Development and Implementation of NURBS Models of Quadratic Curves and Surfaces

This article goes into the development of NURBS models of quadratic curves and surfaces. Curves and surfaces which could be represented by one general equation (one for the curves and one for the surfaces) are addressed. The research examines the curves: ellipse, parabola and hyperbola, the surfaces: ellipsoid, paraboloid, hyperboloid, double hyperboloid, hyperbolic paraboloid and cone, and the cylinders: elliptic, parabolic and hyperbolic. Many real objects which have to be modeled in 3D applications possess specific features. Because of this these geometric objects have been chosen. Using the NURBS models presented here, specialized software modules (plug-ins) have been developed for a 3D graphic system. An analysis of their implementation and the primitives they create has been performed.

Projectively Normal Line Bundles on K-Gonal Curves and Rational Surfaces

2000 Mathematics Subject Classification: 14H50.

Fibrillar Elastomeric Micropatterns Create Tunable Adhesion Even to Rough Surfaces

Acknowledgements V.B., N.K.G., and E.A. contributed with conception and experimental design. V.B. performed the experiments. V.B., R.H., A.G., and R.M.M. carried out analysis and interpretation of data. V.B., R.H., A.G., and E.A. wrote the manuscript. V.B. and R.H. contributed equally to this work. V.B. acknowledges funding by SPP 1420 of the German Science Foundation DFG. E.A., N.K.G., and R.H. acknowledge funding from the European Research Council under the European Union/ERC Advanced Grant “Switch2Stick,” Agreement No. 340929.

The Rotational Evolution and Magnetospheric Emission of the Magnetic Early B-type Stars

How do the magnetic fields of massive stars evolve over time? Are their gyrochronological ages consistent with ages inferred from evolutionary tracks? Why do most stars predicted to host Centrifugal Magnetospheres (CMs) display no H$\alpha$ emission? Does plasma escape from CMs via centrifugal breakout events, or by a steady-state leakage mechanism? This thesis investigates these questions via a population study with a sample of 51 magnetic early B-type stars. The longitudinal magnetic field \bz~was measured from Least Squares Deconvolution profiles extracted from high-resolution spectropolarimetric data. New rotational periods $P_{\rm rot}$ were determined for 15 stars from \bz, leaving only 3 stars for which $P_{\rm rot}$ is unknown. Projected rotational velocities \vsini~were measured from multiple spectral lines. Effective temperatures and surface gravities were measured via ionization balances and line profile fitting of H Balmer lines. Fundamental physical parameters, \bz, \vsini, and $P_{\rm rot}$ were then used to determine radii, masses, ages, dipole oblique rotator model, stellar wind, magnetospheric, and spindown parameters using a Monte Carlo approach that self-consistently calculates all parameters while accounting for all available constraints on stellar properties. Dipole magnetic field strengths $B_{\rm d}$ follow a log-normal distribution similar to that of Ap stars, and decline over time in a fashion consistent with the expected conservation of fossil magnetic flux. $P_{\rm rot}$ increases with fractional main sequence age, mass, and $B_{\rm d}$, as expected from magnetospheric braking. However, comparison of evolutionary track ages to maximum spindown ages $t_{\rm S,max}$ shows that initial rotation fractions may be far below critical for stars with $M_*>10 M_\odot$. Computing $t_{\rm S,max}$ with different mass-loss prescriptions indicates that the mass-loss rates of B-type stars are likely much lower than expected from extrapolation from O-type stars. Stars with H$\alpha$ in emission and absorption occupy distinct regions in the updated rotation-magnetic confinement diagram: H$\alpha$-bright stars are found to be younger, more rapidly rotating, and more strongly magnetized than the general population. Emission strength is sensitive both to the volume of the CM and to the mass-loss rate, favouring leakage over centrifugal breakout.

Internal cooling in rotational molding-A review

Rotational molding suffers from a relatively long cycle time, which hampers more widespread growth of the process. During each cycle, both the polymer and mold must be heated from room temperature to above polymer melting temperature and subsequently cooled to room temperature. The cooling time in this process is relatively long due to the poor thermal conductivity of plastics. Although rapid external cooling is possible, internal cooling rates are the major limitation. This causes the process to be uneconomical for large production runs of small parts. Various researchers have strived to minimize cycle times by applying various internal cooling procedures. This article presents a review of these methods, including computer simulations and practical investigations published to date. The effects of cooling rate on the morphology, shrinkage, warpage, and impact properties of rotationally molded polyolefins are also highlighted. In general, rapid and symmetrical cooling across the mold results in smaller spherulite size, increased mechanical properties and less potential warpage or distortion in moldings. POLYM. ENG. SCI., 2011. ©2011 Society of Plastics Engineers.

