Matrix algebra applied to the calculation of fifth-order aberrations in optical systems.

Thesis (M.A.)--Boston UniversityThis paper is an extension of the work originally done by Dr. Willem Brouwer for his doctoral thesis at Delft University, Delft, Holland. He took the relationships governing:(l) the direction of a light ray before and after refraction at a surface; (2) the coordinates, with respect to the axis, of this light ray at two successive surfaces of an optical system; and set them into matrix form. He was then able to produce a matrix for one surface to obtain image plane coordinates from those in the object plane, when given an initial ray direction, by multiplying in proper syquence two translation and one refraction matrices. He also constructed another objeqt to image matrix which used paraxial magnifications from an object and reference plane, plus unknown coefficients for the higher powers of these two object plane coordinates (i.e. a general series expansion). He modified this basic matrix with another, and its inverse, which contained only powers of the paraxial magnifications. The modification allowed a series of the basic matrices to be multiplied (combining surfaces for a lens system) while causing the coefficients to be only additive for the third-order terms. The conclusions indicate that even preliminary study of the final expression for fifth-order spherical aberration showed that useful information could be derived from examining it in the final form presented

Anisotropic character of talc surfaces as revealed by streaming potential measurements, atomic force microscopy, molecular dynamics simulations and contact angle measurements

Journal ArticleA study of the interfacial properties of the basal plane and the edge surfaces of talc is described in this paper. The isoelectric points measured at two different crystallographic surfaces by the streaming potential method were found to be similar and exist at about pH 3.0. In the case of the edge surface, the zeta potential increases at higher pH values which can be attributed to the hydration of surface magnesium ions. The forces between the edge of a 20 urn talc particle and the two different crystallographic surfaces of talc were measured at various pH values using atomic force microscopy (AFM). These measurements show differences between the properties of the basal plane and edge of the talc. Finally, the differences in the hydration of the basal plane and the edge of talc are revealed from molecular dynamics (MD) simulations. The basal plane of talc is much less hydrated than the edge as can be seen from the water density distribution functions which correlate quite well with the contact angle measurements at the basal plane surface and the edge surface. Improved quality of the edge surface was achieved by sandblasting (erosion with alumina) and research regarding the characteristics of this edge surface is in progress

Growth and dislocation studies of β-HMX

Background: The defect structure of organic materials is important as it plays a major role in their crystal growth properties. It also can play a subcritical role in “hot-spot” detonation processes of energetics and one such energetic is cyclotetramethylene-tetranitramine, in the commonly used beta form (β-HMX). Results: The as-grown crystals grown by evaporation from acetone show prismatic, tabular and columnar habits, all with {011}, {110}, (010) and (101) faces. Etching on (010) surfaces revealed three different types of etch pits, two of which could be identified with either pure screw or pure edge dislocations, the third is shown to be an artifact of the twinning process that this material undergoes. Examination of the {011} and {110} surfaces show only one type of etch pit on each surface; however their natural asymmetry precludes the easy identification of their Burgers vector or dislocation type. Etching of cleaved {011} surfaces demonstrates that the etch pits can be associated with line dislocations. All dislocations appear randomly on the crystal surfaces and do not form alignments characteristic of mechanical deformation by dislocation slip. Conclusions: Crystals of β-HMX grown from acetone show good morphological agreement with that predicted by modelling, with three distinct crystal habits observed depending upon the supersaturation of the growth solution. Prismatic habit was favoured at low supersaturation, while tabular and columnar crystals were predominant at higher super saturations. The twin plane in β-HMX was identified as a (101) reflection plane. The low plasticity of β-HMX is shown by the lack of etch pit alignments corresponding to mechanically induced dislocation arrays. On untwinned {010} faces, two types of dislocations exist, pure edge dislocations with b = [010] and pure screw dislocations with b = [010]. On twinned (010) faces, a third dislocation type exists and it is proposed that these pits are associated with pure screw dislocations with b = [010]

Wetting and contact-line effects for spherical and cylindrical droplets on graphene layers: A comparative molecular-dynamics investigation

