Evaluation of decay times in coupled spaces: Bayesian decay model selection

This paper applies Bayesian probability theory to determination of the decay times in coupled spaces. A previous paper [N. Xiang and P. M. Goggans, J. Acoust. Soc. Am. 110, 1415-1424 (2001)] discussed determination of the decay times in coupled spaces from Schroeder's decay functions using Bayesian parameter estimation. To this end, the previous paper described the extension of an existing decay model [N. Xiang, I. Acoust. Soc. Am. 98, 2112-2121 (1995)] to incorporate one or more decay modes for use with Bayesian inference. Bayesian decay time estimation will obtain reasonable results only when it employs an appropriate decay model with the correct number of decay modes. However, in architectural acoustics practice, the number of decay modes may not be known when evaluating Schroeder's decay functions. The present paper continues the endeavor of the previous paper to apply Bayesian probability inference for comparison and selection of an appropriate decay model based upon measured data. Following a summary of Bayesian model comparison and selection, it discusses selection of a decay model in terms of experimentally measured Schroeder's decay functions. The present paper, along with the Bayesian decay time estimation described previously, suggests that Bayesian probability inference presents a suitable approach to the evaluation of decay times in coupled spaces.     

α decay energies and half-lives from a macroscopic-microscopic model

α decay energies of 323 heavy nuclei with Z≥82 are evaluated with a macroscopic-microscopic model.In this model,the macroscopic part is treated by the continuous medium model and the microscopic part consists of shell and pairing corrections based on the Nilsson potential.α decay half-lives are calculated by Viola-Seaborg formula.The results of α decay energies and half-lives are compared with experimental values and satisfactory agreement is found.The recoiling effect of the daughter nucleus on α decay half-life is also discussed.     

Asymmetric weak decay of polarized hypernuclei

We measured the asymmetric weak decay of the polarized _Λ⁵He hypernuclei. The polarization was derived by the observed asymmetry of the mesonic decay pions for the first time. The asymmetry parameter of the nonmesonic decay has been evaluated using the obtained polarization and the asymmetry of the decay protons. The positive asymmetry parameter contradicts theoretical prediction based on meson exchange model. The present data indicates the limitation of the model in ΛN weak interaction, in particular short range phenomena such the nonmesonic decay of hypernuclei.     

Influence of kinematical constraints on multiplicity distributions and neutral charged correlations in the independent cluster emission model

Energy-momentum conservation in the cluster production process is introduced in the independent cluster emission model using the generating functional formalism. In a simple version of the model clusters are produced which decay into a fixed number of pions. The ?? model and a model with isospin conservation in the cluster decay are used to calculate the charge distribution among the secondaries of cluster decay. Multiplicity characteristics like average multiplicity, second moments and associated average neutral multiplicities and second moments are calculated. The results are compared with experimental data.     

A Simple Derivation of the Luminescence Anisotropy Decay from Randomly Distributed Cylinders Rotating About a Single Axis

A simple derivation is given of the expression describing the anisotropy decay of luminescence for a solution of molecules that can only undergo rotational diffusion about a single cylindrical axis. The usual derivations of the anisotropy decay for this cylindrical model have simply taken limiting cases of the equations resulting from the general treatment of the anisotropy decay of a completely anisotropic rotator or the rotation of an ellipsoid. The arguments presented here can be understood without the mathematical sophistication required to follow the general derivations for the rotational diffusion of a completely anisotropic rotator or ellipsoids. The underlying physical mechanisms leading to a multiple exponential decay of the fluorescence anisotropy signal from a single axis rotating cylinder are clearly shown by following this derivation. The resulting expression for the anisotropy decay is not new. However, the derivation is easily understood, and this article is meant as an introduction to the more advanced treatments of anisotropy decay by rotational diffusion. After presenting the derivation of the rotating cylinder, the corresponding steps of these general treatments and this simple model are indicated. The model is of special interest for describing the anisotropy decay resulting from rotations of proteins within membranes.     

