Homogeneous structures and rigidity of isoparametric submanifolds in Hilbert space

We study isoparametric submanifolds of rank at least two in a separable Hilbert space, which are known to be homogeneous by the main result in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181], and with such a submanifold M and a point x in M we associate a canonical homogeneous structure I" (x) (a certain bilinear map defined on a subspace of T (x) M x T (x) M). We prove that I" (x) , together with the second fundamental form alpha (x) , encodes all the information about M, and we deduce from this the rigidity result that M is completely determined by alpha (x) and (Delta alpha) (x) , thereby making such submanifolds accessible to classification. As an essential step, we show that the one-parameter groups of isometries constructed in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181] to prove their homogeneity induce smooth and hence everywhere defined Killing fields, implying the continuity of I" (this result also seems to close a gap in [U. Christ, J. Differential Geom., 62 (2002), 1-15]). Here an important tool is the introduction of affine root systems of isoparametric submanifolds.

Vascular smooth muscle cells exhibit a progressive loss of rigidity with serial culture passaging

One drawback of in vitro cell culturing is the dedifferentiation process that cells experience. Smooth muscle cells (SMC) also change molecularly and morphologically with long term culture. The main objective of this study was to evaluate if culture passages interfere in vascular SMC mechanical behavior. SMC were obtained from five different porcine arterial beds. Optical magnetic twisting cytometry (OMTC) was used to characterize mechanically vascular SMC from different cultures in distinct passages and confocal microscopy/western blotting, to evaluate cytoskeleton and extracellular matrix proteins. We found that vascular SMC rigidity or viscoelastic complex modulus (G) decreases with progression of passages. A statistically significant negative correlation between G and passage was found in four of our five cultures studied. Phalloidin-stained SMC from higher passages exhibited lower mean signal intensity per cell (confocal microscopy) and quantitative western blotting analysis showed a decrease in collagen I content throughout passages. We concluded that vascular SMC progressively lose their stiffness with serial culture passaging. Thus, limiting the number of passages is essential for any experiment measuring viscoelastic properties of SMC in culture.

Relating network rigidity, time scale hierarchies, and expression noise in gene networks

Fluctuation-dissipation theorems can be used to predict characteristics of noise from characteristics of the macroscopic response of a system. In the case of gene networks, feedback control determines the "network rigidity," defined as resistance to slow external changes. We propose an effective Fokker-Planck equation that relates gene expression noise to topology and to time scales of the gene network. We distinguish between two situations referred to as normal and inverted time hierarchies. The noise can be buffered by network feedback in the first situation, whereas it can be topology independent in the latter.

Judet quadricepsplasty in the treatment of posttraumatic knee rigidity: Long-term outcomes of 45 cases

BACKGROUND: Posttraumatic knee stiffness is a very debilitating condition. Judet's quadricepsplasty technique has been used for more than 50 years. However, few reports of quadricepsplasty results exist in the literature. METHODS: We report the results of 45 cases of posttraumatic arthrofibrosis of the knee treated with Judet's quadricepsplasty. The results of the procedure were analyzed by measuring the degrees of flexion of the operated knees at different time points (before, immediately after, and late postoperatively). RESULTS: The degree of flexion increased from 33.6 degrees (range, 5-80 degrees) preoperatively to 105 degrees (range, 45-160 degrees) immediately after surgery, followed by a slight fall in the range of motion (ROM) in the late postoperative period, which reached an average of 84.8 degrees. There was no significant correlation between knee strength and the patient's gender, but there was a slight trend of lower strength with age. Although Judet's quadricepsplasty technique dates from more than 50 years ago, it still provides good outcomes in the treatment of rigid knees of various etiologies. In general, all cases showed the same pattern of a small decrease in the ROM in the late postoperative period. CONCLUSION: Judet's quadricepsplasty can increase the ROM of rigid knees. The ROM obtained with the surgery persists long term. (J Trauma. 2012; 72: E77-E80. Copyright (C) 2012 by Lippincott Williams & Wilkins)

Rigidity for piecewise smooth homeomorphisms on the circle

We find conditions for two piecewise 'C POT.2+V' homeomorphisms f and g of the circle to be 'C POT.1' conjugate. Besides the restrictions on the combinatorics of the maps (we assume that the maps have bounded combinatorics), and necessary conditions on the one-side derivatives of points where f and g are not differentiable, we also assume zero mean-nonlinearity for f and g.

