients diverge in the absence of coupling between the bilayer and solvents, even when the interleaflet friction is taken into account. In order to corroborate our theory, the effect of the interleaflet friction on the correlated diffusion is examined.