The Mathematics Calendar
http://www.math.psu.edu/seminars/calendar.php
Seminars and special events the Pennsylvania State University Mathematics Department2014-10-31webmaster@math.psu.eduOn computer simulation of multiscale processes in porous electrodes of Li-ion batteries
http://www.math.psu.edu/seminars/meeting.php?id=23563
Speaker(s): Oleg Iliev
Li-ion batteries are widely used in automotive industry, in electronic devices, etc. In this talk we will discuss challenges related to the multiscale nature of batteries, mainly the understanding of processes in the porous electrodes at pore scale and at macroscale. A software tool for simulation of isothermal and non-isothermal electrochemical processes in porous electrodes will be presented. The pore scale simulations are done on 3D images of porous electrodes, or on computer generated 3D microstructures, which have the same characterization as real porous electrodes. Finite Volume and Finite Element algorithms for the highly nonlinear problems describing processes at pore level will be shortly presented. MOR and DEIM-MOR algorithms for acceleration of the computations will be discussed. Next, homogenization of the equations describing the electrochemical processes at the pore scale will be presented, and the results will be compared to the engineering approach based on Newmanâ€™s 1D+1D model. Simulations at battery cell level will also be addressed. Finally, the challenges in modeling and simulation of degradation processes in the battery will be discussed and our first simulation results in this area will be presented.
This is joint work with A.Latz (DLR), M.Taralov, V.Taralova, J.Zausch, S.Zhang from Fraunhofer ITWM, and Y.Efendiev from Texas A&M.2014-10-31T15:30:00CCMA PDEs and Numerical Methods Seminar Seriesfuw7@math.psu.eduqiao_c@math.psu.eduwang_l@math.psu.eduOn time inhomogeneous branching Brownian motion
http://www.math.psu.edu/seminars/meeting.php?id=22064
Speaker(s): Alexei Novikov
A binary branching Brownian motion is a continuous-time Markov branching process that is constructed as follows: start with a single particle which performs a standard Brownian motion x(t) with x(0) = 0 and continues for an exponentially distributed holding time T, independent of x. At time T, the particle splits independently of x and T into 2 offspring with probability p. We discuss what happens if the variance of the Brownian motion depends on time.2014-10-31T15:35:00Probability and Financial Mathematics Seminardenker@math.psu.edumazzucat@math.psu.eduroyer@math.psu.edunistor@math.psu.eduanovikov@math.psu.eduAerodynamic Design Optimization by A Continuous Adjoint Method
http://www.math.psu.edu/seminars/meeting.php?id=22702
Speaker(s): Feng Liu
I will present our latest research progress on the development of a continuous adjoint method to perform aerodynamic design optimization of wings and turbomachinery blade rows. This method requires only about twice the computational effort of flow calculation to obtain the complete gradient information at each operating condition, regardless of the number of design parameters. Therefore, it is orders-of-magnitude more efficient than a conventional finite-difference method for obtaining the gradient information in a optimization procedure when the design parameters are in the hundreds and more. Examples of single and multiple-point design of transonic wings and turbomachinery blade rows will be presented.2014-11-03T12:20:00CCMA Luncheon Seminarshaffer@math.psu.eduliu@math.psu.eduMultiple Numerical Solutions and Stability of Transonic Flows over Airfoils
http://www.math.psu.edu/seminars/meeting.php?id=22719
Speaker(s): Feng Liu
Following a general presentation on the numerical simulation of steady and unsteady transonic flows over wings and turbomachinery blade rows by using computational fluid dynamics, I will focus on the findings of multiple numerical solutions for the Transonic Small-Disturbance equation and the Euler equations. Both symmetric and asymmetric solutions are possible for a symmetric airfoil at zero angle of attack within a certain free-stream Mach number range. The stability of the multiple solutions is analyzed using numerical methods. It is found, the symmetric solutions tend to be unstable, while the asymmetric solutions are stable. I will discuss the relevance of such stability analysis to the intrinsic unsteady behavior of transonic buffet over airfoils and wings.2014-11-03T14:30:00Computational and Applied Mathematics Colloquiumshaffer@math.psu.eduliu@math.psu.eduKrieger's finite generator theorem for ergodic actions of countable groups
http://www.math.psu.edu/seminars/meeting.php?id=22830
Speaker(s): Brandon Seward
The classical Krieger finite generator theorem states that
if a free ergodic probability-measure-preserving action of Z has
entropy less than log(k), then the action admits a generating
partition consisting of k sets. This was extended to actions of
amenable groups independently by Rosenthal and Danilenko-Park. We
introduce the notion of Rokhlin entropy which is defined for actions
of arbitrary countable groups. In the case of actions of amenable
groups, Rokhlin entropy coincides with classical entropy and can thus
be viewed as a natural extension of classical entropy. Using this
notion of entropy, we prove Krieger's finite generator theorem for
actions of arbitrary countable groups.2014-11-03T15:35:00Dynamical systems seminarkatok_s@math.psu.edusaz11@math.psu.edukatok_a@math.psu.eduhertz@math.psu.eduCocycle Reduction and Exponential Drift
http://www.math.psu.edu/seminars/meeting.php?id=23388
Speaker(s): Alex Eskin
I will be discussing how some cocycle reduction results can
be combined with the exponential drift technique of Benoist-Quint to
prove some measure rigidity results, in particular for the SL(2,R)
action on moduli space. This is joint work with Maryam Mirzakhani.
