A blast-tolerant sandwich plate design with a polyurea interlayer

AbstractThis paper presents a study of both conventional and modified sandwich plate designs subjected to blast loads. The conventional sandwich Design (1) consists of thin outer (loaded side) and inner facesheets made of fibrous laminates, separated by a layer of structural foam core. In the modified Design (2), a thin polyurea interlayer is inserted between the outer facesheet and the foam core. Comparisons of the two designs are made during a long time period of 5.0ms, initiated by a pressure impulse lasting 0.05ms applied to a single span of a continuous plate. In the initial response period the overall deflections are limited and significant foam core crushing is caused in the conventional design by the incident compression wave. This type of damage is much reduced in the modified design, by stiffening of the polyurea interlayer under shock compression, which provides support to the outer facesheet and alters propagation of stress waves into the foam core. This benefits the long term, bending response and leads to significant reductions in facesheet strains and overall deflection. The total kinetic energy of the modified sandwich plate is much lower than that of a conventionally designed plate, and so is the stored and dissipated strain energy. Similar reductions are found when the conventional and the enhanced sandwich plates have equal overall thickness or equal total mass

Homotopy techniques for solving sparse column support determinantal polynomial systems

Let $\mathbf{K}$ be a field of characteristic zero with $\overline{\mathbf{K}}$ its algebraic closure. Given a sequence of polynomials $\mathbf{g} = (g_1, \ldots, g_s) \in \mathbf{K}[x_1, \ldots , x_n]^s$ and a polynomial matrix $\mathbf{F} = [f_{i,j}] \in \mathbf{K}[x_1, \ldots, x_n]^{p \times q}$, with $p \leq q$, we are interested in determining the isolated points of $V_p(\mathbf{F},\mathbf{g})$, the algebraic set of points in $\overline{\mathbf{K}}$ at which all polynomials in $\mathbf{g}$ and all $p$-minors of $\mathbf{F}$ vanish, under the assumption $n = q - p + s + 1$. Such polynomial systems arise in a variety of applications including for example polynomial optimization and computational geometry. We design a randomized sparse homotopy algorithm for computing the isolated points in $V_p(\mathbf{F},\mathbf{g})$ which takes advantage of the determinantal structure of the system defining $V_p(\mathbf{F}, \mathbf{g})$. Its complexity is polynomial in the maximum number of isolated solutions to such systems sharing the same sparsity pattern and in some combinatorial quantities attached to the structure of such systems. It is the first algorithm which takes advantage both on the determinantal structure and sparsity of input polynomials. We also derive complexity bounds for the particular but important case where $\mathbf{g}$ and the columns of $\mathbf{F}$ satisfy weighted degree constraints. Such systems arise naturally in the computation of critical points of maps restricted to algebraic sets when both are invariant by the action of the symmetric group

Faster real root decision algorithm for symmetric polynomials

In this paper, we consider the problem of deciding the existence of real solutions to a system of polynomial equations having real coefficients, and which are invariant under the action of the symmetric group. We construct and analyze a Monte Carlo probabilistic algorithm which solves this problem, under some regularity assumptions on the input, by taking advantage of the symmetry invariance property. The complexity of our algorithm is polynomial in $d^s, {{n+d} \choose d}$, and ${{n} \choose {s+1}}$, where $n$ is the number of variables and $d$ is the maximal degree of $s$ input polynomials defining the real algebraic set under study. In particular, this complexity is polynomial in $n$ when $d$ and $s$ are fixed and is equal to $n^{O(1)}2^n$ when $d=n$

Objective Assessment of the Core Laparoscopic Skills Course

Objective. The demand for laparoscopic surgery has led to the core laparoscopic skills course (CLSC) becoming mandatory for trainees in UK. Virtual reality simulation (VR) has a great potential as a training and assessment tool of laparoscopic skills. The aim of this study was to determine the role of the CLSC in developing laparoscopic skills using the VR. Design. Prospective study. Doctors were given teaching to explain how to perform PEG transfer and clipping skills using the VR. They carried out these skills before and after the course. During the course they were trained using the Box Trainer (BT). Certain parameters assessed. Setting. Between 2008 and 2010, doctors attending the CLSC at St Georges Hospital. Participants. All doctors with minimal laparoscopic experience attending the CLSC. Results. Forty eight doctors were included. The time taken for the PEG skill improved by 52%, total left hand and right hand length by 41% and 48%. The total time in the clipping skill improved by 57%. Improvement in clips applied in the marked area was 38% and 45% in maximum vessel stretch. Conclusions. This study demonstrated that CLSC improved some aspects of the laparoscopic surgical skills. It addresses Practice-based Learning and patient care

