The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: (i) an interacting atomic Bose gas, and (ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition is observed in both scenarios. For large attractive values of the atom-atom interaction, the ground state is degenerate. For repulsive and small attractive interaction, the ground state is not degenerate and is well approximated by a boson coherent state. Both systems depict an excited state quantum phase transition. In both cases, a critical energy separates a region in which all the energy levels are degenerate in pairs, from another region in which there are no degeneracies. For the atomic system, the critical point displays a singularity in the density of states, whereas this behavior is largely smoothed for the mixed atom-molecule system.

Understanding the mechanisms of efficient and robust energy transfer in organic systems provides us with insights for the optimal design of artificial systems. In this paper, we explore the dynamics of excitation energy transfer (EET) through a complex quantum network by a toy model consisting of three sites coupled to environments. We study how the coherent evolution and the noise-induced decoherence work together to reach efficient EET and illustrate the role of the phase factor attached to the coupling constant in the EET. By comparing the differences between the Markovian and non-Markovian dynamics, we discuss the effect of environment and the spatial structure of system on the dynamics and the efficiency of EET. A intuitive picture is given to show how the exciton is transferred through the system. Employing the simple model, we show the robustness of EET efficiency under the influence of the environment and elucidate the important role of quantum coherence in EET. We go further to study the quantum feature of the EET dynamics by quantumness and show the importance of quantum coherence from a different perspective. We calculate the energy current in the EET and its quantumness, and results for different system parameters are presented and discussed.

The available kinetic models of assembly of viral protein capsids are focused primarily on the situations in vitro where the amount of protein is fixed. In vivo, however, the viral protein synthesis and capsid assembly occur under transient conditions in parallel with viral genome replication. Herein, a kinetic model describing the latter case of capsid assembly is proposed with emphasis on the period corresponding to the initial stage of viral genome replication. The analysis is aimed at small icosahedral capsids. With biologically reasonable values of model parameters, the model predicts rapid exponential growth of the populations of monomers and fully assembled capsids during the transient period of genome replication. Under the subsequent steady-state conditions with respect to replication, the monomer population is predicted to be nearly constant while the number of fully assembled capsids increases linearly. The kinetics of capsid disassembly, described briefly as well under conditions of negligible monomer concentration, exhibit a short induction period when the number of proteins in a capsid is only slightly smaller than in the beginning, followed by more rapid protein detachment. According to calculations, the latter kinetics may strongly depend on protein degradation.

Helical filaments having sections of reversed chirality are common phenomena in the biological realm. The apparent angle between the two sections of opposite handedness provides information about the geometry and elasticity of the junctional region. In this paper, the governing differential equations for the local helical axis are developed, and asymptotic solutions of the governing equations are solved by perturbation theory. The asymptotic solutions are compared with the corresponding numerical solutions, and the relative error at second order is found to be less than 1.5% over a range of biologically relevant curvature and torsion values from 0 to 1/2 in dimensionless units.

The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The interlayer diffusion constants act as a small parameter in the expansion and the unperturbed state coincides with the limiting setting where the multiplex layers are decoupled. The interaction between adjacent layers can seed the instability of a homogeneous fixed point, yielding self-organized patterns which are instead impeded in the limit of decoupled layers. Patterns on individual layers can also fade away due to cross-talking between layers. Analytical results are compared to direct simulations.

We study a resource utilization scenario characterized by intrinsic fitness. To describe the growth and organization of different cities, we consider a model for resource utilization where many restaurants compete, as in a game, to attract customers using an iterative learning process. Results for the case of restaurants with uniform fitness are reported. When fitness is uniformly distributed, it gives rise to a Zipf law for the number of customers. We perform an exact calculation for the utilization fraction for the case when choices are made independent of fitness. A variant of the model is also introduced where the fitness can be treated as an ability to stay in the business. When a restaurant loses customers, its fitness is replaced by a random fitness. The steady state fitness distribution is characterized by a power law, while the distribution of the number of customers still follows the Zipf law, implying the robustness of the model. Our model serves as a paradigm for the emergence of Zipf law in city size distribution.

