Bogomol'nyi Decomposition for Vesicles of Arbitrary Genus

We apply the Bogomol'nyi technique, which is usually invoked in the study of solitons or models with topological invariants, to the case of elastic energy of vesicles. We show that spontaneous bending contribution caused by any deformation from metastable bending shapes falls in two distinct topological sets: shapes of spherical topology and shapes of non-spherical topology experience respectively a deviatoric bending contribution a la Fischer and a mean curvature bending contribution a la Helfrich. In other words, topology may be considered to describe bending phenomena. Besides, we calculate the bending energy per genus and the bending closure energy regardless of the shape of the vesicle. As an illustration we briefly consider geometrical frustration phenomena experienced by magnetically coated vesicles.Comment: 8 pages, 1 figure; LaTeX2e + IOPar

X-ray time variability across the atoll source states of 4U 1636--53

We have studied the rapid X-ray time variability in 149 pointed observations with the \textit{Rossi X-ray Timing Explorer} (RXTE)'s Proportional Counter Array of the atoll source 4U~1636--53 in the banana state and, for the first time with RXTE, in the island state. We compare the frequencies of the variability components of 4U~1636--53 with those in other atoll and Z-sources and find that 4U~1636--53 follows the universal scheme of correlations previously found for other atoll sources at (sometimes much) lower luminosities. Our results on the hectohertz QPO suggest that the mechanism that sets its frequency differs from that for the other components, while the amplitude setting mechanism is common. A previously proposed interpretation of the narrow low-frequency QPO frequencies in different sources in terms of harmonic mode switching is not supported by our data, nor by some previous data on other sources and the frequency range that this QPO covers is found not to be related to spin, angular momentum or luminosity.Comment: 16 pages, 13 figures, accepted for publication in Ap

Double deletion of Panx1 and Panx3 affects skin and bone but not hearing

Pannexins (Panxs), large-pore channel forming glycoproteins, are expressed in a wide variety of tissues including the skin, bone, and cochlea. To date, the use of single knock-out mouse models of both Panx1 and Panx3 have demonstrated their roles in skin development, bone formation, and auditory phenotypes. Due to sequence homology between Panx1 and Panx3, when one Panx is ablated from germline, the other may be upregulated in a compensatory mechanism to maintain tissue homeostasis and function. To evaluate the roles of Panx1 and Panx3 in the skin, bone, and cochlea, we created the first Panx1/Panx3 double knock-out mouse model (dKO). These mice had smaller litters and reduced body weight compared to wildtype controls. The dKO dorsal skin had decreased epidermal and dermal area as well as decreased hypodermal area in neonatal but not in older mice. In addition, mouse skull shape and size were altered, and long bone length was decreased in neonatal dKO mice. Finally, auditory tests revealed that dKO mice did not exhibit hearing loss and were even slightly protected against noise-induced hearing damage at mid-frequency regions. Taken together, our findings suggest that Panx1 and Panx3 are important at early stages of development in the skin and bone but may be redundant in the auditory system. Key messages Panx double KO mice had smaller litters and reduced body weight. dKO skin had decreased epidermal and dermal area in neonatal mice. Skull shape and size changed plus long bone length decreased in neonatal dKO mice. dKO had no hearing loss and were slightly protected against noise-induced damage

On Density of State of Quantized Willmore Surface-A Way to Quantized Extrinsic String in R^3

Recently I quantized an elastica with Bernoulli-Euler functional in two-dimensional space using the modified KdV hierarchy. In this article, I will quantize a Willmore surface, or equivalently a surface with the Polyakov extrinsic curvature action, using the modified Novikov-Veselov (MNV) equation. In other words, I show that the density of state of the partition function for the quantized Willmore surface is expressed by volume of a subspace of the moduli of the MNV equation.Comment: AMS-Tex Us

On CP1 and CP2 maps and Weierstrass representations for surfaces immersed into multi-dimensional Euclidean spaces

