The dynamics of the fluxon in the Josephson junction is studied. The dielectric layer of the junction has a variable thickness. It is shown that the modified area of the junction acts on the fluxon as a potential barrier. The relation between the critical bias current and the thickness of the dielectric layer is analytically and numerically determined.

While previous works have shown that an overwhelming number of scale-free networks are sparse, there still exist some real-world networks including social networks, urban networks, information networks, which are by observation dense. In this paper, we propose a framework for generating scale-free graphs with a dense feature using two simple yet helpful operations: first-order subdivision and line operation. From the theoretical point of view, our method can be used not only to produce desired scale-free graphs with a density feature, i.e., a power-law exponent $\gamma$ falling into the interval $1<\gamma \le 2$, but also to establish many other unexpected networked models, for instance, power-law models having a large diameter. In addition, the networked models generated upon our framework show an especially assortative structure. That is, their own Pearson correlation coefficients are able to achieve the theoretical upper bound. Last but not the least, we find the sizes of community in the proposed models to follow the power law in a form with respect to modularity maximization.

Predicting missing links in real networks is an important open problem in network science to which considerable efforts have been devoted, giving as a result a vast plethora of link prediction methods in the literature. In this work, we take a different point of view on the problem and focus on predictability instead of prediction. By considering ensembles defined by well-known network models, we prove analytically that even the best possible link prediction method, given by the ensemble connection probabilities, yields a limited precision that depends quantitatively on the topological properties—such as degree heterogeneity, clustering, and community structure—of the ensemble. This suggests an absolute limitation to the predictability of missing links in real networks, due to the irreducible uncertainty arising from the random nature of link formation processes. We show that a predictability limit can be estimated in real networks, and we propose a method to approximate such a bound from real-world networks with missing links. The predictability limit gives a benchmark to gauge the quality of link prediction methods in real networks.

The conformational and dynamical properties of active polymers in solution are determined by the nature of the activity. Here, the behavior of polymers with self-propelled, active Brownian particle-type monomers differs qualitatively from that of polymers with monomers driven externally by colored-noise forces. We present simulation and theoretical results for polymers in solution in the presence of external active noise. In simulations, a semiflexible bead-spring chain is considered, in analytical calculations, a continuous linear wormlike chain. Activity is taken into account by independent monomer or site velocities, with orientations changing in a diffusive manner. In simulations, hydrodynamic interactions (HIs) are taken into account by the Rotne-Prager-Yamakawa tensor or by an implementation of the active polymer in the multiparticle-collision-dynamics approach for fluids. To arrive at an analytical solution, the preaveraged Oseen tensor is employed. The active process implies a dependence of the stationary-state properties on HIs via the polymer relaxation times. With increasing activity, HIs lead to an enhanced swelling of flexible polymers, and the conformational properties differ substantially from those of polymers with self-propelled monomers in the presence of HIs, or free-draining polymers. The polymer mean-square displacement is enhanced by HIs. Over a wide range of timescales, hydrodynamics leads to a subdiffusive regime of the site mean-square displacement for flexible active polymers, with an exponent of $5/7$, larger than that of the Rouse $\left(1/2\right)$ and Zimm $\left(2/3\right)$ models of passive polymers.

We study the possibility of efficient intermittent locomotion for two-link bodies that slide by changing their interlink angle periodically in time. We find that the anisotropy ratio of the sliding friction coefficients is a key parameter, while solutions have a simple scaling dependence on the friction coefficients' magnitudes. With very anisotropic friction, efficient motions involve coasting in low-drag states, with rapid and asymmetric power and recovery strokes. As the anisotropy decreases, burst-and-coast motions change to motions with long power strokes and short recovery strokes, and roughly constant interlink angle velocity on each. These motions are seen in the spaces of sinusoidal and power-law motions described by two and five parameters, respectively. Allowing the duty cycle to vary greatly increases the motions' efficiency compared to the case of symmetric power and recovery strokes. Allowing further variations in the concavity of the power and recovery strokes improves the efficiency further only when friction is very anisotropic. Near isotropic friction, a variety of optimally efficient motions are found with more complex waveforms. Many of the optimal sinusoidal and power-law motions are similar to those that we find with an optimization search in the space of more general periodic functions (truncated Fourier series). When we increase the resistive force's power-law dependence on velocity, the optimal motions become smoother, slower, and less efficient, particularly near isotropic friction.

