# Applied Math Colloquium - Spring 2019

Colloquia are held on Fridays at 11:30 a.m. in Cullimore Lecture Hall II, unless noted otherwise. Refreshments are served at 11:30 a.m.

For questions about the seminar schedule, please contact David Shirokoff.

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Date |
Speaker, Affiliation, and Title |
Host |

January 25 | Leonid Rubchinksky, Indiana University Purdue University Indianapolis (IUPUI)Dynamics of Intermittent Neural Synchronization: Observations, Mechanisms, and Functions
Synchronization of neural activity in the brain is involved in a variety of brain functions including perception, cognition, memory, and motor behavior. Excessively strong, weak, or otherwise improperly organized patterns of synchronous oscillatory activity may contribute to the generation of symptoms of different neurological and psychiatric diseases. However, neuronal synchrony is frequently not perfect, but rather exhibits intermittent dynamics. The same synchrony strength may be achieved with markedly different temporal patterns of activity. I will discuss methods to describe these phenomena and will present the application of this analysis to the neurophysiological data in healthy brain, Parkinson’s disease, and drug addiction disorders. I will finally discuss potential cellular mechanisms and functional advantages of some of the observed temporal patterning of neural synchrony. |
Amitabha Bose |

February 1 | Russel Caflisch, NYU CourantAccelerated Simulation for Plasma Kinetics
This presentation will describe acceleration of simulation methods for the Landau-Fokker-Planck equation, with a focus on a binary collision model that is solved using a Direct Simulation Monte Carlo (DSMC) method. Acceleration of this method is achieved by coupling the particle method to a continuum fluid description. Efficiency of the method is greatly increased by inclusion of particles with negative weights. This significantly complicates the simulation, and many difficulties have plagued earlier efforts to use negatively weighted particles. This talk will describe significant progress that has been made in overcoming those difficulties. |
Michael Siegel |

February 8 | Gillan Queisser, TempleCross-Scale Modeling and Simulation of Biochemical and Electrical Signals in Neurons and Networks
Computational methods that bridge multiple biological scales, including hybrid-dimensional numerical methods and subdivision-optimized geometric multigrid methods, will be presented in this talk. Using these techniques the talk will focus on a study of three-dimensional structure-function interplay at synaptic spines and neuronal dendrites, up to network level dynamics. The main focus will lie on the endoplasmic reticulum (ER), which, under certain structural conditions, gives rise to intracellular calcium waves. The ER forms a complex endomembrane network that reaches into the cellular compartments of a neuron, including dendritic spines. Combining a new 3D spine generator with 3D Ca2+ modeling, this talk addresses the relevance of ER positioning on spine-to-dendrite Ca2+ signaling. Simulations, which account for Ca2+ exchange on the plasma membrane and ER, show that spine ER needs to be present in distinct morphological conformations in order to overcome a barrier between the spine and dendritic shaft. RyR-carrying spine ER promotes spine-to-dendrite Ca2+ signals in a position-dependent manner and simulations indicate that RyR-carrying ER can initiate time-delayed Ca2+ reverberation, depending on the precise position of the spine ER. Upon spine growth, structural reorganization of the ER restores spine-to-dendrite Ca2+ communication, while maintaining aspects of Ca2+ homeostasis in the spine head. The presented work emphasizes the relevance of precise positioning of RyR-containing spine ER in regulating the strength and timing of spine Ca2+ signaling, which could play an important role in tuning spine-to-dendrite Ca2+ communication and homeostasis |
David Shirokoff |

February 15 | Benedetto Piccoli, Rutgers University - CamdenLagrangian and Sparse Control for Multi-Agents Dynamics and Traffic
We review some recent approaches to control large group of systems with sparse controls. At microscopic level we consider a number of multi-particle systems, used in applications to animal groups, opinion dynamics and other, while kinetic models are obtained as mean-field limit (Vlasov-Poisson type). Passing to the limit in the control strategies is particularly delicate and we will discuss some ways of overcoming the technical difficulty. Then we show how these approaches may be applied to control of traffic via autonomous and connected vehicles. Finally, a new class of equations, called Measure Differential Equations, are discussed as a way to encompass mean-field limits. |
Casey Diekman |

