On the stability of the L-p-norm of the Riemannian curvature tensor

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M where R(g) and dv (g) denote the corresponding Riemannian curvature tensor and volume form and p a (0, a). First we prove that the Riemannian metrics with non-zero constant sectional curvature are strictly stable for for certain values of p. Then we conclude that they are strict local minimizers for for those values of p. Finally generalizing this result we prove that product of space forms of same type and dimension are strict local minimizer for for certain values of p.

SOME UNSTABLE CRITICAL METRICS FOR THE L-n/2-NORM OF THE CURVATURE TENSOR

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M given by R-n/2(g) := integral(M) vertical bar R(g)vertical bar(n//2) dv(g) where R(g), dv(g) denote the Riemannian curvature and volume form corresponding to g. We show that there are locally symmetric spaces which are unstable critical points for this functional.

Curvature-constrained trajectory generation for waypoint following for miniature air vehicle

This paper addresses trajectory generation problem of a fixed-wing miniature air vehicle, constrained by bounded turn rate, to follow a given sequence of waypoints. An extremal path, named as g-trajectory, that transitions between two consecutive waypoint segments (obtained by joining two waypoints in sequence) in a time-optimal fashion is obtained. This algorithm is also used to track the maximum portion of waypoint segments with the desired shortest distance between the trajectory and the associated waypoint. Subsequently, the proposed trajectory is compared with the existing transition trajectory in the literature to show better performance in several aspects. Another optimal path, named as loop trajectory, is developed for the purpose of tracking the waypoints as well as the entire waypoint segments. This paper also proposes algorithms to generate trajectories in the presence of steady wind to meet the same objective as that of no-wind case. Due to low computational burden and simplicity in the design procedure, these trajectory generation approaches are implementable in real time for miniature air vehicles.

Trace Formulae for Curvature of Jet Bundles over Planar Domains

For a domain Omega in C and an operator T in B-n(Omega), Cowen and Douglas construct a Hermitian holomorphic vector bundle E-T over Omega corresponding to T. The Hermitian holomorphic vector bundle E-T is obtained as a pull-back of the tautological bundle S(n, H) defined over by Gr(n, H) a nondegenerate holomorphic map z bar right arrow ker(T - z), z is an element of Omega. To find the answer to the converse, Cowen and Douglas studied the jet bundle in their foundational paper. The computations in this paper for the curvature of the jet bundle are rather intricate. They have given a set of invariants to determine if two rank n Hermitian holomorphic vector bundle are equivalent. These invariants are complicated and not easy to compute. It is natural to expect that the equivalence of Hermitian holomorphic jet bundles should be easier to characterize. In fact, in the case of the Hermitian holomorphic jet bundle J(k)(L-f), we have shown that the curvature of the line bundle L-f completely determines the class of J(k)(L-f). In case of rank Hermitian holomorphic vector bundle E-f, We have calculated the curvature of jet bundle J(k)(E-f) and also obtained a trace formula for jet bundle J(k)(E-f).

Influence of curvature on the device physics of thin film transistors on flexible substrates

Thin film transistors (TFTs) on elastomers promise flexible electronics with stretching and bending. Recently, there have been several experimental studies reporting the behavior of TFTs under bending and buckling. In the presence of stress, the insulator capacitance is influenced due to two reasons. The first is the variation in insulator thickness depending on the Poisson ratio and strain. The second is the geometric influence of the curvature of the insulator-semiconductor interface during bending or buckling. This paper models the role of curvature on TFT performance and brings to light an elegant result wherein the TFT characteristics is dependent on the area under the capacitance-distance curve. The paper compares models with simulations and explains several experimental findings reported in literature. (C) 2014 AIP Publishing LLC.

Role of interface curvature on stress distribution under indentation for ZrN/Zr multilayer coating

Contact damage in curved interface nano-layeredmetal/nitride (150 (ZrN)/10 (Zr) nm) multilayer is investigated in order to understand the role of interface morphology on contact damage under indentation. A finite element method (FEM) model was formulated with different wavelengths of 1000 nm, 500 nm, 250 nm and common height of 50 nm, which gives insight on the effect of different curvature on stress field generated under indentation. Elastic-plastic properties were assigned to the metal layer and substrate while the nitride layer was assigned perfectly elastic properties. Curved interface multilayers show delamination along the metal/nitride interface and vertical cracks emanating from the ends of the delamination. FEM revealed the presence of tensile stress normal to the interface even under the contact, along with tensile radial stresses, both present at the valley part of the curve, which leads to vertical cracks associated with interfacial delamination. Stress enhancement was seen to be relatively insensitive to curvature. (C) 2014 Elsevier B.V. All rights reserved.