A turbulent flow is characterized by velocity fluctuations excited in an extremely broad interval of wave numbers $k>{\Lambda }_f$, where ${\Lambda }_f$ is a relatively small set of the wave vectors where energy is pumped into fluid by external forces. Iterative averaging over small-scale velocity fluctuations from the interval ${\Lambda }_f<k\le {\Lambda }_0$, where $\eta =2\pi /{\Lambda }_0$ is the dissipation scale, leads to an infinite number of “relevant” scale-dependent coupling constants (Reynolds numbers) ${\text{Re}}_n\left(k\right)=O\left(1\right)$. It is shown that in the infrared limit $k\to {\Lambda }_f$, the Reynolds numbers $\text{Re}\left(k\right)\to {\text{Re}}_{\text{tr}}$, where ${\text{Re}}_{\text{tr}}$ is the recently numerically and experimentally discovered universal Reynolds number of “smooth” transition from Gaussian to anomalous statistics of spatial velocity derivatives. The calculated relation $\text{Re}\left({\Lambda }_f\right)={\text{Re}}_{\text{tr}}$ “selects” the lowest-order nonlinearity as the only relevant one. This means that in the infrared limit $k\to {\Lambda }_f$, all high-order nonlinearities generated by the scale elimination sum up to zero.

The accuracy of lattice Monte Carlo (LMC) simulation of biased diffusion models is of great importance as far as the simulation credibility is concerned. It is known that the fixed time step LMC algorithm can reproduce the mean and the variance of the particle displacement exactly for all discrete time steps. Thereby, we propose to use the skewness and other quantities to measure the accuracy. For the one-dimensional fixed time step LMC simulation, we obtain an explicit expression for the skewness and find that the algorithm always produces a negative skewness that converges to zero in the long-time limit when the velocity is positive. It is proved that the skewness is inversely proportional to the square root of the number of simulation steps and the first step error only depends on the Péclet number. We further discuss several other measures of the accuracy of the approximation based on appropriately defined mean-square errors, leading to interesting, unexpected results. The accuracy measures can exhibit complicated nonmonotonic behavior and the optimal step size may depend on the measure of accuracy used.

We report a systematic study of the ejected charge dynamics surrounding laser-produced 30-nm warm dense gold films using single-shot femtosecond electron shadow imaging and deflectometry. The results reveal a two-step dynamical process of the ejected electrons under high pump fluence conditions: an initial emission and accumulation of a large amount of electrons near the pumped surface region, followed by the formation of hemispherical clouds of electrons on both sides of the film, which escape into the vacuum at a nearly isotropic and constant velocity with an unusually high kinetic energy of more than 300 eV. We also developed a model of the escaping charge distribution that not only reproduces the main features of the observed charge expansion dynamics but also allows us to extract the number of ejected electrons remaining in the cloud.

In order to explore electric-field-induced transformations of polarization singularities in the polarization-resolved angular (conoscopic) patterns emerging after deformed-helix ferroelectric liquid crystal (DHFLC) cells with subwavelength helix pitch, we combine the transfer matrix formalism with the results for the effective dielectric tensor of biaxial FLCs evaluated using an improved technique of averaging over distorted helical structures. Within the framework of the transfer matrix method, we deduce a number of symmetry relations and show that the symmetry axis of $L$ lines (curves of linear polarization) is directed along the major in-plane optical axis which rotates under the action of the electric field. When the angle between this axis and the polarization plane of incident linearly polarized light is above its critical value, the $C$ points (points of circular polarization) appear in the form of symmetrically arranged chains of densely packed star-monstar pairs. We also emphasize the role of phase singularities of a different kind and discuss the enhanced electro-optic response of DHFLCs near the exceptional point where the condition of zero-field isotropy is fulfilled.

