Mathematical Modeling Doctor of philosophy (Ph.D.) degree

7e9082d0-7a73-4557-8e84-0ff2c9d79793 | 86035

Overview

Mathematical modeling is the process of developing mathematical descriptions, or models, of real-world systems. These models can be linear or nonlinear, discrete or continuous, deterministic or stochastic, and static or dynamic, and they enable investigating, analyzing, and predicting the behavior of systems in a wide variety of fields. Through extensive study and research, graduates of this program will have the expertise not only to use the tools of mathematical modeling in various application settings, but also to contribute in creative and innovative ways to the solution of complex interdisciplinary problems and to communicate effectively with domain experts in various fields.

Plan of study

The degree requires at least 60 credit hours of course work and research. The curriculum consists of three required core courses, three required concentration foundation courses, a course in scientific computing and high-performance computing (HPC), three elective courses focused on the student’s chosen research concentration, and a doctoral dissertation. Elective courses are available from within the School of Mathematical Sciences as well as from other graduate programs at RIT, which can provide application-specific courses of interest for particular research projects. A minimum of 30 credits hours of course work is required. In addition to courses, at least 30 credit hours of research, including the Graduate Research Seminar, and an interdisciplinary internship outside of RIT are required.

Students develop a plan of study in consultation with an application domain advisory committee. This committee consists of the program director, one of the concentration leads, and an expert from an application domain related to the student’s research interest. The committee ensures that all students have a roadmap for completing their degree based on their background and research interests. The plan of study may be revised as needed.

Qualifying examinations

All students must pass two qualifying examinations to determine whether they have sufficient knowledge of modeling principles, mathematics, and computational methods to conduct doctoral research. Students must pass the examinations in order to continue in the Ph.D. program.

The first exam is based on the Numerical Analysis I (MATH-602) and Mathematical Modeling I, II (MATH-622, 722). The second exam is based on the student's concentration foundation courses and additional material deemed appropriate by the committee and consists of a short research project.

Dissertation research adviser and committee

A dissertation research adviser is selected from the program faculty based on the student's research interests, faculty research interest, and discussions with the program director. Once a student has chosen a dissertation adviser, the student, in consultation with the adviser, forms a dissertation committee consisting of at least four members, including the dissertation adviser. The committee includes, in addition to the dissertation adviser, one other member of the mathematical modeling program faculty and an external chair appointed by the dean of graduate education. The external chair must be a tenured member of the RIT faculty who is not a current member of the mathematical modeling program faculty. The fourth committee member must not be a member of the RIT faculty and may be a professional affiliated with industry or with another institution; the program director must approve this committee member.

The main duties of the dissertation committee are administering both the candidacy exam and final dissertation defense. In addition, the dissertation committee assists students in planning and conducting their dissertation research and provides guidance during the writing of the dissertation.

Admission to candidacy

When a student has developed an in-depth understanding of their dissertation research topic, the dissertation committee administers an examination to determine if the student will be admitted to candidacy for the doctoral degree. The purpose of the examination is to ensure that the student has the necessary background knowledge, command of the problem, and intellectual maturity to carry out the specific doctoral-level research project. The examination may include a review of the literature, preliminary research results, and proposed research directions for the completed dissertation. Requirements for the candidacy exam include both a written dissertation proposal and the presentation of an oral defense of the proposal. This examination must be completed at least one year before the student can graduate.

Dissertation defense and final examination

The dissertation defense and final examination may be scheduled after the dissertation has been written and distributed to the dissertation committee and the committee has consented to administer the final examination. Copies of the dissertation must be distributed to all members of the dissertation committee at least four weeks prior to the final examination. The dissertation defense consists of an oral presentation of the dissertation research, which is open to the public. This public presentation must be scheduled and publicly advertised at least four weeks prior to the examination. After the presentation, questions will be fielded from the attending audience and the final examination, which consists of a private questioning of the candidate by the dissertation committee, will ensue. After the questioning, the dissertation committee immediately deliberates and thereafter notifies the candidate and the mathematical modeling graduate director of the result of the examination.

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Curriculum

Mathematical modeling, Ph.D. degree, typical course sequence

Course Sem. Cr. Hrs.
First Year
MATH-602
Numerical Analysis I
This course covers numerical techniques for the solution of nonlinear equations, interpolation, differentiation, integration, and matrix algebra.
3
MATH-622
Mathematical Modeling I
This course will introduce graduate students to the logical methodology of mathematical modeling. They will learn how to use an application field problem as a standard for defining equations that can be used to solve that problem, how to establish a nested hierarchy of models for an application field problem in order to clarify the problem’s context and facilitate its solution. Students will also learn how mathematical theory, closed-form solutions for special cases, and computational methods should be integrated into the modeling process in order to provide insight into application fields and solutions to particular problems. Students will study principles of model verification and validation, parameter identification and parameter sensitivity and their roles in mathematical modeling. In addition, students will be introduced to particular mathematical models of various types: stochastic models, PDE models, dynamical system models, graph-theoretic models, algebraic models, and perhaps other types of models. They will use these models to exemplify the broad principles and methods that they will learn in this course, and they will use these models to build up a stock of models that they can call upon as examples of good modeling practice.
3
MATH-722
Mathematical Modeling II
This course will continue to expose students to the logical methodology of mathematical modeling. It will also provide them with numerous examples of mathematical models from various fields.
3
MATH-606
Graduate Seminar
The course prepares students to engage in activities necessary for independent mathematical research and introduces students to a broad range of active interdisciplinary programs related to applied mathematics.
1
MATH-607
Graduate Seminar
This course is a continuation of Graduate Seminar I. It prepares students to engage in activities necessary for independent mathematical research and introduces them to a broad range of active interdisciplinary programs related to applied mathematics.
1
 
