The α stable distribution model in ocean ambient noise

In view of the non-Gaussian ocean ambient noise,the a stable distribution is applied to the statistical modeling.Firstly,the correspondence between the model characteristic exponent and the sample kurtosis is established based on the similarity in physical meaning of the two.And the kurtosis of the sum of two independent random variables is deduced,and this can be used to explain the kurtosis characteristic of interfered background noise.Secondly,some numerical simulations are made to model samples with higher and lower kurtosis than three,the results show good adaptability in leptokurtic distribution.Finally,three typical samples are taken under quiet environment,air gun interference and ship interference environment.Their Gaussianities are judged by the quantile-quantile plot.And then the four parameters of the model are estimated by the quantile based method and characteristic function based method jointly of the three categories.The statistical law of the characteristic exponent is emphatically analyzed:in the quiet environment,the characteristic exponent is close to 2.0,which is the value of Gaussian model;but for the air gun data,it is between 1.2 and 1.7,which means leptokurtic;and under the interference of the sailing ship,the value of a is related to the ship speed and the distance from the ship source to the receiving location,the more significant the ship impact is,the smaller the characteristic exponent is,which is consistent with the variation of kurtosis of disturbing noise in physical meaning.The results of the model verification show that the a stable distribution behaves well under the above three kinds of trial conditions,especially for the air gun environment which is far superior to the normal distribution.     

On stable variants of Einstein’s static universe

The investigation of the stability properties of certain variants of Einstein’s static universe performed by Carneiro and Tavakol (in Stability of the Einstein static universe in the presence of vacuum energy) is generalized. It is shown that all versions of Einstein’s static universe without interaction between the two fluids it contains are unstable. Interaction between the fluids may stabilize the universe. The condition for stability by perturbation of the scale factor from its static value is deduced for a class of universe models containing those investigated by Carneiro and Tavakol. Stability of the static state requires that energy is transformed to matter during such a perturbation.     

Fractional transport equations for Lévy stable processes

The influence functional method of Feynman and Vernon is used to obtain a quantum master equation for a system subjected to a Lévy stable random force. The corresponding classical transport equations for the Wigner function are then derived, both in the limits of weak and strong friction. These are fractional extensions of the Klein-Kramers and the Smoluchowski equations. It is shown that the fractional character acquired by the position in the Smoluchowski equation follows from the fractional character of the momentum in the Klein-Kramers equation. Connections among fractional transport equations recently proposed are clarified.     

Dual-wavelength stable nanosecond pulses generation from cladding-pumped fiber laser

In this paper, the generation of dual-wavelength stable nanosecond pulses by a laser diode pumped Yb-doped double-clad fiber laser is presented. In the experiment, the fiber laser with two-mirror cavity is approved which operates in a self-Q-switching regime. The Q-switching mechanism is based on stimulated Brillouin scattering (SBS). When the pump power achieves the SBS threshold, the fiber laser changes from the start resonator to the SBS resonator. With different reflectivities of the second mirror, stable dual-wavelength pulses with the pulse width range from 10 ns to less than 2 ns are obtained. The result was explained theoretically by birefringency (including stochastic birefringency and bend birefringency).     

Bose-Einstein correlations for Lévy stable source distributions

The peak of the two-particle Bose-Einstein correlation functions has a very interesting structure. It is often believed to have a multivariate Gaussian form. We show here that for the class of stable distributions, characterized by the index of stability , the peak has a stretched exponential shape. The Gaussian form corresponds then to the special case of . We give examples for the Bose-Einstein correlation functions for univariate as well as multivariate stable distributions, and we check the model against two-particle correlation data.Received: 19 November 2003, Revised: 27 April 2004, Published online: 23 June 2004     

