Hydrodynamic singularities and clustering in a freely cooling inelastic gas

We employ hydrodynamic equations to follow the clustering instability of a freely cooling dilute gas of inelastically colliding spheres into a well-developed nonlinear regime. We simplify the problem by dealing with a one-dimensional coarse-grained flow. We observe that at a late stage of the instability the shear stress becomes negligibly small, and the gas flows solely by inertia. As a result the flow formally develops a finite time singularity, as the velocity gradient and the gas density diverge at some location. We argue that flow by inertia represents a generic intermediate asymptotic of unstable free cooling of dilute inelastic gases.Comment: 4 pages, 4 figure

A Riemannian Approach to Reduced Plate, Shell, and Rod Theories

We derive a dimensionally-reduced limit theory for an $n$-dimensional nonlinear elastic body that is slender along $k$ dimensions. The starting point is to view an elastic body as an $n$-dimensional Riemannian manifold together with a not necessarily isometric $W^{1,2}$-immersion in $n$-dimensional Euclidean space. The equilibrium configuration is the immersion that minimizes the average discrepancy between the induced and intrinsic metrics. The dimensionally reduced limit theory views the elastic body as a $k$-dimensional Riemannian manifold along with an isometric $W^{2,2}$-immersion in $n$-dimensional Euclidean space and linear data in the normal directions. The equilibrium configuration minimizes a functional depending on the average covariant derivatives of the linear data. The dimensionally-reduced limit is obtained using a $\Gamma$-convergence approach. The limit includes as particular cases plate, shell, and rod theories. It applies equally to "standard" elasticity and to "incompatible" elasticity, thus including as particular cases so-called non-Euclidean plate, shell, and rod theories.Comment: 61 pages, added references, fixed typo

The smectic order of wrinkles

A thin elastic sheet lying on a soft substrate develops wrinkled patterns when subject to an external forcing or as a result of geometric incompatibility. Thin sheet elasticity and substrate response equip such wrinkles with a global preferred wrinkle spacing length and with resistance to wrinkle curvature. These features are responsible for the liquid crystalline smectic-like behaviour of such systems at intermediate length scales. This insight allows better understanding of the wrinkling patterns seen in such systems, with which we explain pattern breaking into domains, the properties of domain walls and wrinkle undulation. We compare our predictions with numerical simulations and with experimental observations

Foldable structures made of hydrogel bilayers

We discuss self-folding of a thin sheet by using patterned hydrogel bilayers, which act as hinges connecting flat faces. Folding is actuated by heterogeneous swelling due to different crosslinking densities of the polymer network in the two layers. Our analysis is based on a dimensionally reduced plate model, obtained by applying a recently developed theory [1], which provides us with an explicit connection between (three-dimensional) material properties and the curvatures induced at the hinges. This connection offers a recipe for the fabrication and design of the bilayers, by providing the values of the cross-linking density of each layer that need to be imprinted during polymerization in order to produce a desired folded shape upon swelling

Shape programming for narrow ribbons of nematic elastomers

Using the theory of Γ-convergence, we derive from three-dimensional elasticity new one-dimensional models for non-Euclidean elastic ribbons, i.e., ribbons exhibiting spontaneous curvature and twist. We apply the models to shape-selection problems for thin films of nematic elastomers with twist and splay-bend texture of the nematic director. For the former, we discuss the possibility of helicoid-like shapes as an alternative to spiral ribbons

Methacholine bronchial provocation measured by spirometry versus wheeze detection in preschool children

