Stable variable step stiff methods for ordinary differential equations

The (alpha)-type variable step variable formula method was first shown to be stable by Zlatev in 1978 and more generally in 1981. These methods are studied for their use in the numerical solution of stiff ordinary differential equations with initial conditions;Two parameter families of these (alpha)-type formulas for orders 2-5 are analyzed. Theorems characterizing A(,0)-stability and A-stability are proved. It is shown that no order 5 A(,0)-stable member exists. A((theta))-stability is also discussed;A generalization of the above types of stability is defined for the variable coefficient methods with a variable grid spacing. Theorems for orders 2-3 are proved which provide bounds on the parameters and allowable step size changing sequences in order to increase generalized A((theta))-stability is discussed. A numerical solution for the order 4 case is given. Selection of these formulas is done and comparisons with the variable coefficient backward differentiation formulas are made;A general purpose computer code which uses the (alpha)-type variable step variable formula method is given. Numerical testing on a set of test problems is performed and comparisons are made to three different computer codes

Turbulence measurements in polymer solutions using hot-film anemometry

Hot-film anemometry was used to study the detailed structure of turbulence (intensities, energy spectra, and auto-correlations) in Newtonian solvents, non-drag reducing polymer solutions, and drag reducing polymer solutions. This was done in two smooth wall tubes with diameters of 1.0 inch and 2.0 inches. A probe traversing mechanism was used for measurements at radial positions from the center to as near the wall as possible for both the film probes (r/a=0.85 in the 2-inch tube) and the impact tubes (r/ a=0.98). The impact tubes were used to measure velocities for film probe calibration. The solvents used in this investigation were toluene, cyclohexane, and benzene. Three concentrations of a medium molecular weight polyisobutylene (Vistanex L-80, molecular weight about 720,000) in cyclohexane, two concentrations of the same polymer in benzene, two concentrations of a high molecular weight polymethyl methacrylate (Plexiglas, molecular weight about 1,500,000) in toluene, one concentration of a low molecular weight polymethyl methacrylate (V-100 molding powder, molecular weight about 110,000) in toluene, three concentrations of a high molecular weight polyisobutylene (Vistanex 1-200, molecular weight about 4,700,000) in toluene, and one concentration of the same polymer in cyclohexane were used. In the liquids not showing drag reduction a viscous and/ or elastic effect was found for both turbulence intensities and energy spectra. Turbulence intensities were higher and energy spectrum frequencies were lower for the polymer solutions of high viscosity. Unfortunately the most viscous solutions were also elastic. So purely viscous liquid studies will be necessary to distinguish between elastic and viscous effects. During drag reduction it was found that the energy spectra changed little from purely viscous solvents. The turbulence intensities, however, showed very unusual effects. The intensities relative to friction velocity increased at low drag ratio values (high drag reduction), rather than remain constant as expected from mixing length considerations. This behavior was dependent upon the degree of mechanical polymer degradation, lower intensities occurring for fresh than for degraded solutions during drag reduction. Normal stress differences (P₁₁ - P₂₂) were measured for two of the solutions used in this investigation, one showing drag reduction at attainable flow rates in the l-inch tube, the other showing drag reduction only in 0.5-inch and smaller tubes. Both solutions yielded normal stress differences of about the same level. A quantitative viscoelastic mechanism of drag reduction was tested using the viscosity and normal stress data for the two solutions discussed above. The drag reduction mechanism demonstrated the relative effects of elasticity and viscosity on drag reduction. The adequate prediction of drag ratios for two solutions at two flow rates in each of two tube sizes demonstrated the validity of the mechanism and the reasonableness of the assumptions made --Abstract

Laser assisted milling of difficult to machine materials

Titanium alloys are well known for their excellent strength to weight ratio and corrosion resistance and is highly sought after in the aerospace industry. Additionally, titanium alloys maintain a high biocompatibility for implants and other medical devices. However, these alloys are notorious for their poor machinability. As the demand for these alloys continue to increase, improved methods of manufacture must be explored. ^ This thesis describes Laser Assisted Milling (LAML) of Ti-6AL-4V (Ti-64) alloys, which studies localized preheating of the workpiece by a laser and characterizes the improvements to the machinability of these metals. Laser parameters are determined based on temperature prediction modeling results. Laser preheating is shown to reduce cutting force during the machining process. Machinability improvement is characterized through inspection of flank wear on the cutting tool using LAML and traditional machining methods and comparing total tool life. Systematic characterization of samples is performed using hardness measurements, scanning electron microscopy (SEM), and X-ray diffraction (XRD) to ensure that material properties remained unaltered as a result of laser preheating. ^ An economic analysis is performed to characterize the cost benefit of machining using LAML while considering the additional costs associated with the laser equipment. Economic improvements are shown for the LAML process for Ti-64 alloys. A rotary axis is added to the machining equipment to overcome design constraints from the laser setup and allow for the machining of complex shapes. The feasibility of complex contouring is demonstrated for LAML with the creation of more intricate geometry being performed on a titanium workpiece

Supporting Youth in Transition to Adulthood: Lessons Learned from Child Welfare and Juvenile Justice

The Georgetown Public Policy Institute's Center for Juvenile Justice Reform and the Jim Casey Youth Opportunities Initiative collaborated to publish this paper that describes case assessment, case management, and other practices implemented in the juvenile justice and child welfare systems. The practices highlighted have shown promise in improving outcomes for the transition-age population

The Office of the Indiana Attorney General: Perspectives on Professional Licensing Enforcement and Disciplinary Actions

This presentation details the investigation and litigation processes of the Attorney General’s Office upon receipt of consumer complaints filed against Indiana professional licensees. We will have a round-table discussion with board liaisons from the State Boards of Registrations for Professional Engineers and Professional Surveyors. Time will be reserved for Q&A

Comparison Of Lagrangian Time Correlations Obtained From Dispersion Experiments And From Space‐time Correlation Functions

No Abstracts. Copyright © 1969 American Institute of Chemical Engineer