Stochastic resonance of a tri-stable system with α stable noise

A tri-stable system excited by weak periodic signal is taken as a model and the stochastic resonance phenomenon is investigated by additive α stable noise in this paper. The laws for the resonance system parameters q, p, skewness parameter r and intensity amplification factor Q of α stable noise to act on the resonant output are explored under different stability indicies α and asymmetric skewness β of α stable noise. The results indicate that a weak signal can be realized by tuning the system parameters q, p and r under the joint action of additive α stable noise, and the interval of q and p which can induce stochastic resonance does not change with α or β. Moreover, a certain rule is found in which adjusting the intensity amplification factor Q of α stable noise can also realize a synergistic effect when studying the noise-induced stochastic resonance, and the interval of Q does not change with α or β; the best value of the characteristic index is $\alpha =1$ under any system parameter, and the best value of the symmetry parameter is $\beta =1$ under any system parameter. So, the system performance is best when $\alpha =1$ and $\beta =1$. The results will contribute to a reasonable selection of parameter-induced stochastic resonance system parameters and noise intensity of noise-induced stochastic resonance under α stable noise.     

Is a classical description of stable non-BPS D-branes possible?

We study the classical geometry produced by a stack of stable (i.e., tachyon-free) non-BPS D-branes present in K3 compactifications of type II string theory. This classical representation is derived by solving the equations of motion describing the low-energy dynamics of the supergravity fields which couple to the non-BPS state. Differently from what expected, this configuration displays a singular behaviour: the space–time geometry has a repulson-like singularity. This fact suggests that the simplest setting, namely a set of coinciding non-interacting D-branes, is not acceptable. We finally discuss the possible existence of other acceptable configurations corresponding to more complicated bound states of these non-BPS branes.     

Will a large complex system with time delays be stable?

In 1972 May showed that for a large linear system with random coupling the system size and the average coupling strength must together satisfy a simple inequality to ensure the stability of the equilibrium point. Here we extend the analysis to delay coupled systems. Our calculations establish that the same inequality obtained by May constrains the stability for systems randomly coupled through discrete and distributed delays.     

A construction of stable vector bundles on Calabi–Yau manifolds

In this paper we present a construction of stable bundles on a Calabi–Yau manifold using elementary transformation. As an application, we give examples of stable bundles on certain Calabi–Yau threefolds.     

Photoluminescence decay of silicon nanocrystals and Lévy stable distributions

We incorporate the tools of Lévy processes and distributions to describe the photoluminescence of silicon nanocrystals. The method relies on two novel features: first we use exact forms of one-sided Lévy distributions to get an excellent reproduction of experimental data. Then we show that the dynamics leading to photoluminescence decay can be modelled in terms of fractional Fokker–Planck equation.     

Do stable isotopes reflect the food web development in regenerating ecosystems?

We evaluated the use of delta15N- and delta13C-values to monitor the development of food web complexity and biodiversity in a regenerating ecosystem. Therefore a model food chain was established feeding cultivated woodlice (Porcellio dilatatus) on a cellulolytic fungus (Chaetomium globosum) grown on cellulose paper. Two diets of different quality (C:N ratios of 54 vs. 200) with different delta15N- (1.3% vs. 3.1%) but identical delta13C-values caused low and high dietary stress in animals of treatment A and B, respectively. After an incubation time of 7 weeks amount, elemental and isotopic composition of collected faeces and exuviae as well as woodlice and remaining food were determined. The increase of delta15N-values of woodlice relative to the diet was 5.7% and 2.5% in treatments A and B, respectively, whereas delta13C-shifts were 1.0% and 1.6%, showing a reverse relationship. Modelling of elemental and isotopic mass balances indicated that faeces recycling explains the unexpected high 15N-enrichments. Moreover, 13C-enrichments were positively correlated to the degree of starvation. Considering the effects of starvation and recycling of faeces, stable isotopes represent a useful tool to elucidate trophic interactions in regenerating food webs.     

