TBA

A Lagrangian Vortex Method for Desktop Simulation of Rotor-blade Flows

04/25/2018 - 4:15pm
04/25/2018 - 5:15pm
Speaker: 
Adrin Gharakhani
Abstract: 

There has been significant interest and research activity in the past decade to develop robust methods for simulation of unsteady vortex dominated flow about and due to rotor-blades, not only in the context of traditional helicopters, but more recently for the purpose of design and optimization of wind turbines, as well as multi-copter drones and advanced VTOL (Vertical Take-Off and Landing) aircraft. To this end, flow simulation via traditional low-order grid-based Computational Fluid Dynamics (CFD) methods has proven to be very challenging and highly inefficient, because (1) they suffer from high numerical diffusion, which rapidly dissipates the turbulent vorticity generated by the rotating blades (often within just 2~3 blade rotations); and (2) meshing is often complicated and/or very time consuming, especially due to the relative motion of the blades with respect to each other and stationary objects. To address these challenges, high-order solvers with adaptive mesh refinement are being developed by many researchers.  An alternative approach is to use the Lagrangian vortex particle method (LVPM) – a solution-adaptive meshless method which discretizes the vorticity transport equivalent of the Navier-Stokes equations. In this approach, the Lagrangian evaluation of convection eliminates numerical diffusion and, hence, maintains the compact nature of the blade-induced wake vortices for long distances and times. Further, LVPMs are meshless and obviate the need for volumetric meshing altogether, requiring the meshing of only the boundaries of the objects (and the boundary layer if ultra-high-accuracy simulation is desired). Finally, since LVPMs discretize the vorticity field, the computational domain is compact, often reducing the problem size by 1~2 orders of magnitude compared to traditional CFD.

This presentation will provide a brief, yet comprehensive, introduction to the various computational aspects of developing a robust, high-fidelity LVPM for simulation of unsteady laminar and turbulent vortex dominated flows. Discussion will then focus on our group’s recent activity in modeling and simulation of rotor-blade flows. Validation benchmark data using isolated rotors in hover and forward-flight conditions, as well as preliminary simulation results for a new complex VTOL aircraft design will be presented.

Where: 
Kravis 62, CMC

Geometric Properties of Noncommutative Symmetric Spaces of Measurable Operators and Unitary Matrix Ideals

02/07/2018 - 4:15pm
02/07/2018 - 5:15pm
Speaker: 
Anna Kaminska (U of Memphis)
Abstract: 

This is a survey lecture presenting a number of geometric properties of  noncommutative symmetric spaces of measurable operators $E\Mtau$ and unitary matrix ideals $C_E$, where $\M$ is a von Neumann algebra with  a semi-finite, faithful  and normal trace $\tau$, and  $E$ is a (quasi)Banach function and a sequence lattice, respectively. We provide   auxiliary  definitions, notions,  examples and we discuss a number of properties  that are most often used in studies  of local and global geometry of (quasi) Banach spaces.  We  interpret  the general spaces $E\Mtau$  in the case when $E=L_p$ obtaining $L_p\Mtau$ spaces, and in the case when $E$ is a sequence space we  explain how the unitary matrix space $C_E$ can be in fact identified with the  symmetric  space of measurable operators $G\Mtau$ for some Banach function lattice $G$.  We present the results on (complex) extreme points, (complex) strict convexity, strong extreme points and midpoint local uniform convexity, $k$-extreme points and $k$-convexity,  (complex or local) uniform convexity, smoothness and strong smoothness, (strongly) exposed points, (uniform) Kadec-Klee properties, Banach-Saks properties, Radon-Nikod\'ym property and stability in the sense of Krivine-Maurey. We also present some open problems.

Where: 
Freeberg Forum, LC 62, Kravis Center, CMC

field meeting

01/17/2018 - 4:15pm
01/17/2018 - 5:15pm
Speaker: 
field meeting
Abstract: 

Please come to discuss course offerings and other synergistic items. 

Where: 
HMC SkyCube (Shanahan 3460)

A Moment Closure Technique for a Stochastic Predator-Prey Model

11/08/2017 - 4:15pm
11/08/2017 - 5:15pm
Speaker: 
Jenny Switkes (Cal Poly Pomona)
Abstract: 
The classical deterministic Lotka-Volterra predator-prey model famously leads to closed curves in the predator-prey phase plane. A stochastic version of this model has the form of a simple birth-death process, with the expected values governed by a system of differential equations almost identical in form to the deterministic system, the difference in rate function for each species being proportional to the time-dependent covariance of the populations of the two species. We explore the impact of this covariance term, using a moment closure technique to obtain a closed system of differential equations for the expected values, variances, and covariance of the populations.  This talk will be accessible to students with a background in differential equations; some experience with probability is helpful but not required.
 
Where: 
Argue Auditorium, Millikan, Pomona College

Model Theory and Continuous Logic

10/25/2017 - 4:15pm
10/25/2017 - 5:15pm
Speaker: 
Victoria Noquez (HMC)
Abstract: 

Do you think that considering the abstract notion of a vector space is more fun than doing computations with matrices? Have you ever wondered how you can make that even more abstract? Are you now wondering why anyone ever would?  In this talk we will discuss the kinds of questions which model theorists seek to answer, some applications of these types of results to other branches of math, and ways in which we can generalize the ordinary framework of classical logic to allow for an even wider variety of applications.

 

Where: 
Argue Auditorium, Millikan, Pomona College

Etudes of Spectral Theory

10/18/2017 - 4:15pm
10/18/2017 - 5:15pm
Speaker: 
Victor Ivrii (University of Toronto, visiting Caltech now)
Abstract: 

I briefly describe five old but still actively explored problems of the Spectral Theory of Partial Differential Equations

1.  How eigenvalues are distributed (where eigenvalues often mean squares of the frequencies in the mechanical or electromagnetic problems
or energy levels in the quantum mechanics models) and the relation to the behaviour of the billiard trajectories.
2.  Equidistribution  of eigenfunctions and connection to ergodicity of billiard trajectories
(a quantum chaos and  a classical chaos).

3.  Can one hear the shape of the drum?
4.  Nodal lines and Chladni plates.
5.  Strange spectra of quantum systems.

Where: 
Argue Auditorium, Millikan, Pomona College

Trust your gut: the physics and mathematics behind maintenance of the gastric pH gradient.

10/11/2017 - 4:15pm
10/11/2017 - 5:15pm
Speaker: 
Owen Lewis (U of Utah )
Abstract: 

The gastric mucus layer is widely recognized to serve a protective function, shielding your stomach wall from the extremely low pH and digestive enzymes present in the stomach lumen. Often described as a "diffusion barrier," the mucus is believed to hinder the transport of small diffusive species from the stomach interior (lumen), to the wall (mucosa). However, there is no consensus on the mechanism by which the mucus layer hinders lumen-to-wall transport while allowing acid and enzymes secreted from the mucosa unimpeded transport to the lumen. Using simple physical principles, we develop a mathematical description of electro-diffusion within the stomach, and use it to test physiological hypotheses that are beyond current experimental techniques. Furthermore, we explore what regulatory mechanisms are necessary to segregate an acidic stomach interior from a neutral stomach wall. 

Where: 
Argue Auditorium, Millikan, Pomona College

seminar canceled

10/07/2010 - 4:15pm
10/07/2010 - 5:15pm
Speaker: 
Mark Hansen, UCLA
Abstract: 

TBA

Where: 
Harvey Mudd College 3rd floor Sprague. Refreshments at 4pm.
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