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Current contacts: Benjamin Seibold or Daniel B. Szyld
The Seminar usually takes place on Wednesdays at 4:00 PM in Room 617 on the sixth floor of Wachman Hall. Click on title for abstract.
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The block version of GMRES (BGMRES) is most advantageous over the single right hand side (RHS) counterpart when the cost of communication is high while the cost of floating point operations is not. This is the case on modern Graphics Processing Units(GPUs), while it is generally not the case on traditional Central Processing Units (CPUs). In this talk, experiments on both GPUs and CPUs are shown that compare the performance of BGMRES against GMRES as the number of RHS increases. The experiments indicatethat there are many cases in which BGMRES is slower than GMRES on CPUs, but faster on GPUs. Furthermore, when varying the number of RHS on the GPU, there is an optimal number of RHS where BGMRES is clearly most advantageous over GMRES. A computational modelis developed using hardware specific parameters, showing qualitatively where this optimal number of RHS is, and this model also helps explain the phenomena observed in the experiments.
Rachael Miller Neilan, Duquesne University
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In this talk, I will present an agent-based model (ABM) that simulates the behavior and interactions of neurons in the amygdala for the purpose of studying their impact on pain.
In the ABM, agents represent individual neurons that express either protein kinase C delta (PKC) or somatostatin (SOM). Neurons that express PKC are known to increase pain whereas neurons that express SOM are known to decrease pain. During the model’s initialization, neurons are assigned type-specific parameters based on laboratory data and a location in either the right or left amygdala. A network of directed links is established to allow for the transmission of inhibitory signals between neurons. During each model timestep, neurons accrue damage and the firing rates all of neurons are updated based on the intensity of the external stimulus and the strength of signals transmitted through the network. The ABM outputs an emergent measure of pain, which is calculated in terms of the cumulative pro-nociceptive activity of the PKC neurons and anti-nociceptive activity of the SOM neurons. Results demonstrate the ability of the model to produce changes in pain that are consistent with published studies and highlight the importance of several model parameters.
Undergraduate students contributed to the development and programming of the ABM using NetLogo software.
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Viruses are the most abundant biological entity on Earth and play a pivotal role in regulating the evolution of organisms and the planet's biogeochemistry. Most viruses protect their genome in icosahedral shells made of multiple copies of the same protein. Viral icosahedral shells span two orders of magnitude in size and thousands of different architectures. Yet, the physical mechanisms that have selected such diverse viral structures are unknown. Here, I will share my most recent contributions to this fundamental problem. First, I will introduce the generalized quasi-equivalence theory of icosahedral architectures as a framework to investigate systematically viral architectures and their protein components. Second, I will show how the physical relationship between the protein shell and genome of viruses has opened the door to characterize uncultured viruses, predict the existence of unknown viruses, and engineer new viruses from the environment. Finally, I will discuss a novel physical mechanism that may hold the key to how viruses explore different viral architectures.
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Subaerial biofilms (SABs) are thin layers of densely packed microorganisms, that live in self-organized structures on soil and rock surfaces exposed to the air. Microbial life within these ecosystems is very hard and mainly dependent on the availability of liquid water, essential for microbial metabolic activities. That’s why SAB inhabitants are special microorganisms, able to resist long desiccation periods and loosen the thermodynamic constraints to the water vapor condensation into the SAB.
Here, I will present a multidisciplinary study on subaerial biofilms. First, I will show some confocal microscopy images of SAB microbial colonies, the result of multiple sampling campaigns conducted on the marble surfaces of the Merchants’ Exchange Building (Philadelphia, USA) and on the stone railing of my house in Naples (Italy). Then, I will present a novel theoretical model to predict liquid water availability via microbially-induced condensation and estimate the maximum SAB thickness thermodynamically supported under specific temperature and humidity conditions. Finally, I will apply the present model to a year-long data campaign about temperature and humidity, conducted on the marble roof of the portico of the Thomas Jefferson Memorial (Washington D.C., USA).