Computing critical points for invariant algebraic systems

Let $\mathbf{K}$ be a field and $\phi$, $\mathbf{f} = (f_1, \ldots, f_s)$ in $\mathbf{K}[x_1, \dots, x_n]$ be multivariate polynomials (with $s < n$) invariant under the action of $\mathcal{S}_n$, the group of permutations of $\{1, \dots, n\}$. We consider the problem of computing the points at which $\mathbf{f}$ vanish and the Jacobian matrix associated to $\mathbf{f}, \phi$ is rank deficient provided that this set is finite. We exploit the invariance properties of the input to split the solution space according to the orbits of $\mathcal{S}_n$. This allows us to design an algorithm which gives a triangular description of the solution space and which runs in time polynomial in $d^s$, ${{n+d}\choose{d}}$ and $\binom{n}{s+1}$ where $d$ is the maximum degree of the input polynomials. When $d,s$ are fixed, this is polynomial in $n$ while when $s$ is fixed and $d \simeq n$ this yields an exponential speed-up with respect to the usual polynomial system solving algorithms

Preparation and characterization of avenin-enriched oat protein by chill precipitation for feeding trials in celiac disease

The safety of oats for people with celiac disease remains unresolved. While oats have attractive nutritional properties that can improve the quality and palatability of the restrictive, low fiber gluten-free diet, rigorous feeding studies to address their safety in celiac disease are needed. Assessing the oat prolamin proteins (avenins) in isolation and controlling for gluten contamination and other oat components such as fiber that can cause non-specific effects and symptoms is crucial. Further, the avenin should contain all reported immunogenic T cell epitopes, and be deliverable at a dose that enables biological responses to be correlated with clinical effects. To date, isolation of a purified food-grade avenin in sufficient quantities for feeding studies has not been feasible. Here, we report a new gluten isolation technique that enabled 2 kg of avenin to be extracted from 400 kg of wheat-free oats under rigorous gluten-free and food grade conditions. The extract consisted of 85% protein of which 96% of the protein was avenin. The concentration of starch (1.8% dry weight), β-glucan (0.2% dry weight), and free sugars (1.8% dry weight) were all low in the final avenin preparation. Other sugars including oligosaccharides, small fructans, and other complex sugars were also low at 2.8% dry weight. Liquid chromatography tandem mass spectrometry (LC-MS/MS) analysis of the proteins in these preparations showed they consisted only of oat proteins and were uncontaminated by gluten containing cereals including wheat, barley or rye. Proteomic analysis of the avenin enriched samples detected more avenin subtypes and fewer other proteins compared to samples obtained using other extraction procedures. The identified proteins represented five main groups, four containing known immune-stimulatory avenin peptides. All five groups were identified in the 50% (v/v) ethanol extract however the group harboring the epitope DQ2.5-ave-1b was less represented. The avenin-enriched protein fractions were quantitatively collected by reversed phase HPLC and analyzed by MALDI-TOF mass spectrometry. Three reverse phase HPLC peaks, representing ~40% of the protein content, were enriched in proteins containing DQ2.5-ave-1a epitope. The resultant high quality avenin will facilitate controlled and definitive feeding studies to establish the safety of oat consumption by people with celiac disease

Pressure drop in pulsed extraction columns with internals of discs and doughnuts

A study on the pressure drop in pulsed extraction columns with internals of immobile discs and rings, usually called Discs and Doughnuts Columns (DDC) is carried out. The local pressure at a desired level of the column is obtained by resolving of turbulent flow model based on Reynolds equations coupled with k–ε model of turbulence. Consequently, the pressure drop for a column stage or for a unit of column length is determined. The results are used for development of correlations for determination of pressure drop as a function of plate free area, interplate distance and pulsation parameters - amplitude and frequency. Good correspondence to experimental data is observed. The developed quantitative relations are useful for non-experimental numerical optimization of stage geometry in view of lesser energy consumption