Uniaxial and biaxial soft deformations of nematic elastomers

We give a geometric interpretation of the soft elastic deformation modes of nematic elastomers, with explicit examples, for both uniaxial and biaxial nematic order. We show the importance of body rotations in this non-classical elasticity and how the invariance under rotations of the reference and target states gives soft elasticity (the Golubovic and Lubensky theorem). The role of rotations makes the Polar Decomposition Theorem vital for decomposing general deformations into body rotations and symmetric strains. The role of the square roots of tensors is discussed in this context and that of finding explicit forms for soft deformations (the approach of Olmsted).Comment: 10 pages, 10 figures, RevTex, AmsTe

Smectic-C tilt under shear in Smectic-A elastomers

Stenull and Lubensky [Phys. Rev. E {\bf 76}, 011706 (2007)] have argued that shear strain and tilt of the director relative to the layer normal are coupled in smectic elastomers and that the imposition of one necessarily leads to the development of the other. This means, in particular, that a Smectic-A elastomer subjected to a simple shear will develop Smectic-C-like tilt of the director. Recently, Kramer and Finkelmann [arXiv:0708.2024, Phys. Rev. E {\bf 78}, 021704 (2008)] performed shear experiments on Smectic-A elastomers using two different shear geometries. One of the experiments, which implements simple shear, produces clear evidence for the development of Smectic-C-like tilt. Here, we generalize a model for smectic elastomers introduced by Adams and Warner [Phys. Rev. E {\bf 71}, 021708 (2005)] and use it to study the magnitude of Smectic-C-like tilt under shear for the two geometries investigated by Kramer and Finkelmann. Using reasonable estimates of model parameters, we estimate the tilt angle for both geometries, and we compare our estimates to the experimental results. The other shear geometry is problematic since it introduces additional in-plane compressions in a sheet-like sample, thus inducing instabilities that we discuss.Comment: 8 pages, 5 figure

Interleukin 1: a mitogen for human vascular smooth muscle cells that induces the release of growth-inhibitory prostanoids.

There is much interest in defining the signals that initiate abnormal proliferation of cells in a variety of states characterized by the presence of mononuclear phagocytes. Since IL-1 is a major secretory product of activated human monocytes we examined whether this cytokine can stimulate the growth of human vascular smooth muscle cells (SMC). Neither recombinant IL-1 (rIL-1) alpha (less than or equal to 5.0 ng/ml) nor beta (less than or equal to 100 ng/ml) stimulated SMC growth during 2-d incubations under usual conditions. IL-1 did stimulate SMC to produce prostanoids such as PGE1 or PGE2 that can inhibit SMC proliferation. When prostaglandin synthesis was inhibited by indomethacin or aspirin both rIL-1 alpha and beta (greater than or equal to 1 ng/ml) markedly increased SMC growth. In longer-term experiments (7-28 d) rIL-1 stimulated the growth of SMC even in the absence of cyclooxygenase inhibitors. The addition of exogenous PGE1 or PGE2 (but not PGF1 alpha, PGF2 alpha, PGI2) to indomethacin-treated SMC blocked their mitogenic response to rIL-1. Antibody to IL-1 (but not to platelet-derived growth factor [PDGF]) abolished the mitogenic response of SMC to rIL-1. Exposure of SMC to rIL-1 or PDGF caused rapid (maximal at 1 h) and transient (baseline by 3 h) expression of the c-fos proto-oncogene, determined by Northern analysis. We conclude that IL-1 is a potent mitogen for human SMC. Endogenous prostanoid production simultaneously induced by IL-1 appears to antagonize this growth-promoting effect in the short term (2 d) but not during more prolonged exposures. IL-1 produced by activated monocytes at sites of tissue inflammation or injury may thus mediate both positive and negative effects on SMC proliferation that are temporally distinct

Immune interferon inhibits proliferation and induces 2'-5'-oligoadenylate synthetase gene expression in human vascular smooth muscle cells.