Geometric properties of 2-dimensional minimal surfaces in a sub-Riemannian manifold which models the Visual Cortex

In this paper we study the notion of degree forsubmanifolds embedded in an equiregular sub-Riemannian manifold and we provide the definition of their associated area functional. In this setting we prove that the Hausdorff dimension of a submanifold coincides with its degree, as stated by Gromov. Using these general definitions we compute the first variation for surfaces embedded in low dimensional manifolds and we obtain the partial differential equation associated to minimal surfaces. These minimal surfaces have several applications in the neurogeometry of the visual cortex.

Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities

In this paper we consider instabilities of localised solutions in planar neural field firing rate models of Wilson-Cowan or Amari type. Importantly we show that angular perturbations can destabilise spatially localised solutions. For a scalar model with Heaviside firing rate function we calculate symmetric one-bump and ring solutions explicitly and use an Evans function approach to predict the point of instability and the shapes of the dominant growing modes. Our predictions are shown to be in excellent agreement with direct numerical simulations. Moreover, beyond the instability our simulations demonstrate the emergence of multi-bump and labyrinthine patterns. With the addition of spike-frequency adaptation, numerical simulations of the resulting vector model show that it is possible for structures without rotational symmetry, and in particular multi-bumps, to undergo an instability to a rotating wave. We use a general argument, valid for smooth firing rate functions, to establish the conditions necessary to generate such a rotational instability. Numerical continuation of the rotating wave is used to quantify the emergent angular velocity as a bifurcation parameter is varied. Wave stability is found via the numerical evaluation of an associated eigenvalue problem.

Automorphism groups of non-orientable elliptic-hyperelliptic Klein surfaces with boundary

A classical study about Klein and Riemann surfaces consists in determining their groups of automorphisms. This problem is very difficult in general,and it has been solved for particular families of surfaces or for fixed topological types. In this paper, we calculate the automorphism groups of non-orientable bordered elliptic-hyperelliptic Klein surfaces of algebraic genus p> 5.

Multiscale Modeling and Simulation of Stepped Crystal Surfaces

A primary goal of this dissertation is to understand the links between mathematical models that describe crystal surfaces at three fundamental length scales: The scale of individual atoms, the scale of collections of atoms forming crystal defects, and macroscopic scale. Characterizing connections between different classes of models is a critical task for gaining insight into the physics they describe, a long-standing objective in applied analysis, and also highly relevant in engineering applications. The key concept I use in each problem addressed in this thesis is coarse graining, which is a strategy for connecting fine representations or models with coarser representations. Often this idea is invoked to reduce a large discrete system to an appropriate continuum description, e.g. individual particles are represented by a continuous density. While there is no general theory of coarse graining, one closely related mathematical approach is asymptotic analysis, i.e. the description of limiting behavior as some parameter becomes very large or very small. In the case of crystalline solids, it is natural to consider cases where the number of particles is large or where the lattice spacing is small. Limits such as these often make explicit the nature of links between models capturing different scales, and, once established, provide a means of improving our understanding, or the models themselves. Finding appropriate variables whose limits illustrate the important connections between models is no easy task, however. This is one area where computer simulation is extremely helpful, as it allows us to see the results of complex dynamics and gather clues regarding the roles of different physical quantities. On the other hand, connections between models enable the development of novel multiscale computational schemes, so understanding can assist computation and vice versa. Some of these ideas are demonstrated in this thesis. The important outcomes of this thesis include: (1) a systematic derivation of the step-flow model of Burton, Cabrera, and Frank, with corrections, from an atomistic solid-on-solid-type models in 1+1 dimensions; (2) the inclusion of an atomistically motivated transport mechanism in an island dynamics model allowing for a more detailed account of mound evolution; and (3) the development of a hybrid discrete-continuum scheme for simulating the relaxation of a faceted crystal mound. Central to all of these modeling and simulation efforts is the presence of steps composed of individual layers of atoms on vicinal crystal surfaces. Consequently, a recurring theme in this research is the observation that mesoscale defects play a crucial role in crystal morphological evolution.

