We investigate nondegenerate bound-state solitons systematically in multicomponent Bose-Einstein condensates, through developing the Darboux transformation method to derive exact soliton solutions analytically. In particular, we show that bright solitons with nodes correspond to the excited bound states in effective quantum wells, in sharp contrast to the bright solitons and dark solitons reported before (which usually correspond to ground state and free state, respectively). We further demonstrate that bound-state solitons with nodes are induced by incoherent superposition of solitons in different components. Moreover, we reveal that the interactions between these bound-state solitons are usually inelastic, caused by the incoherent interactions between solitons in different components and the coherent interactions between solitons in the same component. Additionally, the detailed spectral stability analysis demonstrates the stability of nondegenerate bound-state solitons. The bound-state solitons can be used to study many different physical problems, such as beating dynamics, spin-orbit coupling effects, quantum fluctuations, and even quantum entanglement states.

Organisms have evolved in a daily cyclic environment, developing circadian cell-autonomous clocks that temporally organize a wide range of biological processes. Translation is a highly regulated process mainly associated with the activity of microRNAs (miRNAs) at the translation initiation step that impacts on the molecular circadian clock dynamics. Recently, a molecular titration mechanism was proposed to explain the interactions between some miRNAs and their target mRNAs; new evidence also indicates that regulation by miRNA is a nonlinear process such that there is a threshold level of target mRNA below which protein production is drastically repressed. These observations led us to use a theoretical model of the circadian molecular clock to study the effect of miRNA-mediated translational thresholds on the molecular clock dynamics. We model the translational threshold by introducing a phenomenological Hill equation for the kinetics of PER translation and show how the parameters associated with translation kinetics affect the period, amplitude, and time delays between clock mRNA and clock protein expression. We show that our results are useful for analyzing experiments related to the translational regulation of negative elements of transcriptional-translational feedback loops. We also provide new elements for thinking about the translational threshold as a mechanism that favors the emergence of circadian rhythmicity, the tuning of the period-delay relationship and the cell capacity to control the protein oscillation amplitude with almost negligible changes in the mRNA amplitudes.

Microtubules are tubular proteins that form part of the cytoskeleton in eukaryotic cells. Because of their unique mechanical properties, many studies have theorized microtubules could show high-frequency mechanical vibrations. Others have further suggested these vibrations of the electrically polar microtubules could be a source of electric fields inside the cell that could serve some biological function, such as a role in organizing mitosis or also possibly in cell-to-cell communication. In this work, we use a transient method to simulate the electric fields that would be generated from a single microtubule supposing they could sustain vibrations. We evaluate the biological significance of the electric fields and the potential energy microtubules might exert on one another. Our simulation method allows us to evaluate vibrational modes that have not previously been studied. The simulations suggest the acoustic branch flexing mode would actually be the most electrically active. Our results suggest a single vibrating microtubule could potentially exert significant forces (those that exceed thermal energy) on biological dipoles or charges at distances larger then the Debye length, on the order of $10\mathrm{nm}$ from the surface of the microtubule, but interaction is not likely at greater distances.

Language change involves the competition between alternative linguistic forms. The spontaneous evolution of these forms typically results in monotonic growths or decays, such as in winner-take-all attractor behaviors. In the case of the Spanish past subjunctive, the spontaneous evolution of its two competing forms (ending in −ra and −se) was perturbed by the appearance of the Royal Spanish Academy in 1713, which enforced the spelling of both forms as perfectly interchangeable variants, at a moment in which the −ra form was predominant. Time series extracted from a massive corpus of books reveal that this regulation in fact produced a transient renewed interest for the old form −se which, once faded, left the −ra again as the dominant form up to the present day. We show that time series are successfully explained by a two-dimensional linear model that integrates an imitative and a novelty component. The model reveals that the temporal scale over which collective attention fades is in inverse proportion to the verb frequency. The integration of the two basic mechanisms of imitation and attention to novelty allows us to understand diverse competing objects, with lifetimes that range from hours for memes and news to decades for verbs, suggesting the existence of a general mechanism underlying cultural evolution.