In Molecular Dynamics (MD) simulations, interactions between water molecules and graphitic surfaces are often modeled as a simple Lennard-Jones potential between oxygen and carbon atoms. A possible method for tuning this parameter consists of simulating a water nanodroplet on a flat graphitic surface, measuring the equilibrium contact angle, extrapolating it to the limit of a macroscopic droplet and finally matching this quantity to experimental results. Considering recent evidence demonstrating that the contact angle of water on a graphitic plane is much higher than what was previously reported, we estimate the oxygen-carbon interaction for the recent SPC/Fwwater model. Results indicate a value of about 0.2 kJ/mol, much lower than previous estimations. We then perform simulations of cylindrical water filaments on graphitic surfaces, in order to compare and correlate contact angles resulting from these two different systems. Results suggest that modified Young's equation does not describe the relation between contact angle and drop size in the case of extremely small systems and that contributions different from the one deriving from contact line tension should be taken into account.Comment: To be published on Physical Review E (http://pre.aps.org/

Collision of vortex-rings upon V-walls

A study on and 4000 vortex rings colliding with V-walls with included angles of to 120 has been conducted. Along the valley plane, higher Reynolds numbers and/or included angles of lead to secondary/tertiary vortex-ring cores leapfrogging past the primary vortex-ring cores. The boundary layers upstream of the latter separate and the secondary/tertiary vortex-ring cores pair up with these wall-separated vortices to form small daisy-chained vortex dipoles. Along the orthogonal plane, primary vortex-ring cores grow bulbous and incoherent after collisions, especially as the included angle reduces. Secondary and tertiary vortex-ring core formations along this plane also lag those along the valley plane, indicating that they form by propagating from the wall surfaces to the orthogonal plane as the primary vortex ring gradually comes into contact with the entire V-wall. Circulation results show significant variations between the valley and orthogonal plane, and reinforce the notion that the collision behaviour for is distinctively different from those at larger included angles. Vortex-core trajectories are compared to those for inclined-wall collisions, and secondary vortex-ring cores are found to initiate earlier for the V-walls, postulated to be a result of the opposing circumferential flows caused by the simultaneous collisions of both primary vortex-ring cores with the V-wall surfaces. These circumferential flows produce a bi-helical flow mode (Lim, Exp. Fluids, vol. 7, issue 7, 1989, pp. 453-463) that sees higher vortex compression levels along the orthogonal plane, which limit vortex stretching along the wall surfaces and produce secondary vortex rings earlier. Lastly, vortex structures and behaviour of the present collisions are compared to those associated with flat/inclined walls and round-cylinder-based collisions for a more systematic understanding of their differences.Ministry of Education (MOE)The authors acknowledge the support for the study by the School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore, Singapore Ministry of Education AcRF Tier-2 grant (MOE2014-T2-1-002) and National Science Foundation of China grant (grant number: 11772197)

Topology of quasiperiodic functions on the plane

The article describes a topological theory of quasiperiodic functions on the plane. The development of this theory was started (in different terminology) by the Moscow topology group in early 1980s. It was motivated by the needs of solid state physics, as a partial (nongeneric) case of Hamiltonian foliations of Fermi surfaces with multivalued Hamiltonian function. The unexpected discoveries of their topological properties that were made in 1980s and 1990s have finally led to nontrivial physical conclusions along the lines of the so-called geometric strong magnetic field limit. A very fruitful new point of view comes from the reformulation of that problem in terms of quasiperiodic functions and an extension to higher dimensions made in 1999. One may say that, for single crystal normal metals put in a magnetic field, the semiclassical trajectories of electrons in the space of quasimomenta are exactly the level lines of the quasiperiodic function with three quasiperiods that is the dispersion relation restricted to a plane orthogonal to the magnetic field. General studies of the topological properties of levels of quasiperiodic functions on the plane with any number of quasiperiods were started in 1999 when certain ideas were formulated for the case of four quasiperiods. The last section of this work contains a complete proof of these results. Some new physical applications of the general problem were found recently.Comment: latex2e, 27 pages, 7 figure