Force dipoles and stable local defects on fluid vesicles

An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal invariance of the two-dimensional bending energy is used to identify the distribution of energy as well as the stress established in the vesicle. While these states are local minima of the energy, this energy is degenerate; there is a zero mode in the energy fluctuation spectrum, associated with area and volume preserving conformal transformations, which breaks the symmetry between the two points. The volume constraint fixes the distance $S$, measured along the surface, between the two points; if it is relaxed, a second zero mode appears, reflecting the independence of the energy on $S$; in the absence of this constraint a pathway opens for the membrane to slip out of the defect. Logarithmic curvature singularities in the surface geometry at the points of contact signal the presence of external forces. The magnitude of these forces varies inversely with $S$ and so diverges as the points merge; the corresponding torques vanish in these defects. The geometry behaves near each of the singularities as a biharmonic monopole, in the region between them as a surface of constant mean curvature, and in distant regions as a biharmonic quadrupole. Comparison of the distribution of stress with the quadratic approximation in the height functions points to shortcomings of the latter representation. Radial tension is accompanied by lateral compression, both near the singularities and far away, with a crossover from tension to compression occurring in the region between them.Comment: 26 pages, 10 figure

New lanthanide phosphonates structures obtained using XRPD data

5 páginas, 2 figuras, 3 tablas.-- Trabajo presentado como póster a la 12th European Powder Diffraction Conference (EPDIC 2010).-- et al.Seven lanthanide diphosphonates, [H3N(CH2)4NH3]Ln[hedpH][hedpH2] (Ln = La, Pr, Sm, Eu, Gd, Tb, Er; hedp = 1 hydroxyethylidenediphosphonate) have been synthesized with 1,4-diaminobutane as the template. The structures were obtained starting from the known X-ray single crystal model of lanthanum compound, with the X-ray powder diffraction data for these seven compounds. H-atoms were introduced using geometrical considerations. Rietveld fits of the experimental diffractograms confirm the isostructurality of all compounds in the series, and show the different behaviour between the two distances M-M existing in the structures.Financial support from Spanish MICINN (MAT2006-01997, MAT2010-15095 and ‘Factoría de Cristalización’ Consolider Ingenio 2010), Un-iversidad de Oviedo and Banco Santander is acknowledged. FEDER support is also acknowledged.Peer reviewe

Spinor representation of surfaces and complex stresses on membranes and interfaces

Variational principles are developed within the framework of a spinor representation of the surface geometry to examine the equilibrium properties of a membrane or interface. This is a far-reaching generalization of the Weierstrass-Enneper representation for minimal surfaces, introduced by mathematicians in the nineties, permitting the relaxation of the vanishing mean curvature constraint. In this representation the surface geometry is described by a spinor field, satisfying a two-dimensional Dirac equation, coupled through a potential associated with the mean curvature. As an application, the mesoscopic model for a fluid membrane as a surface described by the Canham-Helfrich energy quadratic in the mean curvature is examined. An explicit construction is provided of the conserved complex-valued stress tensor characterizing this surface.Comment: 17 page

Experimental verification of extraordinary transmission without surface plasmons

This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.This letter provides an experimental demonstration of extraordinary transmission in a closed waveguide system loaded with an electrically small diaphragm. This is a situation where the standard surface plasmon polariton SPP theory does not apply. The theoretical explanation is then based on the concept of impedance matching. This concept has previously been applied by some of the authors to account for enhanced transmission in situations where surface plasmon theory can be used: periodic arrays of small holes or slits in flat metal screens. The experiment in this letter supports the impedance matching model, valid for when SPPs are present or not. © 2009 American Institute of PhysicsThe authors would like to acknowledge the support of this research by the Spanish Ministry of Science and Innovation and European Union Feder Funds Grant Nos. TEC2007-65376 and Consolider Ingenio 2010 CSD2008- 00066 and by the Spanish Junta de Andalucía Project No. TIC-25

Experimental verification of extraordinary transmission without surface plasmons

This letter provides an experimental demonstration of extraordinary transmission in a closed waveguide system loaded with an electrically small diaphragm. This is a situation where the standard surface plasmon polariton (SPP) theory does not apply. The theoretical explanation is then based on the concept of impedance matching. This concept has previously been applied by some of the authors to account for enhanced transmission in situations where surface plasmon theory can be used: periodic arrays of small holes or slits in flat metal screens. The experiment in this letter supports the impedance matching model, valid for when SPPs are present or not.Ministerio de Ciencia e Innovación TEC2007-65376, CSD2008- 00066Junta de Andalucía TIC-25

