**NATIONALLY-PROMINENT PROGRAMS:**

MATHEMATICAL SCIENCES

MATHEMATICAL SCIENCES

Under the leadership of Daljit Ahluwalia, NJIT’s Department of Mathematical Sciences is already nationally recognized for quality education and applied research programs. The department currently has more than 100 students enrolled in the BS program and more than 30 doctoral candidates. Its 20 active research projects have more than $1 million in funding from public and private sources including NSF, NIH, NASA, the US Department of Energy, the Air Force Office of Science and Research, and the Whitaker Foundation.

The department aims to become one of the top five applied math departments in the nation within five years. Read an interview with Dr. Ahluwalia in NJIT Alumni Magazine about the departmental goals.

**. . . . . . . The department aims to become one of the top five applied math departments within five years . . . . . . .**

During 2004, the Mathematical Science Department hosted its first international conference, "Frontiers in Applied and Computational Mathematics," which featured presentations by more than 40 world-renowned scientists and mathematicians, including members of the National Academy of Sciences, the National Academy of Engineering, and the National Institute of Medicine. The conference focused on recent advances in mathematical fluid dynamics and mathematical biology, two areas of concentration for NJIT researchers. Read more.

The department’s research programs apply computational techniques to problems in such fields as medicine and biology, the environment and manufacturing. Mathematical biology is the largest area of concentration. Read “Of Crustaceans, Humans and Math” in *NJIT Alumni Magazine*. The department will build on its focus in this area during the coming year as it launches the Undergraduate Biology and Math Training Program with support from the National Science Foundation. This innovative program, directed by Associate Professor Amitabha Bose, will prepare students to be able to do research at the interface of mathematics and biology.

### Projects in Mathematical Biology

**Studying Blood Flow:**Daniel Goldman, assistant professor of mathematical sciences and biomedical engineering, uses realistic mathematical and computational models to study circulation, especially in small blood vessels and how they deliver oxygen to body tissue. Read more.**How the Nervous System Works:**Jorge Golowasch, associate professor of mathematical sciences and biology, studies mechanisms that enable neurons to recover from disruptions due to growth, learning and injury. Read more.**Charting Neural Rhythms:**Farzan Nadim, associate professor of mathematics, studies the nervous systems of crabs and lobsters to gain insights into neurological disorders such as epilepsy. Read more.**Understanding Neural Networks:**New insight into short-term synaptic plasticity (STSP) – the ability of a synapse to change in strength based on how it is being used – is the goal of Amitabha Bose, associate professor of mathematical sciences. Read more.**Improving Microscopy:**In a collaborative project supported by the National Institutes of Health, Assistant Professor Christopher Raymond is developing mathematical models for the process of immunocolloidal labeling, a process which enhances identification of molecules by electron microscopy. Read more.**Analyzing Cell Communication:**Cyrill Muratov, assistant professor of mathematical sciences, is leading a study of cell communication networks in the development of fruitfly eggs. Supported by an NSF grant, the project is a collaboration among investigators combining mechanistic modeling, computational analysis, and experimental techniques of developmental genetics to understand the formation of biological blueprints in genetics. Read a paper by the research team.

### Other Key Research Projects

**Exploring Computational Topology:**Denis Blackmore, professor of mathematical sciences, is one of only a handful of experts nationally to win grant support from the joint NSF/DARPA initiative on Computational and Algorithmic Representations of Geometric Objects (CARGO). Read more.**Dynamics of Granular Materials:**Lou Kondic, associate professor of mathematical sciences, has NASA support for theoretical and computational research on the dynamics of granular materials. Read more.**Microwave Processing of Ceramics:**With funding from the NSF and the US Department of Energy, Gregory Kriegsmann, distinguished professor of mathematical science, is studying how microwave heating processes work and what happens to ceramic materials when they are heated by microwaves. Read more.**Listening to the Ocean:**Underwater sound propagation -- how sound waves move in the ocean and the effects of factors like temperature, ocean depth, seafloor composition and currents – is the research focus of Eliza Michalopoulou, PhD, associate professor of mathematical sciences. Read more.**Analyzing Moving Boundaries:**Moving boundaries -- the evolution of waves on water, the propagation of flame fronts, or the growth of crystals -- are the research specialty of Michael Siegel, associate professor of mathematical sciences. Read more.**Modeling Electromagnetic Wave Propagation:**Peter Petropoulos, associate professor of mathematical sciences, uses numerical modeling and asmptotic analysis to study phsical problems in the areas of transient electromagnetic wave propogation in complex media. Many modern technology applications involve the propagation and scattering of transient electromagnetic signals -- electronic on-chip interconnects, non-destructive testing of concrete structures, and aircraft radar signature analysis. With funding from the Air Force Office of Scientific Research, he is developing explicit four-order accurate schemes for Maxwell's equations and the approximation of impedance boundary conditions.**Hydrodynamics of Bubble Motion:**Demitrios Papageorgiou, associate professor of mathematical sciences, is studying the motion and retardation of bubbles moving through fluids that contain surfactants -- surface active agents. Supported by an NSF grant, this study has applications for enhancing technological processes such as materials processing in microgravity, environmental and chemical processes, biomedical applications and lubrication technologies. Read results of this study. Read another paper on Dr. Papageorgiou's work. He is also studying mathematical problems in electrohydrodynamics.**Modeling Crystalline Growth:**Assistant Professor Christopher Elmer is developing techniques and tools to study spacially discrete reaction-diffusion equations (SDRDEs) and their application to crystalline growth. With a grant from the NSF, he is developing equations to model transitions -- solidification or melting, movement of a grain boundary -- in crystalline materials such as water, metals and salts. He projects that a more accurate mathematical description and understanding of crystalline materials can be useful in such diverse applications as predicting the failure of mechanical parts and growing gem stones.**Capturing Light Waves:**Roy Goodman, assistant professor of mathematical sciences, is studying pulse propagation and capture in Bragg grating optical fibers under an NSF grant. Motivating the study are simulations in which light traveling through a specialized Bragg grating optical fiber is stopped upon reaching a specially engineering defect at a given location in the fiber. This "trapping" of light at a given point in an optical fiber could be useful as a component of an optical communications device. Read more in Dr. Goodman's papers.