Multifacet holographic optical elements

New types of holographic optical elements, combining the flexibility of computer generated holograms with the large space bandwidth product and high diffraction efficiency of interferometrically recorded volume phase holograms, are demonstrated. The optical elements are recorded by subdividing a volume hologram film surface into numerous small areas (facets), each of which is individually exposed under computer control. Each facet is used to produce a portion of the desired final wavefront. Three different optical elements are demonstrated

A NASTRAN DMAP alter for determining a local stiffness modification to obtain a specified eigenvalue

A technique is described which has been programmed as a DMAP Alter to Rigid Format 3, for determining a stiffness matrix modification to obtain a specified eigenvalue for a structure. The stiffness matrix modifications allowable are those that can be described as the product of a single scalar variable and a matrix of constant coefficients input by the user. The program solves for the scalar variable multiplier which will yield a specified eigenvalue for the complete structure (provided it exists), makes the modification to the stiffness matrix, and proceeds in Rigid Format 3 to obtain the eigenvalues and eigenvectors of the modified structure

Accuracy of Three Dimensional Solid Finite Elements

The results of a study to determine the accuracy of the three dimensional solid elements available in NASTRAN for predicting displacements is presented. Of particular interest in the study is determining how to effectively use solid elements in analyzing thick optical mirrors, as might exist in a large telescope. Surface deformations due to thermal and gravity loading can be significant contributors to the determination of the overall optical quality of a telescope. The study investigates most of the solid elements currently available in either COSMIC or MSC NASTRAN. Error bounds as a function of mesh refinement and element aspect ratios are addressed. It is shown that the MSC solid elements are, in general, more accurate than their COSMIC NASTRAN counterparts due to the specialized numerical integration used. In addition, the MSC elements appear to be more economical to use on the DEC VAX 11/780 computer

Improved isoparametric solid and membrane elements

Improvements that were made to the COSMIC NASTRAN elements CIHEX1 and QDMEM1 are described. These elements are isoparametric representations of solid and membrane elastic behavior. Recent papers by the authors have shown the official COSMIC versions of these elements to be inferior to those available in the MacNeal-Schwendler Corporation (MSC) version of NASTRAN in that they are overly stiff for some loadings. Modifications were made to these elements which reduce the order of integration for shear terms and, for the eight-mode solid element, add additional strain functions. The resulting element formulations give behavior similar to that of the MSC elements. The changes made in the element formulations are discussed and results of test problems are compared with results from the official COSMIC elements and with the MSC elements

Effect of Prey Density on Diurnal Activity and Ovarian Development in \u3ci\u3eCalosoma Calidum\u3c/i\u3e (Coleoptera: Carabidae): Implications for Biological Control of the Gypsy Moth, \u3ci\u3eLymantria Dispar (Lepidoptera: Lymantriidae)\u3c/i\u3e in the Midwest

Four feeding treatments were used in the laboratory to study the effects of the availability of prey on diurnal behavior and ovarian development of Calosoma calidum. Activity was closely monitored for six weeks. No significant differences were found between male and female behavior patterns. Diurnal beetle activity was found to be inversely related to prey density; in treatments where prey was available, diurnal activity declined during the course of the experiment. At the end of six weeks, dissections of female beetles showed that ovarian development and fat body quantity were dependent upon the number of prey available for consumption

Saddles, Arrows, and Spirals: Deterministic Trajectories in Cyclic Competition of Four Species

Population dynamics in systems composed of cyclically competing species has been of increasing interest recently. Here, we investigate a system with four or more species. Using mean field theory, we study in detail the trajectories in configuration space of the population fractions. We discover a variety of orbits, shaped like saddles, spirals, and straight lines. Many of their properties are found explicitly. Most remarkably, we identify a collective variable which evolves simply as an exponential: $\mathcal{Q}e^{\lambda t}$, where $\lambda$ is a function of the reaction rates. It provides information on the state of the system for late times (as well as for $t\rightarrow -\infty$). We discuss implications of these results for the evolution of a finite, stochastic system. A generalization to an arbitrary number of cyclically competing species yields valuable insights into universal properties of such systems.Comment: 15 pages, 5 figures, submitted to Physical Review

Coalescence in low-viscosity liquids

The expected universal dynamics associated with the initial stage of droplet coalescence are difficult to study visually due to the rapid motion of the liquid and the awkward viewing geometry. Here we employ an electrical method to study the coalescence of two inviscid droplets at early times. We measure the growth dynamics of the bridge connecting the two droplets and observe a new asymptotic regime inconsistent with previous theoretical predictions. The measurements are consistent with a model in which the two liquids coalesce with a slightly deformed interface.Comment: 4 pages and 4 figure

A knowledge-based approach to configuration layout, justification, and documentation

The design, development, and implementation is described of a prototype expert system which could aid designers and system engineers in the placement of racks aboard modules on Space Station Freedom. This type of problem is relevant to any program with multiple constraints and requirements demanding solutions which minimize usage of limited resources. This process is generally performed by a single, highly experienced engineer who integrates all the diverse mission requirements and limitations, and develops an overall technical solution which meets program and system requirements with minimal cost, weight, volume, power, etc. This system architect performs an intellectual integration process in which the underlying design rationale is often not fully documented. This is a situation which lends itself to an expert system solution for enhanced consistency, thoroughness, documentation, and change assessment capabilities

Accuracy of the TRIA3 thick shell element

The accuracy of the new TRIA3 thick shell element is assessed via comparison with a theoretical solution for thick homogeneous and honeycomb flat simply supported plates under the action of a uniform pressure load. The theoretical thick plate solution is based on the theory developed by Reissner and includes the effects of transverse shear flexibility which are not included in the thin plate solutions based on Kirchoff plate theory. In addition, the TRIA3 is assessed using a set of finite element test problems developed by the MacNeal-Schwendler Corp. (MSC). Comparison of the COSMIC TRIA3 element as well as those from MSC and Universal Analytics Inc. (UAI) for these problems is presented. The current COSMIC TRIA3 element is shown to have excellent comparison with both the theoretical solutions and also those from the two commercial versions of NASTRAN with which it is compared