255 research outputs found
An iterative analytic series method for Laplacian problems with free and mixed boundary conditions
Mixed boundary value problems occur in a wide variety of applications in applied mathematics. These problems are characterised by a combination of Dirichlet and Neumann conditions along at least one boundary. For example, problems in both saturated and unsaturated flow usually contain mixed boundary conditions. Historically, only a small subset of these problems could be solved using analytic series methods, by using an appropriate coordinate transformation or choice of axes. However, there are some striking similarities between the mixed boundary problem and the free boundary problem, where the location of one boundary is initially unknown. This unknown boundary is subject to two boundary conditions, and so the problem can be fully defined. In this paper, I will point out the similarities between mixed boundary and free boundary problems. I will consider mixed boundary conditions of the form ?? where ? satisfies Laplace's equation. Finally, I will present an iterative method to find analytic series solutions for problems of this type
The 4-loop beta-function in the 2D Non-Abelian Thirring model, and comparison with its conjectured "exact" form
Recently, B. Gerganov, A. LeClair and M. Moriconi [Phys. Rev. Lett. 86 (2001)
4753] have proposed an "exact" (all orders) beta-function for 2-dimensional
conformal field theories with Kac-Moody current-algebra symmetry at any level
k, based on a Lie group G, which are perturbed by a current-current
interaction. This theory is also known as the Non-Abelian Thirring model. We
check this conjecture with an explicit calculation of the beta-function to
4-loop order, for the classical groups G= SU(N), SO(N) and SP(N). We find a
contribution at 4-loop order, proportional to a higher-order group-theoretical
invariant, which is incompatible with the proposed beta-function in all
possible regularization schemes.Comment: 26 pages, 24 figures, latex2
Ring exchange, the Bose metal, and bosonization in two dimensions
Motivated by the high-T_c cuprates, we consider a model of bosonic Cooper
pairs moving on a square lattice via ring exchange. We show that this model
offers a natural middle ground between a conventional antiferromagnetic Mott
insulator and the fully deconfined fractionalized phase which underlies the
spin-charge separation scenario for high-T_c superconductivity. We show that
such ring models sustain a stable critical phase in two dimensions, the *Bose
metal*. The Bose metal is a compressible state, with gapless but uncondensed
boson and ``vortex'' excitations, power-law superconducting and charge-ordering
correlations, and broad spectral functions. We characterize the Bose metal with
the aid of an exact plaquette duality transformation, which motivates a
universal low energy description of the Bose metal. This description is in
terms of a pair of dual bosonic phase fields, and is a direct analog of the
well-known one-dimensional bosonization approach. We verify the validity of the
low energy description by numerical simulations of the ring model in its exact
dual form. The relevance to the high-T_c superconductors and a variety of
extensions to other systems are discussed, including the bosonization of a two
dimensional fermionic ring model
Eigenvalue Problem in Two Dimensions for an Irregular Boundary II: Neumann Condition
We formulate a systematic elegant perturbative scheme for determining the
eigenvalues of the Helmholtz equation (\bigtriangledown^{2} + k^{2}){\psi} = 0
in two dimensions when the normal derivative of {\psi} vanishes on an irregular
closed curve. Unique feature of this method, unlike other perturbation schemes,
is that it does not require a separate formalism to treat degeneracies.
Degenerate states are handled equally elegantly as the non-degenerate ones. A
real parameter, extracted from the parameters defining the irregular boundary,
serves as a perturbation parameter in this scheme as opposed to earlier schemes
where the perturbation parameter is an artificial one. The efficacy of the
proposed scheme is gauged by calculating the eigenvalues for elliptical and
supercircular boundaries and comparing with the results obtained numerically.