Concentration Courses
6
 
Elective
3
Second Year
 
Concentration Courses
3
 
Scientific Computing/HPC Course
3
 
Elective
3
 
Research and Thesis
9
Third Year
 
Elective
3
 
Research and Thesis
7
Fourth Year
 
Research and Thesis
6
Fifth Year
 
Research and Thesis
6
Total Semester Credit Hours
60

Faculty

Kara Maki - klmsma

RIT Username
klmsma
Email
klmsma@rit.edu
Courses Taught This Semester
2185-MATH-500-01;2181-MATH-790-08;2181-MATH-622-01;2181-MATH-219-10;2181-MATH-381-03;2181-MATH-622-01;2181-MATH-219-10;2185-MATH-500-01;2181-MATH-790-08;2181-MATH-381-03;
Scholarly Publications
Invited Paper
Maki, Kara L. and David S. Ross. "A New Model for the Suction Pressure Under A Contact Lens." Journal of Biological Systems. (2014). Print.
Journal Paper
Li, Longfei, et al. "Tear Film Dynamics with Evaporation, Wetting, and Time-dependent Flux Boundary Condition on an Eye-shaped Domain." Physics of Fluids 26. 5 (2014): 52101. Print.
Maki, Kara L. and David S. Ross. "Exchange of Tears under a Contact Lens Is Driven by Distortions of the Contact Lens." Integrative and Comparative Biology 54. 6 (2014): 1043-1050. Print.
Lee, S. H., et al. "Gravity-driven Instability of a Thin Liquid Film Underneath a Soft Solid." Physical Review E 90. 5 (2014): 53009. Print.
Huang, J., et al. "Phantom Study of Tear Film Dynamics with Optical Coherence Tomography and Maximum-likelihood Estimation." Optics Letters 38. (2013): 1721-1723. Print.
Huang, J., et al. "Maximum-likelihood Estimation in Optical Coherence Tomography in the Context of the Tear." Biomedical Optics Express 4. (2013): 1806-1816. Print.
Maki, Kara L. and Yuriko Renardy. "The Dynamics of a Viscoelastic Liquid which Displays Thixotropic Yield Stress Behavior." Journal of Non-Newtonian Fluid Mechanics 181. (2012): 30-50. Print.
Maki, Kara L. and Satish Kumar. "Fast Evaporation of Spreading Droplets of Colloidal Suspensions." Langmuir 27. (2011): 11347-11363. Print.
Invited Keynote/Presentation
Maki, Kara L. "Mechanics of the Contact Lens." Indo-American Frontiers of Science Symposium. Indo-US Science & Technology Forum and National Academy of Sciences. Agra, India. 7 Apr. 2013. Conference Presentation.
Maki, Kara L. "Fast Evaporation of Spreading Droplets of Colloidal Suspensions." 1st Int. Workshop on Wetting and Evaporation: Droplets of Pure and Complex Fluids. Aix Marseille Universite. Marseilles, France. 18 Jun. 2013. Lecture.
Maki, Kara Lee and David S. Ross. "Settling Dynamics of the Contact Lens." Applied and Computational Math Seminar. George Mason University. Fairfax, VA. 26 Oct. 2012. Lecture.
Maki, Kara Lee and David Ross. "Settling Dynamics of the Contact Lens." Workshop on Thin Liquid Films and Fluid Interfaces: Models, Experiments and Applications. Banff International Research Station. Banff, Alberta, Canada. 13 Dec. 2012. Conference Presentation.
Maki, Kara Lee and Yuriko Rendary. "Dynamics of a Thixotropic Yield Stress Fluid: A Mathematical Perspective of Ketchup?" Applied Mathematics Seminar. University of Delaware. Newark, DE. 27 Jun. 2012. Lecture.
Maki, Kara Lee and David Ross. "Settling Dynamics of a Contact Lens." Minisymposium on Dynamics and Applications of Thin Liquid Flims. Society for Industrial and Applied Mathematics Annual Meeting. Minneapolis, MN. 12 Jul. 2012. Conference Presentation.
Maki, Kara Lee and Satish Kumar. "Fast Evaporation of Spreading Droplets of Colloidal Suspensions." Workshop on Surfactant Driven Thin Film Flows. Fields Institute for Research in Mathematical Sciences. Toronto, Ontario. 22 Feb. 2012. Conference Presentation.
Maki, Kara Lee and Satish Kumar. "Fast Evaporation of Spreading Droplets of Colloidal Suspensions." Special Session on Mathematics in Industry. Joint Mathematic Meeting. Boston, MA. 4 Jan. 2012. Conference Presentation.
Maki, Kara L. "Skin Formation in Drying Droplets of Colloidal Suspensions." NSF Mathematics Institutes' Modern Math Workshop. The Society for Advancement of Chicanos and Native Americans in Science Annual Conference. San Jose Convention Center, San Jose, CA. 26 Oct. 2011. Conference Presentation.
First Name
Kara
Middle Name
Lee
Last Name
Maki
Phone
585-475-2541
College/Division & Department
Job Title
Instructional Faculty
Professional Roles
College of Science:Instructional Faculty

