Center for Statistical Sciences Seminar Series
Associate Professor, North Carolina State University, Scientist at the Environmental Protection Agency | |
Refreshments beginning at 3:15 pm |
Abstract: Storm surge is the onshore rush of sea water caused by the high winds and to a lesser extent the low pressure associated with a hurricane. Storm surge can compound the effects of inland flooding caused by rainfall, leading to loss of property and loss of life for residents of coastal areas. Numerical ocean models are essential for creating nowcast estimates as well as forecasts for coastal areas that are likely to be impacted by the storm surge. These models are driven primarily by the surface wind forcings. Currently, gridded wind fields used to spin up and force ocean models are specified by deterministic formulas that provide an idealized form of the wind profile based on the central pressure and location of the storm center. While these equations incorporate important physical knowledge about the structure of hurricane surface wind fields, they cannot always capture the asymmetric and dynamic nature of a hurricane. A new Bayesian multivariate spatial temporal statistical modeling framework is introduced to improve the estimation of the wind field inputs. A nonstationary and nonseparable spatial-temporal linear model of coregionalization (LMC) is developed and applied to explain the spatial-temporal variability in the wind vectors (u and v components), as well as the cross-dependency between these two components. This Bayesian framework allows for estimation of the parameters of the multivariate spatial model and the physically based wind model while accounting for potential additive and multiplicative bias in the observed wind data from buoys, ships, aircraft and satellite data. We find that this multivariate spatial model consistently improves parameter estimation and prediction for surface wind data for a case study of Hurricane Charley (2004) when compared to the original physical model. These methods are also shown to improve storm surge estimates when used as the forcing fields for a numerical three dimensional coastal ocean model.
Brown University -
Joint Materials/Solid Mechanics Seminar
Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room 1-272, Cambridge, MA, 02139, USA Email: mbuehler@MIT.EDU, Website: http://web.mit.edu/mbuehler/www/ | |
Abstract: Large-scale molecular dynamics is a useful tool to understand the mechanics of materials from a fundamental viewpoint, providing a unified description of mechanics and chemistry. This link is achieved by employing the new ReaxFF reactive force field that is capable of describing quantum mechanical behavior of atomic bonds under large stretch, including the complexities of bond breaking and formation as materials undergo large deformation and fracture. We exemplify our approach in studies of the nanomechanics of collagen, Nature's most abundant protein material with superior mechanical properties. We report a systematic analysis of the conditions under which entropic elasticity and energetic elasticity govern the elastic deformation behavior. Our results agree quantitatively with experiments of stretching individual tropocollagen (TC) molecules with optical tweezers. Further, we show that it is due to the basis of the collagen structure that leads to its high strength and ability to sustain large deformation, as relevant to its physiological role in tissues such as bone and muscle (M.J. Buehler, P. Natl. Acad. Sci. USA, 2006). Experiment has shown that collagen isolated from different sources of tissues universally displays a design that consists of TC molecules with lengths of approximately 300 nanometers. The reason why stands of amino acids associate to form TC molecules consistently at this length has been an unexplained phenomenon. Using a conbination of theoretical analyses and multi-scale modeling, we have discovered that the characteristic design of collagen displays a clever strategy that enables Nature to take advantage of the nanoscale properties of individual TC molecules at larger scales, leading to a tough material. This is achieved by arranging TC molecules into a staggered assembly at a specific optimal molecular length scale $L_{\chi}$. Our studies exemplify how hierarchical multi-scale modeling can be used to develop quantitative models of chemically complex hierarchical biological materials.
CENTER FOR FLUID MECHANICS
AND
THE FLUIDS, THERMAL AND CHEMICAL PROCESSES GROUP
OF
THE DIVISION OF ENGINEERING
Seminar Series
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA | |
Abstract: This talk begins by pointing out the surprising fact the fundamental equations governing continuum fluid mechanics and transport processes neither explicitly involve, nor require, the notion of velocity. Next, it is pointed out that Euler's (1755) assumption founding fluid mechanics some 250 years ago, namely that* ${\bf m}={\bf n}_{m}$, is a constitutive assumption rather than an empirical fact of nature, contrary to what we learned as students. We discuss evidence for and against his relation. Since the validity of the Navier-Stokes-Fourier equations, and indeed the foundations of fluid mechanics, hinges on the correctness of Euler's implicit hypothesis, the issue is not moot. Irreversible thermodynamics, in the form of the Second law, plays a key role in framing the discussion. We refer here not to the usual side issue of demonstrating the positivity of the fluid's viscosity and thermal conductivity, but rather to the crucial role that Onsager's Reciprocal Theorem plays in resolving the question of whether Euler was right! Finally, some recent applications of the speaker's recent theory of diffuse-volume transport, which is closely related to the Euler question, are cited, including the ability to predict, in nonisothermal liquids, the existence and extent of particle thermophoresis, thermal diffusion, and thermal transpiration. Previously, the mechanism underlying these exotic transport processes was understood only for rarefied gases, and then only in gas-kinetic molecular terms, rather than in terms of hydrodynamic phenomenology.
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*${\bf m}$ = momentum density (per unit volume), a dynamical quantity appearing in the Cauchy linear momentum equation embodying the principle of momentum conservation;
${\bf n}_{m} $= mass flux, a kinematical quantity appearing in the continuity equation embodying the principle of mass conservation.
Euler's hypothesis,${\bf m}$ = ${\bf n}_m$ , is equivalent to supposing that the fluid's "momentum velocity" ${\bf m}/\rho$ is equal to the fluid's " mass velocity"${\bf n}_{m}/\rho$, enabling use of the single symbol ${\bf v}$ as an abbreviation for both of these quantities, and thereby introducing the notion of "velocity" into fluid mechanics.
Brown Analysis Seminar
Abstract:
Walter Rudin proved the following in 1953: let B be a
continuous function on the closed unit disk. Let P be a
polynomial in two variables. Suppose that for a in the
interior of the disk
|P(a,B(a)| <= max|P(z,B(z)| over |z| = 1.
If this holds for every polynomial P and every point a, then
B is analytic on the interior of the disk. I study the analog
of this theorem when the disk is replaced by the punctured
disk, a suitable substitute is assumed for the maximum
principle and the conclusion is that B is holomorphic on the
punctured disk and B has at 0 either a removable singularity
or a pole. The substitute for the maximum principle is taken
from the notion of "projective hull" in complex projective
space, recently introduced by Harvey and Lawson.
Brown University -
Division of Applied Mathematics
Transatlantic Seminar
Scientific Computing Seminar
Marshal University, Huntington, WV | |
Abstract: Symmetric and Asymmetric Radial Basis Function (RBF) collocation methods will be discussed. The focus of the talk will be on issues related to applying the RBF collocation methods to time-dependent PDEs. The issues include: eigenvalue stability, enforcement of boundary conditions, approximating discontinuous functions and a post-processing method to remove Gibbs oscillations.
PDE Seminar
Department of Mathematics Colloquium
<--- 2006 Index