Effects of non-Gaussian noise near supercritical Hopf bifurcation

We have studied the effects of non-Gaussian colored noise in a chemical oscillation system, the well-known Brusselator model, in the parameter region close to the supercritical Hopf bifurcation. With the variation of the parameter q, which quantifies the deviation from Gaussian character, the signal-to-noise ratio of noise induced oscillation exhibits a bell-shaped change, indicating the presence of resonant activity. The cooperative effects of q and the correlation time τ on the performance of noise induced oscillation are also investigated. Interestingly, resonance-like behavior can be induced by either q or τ when the other parameter is properly fixed. Stochastic normal form theory is used to analyze these nontrivial effects and the simulation results are well reproduced. This work provides us comprehensive understanding of how non-Gaussian noise influences the dynamics in chemical oscillation systems.     

Effects of colored noise and noise delay on a calcium oscillation system

As a calcium oscillations system is in steady state, the effects of colored noise and noise delay on the system is investigated using stochastic simulation methods. The results indicate that: (1) the colored noise can induce coherence bi-resonance phenomenon. (2) there exist three peaks in the R–_τ0$R\text{–}{\tau }_0$ (R$R$ is the reciprocal coefficient of variance, and _τ0${\tau }_0$ is the self-correlation time of the colored noise) curves. For the same noise intensity Q=1$Q=1$, the Gaussian colored noise can induce calcium spikes but the white noise cannot do this. (3) the delay time can improve noise induced spikes regularity as _τ0${\tau }_0$ is small, and R$R$ has a significant minimum with increasing τ$\tau$ as _τ0${\tau }_0$ is large. (4) large values of ζ$\zeta$ reduce noise induced spikes regularity.     

Integrable structure of melting crystal model with two -parameters

This paper explores integrable structures of a generalized melting crystal model that has two q-parameters q₁,q₂. This model, like the ordinary one with a single q-parameter, is formulated as a model of random plane partitions (or, equivalently, random 3D Young diagrams). The Boltzmann weight contains an infinite number of external potentials that depend on the shape of the diagonal slice of plane partitions. The partition function is thereby a function of an infinite number of coupling constants t₁,t₂,… and an extra one Q. There is a compact expression of this partition function in the language of a 2D complex free fermion system, from which one can see the presence of a quantum torus algebra behind this model. The partition function turns out to be a tau function (times a simple factor) of two integrable structures simultaneously. The first integrable structure is the bigraded Toda hierarchy, which determines the dependence on t₁,t₂,…. This integrable structure emerges when the q-parameters q₁,q₂ take special values. The second integrable structure is a q-difference analogue of the 1D Toda equation. The partition function satisfies thisq-difference equation with respect to Q. Unlike the bigraded Toda hierarchy, this integrable structure exists for any values of q₁,q₂.     

Oscillations and quantization of resistance at the temperature critical points of PbS-PbTe-PbS three-layer films on (001) KCl

Oscillations and a set of inflection points have been discovered in the temperature dependences of the resistance of single-crystal PbS-PbTe-PbS three-layer films on (001) KCl. Extrema and inflection points are observed at the temperatures (m/n)T ₀ (T ₀=5.238 K), and at these temperature critical points the resistance of the samples takes one of the values (p/q)R _Q , where R _Q =25812.8 Ω is the resistance quantum; and m, n, p, and q are integers. Fiz. Tverd. Tela (St. Petersburg) 41, 1693–1697 (September 1999)     

External noise effects on the fluctuation line width

We calculate stationary state correlation functions of the anharmonic overdamped oscillator driven by multiplicative (white Gaussian) noise of strengthQ together with additive noise of relative strengthq. (i) We donot observe a particular slowing down at the so-called noise induced transition. But there is a region of the oscillator's stiffness parametera neara0 in which the decay time is typically enhanced. (ii) If the phase transition point is defined by the minimum of the decay rate, it lies within the ordered phasea>0 forq1 and shifts down toa=0 forq0. In our approximation it is even in the disordered regiona<0 for very smallq. (iii) As a function of the multiplicative noiseQ the decay ratedecreases with increasingQ if the system is well above or well below threshold. There seem to be experimental indications of this behavior. But within the proper threshold regime of smalla increasing noiseQ increases the decay rate. The valuesa _c where the cross-over occurs depend on the fluctuating variable and onq.     

