The investigator focuses on research and education goals at the crossroads of mathematics with materials science and physics. This research links macroscopic principles for crystal interfacial phenomena to microscale processes. The physical mechanisms are described by discrete "particle" schemes for atomic line defects. However, mesoscopic and macroscopic consequences are best understood via continuous models. Linkages between models are sought by kinetic theory, partial differential equations, and stochastic analysis. The education part includes the training of a graduate student, development of innovative courses in applied mathematics, activities for mathematics awareness and outreach, authorship of a book on integral equations, and organization of working group seminars.
The project addresses fundamental issues in nanotechnology and materials modeling. The investigator uses tools of applied mathematics to study systematically how nano-structures decay on surfaces of technologically important materials. This work is motivated by the pressing need to design increasingly smaller and faster, yet more reliable, devices. The proposed work advances the ability to model and predict by theoretical methods the reliability of devices for the next generation of applications in microelectronics and information technology. The project integrates research and education: Interdisciplinary concepts of applied mathematics are shaped into instruction tools that reach out to students and science experts in diverse areas. This Career award is supported by the MPS Division of Mathematical Sciences and by the MPS Division of Materials Research.
The project of this award focused on research and educational goals at the crossroads of mathematics with materials science and applied physics. The main motivation for the work within this project was to provide quantitative answers to questions emerging from the need to design and fabricate faster and more reliable optoelectronic nano-devices made of crystalline materials. Some of these questions are: How fast do solid structures decay on crystal surfaces? How does the motion of atomic defects in crystals affect the stability of small devices? What is the shape of a stable nanoparticle? The main research achievements from this award include the following: (i) A significantly improved understanding of what kind of physical mechanisms influence the lifetimes of structures that form building blocks of optoelectronic devices. These physical mechanisms involve processes across several length and time scales, from the atomistic scale, where the motion of individual atoms is evident, to the macroscopic scale, where morphological changes on material surfaces are observed. (ii) The systematic description by analytical and numerical means of linkages between these scales. These connections demonstrate how several controlling parameters used in the design of laboratory experiments are related to fundamental atomistic processes. In particular, the principal investigator showed how the presence of certain atomic defects on crystals can affect the evolution of structures at macroscopic scales. (iii) Predictions of quantitative macroscopic laws according to which crystal structures can evolve. These laws tell us how stable certain solid-state devices can be, depending on the temperature and other controlling factors. The main educational achievements from this award include the following: (i) The training by the principal investigator of three graduate students of applied mathematics or physics in a highly interdisciplinary environment. Two of these students already completed their graduate studies at the triple point of mathematics, materials science, and applied physics. (ii) Outreach activities by which aspects of this research were communicated to middle -school students via lectures, lab demonstrations and hands-on exercises offered by the principal investigator. (iii) The creation of a new graduate interdisciplinary course taught by the principal investigator in the University of Maryland. In this course, mathematical methods underlying this research were taught to graduate and advanced undergraduate students of mathematics, engineering, and the physical sciences. (iv) A series of informal seminars (``Research Interaction Teams'') co-organized by the principal investigator, by which results from this research were communicated to postdocs, and graduate and undergraduate students with adjacent interests in the University of Maryland.
