A novel yield function for single crystals based on combined constraints optimization

A novel yield function representing the overall plastic deformation in a single crystal is developed using the concept of optimization. Based on the principle of maximum dissipation during a plastic deformation, the problem of single crystal plasticity is first considered as a constrained optimization problem in which constraints are yield functions for slip systems. To overcome the singularity that usually arises in solving the above problem, a mathematical technique is used to replace the above constrained optimization problem with an equivalent problem which has only one constraint. This single constraint optimization problem, the so-called combined constraints crystal plasticity (CCCP) model, is implemented into a finite element code and the results of modeling the uniaxial tensions of the single crystal copper along different crystallographic directions and also hydroforming of aluminum tubes proved the capability of the proposed CCCP model in accurately predicting the deformation in polycrystalline materials.     

One-pot synthesis of $$\upgamma $$-spiroiminolactones and $$\upgamma $$-dispiroiminolactones using $$\textit{N}{,}{} \textit{N}^{\prime }$$N,N′-disubstituted parabanic acid and thioparabanic acid derivatives

A direct entry and simple process for the synthesis of \(\upgamma \)-spiroiminolactones present in a large number of natural products has been developed. In the first step, the synthesis of parabanic acid derivatives was commenced from the reaction of \(\textit{N}{,}{} \textit{N}^{\prime }\)-disubstituted urea and thiourea with oxalyl chloride, then a three-component reaction was carried out with isocyanides, acetylenic esters, and \(\textit{N}{,}{} \textit{N}^{\prime }\)-disubstituted parabanic acid derivatives. The method allows the construction of a variety of \(\upgamma \)-spiroiminolactone structures in good to high yields starting from readily available precursors. It was found that in the case of \(\textit{N}{,}{} \textit{N}^{\prime }\)-diphenyl thioparabanic acid, additional products of \(\upgamma \)-dispiroiminolactones have been formed due to the higher electrophilicity of \(\upalpha \)-dicarbonyl groups. The structures were fully established using spectroscopic analysis NMR, IR, and Mass spectrometry. The crystal structure of \(\upgamma \)-dispiroiminolactone was confirmed from single-crystal X-ray diffraction study.     

Due date assignment for multistage assembly systems

This paper is concerned with the study of the constant due-date assignment policy in a multistage assembly system. The multistage assembly system is modeled as an open queueing network. It is assumed that the product order arrives according to a Poisson process. In each service station, there is either one or infinite machine with exponentially distributed processing time. The transport times between every pair of service stations are independent random variables with generalized Erlang distributions. It is assumed that each product has a penalty cost that is some linear function of its due-date and its actual completion time. The due date is found by adding a constant to the time that the order arrives. This constant value is the constant lead time that a product might expect between time of placing the order and time of delivery. By applying the longest path analysis in queueing networks, we obtain the distribution function of manufacturing lead time. Then, the optimal constant lead time is computed by minimizing the expected aggregate cost per product. Finally, the results are verified by Monte Carlo simulation.     

Borane–Lewis Base Complexes as Homolytic Hydrogen Atom Donors

Radical stabilization energies (RSE)s have been calculated for a variety of boryl radicals complexed to Lewis bases at the G3(MP2)‐RAD level of theory. These are referenced to the B? H bond dissociation energy (BDE) in BH₃ determined at W4.3 level. High RSE values (and thus low BDE(B? H) values) have been found for borane complexes of a variety of five‐ and six‐membered ring heterocycles. Variations of RSE values have been correlated with the strength of Lewis acid–Lewis base complex formation at the boryl radical stage. The analysis of charge‐ and spin‐density distributions shows that spin delocalization in the boryl radical complexes constitutes one of the mechanisms of radical stabilization.     

Effects of shearing flow with inertia on monolayer mesoscale structure

In an experimental flow system capable of imparting a well-controlled shear-rate distribution with inertia to a monolayer consisting of coexisting phases, we have studied the resulting phase morphology and domain fragmentation. These evolve on distinct time scales: the viscous time associated with the viscosity in the bulk and the Marangoni stress and the fragmentation/relaxation time associated with the phase morphology. A relationship between the microstructure (line tension) and macroflow (shear rate) determining the meso length scale of the coexisting phase domains has been deduced from dimensional analysis and was found to correlate well with the quantitative experimental observations.     