We also present a simple and interesting semi-empirical formula, determining
the eigenspectrum of the 2D Helmholtz equation with the Dirichlet or the
Neumann condition for a supercircular boundary. A comparison of the
eigenspectrum for several low-lying modes obtained by employing the formula
with the corresponding numerical estimates shows good agreement for a wide
range of the supercircular exponent.Comment: 26 pages, 12 figure
Proximity effect at superconducting Sn-Bi2Se3 interface
We have investigated the conductance spectra of Sn-Bi2Se3 interface junctions
down to 250 mK and in different magnetic fields. A number of conductance
anomalies were observed below the superconducting transition temperature of Sn,
including a small gap different from that of Sn, and a zero-bias conductance
peak growing up at lower temperatures. We discussed the possible origins of the
smaller gap and the zero-bias conductance peak. These phenomena support that a
proximity-effect-induced chiral superconducting phase is formed at the
interface between the superconducting Sn and the strong spin-orbit coupling
material Bi2Se3.Comment: 7 pages, 8 figure
Centrality Dependence of the High p_T Charged Hadron Suppression in Au+Au collisions at sqrt(s_NN) = 130 GeV
PHENIX has measured the centrality dependence of charged hadron p_T spectra
from central Au+Au collisions at sqrt(s_NN)=130 GeV. The truncated mean p_T
decreases with centrality for p_T > 2 GeV/c, indicating an apparent reduction
of the contribution from hard scattering to high p_T hadron production. For
central collisions the yield at high p_T is shown to be suppressed compared to
binary nucleon-nucleon collision scaling of p+p data. This suppression is
monotonically increasing with centrality, but most of the change occurs below
30% centrality, i.e. for collisions with less than about 140 participating
nucleons. The observed p_T and centrality dependence is consistent with the
particle production predicted by models including hard scattering and
subsequent energy loss of the scattered partons in the dense matter created in
the collisions.Comment: 7 pages text, LaTeX, 6 figures, 2 tables, 307 authors, resubmitted to
Phys. Lett. B. Revised to address referee concerns. Plain text data tables
for the points plotted in figures for this and previous PHENIX publications
are publicly available at
http://www.phenix.bnl.gov/phenix/WWW/run/phenix/papers.htm
Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration
Extensive experimental data from high-energy nucleus-nucleus collisions were
recorded using the PHENIX detector at the Relativistic Heavy Ion Collider
(RHIC). The comprehensive set of measurements from the first three years of
RHIC operation includes charged particle multiplicities, transverse energy,
yield ratios and spectra of identified hadrons in a wide range of transverse
momenta (p_T), elliptic flow, two-particle correlations, non-statistical
fluctuations, and suppression of particle production at high p_T. The results
are examined with an emphasis on implications for the formation of a new state
of dense matter. We find that the state of matter created at RHIC cannot be
described in terms of ordinary color neutral hadrons.Comment: 510 authors, 127 pages text, 56 figures, 1 tables, LaTeX. Submitted
to Nuclear Physics A as a regular article; v3 has minor changes in response
to referee comments. Plain text data tables for the points plotted in figures
for this and previous PHENIX publications are (or will be) publicly available
at http://www.phenix.bnl.gov/papers.htm
The PHENIX Experiment at RHIC
The physics emphases of the PHENIX collaboration and the design and current
status of the PHENIX detector are discussed. The plan of the collaboration for
making the most effective use of the available luminosity in the first years of
RHIC operation is also presented.Comment: 5 pages, 1 figure. Further details of the PHENIX physics program
available at http://www.rhic.bnl.gov/phenix
Mucedorus: the last ludic playbook, the first stage Arcadia
This article argues that two seemingly contradictory factors contributed to and sustained the success of the anonymous Elizabethan play Mucedorus (c. 1590; pub. 1598). First, that both the initial composition of Mucedorus and its Jacobean revival were driven in part by the popularity of its source, Philip Sidney's Arcadia. Second, the playbook's invitation to amateur playing allowed its romance narrative to be adopted and repurposed by diverse social groups. These two factors combined to create something of a paradox, suggesting that Mucedorus was both open to all yet iconographically connected to an elite author's popular text. This study will argue that Mucedorus pioneered the fashion for “continuations” or adaptations of the famously unfinished Arcadia, and one element of its success in print was its presentation as an affordable and performable version of Sidney's elite work. The Jacobean revival of Mucedorus by the King's Men is thus evidence of a strategy of engagement with the Arcadia designed to please the new Stuart monarchs. This association with the monarchy in part determined the cultural functions of the Arcadia and Mucedorus through the Interregnum to the close of the seventeenth century
Saturation of azimuthal anisotropy in Au + Au collisions at sqrt(s_NN) = 62 - 200 GeV
New measurements are presented for charged hadron azimuthal correlations at
mid-rapidity in Au+Au collisions at sqrt(s_NN) = 62.4 and 200 GeV. They are
compared to earlier measurements obtained at sqrt(s_NN) = 130 GeV and in Pb+Pb
collisions at sqrt(s_NN) = 17.2 GeV. Sizeable anisotropies are observed with
centrality and transverse momentum (p_T) dependence characteristic of elliptic
flow (v_2). For a broad range of centralities, the observed magnitudes and
trends of the differential anisotropy, v_2(p_T), change very little over the
collision energy range sqrt(s_NN) = 62-200 GeV, indicating saturation of the
excitation function for v_2 at these energies. Such a saturation may be
indicative of the dominance of a very soft equation of state for sqrt(s_NN) =
62-200 GeV.Comment: 432 authors, 7 pages text, 4 figures, REVTeX4. To be submitted to
Physical Review Letters. Plain text data tables for the points plotted in
figures for this and previous PHENIX publications are (or will be) publicly
available at http://www.phenix.bnl.gov/papers.htm
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