BACKGROUND: Determination of PC(20)-FEV(1) during Methacholine bronchial provocation test (MCT) is considered to be impossible in preschool children, as it requires repetitive spirometry sets. The aim of this study was to assess the feasibility of determining PC(20)-FEV(1) in preschool age children and compares the results to the wheeze detection (PCW) method. METHODS: 55 preschool children (ages 2.8–6.4 years) with recurrent respiratory symptoms were recruited. Baseline spirometry and MCT were performed according to ATS/ERS guidelines and the following parameters were determined at baseline and after each inhalation: spirometry-indices, lung auscultation at tidal breathing, oxygen saturation, respiratory and heart rate. Comparison between PCW and PC(20)-FEV(1) and clinical parameters at these end-points was done by paired Student's t-tests. RESULTS AND DISCUSSION: Thirty-six of 55 children (65.4%) successfully performed spirometry-sets up to the point of PCW. PC(20)-FEV(1) occurred at a mean concentration of 1.70+/-2.01 while PCW occurred at a mean concentration of 4.37+/-3.40 mg/ml (p < 0.05). At PCW, all spirometry-parameters were markedly reduced: FVC by 41.3+/-16.4% (mean +/-SD); FEV(1) by 44.7+/-14.5%; PEFR by 40.5+/-14.5 and FEF(25–75) by 54.7+/-14.4% (P < 0.01 for all parameters). This reduction was accompanied by de-saturation, hyperpnoea, tachycardia and a response to bronchodilators. CONCLUSION: Determination of PC(20)-FEV(1) by spirometry is feasible in many preschool children. PC(20)-FEV(1) often appears at lower provocation dose than PCW. The lower dose may shorten the test and encourage participation. Significant decrease in spirometry indices at PCW suggests that PC(20)-FEV(1) determination may be safer

Comparison of hemodynamic, biochemical and hematological parameters of healthy pregnant women in the third trimester of pregnancy and the active labor phase

<p>Abstract</p> <p>Background</p> <p>Pregnancy is accompanied by several hemodynamic, biochemical and hematological changes which revert to normal values after labor. The mean values of these parameters have been reported for developed countries, but not for Mexican women. Furthermore, labor constitutes a stress situation, in which these factors may be altered. It is known that serologic increase of heat shock protein (Hsp) 70 is associated with abnormal pregnancies, presenting very low level in normal pregnant women. Nevertheless, there are no studies where these measurements are compared in healthy pregnant women at their third trimester of pregnancy (3TP) and the active labor phase (ActLP).</p> <p>Methods</p> <p>Seventy five healthy Mexican pregnant women were included. Hemodynamic, biochemical and hematological parameters were obtained in all cases, and serum Hsp70 levels were measured in a sample of 15 women at 3TP and at ActLP.</p> <p>Results</p> <p>Significant differences were found in most analysis performed and in Hsp70 concentration at 3TP as compared to ActLP, however all were within normal range in both conditions, supporting that only in pathological pregnancies Hsp70 is drastically increased.</p> <p>Conclusion</p> <p>Results obtained indicate that 3TP and ActLP have clinical similarities in normal pregnancies, therefore if abnormalities are found during 3TP, precautions should be taken before ActLP.</p

Urine/Plasma Neutrophil Gelatinase Associated Lipocalin Ratio Is a Sensitive and Specific Marker of Subclinical Acute Kidney Injury in Mice

Background Detection of acute kidney injury (AKI) is still a challenge if conventional markers of kidney function are within reference range. We studied the sensitivity and specificity of NGAL as an AKI marker at different degrees of renal ischemia. Methods Male C57BL/6J mice were subjected to 10-, 20- or 30-min unilateral renal ischemia, to control operation or no operation, and AKI was evaluated 1 day later by histology, immunohistochemistry, BUN, creatinine, NGAL (plasma and urine) and renal NGAL mRNA expression. Results A short (10-min) ischemia did not alter BUN or kidney histology, but elevated plasma and urinary NGAL level and renal NGAL mRNA expression although to a much smaller extent than longer ischemia. Surprisingly, control operation elevated plasma NGAL and renal NGAL mRNA expression to a similar extent as 10-min ischemia. Further, the ratio of urine to plasma NGAL was the best parameter to differentiate a 10-min ischemic injury from control operation, while it was similar in the non and control-operated groups. Conclusions These results suggest that urinary NGAL excretion and especially ratio of urine to plasma NGAL are sensitive and specific markers of subclinical acute kidney injury in mice