Search results for "Symmetry in biology"
showing 10 items of 11 documents
Radial Symmetry, the Anterior/Posterior Axis, and Echinoderm Hox Genes
2008
20 pages; International audience; The strangeness of echinoderm pentaradiality results from superposition of radial symmetry onto ancestral deuterostome bilaterality. The Extraxial- Axial Theory shows that echinoderms also have an anterior/posterior (A/P) axis developed independently and ontogenetically before radiality. The A/P axis is first established via coelomic stacking in the extraxial region, with ensuing development of the pentamerous hydrocoel in the axial region. This is strongly correlated with a variety of gene expression patterns. The echinoid Hox cluster is disordered into two different sets of genes. During embryogenesis, members of the posterior class demonstrate temporal, …
Radial symmetry of p-harmonic minimizers
2017
"It is still not known if the radial cavitating minimizers obtained by Ball [J.M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. R. Soc. Lond. A 306 (1982) 557--611] (and subsequently by many others) are global minimizers of any physically reasonable nonlinearly elastic energy". The quotation is from [J. Sivaloganathan and S. J. Spector, Necessary conditions for a minimum at a radial cavitating singularity in nonlinear elasticity, Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008), no. 1, 201--213] and seems to be still accurate. The model case of the $p$-harmonic energy is considered here. We prove that the planar radial minimizers are indee…
A note on an overdetermined problem for the capacitary potential
2016
We consider an overdetermined problem arising in potential theory for the capacitary potential and we prove a radial symmetry result.
Arrays in rays: terminal addition in echinoderms and its correlation with gene expression
2005
Summary The echinoderms are deuterostomes that superimpose radial symmetry upon bilateral larval morphology. Consequently, they are not the first animals that come to mind when the concepts of segmentation and terminal addition are being discussed. However, it has long been recognized that echinoderms have serial elements along their radii formed in accordance with the ocular plate rule (OPR). The OPR is a special case of terminal growth, forming elements of the ambulacra that define the rays in echinoderms. New elements are added at the terminus of the ray, which may or may not be marked by a calcified element called the terminal plate (the “ocular” of sea urchins). The OPR operates in eve…
Early decay detection in citrus fruit using laser-light backscattering imaging
2013
Early detection of fungal infections in citrus fruit still remains one of the major problems in postharvest technology. The potential of laser-light backscattering imaging was evaluated for detecting decay in citrus fruit after infection with the pathogen Penicillium digitatum, before the appearance of fruiting structures (green mould). Backscattering images of oranges cv. Navelate with and without decay were obtained using diode lasers emitting at five different wavelengths in the visible and near infrared range for addressing the absorption of fruit carotenoids, chlorophylls and water/carbohydrates. The apparent region of backscattered photons captured by a camera had radial symmetry with…
The rapidity structure of Mach cones and other large angle correlations in heavy-ion collisions
2006
The pattern of angular correlations of hadrons with a (semi-)hard trigger hadron in heavy-ion collisions has attracted considerable interest. In particular, unexpected large angle structures on the away side (opposite to the trigger) have been found. Several explanations have been brought forward, among them Mach shockwaves and Cherenkov radiation. Most of these scenarios are characterized by radial symmetry around the parton axis, thus angular correlations also determine the rapidity dependence of the correlation. If the observed correlations are remnants of an away side parton after interaction with the medium created in the collision, pQCD allows to calculate the distribution $P(y)$ of t…
Lau rings: In-register incoherent superposition of radial self-images
1989
Abstract We describe an optical method for obtaining in-register, incoherent superposition of self-images, with radial symmetry. That is, the Lau effect is implemented, either at infinity or at finite distances, in the form of bright and dark rings of high visibility. This is applied for visualizing radially phase structures, with good-signal-to-noise ratio.
On the stability of the Serrin problem
2008
We investigate stability issues concerning the radial symmetry of solutions to Serrin's overdetermined problems. In particular, we show that, if $u$ is a solution to $\Delta u=n$ in a smooth domain $\Omega \subset \rn$, $u=0$ on $\partial\Omega$ and $|Du|$ is close to 1 on $\partial\Omega$, then $\Omega$ is close to the union of a certain number of disjoint unitary balls.
Stability of radial symmetry for a Monge-Ampère overdetermined problem
2008
Recently the symmetry of solutions to overdetermined problems has been established for the class of Hessian operators, including the Monge-Ampère operator. In this paper we prove that the radial symmetry of the domain and of the solution to an overdetermined Dirichlet problem for the Monge-Ampère equation is stable under suitable perturbations of the data. © 2008 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.
Radial symmetry of minimizers to the weighted Dirichlet energy
2020
AbstractWe consider the problem of minimizing the weighted Dirichlet energy between homeomorphisms of planar annuli. A known challenge lies in the case when the weight λ depends on the independent variable z. We prove that for an increasing radial weight λ(z) the infimal energy within the class of all Sobolev homeomorphisms is the same as in the class of radially symmetric maps. For a general radial weight λ(z) we establish the same result in the case when the target is conformally thin compared to the domain. Fixing the admissible homeomorphisms on the outer boundary we establish the radial symmetry for every such weight.