Graduate Student Computing

Below you will find summaries and links to the various research projects that have benefited from the existence of the cluster.

Spacetime lattice provides a natural regulator for QCD, while the functional integrals of QCD are amenable to Monte Carlo integration techniques. Thus a numerical approach to studying QCD is feasible, with a primary limitation being computational resources. Currently I am developing code to calculate renormalization constants non-perturbatively on the lattice, using staggered fermions. These constants will improve the determination of continuum quantities such as quark masses. The student computer cluster will allow testing of the code as it is scaled up to realistic levels.

I am applying the Single Chain in Mean Field (SCMF) method of M. Müller et al. to bilayers composed of several block copolymer components. The SCMF approach should capture phenomena related to fluctuations in lateral composition and it is hoped that this will shed light on the phase behavior of multicomponent lipid bilayers. I intend also to investigate the behavior of bilayers with asymmetric compositions (specifically, the existence and nature of coupling between the two leaves of the bilayer). Running simulations on this cluster allows me to better understand the behavior of the model as well as the SCMF method as its parameters are varied.

Many features of kinetic roughening phenomena can be described by the Kardar-Parisi-Zhang equation, which in turn is related to the asymmetric simple exclusion process (ASEP) and directed polymers in random media (DPRM). From studies done in the ASEP context (see cond-mat/0307403) and the relationship between ASEP and DPRM, we expect that there should be a localization phase transition in the 1+1 dimensional DPRM with a single line defect.

I am looking for the existence and location of the phase transition numerically using a straightforward transfer matrix method (see Halpin-Healy, Zhang, Phys Rep 254 (1995) 215-414). Use of the Condor cluster allows for the study of larger system sizes and higher precision.

The LHC will provide particle physics with ample data at unprecedented energy scales. However, a major challenge will be finding event samples of new physics processes inside the huge background that QCD provides. To this end, we are studying techniques to characterize event shapes in regions of phase space with a QCD background. Our goal is to develop computational tools to purify event samples, by focusing on methods for distinguishing QCD jets from ones arising from heavy particle or cascade decays.

One of the most crucial components of such a project is the availability of computational resources to build an event library. Our condor cluster enables us to efficiently generate classes of events with the modular Monte Carlo generator MadGraph/MadEvent. Together, these tools let us generate events at the parton level, evolve them to final states, and run them through a detector simulation, enabling us to examine the event from start to finish.

The study of the crossover between Bose-Einstein condensation and BCS pairing in systems of cold atoms has attracted a lot of attention lately, especially since its realization at various laboratories around the world. From the theoretical perspective the middle of the crossover, where the scattering length is infinite (also called the unitary limit), is relevant for models of neutron matter, too. Since these systems are dilute with respect to the range of the interaction, the region of large scattering lengths (i.e. around unitarity) is not amenable to perturbative treatments: there is no (potentially small) dimensionless quantity. As a consequence, study of this interesting problem demands intensive use of computers. Our group implemented a Monte Carlo algorithm and applied it to the case of fermions at unitarity, determining their thermal properties for a wide range of temperatures around the superfluid phase transition (see cond-mat/0505374 or Phys. Rev. Lett. 96, 090404 (2006)).

The usual path integral formulation for scalar particles at finite density involves a sign problem, making numerical simulations impractical. Using our new cluster I explored alternative methods free of this difficulty, and applied them to phi-fourth theory in 2+1 dimensions in the vicinity of the phase transition in the T-mu plane.

An idealized simple model such as an asymmetric exclusion process (ASEP) has been widely studied to understand the universality class encompassing simple and complex non-equilibrium real systems, e.g., sand box avalanche, crystal surface growth, bio-polymerization and traffic flow.

One-species ASEP belongs to KPZ universality class. However, the universality class of two-species ASEP has not known yet. The previous studies are mainly focused on its stationary state and its dynamics of particle cluster growth.

We confirm numerically that the dynamic exponent is equal to z=1.5. This result indicates that the model still belongs to the KPZ universality class. We find numerically that a quasi-particle representation relates all points in the phase diagram to a special line, where the dynamics is directly related to the single species asymmetric exclusion process. The particle two-point correlations decay exponentially, and in such a manner that particles of opposite charge dynamically screen each other.

Quantum chromodynamics (QCD) is the theory of the strong interactions that bind quarks and gluons into the hadrons (protons, neutrons, pions etc) that we observe. QCD is an asymptotically free theory so when energies become large, the strength of the interactions between the quarks and gluons decreases. At the very high energies available in particle accelerators such as the TeVatron, the perturbative methods that work so well in quantum electrodynamics are also applicable in QCD and precise calculations can be performed. In this region, QCD has been well tested and consistenly describes available experimental data. In contrast, at the low energies relevant for the everyday world, quarks and gluons interact so strongly that they are confined and we only ever observe hadrons (protons, neutrons, pions etc.) -- the spectrum of quark and gluon bound states. Thus it is not yet possible to give an analytic expression for such a simple quantity as the proton's mass from QCD.

Lattice QCD is a probabalistic numerical approach to solving QCD that compactifies and discretises space-time to enable the field equations of QCD to be solved on computers. In the limit of vanishing lattice spacing (discretisation) and infinite volume, it is QCD. The condor-cluster is enabling us to perform small scale calculations of hadronic observables such as masses, magnetic moments and electromagnetic and spin polarisabilities. We are also performing further studies in the heavy quark sector.