Inference with progressively censored <Emphasis Type="Italic">k</Emphasis>-out-of-<Emphasis Type="Italic">n</Emphasis> system lifetime data

A system with n independent components which works if and only if a least k of its n components work is called a k-out-of-n system. For exponentially distributed component lifetimes, we obtain point and interval estimators for the scale parameter of the component lifetime distribution of a k-out-of-n system when the system failure time is observed only. In particular, we prove that the maximum likelihood estimator (MLE) of the scale parameter based on progressively Type-II censored system lifetimes is unique. Further, we propose a fixed-point iteration procedure to compute the MLE for k-out-of-n systems data. In addition, we illustrate that the Newton–Raphson method does not converge for any initial value. Finally, exact confidence intervals for the scale parameter are constructed based on progressively Type-II censored system lifetimes.     

The Random <Emphasis Type="Italic">J</Emphasis>-Model with Biquadratic Interaction

The spin-1 model is studied on the Bethe lattice by including the bilinear J and biquadratic K exchange interactions into the Hamiltonian. The effects of J is randomized by using a bimodal random distribution with an adjustable parameter α which allows to study the cases of ±J-model and bond-dilution. The thermal variations of the order-parameters are studied to obtain the possible phase diagrams of the model. It is found that second-order phase transitions lines separate the ordered-phases, ferromagnetic, or antiferromagnetic, from the disordered one, i.e., the paramagnetic phase. The staggered quadrupolar phase lines are also found and only seen for higher negative K values for coordination number q=4 and 6, only. The reentrant behavior is also found for some of the phase transitions lines.     

Testing of multivariate repeated measures data with block exchangeable covariance structure

A new hypothesis testing of equality of mean vectors in two populations using \(D^2\) statistic for multivariate repeated measures data on q response variables at p sites or time points in a block exchangeable covariance matrix setting is proposed. The minimum sample size needed for our new test is only \(q +1\), unlike \(pq +1\) in Hotelling’s \(T^2\) test. The new test is very efficient in small sample scenario, when the number of observations is not adequate to estimate the \(pq \times pq\) dimensional unknown unstructured variance–covariance matrix. Some simulation studies are performed to compare the power of the new \(D^2\) test and the existing \(BT^2\) test. The performance of the proposed \(D^2\) test is demonstrated with the two medical data sets.     

A general near-exact distribution theory for the most common likelihood ratio test statistics used in Multivariate Analysis

In this paper we first show how the exact distributions of the most common likelihood ratio test (l.r.t.) statistics, that is, the ones used to test the independence of several sets of variables, the equality of several variance-covariance matrices, sphericity, and the equality of several mean vectors, may be expressed as the distribution of the product of independent Beta random variables or the product of a given number of independent random variables whose logarithm has a Gamma distribution times a given number of independent Beta random variables. Then, we show how near-exact distributions for the logarithms of these statistics may be expressed as Generalized Near-Integer Gamma distributions or mixtures of these distributions, whose rate parameters associated with the integer shape parameters, for samples of size n, all have the form (n−j)/n for j=2,…,p, where for three of the statistics, p is the number of variables involved, while for the other one, it is the sum of the number of variables involved and the number of mean vectors being tested. What is interesting is that the similarities exhibited by these statistics are even more striking in terms of near-exact distributions than in terms of exact distributions. Moreover all the l.r.t. statistics that may be built as products of these basic statistics also inherit a similar structure for their near-exact distributions. To illustrate this fact, an application is made to the l.r.t. statistic to test the equality of several multivariate Normal distributions.     

Multiscale bifurcation and stability of multilattices

A lattice-level model is developed for active materials, such as shape memory alloys, that undergo martensitic phase transformations. The model is investigated using equilibrium path following and bifurcation techniques. It is shown that a multiscale stability criterion is essential for correctly interpreting the stability of crystal equilibrium configurations under both thermal- and stress-loading conditions. A two-stage temperature-induced phase transformation is predicted from a cubic B2 phase to an orthorhombic Cmmm phase to a final orthorhombic B19 phase. Under stress-loading conditions, martensitic transformations from the B2 austenite phase to a number of possible martensite phases are identified. These include reconstructive transformations to B11, B33, and C2/m structures and proper transformation to a C2/m monoclinic phase which displays characteristic tension-compression asymmetry. The prediction of both temperature-induced and stress-induced proper martensitic transformations indicates the likelihood that the current model will exhibit shape memory behavior.     

