Multifractal characterization of stochastic resonance

We use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable system driven by various input signals. To characterize the response of a stochastic bistable system we introduce a new measure based on the calculation of a singularity spectrum for a return time sequence. We use wavelet transform modulus maxima method for the singularity spectrum computations. It is shown that the degree of multifractality defined as a width of singularity spectrum can be successfully used as a measure of complexity both in the case of periodic and aperiodic (stochastic or chaotic) input signals. We show that in the case of periodic driving force singularity spectrum can change its structure qualitatively becoming monofractal in the regime of stochastic synchronization. This fact allows us to consider the degree of multifractality as a new measure of stochastic synchronization also. Moreover, our calculations have shown that the effect of stochastic resonance can be catched by this measure even from a very short return time sequence. We use also the proposed approach to characterize the noise-enhanced dynamics of a coupled stochastic neurons model.Comment: 10 pages, 21 EPS-figures, RevTe

Constraints on Superfluid Hydrodynamics from Equilibrium Partition Functions

Following up on recent work in the context of ordinary fluids, we study the equilibrium partition function of a 3+1 dimensional superfluid on an arbitrary stationary background spacetime, and with arbitrary stationary background gauge fields, in the long wavelength expansion. We argue that this partition function is generated by a 3 dimensional Euclidean effective action for the massless Goldstone field. We parameterize the general form of this action at first order in the derivative expansion. We demonstrate that the constitutive relations of relativistic superfluid hydrodynamics are significantly constrained by the requirement of consistency with such an effective action. At first order in the derivative expansion we demonstrate that the resultant constraints on constitutive relations coincide precisely with the equalities between hydrodynamical transport coefficients recently derived from the second law of thermodynamics.Comment: 46 page

Codimension-2 surfaces and their Hilbert spaces: low-energy clues for holography from general covariance

We argue that the holographic principle may be hinted at already from low-energy considerations, assuming diffeomorphism invariance, quantum mechanics and Minkowski-like causality. We consider the states of finite spacelike hypersurfaces in a diffeomorphism-invariant QFT. A low-energy regularization is assumed. We note a natural dependence of the Hilbert space on a codimension-2 boundary surface. The Hilbert product is defined dynamically, in terms of transition amplitudes which are described by a path integral. We show that a canonical basis is incompatible with these assumptions, which opens the possibility for a smaller Hilbert-space dimension than canonically expected. We argue further that this dimension may decrease with surface area at constant volume, hinting at holographic area-proportionality. We draw comparisons with other approaches and setups, and propose an interpretation for the non-holographic space of graviton states at asymptotically-Minkowski null infinity.Comment: 13 pages, 9 eps figures. Added Section VI, improved presentation. Expanded and split the Introduction into two sections. Added Section VII. Added reference

Collective dynamics of two-mode stochastic oscillators

We study a system of two-mode stochastic oscillators coupled through their collective output. As a function of a relevant parameter four qualitatively distinct regimes of collective behavior are observed. In an extended region of the parameter space the periodicity of the collective output is enhanced by the considered coupling. This system can be used as a new model to describe synchronization-like phenomena in systems of units with two or more oscillation modes. The model can also explain how periodic dynamics can be generated by coupling largely stochastic units. Similar systems could be responsible for the emergence of rhythmic behavior in complex biological or sociological systems.Comment: 4 pages, RevTex, 5 figure

An Analytical Study of Coupled Two-State Stochastic Resonators

The two-state model of stochastic resonance is extended to a chain of coupled two-state elements governed by the dynamics of Glauber's stochastic Ising model. Appropriate assumptions on the model parameters turn the chain into a prototype system of coupled stochastic resonators. In a weak-signal limit analytical expressions are derived for the spectral power amplification and the signal-to-noise ratio of a two-state element embedded into the chain. The effect of the coupling between the elements on both quantities is analysed and array-enhanced stochastic resonance is established for pure as well as noisy periodic signals. The coupling-induced improvement of the SNR compared to an uncoupled element is shown to be limited by a factor four which is only reached for vanishing input noise.Comment: 29 pages, 5 figure

Anomalies in Superfluids and a Chiral Electric Effect

We analyze the chiral transport terms in relativistic superfluid hydrodynamics. In addition to the spontaneously broken symmetry current, we consider an arbitrary number of unbroken symmetries and extend the results of arXiv:1105.3733. We suggest an interpretation of some of the new transport coefficients in terms of chiral and gravitational anomalies. In particular, we show that with unbroken gauged charges in the system, one can observe a chiral electric conductivity - a current in a perpendicular direction to the applied electric field. We present a motivated proposal for the value of the associated transport coefficient, linking it to the triangle anomaly. Along the way we present new arguments regarding the interpretation of the anomalous transport coefficients in normal fluids. We propose a natural generalization of the chiral transport terms to the case of an arbitrary number of spontaneously broken symmetry currents.Comment: 30 pages; v2: Onsager-relations argument corrected, references added; v3: fixed missing line in eq. (38