A class of stable spectral methods for the Cahn–Hilliard equation

In this work, the initial-boundary value problem of two-dimensional Cahn–Hilliard equation is considered. A class of fully discrete dissipative Fourier spectral schemes are proposed. Moreover, semi-implicit prediction–correction schemes are presented. The numerical simulations are performed to demonstrate the effectiveness of the proposed schemes.     

Spin—orbit stable dirac nodal line in monolayer B6O

The two-dimensional (2D) materials with nodal line band crossing have been attracting great research interest. However, it remains a challenge to find high-stable nodal line structure in 2D systems. Herein, based on the first-principles calculations and theoretical analysis, we propose that monolayer B₆O possesses symmetry protected Dirac nodal line (DNL) state, with its Fermi velocity of 10⁶ m/s in the same order of magnitude as that of graphene. The origin of DNL fermions is induced by coexistence of time-reversal symmetry and inversion symmetry. A two-band tight-binding model is further given to understand the mechanism of DNL. Considering its robustness against spin—orbit coupling (SOC) and high structural stability, these results suggest monolayer B₆O as a new platform for realizing future high-speed low-dissipation devices.     

From meandering to faceting, is step flow growth ever stable?

Based on helium atom beam diffraction and scanning tunneling microscopy data, the coexistence of a meandering and a bunching instability during homoepitaxial step flow growth is established in a class of nonreconstructed, metallic vicinal surfaces, Cu (1,1,n), n=5,9,17. Specifically, the meandering instability is shown to act as a precursor to the bunching instability, indicating that a one-dimensional treatment of bunching in step flow growth is not sufficient. Our findings might be generic to step flow growth in kinetically restricted systems.     

Exact and explicit probability densities for one-sided Lévy stable distributions

We study functions gα(x) which are one-sided, heavy-tailed Lévy stable probability distributions of index α, 0<α<1, of fundamental importance in random systems, for anomalous diffusion and fractional kinetics. We furnish exact and explicit expressions for gα(x), 0 ≤ x<∞, for all α=l/k<1, with k and l positive integers. We reproduce all the known results given by k ≤ 4 and present many new exact solutions for k > 4, all expressed in terms of known functions. This will allow a "fine-tuning" of α in order to adapt gα(x) to a given experimental situation.     

Baryon asymmetry,stable proton and n-n̄ oscillations in superstring models

The violation of baryon number is discussed in the context of a gauge model inspired by the E₈ × E₈ superstring theory. Lepton number is an accidental unbroken symmetry of the model. The proton, as a consequence, is essentially stable. The model yields an acceptable value (∼10⁻¹⁰) for the baryon asymmetry in the universe. It also predicts n-n̄ oscillations at a rate which may be amenable to ongoing experimental searches.     

Numerically stable fluid–structure interactions between compressible flow and solid structures

We propose a novel method to implicitly two-way couple Eulerian compressible flow to volumetric Lagrangian solids. The method works for both deformable and rigid solids and for arbitrary equations of state. The method exploits the formulation of [11] which solves compressible fluid in a semi-implicit manner, solving for the advection part explicitly and then correcting the intermediate state to time tⁿ⁺¹ using an implicit pressure, obtained by solving a modified Poisson system. Similar to previous fluid–structure interaction methods, we apply pressure forces to the solid and enforce a velocity boundary condition on the fluid in order to satisfy a no-slip constraint. Unlike previous methods, however, we apply these coupled interactions implicitly by adding the constraint to the pressure system and combining it with any implicit solid forces in order to obtain a strongly coupled, symmetric indefinite system (similar to [17], which only handles incompressible flow). We also show that, under a few reasonable assumptions, this system can be made symmetric positive-definite by following the methodology of [16]. Because our method handles the fluid–structure interactions implicitly, we avoid introducing any new time step restrictions and obtain stable results even for high density-to-mass ratios, where explicit methods struggle or fail. We exactly conserve momentum and kinetic energy (thermal fluid–structure interactions are not considered) at the fluid–structure interface, and hence naturally handle highly non-linear phenomenon such as shocks, contacts and rarefactions.