A strain model for piezoelectric materials operating in highly hysteretic regimes

Speaker: 

Zhengzheng Hu

Institution: 

NC State

Time: 

Monday, November 14, 2011 - 4:00pm

Location: 

RH 306

Piezoelectric materials exhibit hysteresis in the field-strain relation at
essentially all drive levels. Furthermore, this nonlinear relation is
dependent upon both prestresses and dynamic stresses generated during
employment of the materials. The accurate characterization of this nonlinear
and hysteretic material behavior is critical for material characterization,
device design, and model-based control design. In this talk, we will
discuss the characterization of hysteresis using the homogenized energy
model (HEM) framework. At the mesoscale, energy relations characterizing
field and stress-dependent 90 and 180 degree switching are used to develop
fundamental kernels or hysterons. Material and field nonhomogeneities are
subsequently incorporated by assuming that certain parameters are
manifestations of underlying densities. This yields a macroscopic model
that accurately characterizes the fundamental material behavior yet is
sufficiently efficient for optimization and control implementation.
Attributes of the model will be illustrated through comparison to
experimental data.

Patient-calibrated simulation of ductal carcinoma in situ (DCIS): a small step from the blackboard towards the bedside

Speaker: 

paul macklin

Time: 

Monday, November 21, 2011 - 4:00pm

Location: 

RH 306

Ductal carcinoma in situ (DCIS)--a type of breast cancer whose growth
is confined to the duct lumen--is a significant precursor to invasive
breast carcinoma. DCIS is commonly detected as a subtle pattern of
calcifications in mammograms. Radiologic imaging (including
mammography) is used to plan surgical resection of the tumor
(lumpectomy), but multiple surgeries are often required to fully
eliminate DCIS. On the other hand, pathologists use pre-surgical
biopsies to stage the DCIS, assess its metastatic potential, and
choose adjuvant therapies. There is currently no technique to combine
these data to improve surgical and therapeutic planning. Mechanistic,
patient-tailored computational models may provide such a link between
multiple data types. In this talk, we focus on developing and
calibrating biologically-grounded mathematical models to individual
patients, encouraging (and validated!) results in quantitatively
predicting clinical progression, the implications for making and
quantitatively testing biological hypotheses, and the role of
mathematical modeling in facilitating a deeper understanding of
pathology and mammography.

Speaker: 

Paul Macklin

Institution: 

USC

Time: 

Monday, November 14, 2011 - 12:00pm

Location: 

RH 306

Integrable systems and invariant curve flows in certain geometries

Speaker: 

Professor Changzheng Qu

Institution: 

Northwestern University in Xian, China

Time: 

Tuesday, November 29, 2011 - 4:00pm

Location: 

RH 306

In this talk, the relationship between integrable systems and invariant curve flows is studied. It is shown that many integrable systems including the well-known integrable equations and Camassa-Holm type equations arise from the non-stretching invariant curve flows in Klein geometries. The geometrical formulations to some properties of integrable systems are also given.

The two-variable approach to evaluating the derivative of a p-adic L-function

Speaker: 

Ralph Greenberg

Institution: 

University of Washington

Time: 

Thursday, October 20, 2011 - 3:00pm

Location: 

RH 306

The p-adic L-function attached to an elliptic curve with split, multiplicative reduction at the prime p will vanish at s=1. This is an example of what we call a "trivial zero." This talk will outline the way that Glenn Stevens and I proved a formula for the derivative at s=1 for that function.

Analytic quasi-periodic Schr\"odinger operators - Recovery of spectral data from periodic approximants

Speaker: 

Christoph Marx

Institution: 

UCI

Time: 

Thursday, October 13, 2011 - 2:00pm

Location: 

RH 306

Consider a quasi-periodic Schr\"odinger operator
$H_{\alpha,\theta}$ with analytic potential and Diophantine frequency
$\alpha$. Given any rational approximating $\alpha$, let $S_+$ and $S_-$
denote the union, respectively, the intersection of the spectra taken over
$\theta$. We show that up to sets of zero Lebesgue measure, the absolutely
continuous spectrum can be obtained asymptotically from $S_-$ of the
periodic operators associated with the continued fraction expansion of
$\alpha$. Similarly, from the asymptotics of $S_+$, one recovers the
spectrum of $H_{\alpha,\theta}$ (modulo a set of zero Lebesgue measure).

Optimal Delaunay Triangulation

Speaker: 

Long Chen

Institution: 

UC Irvine

Time: 

Monday, October 10, 2011 - 4:00pm

Location: 

RH 306

Optimal Delaunay triangulations (ODTs) are optimal meshes minimizing the inter- polation error to a convex function in Lp norm. We shall present several applications of ODT.
1. Mesh smoothing and optimization. Meshes with high quality are obtained by minimizing the interpolation error in a weighted L1 norm.

2. Anisotropic mesh adaptation. Optimal anisotropic interpolation error esti- mate is obtained by choosing anisotropic functions. The error estimate is used to produce anisotropic mesh adaptation for convection-dominated problems.

3. Sphere covering and convex polytope approximation. Asymptotic exact and sharp estimate of some constant in these two problems are obtained from ODT.

4. Quantization. Optimization algorithms based on ODT are applied to quanti- zation to speed up the processing.

How Quantum Computers Ruin Everything

Speaker: 

Shane Ryerson

Institution: 

UCI

Time: 

Thursday, October 6, 2011 - 5:00pm

Location: 

RH 306

Almost all forms of communication on the internet are initiated and obfuscated by a method of public key cryptography. Perhaps the most important among these are credit card transactions. This talk will discuss why public key cryptography is considered safe enough for those transactions and how quantum computers are a threat to those methods.

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