Ballistic diffusion induced by non-Gaussian noise

In this letter,we have analyzed the diffusive behavior of a Brownian particle subject to both internal Gaussian thermal and external non-Gaussian noise sources.We discuss two time correlation functions C(t) of the non-Gaussian stochastic process,and find that they depend on the parameter q,indicating the departure of the non-Gaussian noise from Gaussian behavior:for q ≤ 1,C(t) is fitted very well by the first-order exponentially decaying curve and approaches zero in the longtime limit,whereas for q 1,C(t) can be approximated by a second-order exponentially decaying function and converges to a non-zero constant.Due to the properties of C(t),the particle exhibits a normal diffusion for q ≤ 1,while for q 1 the non-Gaussian noise induces a ballistic diffusion,i.e.,the long-time mean square displacement of the free particle reads [x(t)-x(t)]2∝t2.     

中低能非全裸C离子与He原子的碰撞研究

采用反冲离子飞行时间-散射离子位置灵敏符合测量技术，测量了能量范围在0.7v₀—4.4v₀(v₀为玻尔速度)的碳离子C^q+(q=1—4)与He原子碰撞过程不同出射道靶原子的双电离与单电离截面比R，包括入射离子不损失电子(直接电离)的出射道(R_q,q),入射离子俘获一个电子的出射道(R_q,q-1)和入射离子损失一个电子的出射道(R_q,q+1)，并研究了R随入射C离子的能量及电荷态的变化关系.实验表明，对给定电荷态的入射离子，靶原子的双电离与单电离截面比R与出射道有很强的依赖关系，即R_q,q<R_q,q+1<R_q,q-1.直接电离出射道截面比R_q,q与入射离子电荷态几乎无关，而入射离子俘获一个电子的出射道和损失一个电子的出射道靶原子双电离与单电离截面比R_q,q-1和R_q,q+1却与入射离子电荷态有很强的关系.采用原子极化理论和电子屏蔽与反屏蔽作用对实验结果进行了解释. 关键词： 离子-原子碰撞 电离 截面比     

非高斯噪声激励下含周期信号FitzHugh-Nagumo系统的响应特征

研究了非高斯噪声激励下含周期信号的FHN模型的动力学行为. 通过计算神经元的平均响应时间、观察神经元的共振活化和噪声增强稳定现象,分析了非高斯噪声对神经元动力学行为的影响. 发现通过改变非高斯噪声的相关时间可以有效地改变共振活化和噪声增强稳定现象. 观察到在强相关噪声下不同强度的非高斯噪声抑制了神经元的噪声增强稳定现象而共振活化现象几乎不变,也就是非高斯噪声有效地增强了神经响应的效率. 观察了平均响应时间与非高斯噪声参数q之间的关系,当q为一个有限的小于1的值时,平均响应时间取得最小值. 最后表明在一定条件下,非高斯噪声出现重尺度现象,即非高斯噪声产生的效果可以由高斯白噪声来估计. 关键词： FHN神经系统 非高斯噪声 平均响应时间 共振活化现象     

Initial operation at liquid-helium temperature of the M =2270 kg Al 5056 gravitational-wave antenna of the Rome group

Summary We report on the cooling at liquid-helium temperature of our 2270 kg 5056 Al bar at CERN. The liquid-helium container had been filled up to 1500 liters ensuring to keep the antenna cold for more than one month. The antenna is equipped with a resonant capacitive transducer operating at constant electrical charge with a FET low-noise amplifier. The transducer is tuned to the antenna within less than I Hz and the two normal-mode frequencies are ν₋=908.160 Hz and ν₊=924.234 Hz with an applied electrical field in the transducer of 10⁶ V/m. The corresponding overall merit factors areQ ₋=5.20·10⁶ andQ ₊=7.25·10⁶. The transducer has been tested up to an electrical field of 6·10⁶ V/m: in this condition we have βQ≈10⁴. The antenna has been in operation for several weeks giving, for the Brownian noise, values in agreement with the calculated values. We report also on the results of tests performed on a DC SQUID, whose input was connected to a commercial capacitor via a transformer with turn ratio of 1000. Supported in part by Japan Society for the Promotion of Science.     

