Galaxies & Dark Matter Evolution

A dark matter halo distribution in the LasDamas simulations, showing the computational volumes to scale. Smaller boxes allow much higher spatial resolution, to understand faint galaxies, whereas larger boxes are designed to study luminous galaxies and cover a large fraction of the observable universe.

LasDamas (lss.phy.vanderbilt.edu/lasdamas) is an international collaboration among researchers from Vanderbilt University, the University of Washington, the Max Planck Institute of Astronomy, Stanford University — and Roman Scoccimarro of NYU's Center for Cosmology and Particle Physics (FAS). Professor Scoccimarro's interest is in theoretical cosmology, large scale structure of the universe, gravitational clustering, and primordial fluctuations.

Professor Scoccimarro writes, "Large Suite of Dark Matter Simulations (LasDamas) is a project to run a large suite of cosmological N-body simulations that follow the evolution of dark matter in the universe. The project's focus is to obtain adequate resolution in many large boxes, rather than a single realization at high resolution.

"This will result in an enormous volume of data appropriate for statistical studies of galaxies and dark matter halos. We plan to study the clustering of halos as a function of mass and other properties, the internal density and velocity profiles of halos, their three-dimensional shapes, and their mass-accretion and merger histories. Quantifying these properties and their correlations with each other at high signal-to-noise will help improve halo models and will be invaluable for helping to understand the physics of galaxy formation."

Household Investment Behavior

Roine Vestman is completing his Ph.D. at the Department of Economics (FAS) under the supervision of Professor Thomas J. Sargent. His research interest is in macroeconomics and household finance. "This dissertation project," he writes, "uses a dataset with detailed wealth information on a sample of Swedish households, as well as socio-demographic information on these households, to document households' investment behavior as a function of house ownership and other characteristics. The observed investment behavior is compared with the predictions of a state-of-the-art portfolio choice model.

"The purpose is to understand households' financial choices, by taking into account important factors, such as the household's housing situation. Housing wealth is, for most house owners, a large part of total wealth. For renters, housing consumption is a large part of total consumption. So, it's important to incorporate housing in the model, although that makes it more complex."

In the portfolio choice model, the household chooses whether to rent or own its home, as well as the size of the home. Simultaneously, the household makes a financial savings decision. Of particular interest is the choice of the allocation between safe and risky financial assets, the equity share, and how this decision interacts with the housing decision (bottom left panel). The model is solved using dynamic programming methods in FORTRAN.

Viscoelastic Fluid Models

Becca Thomases is an Assistant Professor of Mathematics at the University of California at Davis whose research focuses on analysis and computations of nonlinear partial differential equations (PDE) arising from physical systems. She and NYU Professor Michael Shelley (Mathematics and Neural Science, CIMS) have been using the cluster to work on simulations of viscoelastic fluid models in two- and three-space dimensions. Viscoelastic fluids are relevant to the study of biological fluids, as well as in industrial applications such as the manufacture of petrochemical lubricants and plastics.

"With the aid of Estarose Wolfson, also of CIMS, we have parallelized our pseudo-spectral code to run on multiple processors. The cluster's high level of computational power enables us to get a very high degree of accuracy in our simulations. In two spatial dimensions, the cluster is used to obtain accuracy with n=40962 grid cell points and time steps of .00015. A total of 65536 particle points are updated at every time step."

From left to right: (a) The resolution of very steep gradients as the polymer stress becomes singular exponentially in time; the next step has been to analyze the stability of steady states in the problem. (b) The polymer stress at t=2000 after the onset of a symmetry breaking transition in the flow. (c) & (d) Particle tracers in the fluid; they start out separated into four quadrants and over time ((c) t=500) and ((d) t=2000) become highly mixed by the flow.

Oxygen Pathways in Myoglobin

Above, two isosurfaces of the three dimensional free energy map for ligand migration in Myoglobin (red 2kcal/mol, transparent 7kcal/mol), superimposed on a representation of Myoglobin’s molecular structure. Yellow lines represent minimum free energy paths connecting the binding site to the solvent, and passing through protein internal cavities. White spheres are saddle points along these paths. To obtain this map, about 250 independent calculations of 40 hours of wall-clock time each were performed using the cluster.

As part of an international research group, Luca Maragliano — currently a postdoctoral researcher at the Department of Biochemistry and Molecular Biology, University of Chicago — and NYU Professor Eric Vanden-Eijnden of the Department of Mathematics (CIMS), have recently developed "a method to compute from simulations a three-dimensional free energy landscape for a dissociated ligand inside Myoglobin. Once the map is available, the paths for ligand migration are identified as minimum free energy paths on it. The basic idea of our method is to interpolate the free energy using a set of values of its derivatives, computed at different locations. Such calculations are independent from each other and hence are distributed on different cluster nodes.