Evaluation of decay times in coupled spaces: reliability analysis of Bayeisan decay time estimation

This paper discusses quantitative tools to evaluate the reliability of "decay time estimates" and inter-relationships between multiple decay times for estimates made within a Bayesian framework. Previous works [Xiang and Goggans, J. Acoust. Soc. Am. 110, 1415-1424 (2001); 113, 2685-2697 (2003)] have applied Bayesian framework to cope with the demanding tasks in estimating multiple decay times from Schroeder decay functions measured in acoustically coupled spaces. A parametric model of Schroeder decay function [Xiang, J. Acoust. Soc. Am. 98, 2112-2121 (1995)] has been used for the Bayesian model-based analysis. The relevance of this work is that architectural acousticians need to know how well determined are the estimated decay times calculated within Bayesian framework using Schroeder decay function data. This paper will first address the estimation of global variance of the residual errors between the Schroeder function data and its model. Moreover, this paper discusses how the "landscape" shape of the posterior probability density function over the decay parameter space influences the individual decay time estimates, their associated variances, and their inter-relationships. This paper uses experimental results from measured room impulse responses in real halls to describe a model-based sampling method for an efficient estimation of decay times, and their individual variances. These parameters along with decay times are relevant decay parameters for evaluation and understanding of acoustically coupled spaces.     

Weak radiative decay of baryons

The decay amplitudes and asymmetry parameters for weak radiative decay of baryons are calculated in both pole model and quark model. It is demonstrated that both models give the same results and the results satisfy the symmetry relations we have derived recently. The agreement of the theoretical prediction with the presently measured decay rates and asymmetry is quite good in view of uncertainty in the calculation.     

Nonexponential decay via tunneling in tight-binding lattices and the optical zeno effect

An exactly-solvable model for the decay of a metastable state coupled to a semi-infinite, tight-binding lattice, showing large deviations from exponential decay in the strong coupling regime, is presented. An optical realization of the lattice model, based on discrete diffraction in a semi-infinite array of tunneling-coupled optical waveguides, is proposed to test nonexponential decay and for the observation of an optical analog of the quantum Zeno effect.     

The kinetic Ising model: Exact susceptibilities of two simple examples

The susceptibility of a modified version of the one-dimensional kinetic Ising model is obtained and compared with the susceptibility of the Glauber version of this model. Spin-flip rates in the new model are picked so no spin-flip rate vanishes as the temperature vanishes. Despite the more rapid spin flips, the new model exhibits an infinitely slow approach to equilibrium in the low-temperature limit which is similar to the slowing down exhibited in the Glauber model. The new model also exhibits two different decay rates toward equilibrium, which are called the transient and slow decay rates. The Glauber model is characterized by only a single decay rate toward equilibrium.Work supported in part by National Science Foundation grant DMR 78-03408.     

Spread and Quote-Update Frequency of the Limit-Order Driven Sergei Maslov Model

We perform numerical simulations of the limit-order driven Sergei Maslov （SM） model and investigate the probability distribution and autocorrelation function of the bid-ask spread S and the quote-update frequency U. For the probability distribution, the model successfully reproduces the power law decay of the spread and the exponential decay of the quote-update frequency. For the autocorrelation function, both the spread and the quote-update frequency of the model decay by a power law, which is consistent with the empirical study. We obtain the power law exponent 0.54 for the spread, which is in good agreement with the real financial market.     

Dependence of multiplicity and transverse energy distributions on nuclear geometry at RHIC

We study the dependence of multiplicity and transverse energy on nuclear geometry at RHIC at SNN^1/2 =19.6,130,and 200 GeV basing on ellipsoidal decay model.It is found that the ellipsoidal decay model can describe the data well.     

The microscopic approach to the rates of radioactive decay by emission of heavy clusters

We have applied a simple microscopic decay theory to the analysis of the rare decay modes. The absolute decay rates are estimated by using the shell model and resonance formation factors and optical model penetrabilities. The resonance formation factors are deduced from the strong interaction form of the theory where the wave function in the internal region is represented in terms of compound nucleus decay. In order to account fully for the data, the implication of internal degrees of freedom was found to be necessary, but no adjustment of Gamow factor was needed. The results have been discussed in the light of the previously reported results and data.     

Experimental test for the hyperbolic model of spinodal decomposition in the binary system

A model has been presented for the physical decay with the relaxation of the diffusion flux described by the hyperbolic diffusion equation. The analysis of such a hyperbolic model provides the predictions for the critical parameters of the decay, which are compared with the conclusions of the Cahn-Hilliard theory. It has been shown that the hyperbolic model predicts the nonlinearity of the dispersion curve for the spinodal decay, which is controlled by the ratio of the diffusion and correlation lengths. The predicted behavior of the dispersion curve is compared with the experimental data on phase separation in binary glasses.     

