Courses taught at Northwestern
- ES_APPM 311: Methods of Applied Mathematics
Ordinary differential equations; Sturm-Liouville theory, properties of special functions, solution methods including Laplace transforms. Fourier series: eigenvalue problems and expansions in orthogonal functions. Partial differential equations: classification, separation of variables, solution by series and transform methods. - MATH 228: Multiple Integration and Vector Calculus
Cylindrical and spherical coordinates, double and triple integrals, line and surface integrals. Change of variables in multiple integrals; gradient, divergence, and curl. - ES_APPM 495 Special topics: Theory of Soft and Biological Matter
Soft matter (aka complex fluids) comprise a large class of microstructured materials: from biological membranes to colloidal suspensions. This course aims to bridge the physical chemistry, mechanics and mathematics perspectives in the study of these systems. Since the field is huge, topics will vary from year to year. This year offering will likely focus on interfaces. The question we will explore is “How do interfaces “shape” soft matter, especially out of equilibrium? - ES_APPM 495 Special Topics: Soft and Active Matter
Two module sequence:
First module focuses on the modeling of cell mechanics: Cells and cellular organelles are enveloped by membranes made of lipid bilayers. In this course, we discuss the remarkable mechanical properties of the lipid bilayer (large lateral stability, fluidity, small resistance to bending) and model their role in shaping cells (e.g., why is the red blood cell a biconcave disk?) and in processes such as membrane remodeling and mechanosensing. Topics include geometry of surfaces, Monge parametrization, membrane curvature elasticity, Helfrich theory, the shape equation of vesicles, thermal shape fluctuations.
The second module focuses of the modeling of active fluids: Flocks of birds and schools of fish, are familiar examples of emergent collective behavior, where interactions between self-driven (active) individuals lead to coherent motion (flow) on a scale much larger than the isolated unit. In recent years, similar phenomena have been observed with active micro-units such as bacteria, chemically-activated motile colloids, even microtubule–kinesin bundles (active nematics). This course discusses the hydrodynamics of microswimmers (bacteria, motile colloids). Topics include Stokes equation, scallop theorem, multipole expansion, rheology of active suspensions, active turbulence
Past teaching:
Dartmouth College
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Engs34 |
Fluid Mechanics Junior-level fluid mechanics course. Topic include hydrostatics; mass, momentum, and energy conservation; control volume analysis; Navier-Stokes equations; viscous flow in pipes; lift and drag; compressible flow; and open-channel flows. Laboratory and project |
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Engs30/Phys30 |
Biological Physics (new course) Sophomore-level course introducing physics and engineering approaches to analyze biological problems. Topics include the architecture of biological cells, molecular motion, entropic forces, enzymes and molecular machines, and nerve impulses. |
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Engs156
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Heat, mass, and momentum transfer Advanced undergraduate/beginning graduate course on transport phenomena |
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Engg164 |
Cellular and molecular biomechanics (new course) Advanced undergraduate/beginning graduate course on the engineering principles of cell design. Topics include elasticity of biopolymers and biomembranes, rheology of cytoskeletal components, molecular motors, cell motility. The course connects cell mechanics to micro- and nano- technology. |
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Engs199-02 |
Micro-hydrodynamics (new course) Graduate level course in microscale flows. Topics include Stokes flow, lubrication theory, free-surface flows, hydrodynamic stability, rheology of suspensions. |
Brown University
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ENGN0810
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Fluid Mechanics Junior-level fluid mechanics course. Topic include hydrostatics; mass, momentum, and energy conservation; control volume analysis; Navier-Stokes equations; viscous flow in pipes; lift and drag; compressible flow; and open-channel flows. Laboratory and project |
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ENGN2920 |
Complex fluids: particles and interfaces (new course) Graduate level course introducing disperse systems (colloidal suspensions, emulsions, surfactant solutions, blood) with special attention to the thermodynamics and mechanics of interfaces. The course bridges the physico- chemical and mechanical perspectives in the study of structured fluids |
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ENGN2760
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Heat and mass transfer Graduate level course providing an unified study of momentum, heat and mass transfer; kinetic theory of transport properties; scaling and order-of-magnitude concepts; analytical and approximate solutions to the equations of change; forced and natural convection; radiation; diffusion in mixtures; simultaneous momentum, heat and mass transfer; Taylor dispersion; transport in electrolyte solutions; special topics (e.g., transport at interfaces, porous media) |
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ENGN 2820 |
Fluid Mechanics II This is the second part of a two-semester graduate course following APMA2410/ENGN2810 taught in the Fall. It covers topics from incompressible, Newtonian flows (Stokes flow, lubrication theory, free-surface flows, hydrodynamic stability), electrokinetics, geophysical fluid dynamics, and if time permits explores some more specialized topics of current research interest. The emphasis is on basic physics, scaling and nondimensionalization, and approximations that can be used to obtain analytical solutions. |
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ENGN 0040 |
Dynamics and Vibrations Study of the kinematics and dynamics of particles and rigid bodies. Principles of motion of mechanical systems. Concepts of inertia, work, kinetic energy, linear momentum, angular momentum, and impact. Applications to engineering systems, satellite orbits, harmonic vibrations of one and two degree of freedom systems. Lectures, recitations, and laboratory. |
Lecture Videos
Invited talk at the KITP Program: The Physics of Elastic Films: from Biological Membranes to Extreme Mechanics (May 17 – Jun 18, 2021)
Membrane viscosity effects on the dynamics of fluid bilayers
Lecture at the BIRS workshop on Complex Creeping Fluids: Numerical Methods and Theory, Oaxaca (Mexico) Oct 1-6, 2017
Complex dynamics of soft microparticles in flow and electric fields.
Invited talk at the IMA workshop on Electrohydrodynamics and Electrodiffusion in Material Sciences and Biology, March 12-16, 2018
Electrohydrodynamic instabilities of viscous drops in strong electric fields.