Coherence Resonance and Noise-Induced Synchronization in Globally Coupled Hodgkin-Huxley Neurons

The coherence resonance (CR) of globally coupled Hodgkin-Huxley neurons is studied. When the neurons are set in the subthreshold regime near the firing threshold, the additive noise induces limit cycles. The coherence of the system is optimized by the noise. A bell-shaped curve is found for the peak height of power spectra of the spike train, being significantly different from a monotonic behavior for the single neuron. The coupling of the network can enhance CR in two different ways. In particular, when the coupling is strong enough, the synchronization of the system is induced and optimized by the noise. This synchronization leads to a high and wide plateau in the local measure of coherence curve. The local-noise-induced limit cycle can evolve to a refined spatiotemporal order through the dynamical optimization among the autonomous oscillation of an individual neuron, the coupling of the network, and the local noise.Comment: five pages, five figure

Kelvin Waves and Internal Bores in the Marine Boundary Layer Inversion and Their Relationship to Coastally Trapped Wind Reversals

Detailed observations of a coastally trapped disturbance, or wind reversal, on 10–11 June 1994 along the California coast provide comprehensive documentation of its structure, based on aircraft, wind profiler, radio acoustic sounding system, and buoy measurements. Unlike the expectations from earlier studies based on limited data, which concluded that the deepening of the marine boundary layer (MBL) was a key factor, the 1994 data show that the perturbation was better characterized as an upward thickening of the inversion capping the MBL. As the event propagated over a site, the reversal in the alongshore wind direction occurred first within the inversion and then 3–4 h later at the surface. A node in the vertical structure (defined here as the altitude of zero vertical displacement) is found just above the inversion base, with up to 200-m upward displacements of isentropic surfaces above the node, and 70-m downward displacements below. Although this is a single event, it is shown that the vertical structure observed is representative of most other coastally trapped wind reversals. This is determined by comparing a composite of the 10–11 June 1994 event, based on measurements at seven buoys, with surface pressure perturbations calculated from aircraft data. These results are compared to the composite of many events. In each case a weak pressure trough occurred between 2.4 and 4.0 h ahead of the surface wind reversal, and the pressure rose by 0.32–0.48 mb between the trough and the wind reversal. The pressure rise results from the cooling caused by the inversion’s upward expansion. The propagation and structure of the event are shown to be best characterized as a mixed Kelvin wave–bore propagating within the inversion above the MBL, with the MBL acting as a quasi-rigid lower boundary. If the MBL is instead assumed to respond in unison with the inversion, then the theoretically predicted intrinsic phase speeds significantly exceed the observed intrinsic phase speed. The hybrid nature of the event is indicated by two primary characteristics: 1) the disturbance had a much shallower slope than expected for an internal bore, while at the same time the upward perturbation within the inversion was quasi-permanent rather than sinusoidal, which more closely resembles a bore; and 2) the predicted phase speeds for the ‘‘solitary’’ form of nonlinear Kelvin wave and for an internal bore are both close to the observed intrinsic phase speed

Constraints on Fluid Dynamics from Equilibrium Partition Functions

We study the thermal partition function of quantum field theories on arbitrary stationary background spacetime, and with arbitrary stationary background gauge fields, in the long wavelength expansion. We demonstrate that the equations of relativistic hydrodynamics are significantly constrained by the requirement of consistency with any partition function. In examples at low orders in the derivative expansion we demonstrate that these constraints coincide precisely with the equalities between hydrodynamical transport coefficients that follow from the local form of the second law of thermodynamics. In particular we recover the results of Son and Surowka on the chiral magnetic and chiral vorticity flows, starting from a local partition function that manifestly reproduces the field theory anomaly, without making any reference to an entropy current. We conjecture that the relations between transport coefficients that follow from the second law of thermodynamics agree to all orders in the derivative expansion with the constraints described in this paper.Comment: Typos corrected, References adde

System size resonance in coupled noisy systems and in the Ising model

We consider an ensemble of coupled nonlinear noisy oscillators demonstrating in the thermodynamic limit an Ising-type transition. In the ordered phase and for finite ensembles stochastic flips of the mean field are observed with the rate depending on the ensemble size. When a small periodic force acts on the ensemble, the linear response of the system has a maximum at a certain system size, similar to the stochastic resonance phenomenon. We demonstrate this effect of system size resonance for different types of noisy oscillators and for different ensembles -- lattices with nearest neighbors coupling and globally coupled populations. The Ising model is also shown to demonstrate the system size resonance.Comment: 4 page