Eddy Structures Induced Within a Wedge by a Honing Circular Arc

In this paper we outline an expeditious numerical procedure to calculate the Stokes flow in a corner due to the rotation of a scraping circular boundary. The method is also applicable to other wedge geometries. We employ a collocation technique utilising a basis of eddy (similarity) functions introduced by Moffatt (1964) that allows us to satisfy automatically the governing equations for the streamfunction and all the boundary conditions on the surface of the wedge. The circular honing problem thereby becomes one-dimensional requiring only the satisfaction of conditions on the circular boundary. The advantage of using the Moffatt eddy functions as a basis in wedge geometry is clear and the technique greatly reduces many of the concerns with accuracy and time expenditure associated with alternative numerical methods. An investigation of the details of the eddy structure for our particular geometry is presented

On Intersection Graphs of Arcs and Chords in a Circle

Circular-arc graphs are the intersection graphs of arcs on a circle. We review in this thesis the main results known about this class and we analize some subclasses of it. We show new characterizations for proper circular-arc graphs derived from a characterization formulated by Tucker, and we deduce minimal forbidden structures for circular arc-graphs.All possible intersections of the defined subclasses are studied, showing a minimal example in each one of the generated regions, except one of them that we prove it is empty. From here, we conclude that a clique-Helly and proper no unit circular-arc graph must be Hellycircular-arc graph.Circle graphs are the intersection graphs of chords in a circle. We present also a review of the main results in this class and define the most important subclasses, proving some relations of inclusions between them.We prove a neccesary condition so that a graph is a Helly circle graph and conjecture thatthis condition is sufficient too. If this conjecture becomes true, we would have acharacterization and a polynomial recognition for this subclass.Minimal forbidden structures for circle graphs are shown, using the chacterization of propercircular-arc graphs by Tucker and a characterization theorem for circle graphs by Bouchet.We also analize all the possible intersections between the defined subclasses of circlegraphs, showing a minimal example in each generated region.A superclass of circle graphs is studied: overlap graphs of circular-arc graphs. We show new properties on this class, analizing its relation with circle and circular-arc graphs. A necessary condition for a graph being an overlap graph of circular-arc graphs is shown. We prove that the problem of finding a minimum clique partition for the class of graphs which does not contain either odd holes, or a 3-fan, or a 4-wheel as induced subgraphs, can be solved in polynomial time. We use in the proof results of polyhedral theory for integer linear programming. We extend this result for minimum clique covering by vertices. These results are applied for Helly circle graphs without odd holes. We also show that the problem of minimum clique covering by vertices can be solved in polynomial time for Helly circular-arc graphs. Finally, we present some interesting problems which remain open.Sociedad Argentina de Informática e Investigación Operativ

Effect of transient heating on vibration frequencies of some simple wing structures

Thermal stresses, which may result from transient heating, can cause changes in the effective stiffness of wing structures. Some effects of this change in stiffness were investigated experimentally by radiantly heating three types of simple wing structures: a uniform plate, a solid double-wedge section, and a circular-arc multiweb-wing section. Changes in stiffness were determined by measuring the changes in natural frequency of vibration during transient heating. Some comparisons are made between theoretical calculations and the measured data

Efficient techniques for scattering from planar and cylindrical structures with edges

In this work, we present rigorous and efficient methods for analyzing scattering from the following structures • Tandem Slit loaded with homogeneous material • Eccentrically loaded cylinder with multiple slits • Semicircular cylinder and slit • Dielectric loaded Wedge shaped cylinder • Circular cylinder with resonant cavities and resonant cavities on circular arc. For analyzing the material loaded tandem slit configuration, the boundary value problem is formulated into a pair of simultaneous Wiener-Hopf equations via Fourier transformation. After decoupling these equations by elementary transformation, each modified Wiener-Hopf equation is reduced to a Fredholm integral equation of the second kind. The integral equations are then solved approximately to yield the Fourier transform of the diffracted fields. The inverse transform is evaluated asymptotically to obtain the far field expressions. Measurements and numerical simulations are also performed for several different geometric and material configurations. The analytic solutions compare well with measured and simulated results. The possibility of reducing beamwidth and increasing power coupled through the loaded tandem slit is explored. The analysis of the eccentrically loaded cylindrical cavity with multiple slits under plane wave illumination is formulated using two distinct approaches: (1) an integral equation/combined boundary condition (IE/CBC) formulation and (2) an integral equation/Neumann series expansion (IE/NS) formulation. The IE/NS formulation is shown to converge faster than the IE/CBC formulation based on the proper edge behavior exhibited by the Neumann series current expansion functions. Results for the backscattered radar cross section (RCS) of several geometries are presented, and the relationships between the RCS and the scatterer characteristics are explored. The applicability of the Neumann series method to find a fast method for evaluating scattering from a metallic strip and semicircular cylinder is presented. The Neumann series of different periodicity is used for studying scattering from wedge shaped cylinder. The Neumann series is also applied to study scattering from a circular cylinder with resonant cavities and resonant cavities on a circular arc. These resonant cavities on a circular arc have superdirective properties, which are useful for high gain antenna design