We develop polarized epifluorescence microscopy (PFM), a technique to qualitatively determine a director field, even when refraction effects are too strong to use optical polarized microscopy. We present the basic theory behind the technique and cover in detail the experimental setup. We validate PFM on the well-studied cases of a planar nematic cell, spherical nematic droplets, and a cylindrical capillary filled with nematic liquid crystal. Last, we use nematic capillary bridges to demonstrate that PFM can indeed provide measurements of the director field, even when refraction effects are large.

The present study is devoted to the investigation of spectral properties of an alternated sequence of magnetic and dielectric layers containing a dual defect based on magnetic and nematic layers. Combining the Hydrodynamic Continuum Theory for nematic liquid crystals and Berreman's formalism, we determine how the nematic ordering affects the light localization, polarization rotation, and slow-light phenomena observed in the magnetophotonic system. In particular, we analyze the effects associated with a field-induced reorientation of the director in a nematic defect with strong planar boundary conditions. Our results reveal that field-induced reorientation of the nematic ordering can be used as an efficient mechanism to tune and control the spectral properties of magnetophotonic structure, anomalies in group velocity, and the wavelength mismatch between resonant mode and maximum polarization. The effects of nematic layer thickness are also analyzed.

We studied the paranematic ordering induced by a polymer network in the isotropic phase of a liquid crystal (LC) that occurs in polymer-stabilized cells with bend configuration of the LC director (π cells) fabricated via photopolymerization of photoreactive monomer RM 82 added in small concentrations (3–5 wt %) to a nematic LC [4-cyano-4′-pentylbiphenyl (5CB)] when low voltage was applied across the cell. The polymer network formed in the nematic phase of the LC consists of fine fibrils that are aligned along the LC director and thus mirror the bend deformation of the LC at the time of polymerization. When heated to temperatures above the nematic-to-isotropic (N-I) phase transition such highly ordered polymer network anchors LC molecules providing ordering of the LC around the fibrils which results in unusually high optical retardation of the cell, $R_{\mathrm{cell}}$. We present a theoretical model that relates $R_{\mathrm{cell}}$ to the degree of order of the fibrils, the anchoring energy of the LC molecules on the surface of the polymer fibrils, and the fibril radius $r_0$. Fitting of the experimental $R_{\mathrm{cell}}\left(T\right)$ curves with the developed model reveals correlation of $r_0$ with the nematic correlation length ${\xi }_0$ which characterizes penetration of the nematic order in the isotropic phase of the LC. Accepting ${\xi }_0$ as a material constant of about 1 nm leads to a very small radius of the fibrils, $r_0\sim 1\mathrm{nm}$, which is also supported by other reported experimental data. High optical retardation and fast electro-optical response of the cells at the temperatures deep into the isotropic phase point toward the enhancement of the polymer-induced paranematic order by a well-oriented layer of LC molecules that are absorbed on the surface of fibrils. Application of high voltage at the isotropic phase temperatures results in high variations of the optical retardation of the cells. Characteristic on and off response times were about 10–100 μs, independent of the cell gap. Combination of large voltage-driven changes of the optical retardation occurring in the low-viscosity isotropic state with switching times that are at least two orders of magnitude shorter than the typical relaxation times of the cells operating in the nematic phase make such polymer-stabilized π cells very promising for application in fast electro-optical switches and light modulators.

Magnetic nozzles are convergent-divergent applied magnetic fields which are commonly used in electric propulsion, manufacturing, and material processing industries. This paper studies the previously overlooked physics in confining the thermalized ions injected from a near-uniform inlet in the magnetic nozzle. Through fully kinetic planar-3V particle-in-cell (PIC) modeling and simulation, an electric potential barrier is found on the periphery of the nozzle throat, which serves to confine the thermalized ions by the electric force. With the initial thermal energy as driving force and insufficient magnetic confinement, the ions overshoot the most divergent magnetic line, which results in the accumulation of positive space charges around the throat. The accumulated charges would create an ion-confining potential barrier with limited extent. Apart from the finite-electron Larmor radius (FELR) effect, two more factors are put forward to account for the limited extent of the potential barrier: the depletion of ion thermal energy and the short-circuiting effect. The influences of inlet temperature ratio of ions to electrons and magnetic inductive strength $B_0$ are quantitively investigated using the PIC code. The results indicate that the potential barrier serves as a medium to transfer the gas dynamic thrust to the magnetic nozzle while providing constrain to the ions, like the solid wall in a de Laval nozzle. In high-$B_0$ regime, the finite-ion Larmor radius (FILR) effect becomes dominant rather than the FELR effect in the plasma confinement of magnetic nozzles.

