92,552 research outputs found
ENO-wavelet transforms for piecewise smooth functions
We have designed an adaptive essentially nonoscillatory (ENO)-wavelet transform for approximating discontinuous functions without oscillations near the discontinuities. Our approach is to apply the main idea from ENO schemes for numerical shock capturing to standard wavelet transforms. The crucial point is that the wavelet coefficients are computed without differencing function values across jumps. However, we accomplish this in a different way than in the standard ENO schemes. Whereas in the standard ENO schemes the stencils are adaptively chosen, in the ENO-wavelet transforms we adaptively change the function and use the same uniform stencils. The ENO-wavelet transform retains the essential properties and advantages of standard wavelet transforms such as concentrating the energy to the low frequencies, obtaining maximum accuracy, maintained up to the discontinuities, and having a multiresolution framework and fast algorithms, all without any edge artifacts. We have obtained a rigorous approximation error bound which shows that the error in the ENO-wavelet approximation depends only on the size of the derivative of the function away from the discontinuities. We will show some numerical examples to illustrate this error estimate
Ground-state configuration space heterogeneity of random finite-connectivity spin glasses and random constraint satisfaction problems
We demonstrate through two case studies, one on the p-spin interaction model
and the other on the random K-satisfiability problem, that a heterogeneity
transition occurs to the ground-state configuration space of a random
finite-connectivity spin glass system at certain critical value of the
constraint density. At the transition point, exponentially many configuration
communities emerge from the ground-state configuration space, making the
entropy density s(q) of configuration-pairs a non-concave function of
configuration-pair overlap q. Each configuration community is a collection of
relatively similar configurations and it forms a stable thermodynamic phase in
the presence of a suitable external field. We calculate s(q) by the
replica-symmetric and the first-step replica-symmetry-broken cavity methods,
and show by simulations that the configuration space heterogeneity leads to
dynamical heterogeneity of particle diffusion processes because of the entropic
trapping effect of configuration communities. This work clarifies the fine
structure of the ground-state configuration space of random spin glass models,
it also sheds light on the glassy behavior of hard-sphere colloidal systems at
relatively high particle volume fraction.Comment: 26 pages, 9 figures, submitted to Journal of Statistical Mechanic
First-principles study of phenyl ethylene oligomers as current-switch
We use a self-consistent method to study the distinct current-switch of
-amino-4-ethynylphenyl-4'-ethynylphenyl-5'-nitro-1-benzenethiol, from
the first-principles calculations. The numerical results are in accord with the
early experiment [Reed et al., Sci. Am. \textbf{282}, 86 (2000)]. To further
investigate the transport mechanism, we calculate the switching behavior of
p-terphenyl with the rotations of the middle ring as well. We also study the
effect of hydrogen atom substituting one ending sulfur atom on the transport
and find that the asymmetry of I-V curves appears and the switch effect still
lies in both the positive and negative bias range.Comment: 6 pages, 6 figure
Fermionic R-operator approach for the small-polaron model with open boundary condition
Exact integrability and algebraic Bethe ansatz of the small-polaron model
with the open boundary condition are discussed in the framework of the quantum
inverse scattering method (QISM). We employ a new approach where the fermionic
R-operator which consists of fermion operators is a key object. It satisfies
the Yang-Baxter equation and the reflection equation with its corresponding
K-operator. Two kinds of 'super-transposition' for the fermion operators are
defined and the dual reflection equation is obtained. These equations prove the
integrability and the Bethe ansatz equation which agrees with the one obtained
from the graded Yang-Baxter equation and the graded reflection equations.Comment: 10 page
Quantum integrability and exact solution of the supersymmetric U model with boundary terms
The quantum integrability is established for the one-dimensional
supersymmetric model with boundary terms by means of the quantum inverse
scattering method. The boundary supersymmetric chain is solved by using the
coordinate space Bethe ansatz technique and Bethe ansatz equations are derived.
This provides us with a basis for computing the finite size corrections to the
low lying energies in the system.Comment: 4 pages, RevTex. Some cosmetic changes. The version to appear in
Phys. Rev.
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