A Class of Free Boundary Problems with Onset of a new Phase

A class of diffusion driven Free Boundary Problems is considered which is characterized by the initial onset of a phase and by an explicit kinematic condition for the evolution of the free boundary. By a domain fixing change of variables it naturally leads to coupled systems comprised of a singular parabolic initial boundary value problem and a Hamilton-Jacobi equation. Even though the one dimensional case has been thoroughly investigated, results as basic as well-posedness and regularity have so far not been obtained for its higher dimensional counterpart. In this paper a recently developed regularity theory for abstract singular parabolic Cauchy problems is utilized to obtain the first well-posedness results for the Free Boundary Problems under consideration. The derivation of elliptic regularity results for the underlying static singular problems will play an important role

On the averaging principle for one-frequency systems. An application to satellite motions

This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been introduced to obtain precise, fully quantitative estimates on the averaging error. Here, this procedure is applied to the motion of a satellite in a polar orbit around an oblate planet, retaining only the J_2 term in the multipole expansion of the gravitational potential. To exemplify the method, the averaging errors are estimated for the data corresponding to two Earth satellites; for a very large number of orbits, computation of our estimators is much less expensive than the direct numerical solution of the equations of motion.Comment: LaTeX, 35 pages, 12 figures. The final version published in Nonlinear Dynamic

A Study of the Writing Interests of a Group of Fourth Grade Children

Submitted to the Department of Education and to the Faculty of the Graduate School of the University of Kansas in partial fulfillment of the requirements for the degree of Master of Science in Education

We all live...

I wanted to draw the submarine from \u27Yellow Submarine\u27 as this was the first song I ever listened to from The Beatles. The style of The Beatles from the top-left corner and the Octopus from the bottom-right corner was inspired by The Beatles cartoon and I really like the at style from the cartoon too

Fetal Dystocia

A patient, a seven year old purebred Angus cow, was presented at Stange Memorial Clinic on Jan. 8, 1941. She had begun labor the previous night after having completed a gestation period of supposedly normal length

Momentum transfer during the impact of granular matter with inclined sliding surfaces

© 2017 Elsevier Ltd Increasing the inclination of a rigid surface that is impacted by a collimated granular flow reduces the fraction of granular matter momentum transferred to the surface. Recent studies have shown that the momentum reduction depends upon a frictional interaction between the granular flow and the impacted surface. High coefficient of friction surfaces suffer significantly more momentum transfer than predicted by resolution of the incident momentum onto the inclined plane. This discovery has raised the possibility that inclined surfaces with very low friction coefficients might reduce the impulsive transferred by the impact of high velocity granular matter. Here the use of a lubricated sliding plate is investigated as a means for reducing interfacial friction and impulse transfer to an inclined surface. The study uses a combination of experimental testing and particle-based simulations to investigate impulse transfer to rigid aluminum surfaces inclined either perpendicular or at 53° to synthetic sand that was impulsively accelerated to a velocity of 350–500 m/s. The study shows that impact of this sand with lubricated plates attached to an inclined surface rapidly accelerates them to a velocity of about 55–70 m/s, and reduces the impulse transferred to the inclined surface below. The reduction of impulse by this approach is comparable to that achieved by changing the inclination of the surface.This research was funded by the Defense Advanced Research Projects Agency (DARPA) under grant number W91CRB-11-1-0005 (Program manager, Dr. J. Goldwasser)

A system dynamics approach to educational technology introduction in Developing countries

Thesis (S.M.)--Massachusetts Institute of Technology, System Design and Management Program, 2008.Includes bibliographical references.Developing nations around the globe are focused on ways to use Information and Computing Technologies (ICTs) as springboards to advance their national development in all areas, including education. There are multiple ways in which various organizations are tackling the unique challenges these nations face in equipping their schools with modem educational technologies. This study evaluates two examples of computing technology intended for wide-scale deployment in developing nations. It aims to test the hypothesis that in order to be successful, ICT implementations require adequate funding, available electrical and telecommunication infrastructure, the presence of strong local champions and a local support ecosystem. Interviews were conducted with stakeholders involved in two pilot implementations in Nigeria. A system dynamics model was used to investigate into the relative effects of relevant factors on the speed of ICT deployment. The results from the modeling show the need for a significant increase in financial investment, in order to cover all costs associated with ICT deployments. The results also revealed the daunting task nations face in equipping all students with individual laptops and it presents some alternatives to a wide-scale deployment of one-to-one computing. Finally, the results highlight the necessity of providing economical means of completely powering ICTs in order to rapidly deploy these technologies to the nation's schools. A number of recommendations were made for the consideration of any developing nation undertaking ICT implementations in education.by Trinidad Grange-Kyner.S.M

Renormalization and destruction of 1/γ21/\gamma^2 tori in the standard nontwist map

Extending the work of del-Castillo-Negrete, Greene, and Morrison, Physica D {\bf 91}, 1 (1996) and {\bf 100}, 311 (1997) on the standard nontwist map, the breakup of an invariant torus with winding number equal to the inverse golden mean squared is studied. Improved numerical techniques provide the greater accuracy that is needed for this case. The new results are interpreted within the renormalization group framework by constructing a renormalization operator on the space of commuting map pairs, and by studying the fixed points of the so constructed operator.Comment: To be Submitted to Chao