Emission of relativistic electron bunches in a circular diaphragmatic waveguide

The longitudinally uniform circular diaphragmatic waveguide (CDW) was considered. Expressions for determining the loaded Q-factor of lossy (Q _L1) and lossless (Q _L1⁰) cells and the loaded Q-factor Q _L of a section of length l were derived. An expression for determining the electrical amplitude of the radiation field produced by a relativistic bunch with charge q, moving along the axis of CDW with series resistance R _s was derived. The electron beam energy, radiation power, and electronic efficiency were calculated.     

Unitary representations of suq(2) on the plane for q ∈ R+ or generic q ∈ S1

Some time ago, Rideau and Winternitz introduced a realization of the quantum algebra su _q(2) on a real two-dimensional sphere, or a real plane, and constructed a basis for its representations in terms of q-special functions, which can be expressed in terms of q-Vilenkin functions. In their study, the values of q were implicitly restricted to q R⁺. In the present paper, we extend their work to the case of generic values of q S ¹ (i.e., q values different from a root of unity). In addition, we unitarize the representations for both types of q values, q R⁺ and generic q S ¹, by determining some appropriate scalar products.     

Stochastic resonance in an asymmetric bistable system with coloured noises and periodic rectangular signal

In this paper, we consider the phenomenon of stochastic resonance (SR) in an asymmetric bistable system with coloured noises and periodic rectangular signal. Expression of the signal-to-noise ratio (SNR) has been obtained under the adiabatic limit. We investigate the effect of any system parameter (such as p, q, r, τ₁, τ₂) on the SNR. The plot of SNR-τ₁ shows SR for some values of the additive noise self-correlation time τ₂, but not for the whole range of τ₂. The system bias r suppresses the SNR. When the intensity of additive noise q is increased, the SR phenomenon disappears in the plot of SNR-p, but the plot of SNR-q presents SR for almost all values of the multiplicative noise intensity p.     

Quasi-Stable Configurations of Torus Vortex Knots and Links

The dynamics of torus vortex configurations V_{n, p, q} in a superfluid liquid at zero temperature (n is the number of quantum vortices, p is the number of turns of each filament around the symmetry axis of the torus, and q is the number of turns of the filament around its central circle; radii R₀ and r₀ of the torus at the initial instant are much larger than vortex core width ξ) has been simulated numerically based on the regularized Biot–Savart law. The lifetime of vortex systems till the instant of their substantial deformation has been calculated with a small step in parameter B₀ = r₀/R₀ for various values of parameter Λ = ln(R₀/ξ). It turns out that for certain values of n, p, and q, there exist quasi-stability regions in the plane of parameters (B₀, Λ), in which the vortices remain almost invariable during dozens and even hundreds of characteristic lengths.

     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

Two-dimensional analysis of Bose-Einstein correlationsin hadronic Z decays at LEP

Bose-Einstein correlations are studied in pairs of charged pions from hadronic Z decays, collected by the ALEPH detector. The correlation function, measured using either the unlike-sign or the mixed reference sample, is studied in terms of the Lorentz-invariant four-momentum difference and its transverse, Q _T, and longitudinal, Q _L, components with respect to the longitudinal centre-of-mass system. Values for the correlation radii, R _T and R _L, are obtained from the fit of the Goldhaber parametrisation. The results indicate that the correlation radii values depend on the chosen kind of reference sample and on the two-jet purity.Received: 23 April 2004, Revised: 11 May 2004, Published online: 9 July 2004     

Stochastic resonance in a bistable system with time-delayed feedback and non-Gaussian noise

The phenomenon of stochastic resonance in a bistable system with time-delayed feedback driven by non-Gaussian noise is investigated. Combining the small time delay approximation, the path-integral approach and the unified colored noise approximation, a general approximate Fokker–Planck equation of a stochastic system is obtained. The effects of the parameter q indicating the departure from the Gaussian noise, the delay time τ  , and the correlation time τ₀${\tau }_0$ of the non-Gaussian noise on the quasi-steady-state probability distribution function (SPD) and the signal-to-noise ratio (SNR) are discussed. It is found that the number of peaks in SPD and the reentrant transition between one peak and two peaks and then to one peak again in the curve of SNR depends on the parameter q, the delay time τ  , and the noise correlation time τ₀${\tau }_0$.     

