4,836 research outputs found
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
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, 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
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
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