We present a reconstruction of the mean axisymmetric azimuthal and meridional flows in the Derviche Tourneur Sodium installation in Grenoble liquid sodium experiment. The experimental device sets a spherical Couette flow enclosed between two concentric spherical shells where the inner sphere holds a strong dipolar magnet, which acts as a magnetic propeller when rotated. Measurements of the mean velocity, mean induced magnetic field, and mean electric potentials have been acquired inside and outside the fluid for an inner sphere rotation rate of 9 Hz $\left(\text{Rm}\simeq 28\right)$. Using the induction equation to relate all measured quantities to the mean flow, we develop a nonlinear least-squares inversion procedure to reconstruct a fully coherent solution of the mean velocity field. We also include in our inversion the response of the fluid layer to the nonaxisymmetric time-dependent magnetic field that results from deviations of the imposed magnetic field from an axial dipole. The mean azimuthal velocity field we obtain shows superrotation in an inner region close to the inner sphere where the Lorentz force dominates, which contrasts with an outer geostrophic region governed by the Coriolis force, but where the magnetic torque remains the driver. The meridional circulation is strongly hindered by the presence of both the Lorentz and the Coriolis forces. Nevertheless, it contributes to a significant part of the induced magnetic energy. Our approach sets the scene for evaluating the contribution of velocity and magnetic fluctuations to the mean magnetic field, a key question for dynamo mechanisms.

We apply the Markov-random-field model to linear seismic tomography and propose a method to estimate the hyperparameters for the smoothness and the magnitude of the noise. Optimal hyperparameters can be determined analytically by minimizing the free energy function, which is defined by marginalizing the evaluation function. In synthetic inversion tests under various settings, the assumed velocity structures are successfully reconstructed, which shows the effectiveness and robustness of the proposed method. The proposed mathematical framework can be applied to inversion problems in various fields in the natural sciences.

We use a spring lattice model with springs following a bilinear elastoplastic-brittle constitutive behavior with spatial disorder in the yield and failure thresholds to study patterns of plasticity and damage evolution. The elastic–perfectly plastic transition is observed to follow percolation scaling with the correlation length critical exponent $\nu \approx 1.59$, implying the universality class corresponding to the long-range correlated percolation. A quantitative analysis of the plastic strain accumulation reveals a dipolar anisotropy (for antiplane loading) which vanishes with increasing hardening modulus. A parametric study with hardening modulus and ductility controlled through the spring level constitutive response demonstrates a wide spectrum of behaviors with varying degree of coupling between plasticity and damage evolution.

We employ a primitive path (PP) algorithm and the Gauss linking integral to study the degree of entanglement and knotting characteristics of linear polymer model chains in a melt under the action of a constant pulling force applied to selected chain ends. Our results for the amount of entanglement, the linking number, the average crossing number, the writhe of the chains and their PPs and the writhe of the entanglement strands all suggest a different response at the length scale of entanglement strands than that of the chains themselves and of the corresponding PPs. Our findings indicate that the chains first stretch at the level of entanglement strands and next the PP (tube) gets oriented with the “flow.” These two phases of the extension and alignment of the chains coincide with two phases related to the disentanglement of the chains. Soon after the onset of external force the PPs attain a more entangled conformation, and the number of nontrivially linked end-to-end closed chains increases. Next, the chains disentangle continuously to attain an almost unentangled conformation. Using the linking matrix of the chains in the melt, we furthermore show that these phases are accompanied by a different scaling of the homogeneity of the global entanglement in the system. The homogeneity of the end-to-end closed chains first increases to a maximum and then decreases slowly to a value characterizing a completely unlinked system.

Attosecond bursts of coherent synchrotronlike radiation are found when driving ultrathin relativistic electron disks in a quasi-one-dimensional regime of wakefield acceleration, in which the laser waist is larger than the wake wavelength. The disks of overcritical density shrink radially due to focusing wakefields, thus providing the transverse currents for the emission of an intense, radially polarized, half-cycle pulse of about 100 attoseconds in duration. The electromagnetic pulse first focuses to a peak intensity $\left(7\times {10}^{20}\mathrm{W}/{\mathrm{cm}}^2\right)$ 10 times larger than the driving pulse and then emerges as a conical beam. Basic dynamics of the radiative process are derived analytically and in agreement with particle-in-cell simulations. By making use of gas targets instead of solids to form the ultrathin disks, this method allows for high repetition rates required for applications.

