NJIT Math 451-H Honors Methods of Applied Mathematics II

Spring 2012

Text: (to be provided by the instructor) J. Feder: "Fractals", Plenum Press, New York, 1989 D. Stauffer, A. Aharony, "Introduction to percolation theory", Taylor & Francis, Philadelphia, 2003 Selected research articles

 

Grading policy:: Projects and presentations throughout the semester: 100%

 

Course Outline:

 

Theoretical, computational, and experimental research:

 

Percolation and topological properties of granular media

 

Theoretical component:

(1) Learning the basics about physics of granular systems, including the issues related to the formation of force networks in granular media;

(2) applying novel topological measures to the structures that form when granular systems are exposed to external forcing; (3) analyze percolation properties of these systems; (4) discuss connections between topological measures and percolation properties.

 

Computational component:

(1) Image processing: further develop matlab-based codes used to analyze experimental images; (2) work on developing computational methods for processing data coming out of molecular-dynamics type of simulations; (3)  applying computational homology approach to analyze the results from (1) and (2), including basic properties of force networks.

 

Experimental component:

Performing experiments involving two dimensional particulate systems Visualization of photoelastic granular systems using CCD camera and appropriate software; Data analysis.



NJIT Honor Code: All Students should be aware that the Department of Mathematical Sciences takes the NJIT Honor Code very seriously and enforces it strictly.  This means that there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams.  Under the Honor Code, students are obligated to report any such activities to the Instructor.

Homework Policy: Homework due at the beginning of the class.  There will be a penalty for late homework.

Attendance and participation: Your absences from class will inhibit your ability to fully participate in class discussions, laboratory work, and problem solving sessions and, therefore, affect your grade.  Given the nature of the capstone course, class participation counts for a lot!

Cellular phones: All cellular phones and beepers must be switched off during all class times and project presentations.

IMPORTANT DATES

FIRST DAY OF SEMESTER

January 17, 2012

LAST DAY TO WITHDRAW

March 20, 2012

LAST DAY OF CLASSES

May 2, 2012

FINAL EXAM PERIOD

May 3-9, 2012

 

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