Michael Cromer - mec2sma

RIT Username
mec2sma
Email
mec2sma@rit.edu
Courses Taught This Semester
2191-MATH-495-01;2185-MATH-381-04;2185-MATH-495-02;2191-MATH-495-01;2191-MATH-381-01;2191-MATH-381-01;2185-MATH-790-01;2181-MATH-790-05;2181-MATH-495-03;2181-MATH-326-01;2181-MATH-495-01;2181-MATH-326-04;2181-MATH-326-01;2181-MATH-495-01;2181-MATH-326-04;2181-MATH-495-03;2181-MATH-790-05;2185-MATH-790-01;2185-MATH-495-02;2185-MATH-381-04;2185-MATH-500-02;2185-MATH-500-02;2185-MATH-495-12;2185-MATH-495-12;2185-MATH-495-09;2185-MATH-495-09;2185-MATH-495-11;2185-MATH-495-11;2185-MATH-495-10;2185-MATH-495-10;2185-MATH-495-08;2185-MATH-495-08;2191-MATH-831-01;2191-MATH-831-01;
Additional colleges/divisions
Scholarly Publications
Journal Paper
Cromer, Michael, Glenn H. Fredrickson, and L. Gary Leal. "Concentration Fluctuations in Polymer Solutions Under Mixed Flow." Journal of Rheology 6. 14 (2017): 711-730. Print.
Kalb, Arthur, et al. "Role of Chain Scission in Cross-Slot Flow of Wormlike Micellar Solutions." Physical Review Fluids 2. (2017): 1-10. Print.
Cromer, M. and L. P. Cook. "A Study of Pressure-Driven Flow of Wormlike Micellar Solutions through a Converging/Diverging Channel." Journal of Rheology 60. (2016): 953-972. Web.
Peterson, J. D., et al. "Shear Banding Predictions for the Two-Fluid Rolie-Poly Model." Journal of Rheology 60. (2016): 927-951. Web.
First Name
Michael
Middle Name
E
Last Name
Cromer
Phone
585-475-4078
College/Division & Department
Additional departments
Job Title
Instructional Faculty
Professional Roles
College of Science:Instructional Faculty

