George Hagstrom

• Phd
• PostDoc Position at Princeton University

Hall-MHD is a mixed hyperbolic-parabolic partial differential equation that describes the dynamics of an ideal two fluid plasma with massless electrons. We study the only shock wave family that exists in this system (the other discontinuities being contact discontinuities and not shocks). We study planar travelling wave solutions and we find soluti...

Building on the development of [1], bifurcation of unstable modes that emerge from continu-ous spectra in a class of infinite-dimensional noncanonical Hamiltonian systems is investigated. Of main interest is a bifurcation termed the continuum Hamiltonian Hopf (CHH) bifurcation, which is an infinite-dimensional analog of the usual Hamiltonian Hopf (...

The Caldeira-Leggett model is a Hamiltonian system that describes a simple harmonic oscillator coupled to a continuous spectrum of simple harmonic oscillators. It was invented to study quantum tunnelling in dissipative systems. We show that the damping mechanism in the Caldeira-Leggett model is analogous to Landau damping and derive an integral tra...

The background method is adapted to derive rigorous limits on surface speeds and bulk energy dissipation for shear stress driven flow in two and three dimensional channels. By-products of the analysis are nonlinear energy stability results for plane Couette flow with a shear stress boundary condition: when the applied stress is gauged by a dimensio...

We demonstrate the stable boundary closure of difference methods of order up through 16 for the solution of wave equations in second order form. Our method combines the introduction of 1–2 judiciously placed subcell grid points near the boundary with minimal-stencil, one-sided difference operators of the same order as the interior scheme. The metho...

Phytoplankton stoichiometry modulates the interaction between carbon, nitrogen and phosphorus cycles, yet most biogeochemical models represent phytoplankton C:N:P as constants. This simplification has been linked to Earth System Model (ESM) biases and potential misrepresentation of biogeochemical responses to climate change. Here we integrate key e...

Establishing links between microbial diversity and environmental processes requires resolving the high degree of functional variation among closely related lineages or ecotypes. Here, we implement and validate an improved metagenomic approach that estimates the spatial biogeography and environmental regulation of ecotype-specific replication patter...

Are the oceans turning into deserts? Rising temperature, increasing surface stratification, and decreasing vertical inputs of nutrients are expected to cause an expansion of warm, nutrient deplete ecosystems. Such an expansion is predicted to negatively affect a trio of key ocean biogeochemical features: phytoplankton biomass, primary productivity,...

Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics. Statistical physics first confronted the problem of emergent phenomena such as critical transitions in the 1800s...

Collective behavior is an emergent property of numerous complex systems, from financial markets to cancer cells to predator-prey ecological systems. Characterizing modes of collective behavior is often done through human observation, training generative models, or other supervised learning techniques. Each of these cases requires knowledge of and a...

The ability of marine microbes to navigate toward chemical hotspots can determine their nutrient uptake and has the potential to affect the cycling of elements in the ocean. The link between bacterial navigation and nutrient cycling highlights the need to understand how chemotaxis functions in the context of marine microenvironments. Chemotaxis hin...

Linking ‘omics measurements with biogeochemical cycles is a widespread challenge in microbial community ecology. Here, we propose applying genomic adaptation as ‘biosensors’ for microbial investments to overcome nutrient stress. We then integrate this genomic information with a trait-based model to predict regional shifts in the elemental compositi...

Collective behavior is an emergent property of numerous complex systems, from financial markets to cancer cells to predator-prey ecological systems. Characterizing modes of collective behavior is often done through human observation, training generative models, or other supervised learning techniques. Each of these cases requires knowledge of and a...

A warmer ocean will change plankton physiological rates, alter plankton community composition, and in turn affect ecosystem functions, such as primary production, recycling, and carbon export. To predict how temperature changes affect plankton community dynamics and function, we developed a mechanistic trait‐based model of unicellular plankton (aut...

Marine phytoplankton stoichiometry links nutrient supply to marine carbon export. Deviations of phytoplankton stoichiometry from Redfield proportions (106C : 1P) could therefore have a significant impact on carbon cycling, and understanding which environmental factors drive these deviations may reveal new mechanisms regulating the carbon cycle. To...

