Analysis and implementation of a new constant acceleration subcycling algorithm

An algorithm for explicit integration of structural dynamics problems with multiple time steps is proposed that averages accelerations to obtain subcycle states at a nodal interface between regions integrated with different time steps. With integer time step ratios, the resulting subcycle updates at the interface sum to give the same effect as a central difference update over a major cycle. The algorithm is shown to have good accuracy, and stability properties in linear elastic analysis similar to those of constant velocity subcycling algorithms. The implementation of a generalised form of the algorithm with non-integer time step ratios is presented. (C) 1997 by John Wiley & Sons, Ltd.

The subcycled Newmark algorithm

The popular Newmark algorithm, used for implicit direct integration of structural dynamics, is extended by means of a nodal partition to permit use of different timesteps in different regions of a structural model. The algorithm developed has as a special case an explicit-explicit subcycling algorithm previously reported by Belytschko, Yen and Mullen. That algorithm has been shown, in the absence of damping or other energy dissipation, to exhibit instability over narrow timestep ranges that become narrower as the number of degrees of freedom increases, making them unlikely to be encountered in practice. The present algorithm avoids such instabilities in the case of a one to two timestep ratio (two subcycles), achieving unconditional stability in an exponential sense for a linear problem. However, with three or more subcycles, the trapezoidal rule exhibits stability that becomes conditional, falling towards that of the central difference method as the number of subcycles increases. Instabilities over narrow timestep ranges, that become narrower as the model size increases, also appear with three or more subcycles. However by moving the partition between timesteps one row of elements into the region suitable for integration with the larger timestep these the unstable timestep ranges become extremely narrow, even in simple systems with a few degrees of freedom. As well, accuracy is improved. Use of a version of the Newmark algorithm that dissipates high frequencies minimises or eliminates these narrow bands of instability. Viscous damping is also shown to remove these instabilities, at the expense of having more effect on the low frequency response.

The use of sodium-chloride difference and chloride-sodium ratio as strong ion difference surrogates in the evaluation of metabolic acidosis in critically ill patients

Purpose: Inorganic apparent strong ion difference (SIDai) improves chloride-associated acidosis recognition in dysnatremic patients. We investigated whether the difference between sodium and chloride (Na+-C1-) or the ratio between chloride and sodium (Cl-/Na+) could be used as SIDai surrogates in mixed and dysnatremic patients. Patients and Methods: Two arterial blood samples were collected from 128 patients. Physicochemical analytical approach was used. Correlation, agreement, accuracy, sensitivity, and specificity were measured to examine whether Na(+)-C1(-) and CI(-)/Na(+) could be used instead of SIDai in the diagnosis of acidosis. Results: Na(+)-C1(-) and CF/Na+ were well correlated with SIDai (R = 0.987, P < 0.001 and R = 0.959, P < 0.001, respectively). Bias between Na(+)-C1(-) and SIDai was high (6.384 with a limit of agreement of 4.4638.305 mEq/L). Accuracy values for the identification of SIDai acidosis (<38.9 mEq/L) were 0.989 (95% confidence interval [CI], 0.980-0.998) for Na+-C1- and 0.974 (95% CI, 0.959-0.989) for Cr/Na+. Receiver operator characteristic curve showed that values revealing SIDai acidosis were less than 32.5 mEq/L for Nata- and more than 0.764 for C17Na+ with sensitivities of 94.0% and 92.0% and specificities of 97.0% and 90.0%, respectively. Nata- was a reliable S IDai surrogate in dysnatremic patients. Conclusions: Nata- and CI-/Na+ are good tools to disclose S IDai acidosis. In patients with dysnatremia, Nata- is an accurate tool to diagnose SIDai acidosis. (C) 2010 Elsevier Inc. All rights reserved.