Fluid Models for Kinetic Effects on Coherent Nonlinear Alfven Waves. II. Numerical Solutions

The influence of various kinetic effects (e.g. Landau damping, diffusive and collisional dissipation, and finite Larmor radius terms) on the nonlinear evolution of finite amplitude Alfvenic wave trains in a finite-beta environment is systematically investigated using a novel, kinetic nonlinear Schrodinger (KNLS) equation. The dynamics of Alfven waves is sensitive to the sense of polarization as well as the angle of propagation with respect to the ambient magnetic field. Numerical solution for the case with Landau damping reveals the formation of dissipative structures, which are quasi-stationary, S-polarized directional (and rotational) discontinuities which self-organize from parallel propagating, linearly polarized waves. Parallel propagating circularly polarized packets evolve to a few circularly polarized Alfven harmonics on large scales. Stationary arc-polarized rotational discontinuities form from obliquely propagating waves. Collisional dissipation, even if weak, introduces enhanced wave damping when beta is very close to unity. Cyclotron motion effects on resonant particle interactions introduce cyclotron resonance into the nonlinear Alfven wave dynamics.Comment: 38 pages (including 23 figures and 1 table

The super-n-motifs model : a novel alignment-free approach for representing and comparing RNA secondary structures

Abstract : Motivation: Comparing ribonucleic acid (RNA) secondary structures of arbitrary size uncovers structural patterns that can provide a better understanding of RNA functions. However, performing fast and accurate secondary structure comparisons is challenging when we take into account the RNA configuration (i.e. linear or circular), the presence of pseudoknot and G-quadruplex (G4) motifs and the increasing number of secondary structures generated by high-throughput probing techniques. To address this challenge, we propose the super-n-motifs model based on a latent analysis of enhanced motifs comprising not only basic motifs but also adjacency relations. The super-n-motifs model computes a vector representation of secondary structures as linear combinations of these motifs. Results: We demonstrate the accuracy of our model for comparison of secondary structures from linear and circular RNA while also considering pseudoknot and G4 motifs. We show that the supern- motifs representation effectively captures the most important structural features of secondary structures, as compared to other representations such as ordered tree, arc-annotated and string representations. Finally, we demonstrate the time efficiency of our model, which is alignment free and capable of performing large-scale comparisons of 10 000 secondary structures with an efficiency up to 4 orders of magnitude faster than existing approaches

The Morphology of IRC +10420's Circumstellar Ejecta

Images of the circumstellar ejecta associated with the post-red supergiant IRC +10420 show a complex ejecta with visual evidence for episodic mass loss. In this paper we describe the transverse motions of numerous knots, arcs and condensations in the inner ejecta measured from second epoch {\it HST/WFPC2} images. When combined with the radial motions for several of the features, the total space motion and direction of the outflows show that they were ejected at different times, in different directions, and presumably from separate regions on the surface of the star. These discrete structures in the ejecta are kinematically distinct from the general expansion of the nebula and their motions are dominated by their transverse velocities. They are apparently all moving within a few degrees of the plane of the sky. We are thus viewing IRC +10420 nearly pole-on and looking nearly directly down onto its equatorial plane. We also discuss the role of surface activity and magnetic fields on IRC +10420's recent mass loss history.Comment: 16 pages, 6 figure