An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space

2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.

Measuring higher order optical aberrations of the human eye: techniques and applications

In the present paper we discuss the development of "wave-front", an instrument for determining the lower and higher optical aberrations of the human eye. We also discuss the advantages that such instrumentation and techniques might bring to the ophthalmology professional of the 21st century. By shining a small light spot on the retina of subjects and observing the light that is reflected back from within the eye, we are able to quantitatively determine the amount of lower order aberrations (astigmatism, myopia, hyperopia) and higher order aberrations (coma, spherical aberration, etc.). We have measured artificial eyes with calibrated ametropia ranging from +5 to -5 D, with and without 2 D astigmatism with axis at 45º and 90º. We used a device known as the Hartmann-Shack (HS) sensor, originally developed for measuring the optical aberrations of optical instruments and general refracting surfaces in astronomical telescopes. The HS sensor sends information to a computer software for decomposition of wave-front aberrations into a set of Zernike polynomials. These polynomials have special mathematical properties and are more suitable in this case than the traditional Seidel polynomials. We have demonstrated that this technique is more precise than conventional autorefraction, with a root mean square error (RMSE) of less than 0.1 µm for a 4-mm diameter pupil. In terms of dioptric power this represents an RMSE error of less than 0.04 D and 5º for the axis. This precision is sufficient for customized corneal ablations, among other applications.

A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

Radiant exposure effects on physical properties of methacrylate - and silorane-composites

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 2: shells

Following the approach developed for rods in Part 1 of this paper (Pimenta et al. in Comput. Mech. 42:715-732, 2008), this work presents a fully conserving algorithm for the integration of the equations of motion in nonlinear shell dynamics. We begin with a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, allowing for an extremely simple update of the rotational variables within the scheme. The weak form is constructed via non-orthogonal projection, the time-collocation of which ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that general hyperelastic materials (and not only materials with quadratic potentials) are permitted in a totally consistent way. Spatial discretization is performed using the finite element method and the robust performance of the scheme is demonstrated by means of numerical examples.

An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 1: Rods

A fully conserving algorithm is developed in this paper for the integration of the equations of motion in nonlinear rod dynamics. The starting point is a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, which results in an extremely simple update of the rotational variables. The weak form is constructed with a non-orthogonal projection corresponding to the application of the virtual power theorem. Together with an appropriate time-collocation, it ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that nonlinear hyperelastic materials (and not only materials with quadratic potentials) are permitted without any prejudice on the conservation properties. Spatial discretization is performed via the finite element method and the performance of the scheme is assessed by means of several numerical simulations.

The elements of the differential calculus, comprehending the general theory of curve surfaces, and of curves of double curvature. Intended for the use of mathematical students in schools and universities.

Available on demand as hard copy or computer file from Cornell University Library.

On the determination of the rotational oblateness of Achernar

The recent interferometric study of Achernar, leading to the conclusion that its geometrical oblateness cannot be explained by the Roche approximation, has stirred substantial interest in the community, in view of its potential impact on many fields of stellar astrophysics. It is the purpose of this Letter to reinterpret the interferometric observations with a fast-rotating, gravity-darkened central star surrounded by a small equatorial disk, whose presence is consistent with contemporaneous spectroscopic data. We find that we can fit the available data only assuming a critically rotating central star. We identified two different disk models that simultaneously fit the spectroscopic, polarimetric, and interferometric observational constraints: a tenuous disk in hydrostatic equilibrium (i.e., with small scale height) and a smaller, scale height enhanced disk. We believe that these relatively small disks correspond to the transition region between the photosphere and the circumstellar environment and that they are probably perturbed by some photospheric mechanism. The study of this interface between photosphere and circumstellar disk for near-critical rotators is crucial to our understanding of the Be phenomenon and the mass and angular momentum loss of stars in general. This work shows that it is nowadays possible to directly study this transition region from simultaneous multitechnique observations.

A quasiclassical trajectory study of the OH plus SO reaction: The role of rotational energy

A full dimensional quasiclassical trajectory study of the OH+SO reaction is presented with the aim of investigating the role of the reactants rotational energy in the reactivity. Different energetic combinations with one and both reactants rotationally excited are studied. A passive method is used to correct zero-point-energy leakage in the classical calculations. The reactive cross sections, for each combination, are calculated and fitted to a capturelike model combined with a factor accounting for recrossing effects. Reactivity decreases as rotational energy is increased in any of both reactants. This fact provides a theoretical support for the experimental dependence of the rate constant on temperature.

