Exact Algorithm for Sampling the 2D Ising Spin Glass

A sampling algorithm is presented that generates spin glass configurations of the 2D Edwards-Anderson Ising spin glass at finite temperature, with probabilities proportional to their Boltzmann weights. Such an algorithm overcomes the slow dynamics of direct simulation and can be used to study long-range correlation functions and coarse-grained dynamics. The algorithm uses a correspondence between spin configurations on a regular lattice and dimer (edge) coverings of a related graph: Wilson's algorithm [D. B. Wilson, Proc. 8th Symp. Discrete Algorithms 258, (1997)] for sampling dimer coverings on a planar lattice is adapted to generate samplings for the dimer problem corresponding to both planar and toroidal spin glass samples. This algorithm is recursive: it computes probabilities for spins along a "separator" that divides the sample in half. Given the spins on the separator, sample configurations for the two separated halves are generated by further division and assignment. The algorithm is simplified by using Pfaffian elimination, rather than Gaussian elimination, for sampling dimer configurations. For n spins and given floating point precision, the algorithm has an asymptotic run-time of O(n^{3/2}); it is found that the required precision scales as inverse temperature and grows only slowly with system size. Sample applications and benchmarking results are presented for samples of size up to n=128^2, with fixed and periodic boundary conditions.Comment: 18 pages, 10 figures, 1 table; minor clarification

Irrational mode locking in quasiperiodic systems

A model for ac-driven systems, based on the Tang-Wiesenfeld-Bak-Coppersmith-Littlewood automaton for an elastic medium, exhibits mode-locked steps with frequencies that are irrational multiples of the drive frequency, when the pinning is spatially quasiperiodic. Detailed numerical evidence is presented for the large-system-size convergence of such a mode-locked step. The irrational mode locking is stable to small thermal noise and weak disorder. Continuous time models with irrational mode locking and possible experimental realizations are discussed.Comment: 4 pages, 3 figures, 1 table; revision: 2 figures modified, reference added, minor clarification

Richard Smalley and the Materials of Tomorrow: the discovery, properties, and science of fullerenes

These are slides accompanying a presentation given at the Natural Sciences Poster Session at Parkland College outlining the properties of and ongoing research pertaining to fullerenes in materials science

Freedom and the Ideal Republican State: Kant, Jefferson, and the Place of Individual Freedom in the Republican Constitutional State

Of the questions concerning the many great minds of the European Enlightenment, the question of what constitutes right and proper government perhaps had the most enduring influence on the world stage. Both Thomas Jefferson and Immanuel Kant attempted to answer the question of what constitutes right government, in particular by basing the system upon the idea of human freedom as an inalienable right. This project is an attempt to compare the systems proposed by these two authors, as well as to critique each on its ability to protect and foster individual freedom. It is my opinion that neither manages to do what it is constructed to do, as each fails to fully protect individual freedom, and each has as part of it a component which conflicts with individual freedom

Richard Smalley and the Materials of Tomorrow: The Discovery and Science of Fullerenes

This poster for the Natural Sciences Poster Session at Parkland College details the contributions of Richard Smalley to organic chemistry, specifically the discovery of fullerenes in 1984, which led to advancements in the field of nanoscience. Fullerene use in materials science, Single-walled and multi-walled nanotubes and use of fullerenes in biology are also outlined

Decoding the Double Helix: Frederick Sanger and Sanger Sequencing

This is a poster presented at the Natural Sciences Poster Session at Parkland College, which summarizes the work of Frederick Sanger, a British biochemist and the only recipient of two separate Nobel Prizes in the field of chemistry. His first prize was awarded for his work deciphering the structure of the protein insulin. This discovery would go on to influence research on proteins and DNA as it determined that proteins had definite structures and led to the theory that DNA directed the construction of proteins. His second was awarded for this work on the Sanger method of DNA sequencing and was shared with Walter Gilbert