Using direct numerical simulations, we study dynamo action under Taylor-Green forcing for a magnetic Prandtl number of $0.5$. We observe bistability with weak- and strong-magnetic-field branches. Both the dynamo branches undergo subcritical dynamo transition. We also observe a host of dynamo states including constant, periodic, quasiperiodic, and chaotic magnetic fields. One of the chaotic states originates through a quasiperiodic route with phase locking, while the other chaotic attractor appears to follow the Newhouse-Ruelle-Takens route to chaos. We also observe intermittent transitions between quasiperiodic and chaotic states for a given Taylor-Green forcing.

We study the propagation of highly nonlinear waves in a branched (Y-shaped) granular crystal composed of chains of spherical particles of different materials, arranged at variable branch angles. We experimentally test the dynamic behavior of a solitary pulse, or of a train of solitary waves, crossing the Y-junction interface, and splitting between the two branches. We describe the dependence of the split pulses’ speed and amplitude on the branch angles. Analytic predictions based on the quasiparticle model and numerical simulations based on Hertzian interactions between the particles are found to be in excellent agreement with the experimental data.

The aim of this paper is to study the periodic orbits of the generalized van der Waals Hamiltonian system. The tool for studying such periodic orbits is the averaging theory. Moreover, for this Hamiltonian system we provide information on its ${\mathcal{C}}^1$ nonintegrability, i.e., on the existence of a second first integral of class ${\mathcal{C}}^1$.

We obtain an exact solution for the motion of a particle driven by a spring in a Brownian random-force landscape, the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model. Many experiments on quasistatic driving of elastic interfaces (Barkhausen noise in magnets, earthquake statistics, shear dynamics of granular matter) exhibit the same universal behavior as this model. It also appears as a limit in the field theory of elastic manifolds. Here we discuss predictions of the ABBM model for monotonous, but otherwise arbitrary, time-dependent driving. Our main result is an explicit formula for the generating functional of particle velocities and positions. We apply this to derive the particle-velocity distribution following a quench in the driving velocity. We also obtain the joint avalanche size and duration distribution and the mean avalanche shape following a jump in the position of the confining spring. Such nonstationary driving is easy to realize in experiments, and provides a way to test the ABBM model beyond the stationary, quasistatic regime. We study extensions to two elastically coupled layers, and to an elastic interface of internal dimension $d$, in the Brownian force landscape. The effective action of the field theory is equal to the action, up to one-loop corrections obtained exactly from a functional determinant. This provides a connection to renormalization-group methods.

The behavior of thermodynamic response functions and the thermodynamic scalar curvature in the supercritical region have been studied for a Lennard-Jones fluid based on a revised modified Benedict-Webb-Rubin equation of state. Response function extrema are sometimes used to estimate the Widom line, which is characterized by the maxima of the correlation lengths. We calculated the Widom line for the Lennard-Jones fluid without using any response function extrema. Since the volume of the correlation length is proportional to the Riemannian thermodynamic scalar curvature, the locus of the Widom line follows the slope of maximum curvature. We show that the slope of the Widom line follows the slope of the isobaric heat capacity maximum only in the close vicinity of the critical point and that, therefore, the use of response function extrema in this context is problematic. Furthermore, we constructed the vapor-liquid coexistence line for the Lennard-Jones fluid using the fact that the correlation length, and therefore the thermodynamic scalar curvature, must be equal in the two coexisting phases. We compared the resulting phase envelope with those from simulation data where multiple histogram reweighting was used and found striking agreement between the two methods.

Statistical behaviors of packing collections of granular chains in a two-dimensional container have been investigated experimentally. On compaction from their own gravity, the longer chains pack into a structure with lower packing density due to the prevalence of backbone loops. The packing of chains can be considered as the jamming of the granular system. The structure factor of packing chains shows scaling behavior $g\left(q\right)\sim q^{-2}$ in good agreement with dense polymer solutions. In addition, we compute various probability distributions of distances and estimate three crucial contact exponents, finding that the scaling behavior from granular chains is in accord with the theoretical expectation of polymers. Finally, an orientational anticorrelation of granular chains is observed by bond-bond correlation function, which agrees with the results in the two-dimensional model of compact polymers.

The stationary to drifting transition of a subharmonic wave pattern is studied in the presence of inhomogeneities and drift forces as the pattern wavelength is comparable with the system size. We consider a pinning-depinning transition of stationary subharmonic waves in a tilted quasi-one-dimensional fluidized shallow granular bed driven by a periodic air flow in a small cell. The transition is mediated by the competition of the inherent periodicity of the subharmonic pattern, the asymmetry of the system, and the finite size of the cell. Measurements of the mean phase velocity of the subharmonic pattern are in good agreement with those inferred from an amplitude equation, which takes into account asymmetry and finite-size effects of the system, emphasizing the main ingredients and mechanism of the transition.

