We consider how to control the extension of curvature-induced defects in the hexagonal order covering different curved surfaces. In these frames we propose a physical mechanism for improving structures of two-dimensional spherical colloidal crystals (SCCs). For any SCC comprising of about 300 or less particles the mechanism transforms all extended topological defects (ETDs) in the hexagonal order into the point disclinations. Perfecting the structure is carried out by successive cycles of the particle implantation and subsequent relaxation of the crystal. The mechanism is potentially suitable for obtaining colloidosomes with better selective permeability. Our approach enables modeling the most topologically regular tubular and conical two-dimensional nanocrystals including various possible polymorphic forms of the HIV viral capsid. Different HIV-like shells with an arbitrary number of structural units (SUs) and desired geometrical parameters are easily formed. Faceting of the obtained structures is performed by minimizing the suggested elastic energy.

The shock wave in one-dimensional bead chain is studied numerically. When the shock wave arrives, the bead velocity oscillates around the piston velocity. It is found that the shock front is composed of several solitary waves and the limitation of the maximum bead velocity is 2 times the piston velocity in the limiting case where the initial overlap is zero. If the initial overlap is not zero, then the maximum bead velocity is less than 2 times the piston velocity but larger than the piston velocity. As the initial overlap increases from zero to the finite value, the shock velocity depends on not only the piston velocity but also the initial overlap. The crossover of the dependence of the shock velocity on the piston velocity from the zero initial prestress to the finite value is obtained in the present manuscript. It is an improvement of the results presented in Phys. Rev. Lett. 108, 058001 (2012). In other words, the dependence of the shock velocity on the parameters of the granular materials is given.

Using the field theoretic renormalization group technique in the two-loop approximation, turbulent Prandtl numbers are obtained in the general $A$ model of passive vector advected by fully developed turbulent velocity field with violation of spatial parity introduced via the continuous parameter $\rho$ ranging from $\rho =0$ (no violation of spatial parity) to $\left|\rho \right|=1$ (maximum violation of spatial parity). Values of $A$ represent a continuously adjustable parameter which governs the interaction structure of the model. In nonhelical environments, we demonstrate that $A$ is restricted to the interval $-1.723\le A\le 2.800$ (rounded to 3 decimal places) in the two-loop order of the field theoretic model. However, when $\rho >0.749$ (rounded to 3 decimal places), the restrictions may be removed, which means that presence of helicity exerts a stabilizing effect onto the possible stationary regimes of the system. Furthermore, three physically important cases $A\in \{-1,0,1\}$ are shown to lie deep within the allowed interval of $A$ for all values of $\rho$. For the model of the linearized Navier-Stokes equations ($A=-1$) up to date unknown helical values of the turbulent Prandtl number have been shown to equal 1 regardless of parity violation. Furthermore, we have shown that interaction parameter $A$ exerts strong influence on advection-diffusion processes in turbulent environments with broken spatial parity. By varying $A$ continuously, we explain high stability of the kinematic MHD model ($A=1$) against helical effects as a result of its proximity to the $A=0.912$ (rounded to 3 decimal places) case where helical effects are completely suppressed. Contrary, for the physically important $A=0$ model, we show that it lies deep within the interval of models where helical effects cause the turbulent Prandtl number to decrease with $\left|\rho \right|$. We thus identify internal structure of interactions given by the parameter $A$, and not the vector character of the admixture itself being the dominant factor influencing diffusion-advection processes in the helical $A$ model.

Signal inference problems with non-Gaussian posteriors can be hard to tackle. Through using the concept of Gibbs free energy these posteriors are rephrased as Gaussian posteriors for the price of computing various expectation values with respect to a Gaussian distribution. We present a way of translating these expectation values to a language of operators which is similar to that in quantum mechanics. This simplifies many calculations, for instance such as those involving log-normal priors. The operator calculus is illustrated by deriving a self-calibrating algorithm which is tested with mock data.

We have studied the folding of ribonuclease A by mapping it onto coarse-grained lattice protein models. With replica exchange Wang-Landau sampling, we calculated the free energy vs end-to-end distance as a function of temperature. A mapping to the famous hydrophobic-polar (HP) model shows a relatively shallow folding funnel and flat free energy minimum, reflecting the high degeneracy of the ground state. In contrast, extending the HP model with an additional “neutral” monomer type (i.e., a mapping to the three-letter H0P model) has a well developed, rough free energy funnel with a low degeneracy ground state. In both cases, folding funnels are asymmetric with temperature dependent shape.

In the recent progress in nonequilibrium thermodynamics, information has been recognized as a kind of thermodynamic resource that can drive thermodynamic current without any direct energy injection. In this paper, we establish the framework of linear irreversible thermodynamics for a broad class of autonomous information processing. In particular, we prove that the Onsager reciprocity holds true with information: The linear response matrix is well-defined and is shown symmetric with both of the information affinity and the conventional thermodynamic affinity. As an application, we derive a universal bound for the efficiency at maximum power for information-driven engines in the linear regime. Our result reveals the fundamental role of information flow in linear irreversible thermodynamics.