A statistical framework for the classification of tensor morphologies in diffusion tensor images

Tractography algorithms for diffusion tensor (DT) images consecutively connect directions of maximal diffusion across neighboring DTs in order to reconstruct the 3-dimensional trajectories of white matter tracts in vivo in the human brain. The performance of these algorithms, however, is strongly influenced by the amount of noise in the images and by the presence of degenerate tensors-- i.e., tensors in which the direction of maximal diffusion is poorly defined. We propose a simple procedure for the classification of tensor morphologies that uses test statistics based on invariant measures of DTs, such as fractional anisotropy, while accounting for the effects of noise on tensor estimates. Examining DT images from seven human subjects, we demonstrate that this procedure validly classifies DTs at each voxel into standard types (nondegenerate DTs, as well as degenerate oblate, prolate or isotropic DTs), and we provide preliminary estimates for the prevalence and spatial distribution of degenerate tensors in these brains. We also show that the P values for test statistics are more sensitive tools for classifying tensor morphologies than are invariant measures of anisotropy alone.     

The CoMirror algorithm for solving nonsmooth constrained convex problems

We introduce a first-order Mirror-Descent (MD) type algorithm for solving nondifferentiable convex problems having a combination of simple constraint set X (ball, simplex, etc.) and an additional functional constraint. The method is tuned to exploit the structure of X by employing an appropriate non-Euclidean distance-like function. Convergence results and efficiency estimates are derived. The performance of the algorithm is demonstrated by solving certain image deblurring problems.     

A new approach to the credibility formula

The usual credibility formula holds whenever, (i) claim size distribution is a member of the exponential family of distributions, (ii) prior distribution conjugates with claim size distribution, and (iii) square error loss has been considered. As long as, one of these conditions is violent, the usual credibility formula no longer holds. This article, using the mean square error minimization technique, develops a simple and practical approach to the credibility theory. Namely, we approximate the Bayes estimator with respect to a general loss function and general prior distribution by a convex combination of the observation mean and mean of prior, say, approximate credibility formula. Adjustment of the approximate credibility for several situations and its form for several important losses are given.     

Multiproduct single-machine production system with stochastic scrapped production rate, partial backordering and service level constraint

In this paper, a multiproduct single-machine production system under economic production quantity (EPQ) model is studied in which the existence of only one machine causes a limited production capacity for the common cycle length of all products, the production defective rates are random variables, shortages are allowed and take a combination of backorder and lost sale, and there is a service rate constraint for the company. The aim of this research is to determine the optimal production quantity, the allowable shortage level, and the period length of each product such that the expected total cost, including holding, shortage, production, setup and defective items costs, is minimized. The mathematical model of the problem is derived for which the objective function is proved to be convex. Then, a derivative approach is utilized to obtain the optimal solution. Finally, two numerical examples in each of which a sensitivity analysis is performed on the model parameters, are provided to illustrate the practical usage of the proposed methodology.     

Determination of the thermal stress wave propagation in orthotropic hollow cylinder based on classical theory of thermoelasticity

The thermoelasticity problem in a thick-walled orthotropic hollow cylinder is solved analytically using finite Hankel transform and Laplace transform. Time-dependent thermal and mechanical boundary conditions are applied on the inner and the outer surfaces of the cylinder. For solving the energy equation, the temperature itself is considered as boundary condition to be applied on both the inner and the outer surfaces of the orthotropic cylinder. Two different cases are assumed for solving the equation of motion: traction–traction problem (tractions are prescribed on both the inner and the outer surfaces) and traction–displacement (traction is prescribed on the inner surface and displacement is prescribed on the outer surface of the hollow orthotropic cylinder). Due to considering uncoupled theory, after obtaining temperature distribution, the dynamical structural problem is solved and closed-form relations are derived for radial displacement, radial and hoop stress. As a case study, exponentially decaying temperature with respect to time is prescribed on the inner surface of the cylinder and the temperature of the outer surface is considered to be zero. Owing to solving dynamical problem, the stress wave propagation and its reflections were observed after plotting the results in both cases.