A theoretical study of the origin of rotational barriers in push-pull ethylenes

Using the B3LYP/6-31G* ab initio method, we have studied the rotation about the C=C bonds in 15 push-pull ethylenes of the general formula (X,Y)C=C(CHO)(2) [X, Y = NH2, NHCH3, N(CH3)(2), OCH3, SCH3] in the gas phase. Two stationary points (minimum and transition state) were located for all compounds. The geometry, dipole moments, natural bond orbital atomic charges, as well as the rotational barriers were examined. The torsion angle 0 depends essentially on the presence or absence of intramolecular hydrogen bonds, and the barrier is a function of the torsion angle. (C) 2002 Elsevier Science B.V. All rights reserved.

Diseño y desarrollo de superficies modificadas. Aplicaciones ambientales, biomédicas y farmacéuticas. Design and development of modified surfaces. Environmental, biomedical and pharmaceutical applications.

El objetivo general de este proyecto de investigación es diseñar, desarrollar y optimizar superficies con propiedades especificas para ser utilizadas como sensores y biosensores, materiales biocompatibles, columnas para separaciones por electroforesis capilar, matrices para la liberación controlada de fármacos y sorbentes para remediación ambiental. Para concretar este objetivo, se propone específicamente modificar superficies o particulas apuntando a optimizar un sistema concreto relevante en aplicaciones farmaceuticas, ambientales o biomedicas: 1. Modificacion de arcillas naturales o sinteticas para desarrollar matrices portadoras de farmacos o sorbentes para remediacion ambiental:1.1 Estudiar ilitas modificadas con Fe(III) para maximizar las propiedades adsortivas frente a aniones contaminantes como arsenico. 1.2 Sintetizar LDH de Al y Mg modificados con compuestos de interés farmacéutico para diseñar sistemas de liberación controlada.2. Modificación de canales de chips y electrodos para optimizar la separación, detección y cuantificación de compuestos farmacéutico: 2.1 Diseñar y construir microchips para la separación por EC de compuestos de base fenólica.2.2 Evaluar polímeros que mejoren la respuesta y/o estabilidad de electrodos de Carbono para ser usados como detectores amperométrico de compuestos de base fenólica en sistemas FIA y miniaturizados de análisis integrados.3. Modificación de superficies sólidas con biomoléculas para el desarrollo y optimización de superficies de bio-reconocimiento:3.1 Evaluar el comportamiento de superficies de titanio modificadas con TiO2 y depósitos inorgánicos frente a la interacción con proteínas plasmáticas (PP) para el análisis de la biocompatibilidad superficial.3.2 Diseñar y desarrollar superficies biofuncionales para el reconocimiento especifico de D-aminoácidos, anticuerpos en pacientes chagásicos y simple hebra de ADN. Las técnicas que se emplearán para llevar a cabo el proyecto dependen del tipo de sistema de estudio. En particular los estudios correspondientes al objetivo 1 se realizarán mediante análisis químicos, térmico, DXR, SEM, IR, BET así como mediante titulaciones ácido-base potenciométricas, movilidades electroforéticas, cinética e isotermas de adsorción.En general para desarrollar el objetivo 2 se utilizarán técnicas electroquímicas clásicas para la caracterización de los electrodos, los que luego se utilizarán como detectores en un sistema FIA amperométrico, mientras que los microchips se emplearán en electroforesis capilar para la separación de diferentes compuestos de interés farmacéutico.Finalmente, el objetivo 3 se llevará a cabo por un lado modificando electrodos de titanio con distintos depósitos (electroquímicas, sol-gel, térmicas) de TiO2 e hidroxiapatita y evaluando la interacción con proteínas plasmáticas para analizar la biocompatibilidad de los materiales preparados. Por otro lado, se estudiará el proceso de adsorción-desorción de D-aminoácido oxidasa, antígenos del T. Cruzi y ADN de simple hebra para optmizar la capacidad de bio-reconocimiento superficial de D-aminoácidos, anticuerpos de chagásicos y de cadena complementaria de ADN. Para concretar este objetivo se utilizarán técnicas electroquímicas, espectroscópicas y microscopias.Debido al carácter multidisciplinario del presente proyecto de investigación, su ejecución se llevara a cabo a través de la colaboración de investigadores pertenecientes a distintas áreas de la Química y permitirá continuar con la formación de recursos humanos mediante la realización de tesis doctorales y estadías postdoctorales.

Random graphs on surfaces

Counting labelled planar graphs, and typical properties of random labelled planar graphs, have received much attention recently. We start the process here of extending these investigations to graphs embeddable on any fixed surface S. In particular we show that the labelled graphs embeddable on S have the same growth constant as for planar graphs, and the same holds for unlabelled graphs. Also, if we pick a graph uniformly at random from the graphs embeddable on S which have vertex set {1, . . . , n}, then with probability tending to 1 as n → ∞, this random graph either is connected or consists of one giant component together with a few nodes in small planar components.