On bifurcation of solutions of the Yamabe problem in product manifolds

We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non-homothetic solutions of the Yamabe problem. Using local rigidity and some compactness results for solutions of the Yamabe problem, we also exhibit new examples of conformal classes (with positive Yamabe constant) for which uniqueness holds. (C) 2011 Elsevier Masson SAS. All rights reserved.

New characterizations for hyperbolic cylinders in anti-de Sitter spaces

In this paper we study complete maximal spacelike hypersurfaces in anti-de Sitter space H-1(n+1) with either constant scalar curvature or constant non-zero Gauss-Kronecker curvature. We characterize the hyperbolic cylinders H-m(c(1)) x Hn-m(c(2)), 1 <= m <= n - 1, as the only such hypersurfaces with (n - 1) principal curvatures with the same sign everywhere. In particular we prove that a complete maximal spacelike hypersurface in H-1(5) with negative constant Gauss-Kronecker curvature is isometric to H-1(c(1)) x H-3(c(2)). (C) 2012 Elsevier Inc. All rights reserved.

Dynamic Viscosity of Implantable Autologous Materials Into the Vocal Fold

Objective. To compare the dynamic viscosity (DV) of superficial layer of temporalis fascia (SLTF) with that of other biological tissues traditionally used for vocal fold implants to treat vocal fold rigidity. Study Design. Experimental. Method. Measurement of DV of samples of SLTF, deep layer of temporalis fascia (DLTF), and abdominal fat of 12 cadavers. Results. DV values of the different samples were presented in the following increasing order: SLTF, DLTF, and abdominal fat. There was statistical difference between the samples. Conclusion. DV of SLTF is lower than of other tissues tested.

The influence of rifting on escarpment migration on high elevation passive continental margins

Using numerical models that couple surface processes, flexural isostasy, faulting and the thermal effects of rifting, we show that fault-bounded escarpments created at rift flanks by mechanical unloading and flexural rebound have little potential to "survive" as retreating escarpments if the lower crust under the rift flank is substantially stretched. In this configuration, a drainage divide that persists through time appears landward of the initial escarpment in a position close to a secondary bulge that is created during the rifting event at a distance that depends on the flexural rigidity of the upper crust. Moreover, the migration of the escarpment to the secondary bulge occurs when the pre-rift topography dips landward, otherwise the evolution of the escarpment is guided by the pre-existing inland drainage divide. To illustrate this new mechanism for the evolution of passive margins, we study the examples of Southeastern Australia and Southeastern Brazil. We propose that a pre-existing inland drainage divide with rift related flank uplift can produce the double drainage divide observed in Southeastern Australia. On the other hand, we conclude that it is possible that the Serra do Mar escarpments on the Southeastern Brazilian margin originated as a secondary flexural bulge during rifting that persisted through time. In both cases, the retreating escarpment scenario is unlikely and the present-day margin morphology can be explained as resulting from rift-related vertical motions alone, without requiring significant post-rift "rejuvenation".

