The Mathematics Calendar
http://www.math.psu.edu/seminars/calendar.php
Seminars and special events the Pennsylvania State University Mathematics Department2015-03-26webmaster@math.psu.eduExistence of a dynamic system of ionic electrodiffusion
http://www.math.psu.edu/seminars/meeting.php?id=25859
Speaker(s): Tao Huang
We consider a dynamic system of ionic electrodiusion which can be considered as a special case of cardiac bidomain model. A global weak solution has been constructed by Galerkin argument and maximum principle.2015-03-27T13:00:00CCMA PDEs and Numerical Methods Seminar Seriesqiao_c@math.psu.edusaz11@math.psu.edufuw7@math.psu.edusxw58@math.psu.eduG/G/N Queues with Service Interruptions in the Halfin-Whitt Regime
http://www.math.psu.edu/seminars/meeting.php?id=24883
Speaker(s): Guodong Pang
We consider G/G/N queues with renewal alternating service interruptions. The arrival process is general and the service times forms a stationary and weakly dependent sequence satisfying some strong mixing condition. The system experiences up and down alternating periods. Both the arrival and service processes operate normally in the up periods. In the down periods, arrivals continue entering the system, but all servers break down and the amount of service a customer has received will be conserved and resumed when the next up period starts. We assume that the up times are of the same order as the service times but the down times are asymptotically negligible compared with the service times. In the QD and QED regimes, we prove FLLNs and FCLTs for the total count processes and the two-parameter queueing processes tracking elapsed or residual times. The limit processes in the FCLTs are characterized via stochastic integral equations with jumps, and the convergence requires Skorohod M_1 topology in the spaces D([0,T], R) and D([0, T], D([0, T], R)). (This is joint work with Yuhang Zhou and Hongyuan Lu.)2015-03-27T15:35:00Probability and Financial Mathematics Seminardenker@math.psu.eduanovikov@math.psu.edumazzucat@math.psu.eduroyer@math.psu.edunistor@math.psu.eduEnergy-Stable Open Boundary Conditions for Two-Phase Outflows
http://www.math.psu.edu/seminars/meeting.php?id=26487
Speaker(s): Suchuan Steven Dong
This talk focuses on the motion of a mixture of two immiscible incompressible fluids in a domain with open boundaries. The domain boundary is open in the sense that the fluids can freely leave or even enter the domain through such boundaries. In particular, we concentrate on situations where the interface formed between the two fluids passes through the open portions of the domain boundary. The problem therefore involves truly two-phase outflow/open boundaries.
The challenge facing the design of effective techniques for treating two-phase outflows in numerical simulations is manifold. Some of the primary issues are associated with the viscosity contrasts, density contrasts, surface tension, and the presence of fluid interface, backflows or strong vortices on the open boundaries. Large density ratios and large viscosity ratios of the two fluids make two-phase outflow simulations tremendously challenging.
In this talk we present a set of boundary conditions, and an associated numerical algorithm, for two-phase outflow simulations within the phase field framework. These open boundary conditions have the characteristic that they all ensure the energy stability of the two-phase system, even in situations where strong vortices, backflows, large density contrast and
large viscosity contrast are present at the open boundaries. We will show the physical accuracy of the method by comparing simulation results with the theory and experimental data. Numerical experiments will be presented to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows are present at the outflow/open boundaries.2015-03-30T12:20:00CCMA Luncheon Seminarmsm37@math.psu.edushaffer@math.psu.eduliu@math.psu.eduIncompressible N-Phase Flows: Physical Formulation and Numerical Algorithm
http://www.math.psu.edu/seminars/meeting.php?id=25569
Speaker(s): Suchuan Steven Dong
This talk focuses on simulating the motion of a mixture of N (N>=2) immiscible incompressible fluids with given densities, dynamic viscosities and pairwise surface tensions. We present an N-phase formulation within the phase field framework that is thermodynamically consistent, in the sense that the formulation satisfies the conservations of mass/momentum, the second law of thermodynamics and Galilean invariance. In addition, we also present an efficient algorithm for numerically simulating the N-phase system that has overcome the issues caused by the variable mixture density/viscosity and the couplings among the (N-1) phase field variables and the flow variables. We compare simulation results with the Langmuir-de Gennes theory to demonstrate that the presented method produces physically accurate results for multiple fluid phases. Numerical experiments will be presented for several problems involving multiple fluid phases, large density contrasts and large viscosity contrasts to demonstrate the capabilities of the method for studying the interactions among multiple types of fluid interfaces.2015-03-30T14:30:00Computational and Applied Mathematics Colloquiummsm37@math.psu.edushaffer@math.psu.eduliu@math.psu.edufuw7@math.psu.eduKolmogorov and Bernoulli property for partially hyperbolic diffeomorphisms
http://www.math.psu.edu/seminars/meeting.php?id=24801
Speaker(s): Ali Tahzibi
There is a hierarchy among the order of unpredictability of dynamical systems. The Bernoulli property (conjugacy with a Bernoulli Shift) is the strongest form of unpredictability. Each Bernoulli system, in particular, is a Kolmogorov system. However, the inverse is not always true. In this talk we review some known results and prove the equivalence between Kolmogorov and Bernoullicity of volume measure for partially hyperbolic systems which are derived from Anosov and have one dimensional central bundle on Torus. In particular we announce some recent results on disintegration of measures along central foliation of partially hyperbolic dynamics. This is a joint work with J.R.VarĂ£o and G. Ponce.2015-03-30T15:35:00Dynamical systems seminarkatok_a@math.psu.edusaz11@math.psu.edukatok_s@math.psu.eduhertz@math.psu.eduTBA