February 22 | Lydia Bourouiba, MITUnsteady Fluid Fragmentation
Understanding secondary droplet formation from fluid fragmentation is critical for industrial, environmental, and health processes including for predicting and controlling the transport of pathogen-bearing droplets created from contaminated fluids or surfaces. Despite the complexity and diversity of modes of unsteady fluid fragmentation into secondary droplets, universality across geometry and fluid systems emerges. We will discuss results from our recent joint experimental and theoretical investigations elucidating the role of unsteadiness in shaping a ubiquitous, yet neglected class of fluid fragmentation problems. In particular, we revisit fundamental assumptions of hydrodynamic instability and reveal how unsteadiness and multi-scale dynamics couple to select the sizes and speeds of secondary droplets generated. The implications for human health and food safety will be discussed. |
Yassine Boubendir |

March 1 | Jeff Moehlis , UCSBControlling Populations of Neural Oscillators
Some brain disorders are hypothesized to have a dynamical origin; in particular, it has been been hypothesized that some symptoms of Parkinson's disease are due to pathologically synchronized neural activity in the motor control region of the brain. This talk will describe several different approaches for desynchronizing the activity of a group of neurons, including maximizing the Lyapunov exponent associated with their phase dynamics, optimal phase resetting, controlling the phase density, and controlling the population to have clustered dynamics. It is hoped that this work will ultimately lead to improved treatment of Parkinson's disease via targeted electrical stimulation. |
Yuan-nan Young |

March 8 | Govind Menon, Brown/IASRandom Conformal Maps with Branching
Basic examples in phase transitions, such as the formation of crystals or the separation of phases, give rise to intricate random geometries with astonishing empirical universality. Physicists have invented several minimal models that attempt to capture the essence of these processes, one of which is diffusion limited aggregation (DLA). Despite an extensive physics literature, very little is known mathematically about DLA and its close relative, the Hastings-Levitov model for iterated conformal maps. I will describe a new model, that `interpolates' between these models and the Loewner theory for conformal maps. The main point of our model is its ease of description and analysis. In particular, it yields explicit stochastic PDE that are at least formally, the scaling limits of these processes. No background beyond basic familiarity with conformal maps will be presumed in this talk. This is joint work with Vivian Olsiewski Healey (University of Chicago). |
David Shirokoff |

March 15 | Judith R. Miller, Georgetown UniversitySpatial Population Dynamics with Adaptation to a Heterogeneous Environment
We model the joint evolution of a population density and the mean, and sometimes variance, of a quantitative trait (that is, a continuous random variable such as flowering time in plants) subject to selection toward an optimum value that varies in space. To do so, we study a family of deterministic models originating from the Kirkpatrick-Barton (1997) reaction-diffusion system. We use analysis and numerics to identify conditions under which the models predict range pinning due to an influx of locally maladapted individuals from the center of a species' range to its borders (“genetic swamping”) versus invasions represented as travelling waves. We highlight differences between the predictions of the Kirkpatrick-Barton model and those of related models incorporating features, such as non-Gaussian dispersal kernels and patchy habitat, that are often represented in nongenetic invasion models. |
Amitabha Bose |

March 29 | Daniel Harris, Brown UniversityForces on Capillary DisksUnderstanding the forces on small bodies at a fluid interface has significant relevance to a range of natural and artificial systems. In this talk, I will discuss two recent investigations in my lab where we’ve developed custom experiments to explore different forces on “capillary disks”: centimeter-scale hydrophobic disks trapped at an air-water interface. In the first part, we investigate the friction experienced by a capillary disk sliding along the interface. We demonstrate that the motion is dominated by skin friction due to the viscous boundary layer that forms in the fluid beneath the moving body. We develop a simple model that considers the boundary layer as quasi-steady, and that is able to capture the experimental behavior for a range of disk radii, masses, and fluid viscosities. Furthermore, we explore the influence of the body’s shape as well as the topography of its bottom surface on the friction. In the second part, we present direct measurements of the attractive force between capillary disks. It is well known that objects at a fluid interface may interact due to the mutual deformation they induce on the free surface, however very few direct measurements of such forces have been reported. In the present work, we characterize how the attraction force depends on the disk radius, mass, and relative spacing. The magnitudes of the measured forces are rationalized with a simple scaling argument and compared directly to theoretical predictions. Future directions in this area will also be discussed, in particular, we are beginning to investigate the motion and interactions of “active” capillary disks at the interface. |
Anand Oza |