Comparison of renal transplantation outcomes in children with and without bladder dysfunction. A customized approach equals the difference

Purpose: We examined the development of urological abnormalities in a group of pediatric renal transplant recipients. Materials and Methods: We reviewed 211 patients younger than 19 years who underwent 226 renal transplants. Three groups of patients were studied-136 children with end stage renal disease due to a nonurological cause (group 1), 56 children with a urological disorder but with an adequate bladder (group 2a) and 19 children with lower urinary tract dysfunction and/or inadequate bladder drainage (group 2b). A total of 15 children in group 2b underwent bladder augmentation (ureterocystoplasty in 6, enterocystoplasty in 9), 2 underwent continent urinary diversion, 1 underwent autoaugmentation and 1 underwent a Mitrofanoff procedure at the bladder for easier drainage. Kidney transplantation was performed in the classic manner by extraperitoneal access, and whenever possible the ureter was reimplanted using an antireflux procedure. Results: At a mean followup of 75 months 13 children had died, 59 grafts were lost and 15 children had received a second transplant. Two patients in group 2a required a complementary urological procedure to preserve renal function (1 enterocystoplasty, 1 vesicostomy). A total of 12 major surgical complications occurred in 226 kidney transplants (5.3%), with a similar incidence in all groups. The overall graft survival at 5 years was 75%, 74% and 84%, respectively, in groups 1, 2a and 2b. Conclusions: With individualized treatment children with severely inferior lower urinary tract function may undergo renal transplantation with a safe and adequate outcome.

Representational Difference Analysis (RDA) reveals differential expression of conserved as well as novel genes during caste-specific development of the honey bee (Apis mellifera L.) ovary

In highly eusocial insects, such as the honey bee, Apis mellifera, the reproductive bias has become embedded in morphological caste differences. These are most expressively denoted in ovary size, with adult queens having large ovaries consisting of 150-200 ovarioles each, while workers typically have only 1-20 ovarioles per ovary. This morphological differentiation is a result of hormonal signals triggered by the diet change in the third larval instar, which eventually generate caste-specific gene expression patterns. To reveal these we produced differential gene expression libraries by Representational Difference Analysis (RDA) for queen and worker ovaries in a developmental stage when cell death is a prominent feature in the ovarioles of workers, whereas all ovarioles are maintained and extend in length in queens. In the queen library, 48% of the gene set represented homologs of known Drosophila genes, whereas in the worker ovary, the largest set (59%) were ESTs evidencing novel genes, not even computationally predicted in the honey bee genome. Differential expression was confirmed by quantitative RT-PCR for a selected gene set, denoting major differences for two queen and two worker library genes. These included two unpredicted genes located in chromosome 11 (Group11.35 and Group11.31, respectively) possibly representing long non-coding RNAs. Being candidates as modulators of ovary development, their expression and functional analysis should be a focal point for future studies. (C) 2011 Elsevier Ltd. All rights reserved.

A simple solution of the laminar dam break wave

The sudden release of a mass of fluid in a channel generates a highly unsteady flow motion, called dam break wave. While industrial fluids exhibit sometimes non-Newtonian behaviours, the viscous fluid flow assumption remains a useful approximation for simplified analyses. In this study, new solutions of laminar dam break wave are proposed for a semi-infinite reservoir based upon the method of characteristics. The solutions yield simple explicit expressions of the wave front location, wave front celerity and instantaneous free-surface profiles that compare favourably with experimental observations. Both horizontal and sloping channel configurations are treated. The simplicity of the equations may allow future extension to more complicated fluid flows.

Stability of nonlinear difference inclusions

The stability of difference inclusions x(k+1) is an element of F(x(k)) is studied, where F(x) = {F(x, gimel) : is an element of Lambda} and the selections F(., gimel) : E -->E assume values in a Banach space E, partially ordered by a cone K. It is assumed that the operators F(.,gimel) are heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, and include the case of a single equilibrium point. The results are applied to a number of practical problems.

Stability of linear difference and differential inclusions

Any given n X n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N x N matrix B of spectral radius p(B) arbitrarily close to p(A). A difference inclusion x(k+1) is an element of Ax(k), where A is a compact set of matrices, is asymptotically stable if and only if A can be extended to a set B of nonnegative matrices B with \ \B \ \ (1) < 1 or \ \B \ \ (infinity) < 1. Similar results are derived for differential inclusions.