We study work extraction from the Dicke model achieved using simple unitary cyclic transformations keeping into account both a nonoptimal unitary protocol and the energetic cost of creating the initial state. By analyzing the role of entanglement, we find that highly entangled states can be inefficient for energy storage when considering the energetic cost of creating the state. Such a surprising result holds notwithstanding the fact that the criticality of the model at hand can sensibly improve the extraction of work. While showing the advantages of using a many-body system for work extraction, our results demonstrate that entanglement is not necessarily advantageous for energy storage purposes, when nonoptimal processes are considered. Our work shows the importance of better understanding the complex interconnections between nonequilibrium thermodynamics of quantum systems and correlations among their subparts.

Atomic mass and interatomic interaction are the two key quantities that significantly affect the heat conduction carried by phonons. Here, we study the effects of long-range (LR) interatomic interaction and mass disorder on the phonon transport in a one-dimensional harmonic chain with up to ${10}^5$ atoms. We find that while LR interaction reduces the transmission of low-frequency phonons, it enhances the transmission of high-frequency phonons by suppressing the localization effects caused by mass disorder. Therefore, LR interaction is able to boost heat conductance in the high-temperature regime or in the large size regime, where the high-frequency modes are important.

The influence of potential asymmetries on stochastic resonance (SR) subject to both multiplicative and additive noise is studied by using two-state theory, where three types of asymmetries are introduced in double-well potential by varying the depth, the width, and both the depth and the width of the left well alone. The characteristics of SR in the asymmetric cases are different from symmetric ones, where asymmetry has a strong influence on output signal-to-noise ratio (SNR) and optimal noise intensity. Even optimal noise intensity is also associated with the steepness of the potential-barrier wall, which is generally ignored. Moreover, the largest SNR in asymmetric SR is found to be relatively larger than the symmetric one, which also closely depends on noise intensity ratio. In addition, a moderate cross-correlation intensity between two noises is good for improving the output SNR. More interestingly, a double SR phenomenon is observed in certain cases for two correlated noises, whereas it disappears for two independent noises. The above clues are helpful in achieving weak signal detection under heavy background noise.

In this work we study quantum signatures of charge flipping vortices, found in the classical discrete nonlinear Schrödinger trimer, by use of the Bose-Hubbard model. We are able to identify such signatures in the quantum energy eigenstates, for instance when comparing the site amplitudes of the classical charge flipping vortices with the probability distribution over different particle configurations. It is also discussed how to construct quantum states that correspond to the classical charge flipping vortices and which effects can lead to deviations between the classical and quantum dynamics. We also examine properties of certain coherent states: classical-like quantum states that can be used to derive the classical model. Several quantum signatures are identified when studying the dynamics of these coherent states, for example, when comparing the average number of particles on a site with the classical site amplitude, when comparing the quantum and classical currents and topological charge, and when studying the evolution of the quantum probability amplitudes. The flipping of the quantum currents are found to be an especially robust feature of these states.

The hierarchical product of two graphs represents a natural way to build a larger graph out of two smaller graphs with less regular and therefore more heterogeneous structure than the Cartesian product. Here we study the eigenvalue spectrum of the adjacency matrix of the hierarchical product of two graphs. Introducing a coupling parameter describing the relative contribution of each of the two smaller graphs, we perform an asymptotic analysis for the full spectrum of eigenvalues of the adjacency matrix of the hierarchical product. Specifically, we derive the exact limit points for each eigenvalue in the limits of small and large coupling, as well as the leading-order relaxation to these values in terms of the eigenvalues and eigenvectors of the two smaller graphs. Given its central roll in the structural and dynamical properties of networks, we study in detail the Perron-Frobenius, or largest, eigenvalue. Finally, as an example application we use our theory to predict the epidemic threshold of the susceptible-infected-susceptible model on a hierarchical product of two graphs.

Using coarse-grained molecular dynamics simulations, we study the relaxation of bilayer vesicles, uniaxially compressed by an atomic force microscope cantilever. The relaxation time exhibits a strong force dependence. Force-compression curves are very similar to recent experiments wherein giant unilamellar vesicles were compressed in a nearly identical manner.

Droplets can bounce indefinitely on a liquid bath vertically vibrated in a sinusoidal fashion. We here present experimental results that extend this observation to forcing signals composed of a combination of two commensurable frequencies. The Faraday and Goodridge thresholds are characterized. Then a number of vertical bouncing modes are reported, including walkers. The vertical motion can become chaotic, in which case the horizontal motion is an alternation of walk and stop.