What is the ultimate limiting nutrient in the ocean? The dominant theory, which was first proposed by Redfield and later formalized by Tyrrell[1, 2], states that despite the scarcity of fixed nitrogen (N) in the surface ocean, phosphorus (P) availability ultimately determines primary productivity. Two recent findings directly challenge the assumpti...

Marine phytoplankton stoichiometry links nutrient supply to marine carbon export. Deviations of phytoplankton stoichiometry from Redfield proportions (106C : 1P) could therefore have a significant impact on carbon cycling, and understanding which environmental factors drive these deviations may reveal new mechanisms that regulate the carbon cycle....

Complex adaptive systems provide a unified framework for explaining ecosystem phenomena. In the past 20 years, complex adaptive systems have been sharpened from an abstract concept into a series of tools that can be used to solve concrete problems. These advances have been led by the development of new techniques for coupling ecological and evoluti...

Complex adaptive systems provides a unified framework for explaining ecosystem phenomena. In the past twenty years, complex adaptive systems has been sharpened from an abstract concept into a series of tools that can be used to solve concrete problems. These advances have been led by the development of new techniques for coupling ecological and evo...

Hall-magnetohydrodynamics (HMHD) is a mixed hyperbolic-parabolic partial differential equation that describes the dynamics of an ideal two fluid plasma with massless electrons. We study the only shock wave family that exists in this system (the other discontinuities being contact discontinuities and not shocks). We study planar traveling wave solut...

Hamiltonian bifurcations in the context of noncanonical Hamiltonian matter models are described. First, a large class of 1 + 1 Hamiltonian multi-fluid models is considered. These models have linear dynamics with discrete spectra, when linearized about homogeneous equilibria, and these spectra have counterparts to the steady state and Hamiltonian Ho...

Poster presentation at the 2012 APS DPP meeting

Hall-MHD is a partial differential equation of degenerate parabolic type that describes the dynamics of an ideal two fluid plasma with massless electrons. We study shock waves and discontinuities in this system. We characterize planar travelling wave solutions and find solutions with discontinuities in the hydrodynamic variables. These solutions, w...

The Caldeira-Leggett Hamiltonian describes the interaction of a discrete harmonic oscillator with a continuous bath of harmonic oscillators. This system is a standard model of dissipation in macroscopic low temperature physics, and has applications to superconductors, quantum computing, and macroscopic quantum tunneling. The similarities between th...

The Caldeira-Leggett Hamiltonian (Eq. (1) below) describes the interaction of a discrete harmonic oscillator with a continuous bath of harmonic oscillators. This system is a standard model of dissipation in macroscopic low temperature physics, and has applications to superconductors, quantum computing, and macroscopic quantum tunneling. The similar...

For Pearson's model of B\'enard-Marangoni convection, the Nusselt number Nu is proven to be bounded as a function Marangoni number Ma according to $\text{Nu}$\le${}0.838\ifmmode\times\else\texttimes\fi{}{\text{Ma}}^{2/7}$ for infinite Prandtl number and according to $\text{Nu}$\lesssim${}{\text{Ma}}^{1/2}$ uniformly for finite Prandtl number. The a...

The notions of spectral stability and the spectrum for the Vlasov-Poisson system linearized about homogeneous equilibria, f 0(v), are reviewed. Structural stability is reviewed and applied to perturbations of the linearized Vlasov operator through perturbations of f 0. We prove that for each f 0 there is an arbitrarily small δf′0 in such that f 0+δ...

We consider the linearized Vlasov-Poisson equation in the Banach space with the norm |fk|=∑kk^2|fk|W1,1. We perturb the equations by changing the equillibrium solution f0. We prove that that always exists an infinitesimal perturbation of f0' in the W1,1 norm can create an instability at any solution of the equation f0'(v)=0. If we restrict to dynam...

We use the background method to prove rigorous upper bounds on the Nusselt number in terms of the Marangoni number in Marangoni convection. When the Prandtl number is infinite Nu

We construct stable, maximal order boundary closures for high order central difference methods. The stability is achieved by adding a small number of additional subcell nodes near the boundaries at experimentally determined locations. We find that methods up through 8th order can be stabilized by the addition of a single node, up through 16th order...

Phylogenetic trees group organisms by their ancestral relationships. There are a number of distinct algorithms used to reconstruct these trees from molecular sequence data, but different methods sometimes give conflicting results. Since there are few precisely known phylogenies, simulations are typically used to test the quality of reconstruction a...