Baasansuren Jadamba - bxjsma

RIT Username
bxjsma
Email
bxjsma@rit.edu
Courses Taught This Semester
2185-MATH-741-01;2185-MATH-233-02;2185-MATH-233-02;2185-MATH-741-01;2191-MATH-181-13;2191-MATH-181-13;2191-MATH-181-05;2191-MATH-181-05;
Additional colleges/divisions
Scholarly Publications
Journal Paper
Jadamba, Baasansuren, et al. "Elliptic Inverse Problems of Identifying Nonlinear Parameters." Pure and Applied Functional Analysis 3. 2 (2018): 309-326. Print.
Jadamba, Baasansuren, Akhtar A. Khan, and Miguel Sama. "Stable Conical Regularization by Constructible Dilating Cones with an Application to Lp-constrained Optimization Problems." Taiwanese Journal of Mathematics. (2018): 1-23. Web.
Causa, Antonio, Baasansuren Jadamba, and Fabio Raciti. "A migration Equilibrium Model with Uncertain Data and Movement Costs." Decisions in Economics and Finance 40. 1-2 (2017): 159-175. Print.
Jadamba, Baasansuren, et al. "On Convex Modified Output Least-Squares for Elliptic Inverse Problems: Stability, Regularization, Applications, and Numerics." Optimization 60. (2017): 983-1012. Print.
Jadamba, Baasansuren, et al. "First-Order and Second-Order Adjoint Methods for Parameter Identification Problems with an Application to the Elasticity Imaging Inverse Problem." Inverse Problems in Science and Engineering 25. 12 (2017): 1-21. Print.
Gwinner, Joachim, et al. "Identification in Variational and Quasi-Variational Inequalities." J. Convex Analysis 25. 1-26 (2018): 545-569. Print.
Jadamba, Baasansuren, Massimo Pappalardo, and Fabio Raciti. "Efficiency and Vulnerability Analysis for Congested Networks with Random Data." J. Optim. Theory Appl.. (2018): 1-21. Web.
Faraci, F., B. Jadamba, and F. Raciti. "On Stochastic Variational Inequalities with Mean Value Constraints." J. Optim. Theory Appl. 171. 2 (2016): 675-693. Print.
Jadamba, B., A. Khan, and M. Sama. "Error Estimates for Integral Constraint Regularization of State-Constrained Elliptic Control Problems." Comput. Optim. Appl.. (2016): 1-33. Web.
Jadamba, Baasansuren, et al. "Identification of Flexural Rigidity in a Kirchhoff Plates Model Using a Convex Objective and Continuous Newton Method." Mathematical Problems in Engineering 2015. Article ID 290301 (2015): 11. Web.
Bush, Nathan, et al. "Identification Of A Parameter In Fourth-Order Partial Differential Equations By An Equation Error Approac." Math. Slovaca 65. 5 (2015): 1-13. Print.
Jadamba, Baasansuren and Fabio Raciti. "Variational Inequality Approach to Stochastic Nash Equilibrium Problems with an Application to Cournot Oligopoly." Journal of Optimization Theory and Applications 165. (2015): 1050-1070. Print.
Doyley, Marvin, et al. "A New Energy Inversion for Parameter Identification in Saddle Point Problems with an Application to the Elasticity Imaging Inverse Problem of Predicting Tumor Location." Numerical Functional Analysis and Optimization 35. 7-9 (2014): 984-1017. Print.
Jadamba, Baasansuren, et al. "A New Convex Inversion Framework for Parameter Identification in Saddle Point Problems with an Application to the Elasticity Imaging Inverse Problem of Predicting Tumor Location." SIAM Journal on Applied Mathematics 74. 5 (2014): 1486-1510. Print.
Gibali, Aviv, et al. "Gradient and Extragradient Methods for an Elliptic Inverse Problem of Parameter Identification: A Numerical Study." Indian J. Indust. Appl. Math 4. 1 (2013): 33-51. Print.
Jadamba, Baasansuren and Fabio Raciti. "On the Modelling of some Environmental Games with Uncertain Data." J. of Optim. Theory and Appl 167. (2015): 959-968. Print.
Cahill, Nathan, et al. "A First-Order Adjoint and A Second-Order Hybrid Method for an Energy Output Least Squares for Elastography Inverse Problem." Boundary Value Problems. (2013): 263-277. Web.
Jadamba, Baasansuren, Akhtar A. Khan, and Miguel Sama. "Regularization for State Constrained Optimal Control Problems by Half Spaces Based Decoupling." Systems and Control Letters 61. (2012): 707-713. Print.
Baasansuren, Jadamba, et al. "Proximal Point Methods for the Inverse Problem of Identifying Parameter in Beam Models." Emerging Applications of Wavelet Methods 1463. (2012): 16-38. Print.
Baasansuren, Jadamba and Fabio Raciti. "A Variational Inequality Approach to a Class of Environmental Equilibrium Problems." Applied Mathematics 3. (2012): 1723-1728. Web.
Jadamba, Baasansuren, Akhtar A. Khan, and Miguel Sama. "Generalized Solutions of Quasi Variational Inequalities." Optimization Letters 6. (2012): 1221-1231. Print.
Book Chapter
Strychalski, Wanda, et al. "Fluid Dynamics of Nematocyst Prey Capture." Understanding Complex Biological Systems with Mathematics. Ed. Amy Radunskaya, Rebecca Segal, and Blerta Shtylla. New York, NY: Springer, 2018. 123-144. Print.
Cho, Manki, et al. "First-Order and Second-Order Adjoint Methods for the Inverse Problem of Identifying Nonlinear Parameters in PDEs." Industrial Mathematics and Complex Systems. New York, NY: Springer, 2017. 147-163. Print.
Chugunova, M., et al. "Study of a Mixed Dispersal Population Dynamics Model." The IMA Volumes in Mathematics and its Applications: Numerical Partial Differential Equations and Scientific Computing. Ed. Susanne Brenner. New York, NY: Springer, 2016. 51-77. Print.
