Area spectrum of slowly rotating black holes

We investigate the area spectrum for rotating black holes which are Kerr and BTZ black holes. For slowly rotating black holes, we use the Maggiore's idea combined with Kunstatter's method to derive their area spectra, which are equally spaced.     

Exponential transient rotating waves in a bistable ring of unidirectionally coupled maps

Properties of transient rotating waves in a bistable ring of unidirectionally coupled antisymmetric cubic maps are studied. A kinematical model shows that the duration of rotating waves increases exponentially with the number of elements. The probability density function of the duration of rotating waves generated under random initial conditions has a power law form up to a cut-off. In addition, spatiotemporal noise of intermediate intensity makes the duration of rotating waves increase. Further, rotating waves are stabilized through bifurcations of steady states as coupling strength increases.     

Synchronization,zero-resistance states and rotating Wigner crystal

We show, in a framework of a classical nonequilibrium model, that rotational angles of electrons moving in two dimensions (2D) in a perpendicular magnetic field can be synchronized by an external microwave field whose frequency is close to the Larmor frequency. The synchronization eliminates collisions between electrons and thus creates a regime with zero diffusion corresponding to the zero-resistance states observed in experiments with high mobility 2D electron gas (2DEG). For long range Coulomb interactions electrons form a rotating hexagonal Wigner crystal. Possible relevance of this effect of synchronization-induced self-assembly for planetary rings is discussed.     

Dynamics of rotating two-component Bose-Einstein condensates and its efficient computation

In this paper, we investigate the dynamics of rotating two-component Bose-Einstein condensates (BEC) based on the coupled Gross-Pitaevskii equations (CGPEs) with an angular momentum rotation term and an external driving field, and propose an efficient and accurate method for numerical simulations. We prove the conservation of the angular momentum expectation, derive the dynamic laws for the density of each component and condensate widths, and analyze the dynamics of a stationary state with its center shifted from the trap center. By formulating the CGPEs in either 2D (two-dimensional) polar coordinate or 3D cylindrical coordinate system, the angular momentum rotation term becomes a term with constant coefficients. This allows us to develop an efficient time-splitting method which is time reversible, time transverse invariant, unconditionally stable, efficient and accurate for the problem. Moreover, it conserves the total position density in the discretized level. The numerical method is applied to verify our analytical results and study the dynamics of quantized vortex lattices in rotating two-component BEC with/without an external driving field.     

Synchronization of phase oscillators with heterogeneous coupling: A solvable case

We consider an extension of Kuramoto’s model of coupled phase oscillators where oscillator pairs interact with different strengths. When the coupling coefficient of each pair can be separated into two different factors, each one associated to an oscillator, Kuramoto’s theory for the transition to synchronization can be explicitly generalized, and the effects of coupling heterogeneity on synchronized states can be analytically studied. The two factors are respectively interpreted as the weight of the contribution of each oscillator to the mean field, and the coupling of each oscillator to that field. We explicitly analyze the effects of correlations between those weights and couplings, and show that synchronization can be completely inhibited when they are strongly anti-correlated. Numerical results validate the theory, but suggest that finite-size effect are relevant to the collective dynamics close to the synchronization transition, where oscillators become entrained in synchronized frequency clusters.     

Synchronization in an array of coupled Boolean networks

This Letter presents an analytical study of synchronization in an array of coupled deterministic Boolean networks. A necessary and sufficient criterion for synchronization is established based on algebraic representations of logical dynamics in terms of the semi-tensor product of matrices. Some basic properties of a synchronized array of Boolean networks are then derived for the existence of transient states and the upper bound of the number of fixed points. Particularly, an interesting consequence indicates that a “large” mismatch between two coupled Boolean networks in the array may result in loss of synchrony in the entire system. Examples, including the Boolean model of coupled oscillations in the cell cycle, are given to illustrate the present results.     

Lengths on rotating platforms

The paper treats the issue of the length of a rotating circumference as seen from on board the moving disk and from an inertial reference frame. It is shown that, properly defining a measuring process, the result is in both cases 2πR thus dissolving the Ehrenfest paradox. The same holds good when considering that, for the rotating observer, the perceived radius coincides with the curvature radius of a space-time helix and a complete round trip corresponds to an angle which differs from the one seen by the inertial observer. The apparent contradiction with the Lorentz contraction is discussed.     