On the curvature ODE associated to the Ricci flow

In the vector space of algebraic curvature operators we study the reaction ODE which is associated to the evolution equation of the Riemann curvature operator along the Ricci flow. More precisely, we give a partial classification of the zeros of this ODE up to suitable normalization and analyze the stability of a special class of zeros of the same. In particular, we show that the ODE is unstable near the curvature operators of the Riemannian product spaces where is an Einstein (locally) symmetric space of compact type and not a spherical space form when .

The tarani mutation alters surface curvature in Arabidopsis leaves by perturbing the patterns of surface expansion and cell division

The leaf surface usually stays flat, maintained by coordinated growth. Growth perturbation can introduce overall surface curvature, which can be negative, giving a saddle-shaped leaf, or positive, giving a cup-like leaf. Little is known about the molecular mechanisms that underlie leaf flatness, primarily because only a few mutants with altered surface curvature have been isolated and studied. Characterization of mutants of the CINCINNATA-like TCP genes in Antirrhinum and Arabidopsis have revealed that their products help maintain flatness by balancing the pattern of cell proliferation and surface expansion between the margin and the central zone during leaf morphogenesis. On the other hand, deletion of two homologous PEAPOD genes causes cup-shaped leaves in Arabidopsis due to excess division of dispersed meristemoid cells. Here, we report the isolation and characterization of an Arabidopsis mutant, tarani (tni), with enlarged, cup-shaped leaves. Morphometric analyses showed that the positive curvature of the tni leaf is linked to excess growth at the centre compared to the margin. By monitoring the dynamic pattern of CYCLIN D3;2 expression, we show that the shape of the primary arrest front is strongly convex in growing tni leaves, leading to excess mitotic expansion synchronized with excess cell proliferation at the centre. Reduction of cell proliferation and of endogenous gibberellic acid levels rescued the tni phenotype. Genetic interactions demonstrated that TNI maintains leaf flatness independent of TCPs and PEAPODs.

Expression of Bioactive Callithrix jacchus Follicle-Stimulating Hormone in Pichia pastoris

Callithrix jacchus (common marmoset) is a New World primate monkey, used as an animal model in biomedical research. Marmoset-specific follicle-stimulating hormone (FSH) preparation is required to improve superovulation protocols and to develop homologous FSH monitoring assays in these monkeys. In this study, we document the large-scale expression of recombinant marmoset FSH in methylotropic yeast, Pichia pastoris. The recombinant preparation was found to be immunologically active in Western blotting and radioimmunoassay. The preparation displayed receptor binding ability in radioreceptor assay. Based on the receptor binding ability, the yield of fermentation was estimated to be 7.2 mg/L. FSH-induced cAMP assay and estradiol assay revealed that the recombinant hormone is able to induce signal transduction. Both immunological and in vitro biological activity of marmoset FSH was found to be comparable to purified human pituitary FSH, which served as reference hormone for these assays. Thus, the study suggests that a Pichia expression system can be used for large-scale expression of bioactive recombinant marmoset FSH.

NON-COERCIVE RICCI FLOW INVARIANT CURVATURE CONES

This note is a study of nonnegativity conditions on curvature preserved by the Ricci flow. We focus on a specific class of curvature conditions which we call non-coercive: These are the conditions for which nonnegative curvature and vanishing scalar curvature does not imply flatness. We show, in dimensions greater than 4, that if a Ricci flow invariant nonnegativity condition is satisfied by all Einstein curvature operators with nonnegative scalar curvature, then this condition is just the nonnegativity of scalar curvature. As a corollary, we obtain that a Ricci flow invariant curvature condition, which is stronger than a nonnegative scalar curvature, cannot be strictly satisfied by curvature operators (other than multiples of the identity) of compact Einstein symmetric spaces. We also investigate conditions which are satisfied by all conformally flat manifolds with nonnegative scalar curvature.