Waveguide Bandpass Filters for Millimeter-Wave Radiometers

A fundamental requirement for most mm-wave heterodyne receivers is the rejection of the input image signal which is located close to the local oscillator frequency. For this purpose we use a bandpass filter, which for heterodyne receivers is also called an image rejection filter. In this paper we present a systematic approach to the design of a waveguide bandpass filter with a passband from 100 to 110 GHz and upper rejection bandwidth in the range from 113 to 145 GHz. We consider two non-tunable filter configurations: the first one is relatively selective with 11 sections (poles) whereas the second one is simpler with 5 sections. We used established design equations to propose an initial guess for the geometries of the filters, optimized the geometries, constructed the filters using two different milling methods, measured their transmission and reflection characteristics, and compared the measurements with numerical simulations. Measurements of both filters agree well with simulations in frequency response and rejection bandwidth. The insertion loss of the 11-pole filter is better than 10 dB and that of the 5-pole filter is better than 5 dB. The 11-pole filter has a sharper attenuation roll-off compared with the 5-pole filter. The upper out-of-band rejection is better than 40 dB up to 145 GHz for the 11-pole filter and up to 155 GHz for the 5-pole filter

Quantization of pure gravitational plane waves

Pure gravitational plane waves are considered as a special case of spacetimes with two commuting spacelike Killing vector fields. Starting with a midisuperspace that describes this kind of spacetimes, we introduce gauge-fixing and symmetry conditions that remove all non-physical degrees of freedom and ensure that the classical solutions are plane waves. In this way, we arrive at a reduced model with no constraints and whose only degrees of freedom are given by two fields. In a suitable coordinate system, the reduced Hamiltonian that generates the time evolution of this model turns out to vanish, so that all relevant information is contained in the symplectic structure. We calculate this symplectic structure and particularize our discussion to the case of linearly polarized plane waves. The reduced phase space can then be described by an infinite set of annihilation and creation like variables. We finally quantize the linearly polarized model by introducing a Fock representation for these variables.Comment: 11 pages, Revtex, no figure

Characterization of multiple sclerosis lesions with distinct clinical correlates through quantitative diffusion MRI

Diffusion magnetic resonance imaging can reveal quantitative information about the tissue changes in multiple sclerosis. The recently developed multi-compartment spherical mean technique can map different microscopic properties based only on local diffusion signals, and it may provide specific information on the underlying microstructural modifications that arise in multiple sclerosis. Given that the lesions in multiple sclerosis may reflect different degrees of damage, we hypothesized that quantitative diffusion maps may help characterize the severity of lesions "in vivo" and correlate these to an individual's clinical profile. We evaluated this in a cohort of 59 multiple sclerosis patients (62% female, mean age 44.7 years), for whom demographic and disease information was obtained, and who underwent a comprehensive physical and cognitive evaluation. The magnetic resonance imaging protocol included conventional sequences to define focal lesions, and multi-shell diffusion imaging was used with b-values of 1000, 2000 and 3000 s/mm2 in 180 encoding directions. Quantitative diffusion properties on a macro- and micro-scale were used to discriminate distinct types of lesions through a k-means clustering algorithm, and the number and volume of those lesion types were correlated with parameters of the disease. The combination of diffusion tensor imaging metrics (fractional anisotropy and radial diffusivity) and multi-compartment spherical mean technique values (microscopic fractional anisotropy and intra-neurite volume fraction) differentiated two type of lesions, with a prediction strength of 0.931. The B-type lesions had larger diffusion changes compared to the A-type lesions, irrespective of their location (P < 0.001). The number of A and B type lesions was similar, although in juxtacortical areas B-type lesions predominated (60%, P < 0.001). Also, the percentage of B-type lesion volume was higher (64%, P < 0.001), indicating that these lesions were larger. The number and volume of B-type lesions was related to the severity of disease evolution, clinical disability and cognitive decline (P = 0.004, Bonferroni correction). Specifically, more and larger B-type lesions were correlated with a worse Multiple Sclerosis Severity Score, cerebellar function and cognitive performance. Thus, by combining several microscopic and macroscopic diffusion properties, the severity of damage within focal lesions can be characterized, further contributing to our understanding of the mechanisms that drive disease evolution. Accordingly, the classification of lesion types has the potential to permit more specific and better-targeted treatment of patients with multiple sclerosis

Plane waves in quantum gravity: breakdown of the classical spacetime

Starting with the Hamiltonian formulation for spacetimes with two commuting spacelike Killing vectors, we construct a midisuperspace model for linearly polarized plane waves in vacuum gravity. This model has no constraints and its degrees of freedom can be interpreted as an infinite and continuous set of annihilation and creation like variables. We also consider a simplified version of the model, in which the number of modes is restricted to a discrete set. In both cases, the quantization is achieved by introducing a Fock representation. We find regularized operators to represent the metric and discuss whether the coherent states of the quantum theory are peaked around classical spacetimes. It is shown that, although the expectation value of the metric on Killing orbits coincides with a classical solution, its relative fluctuations become significant when one approaches a region where null geodesics are focused. In that region, the spacetimes described by coherent states fail to admit an approximate classical description. This result applies as well to the vacuum of the theory.Comment: 11 pages, no figures, version accepted for publication in Phys. Rev.