Development of thermodynamic induction up to second order gives a dynamical bifurcation for thermodynamic variables and allows for the prediction and detailed explanation of nonequilibrium phase transitions with associated spontaneous symmetry breaking. By taking into account nonequilibrium fluctuations, long-range order is analyzed for possible pattern formation. Consolidation of results up to second order produces thermodynamic potentials that are maximized by stationary states of the system of interest. These potentials differ from the traditional thermodynamic potentials. In particular a generalized entropy is formulated for the system of interest which becomes the traditional entropy when thermodynamic equilibrium is restored. This generalized entropy is maximized by stationary states under nonequilibrium conditions where the standard entropy for the system of interest is not maximized. These nonequilibrium concepts are incorporated into traditional thermodynamics, such as a revised thermodynamic identity and a revised canonical distribution. Detailed analysis shows that the second law of thermodynamics is never violated even during any pattern formation, thus solving the entropic-coupling problem. Examples discussed include pattern formation during phase front propagation under nonequilibrium conditions and the formation of Turing patterns. The predictions of second-order thermodynamic induction are consistent with both observational data in the literature as well as the modeling of this data.

The features for the unsteady process of thermal equilibration (“the fast motions”) in a one-dimensional harmonic crystal lying in a viscous environment (e.g., a gas) are under investigation. It is assumed that initially the displacements of all the particles are zero and the particle velocities are random quantities with zero mean and a constant variance, thus, the system is far away from the thermal equilibrium. It is known that in the framework of the corresponding conservative problem the kinetic and potential energies oscillate and approach the equilibrium value that equals a half of the initial value of the kinetic energy. We show that the presence of the external damping qualitatively changes the features of this process. The unsteady process generally has two stages. At the first stage oscillations of kinetic and potential energies with decreasing amplitude, subjected to exponential decay, can be observed (this stage exists only in the underdamped case). At the second stage (which always exists), the oscillations vanish, and the energies are subjected to a power decay. The large- time asymptotics for the energy is proportional to $t^{-3/2}$ in the case of the potential energy and to $t^{-5/2}$ in the case the kinetic energy. Hence, at large values of time the total energy of the crystal is mostly the potential energy. The obtained analytic results are verified by independent numerical calculations.

Final-state sensitivity in a system with intermingled basins is investigated. Under a scaling assumption a dimension of the basins, referred to as the conditional external dimension, is introduced by which the uncertainty exponent is expressed. For an analytically tractable model, which is not a skew product type system, a multifractal analysis on the basin structure is performed. It is shown that the scaling assumption is valid and the conditional external dimension as the left end-point value of the singularity spectrum is determined by the transient motions converging to neither of the chaotic attractors. It is also shown that such transient motions bring about a phase transition in the singularity spectrum.

Dynamical processes in various natural and social phenomena have been described by a series of events or event sequences showing non-Poissonian, bursty temporal patterns. Temporal correlations in such bursty time series can be understood not only by heterogeneous interevent times (IETs) but also by correlations between IETs. Modeling and simulating various dynamical processes requires us to generate event sequences with a heavy-tailed IET distribution and memory effects between IETs. For this, we propose a Farlie-Gumbel-Morgenstern copula-based algorithm for generating event sequences with correlated IETs when the IET distribution and the memory coefficient between two consecutive IETs are given. We successfully apply our algorithm to the cases with heavy-tailed IET distributions. We also compare our algorithm to the existing shuffling method to find that our algorithm outperforms the shuffling method for some cases. Our copula-based algorithm is expected to be used for more realistic modeling of various dynamical processes.

We study the relaxation dynamics of the polymer networks that are constructed based on a degree distribution specific to small-world networks. The employed building algorithm generates polymers with a large variety of architectures, thus allowing for a detailed study of the structural transition from a pure linear chain to dendritic polymer networks. This is done by varying a single parameter $p$, which measures the randomness in the degree of the network's nodes. The dynamics is investigated in the framework of the generalized Gaussian structures model by monitoring the influence of the parameter $p$ and of the stiffness parameter $q$ on the behavior of the relaxation quantities: averaged monomer displacement, storage modulus, and loss modulus. The structure properties of the constructed polymers are described by the mean-square radius of gyration. In the absence of stiffness, in the intermediate frequencies domain of the dynamical quantities we encounter different behaviours, such as a dendritic behavior followed by a linear one for very small values of $p$ or a single well-marked dendritic behavior for higher values of $p$. The stiffness parameter $q$ influences drastically the relaxation dynamics of these polymer networks and in general no evident scaling regions were encountered. However, for some values of the parameter set $(p,q)$, such as $(0.8,0.4)$, an extremely short constant slope region, less than one order of magnitude, was found.