http://www.math.psu.edu/seminars/meeting.php?id=27457
Speaker(s): Atendees
2015-03-31T12:20:00Teaching Mathematics Discussion Group Seminarzach@math.psu.eduzelenberg@math.psu.eduA game-theoretic dispersal mechanism in PDE models of interacting populations
http://www.math.psu.edu/seminars/meeting.php?id=24701
Speaker(s): Russ deForest
We adapt a fitness from evolutionary game theory as a dispersal mechanism in
spatial PDE models of interacting populations. Evolutionary games are used to model selection dynamics among competing traits or strategies. The relative frequencies of competing strategies evolve according to an ODE model governed by a replicator equation. We spatially extend these models by allowing populations to travel up a fitness gradient. We discuss results for some two-species models, including cross-diffusive instabilities and pattern formation in a spatial Lotka-Volterra model. Some background on PDE models for interacting populations and spatial games will be given with a focus on PDE systems that are normally parabolic, but in general non-coercive.2015-03-31T13:00:00Theoretical Biology Seminartreluga@math.psu.educpc16@math.psu.eduGravity in three dimensions: mathematical foundations
http://www.math.psu.edu/seminars/meeting.php?id=24758
Speaker(s): Marc Geiller
The year 2015 marks the centennial anniversary of the birth of Einstein's theory of general relativity, which is so far the most successful and experimentally tested description of the gravitational interaction. Although the physical spacetime around us is four-dimensional, general relativity, because of its geometrical nature, can also be formulated in three spacetime dimensions. There it exhibits special mathematical structure, and can be studied in exactly soluble ways. The goal of this series of lectures is to present some aspects of the rich interplay that exists between mathematics and physics within the context of three-dimensional gravity.
Part 1: Physical foundations
Part 2: Mathematical formulations
Part 3: Quantization via loop groups
Part 4: Path integral quantization and topological invariants2015-03-31T14:30:00GAP Seminarhigson@math.psu.edustienon@math.psu.eduping@math.psu.eduroyer@math.psu.eduDeformations of boundary distances and geodesic flows
http://www.math.psu.edu/seminars/meeting.php?id=24829
Speaker(s): Sergei Ivanov
This is a joint work with Dima Burago. We show that a simple Finsler metric
on the n-disc can be deformed so as to induce an arbitrary perturbation
of the boundary distance function, or an arbitrary symplectic perturbation
of the geodesic scattering map. Among the applications is a construction
of a metric on the 4-sphere arbitrarily close to the standard "round" metric
and having positive metric entropy of its geodesic flow (which is regarded as
a Hamiltonian flow).2015-03-31T14:30:00Center for Dynamics and Geometry Colloquiumkatok_s@math.psu.edukatok_a@math.psu.edusaz11@math.psu.eduhertz@math.psu.eduNo Seminar this week
http://www.math.psu.edu/seminars/meeting.php?id=24910
Speaker(s): No Seminar this week
2015-03-31T14:30:00Logic Seminarjmr71@math.psu.edusimpson@math.psu.edureimann@math.psu.eduDynamics in threshold-linear networks
http://www.math.psu.edu/seminars/meeting.php?id=25365
Speaker(s): Carina Curto
Threshold-linear networks are simplified models of neural networks in the brain. I will first describe how these networks can operate as traditional attractor neural networks (similar to the Hopfield model), and what we can say about the set of stable fixed points. I will then show how we can construct networks without fixed points, and state a conjecture about the dynamics in this regime.2015-03-31T15:30:00Working Seminar: Dynamics and its Working Toolskatok_a@math.psu.edusaz11@math.psu.eduhertz@math.psu.edukalinin@math.psu.eduHomogeneous additive equations over p-adic fields
http://www.math.psu.edu/seminars/meeting.php?id=24851
Speaker(s): Mike Knapp
In this talk, we will study solutions of the equation a_1x_1^d + a_2x_2^d + ... + a_sx_s^d = 0 in p-adic integers. It has been known since the 1960s that if s>= d^2 + 1, then this equation will have nontrivial p-adic solutions for any prime p, regardless of the coefficients. This bound is sharp when $d+1$ is prime, but can be reduced when $d+1$ is composite. Given a degree d, we define \Gamma^*(d) to be the smallest number of variables which guarantees that the above equation has nontrivial p-adic solutions for all p. In the first half of the talk, we will evaluate the exact values of \Gamma^*(d) for some small degrees. After that, we will focus specifically on the 2-adic version of the problem and give an exact formula for the smallest number of variables which guarantees that the equation has nontrivial 2-adic solutions.2015-04-02T11:15:00Algebra and Number Theory Seminarrvaughan@math.psu.edupapikian@math.psu.eduyee@math.psu.edueisentra@math.psu.eduGravity in three dimensions: quantization via loop groups
http://www.math.psu.edu/seminars/meeting.php?id=25493
Speaker(s): Marc Geiller
The year 2015 marks the centennial anniversary of the birth of Einstein's theory of general relativity, which is so far the most successful and experimentally tested description of the gravitational interaction. Although the physical spacetime around us is four-dimensional, general relativity, because of its geometrical nature, can also be formulated in three spacetime dimensions. There it exhibits special mathematical structure, and can be studied in exactly soluble ways. The goal of this series of lectures is to present some aspects of the rich interplay that exists between mathematics and physics within the context of three-dimensional gravity.
Part 1: Physical foundations
Part 2: Mathematical formulations
Part 3: Quantization via loop groups
Part 4: Path integral quantization and topological invariants2015-04-02T14:30:00Noncommutative Geometry Seminarhigson@math.psu.edusaz11@math.psu.edu