Rotational and ro-vibrational spectroscopy of small nitrogen-containing species and their astrophysical applications

This thesis presents the study of small nitrogen-bearing molecules, from diatomic radicals to complex organic molecules, by means of rotational and ro-vibrational spectroscopy. Besides their theoretical relevance, which spans from anharmonic force field analyses to energetic and structural properties, I have chosen this family of species because of their astrochemical importance. After some basic knowledge of molecular spectroscopy and astrochemistry is introduced, the instrumentation used during the course of my PhD school is described. Then, the most relevant studies I conducted during the last three years are presented. Generally speaking, a number of molecules of astrophysical relevance have been characterized by means of rotational and ro-vibrational spectroscopy. The sample of studied species is constituted by small radicals (imidogen, amidogen, and titanium nitride), cyanopolyynes (cyanoacetylene) and pre-biotic molecules (aminoacetonitrile): these studies are presented in great detail. Among the results, the first astronomical detection of two deuterated radicals (NHD and ND2) is presented in this thesis.Thanks to our studies, it was possible to clearly identify molecular absorptions of these species towards the pre-stellar core IRAS16293-2422, as recorded by the Herschel Space Observatory mission. These observations confirm the strong deuterium enhancement generally observed in this cloud but they reveal that models underestimate the abundances of NHD and ND2. I also report the detection of vibrationally excited aminoacetonitrile (NH2CH2CN) in Sagittarius B2, as observed in the ReMoCa survey. This is the second detection of aminoacetonitrile in the interstellar medium and the first astronomical observation of its vibrationally hot lines. This represents a small step toward the comprehension on how complex organic molecules are formed and which processes can lead to the formation of glycine. Finally, few general remarks are discussed and the importance of future laboratory studies is pointed out, along with possible perspectives.

Excited state energy surfaces of flexible emitters for thermally activated delayed fluorescence

Organic Light-Emitting Diodes (OLEDs) technology has matured over recent years, reaching the commercialization level and being used in various applications. The required efficiency can be achieved by transforming triplet excitons into singlet states via Reverse InterSystem Crossing (RISC), which a general mechanism called thermally activated delayed fluorescence (TADF). Two prototypical molecules in the field, 2CzBN and 4CzBN, Carbazole Benzonitrile (donor-acceptor) derivatives, possess similar energy gap between singlet and triplet (∆EST, a key parameter in the RISC rate), but different TADF performance. In this sense, other parameter must be considered to explain these different behaviors. In this work, we theoretically investigate 2CzBN and 4CzBN and address the problem of how flexible donor-acceptor (D-A) or donor-acceptor-donor (D-A-D) molecular architectures affect the nature of excited state, and the oscillator strength. Furthermore, we analyze the RISC rates as a function of the conformation of the carbazole side groups, considering the S0, S1, T1 and T2 states. The oscillator strength of 4CzBN is higher than of 2CzBN, which, in turn, is almost vanishing, resulting in only 4CzBN being a TADF active molecule. We also note the presence of a second triplet state T2 lower in energy than S1, and that the reorganization energies, associated to the RISC processes involving T1 and T2, are both important factor in differentiating the rates in 2CzBN and 4CzBN. However, the 4CzBN RISC rate from T2 to S1 is surprisingly high with respect to the one from T1 to S1, although, according to EL-Sayed rules, since T2 (CT/LE) is more similar to S1 (CT) than in 2CzBN (LE, CT), this transition should be less favored. These insights are important to understand the photophysics of the TADF process and to design novel TADF emitters based on the benzo-carbazole architecture.

Study of the rotational state of Titan using radio tracking data of the Dragonfly mission