Performance of polymeric reinforcements in vehicle structures submitted to frontal impact

Preformed structural reinforcements have shown good performance in crash tests, where the great advantage is their weight. These reinforcements are designed with the aim of increasing the rigidity of regions with large deformations, thus stabilising sections of the vehicle that work as load path during impact. The objective of this work is to show the application of structural reinforcements made of polymeric material PA66 in the field of vehicle safety, through finite element simulations. Simulations of frontal impact at 50 km/h and in ODB (offset deformable barrier) at 57 km/h configurations (standards such as ECE R-94 and ECE R-12) were performed in the software LS-DYNA R (R) and MADYMO (R). The simulations showed that the use of polymeric reinforcements leads to a 70% reduction in A-pillar intrusion, a 65% reduction in the displacement of the steering column and a 59% reduction in the deformation in the region of the occupant legs and feet. The level of occupant injuries was analysed by MADYMO (R) software, and a reduction of 23.5% in the chest compression and 80% in the tibia compression were verified. According to the standard, such conditions lead to an improvement in the occupant safety in a vehicle collision event.

The 1420 Ma Indiavai Mafic Intrusion (SW Amazonian Craton): Paleomagnetic results and implications for the Columbia supercontinent

The configuration and the timing of assembly and break-up of Columbia are still matter of debate. In order to improve our knowledge about the Mesoproterozoic evolution of Columbia, a paleomagnetic study was carried out on the 1420 Ma Indiavai mafic intrusive rocks that crosscut the polycyclic Proterozoic basement of the SW Amazonian Craton, in southwestern Mato Grosso State (Brazil). Alternating field and thermal demagnetization revealed south/southwest ChRM directions with downward inclinations for sixteen analyzed sites. These directions are probably carried by SD/PSD magnetite with high coercivities and high unblocking temperatures as indicated by additional rock magnetic tests, including thermomagnetic data, hysteresis data and the progressive acquisition of isothermal remanent magnetization. Different stable magnetization components isolated in host rocks from the basement 10 km NW away to the Indiavai intrusion, further support the primary origin of the ChRM. A mean of the site mean directions was calculated at Dm = 209.8 degrees, Im = 50.7 degrees (alpha(95) = 8.0 degrees, K = 22.1), which yielded a paleomagnetic pole located at 249.7 degrees E, 57.0 degrees S (A(95) = 8.6 degrees). The similarity of this pole with the recently published 1420 Ma pole from the Nova Guarita dykes in northern Mato Grosso State suggests a similar tectonic framework for these two sites located 600 km apart, implying the bulk rigidity of the Rondonian-San Ignacio crust at that time. Furthermore these data provide new insights on the tectonic significance of the 1100-1000 Ma Nova Brasilandia belt-a major EW feature that cuts across the basement rocks of this province, which can now be interpreted as intracratonic, in contrast to previous interpretation. From a global perspective, a new Mesoproterozoic paleogeography of Columbia has been proposed based on comparison of these 1420 Ma poles and a 1780 Ma pole from Amazonia with other paleomagnetic poles of similar age from Baltica and Laurentia, a reconstruction in agreement with geological correlations. (C) 2012 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.

Energy-level statistics of interacting trapped bosons

It is a well-established fact that statistical properties of energy-level spectra are the most efficient tool to characterize nonintegrable quantum systems. The statistical behavior of different systems such as complex atoms, atomic nuclei, two-dimensional Hamiltonians, quantum billiards, and noninteracting many bosons has been studied. The study of statistical properties and spectral fluctuations in interacting many-boson systems has developed interest in this direction. We are especially interested in weakly interacting trapped bosons in the context of Bose-Einstein condensation (BEC) as the energy spectrum shows a transition from a collective nature to a single-particle nature with an increase in the number of levels. However this has received less attention as it is believed that the system may exhibit Poisson-like fluctuations due to the existence of an external harmonic trap. Here we compute numerically the energy levels of the zero-temperature many-boson systems which are weakly interacting through the van der Waals potential and are confined in the three-dimensional harmonic potential. We study the nearest-neighbor spacing distribution and the spectral rigidity by unfolding the spectrum. It is found that an increase in the number of energy levels for repulsive BEC induces a transition from a Wigner-like form displaying level repulsion to the Poisson distribution for P(s). It does not follow the Gaussian orthogonal ensemble prediction. For repulsive interaction, the lower levels are correlated and manifest level-repulsion. For intermediate levels P(s) shows mixed statistics, which clearly signifies the existence of two energy scales: external trap and interatomic interaction, whereas for very high levels the trapping potential dominates, generating a Poisson distribution. Comparison with mean-field results for lower levels are also presented. For attractive BEC near the critical point we observe the Shnirelman-like peak near s = 0, which signifies the presence of a large number of quasidegenerate states.