The motion induced by the orthogonal stretching and shearing of a membrane beneath a quiescent fluid

The flow induced above an impermeable membrane undergoing orthogonal linear stretching and orthogonal linear shearing is investigated. For an exact solution of the Navier–Stokes equations, the orthogonal shearing motions must be related through the constant σ = γ δ, where γ and δ are the dimensionless streamwise and transverse shear rates, respectively. The resulting similarity reduction leads to three nonlinearly coupled ordinary differential equations governed by σ and the ratio of membrane stretch rates β. All possible solutions of these equations are found either numerically or, in special cases, analytically. Features of the σ = 0 solutions at β = 0 and asymptotically as β → ∞ are found to be in excellent agreement with numerical calculations. An aside calculation shows that orthogonal shearing in the absence of any plate stretching cannot exist. However, shearing in one coordinate direction is possible as long as the membrane stretches in at least one direction with the caveat that there exists uniform suction through a porous membrane.     

Solution of the Landau–Ginzburg Equations Using Lattice–Boltzmann

In this paper, we solve the time dependent Ginzburg–Landau (TDGL) equations in two dimensions, using Lattice–Boltzmann (LB) technique and the velocity discretization scheme D2Q9, for a square region with periodic boundary conditions. In order to obtain the solution, we use three distribution functions, each of them obeying the LB equation, and making a proper redefinition of the tensor Π ⁰, we find the (TDGL) equations. Further, we obtain the equilibrium distribution functions for the three LB equations, and then the solution for the components of the magnetic potential vector and the order parameter.     

High-temperature behavior and degradation mechanism of SiC fibers annealed in Ar and N<Subscript>2</Subscript> atmospheres

The thermal and mechanical stability of SiC fibers at elevated temperature is an important property for the practical application of SiC fiber-reinforced ceramic matrix composites and is related to the heat-treating atmosphere. In this study, the high-temperature behavior of KD SiC fibers with low oxygen content was investigated in both Ar and N₂ at temperatures from 1400 to 1800 °C through scanning electron microscopy, X-ray diffraction, X-ray photoelectron spectroscopy, Auger electron spectroscopy, resistivity measurements, and tensile tests in order to understand the effects of atmospheres on the degradation of the fibers. The results show that high-temperature treatment caused more severe strength degradation in Ar than in N₂. In particular, the fibers heat treated in N₂ at 1700 °C retained a relatively high strength of 1.52 GPa, 60 % of their original strength, while the fiber strength was completely lost after heat treatment in Ar. Fiber strength degradation was mainly caused by a combination of crystal growth and surface flaws. The formation of huge grains and porosity in the fiber surfaces, owing to the thermal decomposition of the SiC _x O _y N _z and SiC _x O _y phases, significantly degraded the strength for fibers heat treated in Ar. However, the suppressing effect of N₂ on the decomposition of the SiC _x O _y N _z phase in the fiber surfaces and nitrided case on the decomposition of the SiC _x O _y phase in the fiber cores, led to higher SiC fiber temperature stability in N₂ rather than Ar.     

Effects of <Emphasis Type="Italic">β</Emphasis>-Sn grain <Emphasis Type="Italic">c</Emphasis>-axis on electromigration behavior in BGA Sn3.0Ag0.5Cu solder interconnects

The anisotropy of β-Sn grain can significantly affect the electromigration (EM) behavior in Sn3.0Ag0.5Cu (SAC305) solder interconnects. A real ball grid array (BGA) specimen with a cross sectioned edge row suffered electromigration for 600 h to investigate the effects of β-Sn c-axis on the behavior of electromigration in SAC305 solder interconnects. Scanning electron microscopy (SEM) and electron backscattered diffraction (EBSD) were used to obtain the microstructure and orientation of β-Sn grains in as-reflowed and low current density conditions. Besides, the orientation of c-axis had a great effect on the growth direction of IMCs in solder matrix. The solder interconnect with the Sn grain c-axis pointing the positive direction of ND would emerge serious electromigration phenomena. The density of Cu₆Sn₅ IMCs distributing at the surface of solder matrix increased obviously. However, when Sn grain c-axis was in the same direction with the opposite direction of ND, the original Cu₆Sn₅ IMCs in as-reflowed solder interconnect disappeared. Therefore, the results show that the solder interconnects will performance a different electromigration behavior due to the direction of c-axis in Sn grain: the growth direction of Cu₆Sn₅ IMCs in solder matrix will along the c-axis accompanied growing into solder matrix or gathering at the surface of the cross section.     