Our solar system contains an impressive amount of celestial bodies. For example Saturn posses a huge variety of natural satellites, the diversity in size and physical proprieties of which might amaze imagination. The observational data gathered in 30 years range of deep space missions revealed, that some of these bodies can hide subsurface oceans under their crust. The water, as we know, serves as a fundamental base for a possible appearance of life. This statement is quite exited for the scientific society and serves as a reason for studying so called ”ocean worlds”. In order to detect the celestial bodies with the hidden subsurface ocean, one of the key aspects is the study of their rotational state, which is strongly coupled with the body internal structure. It can be done through the various techniques mentioned in Chapter 1. The main goal of the thesis is the study of rotational state of Titan, whose interior structure expectedly contains liquid ocean layer under its icy crust. Titan is the largest moon of Saturn and it is the second largest moon in the solar system in general. This natural satellite is of particular scientific interest, because it is one of a kind which has substantial atmosphere. The present work was done using radio tracking data of the Dragonfly mission which is one of the next NASA’s missions destined for Titan selected as a part of the New Frontiers Program in 2019. The detailed characteristic of the Dragonfly regarding the landing site and mission lifetime was reported in Chapter 2. The radio-tracking communication link from Titan side was performed using Dragonfly X band transponder according to the schedule tracking opportunity. From Earth side according to the mission, Deep Space Station 25 which is a part of NASA’s Deep Space Network was considered. Only Doppler data was used for studying Titan rotational state, even though there are other reliable techniques described in Chapter 3, that in general could be implemented.

Electronic And Structural Study Of Pt-modified Au Vicinal Surfaces: A Model System For Pt-au Catalysts.

Two single crystalline surfaces of Au vicinal to the (111) plane were modified with Pt and studied using scanning tunneling microscopy (STM) and X-ray photoemission spectroscopy (XPS) in ultra-high vacuum environment. The vicinal surfaces studied are Au(332) and Au(887) and different Pt coverage (θPt) were deposited on each surface. From STM images we determine that Pt deposits on both surfaces as nanoislands with heights ranging from 1 ML to 3 ML depending on θPt. On both surfaces the early growth of Pt ad-islands occurs at the lower part of the step edge, with Pt ad-atoms being incorporated into the steps in some cases. XPS results indicate that partial alloying of Pt occurs at the interface at room temperature and at all coverage, as suggested by the negative chemical shift of Pt 4f core line, indicating an upward shift of the d-band center of the alloyed Pt. Also, the existence of a segregated Pt phase especially at higher coverage is detected by XPS. Sample annealing indicates that the temperature rise promotes a further incorporation of Pt atoms into the Au substrate as supported by STM and XPS results. Additionally, the catalytic activity of different PtAu systems reported in the literature for some electrochemical reactions is discussed considering our findings.

Triboelectricity In Insulating Polymers: Evidence For A Mechanochemical Mechanism.

Transfer of reaction products formed on the surfaces of two mutually rubbed dielectric solids makes an important if not dominating contribution to triboelectricity. New evidence in support of this statement is presented in this report, based on analytical electron microscopy coupled to electrostatic potential mapping techniques. Mechanical action on contacting surface asperities transforms them into hot-spots for free-radical formation, followed by electron transfer producing cationic and anionic polymer fragments, according to their electronegativity. Polymer ions accumulate creating domains with excess charge because they are formed at fracture surfaces of pulled-out asperities. Another factor for charge segregation is the low polymer mixing entropy, following Flory and Huggins. The formation of fractal charge patterns that was previously described is thus the result of polymer fragment fractal scatter on both contacting surfaces. The present results contribute to the explanation of the centuries-old difficulties for understanding the triboelectric series and triboelectricity in general, as well as the dissipative nature of friction, and they may lead to better control of friction and its consequences.

Analysis Of The Fluorescence Of Body Fluids On Different Surfaces And Times.

The use of screening techniques, such as an alternative light source (ALS), is important for finding biological evidence at a crime scene. The objective of this study was to evaluate whether biological fluid (blood, semen, saliva, and urine) deposited on different surfaces changes as a function of the age of the sample. Stains were illuminated with a Megamaxx™ ALS System and photographed with a Canon EOS Utility™ camera. Adobe Photoshop™ was utilized to prepare photographs for analysis, and then ImageJ™ was used to record the brightness values of pixels in the images. Data were submitted to analysis of variance using a generalized linear mixed model with two fixed effects (surface and fluid). Time was treated as a random effect (through repeated measures) with a first-order autoregressive covariance structure. Means of significant effects were compared by the Tukey test. The fluorescence of the analyzed biological material varied depending on the age of the sample. Fluorescence was lower when the samples were moist. Fluorescence remained constant when the sample was dry, up to the maximum period analyzed (60 days), independent of the substrate on which the fluid was deposited, showing the novelty of this study. Therefore, the forensic expert can detect biological fluids at the crime scene using an ALS even several days after a crime has occurred.