In this work, we studied the stopping power of deuterium-tritium (DT) plasmas mixed with impurities to the injected charged particles. Based on the Brown-Preston-Singleton model, the analytical expression for the change ratio of stopping power (denoted by $\eta )$ induced by impurities in DT plasmas is developed, in which both classical short-distance collision part and quantum correction contribution are purely linear response to the impurity concentration ${\xi }_X$, while the classical long-range collision brings about higher-order nonlinear response to ${\xi }_X$. Furthermore, the expression for change ratio of deposition depth (denoted by $\chi )$ of charged particles induced by impurities in DT plasmas is also derived. As applications, we systemically investigated the energy loss of $\alpha$ particles deposited into a hot dense DT plasma mixed with impurity $X(X=\mathrm{C}$, Si, Ge), where the temperature and density of DT are smaller than 10 keV and 500 g/${\mathrm{cm}}^3$ and the concentration of $X{\xi }_X$ is less than $5\%$. The numerical results suggest that (i) for the case of C mixed into DT, both change ratios of stopping power and deposition depth of $\alpha$ particles (i.e., $\eta$ and $\chi )$ are linear response to the concentration of C ${\xi }_C$; (ii) for the case of Si mixed into DT, the second-order nonlinear response of $\eta$ and $\chi$ to ${\xi }_{\text{Si}}$ cannot be ignored when the densities of DT are larger than 200 g/${\mathrm{cm}}^3$; and (iii) for the case of Ge mixed into DT, the second- and third-order nonlinear response of $\eta$ and $\chi$ to ${\xi }_{\text{Ge}}$ are very remarkable because of the higher ionization degree and heavier atomic mass of Ge. The formulas and findings in this work may be helpful to the research of internal confinement fusion (ICF) related implosion physics and may provide useful theoretical guidance and data for the design of ICF target.

Nuclear mass measurements by means of Schottky mass spectrometry critically rely on an accurate determination of revolution frequencies of the circulating ions in a storage ring. Such a harmonic retrieval problem is conventionally tackled via the periodogram of the Schottky data, where the ion peaks are identified and their spectral locations are obtained by fittings. However, the discrete frequency grid of the periodogram has unfortunately hampered a fine resolution of two closely spaced harmonics. We thereby propose a method based on the state space representation in the frequency domain to overcome this limit. Moreover, its frequency-selective merit has allowed the method to focus only on a narrow band and thus greatly reduced the computational cost while still retaining superb accuracy. With the real Schottky data from an isochronous-Schottky beam time at the experimental cooler-storage ring in Lanzhou, the accuracy of the retrieved harmonics is demonstrated to be around 1 ppm, as limited by the anisochronism effect of the ion optics.

We present a concise, general, and efficient procedure for calculating the cluster integrals that relate thermodynamic virial coefficients to molecular interactions. The approach encompasses nonpairwise intermolecular potentials generated from quantum chemistry or other sources; a simple extension permits efficient evaluation of temperature and other derivatives of the virial coefficients. We demonstrate with a polarizable model of water. We argue that cluster-integral methods are a potent yet underutilized instrument for the development and application of first-principles molecular models and methods.

We consider the additive superimposition of an extensive number of independent Euclidean Random Matrices in the high-density regime. The resolvent is computed with techniques from free probability theory, as well as with the replica method of statistical physics of disordered systems. Results for the spectrum and eigenmodes are shown for a few applications relevant to computational neuroscience, and are corroborated by numerical simulations.

The exchange-driven growth model describes the mean-field kinetics of a population of composite particles (clusters) subject to pairwise exchange interactions. Exchange in this context means that upon interaction of two clusters, one loses a constituent unit (monomer) and the other gains this unit. Two variants of the exchange-driven growth model appear in applications. They differ in whether clusters of zero size are considered active or passive. In the active case, clusters of size zero can acquire a monomer from clusters of positive size. In the passive case they cannot, meaning that clusters reaching size zero are effectively removed from the system. We show that the large-time behavior is very different for the two variants of the model. We first consider an isolated system. In the passive case, the cluster size distribution tends towards a self-similar evolution and the typical cluster size grows as a power of time. In the active case, we identify a broad class of kernels for which the the cluster size distribution tends to a nontrivial time-independent equilibrium in which the typical cluster size is finite. We next consider a nonisolated system in which monomers are input at a constant rate. In the passive case, the cluster size distribution again attains a self-similar profile in which the typical cluster size grows as a power of time. In the active case, a surprising new behavior is found: the cluster size distribution asymptotes to the same equilibrium profile found in the isolated case but with an amplitude that increases linearly with time.