Turbulence modeling in practice requires predicting averages of solutions of the Navier-Stokes equations. We examine eddy viscosity RANS models based on the 1-equation model of Prandtl and Kolmogorov. Many of these models fail due to overdissipation in the near wall region. For general eddy viscosity models, we show that the ratio of the near wall average viscosity to the effective global viscosity is the key parameter. This result is then applied to the 1-equation, URANS model of turbulence for which this ratio depends on the specification of the turbulence length scale. We propose a modification to traditional choices of l: away from walls, interpreting an early suggestion of Prandtl, we set l=√2k^{+1/2}τ, where τ=selected time scale. In the near wall region analysis suggests replacing the traditional l=0.41d (d=wall normal distance) with l=0.41d√(d/L)giving, e.g., l=min{√2k^{+1/2}τ, 0.41d√(d/L)}. This l(⋅) results in a simpler model with correct near wall asymptotics. Its energy dissipation rate scales no larger than the physically correct O(U^{3}/L), balancing energy input with energy dissipation.
Several neuron types have been shown to exhibit (subthreshold) membrane potential resonance (MPR), defined as the occurrence of a peak in their voltage amplitude response to oscillatory input currents at a preferred (resonant) frequency. MPR has been investigated both experimentally and theoretically. However, whether MPR is simply an epiphenomenon or it plays a functional role for the generation of neuronal network oscillations, and how the latent time scales present in individual, non-oscillatory cells affect the properties of the oscillatory networks in which they are embedded are open questions. We address these issues by investigating a minimal network model consisting of (i) a non-oscillatory linear resonator (band-pass filter) with 2D dynamics, (ii) a passive cell (low-pass filter) with 1D linear dynamics, and (iii) nonlinear graded synaptic connections (excitatory or inhibitory) with instantaneous dynamics. We demonstrate that (i) the network oscillations crucially depend on the presence of MPR in the resonator, (ii) they are amplified by the network connectivity, (iii) they develop relaxation oscillations for high enough levels of mutual inhibition/excitation, and (iv) the network frequency monotonically depends on the resonator’s resonant frequency. We explain these phenomena using a reduced adapted version of the classical phase-plane analysis that helps uncovering the type of effective network nonlinearities that contribute to the generation of network oscillations. We extend our results to the so-called firing rate models with adaption. Our results have direct implications for neuronal network oscillations in more complex systems and other biological oscillatory networks (e.g, biochemical, genetic).
Heterogeneous problems that take place at multiple scales are ubiquitous in science and engineering. Examples are wind turbines made from composites or groundwater flow relevant e.g., for the design of flood prevention measures. However, finite element or finite volume methods require an often prohibitively large amount of computational time for such tasks. Multiscale methods that are based on ansatz functions which incorporate the local behavior of the (numerical) solution of the partial differential equations (PDEs) have been developed to tackle these heterogeneous problems. Heterogeneous problems also pose a challenge for iterative linear system of equations solvers as the condition number of the preconditioned system generally depends on the contrast of the coefficient function leading to a deterioration of convergence.Two-level domain decomposition preconditioners with so-called adaptive coarse spaces constructed from suitable local eigenvalue problems restore robust, contrast-independent convergence. However, these eigenvalue problems typically rely on non-algebraic information, such that the adaptive coarse spaces cannot be constructed from the fully assembled system matrix
In this talk we will present optimal local approximation spaces for multiscale methods, whose local ansatz functions can be constructed by solving the PDE on small subdomains, and that allow controlling the error due to localization and the (global) approximation error at a (quasi-optimal) rate without relying on structural assumptions such as scale separation or periodicity. In addition, we will show how these optimal local approximation spaces can be used to generate two-level overlapping Schwarz preconditioners that are both fully algebraic and robust in the sense that we can show an upper bound for the condition number that is independent of the contrast.
This talk focuses on developing time integration strategies for thedispersive shallow water equations (DSWE)—which are fluid models, applicable tocoastal regions that include additional physics (such as dispersion) to thewell-known shallow water equations. The DSWEs contain nonlinear,"mixed" space and time derivatives that create computational challengesin the numerical time integration of the equations. We devise a constantcoefficient preconditioner that may be used to handle the time integration ofthe mixed derivative terms in the DSWE via preconditioned Krylov methods. A key feature of the approach is that the results may be applied to varyingbottom topographies. Concepts from the preconditioner also enablethe development of computationally advantageous IMEX approaches that treat someterms in the time integration implicitly (Im) and others explicitly (Ex).