Estimation of stochastic environment force for master–slave robotic system

The aim of this work is to obtain the maximum likelihood estimate (MLE) of controller-gain parameters \(\widehat{K} \) of the slave robot to determine the stochastic environment force. This is accomplished by measuring the joint positions of master and slave for a known master torque using stochastic difference equation. Here, the environmental force is modelled as a zero-mean white Gaussian random process. Therefore, the joint probability distribution function (pdf) of the slave angle over a given time duration can be computed as a function of the parameters ‘K’. This pdf is maximized with respect to ‘K’ to obtain the MLE of controller-gain parameters. Subsequently, convergence analysis of error in the estimates is performed. Also, an expression of the Cramer–Rao lower bound (CRLB) is derived to measure accuracy of the estimation. Comparison of CRLB with variance of MLE supports that our estimates are asymptotically efficient. The estimation performance is validated analytically and through simulations carried out on a two-link master–slave robotic system.     

Data clustering using <Emphasis Type="Italic">K</Emphasis>-Means based on Crow Search Algorithm

Cluster analysis is one of the popular data mining techniques and it is defined as the process of grouping similar data. K-Means is one of the clustering algorithms to cluster the numerical data. The features of K-Means clustering algorithm are easy to implement and it is efficient to handle large amounts of data. The major problem with K-Means is the selection of initial centroids. It selects the initial centroids randomly and it leads to a local optimum solution. Recently, nature-inspired optimization algorithms are combined with clustering algorithms to obtain the global optimum solution. Crow Search Algorithm (CSA) is a new population-based metaheuristic optimization algorithm. This algorithm is based on the intelligent behaviour of the crows. In this paper, CSA is combined with the K-Means clustering algorithm to obtain the global optimum solution. Experiments are conducted on benchmark datasets and the results are compared to those from various clustering algorithms and optimization-based clustering algorithms. Also the results are evaluated with internal, external and statistical experiments to prove the efficiency of the proposed algorithm.     

The thermal properties of water-ethanol system in the near-critical and supercritical states

Experimental p, ρ, T, x-data are given for water-ethanol mixtures at temperatures up to 673.15 K, including the saturation curve and the critical and supercritical regions, and at pressures up to 50 MPa for ethanol concentrations of 0.2, 0.5, and 0.8 mole fraction. The data of p, ρ, T, x-measurements are used to determine the critical parameters of mixtures. The thermal decomposition of ethanol molecules is observed at a temperature above 623.15 K.     

Effect of restricted geometry and external pressure on the phase transitions in ammonium hydrogen sulfate confined in a nanoporous glass matrix

A study of heat capacity, thermal dilatation, susceptibility to hydrostatic pressure, permittivity and polarization loops was carried out on NH₄HSO₄–porous glass nanocomposites (AHS?+?PG) as well as empty glass matrices. The formation of dendrite clusters of AHS with a size, d_cryst, exceeding the pore size was found. An insignificant anisotropy of thermal expansion of AHS?+?PG showing statistically uniform distribution of AHS with random orientations of nanocrystallites over the matrix was observed. The effect of internal and external pressures on thermal properties and permittivity was studied. At the phase transition P-1???Pc, a strongly nonlinear decrease in the entropy ΔS₂ and volume strain (ΔV/V)_T2 was observed with decreasing d_cryst. The linear change in temperatures of both phase transitions P-1???Pc???P2₁/c under hydrostatic pressure is accompanied by the expansion of the temperature range of existence of the ferroelectric phase Pc, while this interval narrows as d_cryst decreases.     

A procedure for outlier identification in data sets from continuous distributions

We propose a procedure, based on sums of reciprocals ofp-values, for the identification of outliers in univariate or multivariate data sets coming from continuous distributions. Using results of Csörg? (1990), we find the limiting distribution of the relevant statistic for completely specified models. By simulations, we obtain approximate quantiles for the asymptotic distribution, (which does not depend on the specific model or the dimension where the data live) and for the finite sample distribution in different dimensions of our statistic when parameters are estimated, for the multivariate Gaussian model and a multivariate double exponential model with independent coordinates. Monte Carlo evaluation shows that the procedure proposed is effective in the identification of outliers, and that it is sensitive to sample size, a feature seldom found in outlier identification methods.     

The effect of the flow-to-wall temperature ratio on strong condensation of gas

The method of direct statistical simulation is used to investigate the effect of the flow-to-wall temperature ratio T on the strong subsonic condensation of monatomic gas. It is demonstrated that the dependence of relative pressure at the boundary of the Knudsen layer on relative temperature at a fixed value of the Mach number M has a minimum. In so doing, the marked supercooling of condensing gas (T < 1) causes an abrupt increase in relative pressure. At the same time, for a “moderately cold” wall (1.5 < T < 10), the dependence of relative pressure on relative temperature at a fixed value of M is very weak. It is demonstrated that, in the case of supersonic condensation, the dependence of minimal possible relative pressure on T at a fixed value of M likewise has a minimum. The calculation results agree well with the results of calculations by the method of moments using the suggested approximation of the molecule distribution function.     