Jadamba, B., et al. "Iterative Methods for the Elastography Inverse Problem of Locating Tumors." Essays in Mathematics and its Applications. Ed. T. M. Rassias and P. Pardalos. Cham, Switzerland, NA: Springer, 2016. 101-131. Print.
Jadamba, Baasansuren and Fabio Raciti. "A Stochastic Model of Oligopolistic Market Equilibrium Problems." Optimization in Science and Engineering. Ed. T. M. Rassias, C. A. Floudas, and S. Butenko. Berlin, Germany: Springer, 2014. 263-271. Print.
Jadamba, Baasansuren, Akhtar A. Khan, and Miguel Sama. "Inverse Problems on Parameter Identification in Partial Differential Equations." Mathematical Methods, Models and Algorithms in Science and Technology. Singapore: World Scientific, 2011. 228-258. Print.
Invited Keynote/Presentation
Jadamba, Baasansuren. "Optimization Methods for the Elastography Inverse Problem." Inverse Problems Symposium. Michigan State University. East Lansing, MI. 4 Jun. 2018. Conference Presentation.
Jadamba, Baasansuren. "Minimization of a principal eigenvalue in a mixed dispersal model." Canadian Mathematical Society Winter Meeting. Canadian Mathematical Society. Niagara Falls, Ontario. 3 Nov. 2016. Conference Presentation.
Jadamba, Baasansuren. "First- and second-order adjoint method for parameter identification." Modeling and Optimization: Theory and Applications (MOPTA). Lehigh University. Bethlehem, PA. 17 Aug. 2016. Conference Presentation.
Jadamba, Baasansuren. "Nonlinear Parameter Identification in Variational Problems." 11th AIMS Conference on Dynamical Systems, Differential Equations. American Institute of Mathematical Sciences. Orlando, FL. 3 Jul. 2016. Conference Presentation.
Jadamba, Baasansuren. "Non-smooth Optimization Framework for Elastography Inverse Problem of Tumor Identification." SIAM Conference on Optimization. Society for Industrial and Applied Mathematics. Vancouver, BC. 24 May 2017. Conference Presentation.
Jadamba, Baasansuren. "Mixed Dispersal Model of Population Dynamics." Department of Mathematics and its Applications Colloquium. UNED. Madrid, Spain, Madrid. 4 Jul. 2017. Guest Lecture.
Jadamba, Baasansuren. "Study of a Mixed Dispersal Model of Population Dynamics." Institute of Mathematics Colloquium. Martin-Luther University of Halle-Wittenberg. Halle, Germany, Sachsen-Anhalt. 22 Jun. 2017. Guest Lecture.
Jadamba, Baasansuren. "Stability of an Equation Error Approach for an Inverse Problem." Joint Mathematics Meeting. American Mathematical Society. San Antonio, TX. 10 Jan. 2015. Conference Presentation.
Jadamba, Baasansuren. "Equation Error Approach for Elasticity Imaging Inverse Problem." Modeling and Optimization: Theory and Applications (MOPTA). Lehigh University. Bethlehem, PA. 20 Jul. 2015. Conference Presentation.
Jadamba, Baasansuren. "Minimization of a Principal Eigenvalue of a Mixed Dispersal Model." 22nd International Symposium on Mathematical Programming. Mathematical Optimization Society. Pittsburgh, PA. 13 Jul. 2015. Conference Presentation.
Jadamba, Baasansuren. "An Equation Error Approach for the Elasticity Imaging Inverse Problem." Inverse Problems: Modeling and Simulation. Izmir University. Fethiye, Turkey. 29 May 2014. Conference Presentation.
Baasansuren, Jadamba. "Finite Element Error Estimates for a Phase Field Model for Mixtures." Department Colloquium. University of Catania. Catania, Italy. 7 Mar. 2012. Guest Lecture.
Baasansuren, Jadamba. "Regularization of Stochastic Variational Inequalities and Comparison of an Lp and a Sample-Path Approach." 21st International Symposium on Mathematical Programming. Mathematical Optimization Society. Berlin, Germany. 24 Aug. 2012. Conference Presentation.
Baasansuren, Jadamba. "Regularization of Stochastic Variational Inequalities and Comparison of an Lp and a Sample-Path Approach." Eastern Sectional Meeting. American Mathematical Society. Rochester, NY. 22 Sep. 2012. Conference Presentation.
Jadamba, Baasansuren. "Error Estimates for Modified Output Least Squares for Elliptic Partial Differential Equations." International Congress on Industrial and Applied Mathematics. SIAM. Vancouver Convention Centre, Vancouver, Canada. 18 Jul. 2011. Conference Presentation.
Published Conference Proceedings
Jadamba, Baasansuren and Fabio Raciti. "A Variational Inequality Formulation of a Migration Model with Random Data." Proceedings of the Modeling and Optimization: Theory and Applications. Ed. Martin Takac, Tamas Terlaky. New York, NY: Springer, 2017. Print.
Cho, Manki, et al. "Identification in Mixed Variational Problems by Adjoint Methods with Applications." Proceedings of the Modeling and Optimization: Theory and Applications. Ed. Martin Takac, Tamas Terlaky. New York, NY: Springer, 2017. Print.
Published Article
Eck, Ch., B. Jadamba and P. Knabner. “Error Estimates for a Finite Element Discretization of a Phase Field Model for Mixtures.” SIAM Journal on Numerical Analysis, 47.6 (2010):4429-4445. Print. *
First Name
Baasansuren
Last Name
Jadamba
Phone
585-475-3994
College/Division & Department
Additional departments
Job Title
Instructional Faculty
Professional Roles
College of Science:Instructional Faculty