April 5 | Jörn Dunkel, MITWrinkles, Spaghetti & KnotsBuckling, twisting and fracture are ubiquitous phenomena that, despite having been studied for centuries, still pose many interesting conceptual and practical challenges. In this talk, I will summarize recent theoretical and experimental work that aims to understand the role of curvature and torsion in wrinkle pattern selection, fragmentation cascades and knots. First, we will show how changes in curvature can induce phase transitions and topological defects in the wrinkling patterns on curved elastic surfaces. Thereafter, we will revisit an observation by Feynman who noted that dry spaghetti appears to fragment into at least three (but hardly ever two) pieces when placed under large bending stresses. Using a combination of experiments, simulations and analytical scaling arguments, we will demonstrate how twist can be used to control binary fracture of brittle elastic rods. Finally, in the last part, we will try to shed some light on how topology and torsion affect the stability of knots. |
Anand Oza |

April 12 | Tepper Gill, Howard UniversityA Little Physics, Can Lead to a Lot of Mathematics and Vis-Versa |
Denis Blackmore |

April 26 | Francesco Maggi, University of TexasAlmost Minimal and Almost Constant Mean Curvature Surfaces in Surface Tension Driven PhenomenaMinimal and constant mean curvature surfaces arise in mathematical models for surface tension. We illustrate various situations where these conditions needs to be perturbed and some related mathematical results obtained in collaboration with Giulio Ciraolo, Matias Delgadino, Darren King, Cornelia Mihaila, Robin Neumayer, Antonello Scardicchio and Salvatore Stuvard. |
Cyrill Muratov |

May 3 | Tore Magnus Arnesen Taklo, NJIT
Resonance Between Surface and Internal Gravity WavesThe ocean is stratified into a lower layer of cold, salty and dense water and an upper layer of warmer, sweeter and lighter water due to the transport of fresh water from river deltas, estuaries and heavy rainfall over the ocean surface. In between these layers, internal gravity waves are generated by disturbances caused by tidal currents that flows over ocean floor bathymetry such as continental shelfs or ocean floor hills or mountains. In height, a wave may rise to hundreds of feet and in length, a wave train may propagate for hundreds of miles. Being ubiquitous, due the periodic motion of the moon and the tides, it is believed that internal waves play a significant role in transferring heat and nutrients between ocean layers. Satellite images from NASA's archive will be presented. For a two-layer fluid, a closed Hamiltonian system of second-order nonlinear evolution equations was derived in Choi (2019). A numerical solution, employing a pseudo-spectral (PS) method, is presented. A triad of internal and surface gravity waves can resonate at second-order nonlinearity. The resonance may transfer energy from a internal wave to surface waves in which a monochromatic and uniform surface wave may become modulated and evolve into envelopes. Resonance conditions are presented with special emphasis on the group resonance which is admissible when the group velocity of the surface waves coincides with the phase speed of the internal wave. The PS model is compared to experiments and modulation theory of Lewis, Lake, and Ko (1974). For the initial wave evolution the PS model affirms the experiments and theory. The modulation theory is revisited and the governing equations are solved as an initial value problem to suit the PS model. Simulations with higher nonlinearity and with realistic ocean parameters are performed and compared to the theory. The results will be presented along with a series of wave animations. ReferencesW. Choi. Nonlinear interaction between surface and internal waves. Part I: Nonlinear models and spectral formulation. Preprint, 2019. J. E. Lewis, B. M. Lake, and D. R. S. Ko. On the interaction of internal waves and surface gravity waves. J. Fluid Mech., 63:773-800, 1974. |
Anand Oza |

*Updated: May 2, 2019*