Quantization in generalized coordinates III-Lagrangian formulation

It is shown that if one incorporates the generalized coordinate quantum velocitiesQ ¹ as given byQ ¹=l[H,Q ¹](h=1) into the generalized classical Lagrangian for a free particle (the total energy),L=1/2Q ¹ g _tk Q ^k one does not obtain (no matter what ordering of the operatorsq ^l ,q ^k andg _lkwe choose the correct quantum Lagrangian operator which is a transformation from -1/2V² to generalized coordinates (Gruber, 1971, 1972).q ^l as given byq ^l=i[H,q ^l] turns out to be the Hermitian part of a more generaiized operator which we call the total generalized velocity operator similar to the notation in ear previous articles (Gruber, 1971, 1972). This total velocity operator really determines the fundamental structure governing our system in the Lagrangian formulation. We show that ft is through the total velocity operator that we make the transition from classical to quantum mechanics and through our procedure we arrive at the correct quantum Lagrangian operator.     

Nonlinear statistical coupling

By considering a nonlinear combination of the probabilities of a system, a physical interpretation of Tsallis statistics as representing the nonlinear coupling or decoupling of statistical states is proposed. The escort probability is interpreted as the coupled probability, with Q=1−q defined as the degree of nonlinear coupling between the statistical states. Positive values of Q have coupled statistical states, a larger entropy metric, and a maximum coupled-entropy distribution of compact-support coupled-Gaussians. Negative values of Q have decoupled statistical states and for −2<Q<0 a maximum coupled-entropy distribution of heavy-tail coupled-Gaussians. The conjugate transformation between the heavy-tail and compact-support domains is shown to be for coupled-Gaussian distributions. This conjugate relationship has been used to extend the generalized Fourier transform to the compact-support domain and to define a scale-invariant correlation structure with heavy-tail limit distribution. In the present paper, we show that the conjugate is a mapping between the source of nonlinearity in non-stationary stochastic processes and the nonlinear coupling which defines the coupled-Gaussian limit distribution. The effects of additive and multiplicative noise are shown to be separable into the coupled-variance and the coupling parameter Q, providing further evidence of the importance of the generalized moments.     

Glassy dynamics of simulated polymer melts: Coherent scattering and van Hove correlation functions

Whereas the first part of this paper dealt with the relaxation in the β-regime, this part investigates the final relaxation (α-relaxation) of a simulated polymer melt consisting of short non-entangled chains in the supercooled state above the critical temperature of ideal mode-coupling theory (MCT). The temperature range covers the onset of a two-step relaxation behaviour down to a temperature merely 2% above . We monitor the incoherent intermediate scattering function as well as the coherent intermediate scattering function of both a single chain and the melt over a wide range of wave numbers q. Upon approaching the coherent α-relaxation time of the melt increases strongly close to the maximum q _max of the collective static structure factor S_q and roughly follows the shape of S_q for q q _max. For smaller q-values corresponding to the radius of gyration the relaxation time exhibits another maximum. The temperature dependence of the relaxation times is well described by a power law with a q-dependent exponent in an intermediate temperature range. Deviations are found very close to and far above , the onset of which depends on q. The time-temperature superposition principle of MCT is clearly borne out in the whole range of reciprocal vectors. An analysis of the α-decay by the Kohlrausch-Williams-Watts (KWW) function reveals that the collective KWW stretching exponent and KWW relaxation time show a modulation with S_q. Furthermore, both incoherent and coherent KWW times approach the large-q prediction of MCT already for q > q _max. At small q, a q^-3 power law is found for the coherent chain KWW times similar to that of recent experiments.