Moumita Das - modsps

RIT Username
modsps
Email
modsps@rit.edu
Courses Taught This Semester
2185-PHYS-415-01;2185-MATH-790-05;2185-MATH-790-05;2181-MATH-790-04;2181-MATH-790-04;2181-PHYS-214-01;2185-PHYS-415-01;2185-MTSE-790-01;2181-MTSE-790-10;2181-MTSE-790-10;2185-MTSE-790-01;2181-PHYS-214-01;2191-MATH-790-04;2191-MATH-790-04;2191-PHYS-214-01;2191-PHYS-214-01;
Additional colleges/divisions
Scholarly Publications
Journal Paper
Das, Moumita, et al. "Chase and Run Dynamics and Molecular Rupture of Interacting Elastic Dimers." arXiv: 1612.09052. (2016): 1-6. Print.
Das, Moumita, et al. "Dynamic Self-Organization of Microwell-Aggregated Cellular Mixtures." Soft Matter 12. (2016): 5739--5746. Print.
Moumita, Das. "Redundancy and Cooperativity in the Mechanics of Compositely Crosslinked Filamentous Networks." PloS one 7. (2012): 35939. Web.
Invited Keynote/Presentation
Das, Moumita. "The Cell Cytoskeleton as a Composite: Mechanics and Force Transmission." Physical Sciences Oncology Center, Johns Hopkins University. Baltimore, Maryland. 27 Feb. 2013. Guest Lecture.
Das, Moumita. "The Cell Cytoskeleton as a Composite: Mechanics and Force Transmission." Materials Research Science and Engineering Center, Brandeis University. Waltham, Massachussetts. 7 Nov. 2013. Guest Lecture.
Das, Moumita. "Mechanics of Composite Cytoskeletal and Extracellular Networks." Syracuse University, Department of Physics. Syracuse, NY. 5 Dec. 2013. Guest Lecture.
Das, Moumita. "Simulation and Modeling of Biopolymer Networks." Physics of Functional Biological Assemblies: Pushing, Pulling and Sensing. Aspen Center for Physics. Aspen, Colorado. 31 May 2013. Lecture.
Shows/Exhibits/Installations
Das, Moumita. Touchy Feely Life of Cells. 16 Nov. 2013. Rochester Museum and Science Center, Rochester, NY. Performance.
First Name
Moumita
Last Name
Das
Phone
585-475-5135
Programs Taught Under
College/Division & Department
Additional departments
Job Title
Instructional Faculty
Professional Roles
College of Science:Instructional Faculty
College of Science:Associate Professor