Based on Fick's second law and Cahn-Hilliard theory, a conservative phase-field model is developed to track interface. The phase-field variable changes in a hyperbolic tangent behavior across the diffuse interface over which the interface curvature can be easily calculated. Different from the frequently used lattice-Boltzmann–based discrete method, the phase-field equation is discretized using a fourth-order Runge-Kutta method. Accordingly, the present numerical scheme alleviates the programming burden, reduces the memory usage, but maintains a high numerical accuracy. To achieve large-scale interface tracking, a parallel and adaptive-mesh-refinement algorithm is developed to reduce the computing overhead. Various cases of the interface evolutions under steady flow fields indicate that the proposed numerical scheme can capture the interface with high accuracy. Furthermore, the robustness of the numerical scheme is validated by simulating the Rayleigh-Taylor instability, and good agreement with previous work is achieved.

We consider the overdamped motion of a Brownian particle in an unbiased force field described by a periodic function of coordinate and time. A compact analytical representation has been obtained for the average particle velocity as a series in the inverse friction coefficient, from which follows a simple and clear proof of hidden symmetries of ratchets, reflecting the symmetry of summation indices of the applied force harmonics relative to their numbering from left to right and from right to left. We revealed the conditions under which (i) the ratchet effect is absent; (ii) the ratchet average velocity is an even or odd functional of the applied force, whose dependences on spatial and temporal variables are characterized by periodic functions of the main types of symmetries: shift, symmetric, and antisymmetric, and universal, which combines all three types. These conditions have been specified for forces with those dependences of a multiplicative (or additive-multiplicative) and additive structure describing two main ratchet types, pulsating and forced ratchets. We found the fundamental difference in dependences of the average velocity of pulsating and forced ratchets on parameters of spatial and temporal asymmetry of potential energy of a particle for systems in which the spatial and temporal dependence is described by a sawtooth potential and a deterministic dichotomous process, respectively. In particular, it is shown that a pulsating ratchet with a multiplicative structure of its potential energy cannot move directionally if the energy is of the universal symmetry type in time; this restriction is removed in the inertial regime, but only if the coordinate dependence of the energy does not belong to either symmetric or antisymmetric functions.

We study oscillatory and oscillation suppressed phases in coupled counter-rotating nonlinear oscillators. We demonstrate the existence of limit cycle, amplitude death, and oscillation death, and also clarify the Hopf, pitchfork, and infinite period bifurcations between them. Especially, the oscillation death is a new type of oscillation suppressions of which the inhomogeneous steady states are neutrally stable. We discuss the robust neutral stability of the oscillation death in non-conservative systems via the anti-parity-time-symmetric phase transitions at exceptional points in terms of non-Hermitian systems.

In this work, we explore a massless nonlinear Dirac equation, i.e., a nonlinear Weyl equation. We study the dynamics of its pulse solutions and find that a localized one-hump initial condition splits into a localized two-hump pulse, while an associated phase structure emerges in suitable components of the spinor field. For times larger than a transient time $t_s$ this pulse moves with the speed of light, effectively featuring linear wave dynamics and maintaining its shape (both in two and three dimensions). We show that for the considered nonlinearity, this pulse represents an exact solution of the nonlinear equation. Finally, we briefly comment on the generalization of the results to a broader class of nonlinearities.

Network geometry is currently a topic of growing scientific interest, as it opens the possibility to explore and interpret the interplay between structure and dynamics of complex networks using geometrical arguments. However, the field is still in its infancy. In this work we investigate the role of network geometry in determining the nature of the percolation transition in planar hyperbolic manifolds. Boettcher et al. [Nat. Comm. 3, 787 (2012)] have shown that a special type of two-dimensional hyperbolic manifolds, the Farey graphs, display a discontinuous transition for ordinary link percolation. Here we investigate using the renormalization group the critical properties of link percolation on a wider class of two-dimensional hyperbolic deterministic and random manifolds constituting the skeletons of two-dimensional cell complexes. These hyperbolic manifolds are built iteratively by subsequently gluing $m$-polygons to single edges. We show that when the size $m$ of the polygons is drawn from a distribution $q_m$ with asymptotic power-law scaling $q_m\simeq C{m}^{-\gamma }$ for $m\gg 1$, different universality classes can be observed depending on the value of the power-law exponent $\gamma$. Interestingly, the percolation transition is hybrid for $\gamma \in (3,4)$ and becomes continuous for $\gamma \in (2,3]$.