An extension of the classic Enneper-Weierstrass representation for conformally parametrised surfaces in multi-dimensional spaces is presented. This is based on low dimensional CP^1 and CP^2 sigma models which allow the study of the constant mean curvature (CMC) surfaces immersed into Euclidean 3- and 8-dimensional spaces, respectively. Relations of Weierstrass type systems to the equations of these sigma models are established. In particular, it is demonstrated that the generalised Weierstrass representation can admit different CMC-surfaces in R^3 which have globally the same Gauss map. A new procedure for constructing CMC-surfaces in R^n is presented and illustrated in some explicit examples.Comment: arxiv version is already officia

Quantum deformations of associative algebras and integrable systems

Quantum deformations of the structure constants for a class of associative noncommutative algebras are studied. It is shown that these deformations are governed by the quantum central systems which has a geometrical meaning of vanishing Riemann curvature tensor for Christoffel symbols identified with the structure constants. A subclass of isoassociative quantum deformations is described by the oriented associativity equation and, in particular, by the WDVV equation. It is demonstrated that a wider class of weakly (non)associative quantum deformations is connected with the integrable soliton equations too. In particular, such deformations for the three-dimensional and infinite-dimensional algebras are described by the Boussinesq equation and KP hierarchy, respectively.Comment: Numeration of the formulas is correcte

A classification theorem for Helfrich surfaces

In this paper we study the functional \SW_{\lambda_1,\lambda_2}, which is the the sum of the Willmore energy, $\lambda_1$-weighted surface area, and $\lambda_2$-weighted volume, for surfaces immersed in $\R^3$. This coincides with the Helfrich functional with zero `spontaneous curvature'. Our main result is a complete classification of all smooth immersed critical points of the functional with $\lambda_1\ge0$ and small $L^2$ norm of tracefree curvature. In particular we prove the non-existence of critical points of the functional for which the surface area and enclosed volume are positively weighted.Comment: 21 page

Surfaces immersed in su(N+1) Lie algebras obtained from the CP^N sigma models

We study some geometrical aspects of two dimensional orientable surfaces arrising from the study of CP^N sigma models. To this aim we employ an identification of R^(N(N+2)) with the Lie algebra su(N+1) by means of which we construct a generalized Weierstrass formula for immersion of such surfaces. The structural elements of the surface like its moving frame, the Gauss-Weingarten and the Gauss-Codazzi-Ricci equations are expressed in terms of the solution of the CP^N model defining it. Further, the first and second fundamental forms, the Gaussian curvature, the mean curvature vector, the Willmore functional and the topological charge of surfaces are expressed in terms of this solution. We present detailed implementation of these results for surfaces immersed in su(2) and su(3) Lie algebras.Comment: 32 pages, 1 figure; changes: major revision of presentation, clarifications adde

Index-free Heat Kernel Coefficients

Using index-free notation, we present the diagonal values of the first five heat kernel coefficients associated with a general Laplace-type operator on a compact Riemannian space without boundary. The fifth coefficient appears here for the first time. For a flat space with a gauge connection, the sixth coefficient is given too. Also provided are the leading terms for any coefficient, both in ascending and descending powers of the Yang-Mills and Riemann curvatures, to the same order as required for the fourth coefficient. These results are obtained by directly solving the relevant recursion relations, working in Fock-Schwinger gauge and Riemann normal coordinates. Our procedure is thus noncovariant, but we show that for any coefficient the `gauged' respectively `curved' version is found from the corresponding `non-gauged' respectively `flat' coefficient by making some simple covariant substitutions. These substitutions being understood, the coefficients retain their `flat' form and size. In this sense the fifth and sixth coefficient have only 26 and 75 terms respectively, allowing us to write them down. Using index-free notation also clarifies the general structure of the heat kernel coefficients. In particular, in flat space we find that from the fifth coefficient onward, certain scalars are absent. This may be relevant for the anomalies of quantum field theories in ten or more dimensions.Comment: 38 pages, LaTe