Aleks Donev's expertise is in the areas of applied and computational mathematics, computational materials science, and computational physics. He works on developing algorithms that accelerate or systematically coarse-grain traditional methods such as Molecular Dynamics or (Kinetic) Monte Carlo, as well as multi-scale (hybrid) methods combining particle with stochastic (fluctuating) coarse-grained models. His present focus is on fluid dynamics at small scales, and in particular, fluctuating hydrodynamics and colloidal suspensions.
Miranda Holmes-Cerfon is applied mathematician, who uses and develops tools to address problems in science and engineering. Her mathematical work draws on many areas of pure and applied mathematics, but areas of particular interest include stochastic analysis, statistical mechanics, computational geometry, and rigidity theory. Her past areas of application include materials science, fluid dynamics, soft-matter physics, geophysics, and oceanography. Her curent work is mainly focused on building the theoretical and computational tools to study nano- or micro-scale particles or materials building blocks, with the aim of identifying which structures or materials can be assembled efficiently.
Charles S. Peskin
Charlie Peskin is a world leader in mathematical modeling and computer simulation, with special expertise on applications in the biomedical sciences. He is the creator of the
immersed boundary (IB) method, which has grown from a method to study the fluid dynamics of heart valves and cardiac flows to a generally useful tool for fluid-structure interactions. In addition to fluid interactions, the heart modeling effort now encompasses realistic fiber architecture of the muscular heart walls and electro-mechanical couplings. The IB method has also been applied to small-scale phenomena, such as the dynamics of bacterial flagella and the collective motion of micro-swimmer suspensions. Beyond IB, recent studies in Peskin's group pertain to stochastic gene expression, the mammalian circadian clock, the role of flexibility in chromosome transport, among many others.
Leif Ristroph is an experimental physicist and applied mathematician who specializes in fluid dynamics, with a particular emphasis on fluid-structure interactions as applied to biological and geophysical flows. His biophysical work includes studies of the aerodynamics and stabilization of insect flight as well as the hydrodynamics of schooling and flow-sensing in swimming fish. Relevant to geophysical flows, he is interested in problems ranging from instabilities of interfacial flows to the evolution of shape during fluid mechanical erosion.
Esteban G. Tabak
Esteban Tabak works in various areas of applied mathematics, including Fluid Dynamics, Data Science and Optimization. His recent work in fluid dynamics has been mostly concerned with the physical and numerical modeling of large-scale flows applied to understanding the dynamics of the Atmosphere and the Ocean. In data science, he has developed new tools in density estimation and optimal transport and applied them to general problems in classification, regression, clustering and time-series analysis. In optimization, he has developed a new general methodology to solve constrained optimization problems, both continuous and discrete, through a dynamical two-person game with evolving strategies represented by the primal and dual variables.
Charles Pueltz is currently a postdoc working with Boyce Griffith in his Cardiovascular Modeling and Simulation Lab. He will join the RTG as a Courant Instructor in the Fall of 2018. His research interests are in mathematical modeling and numerical methods for partial differential equations. He is particularly interested in research questions related to cardiovascular mechanics and fluid dynamics.
Pejman Sanaei is a Courant instructor working on mathematical modleling and simulation in the Applied Math Lab (AML). He has expertise in fluid mechanics, deterministic and stochastic approaches to mathematical modeling, tissue engineering, applications of mathematics to industry and in particular his dissertation topic was mathematical modeling of membrane filtration.
Tristan Goodwill is a PhD student advised by Miranda Holmes-Cerfon. He is interested in studying systems arising from statistical mechanics and materials science through the tools of stochastic analysis and simulations. Specifically, his current work aims to better understand the behaviour of DNA-coated colloidal particles in a fluid.
Jason Kaye is a PhD student working with Leslie Greengard. His interests are in developing fast numerical algorithms to solve PDEs and integral equations arising in computational physics problems.
Karina Koval is PhD candidate advised by Georg Stadler. Her primary interests include numerical methods, optimization under uncertainty and uncertainty quantification. Currently her research involves inverse problems governed by partial differential equations.
Anthony S Trubiano
Anthony Trubiano is a PhD student working with Miranda Holmes-Cerfon. He is interested in the mathematical modeling of physical systems in various fields of science and the methods of applied and computational mathematics in analyzing them. Particular interests include stochastic analysis, statistical mechanics, Monte Carlo methods, and other numerical solution algorithms. He is currently studying the behavior of hard sphere packings in the presence of a long range potential.
Undergraduate Students (participated in AM-SURE, 2018)
As a math major on the pre-health track, I am interested in how mathematical modeling of physiological systems can help determine the most efficient courses of treatment. I am particularly interested in the human cardiac system. This summer, I am working with Professor Peskin on creating a robust, fluid dynamics model of fetal congenital heart disease, which will hopefully be able to demonstrate how surgical corrections are able to resolve the disease's complications.
Ling Lan is a senior student who is major in Honors Mathematics and minor in computer science. She is interested in numerical methods and in mathematical modeling of various fields. In summer 2018, Ling is working with Miranda Holmes-Cerfon on modeling and simulating self-folding origami.
Nick Lewis is a senior majoring in Math at the College of Arts & Sciences (CAS). His primary interests include fluid dynamics and biophysics. Currently, he is working under the supervision of Professor Leif Ristroph to investigate the existence of stable points in migratory bird flight formations.
As a mathematics major and pre-medical student, I am particularly interested in how mathematics can be applied to biology through the use of mathematical models and simulations. I am currently working on creating a model for motor neuron stimulation of muscle contractions and the force that is produced as a result. Through the use of ODEs to describe calcium dynamics and muscle force generation, coupled to action potentials in the neuromuscular junction, I hope to not only model this as a healthy process but also model where problems occur in a variety of neuromuscular diseases.
I'm Guanhua, a math major senior. My project aims to simulate an experiment, conducted by AML, in investigating a fluid dynamics phenomenon ("unidirectional flow") that observed in avian respiratory systems. By simulations we wish to understand more about the phenomenon, and extend those understandings to similar fields. I'm advised by Prof. Charles Peskin and the AML (Applied Mathematics Lab).
Tianrui Xu is an Undergraduate student advised by Charles S. Peskin. Her interests are in mathematical modeling and probability theory. She is currently working on the mathematical models for red blood cell and its exocytosis process.
Peilin Zhen is a rising junior working with Dimitris Giannakis. Her interests lie in the interdisciplinary applications of data science and machine learning. Currently she is working on observing and characterizing the pattern of climate phenomena such as El Nino Southern Oscillation using Reproducing Kernel Hilbert Space techniques to identify coherent temporal patterns in sea surface temperature data.