Identifying and removing spurious links in complex networks is meaningful for many real applications and is crucial for improving the reliability of network data, which, in turn, can lead to a better understanding of the highly interconnected nature of various social, biological, and communication systems. In this paper, we study the features of different simple spurious link elimination methods, revealing that they may lead to the distortion of networks’ structural and dynamical properties. Accordingly, we propose a hybrid method that combines similarity-based index and edge-betweenness centrality. We show that our method can effectively eliminate the spurious interactions while leaving the network connected and preserving the network's functionalities.

Wave scattering in chaotic systems can be characterized by its spectrum of resonances, $z_n=E_n-i\frac{{\Gamma }_n}{2}$, where $E_n$ is related to the energy and ${\Gamma }_n$ is the decay rate or width of the resonance. If the corresponding ray dynamics is chaotic, a gap is believed to develop in the large-energy limit: almost all ${\Gamma }_n$ become larger than some $\gamma$. However, rare cases with $\Gamma <\gamma$ may be present and actually dominate scattering events. We consider the statistical properties of these supersharp resonances. We find that their number does not follow the fractal Weyl law conjectured for the bulk of the spectrum. We also test, for a simple model, the universal predictions of random matrix theory for density of states inside the gap and the hereby derived probability distribution of gap size.

Solutions for characterizing both electromagnetic wave propagation in, and scattering by, a gyrotropic sphere are obtained based on some recently published literature. Both gyrotropic permittivity and permeability tensors are considered herein, and both transmitted internal fields and scattered external fields are derived theoretically. Compared with problems of a uniaxial sphere, a gyroelectric sphere, and a gyromagnetic sphere, the scattering problem considered here is found to be astonishingly complicated but more generalized in formulation and solution procedure. Numerical validations are made by reducing our results to a gyromagnetic sphere and comparing them with the results obtained using the Fourier transform method, where excellent agreements are observed. Then, radar cross sections (RCSs) versus electric and magnetic gyrotropy ratios are computed, while hybrid effects due to both electric and magnetic gyrotropies are studied extensively, where some special cases of uniaxial spheres are demonstrated. It is shown that characteristics of gyrotropy parameters in Cartesian coordinates may lead to considerably large variations in RCS values, elucidating physical significance of gyrotropy and anisotropy ratios in scattering control. The generalized formulation of the problem is expected to have wide practical applications, while some features of this gyrotropic sphere may help other researchers or engineers to understand more physical insight. In addition, some critical mistakes made in literature were corrected.

The conical-boundary-integral-equation method has been proposed for calculation of the sensitive optical response of two-dimensional photonic band gaps (PBGs), including dielectric, absorbing, and high-conductive rods of various shapes working in any wavelength range. It is possible to determine the diffracted field by computing the scattering matrices separately for any grating boundary profile. The computation of the matrices is based on the solution of a $2\times 2$ system of singular integral equations at each interface between two different materials. The advantage of our integral formulation is that the discretization of the integral equation system and the factorization of the discrete matrices, which takes the majority of the computing time, are carried out only once for a boundary. It turns out that a small number of collocation points per boundary combined with a high convergence rate can provide an adequate description of the dependence on diffracted energy of very different PBGs illuminated at arbitrary incident and polarization angles. The numerical results presented describe the significant impact of rod shape on diffraction in PBGs supporting polariton-plasmon excitation, particularly in the vicinity of resonances and at high filling ratios. The diffracted energy response calculated vs the array cell geometry parameters was found to vary from a few up to a few hundred percent. The influence of other types of anomalies (i.e., waveguide anomalies, cavity modes, Fabry-Perot and Bragg resonances, Rayleigh orders, etc.), conductivity, and polarization states on the optical response is demonstrated.

While worldwide census data provide statistical evidence that firmly link the population density with several indicators of social welfare, the precise mechanisms underlying these observations are largely unknown. Here we study the impact of population density on the evolution of public cooperation in structured populations and find that the optimal density is uniquely related to the percolation threshold of the host graph irrespective of its topological details. We explain our observations by showing that spatial reciprocity peaks in the vicinity of the percolation threshold, when the emergence of a giant cooperative cluster is hindered neither by vacancy nor by invading defectors, thus discovering an intuitive yet universal law that links the population density with social prosperity.

The BFW model introduced by Bohman, Frieze, and Wormald [Random Struct. Algorithms, 25, 432 (2004)], and recently investigated in the framework of discontinuous percolation by Chen and D'Souza [Phys. Rev. Lett. 106, 115701 (2011)], is studied on the square and simple-cubic lattices. In two and three dimensions, we find numerical evidence for a strongly discontinuous transition. In two dimensions, the clusters at the threshold are compact with a fractal surface of fractal dimension $d_f=1.49\pm 0.02$. On the simple-cubic lattice, distinct jumps in the size of the largest cluster are observed. We proceed to analyze the tree-like version of the model, where only merging bonds are sampled, for dimension two to seven. The transition is again discontinuous in any considered dimension. Finally, the dependence of the cluster-size distribution at the threshold on the spatial dimension is also investigated.