We present comprehensive molecular dynamics results for phase-separation kinetics of fluids in a porous medium. This system is modeled by a symmetric Lennard-Jones fluid mixture with a quenched random field. The presence of disorder slows down domain growth from power-law to a logarithmic form. It also modifies the correlation functions and structure factors which characterize the morphology. In particular, the structure-factor tail shows a non-Porod behavior, which is the consequence of scattering from rough interfaces.

Ensemble-averaged high resolution direct numerical simulations of reverse spectral transfer are presented, extending on the many single realization numerical studies done up to now. This identifies this type of spectral transfer as a statistical property of magnetohydrodynamic turbulence and thus permits reliable numerical exploration of its dynamics. The magnetic energy decay exponent from these ensemble runs has been determined to be $n_E=(0.47\pm 0.03)+(13.9\pm 0.8)/R_{\lambda }$ for initially helical magnetic fields. We show that even after removing the Lorentz force term in the momentum equation, thus decoupling it from the induction equation, reverse spectral transfer still persists. The induction equation is now linear with an externally imposed velocity field, thus amenable to numerous analysis techniques. A new door has opened for analyzing reverse spectral transfer, with various ideas discussed.

We study the Riemannian metric and the Euler characteristic number of the Bloch band in a one-dimensional spin model with multisite spins exchange interactions. The Euler number of the Bloch band originates from the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. We study this approach analytically in a transverse field $XY$ spin chain with three-site spin coupled interactions. We define a class of cyclic quantum distance on the Bloch band and on the ground state, respectively, as a local characterization for quantum phase transitions. Specifically, we give a general formula for the Euler number by means of the Berry curvature in the case of two-band models, which reveals its essential relation to the first Chern number of the band insulators. Finally, we show that the ferromagnetic-paramagnetic phase transition in zero temperature can be distinguished by the Euler number of the Bloch band.

The traveler's dilemma game and the minimum-effort coordination game are social dilemmas that have received significant attention resulting from the fact that the predictions of classical game theory are inconsistent with the results found when the games are studied experimentally. Moreover, both the traveler's dilemma and the minimum-effort coordination games have potentially important applications in evolutionary biology. Interestingly, standard deterministic evolutionary game theory, as represented by the replicator dynamics in a well-mixed population, is also inadequate to account for the behavior observed in these games. Here we study the evolutionary dynamics of both these games in populations with interaction patterns described by a variety of complex network topologies. We investigate the evolutionary dynamics of these games through agent-based simulations on both model and empirical networks. In particular, we study the effects of network clustering and assortativity on the evolutionary dynamics of both games. In general, we show that the evolutionary behavior of the traveler's dilemma and minimum-effort coordination games on complex networks is in good agreement with that observed experimentally. Thus, formulating the traveler's dilemma and the minimum-effort coordination games on complex networks neatly resolves the paradoxical aspects of these games.

Delayed dynamics result from finite transmission speeds of a signal in the form of energy, mass, or information. In stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic, oscillatory, and unstable evolution. Despite the vast literature, quantifying this rich behavior is limited by a lack of explicit analytic studies of high-dimensional stochastic delay systems. Here we fill this gap for systems governed by a linear Langevin equation of any number of delays and spatial dimensions with additive Gaussian noise. By exploiting Laplace transforms we are able to derive an exact time-dependent analytic solution of the Langevin equation. By using characteristic functionals we are able to construct the full time dependence of the multivariate probability distribution of the stochastic process as a function of the delayed and nondelayed random variables. As an application we consider interactions in animal collective movement that go beyond the traditional assumption of instantaneous alignment. We propose models for coordinated maneuvers of comoving agents applicable to recent empirical findings in pigeons and bats whereby individuals copy the heading of their neighbors with some delay. We highlight possible strategies that individual pairs may adopt to reduce the variance in their velocity difference and/or in their spatial separation. We also show that a minimum in the variance of the spatial separation at long times can be achieved with certain ratios of measurement to reaction delay.