Path thermodynamic formulation of nonequilibrium reactive systems is considered. It is shown through simple practical examples that this approach can lead to results that contradict well established thermodynamic properties of such systems. Rigorous mathematical analysis confirming this fact is presented.

Stochasticity is introduced to a well studied class of recursively grown graphs: $(u,v)$-flower nets, which have power-law degree distributions as well as small-world properties (when $u=1)$. The stochastic variant interpolates between different (deterministic) flower graphs thus adding flexibility to the model. The random multiplicative growth process involved, however, leads to a spread ensemble of networks with finite variance for the number of links, nodes, and loops. Nevertheless, the degree exponent and loopiness exponent attain unique values in the thermodynamic limit of infinitely large graphs. We also study a class of mixed flower networks, closely related to the stochastic flowers, but which are grown recursively in a deterministic way. The deterministic growth of mixed flower-nets eliminates ensemble spreads, and their recursive growth allows for exact analysis of their (uniquely defined) mixed properties.

We study the homogeneous symmetrical threshold model with independence (noise) by pair approximation and Monte Carlo simulations on Erdős-Rényi and Watts-Strogatz graphs. The model is a modified version of the famous Granovetter's threshold model: with probability $p$ a voter acts independently, i.e., takes randomly one of two states $\pm 1$; with complementary probability $1-p$, a voter takes a given state, if a sufficiently large fraction (above a given threshold $r)$ of individuals in its neighborhood is in this state. We show that the character of the phase transition, induced by the noise parameter $p$, depends on the threshold $r$, as well as graph's parameters. For $r=0.5$ only continuous phase transitions are observed, whereas for $r>0.5$ discontinuous phase transitions also are possible. The hysteresis increases with the average degree $\langle k\rangle$ and the rewriting parameter $\beta$. On the other hand, the dependence between the width of the hysteresis and the threshold $r$ is nonmonotonic. The value of $r$, for which the maximum hysteresis is observed, overlaps pretty well with the size of the majority used for the descriptive norms in order to manipulate people within social experiments. We put the results obtained within this paper into a broader picture and discuss them in the context of two other models of binary opinions: the majority-vote and the $q$-voter model. Finally, we discuss why the appearance of social hysteresis in models of opinion dynamics is desirable.

Modeling stochastic gene expression has long relied on Markovian hypothesis. In recent years, however, this hypothesis is challenged by the increasing availability of time-resolved data. Correspondingly, there is considerable interest in understanding how non-Markovian reaction kinetics of gene expression impact protein variations across a population of genetically identical cells. Here, we analyze a stochastic model of gene expression with arbitrary waiting-time distributions, which includes existing gene models as its special cases. We find that stationary probabilistic behavior of this non-Markovian system is exactly the same as that of an equivalent Markovian system with the same substrates. Based on this fact, we derive analytical results, which provide insight into the roles of feedback regulation and molecular memory in controlling the protein noise and properties of the steady states, which are inaccessible via existing methodology. Our results also provide quantitative insight into diverse cellular processes involving stochastic sources of gene expression and molecular memory.

The genetic composition of a naturally developing population is considered as due to mutation, selection, genetic drift, and recombination. Selection is modeled as single-locus terms (additive fitness) and two-loci terms (pairwise epistatic fitness). The problem is posed to infer epistatic fitness from population-wide whole-genome data from a time series of a developing population. We generate such data in silico and show that in the quasilinkage equilibrium phase of Kimura, Neher, and Shraiman, which pertains at high enough recombination rates and low enough mutation rates, epistatic fitness can be quantitatively correctly inferred using inverse Ising-Potts methods.

We derive hydrodynamics of a prototypical one-dimensional model, having variable-range hopping, which mimics passive diffusion and ballistic motion of active, or self-propelled, particles. The model has two main ingredients—the hardcore interaction and the competing mechanisms of short- and long-range hopping. We calculate two density-dependent transport coefficients—the bulk-diffusion coefficient and the conductivity, the ratio of which, despite violation of detailed balance, is connected to particle-number fluctuation by an Einstein relation. In the limit of infinite-range hopping, the model exhibits, upon tuning density $\rho$ (or activity), a “superfluidlike” transition from a finitely conducting fluid phase to an infinitely conducting “superfluid” phase, characterized by a divergence in conductivity $\chi \left(\rho \right)\sim {(\rho -{\rho }_c)}^{-1}$ with ${\rho }_c$ being the critical density. The diverging conductivity greatly increases particle (or vacancy) mobility and thus induces “giant” number fluctuations in the system.