We show that in a variant of the minority game problem, the agents can reach a state of maximum social efficiency, where the fluctuation between the two choices is minimum, by following a simple stochastic strategy. By imagining a social scenario where the agents can only guess about the number of excess people in the majority, we show that as long as the guessed value is sufficiently close to the reality, the system can reach a state of full efficiency or minimum fluctuation. A continuous transition to less efficient condition is observed when the guessed value becomes worse. Hence, people can optimize their guess for excess population to optimize the period of being in the majority state. We also consider the situation where a finite fraction of agents always decide completely randomly (random trader) as opposed to the rest of the population who follow a certain strategy (chartist). For a single random trader the system becomes fully efficient with majority-minority crossover occurring every 2 days on average. For just two random traders, all the agents have equal gain with arbitrarily small fluctuations.

To explain the appearance of heterogeneities in the plasma membrane, I propose a hypothesis which begins with the observation that fluctuations in the membrane curvature are coupled to the difference between compositions of one leaf and the other. Because of this coupling, the most easily excited fluctuations can occur at nonzero wave numbers. When the coupling is sufficiently strong, it is well-known that it leads to microphase separation and modulated phases. I note that when the coupling is less strong, the tendency toward modulation remains manifest in a liquid phase that exhibits a transient structure of a characteristic size, that is, it is a microemulsion. The characteristic size of the fluctuating domains is estimated to be on the order of 100 nm, and experiments to verify this hypothesis are proposed.

We investigate an analytically tractable toy model for thermally induced polymorphic dynamics of cooperatively rearranging biofilaments-like microtubules. The proposed four-block model, which can be seen as a coarse-grained approximation of the full polymorphic tube model, permits a complete analytical treatment of all thermodynamic properties including correlation functions and angular Fourier mode distributions. Due to its mathematical tractability the model straightforwardly leads to some physical insights in recently discussed phenomena like the “length dependent persistence length.” We show that a polymorphic filament can disguise itself as a classical worm-like chain on small and on large scales and yet display distinct anomalous tell-tale features indicating an inner switching dynamics on intermediate length scales.

An algorithm for identifying parameters in dynamical systems is developed in this work using homotopy transformations and the single-shooting method. The equations governing the dynamics of the mathematical model are augmented with observer-like homotopy terms that smooth the objective function. As a result, premature convergence to a local minimum is avoided and the obtained parameter estimates are globally optimal. Numerical examples are presented to demonstrate the application of the proposed approach to chaotic systems.

In quantum spin chains at criticality, two types of scaling for the entanglement entropy exist: one comes from conformal field theory (CFT), and the other is for entanglement support of matrix product state (MPS) approximation. On the other hand, the quantum spin-chain models can be mapped onto two-dimensional (2D) classical ones by the Suzuki-Trotter decomposition. Motivated by the scaling and the mapping, we introduce information entropy for 2D classical spin configurations as well as a spectrum, and examine their basic properties in the Ising and the three-state Potts models on the square lattice. They are defined by the singular values of the reduced density matrix for a Monte Carlo snapshot. We find scaling relations of the entropy compatible with the CFT and the MPS results. Thus, we propose that the entropy is a kind of “holographic” entanglement entropy. At $T_c$, the spin configuration is fractal, and various sizes of ordered clusters coexist. Then, the singular values automatically decompose the original snapshot into a set of images with different length scales, respectively. This is the origin of the scaling. In contrast to the MPS scaling, long-range spin correlation can be described by only few singular values. Furthermore, the spectrum, which is a set of logarithms of the singular values, also seems to be a holographic entanglement spectrum. We find multiple gaps in the spectrum, and in contrast to the topological phases, the low-lying levels below the gap represent spontaneous symmetry breaking. These contrasts are strong evidence of the dual nature of the holography. Based on these observations, we discuss the amount of information contained in one snapshot.

Recent work by Teifel and Mahler [Eur. Phys. J. B 75, 275 (2010)] raises legitimate concerns regarding the validity of quantum nonequilibrium work relations in processes involving moving hard walls. We study this issue in the context of the rapidly expanding one-dimensional quantum piston. Utilizing exact solutions of the time-dependent Schrödinger equation, we find that the evolution of the wave function can be decomposed into static and dynamic components, which have simple semiclassical interpretations in terms of particle-piston collisions. We show that nonequilibrium work relations remain valid at any finite piston speed, provided both components are included, and we study explicitly the work distribution for this model system.