Carlos Lousto - colsma

RIT Username
colsma
Email
colsma@rit.edu
Courses Taught This Semester
2185-MATH-790-03;2181-MATH-790-07;2181-ASTP-890-08;2181-ASTP-790-07;2185-ASTP-610-01;2185-ASTP-890-08;2185-ASTP-790-07;2181-MATH-411-01;2181-ASTP-890-08;2181-ASTP-790-07;2185-ASTP-610-01;2185-ASTP-890-08;2185-ASTP-790-07;2181-MATH-411-01;2181-MATH-790-07;2185-MATH-790-03;2195-ASTP-790-07;2188-ASTP-890-07;2188-ASTP-890-07;2188-ASTP-790-07;2188-ASTP-790-07;2191-ASTP-790-07;2191-ASTP-790-07;2191-ASTP-890-08;2191-ASTP-890-08;2191-MATH-326-01;2191-MATH-326-01;2191-MATH-326-05;2191-MATH-326-05;2195-ASTP-890-08;2195-ASTP-890-08;2195-ASTP-790-07;2191-MATH-790-03;2191-MATH-790-03;
Additional colleges/divisions
Scholarly Publications
Journal Paper
Zlochower, Yosef, Marcelo Ponce, and Carlos Lousto. "Accuracy Issues for Numerical Waveforms." Physical Review D86. (2012): 104056. Print.
Lousto, Carlos, et al. "Study of Conformally Flat Initial Data for Highly Spinning Black Holes and their Early Evolutions." Physical Review D85. (2012): 124013. Print.
Ajith, P. and Carlos Lousto. "The NINJA-2 Catalog of Hybrid Post-Newtonian/numerical-relativity Waveforms for Non-precessing Black-hole Binaries." Class.Quant.Grav. 29. (2012): 124001. Print.
Cardoso, Vitor and Carlos Lousto. "NR/HEP: roadmap for the future." Class.Quant.Grav. 29. (2012): 244001. Print.
Lousto, Carlos, et al. "Gravitational Recoil From Accretion-Aligned Black-Hole Binaries." Physical Review D85. (2012): 84015. Print.
Nakano, Hiroyuki, et al. "Intermediate-mass-ratio Black Hole Binaries II: Modeling Trajectories and Gravitational Waveforms." Physical Review D84. (2011): 12400601-12400622. Print.
Lousto, Carlos Oscar and Yosef Zlochower. "Hangup Kicks: Still Larger Recoils by Partial Spin/Orbit Alignment of Black-Hole Binaries." Physical Review Letters 107. (2011): 2311021-2311025. Print.
Nakano, Hiroyuki, et al. "Perturbative Effects of Spinning Black Holes with Applications to Recoil Velocities." Classical and Quantum Gravity 28. (2011): 13400501-13400512. Print.
Zlochower, Yosef, Manuela Campanelli, and Carlos Oscar Lousto. "Modeling Gravitational Recoil Using Numerical Relativity." Classical and Quantum Gravity 28. (2011): 11401501-11401512. Print.
Lousto, Carlos Oscar and Yosef Zlochower. "Modeling Maximum Astrophysical Gravitational Recoil Velocities." Physical Review D83. (2011): 0240031-0240038. Print.
Lousto, Carlos Oscar and Yosef Zlochower. "Orbital Evolution of Extreme-Mass-Ratio Black-Hole Binaries with Numerical Relativity." Physical Review Letters 106. (2011): 0411011-0411014. Print.
Ponce, Marcelo, Carlos Oscar Lousto, and Yosef Zlochower. "Seeking for Toroidal Event Horizons from Initially Stationary BH Configurations." Classical and Quantum Gravity 28. (2011): 14502701-14502718. Print.
Jaramillo, Gabriela and Carlos Oscar Lousto. "Study of Multi Black Hole and Ring Singularity Apparent Horizons." Physical Review D84. (2011): 10401101-10401116. Print.
External Scholarly Fellowships/National Review Committee
10/1/2012 - 9/30/2013
     (XSEDE) is supported by the National Science Foundation
     Amount: 17259113 SU
Invited Keynote/Presentation
Lousto, Carlos. "Binary Black Hole Mergers in Numerical Relativistic Astrophysics." XXVI Texas Symposium on Relativistic Astrophysics. INPE. Sao Paulo, Brazil. 19 Dec. 2012. Conference Presentation.
Lousto, Carlos. "Gravitational Recoil From Black-Hole Binaries." Nishinomiya Yukawa Symposium: New Waves in Gravity and Cosmology. Yukawa Institute. Kyoto, Japan. 5 Dec. 2012. Conference Presentation.
Lousto, Carlos. "Gravitational Recoil From Merging Black-Hole Binaries." Conference: AMS 2012 Eastern Sectional Meeting. RIT. Rochester, NY. 22 Sep. 2012. Conference Presentation.
Lousto, Carlos. "Gravitational Recoil From Accretion-Aligned Black-Hole Binaries." 13th Marcel Grossmann Meeting. Marcel Grossmann Meeting. Stockholm, Sweden. 4 Jul. 2012. Conference Presentation.
Published Article
Zlochower, Yosef, M. Campanelli, C.O. Lousto. “Modeling Gravitational Recoil Using NumericalRelativity.” Physical Review D, 82 (2010): 104057. Web. ≠ «
Lousto, Carlos O., M. Campanelli, Y. Zlochower. “Remnant Masses, Spins and Recoils from the Mergerof Generic Black-Hole Binaries.” Physical Review D, 81 (2010): 084023. Web. ≠ «
Lousto, Carlos O., M. Campanelli, Y. Zlochower. “Remnant Masses, Spins and Recoils from the Merger of Generic Black-Hole Binaries.” Classical Quantum Gravity, 27 (2010):114006. Print. ≠ «
Lousto, Carlos O.,H. Nakano, Y. Zlochower, M. Campanelli. “Intermediate Mass Ratio Black HoleBinaries: Numerical Relativity meets Perturbation Theory.” Physical Review Letters, 104 (2010): 211101. Web. ≠ «
Campanelli, Manuela, C.O. Lousto, B.C Mundim, H. Nakano, Y. Zlochower, Hans-Peter Bischof. “Advances in Simulations of Generic Black-HoleBinaries.” Classical Quantum Gravity, 27 (2010): 084034. Print. ≠ «
Lousto, Carlos O., H. Nakano, Y. Zlochower, M. Campanelli. “Intermediate mass-ratio black hole binaries: Intertwining numerical and perturbative techniques.” Physical Review D, 82 (2010): 104057. Web. ≠ «
Nakano, Hiroyuki, Manuela Campanelli, Carlos Lousto, and Yosef Zlochower. “Perturbative effects of spinning black holes with applications to recoil velocities.” Proceedings of theTheory Meets Data Analysis at Comparable and Extreme Mass Ratios Conference, 20-26 June 2010. n.p. Web. ≠ «
Formal Presentation
Lousto, Carlos.“Extreme-Mass-Ratio-Black-Hole-Binary Evolutions with Numerical Relativity.” 20th Annual Midwest Relativity Meeting. Guelph, Canada. 5-6 Nov. 2010. Presentation.
Lousto, Carlos.“Statistical Studies of Spinning Black-Hole Binaries.” American PhysicalSociety Meeting. Washington, DC.13-16 Feb. 2010. Presentation.
First Name
Carlos
Last Name
Lousto
Phone
585-475-2219
Rank
College/Division & Department
Additional departments
Job Title
Instructional Faculty
Professional Roles
College of Science:Instructional Faculty
College of Science:Professor

