783 research outputs found
Skyrmions in Higher Landau Levels
We calculate the energies of quasiparticles with large numbers of reversed
spins (``skyrmions'') for odd integer filling factors 2k+1, k is greater than
or equals 1. We find, in contrast with the known result for filling factor
equals 1 (k = 0), that these quasiparticles always have higher energy than the
fully polarized ones and hence are not the low energy charged excitations, even
at small Zeeman energies. It follows that skyrmions are the relevant
quasiparticles only at filling factors 1, 1/3 and 1/5.Comment: 10 pages, RevTe
Exact solution of the six-vertex model with domain wall boundary condition. Critical line between ferroelectric and disordered phases
This is a continuation of the papers [4] of Bleher and Fokin and [5] of
Bleher and Liechty, in which the large asymptotics is obtained for the
partition function of the six-vertex model with domain wall boundary
conditions in the disordered and ferroelectric phases, respectively. In the
present paper we obtain the large asymptotics of on the critical line
between these two phases.Comment: 22 pages, 6 figures, to appear in the Journal of Statistical Physic
Second-order corrections to mean field evolution for weakly interacting Bosons. I
Inspired by the works of Rodnianski and Schlein and Wu, we derive a new
nonlinear Schr\"odinger equation that describes a second-order correction to
the usual tensor product (mean-field) approximation for the Hamiltonian
evolution of a many-particle system in Bose-Einstein condensation. We show that
our new equation, if it has solutions with appropriate smoothness and decay
properties, implies a new Fock space estimate. We also show that for an
interaction potential , where is
sufficiently small and , our program can be easily
implemented locally in time. We leave global in time issues, more singular
potentials and sophisticated estimates for a subsequent part (part II) of this
paper
Hund's Rule for Composite Fermions
We consider the ``fractional quantum Hall atom" in the vanishing Zeeman
energy limit, and investigate the validity of Hund's maximum-spin rule for
interacting electrons in various Landau levels. While it is not valid for {\em
electrons} in the lowest Landau level, there are regions of filling factors
where it predicts the ground state spin correctly {\em provided it is applied
to composite fermions}. The composite fermion theory also reveals a
``self-similar" structure in the filling factor range .Comment: 10 pages, revte
Duality-based two-level error estimation for time-dependent PDEs: application to linear and nonlinear parabolic equations
We introduce a duality-based two-level error estimator for linear and nonlinear time-dependent problems. The error measure can be a space-time norm, energy norm, final-time error or other error related functional. The general methodology is developed for an abstract nonlinear parabolic PDE and subsequently applied to linear heat and nonlinear Cahn-Hilliard equations. The error due to finite element approximations is estimated with a residual weighted approximate-dual solution which is computed with two primal approximations at nested levels. We prove that the exact error is estimated by our estimator up to higher-order remainder terms. Numerical experiments confirm the theory regarding consistency of the dual-based two-level estimator. We also present a novel space-time adaptive strategy to control errors based on the new estimator
Synthesis of Bio-Dimethyl Ether Based on Carbon Dioxide-Enhanced Gasification of Biomass: Process Simulation Using Aspen Plus
YesProcess simulation of a single-step synthesis of DME based on CO2-enhanced gasification of rice straw was conducted using Aspen PlusTM. The process consists of gasification unit, heat recovery unit, gas purification unit, single-step DME synthesis, and DME separation unit. In the simulation, highly pure DME was produced by the control of CO2 concentration in syngas to a very low level prior to synthesis. A gasification system efficiency of 36.7% and CO2 emission of 1.31 kg/kg of DME were achieved. Bio-DME production based on CO2-enhanced gasification of biomass was found to be more cost-effective as it required 19.6% less biomass than that of DME production based on conventional biomass gasification. The performance and environmental benefits of the proposed process could be further improved by the utilization of unreacted gases and the handling of CO2 generated via incorporating poly-generation concept or carbon storage, which could also potentially improve process economics.Ningbo Bureau of Science and Technology; Innovation Team Scheme; Major R&D Programme; Provincial Innovation Team on the Commercialisation of SOx and NOx Removal Technologies; University of Nottingham Ningbo Chin
A-posteriori error estimation and adaptivity for nonlinear parabolic equations using IMEX-Galerkin discretization of primal and dual equations
While many methods exist to discretize nonlinear time-dependent partial differential equations (PDEs), the rigorous estimation and adaptive control of their discretization errors remains challenging. In this paper, we present a methodology for duality-based a posteriori error estimation for nonlinear parabolic PDEs, where the full discretization of the PDE relies on the use of an implicit-explicit (IMEX) time-stepping scheme and the finite element method in space. The main result in our work is a decomposition of the error estimate that allows to separate the effects of spatial and temporal discretization error, and which can be used to drive adaptive mesh refinement and adaptive time-step selection. The decomposition hinges on a specially-tailored IMEX discretization of the dual problem. The performance of the error estimates and the proposed adaptive algorithm is demonstrated on two canonical applications: the elementary heat equation and the nonlinear Allen-Cahn phase-field model
Skyrmion Excitations in Quantum Hall Systems
Using finite size calculations on the surface of a sphere we study the
topological (skyrmion) excitation in quantum Hall system with spin degree of
freedom at filling factors around . In the absence of Zeeman energy, we
find, in systems with one quasi-particle or one quasi-hole, the lowest energy
band consists of states with , where and are the total orbital and
spin angular momentum. These different spin states are almost degenerate in the
thermodynamic limit and their symmetry-breaking ground state is the state with
one skyrmion of infinite size. In the presence of Zeeman energy, the skyrmion
size is determined by the interplay of the Zeeman energy and electron-electron
interaction and the skyrmion shrinks to a spin texture of finite size. We have
calculated the energy gap of the system at infinite wave vector limit as a
function of the Zeeman energy and find there are kinks in the energy gap
associated with the shrinking of the size of the skyrmion. breaking ground
state is the state with one skyrmion of infinite size. In the presence of
Zeeman energy, the skyrmion size is determined by the interplay of the Zeeman
energy and electron-electronComment: 4 pages, 5 postscript figures available upon reques
Fractional Quantum Hall States in Low-Zeeman-Energy Limit
We investigate the spectrum of interacting electrons at arbitrary filling
factors in the limit of vanishing Zeeman splitting. The composite fermion
theory successfully explains the low-energy spectrum {\em provided the
composite fermions are treated as hard-core}.Comment: 12 pages, revte
Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings
We present exact results on the partition function of the -state Potts
model on various families of graphs in a generalized external magnetic
field that favors or disfavors spin values in a subset of
the total set of possible spin values, , where and are
temperature- and field-dependent Boltzmann variables. We remark on differences
in thermodynamic behavior between our model with a generalized external
magnetic field and the Potts model with a conventional magnetic field that
favors or disfavors a single spin value. Exact results are also given for the
interesting special case of the zero-temperature Potts antiferromagnet,
corresponding to a set-weighted chromatic polynomial that counts
the number of colorings of the vertices of subject to the condition that
colors of adjacent vertices are different, with a weighting that favors or
disfavors colors in the interval . We derive powerful new upper and lower
bounds on for the ferromagnetic case in terms of zero-field
Potts partition functions with certain transformed arguments. We also prove
general inequalities for on different families of tree graphs.
As part of our analysis, we elucidate how the field-dependent Potts partition
function and weighted-set chromatic polynomial distinguish, respectively,
between Tutte-equivalent and chromatically equivalent pairs of graphs.Comment: 39 pages, 1 figur
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