Synchronization in lattice-embedded scale-free networks

In this work, we study the effects of embedding a system of non-linear phase oscillators in a two-dimensional scale-free lattice. In order to analyze the effects of the embedding, we consider two different topologies. On the one hand, we consider a scale-free complex network where no constraint on the length of the links is taken into account. On the other hand, we use a method recently introduced for embedding scale-free networks in regular Euclidean lattices. In this case, the embedding is driven by a natural constraint of minimization of the total length of the links in the system. We analyze and compare the synchronization properties of a system of non-linear Kuramoto phase oscillators, when interactions between the oscillators take place in these networks. First, we analyze the behavior of the Kuramoto order parameter and show that the onset of synchronization is lower for non-constrained lattices. Then, we consider the behavior of the mean frequency of the oscillators as a function of the natural frequency for the two different networks and also for different values of the scale-free exponent. We show that, in contrast to non-embedded lattices that present a mean-field-like behavior characterized by the presence of a single cluster of synchronized oscillators, in embedded lattices the presence of a diversity of synchronized clusters at different mean frequencies can be observed. Finally, by considering the behavior of the mean frequency as a function of the degree, we study the role of hubs in the synchronization properties of the system.     

Delay-coupled discrete maps: Synchronization, bistability, and quasiperiodicity

The synchronization transition is studied in delay-coupled logistic maps. For low coupling, in-phase and out-of-phase synchronous dynamics coexist, and with increasing coupling there is a regime of quasiperiodicity before eventual attraction to a fixed point at a critical value of coupling that depends on the nonlinearity. The presence of a region of asynchrony separating two synchronized regimes—termed anomalous behaviour—has been observed earlier in continuous systems and is shown here to occur in delay mappings as well. There are regions of in-phase, anti-phase, and out-of-phase dynamics of periodic as well as chaotic attractors.     

Dynamics at the interface dividing collective chaotic and synchronized periodic states in a CML

A study is developed focusing the loss of stability of the interface dividing two regions of different spatial patterns on a coupled map lattice using coupling as the parameter guiding the transition. These patterns are constructed over local periodic/chaotic attractors generating regions of synchronized/collective behavior. The discrete feature of the underlying lattice, the anisotropy that stems from such discreteness and its possible change to an isotropic system through coupling with large number of neighbors are also investigated.     

Optical bistability without the rotating wave approximation

Optical bistability for two-level atomic system in a ring cavity is investigated outside the rotating wave approximation (RWA) using non-autonomous Maxwell-Bloch equations with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or closed loop bistability simultaneously with the usual (anti-clockwise) bistability in the fundamental field component.     

The dynamics of co- and counter rotating coupled spherical pendula

The dynamics of co- and counter-rotating coupled spherical pendula (two lower pendula are mounted at the end of the upper pendulum) is considered. Linear mode analysis shows the existence of three rotating modes. The linear modes allow us to understand the nonlinear normal modes, which are visualized in frequency-energy plots. With the increase of energy in one mode we observe a symmetry breaking pitchfork bifurcation. In the second part of the paper we consider energy transfer between pendula having different energies. The results for co-rotating (all pendula rotate in the same direction) and counter-rotating motion (one of lower pendula rotates in the opposite direction) are presented. In general, the energy fluctuations in counter-rotating pendula are found to be higher than in the co-rotating case.     

Transition from the self-organized to the driven dynamical clusters

We study the mechanism of formation of synchronized clusters in coupled maps on networks with various connection architectures. The nodes in a cluster are self-synchronized or driven-synchronized, based on the coupling strength and underlying network structures. A smaller coupling strength region shows driven clusters independent of the network rewiring strategies, whereas a larger coupling strength region shows the transition from the self-organized cluster to the driven cluster as network connections are rewired to the bi-partite type. Lyapunov function analysis is performed to understand the dynamical origin of cluster formation. The results provide insights into the relationship between the topological clusters which are based on the direct connections between the nodes, and the dynamical clusters which are based on the functional behavior of these nodes.     

Cold matter trapping via slowly rotating helical potential

We consider the cold bosonic ensemble trapped by a helical interference pattern in the optical loop scheme. This rotating helical potential is produced by the two slightly detuned counter-propagating Laguerre-Gaussian laser beams with counter-directed orbital angular momenta ±??. The detuning δω may occur due to rotational Doppler effect. The superfluid hydrodynamics is analyzed for the large number of trapped atoms in Thomas-Fermi approximation. For the highly elongated trap the Gross-Pitaevskii equation is solved in a slowly varying envelope approximation. The speed of axial translation and angular momenta of interacting atomic cloud are evaluated. In the T→0 limit the angular momentum of the helical cloud is expected to be zero while toroidal trapping geometry leads to 2?? angular momentum per trapped atom.     