Internal bremsstrahlung of strongly interacting charged particles

A universal theoretical model intended for calculating internal-bremsstrahlung spectra is proposed. In this model, which can be applied to describing nuclear decays of various type (such as alpha decay, cluster decay, and proton emission), use is made of realistic nucleus–nucleus potentials. Theoretical internal-bremsstrahlung spectra were obtained for the alpha decay of the ²¹⁴Po nucleus, as well as for the decay of the ²²²Ra nucleus via the emission of a ¹⁴C cluster and for the decay of the ¹¹³Cs nucleus via proton emission, and the properties of these spectra were studied. The contributions of various regions (internal, subbarrier, and external) to the internal-bremsstrahlung amplitude were analyzed in detail. It is shown that the contribution of the internal region to the amplitude for internal bremsstrahlung generated in nuclear decay via proton emission is quite large, but that this is not so for alpha decay and decay via cluster emission. Thus, a process in which strong interaction of nuclear particles affects the internal-bremsstrahlung spectrum if found.     

Long-term charge retention on PWBs

A sample of printed wiring boards, isolated from ground, has been charged tribo-electrically and the charge decay process has been studied with focus on the long-term charge decay behaviour. It was found that the time constant 1/e did not say much about the proceeding decay process. Instead a second-order approximation model for the measured decay curves has been suggested.     

Dependence of multiplicity and transverse energy distributions on nuclear geometry at RHIC

We study the dependence of multiplicity and transverse energy on nuclear geometry at RHIC at √s_NN=19.6, 130, and 200 GeV basing on ellipsoidal decay model. It is found that the ellipsoidal decay model can describe the data well.     

Quantum mechanical look at the radioactive-like decay of metastable dark energy

We derive the Shafieloo, Hazra, Sahni and Starobinsky (SHSS) phenomenological formula for the radioactive-like decay of metastable dark energy directly from the principles of quantum mechanics. To this aim we use the Fock–Krylov theory of quantum unstable states. We obtain deeper insight on the decay process as having three basic phases: the phase of radioactive decay, the next phase of damping oscillations, and finally the phase of power-law decay. We consider the cosmological model with matter and dark energy in the form of decaying metastable dark energy and study its dynamics in the framework of non-conservative cosmology with an interacting term determined by the running cosmological parameter. We study the cosmological implications of metastable dark energy and estimate the characteristic time of ending of the radioactive-like decay epoch to be \(2.2\times 10^4\) of the present age of the Universe. We also confront the model with astronomical data which show that the model is in good agreement with the observations. Our general conclusion is that we are living in the epoch of the radioactive-like decay of metastable dark energy which is a relict of the quantum age of the Universe.     

Nonexponential <Superscript>125m</Superscript>Te radioactive decay

Nonexponential decay of isomeric ^125mTe nuclei having intermediate Mössbauer levels and surrounded by their own decay products is observed and studied. A collective decay model is suggested for the nuclear systems of this type.     

Direct observation of two protons in the decay of 54Zn

The two protons emitted in the decay of 54Zn have been individually observed for the first time in a time projection chamber. The total decay energy and the half-life measured in this work agree with the results obtained in a previous experiment. Angular and energy correlations between the two protons are determined and compared to theoretical distributions of a three-body model. Within the shell model framework, the relative decay probabilities show a strong contribution of the p2 configuration for the two-proton emission. After 45Fe, the present result on 54Zn constitutes only the second case of a direct observation of the ground state two-proton decay of a long-lived isotope.     

Fluorescence decay time of single semiconductor nanocrystals

We present fluorescence decay measurements of single ZnS covered CdSe nanocrystals. It is shown that the fluorescence decay time is fluctuating during the investigation leading to a multiexponential decay even for a single nanocrystal. In combination with measurements of the fluorescence blinking behavior we find that a high fluorescence intensity is correlated with a long fluorescence decay time. This is consistent with a model of fluctuating nonradiative decay channels leading to variable dynamic quenching processes of the excited state.