Optimum step-stress accelerated degradation test for Wiener degradation process under constraints

To assess a product's reliability for subsequent managerial decisions such as designing an extended warranty policy and developing a maintenance schedule, Accelerated Degradation Test (ADT) has been used to obtain reliability information in a timely manner. In particular, Step-Stress ADT (SSADT) is one of the most commonly used stress loadings for shortening test duration and reducing the required sample size. Although it was demonstrated in many previous studies that the optimum SSADT plan is actually a simple SSADT plan using only two stress levels, most of these results were obtained numerically on a case-by-case basis. In this paper, we formally prove that, under the Wiener degradation model with a drift parameter being a linear function of the (transformed) stress level, a multi-level SSADT plan will degenerate to a simple SSADT plan under many commonly used optimization criteria and some practical constraints. We also show that, under our model assumptions, any SSADT plan with more than two distinct stress levels cannot be optimal. These results are useful for searching for an optimum SSADT plan, since one needs to focus only on simple SSADTs. A numerical example is presented to compare the efficiency of the proposed optimum simple SSADT plans and a SSADT plan proposed by a previous study. In addition, a simulation study is conducted for investigating the efficiency of the proposed SSADT plans when the sample size is small.     

Exponentially modified Gaussian relevance to the distributions of translocation events in nanopore-based single molecule detection

Nanopore technique plays an important role in single molecule detection, which illuminates the properties of an individual molecule by analyzing the blockage durations and currents. However, the traditional exponential function is lack of efficiency to describe the distributions of blockage durations in nanopore experiments. Herein, we introduced an exponentially modified Gaussian （EMG） function to fit the duration histograms of both simulated events and experimental events. In comparison with the traditional exponential function, our results demonstrated that the EMG provides a better fit while covers the entire range of the distributions. In particular, the fitted parameters of EMG could be directly used to discriminate the sequence length of the oligonucleotides at single molecule level.     

G-Protein-Coupled Receptor–Membrane Interactions Depend on the Receptor Activation State

G-protein-coupled receptors (GPCRs) are the largest family of human membrane proteins and serve as primary targets of approximately one-third of currently marketed drugs. In particular, adenosine A₁ receptor (A₁AR) is an important therapeutic target for treating cardiac ischemia–reperfusion injuries, neuropathic pain, and renal diseases. As a prototypical GPCR, the A₁AR is located within a phospholipid membrane bilayer and transmits cellular signals by changing between different conformational states. It is important to elucidate the lipid–protein interactions in order to understand the functional mechanism of GPCRs. Here, all-atom simulations using a robust Gaussian accelerated molecular dynamics (GaMD) method were performed on both the inactive (antagonist bound) and active (agonist and G-protein bound) A₁AR, which was embedded in a 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC) lipid bilayer. In the GaMD simulations, the membrane lipids played a key role in stabilizing different conformational states of the A₁AR. Our simulations further identified important regions of the receptor that interacted distinctly with the lipids in highly correlated manner. Activation of the A₁AR led to differential dynamics in the upper and lower leaflets of the lipid bilayer. In summary, GaMD enhanced simulations have revealed strongly coupled dynamics of the GPCR and lipids that depend on the receptor activation state. © 2019 Wiley Periodicals, Inc.     

Effect of Gaussian size distribution width on minimum fluidization velocity in tapered gas–solid fluidized beds

This paper investigated the effect of Gaussian distribution width, average particle diameter, particle loading, and the tapered angle on minimum fluidization velocity (U_mf) by conducting extensive experiments in tapered fluidized beds. Three powders with Gaussian size distribution and different distribution widths were used in the experiments. An increase in U_mf with increasing the average particle diameter, particle loading, and the tapered angle was observed. There was also a nonmonotonic behavior of U_mf as the Gaussian distribution width increased. An empirical correlation including dimensionless groups for predicting U_mf in tapered beds was developed in which the effect of distribution width was considered. The proposed correlation predictions were in good agreement with the experimental data, with a maximum deviation of 16.5% and average and standard deviations of, respectively, 6.4% and 7.4%. The proposed correlation was also compared with three earlier models, and their accuracy was discussed.     

RPA calculations with Gaussian expansion method

The Gaussian expansion method (GEM) is applied to calculations of the nuclear excitations in the random-phase approximation (RPA). We adopt the mass-independent basis-set that is successful in the mean-field calculations. The RPA results obtained by the GEM are compared with those obtained by several other available methods in Ca isotopes, by using a density-dependent contact interaction along with the Woods–Saxon single-particle states. It is confirmed that energies, transition strengths and widths of their distribution are described by the GEM with good precision, for the 1⁻, 2⁺ and 3⁻ collective states. The GEM is then applied to the self-consistent RPA calculations with the finite-range Gogny D1S interaction. The spurious center-of-mass motion is well separated from the physical states in the E1 response, and the energy-weighted sum rules for the isoscalar transitions are fulfilled reasonably well. Properties of low-energy transitions in ⁶⁰Ca are investigated in some detail.     

Circular partially coherent flattened Gaussian beam

An alternative theoretical model called circular partially coherent flattened Gaussian beam (FGB) is developed to describe a circular partially coherent beam with a flat-topped spatial profile. Explicit expression for the propagation factor of a circular partially coherent FGB is derived. We drive the analytical formulae for the cross-spectral density and mean-squared beam width of a circular partially coherent FGB propagating through a paraxial ABCD optical system based on the generalized Collins formula. The intensity, spreading and directionality properties of a circular partially coherent FGB propagating in free space are studied as numerical examples. The propagation properties of a circular partially coherent FGB agree well with those of a partially coherent flat-topped beam reported in the literature. Thus, our model provides an alternative but reliable model for describing a circular partially coherent beam with flat-topped profile.     

On Pseudo-Holomorphic Curves from Two-Spheres into a Complex Grassmannian G（2, 5）

Let s ： S2 → G（2, 5） be a linearly full totally unramified pseudo-holomorphic curve with constant Gaussian curvature K in a complex Grassmann manifold G（2, 5）. It is prove that K is either 1 4 1 or 4/5 if s is non-±holomorphic. Furthermore, K = 1/3 if and only if s is totally real. We also prove that the Gaussian curvature K is either 1 or -4/3 if s is a non-degenerate holomorphic curve under some conditions.     

Relativistic correlating basis sets for 57La and 89Ac

Developed and reported are compact yet efficient correlating basis sets for the ₅₇La and ₈₉Ac atoms, missing in the literature. Good performance of these correlating sets is exemplified in molecular applications to diatomic oxides and fluorides. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Fast Gaussian wavepacket transforms and Gaussian beams for the Schrödinger equation

This paper introduces a wavepacket-transform-based Gaussian beam method for solving the Schrödinger equation. We focus on addressing two computational issues of the Gaussian beam method: how to generate a Gaussian beam representation for general initial conditions and how to perform long time propagation for any finite period of time. To address the first question, we introduce fast Gaussian wavepacket transforms and develop on top of them an efficient initialization algorithm for general initial conditions. Based on this new initialization algorithm, we address the second question by reinitializing the beam representation when the beams become too wide. Numerical examples in one, two, and three dimensions demonstrate the efficiency and accuracy of the proposed algorithms. The methodology can be readily generalized to deal with other semi-classical quantum mechanical problems.     

The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation

We propose the backward phase flow method to implement the Fourier–Bros–Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schrödinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in [12]. In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.