Instabilities in a two-dimensional polar-filament-motor system

The dynamical interaction between filaments and motor proteins is known for their propensity to self-organize into spatio-temporal patterns. Since the filaments are polar in the sense that motors define a direction of motion on them, the system can display a spatially homogeneous polar-filament orientation. We show that the latter anisotropic state itself may become unstable with respect to inhomogeneous fluctuations. This scenario shares similarities with instabilities in planarly aligned nematic liquid crystals: in both cases the wave vector of the instability may be oriented either parallel or oblique to the polarity axis. However, the encountered instabilities here are long-wave instead of short-wave and the destabilizing modes are drifting ones due to the polar symmetry. Additionally a nonpropagating transverse instability is possible. The stability diagrams related to the various wave vector orientations relative to the polarity axis are determined and discussed for a specific model of motor-filament interactions.     

Estimating the half-life of 241Pu and its uncertainty

Measuring the double isotope atomic abundance ratio as function of time of a homogenized stock of plutonium using mass spectroscopy provides a means to estimate the half-life of ²⁴¹Pu, denoted here as t_1/2,241. After a logarithmic transformation, estimating t_1/2,241 along with a justifiable associated uncertainty is reduced to the analysis of a linear relationship, as illustrated in this paper using 15 published data pairs (time, log(double isotope ratio)) of Wellum et al. (2009) that span approximately 31 years (greater than two half-lives). However, as noted by Wellum et al. (2009), the published 15 data pairs exhibit inconsistencies that indicate possible underestimation of individual experimental uncertainties. Similar inconsistencies often arise in multi-experiment comparisons of the same estimated quantity, typically because some components of uncertainty such as individual experimental biases are difficult to identify and assess. It is therefore an important and common problem. In such cases the experimental data must be supplemented with other information to make plausible uncertainty estimates. We therefore analyze the data pairs under several different assumptions regarding total experimental uncertainties and show quantitatively that the best estimate of t_1/2,241 and of its uncertainty depend on the assumptions regarding experimental uncertainties. It is unlikely in this context that the 15 data pairs and associated estimated experimental uncertainties could guide one toward a very certain choice among the reasonable sets of assumptions regarding total experimental uncertainties. Thus a definitive recommendation cannot be singled out. Fortunately, the best estimates and associated uncertainties arising from different yet tenable assumptions regarding experimental uncertainties are all in reasonably close agreement. And, one of those best estimates we provide (with approximately 95% confidence limits) is (14.329 ± 0.006[fit] ± 0.029[bias]) years, which uses similar data stratification arguments as in Wellum et al. (2009) but a completely different approach. Furthermore, this estimate of t_1/2,241 agrees closely with the value recommended in Wellum et al. (2009) of (14.325 ± 0.024) years. We conclude that the value of t_1/2,241 supported by the available data is robust, despite evidence of some non-ideal behavior, and that alternative means of estimating t_1/2,241 and its uncertainty yield reasonably similar results.     

关于Reissner-Mindlin板问题的线性格式

本文给出Ｒｅｉｓｓｎｅｒ－Ｍｉｎｄｌｉｎ板问题的线性格式[1]中的汽泡函数的最优选取。     

稀土离子激活发光材料中能级跃迁的选择定则

能级跃迁的选择定则可用于判别含稀土离子的发光材料中的光吸收、能量传递和发光及非辐射能量弛豫过程是否发生.本研究中,我们根据跃迁所涉及到的电子组态、稀土离子所处格位的对称性、跃迁所涉及到的多重态及晶格振动情况进行了细致地讨论分析.对于光吸收和发射过程,我们得到了和相关文献报道一致的结果,并对有些结果进行了更细致的解释.对...     

Covariance identities for normal variables via convex polytopes

Siegel (1993) presented a covariance identity involving normal variables that seems to flout notions of dependence. Here we show that it has an explanation from an unexpected quarter: convex geometry and the centroid known as the Steiner point.     

Perturbation solution of optimal portfolio theory with transaction costs for any utility function

The solution to the optimal portfolio selection and consumptionrule with small transaction costs is derived via the use ofperturbation analysis for the case when one risky and one risklessasset are available for investment. This methodology allowsus to apply a broader specification for the utility function.     

On Bayesian Adaptation

We show that Bayes estimators of an unknown density can adapt to unknown smoothness of the density. We combine prior distributions on each element of a list of log spline density models of different levels of regularity with a prior on the regularity levels to obtain a prior on the union of the models in the list. If the true density of the observations belongs to the model with a given regularity, then the posterior distribution concentrates near this true density at the rate corresponding to this regularity.     

Covariance kernel and the central limit theorem in the total variation distance

We modify and generalize the idea of covariance kernels for Borel probability measures on R^d, and study the relation between the central limit theorem in the total variation distance and the convergence of covariance kernels.