Dynamic estimation of three-dimensional cerebrovascular deformation from rotational angiography

Purpose: The objective of this study is to investigate the feasibility of detecting and quantifying 3D cerebrovascular wall motion from a single 3D rotational x-ray angiography (3DRA) acquisition within a clinically acceptable time and computing from the estimated motion field for the further biomechanical modeling of the cerebrovascular wall. Methods: The whole motion cycle of the cerebral vasculature is modeled using a 4D B-spline transformation, which is estimated from a 4D to 2D + t image registration framework. The registration is performed by optimizing a single similarity metric between the entire 2D + t measured projection sequence and the corresponding forward projections of the deformed volume at their exact time instants. The joint use of two acceleration strategies, together with their implementation on graphics processing units, is also proposed so as to reach computation times close to clinical requirements. For further characterizing vessel wall properties, an approximation of the wall thickness changes is obtained through a strain calculation. Results: Evaluation on in silico and in vitro pulsating phantom aneurysms demonstrated an accurate estimation of wall motion curves. In general, the error was below 10% of the maximum pulsation, even in the situation when substantial inhomogeneous intensity pattern was present. Experiments on in vivo data provided realistic aneurysm and vessel wall motion estimates, whereas in regions where motion was neither visible nor anatomically possible, no motion was detected. The use of the acceleration strategies enabled completing the estimation process for one entire cycle in 5-10 min without degrading the overall performance. The strain map extracted from our motion estimation provided a realistic deformation measure of the vessel wall. Conclusions: The authors' technique has demonstrated that it can provide accurate and robust 4D estimates of cerebrovascular wall motion within a clinically acceptable time, although it has to be applied to a larger patient population prior to possible wide application to routine endovascular procedures. In particular, for the first time, this feasibility study has shown that in vivo cerebrovascular motion can be obtained intraprocedurally from a 3DRA acquisition. Results have also shown the potential of performing strain analysis using this imaging modality, thus making possible for the future modeling of biomechanical properties of the vascular wall.

Model for the emission of Si+ ions during oxygen bombardment of Si(100) surfaces

The variation in the emission of Si+ ions from ion-beam-induced oxidized silicon surfaces has been studied. The stoichiometry and the electronic structure of the altered layer has been characterized using x-ray photoelectron spectroscopy (XPS). The XPS analysis of the Si 2p core level indicates the strong presence of suboxide chemical states when bombarding at angles of incidence larger than 30 °. Since the surface stoichiometry or degree of oxidation varies with the angle of incidence, the corresponding valence-band structures also differ among each other. A comparison between experimental measurements and theoretically calculated Si and SiO2 valence bands indicates that the valence bands for the altered layers are formed by a combination of those two. Since Si-Si bonds are present in the suboxide molecules, the top of the respective new valence bands are formed by the corresponding 3p-3p Si-like subbands, which extend up to the Si Fermi level. The changes in stoichiometry and electronic structure have been correlated with the emission of Si+ ions from these surfaces. From the results a general model for the Si+ ion emission is proposed combining the resonant tunneling and local-bond-breaking models.

Thin Maintenance Surfaces for Municipalities, TR-507, 2007

As streets age, officials must deal with rehabilitating and reconstructing these pavements to maintain a safe and comfortable ride. In light of nationwide budget shortfalls, cost-effective methods of extending pavement service life must be developed or the overall condition of street systems will continue to fall. Thin maintenance surfaces (TMSs) are a set of cost-effective preventive maintenance surfacing techniques that can be used to extend the life of bituminous pavement—pavement built with hot mix asphalt, hot mix asphalt overlays of portland cement concrete pavements, built-up seal coat (chip seal), stabilized materials, or a combination of these. While previous phases of TMS research have provided information about the uses of thin maintenance surfaces in rural settings, urban areas have different road maintenance challenges that should be considered separately. This research provides city street officials with suggestions for TMS techniques that street departments can easily test and include into their current programs. This research project facilitated the construction of TMS test sections in Cedar Rapids, Council Bluffs, and West Des Moines (all urban settings in Iowa). Test section sites and surfaces were selected to suit the needs of municipalities and were applied to roads with an array of various distresses and maintenance needs. Condition surveys of each test section were performed before construction, after construction, and after the first winter to record the amount and severity of existing distress and calculate the pavement condition index. Because conditions of the test sections varied greatly, determining which surface was most successful by comparing case studies was not feasible. However, some general conclusions can be made from this research. TMSs are suitable preventive maintenance techniques for a municipal street department’s program for preserving existing pavements. Careful attention should be paid to proper planning, quality control during construction, aggregate and binder selection, and aggregate embedment in order to support successful TMS application.