Superconductor-Semiconductor Metamaterial Photonic Crystals

We constructed theoretically one-dimensional photonic crystal (1DPC) by using a semiconductor metamaterial in the near-infrared range(NIR) which is composed of Al-doped Z n O(A Z O) and Z n O. The construction of this photonic crystal (PC) is based on a high-temperature superconductor material with the semiconductor metamaterial as constituent layers for this PC. The electromagnetic interactions with this periodic structure are investigated using the transfer matrix method (TMM) in the NIR range. The investigation shows that the reflectance spectra are depending on some parameters of the periodic structure such as the thicknesses of the constituent layers, temperature, and the angle of incidence.     

Wetting and Layering Transitions in a Nano-Square Structure: Monte Carlo Study

In this work, we study the magnetic wetting and layering transitions in a nano-square structure. The system is consisting of particles with spins s= 1/2 and S=1 placed at the square sites. We study the effect of the exchange couplings between different spins, namely, s- s, S- s, and S-S. The wetting phenomena and layering transitions are found under the effect of the temperature and the external magnetic field, for fixed values of the exchange coupling parameters. When studying the temperature effect on the magnetizations, using Monte Carlo simulations, the ground-state phase diagrams confirm these results for very low temperatures. Over the 2 × 2 × 2 × 3 = 24 possible configurations, only 6 configurations are found to be stable in the ground-state phase diagrams. Though the model established equations are valid for any system sizes, we give results and numerical values for a fixed system size formed only by four square layers.     

Block-simultaneous direction method of multipliers: a proximal primal-dual splitting algorithm for nonconvex problems with multiple constraints

We introduce a generalization of the linearized Alternating Direction Method of Multipliers to optimize a real-valued function f of multiple arguments with potentially multiple constraints \(g_\circ\) on each of them. The function f may be nonconvex as long as it is convex in every argument, while the constraints \(g_\circ\) need to be convex but not smooth. If f is smooth, the proposed Block-Simultaneous Direction Method of Multipliers (bSDMM) can be interpreted as a proximal analog to inexact coordinate descent methods under constraints. Unlike alternative approaches for joint solvers of multiple-constraint problems, we do not require linear operators \({{\mathsf {L}}}\) of a constraint function \(g({{\mathsf {L}}}\ \cdot )\) to be invertible or linked between each other. bSDMM is well-suited for a range of optimization problems, in particular for data analysis, where f is the likelihood function of a model and \({{\mathsf {L}}}\) could be a transformation matrix describing e.g. finite differences or basis transforms. We apply bSDMM to the Non-negative Matrix Factorization task of a hyperspectral unmixing problem and demonstrate convergence and effectiveness of multiple constraints on both matrix factors. The algorithms are implemented in python and released as an open-source package.     

Development of a spinodal decomposition model for the example of a heterostructure based on silicon carbide polytypes

The transition region of a 3C-SiC/4H-SiC heterostructure constituted by layers of the 3C and 4H polytypes has been studied. A previously proposed spinodal decomposition model was used to estimate the thickness ratio of 4H and 3C layers in comparison with the image furnished by transmission electron microscopy.     

The Impact of Hypergravity and Vibration on Gene and Protein Expression of Thyroid Cells

Experiments in space either on orbital missions on-board the ISS, or in suborbital missions using sounding rockets, like TEXUS as well as parabolic flight campaigns are still the gold standard to achieve real microgravity conditions in the field of gravitational biology and medicine. However, during launch, and in flight, hypergravity and vibrations occur which might interfere with the effects of microgravity. It is therefore important to know these effects and discriminate them from the microgravity effects. This can be achieved by ground-based facilities like centrifuges or vibration platforms. Recently, we have conducted several experiments with different thyroid cancer cell lines. This study, as part of the ESA-CORA-GBF 2010-203 project, focused on the influence of vibration and hypergravity on benign human thyroid follicular epithelial cells (Nthy-ori 3-1 cell line). Gene and in part protein expression regulation under both conditions were analyzed for VCAN, ITGA10, ITGB1, OPN, ADAM19, ANXA1, TNFA, ABL2, ACTB, PFN2, TLN1, EZR, RDX, MSN, CTGF, PRKCA, and PRKAA1 using quantitative real-time PCR and Western Blot. We found that hypergravity and vibration affected genes and proteins involved in the extracellular matrix, the cytoskeleton, apoptosis, cell growth and signaling. Vibration always led to a down-regulation, whereas hypergravity resulted in a more heterogeneous expression pattern. Overall we conclude that both conditions can influence gene regulation and production of various genes and proteins. As a consequence, it is important to perform control experiments on hypergravity and vibration facilities in parallel to flight experiments.