Critical condition of inner cylinder radius for sustaining rotating detonation waves in rotating detonation engine thruster

We describe the critical condition necessary for the inner cylinder radius of a rotating detonation engine (RDE) used for in-space rocket propulsion to sustain adequate thruster performance. Using gaseous C₂H₄ and O₂ as the propellant, we measured thrust and impulse of the RDE experimentally, varying in the inner cylinder radius r_i from 31 mm (typical annular configuration) to 0 (no-inner-cylinder configuration), while keeping the outer cylinder radius (r_o = 39 mm) and propellant injector position (r_inj = 35 mm) constant. In the experiments, we also performed high-speed imaging of self-luminescence in the combustion chamber and engine plume. In the case of relatively large inner cylinder radii (r_i = 23 and 31 mm), rotating detonation waves in the combustion chamber attached to the inner cylinder surface, whereas for relatively small inner cylinder radii (r_i = 0, 9, and 15 mm), rotating detonation waves were observed to detach from the inner cylinder surface. In these small inner radii cases, strong chemical luminescence was observed in the plume, probably due to the existence of soot. On the other hand, for cases where r_i = 15, 23, and 31 mm, the specific impulses were greater than 80% of the ideal value at correct expansion. Meanwhile, for cases r_i = 0 and 9 mm, the specific impulses were below 80% of the ideal expansion value. This was considered to be due to the imperfect detonation combustion (deflagration combustion) observed in small inner cylinder radius cases. Our results suggest that in our experimental conditions, r_i = 15 mm was close to the critical condition for sustaining rotating detonation in a suitable state for efficient thrust generation. This condition in the inner cylinder radius corresponds to a condition in the reduced unburned layer height of 4.5–6.5.     

Fixed lock-time relaxation dispersion in the rotating frame

The spin-lattice relaxation dispersion may be probed in the laboratory frame through field-cycling NMR relaxometry. The experiment, as usually done, has the basic weakness that the low frequency end of the measured dispersion can be blurred by the presence of local fields. An understanding of the nature of such local fields was found to be essential to the interpretation of the dispersion profile. In this work, an attempt was made to determine the extent to which specific information can be obtained from a rotating frame experiment. The technique consists in the study of the NMR signal dispersion at a fixed spin-lock time, as a function of the radio frequency field intensity. Within this scheme, a strong dispersion can be attributed to the presence of a non-zero magnetic field component along the laboratory-frame Zeeman-axis in the rotating-frame. At on-resonance condition, this component is exclusively due to the presence of local fields as projected on that axis.     

Effect of high hydrostatic pressure on the profile of proteins extracted from Betula pendula pollens

High hydrostatic pressure (HHP) has high success potential in pollen protein extraction, but its effect on pollen protein profiles has not been studied yet. The aim of this study is to put forward whether HHP processing causes a change in the protein profiles extracted from pollens or not. In this study, proteins extracted from Betula pendula pollens were studied at 100, 200 and 300?MPa at room temperature for 5?min. In addition, the efficiency of three different extraction solvents, namely phosphate buffer saline (PBS) buffer pH 7.5, trichloroacetic acid–acetone and Tris–HCl buffer pH 8.8, was also observed, and the results were compared with the conventional pollen protein extraction procedure. As a result, it is concluded that 200?MPa for 5?min has extracted similar amounts of protein compared with the conventional extraction method which lasted for 24?h, which lasted for 24 h. On the other hand, the application time for 200 MPa for 5 min is extremely shorter when it is compared to the conventional extraction method.     

Nonlinear dynamics and synchronisation of pendula attached to a rotating hub

A model of a nonlinear system composed of a hub with attached two pendula rotating in a horizontal plane is studied in the paper. Each single pendulum, treated as a stiff and massless rod with a lumped mass, is connected to the hub by a flapping hinge. Nonlinear stiffness and viscous damping of the hinge is taken into consideration. The system is excited by an external torque generated by a DC motor which is considered as an ideal system with torque given by a harmonic function. For small oscillations the problem is linearised and then solved analytically. An influence of the structural parameters like mass of the hub and pendula length on natural end excited vibrations is presented. Large oscillations are studied by a continuation technique, directly from the original Ordinary Differential Equations of motion (ODE). The complete synchronisation, phase synchronisation, bifurcations and transition through resonances are analysed considering the influence of the mass of the hub. The existence of chaotic oscillations of the system and paths leading to chaos are demonstrated as well.     

Synchronization time in a hyperbolic dynamical system with long-range interactions

We show that the threshold of complete synchronization in a lattice of coupled non-smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace. We examine carefully the synchronization time and show that an inadequate observation of the system evolution leads to wrong results. We present both careful numerical experiments and a rigorous mathematical explanation confirming this fact, allowing for a generalization involving hyperbolic coupled map lattices.     

Angular interferometer using calcite prism and rotating analyzer

An interferometer using a calcite prism and rotating analyzer is proposed for angular displacement determinations. The calcite prism senses the angular displacements and the rotating analyzer transfers the interference signals from dc-type into ac-type. Compact optical setup and using low-cost devices are thus the advantages of the interferometer. The theory of the interferometer is first demonstrated. A setup constructed to realize the interferometer and the results of using this setup are then presented.