We study the polygons governing the convex hull of a point set created by the steps of $n$ independent two-dimensional random walkers. Each such walk consists of $T$ discrete time steps, where $x$ and $y$ increments are independent and identically distributed Gaussian. We analyze area $A$ and perimeter $L$ of the convex hulls. We obtain probability densities for these two quantities over a large range of the support by using a large-deviation approach allowing us to study densities below ${10}^{-900}$. We find that the densities exhibit in the limit $T\to \infty$ a time-independent scaling behavior as a function of $A/T$ and $L/\sqrt{T}$, respectively. As in the case of one walker $\left(n=1\right)$, the densities follow Gaussian distributions for $L$ and $\sqrt{A}$, respectively. We also obtained the rate functions for the area and perimeter, rescaled with the scaling behavior of their maximum possible values, and found limiting functions for $T\to \infty$, revealing that the densities follow the large-deviation principle. These rate functions can be described by a power law for $n\to \infty$ as found in the $n=1$ case. We also investigated the behavior of the averages as a function of the number of walks $n$ and found good agreement with the predicted behavior.

The well-established method of phase reduction neglects information about a limit-cycle oscillator's approach towards its periodic orbit. Consequently, phase reduction suffers in practicality unless the magnitude of the Floquet multipliers of the underlying limit cycle are small in magnitude. By defining isostable coordinates of a periodic orbit, we present an augmentation to classical phase reduction which obviates this restriction on the Floquet multipliers. This framework allows for the study and understanding of periodic dynamics for which standard phase reduction alone is inadequate. Most notably, isostable reduction allows for a convenient and self-contained characterization of the dynamics near unstable periodic orbits.

The concept of sequential visibility graph motifs—subgraphs appearing with characteristic frequencies in the visibility graphs associated to time series—has been advanced recently along with a theoretical framework to compute analytically the motif profiles associated to horizontal visibility graphs (HVGs). Here we develop a theory to compute the profile of sequential visibility graph motifs in the context of natural visibility graphs (VGs). This theory gives exact results for deterministic aperiodic processes with a smooth invariant density or stochastic processes that fulfill the Markov property and have a continuous marginal distribution. The framework also allows for a linear time numerical estimation in the case of empirical time series. A comparison between the HVG and the VG case (including evaluation of their robustness for short series polluted with measurement noise) is also presented.

The robustness of controlling complex networks is significant in network science. In this paper, we focus on evaluating and analyzing the robustness of controlling edge dynamics in complex networks against node failure. Using three categories of all nodes to quantify the robustness, we find that the percentages of the three types of nodes are mainly related to the degree distribution of networks. The simulation results of model networks and analytic calculations show that the sparse inhomogeneous networks, which emerge in many real complex networks, have strong control robustness from the point of the number of ordinary nodes, but the strong positive correlation between in and out degrees reduces the control robustness. Evaluation of real-world networks indicates that most of them have few or no critical nodes, that is, they do not need to increase driver nodes to maintain control for most of node failures. Then an adding circuit-link strategy is proposed to optimize the robustness of edge controllability.

In the present paper, the locking phenomenon induced by distance-dependent delay in ring structured neuronal networks is investigated, wherein each neuron is modeled by a FitzHugh-Nagumo neuron. Through increasing the element time delay, the different spatiotemporal patterns are observed. By calculating the interspike interval and its value that is divided by the delay of the nearest neurons, it is found that these patterns are actually the lockings between the period of spiking and the distance-dependent delay of the connected neurons. The lockings could also be revealed by the mean time lag of the neurons and in different connection topologies. Furthermore, the influences of the network size and the coupling strength are investigated, wherein the former seems to play a negligible role on these locking patterns; in contrast, too small coupling strengths will blur the boundaries of different patterns and too large ones may destroy the high ratio locking patterns. Finally, one may predict the locking order which determines the emergence order of the patterns in the networks.

The description of the dynamics of a complex, high-dimensional system in terms of a low-dimensional set of collective variables $Y$ can be fruitful if the low-dimensional representation satisfies a Langevin equation with drift and diffusion coefficients that depend only on $Y$. We present a computational scheme to evaluate whether a given collective variable provides a faithful low-dimensional representation of the dynamics of a high-dimensional system. The scheme is based on the framework of a finite-difference Langevin equation, similar to that used for molecular-dynamics simulations. This allows one to calculate the drift and diffusion coefficients in any point of the full-dimensional system. The width of the distribution of drift and diffusion coefficients in an ensemble of microscopic points at the same value of $Y$ indicates to what extent the dynamics of $Y$ is described by a simple Langevin equation. Using a simple protein model, we show that collective variables often used to describe biopolymers display a non-negligible width both in the drift and in the diffusion coefficients. We also show that the associated effective force is compatible with the equilibrium free energy calculated from a microscopic sampling, but it results in markedly different dynamical properties.