Unstable crack motion is predictable

Yoffe's linear theory of dynamic brittle fracture suggests that crack motion will be unstable beyond ∼70% of the Rayleigh speed, a prediction that is not supported by experiment. We show by atomistic simulations that hyperelasticity, the elasticity of large strains, plays a governing role in the instability dynamics of brittle fracture. A simple, yet remarkable, scaling model based on an effective elastic modulus (the secant modulus at the stability limit) gives successful predictions for the onset speed of the crack instability.     

Gold catalysis in organic transformations: A review

This review updates the explosive development of gold catalysis for organic transformation focusing on the current literature over last 3 years. Recent investigations have shown that gold catalysis provides catalytically active systems, whereas selectivity and reusability are advantages over noncatalyzed organic transformations. The collected literature is focusing for new organic reactions and synthetic methodologies. Gold can also be suggested for green processes dedicated to fine chemicals, pharmaceuticals, and the food industry due to its recognized biocompatibility. The current review is focused on new methods in the organic synthesis that could be of interest in the wide area of organic chemistry for developing new catalytic pathways.     

On toric locally conformally Kähler manifolds

We study compact toric strict locally conformally Kähler manifolds. We show that the Kodaira dimension of the underlying complex manifold is \(-\infty \), and that the only compact complex surfaces admitting toric strict locally conformally Kähler metrics are the diagonal Hopf surfaces. We also show that every toric Vaisman manifold has lcK rank 1 and is isomorphic to the mapping torus of an automorphism of a toric compact Sasakian manifold.     

Computation of the Coefficients Appearing in the Uniform Asymptotic Expansions of Integrals

The coefficients that appear in uniform asymptotic expansions for integrals are typically very complicated. In the existing literature, the majority of the work only give the first two coefficients. In a limited number of papers where more coefficients are given, the evaluation of the coefficients near the coalescence points is normally highly numerically unstable. In this paper, we illustrate how well‐known Cauchy‐type integral representations can be used to compute the coefficients in a very stable and efficient manner. We discuss the cases: (i) two coalescing saddles, (ii) two saddles coalesce with two branch points, and (iii) a saddle point near an endpoint of the interval of integration. As a special case of (ii), we give a new uniform asymptotic expansion for Jacobi polynomials in terms of Laguerre polynomials as that holds uniformly for z near 1. Several numerical illustrations are included.     

Disorder effect on heat capacity,self-diffusion coefficient,and choosing best potential model for melting temperature,in gold–copper bimetallic nanocluster with 55 atoms

Molecular dynamics simulation has been implemented for doping effect on melting temperature, heat capacity, self-diffusion coefficient of gold–copper bimetallic nanostructure with 55 total gold and copper atom numbers and its bulk alloy. Trend of melting temperature for gold–copper bimetallic nanocluster is not same as melting temperature copper–gold bulk alloy. Molecular dynamics simulation of our result regarding bulk melting temperature is consistence with available experimental data. Molecular dynamics simulation shows that melting temperature of gold–copper bimetallic nanocluster increases with copper atom fraction. Semi-empirical potential model and quantum Sutton–Chen potential models do not change melting temperature trend with copper doping of gold–copper bimetallic nanocluster. Self-diffusion coefficient of copper atom is greater than gold atom in gold–copper bimetallic nanocluster. Semi-empirical potential within the tight-binding second moment approximation as new application potential model for melting temperature of gold–copper bulk structure shows better result in comparison with EAM, Sutton–Chen potential, and quantum Sutton–Chen potential models.     

Optimal partitions for first eigenvalues of the Laplace operator

Given a bounded open set , we present numerical approximations for two problems related to minimal partitioning of the first eigenvalues of the Dirichlet Laplacian. The first problem is about minimizing the sum of first eigenvalues of the Dirichlet Laplacian. This partitioning problem arises as a steady state of a reaction‐diffusion process. To do this, a new idea to approximate the second eigenfunction and second eigenvalue is presented. We use the qualitative properties of the minimization problem to construct a numerical algorithm to approximate optimal configurations. A rigorous analysis to show the convergence and the rate of convergence is given. Moreover, we discuss the numerical implementation of the resulting approach and present computational tests confirming the expected asymptotic behavior of optimal partitions with large numbers of partitions. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 923–949, 2015     

Preparation,characterization and application of silica‐supported palladium complex as a new and heterogeneous catalyst for Suzuki and Sonogashira reactions

An efficient heterogeneous Pd catalytic system has been developed, based on immobilization of Pd nanoparticles (PNPs) on a silica‐bonded propylamine–cyanuric–cysteine (SiO₂–pA–Cyan–Cys) substrate. The synthesized catalyst was characterized by transmission electron microscopy, scanning electron microscopy, FT‐IR, N₂ adsorption analysis (BET), TGA and inductively coupled plasma/atomic emission spectroscopy, and catalytic activity of this catalyst was investigated in the Suzuki and Sonogashira cross‐coupling reactions. The catalysts showed excellent performance in these two reactions, including various aryl halide derivatives (except aryl chloride derivatives) with phenylboronic acid and phenylacetylene under green conditions. Moreover, the catalyst was recycled for several runs without any significant loss of catalytic activity. Copyright © 2014 John Wiley & Sons, Ltd.     

Long‐term consequences of single and multiple mild blast exposure on select physiological parameters and blood‐based biomarkers

Mild traumatic brain injury (mTBI), especially when it is repeated (rmTBI), can lead to progressive degenerative diseases and lasting neuropsychiatric abnormalities. To better understand the long‐term pathobiological changes in mTBI and rmTBI, we exposed rats to single or repeated (5 total; administered on consecutive days) mild blast overpressure, monitored changes in physiological parameters, and determined the plasma levels of select biomarkers at 42 days post injury by proteomics. We unexpectedly found comparable changes in arterial oxygen saturation levels and heart rates of single‐injured (SI) and multiple‐injured (MI) rats throughout the observation period. Our analyses indicated lasting oxidative stress, vascular abnormalities, and neuronal and glial cell loss in both injured groups. However, MI rats exhibited a relatively more pronounced increase in the plasma levels of most of the tested markers—particularly those associated with inflammation—albeit the differences between the two injured groups were not statistically significant. Our findings indicate that the frequency of blast exposures is an important determinant of the resulting cumulative damage in rmTBI.     

On the Numerical Range of Operator Polynomials

An upper bound for the number of components of the numerical range of matrix polynomials is established. We also establish a necessary condition and a sufficient condition for the connectedness of the numerical range of a quadratic selfadjoint matrix polynomial. The boundary of the numerical range of linear matrix polynomials is also considered.     

Estimating arrival rate of nonhomogeneous Poisson processes with semidefinite programming

We present a summary of methods based on semidefinite programming for estimating arrival rate of nonhomogeneous Poisson processes from a finite set of observed data. Both one-dimensional time dependent, and multi-dimensional time and location dependent rates are considered. The arrival rate is a nonnegative function of time (or time and location). We also assume that it is a smooth function with continuous derivatives of up to certain order k. We estimate the rate function by one or multi-dimensional splines, with the additional condition that the underlying rate function is nonnegative. This approach results in an optimization problem over nonnegative polynomials, which can be modeled and solved using semidefinite programming. We also describe a method which requires only linear constraints. Numerical results based on e-mail arrival and highway accidents are presented.