Proliferation of vascular smooth muscle cells (SMC) contributes to formation of the complicated human atherosclerotic plaque. These lesions also contain macrophages, known to secrete SMC mitogens, and T lymphocytes. Many of the SMC in the lesions express class II major histocompatibility antigens, an indication that activated T cells secrete immune IFN-gamma locally in the plaque. We therefore studied the effect of IFN-gamma on the proliferation of cultured SMC derived from adult human blood vessels. IFN-gamma (1,000 U/ml) reduced [3H]thymidine (TdR) incorporation into DNA by SMC stimulated with the well-defined mitogens IL 1 (from 15.3 +/- 0.7 to 6.2 +/- 0.7 dpm X 10(-3)/24 h) or platelet-derived growth factor (PDGF) (from 18.5 +/- 1.0 to 7.3 +/- 0.7 dpm X 10(-3)/24 h). Kinetic and nuclear labeling studies indicated that this effect of IFN-gamma was not due to altered thymidine transport or specific radioactivity of TdR in the cell. In longer term experiments (4-16 d) IFN-gamma prevented net DNA accumulation by SMC cultures stimulated by PDGF. IFN-gamma also delayed (from 30 to 60 min) the time to peak level of c-fos RNA in IL 1-treated SMC. It is unlikely that cytotoxicity caused these effects of IFN-gamma, as the inhibition of growth was reversible and we detected no cell death in SMC cultures exposed to this cytokine. Activation of 2'-5' oligoadenylate synthetase gene expression may mediate certain antiproliferative and antiviral effects of interferons. Both IFN-gamma and type I IFNs (IFN-alpha or IFN-beta) induced 2'-5' oligoadenylate synthetase mRNA and enzyme activity in SMC cultures, but with concentration dependence and time course that may not account for all of IFN-gamma's cytostatic effect on SMC. The accumulation of SMC in human atherosclerotic lesions is a long-term process that must involve altered balance between growth stimulatory and inhibitory factors. The cytostatic effect of IFN-gamma on human SMC demonstrated here may influence this balance during human atherogenesis, because T cells present in the complicated atherosclerotic plaque likely produce this cytokine

Deformed Gaussian Orthogonal Ensemble Analysis of the Interacting Boson Model

A Deformed Gaussian Orthogonal Ensemble (DGOE) which interpolates between the Gaussian Orthogonal Ensemble and a Poissonian Ensemble is constructed. This new ensemble is then applied to the analysis of the chaotic properties of the low lying collective states of nuclei described by the Interacting Boson Model (IBM). This model undergoes a transition order-chaos-order from the $SU(3)$ limit to the $O(6)$ limit. Our analysis shows that the quantum fluctuations of the IBM Hamiltonian, both of the spectrum and the eigenvectors, follow the expected behaviour predicted by the DGOE when one goes from one limit to the other.Comment: 10 pages, 4 figures (avaiable upon request), IFUSP/P-1086 Replaced version: in the previous version the name of one of the authors was omitte

Sobolev Inequalities for Differential Forms and Lq,pL_{q,p}-cohomology

We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold $(M,g)$ and the $L_{q,p}$-cohomology of that manifold. The $L_{q,p}$-cohomology of $(M,g)$ is defined to be the quotient of the space of closed differential forms in $L^p(M)$ modulo the exact forms which are exterior differentials of forms in $L^q(M)$.Comment: This paper has appeared in the Journal of Geometric Analysis, (only minor changes have been made since verion 1

The Interpretations For the Low and High Frequency QPO Correlations of X-ray Sources Among White Dwarfs, Neutron Stars and Black Holes

It is found that there exists an empirical linear relation between the high frequency \nhigh and low frequency \nlow of quasi-periodic oscillations (QPOs) for black hole candidate (BHC), neutron star (NS) and white dwarf (WD) in the binary systems, which spans five orders of magnitude in frequency. For the NS Z (Atoll) sources, $\nu_{high}$ and $\nu_{low}$ are identified as the lower kHz QPO frequency and horizontal branch oscillations (HBOs) \nh (broad noise components); for the black hole candidates and low-luminosity neutron stars, they are the QPOs and broad noise components at frequencies between 1 and 10 Hz; for WDs, they are the ``dwarf nova oscillations'' (DNOs) and QPOs of cataclysmic variables (CVs). To interpret this relation, our model ascribes $\nu_{high}$ to the Alfv\'en wave oscillation frequency at a preferred radius and $\nu_{low}$ to the same mechanism at another radius. Then, we can obtain \nlow = 0.08 \nhigh and the relation between the upper kHz QPO frequency \nt and HBO to be \nh \simeq 56 ({\rm Hz}) (\nt/{\rm kHz})^{2}, which are in accordance with the observed empirical relations. Furthermore, some implications of model are discussed, including why QPO frequencies of white dwarfs and neutron stars span five orders of magnitude in frequency. \\Comment: 11 pages, 1 figure, accepted by PAS

Visualizing the motion of graphene nanodrums

Membranes of suspended two-dimensional materials show a large variability in mechanical properties, in part due to static and dynamic wrinkles. As a consequence, experiments typically show a multitude of nanomechanical resonance peaks, which makes an unambiguous identification of the vibrational modes difficult. Here, we probe the motion of graphene nanodrum resonators with spatial resolution using a phase-sensitive interferometer. By simultaneously visualizing the local phase and amplitude of the driven motion, we show that unexplained spectral features represent split degenerate modes. When taking these into account, the resonance frequencies up to the eighth vibrational mode agree with theory. The corresponding displacement profiles however, are remarkably different from theory, as small imperfections increasingly deform the nodal lines for the higher modes. The Brownian motion, which is used to calibrate the local displacement, exhibits a similar mode pattern. The experiments clarify the complicated dynamic behaviour of suspended two-dimensional materials, which is crucial for reproducible fabrication and applications