Matthew Hoffman - mjhsma

RIT Username
mjhsma
Email
mjhsma@rit.edu
Courses Taught This Semester
2185-IMGS-890-26;2188-IMGS-699-09;2188-IMGS-699-09;2185-IMGS-699-04;2181-IMGS-699-08;2181-IMGS-890-26;2185-MATH-790-02;2191-MATH-602-01;2191-MATH-602-01;2181-MATH-606-01;2181-MATH-791-01;2181-MATH-602-01;2181-MATH-790-01;2181-MATH-790-14;2185-MATH-607-01;2181-MATH-606-01;2181-MATH-791-01;2181-MATH-602-01;2181-MATH-790-01;2181-MATH-790-14;2185-MATH-607-01;2185-MATH-790-02;2181-IMGS-890-26;2181-IMGS-699-08;2185-IMGS-699-04;2185-IMGS-890-26;2188-IMGS-890-14;2188-IMGS-890-14;2191-MATH-606-01;2191-MATH-606-01;2191-MATH-790-06;2191-MATH-790-06;
Additional colleges/divisions
Scholarly Publications
Journal Paper
Uzkent, Burak, Matthew J. Hoffman, and Anthony Vodacek. "Spectral Validation of Measurements in a Vehicle Tracking DDDAS." Procedia Computer Science 51. (2015): 2493—2502. Web.
Hoffman, Matthew J., et al. "Feature Matching with an Adaptive Optical Sensor in a Ground Target Tracking System." IEEE Sensors Journal 15. 1 (2015): 510--519. Print.
Hoffman, Matthew J., et al. "Integrating Hyperspectral Likelihoods in a Multi-dimensional Assignment Algorithm for Aerial Vehicle Tracking." IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing. (2015): --. Print.
Greybush, S. J., et al. "Ensemble Kalman Filter Data Assimilation of Thermal Emission Spectrometer Temperature Retrievals into a Mars GCM." Journal of Geophysical Research: Planets 117. E11 (2012) Web.
Hoffman, M. J., et al. "An Advanced Data Assimilation System for the Chesapeake Bay: Performance Evaluation." J. Atmos. Oceanic Technol. 29. (2012): 1542-1557. Print.
Greybush, Steven J., et al. "Identifying Martian atmospheric instabilitiesand their physical origins using bred vectors." Quarterly Journal of the Royal Meteorological Society. (2012) Print.
Urquhart, E., et al. "Remotely Sensed Estimates of Surface Salinity in the Chesapeake Bay." Remote Sensing of the Environment 23. (2012): 522-531. Print.
Hoffman, M. J., et al. "Assessment of Mars Atmospheric Temperature Retrievals from the Thermal Emission Spectrometer Radiances." Icarus 220. 2 (2012): 1031-1039. Print.
Published Conference Proceedings
Uzkent, Burak, Matthew J. Hoffman, and Anthony Vodacek. "Efficient integration of spectral features for vehicle tracking utilizing an adaptive sensor." Proceedings of the SPIE Conference on Video Surveillance and Transportation Imaging Applications. Ed. Robert Loce and Eli Saber. San Francisco, CA: n.p., 2015. Web.
Uzkent, Burak, et al. "Background image understanding and adaptive imaging for vehicle tracking." Proceedings of the SPIE Conference on Airborne Intelligence, Surveillance, Reconnaissance (ISR) Systems and Applications XII. Ed. Daniel J. Henry, et al. Baltimore, MD: n.p., 2015. Web.
Hoffman, Matthew J. "Spectral Validation of Measurements in a Vehicle Tracking DDDAS." Proceedings of the Procedia Computer Science. , Reykjavik: , 2015. Print.
Hoffman, Matthew J. "Background Image Understanding and Adaptive Imaging for Vehicle Tracking." Proceedings of the SPIE Defense + Security. Baltimore, Maryland: SPIE, 2015. Print.
Hoffman, Matthew J. "Efficient Integration of Spectral Features for Vehicle Tracking Utilizing an Adaptive Sensor." Proceedings of the IS&T/SPIE Electronic Imaging 2015. San Francisco, California: SPIE, 2015. Print.
Uzkent, Burak, et al. "Feature Matching and Adaptive Prediction Models in an Object Tracking DDDAS." Proceedings of the Procedia Computer Science. n.p., 2013. Print.
Invited Keynote/Presentation
Hoffman, Matthew J. "Ground Target Tracking Utilizing DDDAS Based Control of an Adaptive Optical Sensor." IEEE Geoscience and Remote Sensing Joint Chapter Meeting. IEEE Geoscience and Remote Sensing Joint Chapter. Rochester, NY. 31 Mar. 2015. Lecture.
First Name
Matthew
Middle Name
Joseph
Last Name
Hoffman
Phone
585-475-4209
College/Division & Department
Additional departments
Job Title
Instructional Faculty
Professional Roles
College of Science:Associate Professor
College of Science:Instructional Faculty

Admission Requirements

To be considered for admission to the Ph.D. program in mathematical modeling, candidates must fulfill the following requirements:

  • Complete a graduate application.
  • Hold a baccalaureate degree (or equivalent) from an accredited university or college.
  • Submit official transcripts (in English) of all previously completed undergraduate and graduate course work.
  • Have a minimum cumulative GPA of 3.0 (or equivalent) in a primary field of study.
  • Submit scores from the GRE.
  • Submit a personal statement of educational objectives and research interests.
  • Submit a current resume or curriculum vitae.
  • Submit a minimum of two letters of recommendation from academic or professional sources.
  • International applicants whose native language is not English must submit scores from the TOEFL, IELTS, or PTE. A minimum TOEFL score of 100 (internet-based) is required. A minimum IELTS score of 7.0 is required. The English language test score requirement is waived for native speakers of English or for those submitting transcripts from degrees earned at American institutions.

Mathematical modeling encompasses a wide variety of scientific disciplines, and candidates from diverse backgrounds are encouraged to apply. If applicants have not taken expected foundational course work, the program director may require the student to successfully complete foundational courses prior to matriculating into the Ph.D. program. Typical foundation course work includes calculus through multivariable and vector calculus, differential equations, linear algebra, probability and statistics, one course in computer programming, and at least one course in real analysis, numerical analysis, or upper-level discrete mathematics.

Learn about admissions and financial aid 

Additional Info

Financial aid, scholarships, and assistantships

Graduate assistantships and tuition remission scholarships are available to qualified students. Applicants seeking financial assistance must submit all application documents to the Office of Graduate and Part-time Enrollment. Please contact the office for current application materials and deadlines. Students whose native language is not English are advised to obtain as high a TOEFL or IELTS score as possible if they wish to apply for a teaching or research assistantship. These candidates also are encouraged to take the Test of Spoken English in order to be considered for financial assistance.

Residency

All students in the program must spend at least two consecutive semesters (summer excluded) as resident full-time students to be eligible to receive the doctoral degree.

Maximum time limitations

University policy requires that doctoral programs be completed within seven years of the date of the student passing the qualifying exam. All candidates must maintain continuous enrollment during the research phase of the program. Such enrollment is not limited by the maximum number of research credits that apply to the degree.