MS3ALIGN: an efficient molecular surface aligner using the topology of surface curvature

Background: Aligning similar molecular structures is an important step in the process of bio-molecular structure and function analysis. Molecular surfaces are simple representations of molecular structure that are easily constructed from various forms of molecular data such as 3D atomic coordinates (PDB) and Electron Microscopy (EM) data. Methods: We present a Multi-Scale Morse-Smale Molecular-Surface Alignment tool, MS3ALIGN, which aligns molecular surfaces based on significant protrusions on the molecular surface. The input is a pair of molecular surfaces represented as triangle meshes. A key advantage of MS3ALIGN is computational efficiency that is achieved because it processes only a few carefully chosen protrusions on the molecular surface. Furthermore, the alignments are partial in nature and therefore allows for inexact surfaces to be aligned. Results: The method is evaluated in four settings. First, we establish performance using known alignments with varying overlap and noise values. Second, we compare the method with SurfComp, an existing surface alignment method. We show that we are able to determine alignments reported by SurfComp, as well as report relevant alignments not found by SurfComp. Third, we validate the ability of MS3ALIGN to determine alignments in the case of structurally dissimilar binding sites. Fourth, we demonstrate the ability of MS3ALIGN to align iso-surfaces derived from cryo-electron microscopy scans. Conclusions: We have presented an algorithm that aligns Molecular Surfaces based on the topology of surface curvature. Awebserver and standalone software implementation of the algorithm available at http://vgl.serc.iisc.ernet. in/ms3align.

Positive isotropic curvature and self-duality in dimension 4

We study a positivity condition for the curvature of oriented Riemannian 4-manifolds: the half-PIC condition. It is a slight weakening of the positive isotropic curvature (PIC) condition introduced by M. Micallef and J. Moore. We observe that the half-PIC condition is preserved by the Ricci flow and satisfies a maximality property among all Ricci flow invariant positivity conditions on the curvature of oriented 4-manifolds. We also study some geometric and topological aspects of half-PIC manifolds.

Smooth Path Planning for Passages with Heading and Curvature Discontinuities

The problem of continuous curvature path planning for passages is considered. This problem arises when an autonomous vehicle traverses between prescribed boundaries such as corridors, tunnels, channels, etc. Passage boundaries with curvature and heading discontinuities pose challenges for generating smooth paths passing through them. Continuous curvature half-S shaped paths derived from the Four Parameter Logistic Curve family are proposed as a prospective path planning solution. Analytic conditions are derived for generating continuous curvature paths confined within the passage boundaries. Zero end curvature highlights the scalability of the proposed solution and its compatibility with other path planners in terms of larger path planning domains. Various scenarios with curvature and heading discontinuities are considered presenting viability of the proposed solution.

Curvature Management in Buffer Layer for Device Quality GaN Growth on Si (111)

An efficient buffer layer scheme has been designed to address the issue of curvature management during metalorganic chemical vapour deposition growth of GaN on Si (111) substrate. This is necessary to prevent cracking of the grown layer during post-growth cooling down from growth temperature to room temperature and to achieve an allowable bow (<40 m) in the wafer for carrying out lithographic processes. To meet both these ends simultaneously, the stress evolution in the buffer layers was observed carefully. The reduction in precursor flow during the buffer layer growth provided better control over curvature evolution in the growing buffer layers. This has enabled the growth of a suitable high electron mobility transistor (HEMT) stack on 2'' Si (111) substrate of 300 m thickness with a bow as low as 11.4 m, having a two-dimensional electron gas (2DEG) of mobility, carrier concentration, and sheet resistance values 1510 cm(2)/V-s, 0.96 x 10(13)/cm(2), and 444 /, respectively. Another variation of similar technique resulted in a bow of 23.4 m with 2DEG mobility, carrier concentration, and sheet resistance values 1960 cm(2)/V-s, 0.98 x 10(13)/cm(2), and 325 /, respectively.

Curvature and wrinkling of premixed flame kernels-comparisons of OH PLIF and DNS data

The effects of curvature and wrinkling on the growth of turbulent premixed flame kernels were studied using both two-dimensional OH Planar Laser-Induced Fluorescence (PLIF) and three-dimensional Direct Numerical Simulation (DNS). Comparisons of results between the two approaches showed a high level of agreement, providing confidence in the simplified chemistry treatment employed in the DNS, and indicating that chemistry might have only a limited influence on the evolution of the freely propagating flame. The usefulness of PLIF in providing data over a wide parameter range was illustrated using statistics obtained from both CH4/air and H2/air mixtures, which show markedly different behavior due to their different thermo-diffusive properties. The results provided a demonstration of the combined power of PLIF and DNS for flame investigation. Each technique compensate for the weaknesses of the other, and to reinforce the strengths of both.