Industry members have submitted proposals for current technical problem that is seen as an unsolved challenge to their industry. These problems will be studied during the workshop in working sessions with Harvard faculty and student researchers. The outcome of the study group will be a brief technical presentation (e.g. PowerPoint) summarizing the results achieved during this workshop.
Predicting the whirling behavior of a rotating cylinder
Suggested by Jahir Pabon
Consider a slender elastic cylinder (L ~ 60*Do), suspended horizontally with bearings at the ends, and passing through a plate with a cylindrical hole. Assume a configuration with the cylinder centered in the hole in the static configuration (a possible suggestion is to neglect the effect of gravity as a first step). Assume the cylinder to have a perfectly cylindrical outer geometry, however not perfectly uniform mass distribution, so that the center of mass is not aligned with the geometric center of the cylinder. Assume an external torsional source forces the cylinder into rotation. Due to the uneven distribution of mass, the cylinder will exhibit a “forward whirling” behavior, in which the geometric center of the cylinder will turn around in the same direction as the rotation of the cylinder. As the amplitude of that forward whirling increases (usually as the rotation speed becomes closer to the resonant frequency of the suspended cylinder), its outer surface will start to interact/interfere/collide with the inner wall of the hole in the plate. Under some conditions, for instance when the friction coefficient between the cylinder and the plate is high enough, after some transient, seemingly chaotic behavior, the cylinder will end up whirling backwards, that is, rolling on the inner wall of the hole so that its center is turning in a direction opposite to the rotation of the cylinder.
We are able to run time transient finite difference simulations of this problem, which can reasonably predict the behavior observed in lab experiments. However, those simulations are time consuming, and do not necessarily lead to prediction of possible behavior under slightly modified parameters (such as friction, speed of rotation, etc).
What is wanted is some sort of solution of the problem that can give a “reasonable” prediction of the behavior, e.g. whether the cylinder will experience pure forward whirling (for instance in the absence of friction it will purely slide on the inner wall), backward whirling, or “something in between”.
Modeling water transport trough stratum corneum at low humidity
Suggested by Eugene Pashkovski and Alex Lips
The mammalian skin separates the organism from the environment. The top layer of skin, epidermis prevents the inner body from chemicals, bacteria, and controls the water transport across the skin. The water gradient across stratum corneum (the top layer of epidermis) depends on the environmental humidity. When the gradient increases (humidity decreases), the water loss also increases provided that the permeability of corneum remains unchanged. However, there are several possible mechanisms that may account for the decrease in permeability at low humidity and play a role in adaptation of stratum corneum to the dry environment. These mechanisms are purely hypothetical and were not disclosed in the literature.
The permeability of stratum corneum is defined by two subsystems, cornified keratinous cells (corneocytes) and lipid extracellular matrix (LM). Corneocytes have porous structure filled with water solution of amino acids. As water evaporates, this solution becomes very viscous so the water diffusion slows down. Both, the geometry of porous structures in corneocytes and viscosity-humidity relationship of solutions are known.
LM becomes less permeable to water due to the decrease in the bilayer thickness. There are several models in the literature that relate lipid permeability with the bilayer organization.
We assume that stratum corneum may respond rapidly on sudden environmental changes, i.e. the transient behavior of skin is controlled by the negative feedback between the water gradient and permeability. It is interesting to model the transient response and find the critical parameters that control the proposed mechanism.
Performance comparison of extended and unscented Kalman filters
Suggested by J. Ashmore
In the four decades since Kalman first proposed his Kalman filtering has become a well-established method that is used to reduce noise in a wide variety of applications. More sophisticated approaches that build on the basic principles of the Kalman filter, included extended  and unscented [3,4] versions, have been developed in order to address nonlinear problems. While the flexibility of Kalman filters is a significant benefit, it is important to choose the filter design carefully for a given application in order that reliable and robust results are achieved.
TIAX is in the process of developing Kalman filters for orientation sensors that incorporate two types of sensors with different noise characteristics. The state equation is nonlinear and therefore either an extended or an unscented Kalman filter must be used. An important set of questions concern:
TIAX will provide a sample data set to use as a benchmark for the performance of the different filters developed. The results will assist us in our efforts to design and implement the filter that best matches our performance requirements.
- In the scenarios we are concerned with, is the performance of an unscented Kalman filter significantly superior to that of an extended Kalman filter?
- If so, is the performance improvement general to a variety of different types of noise?
- For given input noise levels, can we predict the reduction in noise that the different types of filter can provide?
- What are the differences in computational efficiency of the different types of filters?
Hydrodynamic dispersion in a Channel
Suggested by Pabitra N. Sen
• On the Dispersion of a Solute in a Fluid Flowing Through a Tube
• Experimental Characterization of Hydrodynamic Dispersion in Shallow Microchannels
• Hydrodynamic Dispersion in Shallow Microchannels: the Effect of Cross-Sectional Shape
Dispersions of strongly interacting particles
Proctor and Gamble
Suggested by Matt Lynch