Two coupled climate models, GFDL-CM4and GFDL-ESM4, are used to investigate the physical response of the SouthernOcean to changes in surface wind stress, increased Antarctic meltwater, and thecombined forcing of the two in a pre-industrial control simulation. Themeltwater cools the ocean surface in all regions except the Weddell Sea, wherethe wind stress drives a warming of the near-surface layer. The limitedsensitivity of the Weddell Sea surface layer to the meltwater is a result ofthe spatial distribution of the imposed meltwater fluxes, regional bathymetry,and large-scale circulation patterns. The models yield strikingly differentresponses on the West Antarctic shelf. The disagreement is attributable to themean-state representation and meltwater-driven acceleration of the AntarcticSlope Current (ASC). In CM4, the meltwater is efficiently trapped on the shelfby a strong, and accelerating ASC which isolates the West Antarctic shelf fromwarm offshore waters, leading to strong subsurface cooling. In ESM4, a weakerand diffuse ASC allows more meltwater to escape from the shelf and there is noisolation mechanism in West Antarctica. Instead, the subsurface warms in thisregion in ESM4. The CM4 results suggest a possible negative feedback mechanismthat acts to limit future melting, while the ESM4 results suggest a possiblepositive feedback mechanism that acts to accelerate melt. Our resultsdemonstrate the strong influence the ASC has on governing changes along theshelf, highlighting the importance of coupling interactive ice sheet models toocean models that can resolve these dynamical processes.
Sea ice, which covers a significant portion of the earth's surface, is a
interestingly complicated material consisting of a mixture of solid
ice and liquid brine phases which are coupled by thermodynamic considerations.
It also is a platform for microbial life, lots of
it in fact, that uses the ice as a sort of shelter though eventually
becoming part of the local food chain. A model will be presented that
hypothesizes that, in turn, the resident microbial population might
impact sea ice structure.
I will review basic properties of Newton's method for solving
nonlinear equations. For difficult nonlinearities it can be beneficial
to lift the nonlinear systems to a higher-dimensional space, linearize
there and reduce the linearization to the original space before
solving the linearized system. The resulting algorithms may yield
favorable convergence properties. I will illustrate the ideas on a
simple example, and show connections to primal-dual interior point
methods. The resulting Newton solvers will be used for the solution of
flow problems with visco-plastic constitutive relations arising in the
geosciences. This is joint work with Johann Rudi (Virginia Tech) and
Melody Shih (NYU).
More than 99% of the mass of the visible matter resides in hadrons
which are bound states of quarks and gluons, collectively called
partons. These are the fundamental constituents of Quantum
Chromodynamics (QCD), the theory of strong interactions. While QCD is
a very elegant theory, it is highly non-linear and cannot be solved
analytically, posing severe limitations on our knowledge of the
structure of the hadrons. Lattice QCD is a powerful first-principle
formulation that enables the study of hadrons numerically, which is
done by defining the continuous equations on a discrete Euclidean
four-dimensional lattice.
Hadron structure is among the frontiers of Nuclear and Particle
Physics. Among the high-priority science questions identified by
the National Academies of Sciences, Engineering, and Medicine
are:
1. How does the mass of the nucleon arise?
2. How does the spin of the nucleon arise?
In this talk, I will discuss how mathematical methods,
algorithms and access to large-scale computational resources
are critical in addressing the above questions.
The National Institute of Standards and Technology (NIST), founded in 1901, is a government agency under the Department of Commerce that conducts research in measurement science and other areas of the mathematical and physical sciences to enhance US industrial competitiveness. Researchers in the Applied and Computational Mathematics Division (ACMD), located in the Information Technology Laboratory(ITL) at NIST, work with members of the division, collaborate with scientists from other NIST labs, and often foster interdisciplinary collaborations at research institutions and universities external to NIST. The speaker will discuss her involvement, research and outside collaborations related to the NIST Digital Library of Mathematical Functions (DLMF), https://dlmf.nist.gov , one of the signature projects ofACMD, and look at additional projects in ACMD that showcase the breadth of research being conducted. Opportunities for internships and postdocs at NIST will also be discussed.
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