Note: this talk will be self-contained, and no knowledge of
Teichmuller theory will be assumed (or needed).2014-11-04T14:30:00Center for Dynamics and Geometry Colloquiumkatok_s@math.psu.edusaz11@math.psu.edukatok_a@math.psu.eduhertz@math.psu.eduPointwise convergence of multiple ergodic averages and strictly ergodic models
http://www.math.psu.edu/seminars/meeting.php?id=22808
Speaker(s): Xiangdong Ye
In this talk we discuss the pointwise convergence. By building some suitable strictly ergodic models, we prove that for an ergodic system $(X,\mathcal{X},\mu, T)$, $d\in\N$, $f_1, \ldots, f_d \in L^{\infty}(\mu)$, the averages
$$\frac{1}{N^2} \sum_{(n,m)\in [0,N-1]^2} f_1(T^nx)f_2(T^{n+m}x)\ldots f_d(T^{n+(d-1)m}x)$$
converge $\mu$ a.e.
Deriving some results from the construction, for distal systems we answer positively the question if the multiple ergodic averages converge a.e. That is, we show that if $(X,\mathcal{X},\mu, T)$ is an ergodic distal system, and $f_1, \ldots, f_d \in L^{\infty}(\mu)$, then the multiple ergodic averages
$$\frac 1 N\sum_{n=0}^{N-1}f_1(T^nx)\ldots f_d(T^{dn}x)$$
converge $\mu$ a.e..
The two talks are mainly based on the following papers.
a. S. Shao and X.Ye, Regionally proximal relation of order d is an equivalence one for minimal systems and a combinatorial consequence,Adv. in Math.,231(2012), 1786-1817.
b. W. Huang, S. Shao and X. Ye,Nil Bohr-sets and almost automorphy of higher order, arXiv:1407.1179v1[math.DS], Memoirs of Amer. Math. Soc., to appear.
c. W. Huang, S. Shao and X Ye, Pointwise convergence of multiple ergodic averages and strictly ergodic models, arXiv:1406.5930v1[math.DS], submitted.2014-11-04T15:30:00Working Seminar: Dynamics and its Working Toolskatok_a@math.psu.eduhertz@math.psu.edukalinin@math.psu.eduExtremality, uniqueness and optimality of transference plans.
http://www.math.psu.edu/seminars/meeting.php?id=22200
Speaker(s): Stefano Bianchini
For the transportation problem
\[
\inf \int c(x,y) \pi
\]
where $\pi$ (the transference plan) is a probability measure with given
marginals, and $c$ is a Borel cost, we are interested in the
characterization of the minimizers (optimal plans).
Analogous problems are the characterization of extremal points of the
set of transference plans and its uniqueness.
Even if the result is measure theoretic, it has applications to the
solution of the Monge problem (existence of an optimal map) for convex
l.s.c. costs.2014-11-04T16:00:00Applied Analysis Seminaranovikov@math.psu.edulevi@math.psu.eduberlyand@math.psu.edupesin@math.psu.eduProficiency to Mastery (Week 1 of 3)
http://www.math.psu.edu/seminars/meeting.php?id=23978
Speaker(s): Attendees
For the next three weeks, we discuss what it means for a student to be proficient and to develop mastery. We will be reading excerpts from Adding it Up and How Learning Works. This week, we read the description of proficiency from Adding It Up.
<br>
Kilpatrick, Jeremy, Jane Swafford, and Bradford Findell. "The Strands of Mathematical Proficiency." <i>Adding It Up: Helping Children Learn Mathematics.</i> Washington, DC: National Academy, 2001. 115-35. Print.2014-11-05T15:35:00Teaching Mathematics Discussion Group Seminarjamshidi@math.psu.eduPortraits of rational functions modulo primes
http://www.math.psu.edu/seminars/meeting.php?id=21889
Speaker(s): Tom Tucker
Let F be a rational function of degree > 1 over a number
field or function field K and let z be a point that is not preperiodic. Ingram and Silverman conjecture that for all but finitely many positive integers (m,n), there is a prime p such that z has exact preperiodic m and exact period n (we call this pair (m,n) the portrait of z modulo p). We present some counterexamples to this conjecture and show that a generalized form of abc implies -- one that is true for function fields -- implies that these are the only counterexamples. One may also ask a similar question for tuples of portraits for several point in a number field or function field. This work is still in progress. The talk represents joint work with several other authors.2014-11-06T11:15:00Algebra and Number Theory Seminarrvaughan@math.psu.eduschwede@math.psu.edupapikian@math.psu.eduyee@math.psu.eduSolutions to polynomials in two variables
http://www.math.psu.edu/seminars/meeting.php?id=24063
Speaker(s): Thomas Tucker
You may remember the quadratic formula for finding solutions
to quadratic polynomials in one variable. It is natural to ask: are
there formulas like this for polynomials of higher degree? The
answer, roughly speaking, is yes. Going further, one might ask: what
about polynomials in more than one variable? Here, the answer is far
more complicated, and involves geometry in what may seem a surprising
way. One famous example of this type of polynomial equation is the
Fermat equation x^n + y^n = z^n.2014-11-06T13:25:00MASS Colloquiumvxs137@math.psu.edudunlop@math.psu.edu