Numerical investigation of a binary solidification design problem

This exposition presents the development and application of a methodology for control of unidirectional solidification of a binary alloy. In particular, it is desired to produce a casting that has a uniform cast structure throughout its entire length. Furthermore, the methodology allows the specification, a priori, of the cast structure with respect to both scale, i.e., fine or coarse, and mor- phology, i.e., dentritic or cellular. This specification is in the form of a map that relates solidification characteristics, i.e., scale and morphology, to the solidification velocity and liquid-side interfacial temperature gradient. Thus design is accomplished by controlling these two parameters during the solidification process. With this in mind, the goal of what is termed the binary solidification design problem is the prediction of a set of boundary temperatures and heat fluxes which when applied will result in the desired interfacial motion and temperature gradient and therefore cast structure. Mathematical models for problems of this type lead to what are termed ill-posed systems in that they may not exhibit existence, uniqueness, or continuous dependence on boundary data. The resolution of this class of problems requires advanced techniques to overcome the instabilities encountered due to their ill-posed nature. The methodology developed herein employs the classical weight residual approach in a innovative manner. Normally, in the solution of a parabolic partial differential equation, such as the heat equation, a spatial series expansion with time varying coefficients is utilized along with a minimiza- tion technique to reduce the partial differential equation to a set of first order ordinary differential equations. This set can be solved using any number of numerical technique, i.e, Runge-Kutta, to obtain the temporal variation of the coefficientsThese types of time stepping techniques eventually lead to the onset of instability when employed for the resolution of ill-posed problems due to the build-up of round-off errors. In this exposition, time stepping is replaced by the further expansion of the time varying expansion coefficients into a series unto itself. Minimization in both space and time is simultaneously applied leading to a set of algebraic equations whose solution leads to the resolution of the entire space-time domain. This treatment of time in an elliptic fashion stabilizes the solution of the ill-posed problem and forms the basis of what is termed the Global Time Method, GTM. The results obtained for the control boundaries indicate that the control measures required to accomplish the design solidification are not only physically realistic but relatively undemanding to implement. Furthermore, under the design solidification conditions, it was observed that once formed, a mushy zone of constant thickness was maintained throughout the transient. This observation gave rise to a quasi-steady state analysis of the mushy zone which lead to the development of a set of design tools

Leading Your Leaders

Even though working on a problem has been your primary effort for the past year, your leadership may have heard about this once in a briefing a decade ago. Now they are basically clueless. Pretend that you are talking to your daughter's fifth-grade class. Explain how your complicated gizmo works. If possible, do not use acronyms. Define your terms. Put your work in context. Assume your leader has no idea what you do, who you work for, or what your gizmo does. That is a good place to start. Remember, taking the next century to study the problem or spending the Gross National Product to invent a new solution are probably not going to be acceptable solutions. Real engineers and technicians build real hardware that works in the real world in a reasonable manner within a reasonable time at a reasonable cost. True, skimping on time or money can cause mistakes, but folks whose gizmos are delayed unreasonably or cost more than is practical get their programs canceled, force the business into bankruptcy, or give the market over to the competition. Real engineers and technicians always consider cost and schedule in their work. Raising questions is important. However, we are in the business of doing things. Engineers and technicians are paid to get things done. Yes, you have to identify the problem, frame the design, identify the tests, perform the analysis, and assemble the hardware. But the goal is to solve the problem. Nobody ever said flying in space was easy. We make it look easy the same way that an Olympic champion makes her sport look easy: by working hard at improving performance every day. Better are the results of a well-defined test. Remember that a test on a laboratory bench is always an approximation of reality, and rules similar to those for good analysis also apply. One should always be mindful of Mechelay's rule: "It is better to be stupid than to run a stupid test." Often we try to overtest. If a piece of hardware passes an unbelievably difficult test, then life is good. More often when an unbelievably difficult test fails, we are left with a very long discussion of why and what was wrong in the design or execution of the test. Make sure that the test is well defined. Even then, it is important to explain to your leaders what inherent accuracy (or error) the test conditions or equipment have and what the assumptions or initial conditions were for the test. Test results without a good understanding of the test's accuracy or the pedigree of the test assumptions are worth very little. Finally, there is flight test data. Always limited, never at the edge of the envelope, it still shows how the real hardware works in a combined environment. Flight experience is dangerous because it typically doesn't show how close to the edge of the cliff the equipment is operating, but it does demonstrate how the hardware really works. A flight test is the ultimate test, again taken with the knowledge that it is probably not the extreme but something more like the middle of the environmental and systems performance. Good understanding of a problem and its solution always relies on a combination of all these methods. Be sure to lead your leaders by using all the tools you have at your disposal. At the end of the day, decisions in space flight always come down to a risk trade. Our business is not remotely safe, not in the sense that the public, the media, or our legislators use the term. Everything we do has a risk, cost, schedule, or performance trade-off. For your leaders to make an appropriate decision, you need to educate them, lead them, talk with them, and engage them in the discussion until full understanding takes place. It's your job.

Does microalbuminuria screening in diabetes prevent complications?