"Myoglobin is the first protein whose atomic structure was revealed by X-rays. It binds molecular oxygen (O2) at a reaction center in its interior, keeping it available for use by muscles, or oxygen compounds as CO. The binding site is buried in the protein inside, and no clear path to it can be observed by looking at the molecular surface. Indeed, finding the pathways of ligand entrance and exit in Myoglobin is one of the oldest problems in molecular biophysics."

Arctic Shelf Systems' Behaviors

Tasha Reddy, Ph.D., is a postdoctoral fellow at NYU's Center for Atmospheric and Ocean Science (CIMS). Her research involves studying Antarctic and Arctic open water ecosystems and sea ice using a combination of numerical modeling, satellite remote sensing, and field studies.

"The multi-year ice pack that covers the central Arctic Ocean has thinned from 3.1 m in the 1960's to 1.8 m in the 1990's. Over this time period, the long-term areal extent of sea ice has decreased by 14%. Although these changes could represent a component in a natural cycle, this trend could also harbinger the "meltdown' of the Arctic in response to anthropogenic climate warming.

"In recent years, two major observational programs have been launched and have garnished significant physical, geochemical, and biological data over specific Arctic shelves. The successful Shelf-Basin Interaction (SBI) project over the Alaskan Shelf and Canadian Arctic Shelf Exchange Study (CASES) over the Mackenzie shelf represent a major step forward in quality and quantity of observational data upon which a model of the present and future behavior of the Arctic shelf systems can be constructed.

"The purpose of this project is to construct a robust, coupled physical and biological model of the Alaskan and Mackenzie shelf ecosystems and their interaction with the Arctic basin, based on the observational data sets of the SBI and CASES programs."

Observed winter (A) and summer (B) ice cover concentrations over the Arctic compared to modeled winter (C) and summer (D) ice concentrations. (Dark grey shows land mass, and colors show percent ice concentration.)

Comparing Entrepreneurs' & Wage Workers' Earnings

Chloe Tergiman is a graduate of MIT and a current student at NYU's Department of Economics (FAS). Her research interest is entrepreneurship and political economics, and her academic advisors are Professors Guillaume Frechette and Boyan Jovanovic.

"If we focus on the earnings of the median entrepreneur and compare it with the earnings of the median wageworker, data show that the median entrepreneur fares less well than his wageworker counterpart. This is true for any level of tenure, and the difference in their earnings increases with time. In other words, if we take an individual who has been an entrepreneur for 10 years say, and compare his earnings with the earnings of a worker who has worked for 10 years, the entrepreneur makes less money. After 10 years of tenure, this difference can reach 30%. This raises a significant puzzle: if the returns to entrepreneurship are so low, why are there so many entrepreneurs?

"The mathematical problems involved are all non-linear constrained optimizations with no closed form solutions. Further, because I chose to endogenize all the "economic variables,' I needed to write code that could easily handle symbolic calculations. Mathematica (www.wolfram.com) was perfectly suited. I am currently expanding my model to a multi-sector economy (with different goods being produced by different entrepreneurs), thus expanding my computing needs."

Predicting Ice Sheet Instability

Daniel Goldberg, a Ph.D. student at NYU's Center for Atmosphere Ocean Science (CAOS, CIMS), is studying the dynamics of Antarctic ice shelves and fast-moving ice streams, using mathematical and numerical modeling, under the supervison of his advisor, CAOS Director David Holland (Department of Mathematics, CIMS). He writes:

"The West Antarctic Ice Sheet is a marine ice sheet, meaning that its base is below sea level. As such, there are strong interactions between the ice sheet's streams and their floating ice shelves. This implies that factors affecting ice shelves, such as ocean melting and the breaking off of large pieces of shelves, can feed back on the ice sheet's dynamics. The boundary between grounded and floating ice, also referred to as the grounding line, can change due to mass flux imbalances, which in turn can modify the flow of the streams.

"Using the deal.II software library (dealii.org), I have developed a model that makes use of the finite element and finite volume methods to solve the time-dependent Shelfy-Stream approximation to the governing glaciological equations [1]. Running this model on the cluster and using up to 16 CPUs simultaneously, I have carried out experiments to determine how both ice shelf buttressing and ice rises affect the instability to collapse predicted for an ice sheet on a foredeepened bed — that is, a bed that deepens moving inland."

Seaward velocity after 1000 years (simulated time)

Marine ice sheet with initially partly grounded shelf (ice rise). The sheet is cut away to reveal the seamount.