Child Physical Abuse: Evaluating Psychological Risk Factors in Accused Caregivers

It was verified to what extent cognitive and affective/emotional variables could distinguish caregivers accused of committing physical abuse (G1) from those without physical abuse records (G2). The Child Abuse Potential Inventory (CAP), which is an instrument designed to assess psychological risk factors in caregivers, was used. A questionnaire on socio-demographic characterization and another on economic classification were also employed to equate the groups. G1 presented a greater potential risk than G2, higher levels of Distress, Rigidity, Problems with the Child and with Themselves, Problems with Others, and a lower level of Ego Strength. These variables contribute with the composition of physical abuse risk, since, in agreement with the Social Information Processing Model, they would be related to cognitive and affective basic processes which are veiled to the perceptions and evaluation/interpretations, associated to abusive parental behavior.

Steel fiber reinforced concrete pipes: part 1: technological analysis of the mechanical behavior

This paper is the first part of an extensive work focusing the technological development of steel fiber reinforced concrete pipes (FRCP). Here is presented and discussed the experimental campaign focusing the test procedure and the mechanical behavior obtained for each of the dosages of fiber used. In the second part ("Steel fiber reinforced concrete pipes. Part 2: Numerical model to simulate the crushing test"), the aspects of FRCP numerical modeling are presented and analyzed using the same experimental results in order to be validated. This study was carried out trying to reduce some uncertainties related to FRCP performance and provide a better condition to the use of these components. In this respect, an experimental study was carried out using sewage concrete pipes in full scale as specimens. The diameter of the specimens was 600 mm, and they had a length of 2500 mm. The pipes were reinforced with traditional bars and different contents of steel fibers in order to compare their performance through the crushing test. Two test procedures were used in that sense. In the 1st Series, the diameter displacement was monitored by the use of two LVDTs positioned at both extremities of the pipes. In the 2nd Series, just one LVDT is positioned at the spigot. The results shown a more rigidity response of the pipe during tests when the displacements were measured at the enlarged section of the socket. The fiber reinforcement was very effective, especially when low level of displacement was imposed to the FRCP. At this condition, the steel fibers showed an equivalent performance to superior class pipes made with traditional reinforced. The fiber content of 40 kg/m3 provided a hardening behavior for the FRCP, and could be considered as equivalent to the critical volume in this condition.

The study the properties structurals and elastics of phases lamellar of lipid.

Lamellar systems composed of lipid bilayers have been widely used as model system for investigating properties of biological membranes, interactions between membranes and with biomolecules. The composition of the membrane determines its three dimensional shape and its properties such as rigidity and compressibility which play an important role on membrane fusion, protein adhesion, interactions between proteins, etc. We present a systematic study of a lamellar system composed of lecithin and a commercial co-surfactant (Simusol), which is a mixture of ethoxylated fatty acids. Using X ray scattering and a new procedure to fit X-ray experimental data, we determine relevant parameters characterizing the lamellar structure, varying membrane composition from 100% of lecithin to 100% of Simulsol. We present experimental data illustrating the swelling behavior for the membrane of different compositions and the respective behavior of the Caillé parameter. From and GISAXS experiments on oriented films under controlled humidity we investigate the compressibility of the lamellar phase and the effect of incorporating co-surfactant. Combining the Caillé parameter and compressibility studies we determine the bending rigidity of membranes. The results obtained with this experimental approach and new procedure to fit X-ray experimental allows us to identify structural changes in the bilayer depending both on hydration and co-surfactant content, with implications on elastic properties of membranes.