Single kinesin molecular motors can processively move along a microtubule (MT) a few micrometers on average before dissociating. However, cellular length scales over which transport occurs are several hundred microns and more. Why seemingly unreliable motors are used to transport cellular cargo remains poorly understood. We propose a theory for how low processivity, the average length of a single bout of directed motion, can enhance cellular transport when motors and cargos must first diffusively self-assemble into complexes. We employ stochastic modeling to determine the effect of processivity on overall cargo transport flux. We show that, under a wide range of physiologically relevant conditions, possessing “infinite” processivity does not maximize flux along MTs. Rather, we find that lowering processivity, i.e., weaker binding of motors to MTs, can improve transport flux. These results shed light on the relationship between processivity and transport efficiency and offer a theory for the physiological benefits of low motor processivity.

Instabilities in thin elastic sheets, such as wrinkles, are of broad interest both from a fundamental viewpoint and also because of their potential for engineering applications. Nematic liquid crystal elastomers offer a new form of control of these instabilities through direct coupling between microscopic degrees of freedom, resulting from orientational ordering of rodlike molecules, and macroscopic strain. By a standard method of dimensional reduction, we construct a plate theory for thin sheets of nematic elastomer. We then apply this theory to the study of the formation of wrinkles due to compression of a thin sheet of nematic liquid crystal elastomer atop an elastic or fluid substrate. We find the scaling of the wrinkle wavelength in terms of material parameters and the applied compression. The wavelength of the wrinkles is found to be nonmonotonic in the compressive strain due to the presence of the nematic. Finally, due to soft modes, the critical stress for the appearance of wrinkles can be much higher than in an isotropic elastomer and depends nontrivially on the manner in which the elastomer was prepared.

We employ a version of classical density functional theory to study the phase behavior of a simple model liquid crystal in an external field. The uniaxially symmetric molecules have a spherically symmetric core with superimposed orientation-dependent attractions. The interaction between the cores consists of a hard-sphere repulsion plus an isotropic square-well attraction. The anisotropic part of the interaction potential allows for the formation of a uniaxially symmetric nematic phase. The orientation of the molecules couples to an external polar field. The external field is capable of rotating the nematic director $\widehat{\mathit{n}}$ in the $x-z$ plane. The field is also capable of changing the topology of the phase diagram in that it suppresses the phase coexistence between an isotropic liquid and a nematic phase observed in the absence of the field. We study the transition from an unpolar to a polar nematic phase in terms of the orientation-distribution function (odf), nematic and polar order parameters, and components of $\widehat{\mathit{n}}$. If represented suitably the odf allows us to study orientational changes during the switching process between nonpolar and polar nematic phases. We also give a simple argument that explains why nematic order is lost whereas polar order persists up to the gas-liquid critical point along the coexistence curve. We also discuss the relevance of our theory for future experimental studies.

Molecular dynamics simulations of equilibrium structures and flows of nonpolar argon atoms confined by single-walled carbon nanotubes (SWCNTs) with circular cross section and rectangular cross section having the same area and the ratio between its sides $1:4$ have been performed. It has been shown that, inside these SWCNTs, argon atoms form the spatially ordered structures and, under action of external driving forces they move collectively along SWCNT's axes. It has been also obtained that there are two regimes of such collective movement. In the first regime, when the driving external force $f_{x0}$ is lower than a certain critical value $f_{xc}$, argon atoms flow through these SWCNTs with the finite average flow velocity. In the second regime, when the driving external force $f_{x0}$ exceeds $f_{xc}$, the retarding friction force acting on argon atoms from bounding wall carbon atoms gradually drops to zero and the average flow velocity exhibits an unlimited growth. Moreover, when the retarding friction force becomes close to zero, the fluid will continue to flow with the same constant velocity at switched off external driving force. Hence, in the second regime, argon atoms inside the above-mentioned SWCNTs demonstrate the ballistic frictionless flows which resemble the superfluidic liquid flow. It has been shown that collective frictionless ballistic flows of argon atoms through SWCNTs are caused by the crystalline structure of SWCNT's bounding walls and, for the same SWCNTs with random distribution of carbon atoms on the bounding walls, one can observe only the first regime of the argon atom flows.

A broad survey of viscoelastic data demonstrates that van der Waals, hydrogen-bonded, and ionic liquids, as well as polymeric, inorganic, and metallic melts share a structural relaxation pattern virtually insensitive to their morphological details. This mechanical simplicity is connected with that characterizing the fast reorientation dynamics prevailing in liquids devoid of a distinguishable secondary susceptibility peak. By these means one is able to uncover a generic spectral pattern which rationalizes the recently reported “universality” of relaxation strength vs stretching of the dielectric response of viscous liquids, significantly broadening the framework in which their relaxation behavior is assessed.