Screening diabetic patients for microalbuminuria identifies those who may benefit from treatments that delay progression to renal failure (strength of recommendation: B, based on extrapolation from Level 1 treatment studies of patients with microalbuminuria). No research has determined the best method for screening for microalbuminuria, or whether screening in primary care populations will produce better long-term outcomes. No studies have examined the role of microalbuminuria screening after angiotensin-converting enzyme (ACE) inhibitors or angiotensin receptor blockers (ARBs) have been instituted for other indications

Is folate supplementation indicated for patients with CAD?

There is insufficient evidence to advocate the routine use of folate supplementation for the treatment of coronary artery disease (CAD). High levels of serum homocysteine have been associated in several studies with an increased risk for CAD (strength of recommendation [SOR]: B, associated in case-control studies). Folate supplementation decreases the level of serum homocysteine (SOR: A, meta-analysis of randomized controlled trials). This indirect evidence suggests that folate supplementation may be of benefit in slowing the progress of arteriosclerosis

Does quinine reduce leg cramps for young athletes?

Very little evidence exists regarding the use of quinine for cramps in young adult athletes. Quinine may be an effective treatment for heat cramps in athletes (strength of recommendation [SOR]: C, 1 case series involving 2 patients). Quinine is better established as an effective treatment for nocturnal leg cramps in the general adult population (SOR: A, 1 meta-analysis and 2 randomized controlled trials)

Does postcoital voiding prevent urinary tract infections in young women?

Healthy women who urinate within 15 minutes of sexual intercourse may be slightly less likely to develop a urinary tract infection (UTI) than women who do not urinate afterward (grade of recommendation: D, extrapolation of single case-control study with nonsignificant findings)

Wings in Orbit: Scientific and Engineering Legacies of the Space Shuttle, 1971-2010

The Space Shuttle is an engineering marvel perhaps only exceeded by the station itself. The shuttle was based on the technology of the 1960s and early 1970s. It had to overcome significant challenges to make it reusable. Perhaps the greatest challenges were the main engines and the Thermal Protection System. The program has seen terrible tragedy in its 3 decades of operation, yet it has also seen marvelous success. One of the most notable successes is the Hubble Space Telescope, a program that would have been a failure without the shuttle's capability to rendezvous, capture, repair, as well as upgrade. Now Hubble is a shining example of success admired by people around the world. As the program comes to a close, it is important to capture the legacy of the shuttle for future generations. That is what "Wings In Orbit" does for space fans, students, engineers, and scientists. This book, written by the men and women who made the program possible, will serve as an excellent reference for building future space vehicles. We are proud to have played a small part in making it happen. Our journey to document the scientific and engineering accomplishments of this magnificent winged vehicle began with an audacious proposal: to capture the passion of those who devoted their energies to its success while answering the question "What are the most significant accomplishments?" of the longestoperating human spaceflight program in our nation s history. This is intended to be an honest, accurate, and easily understandable account of the research and innovation accomplished during the era

Decision-making capacity for treatment in psychiatric and medical in-patients: Cross-sectional, comparative study

BackgroundIs the nature of decision-making capacity (DMC) for treatment significantly different in medical and psychiatric patients?AimsTo compare the abilities relevant to DMC for treatment in medical and psychiatric patients who are able to communicate a treatment choice.MethodA secondary analysis of two cross-sectional studies of consecutive admissions: 125 to a psychiatric hospital and 164 to a medical hospital. The MacArthur Competence Assessment Tool – Treatment and a clinical interview were used to assess decision-making abilities (understanding, appreciating and reasoning) and judgements of DMC. We limited analysis to patients able to express a choice about treatment and stratified the analysis by low and high understanding ability.ResultsMost people scoring low on understanding were judged to lack DMC and there was no difference by hospital (P=0.14). In both hospitals there were patients who were able to understand yet lacked DMC (39% psychiatric v. 13% medical in-patients, P&lt;0.001). Appreciation was a better ‘test’ of DMC in the psychiatric hospital (where psychotic and severe affective disorders predominated) (P&lt;0.001), whereas reasoning was a better test of DMC in the medical hospital (where cognitive impairment was common) (P=0.02).ConclusionsAmong those with good understanding, the appreciation ability had more salience to DMC for treatment in a psychiatric setting and the reasoning ability had more salience in a medical setting.</jats:sec

Phase Slips and the Eckhaus Instability

We consider the Ginzburg-Landau equation, $\partial_t u= \partial_x^2 u + u - u|u|^2$, with complex amplitude $u(x,t)$. We first analyze the phenomenon of phase slips as a consequence of the {\it local} shape of $u$. We next prove a {\it global} theorem about evolution from an Eckhaus unstable state, all the way to the limiting stable finite state, for periodic perturbations of Eckhaus unstable periodic initial data. Equipped with these results, we proceed to prove the corresponding phenomena for the fourth order Swift-Hohenberg equation, of which the Ginzburg-Landau equation is the amplitude approximation. This sheds light on how one should deal with local and global aspects of phase slips for this and many other similar systems.Comment: 22 pages, Postscript, A