90 research outputs found
Assessment of Streams and Watersheds in Illinois: Development of a Stream Classification System and Fish Sampling Protocols
Final Report issued October 1, 2003.Report issued on: October 1, 2003INHS Technical Report prepared for Illinois Department of Natural Resources, Office of
Resource Conservation and Illinois Environmental Protection Agency, Bureau of Wate
Conformal Symmetries of the Self-Dual Yang-Mills Equations
We describe an infinite-dimensional Kac-Moody-Virasoro algebra of new hidden
symmetries for the self-dual Yang-Mills equations related to conformal
transformations of the 4-dimensional base space.Comment: 12 pages, Late
The Information Geometry of the Ising Model on Planar Random Graphs
It has been suggested that an information geometric view of statistical
mechanics in which a metric is introduced onto the space of parameters provides
an interesting alternative characterisation of the phase structure,
particularly in the case where there are two such parameters -- such as the
Ising model with inverse temperature and external field .
In various two parameter calculable models the scalar curvature of
the information metric has been found to diverge at the phase transition point
and a plausible scaling relation postulated: . For spin models the necessity of calculating in
non-zero field has limited analytic consideration to 1D, mean-field and Bethe
lattice Ising models. In this letter we use the solution in field of the Ising
model on an ensemble of planar random graphs (where ) to evaluate the scaling behaviour of the scalar curvature, and find
. The apparent discrepancy is traced
back to the effect of a negative .Comment: Version accepted for publication in PRE, revtex
The Information Geometry of the Spherical Model
Motivated by previous observations that geometrizing statistical mechanics
offers an interesting alternative to more standard approaches,we have recently
calculated the curvature (the fundamental object in this approach) of the
information geometry metric for the Ising model on an ensemble of planar random
graphs. The standard critical exponents for this model are alpha=-1, beta=1/2,
gamma=2 and we found that the scalar curvature, R, behaves as
epsilon^(-2),where epsilon = beta_c - beta is the distance from criticality.
This contrasts with the naively expected R ~ epsilon^(-3) and the apparent
discrepancy was traced back to the effect of a negative alpha on the scaling of
R.
Oddly,the set of standard critical exponents is shared with the 3D spherical
model. In this paper we calculate the scaling behaviour of R for the 3D
spherical model, again finding that R ~ epsilon^(-2), coinciding with the
scaling behaviour of the Ising model on planar random graphs. We also discuss
briefly the scaling of R in higher dimensions, where mean-field behaviour sets
in.Comment: 7 pages, no figure
Unified description of ballistic and diffusive carrier transport in semiconductor structures
A unified theoretical description of ballistic and diffusive carrier
transport in parallel-plane semiconductor structures is developed within the
semiclassical model. The approach is based on the introduction of a
thermo-ballistic current consisting of carriers which move ballistically in the
electric field provided by the band edge potential, and are thermalized at
certain randomly distributed equilibration points by coupling to the background
of impurity atoms and carriers in equilibrium. The sum of the thermo-ballistic
and background currents is conserved, and is identified with the physical
current. The current-voltage characteristic for nondegenerate systems and the
zero-bias conductance for degenerate systems are expressed in terms of a
reduced resistance. For arbitrary mean free path and arbitrary shape of the
band edge potential profile, this quantity is determined from the solution of
an integral equation, which also provides the quasi-Fermi level and the
thermo-ballistic current. To illustrate the formalism, a number of simple
examples are considered explicitly. The present work is compared with previous
attempts towards a unified description of ballistic and diffusive transport.Comment: 23 pages, 10 figures, REVTEX
Probing the fuzzy sphere regularisation in simulations of the 3d \lambda \phi^4 model
We regularise the 3d \lambda \phi^4 model by discretising the Euclidean time
and representing the spatial part on a fuzzy sphere. The latter involves a
truncated expansion of the field in spherical harmonics. This yields a
numerically tractable formulation, which constitutes an unconventional
alternative to the lattice. In contrast to the 2d version, the radius R plays
an independent r\^{o}le. We explore the phase diagram in terms of R and the
cutoff, as well as the parameters m^2 and \lambda. Thus we identify the phases
of disorder, uniform order and non-uniform order. We compare the result to the
phase diagrams of the 3d model on a non-commutative torus, and of the 2d model
on a fuzzy sphere. Our data at strong coupling reproduce accurately the
behaviour of a matrix chain, which corresponds to the c=1-model in string
theory. This observation enables a conjecture about the thermodynamic limit.Comment: 31 pages, 15 figure
Non-local charges on AdS_5 x S^5 and PP-waves
We show the existence of an infinite set of non-local classically conserved
charges on the Green-Schwarz closed superstring in a pp-wave background. We
find that these charges agree with the Penrose limit of non-local classically
conserved charges recently found for the Green-Schwarz
superstring. The charges constructed in this paper could help to understand the
role played by these on the full background.Comment: 20 pages. JHEP. v2:references adde
Insights from a Convocation: Integrating Discovery-Based Research into the Undergraduate Curriculum
The National Academies of Sciences, Engineering, and Medicine organized a convocation in 2015 to explore and elucidate opportunities, barriers, and realities of course-based undergraduate research experiences, known as CUREs, as a potentially integral component of undergraduate science, technology, engineering, and mathematics education. This paper summarizes the convocation and resulting report
Different definitions of the chemical potential with identical partition function in QCD on a lattice
It is shown that starting from one and the same transfer matrix formulation
of QCD on a lattice, it is possible to obtain both the action of Hasenfratz and
Karsch as well as an action where the chemical potential is not coupled to the
temporal links.Comment: 4 page
A Conformally Invariant Holographic Two-Point Function on the Berger Sphere
We apply our previous work on Green's functions for the four-dimensional
quaternionic Taub-NUT manifold to obtain a scalar two-point function on the
homogeneously squashed three-sphere (otherwise known as the Berger sphere),
which lies at its conformal infinity. Using basic notions from conformal
geometry and the theory of boundary value problems, in particular the
Dirichlet-to-Robin operator, we establish that our two-point correlation
function is conformally invariant and corresponds to a boundary operator of
conformal dimension one. It is plausible that the methods we use could have
more general applications in an AdS/CFT context.Comment: 1+49 pages, no figures. v2: Several typos correcte
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