43,829 research outputs found
Quantitative Description of by the Hubbard Model in Infinite Dimensions
We show that the analytic single-particle density of states and the optical
conductivity for the half-filled Hubbard model on the Bethe lattice in infinite
dimensions describe quantitatively the behavior of the gap and the kinetic
energy ratio of the correlated insulator . The form of the optical
conductivity shows rising and is quite similar to the
experimental data, and the density of states shows behavior near
the band edges.Comment: 9 pages, revtex, 4 figures upon reques
Provable Deterministic Leverage Score Sampling
We explain theoretically a curious empirical phenomenon: "Approximating a
matrix by deterministically selecting a subset of its columns with the
corresponding largest leverage scores results in a good low-rank matrix
surrogate". To obtain provable guarantees, previous work requires randomized
sampling of the columns with probabilities proportional to their leverage
scores.
In this work, we provide a novel theoretical analysis of deterministic
leverage score sampling. We show that such deterministic sampling can be
provably as accurate as its randomized counterparts, if the leverage scores
follow a moderately steep power-law decay. We support this power-law assumption
by providing empirical evidence that such decay laws are abundant in real-world
data sets. We then demonstrate empirically the performance of deterministic
leverage score sampling, which many times matches or outperforms the
state-of-the-art techniques.Comment: 20th ACM SIGKDD Conference on Knowledge Discovery and Data Minin
Crumpling wires in two dimensions
An energy-minimal simulation is proposed to study the patterns and mechanical
properties of elastically crumpled wires in two dimensions. We varied the
bending rigidity and stretching modulus to measure the energy allocation,
size-mass exponent, and the stiffness exponent. The mass exponent is shown to
be universal at value . We also found that the stiffness exponent
is universal, but varies with the plasticity parameters and
. These numerical findings agree excellently with the experimental
results
Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian
Based on the technique of integration within an ordered product (IWOP) of
operators we introduce the Fresnel operator for converting Caldirola-Kanai
Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel
operator with the parameters A,B,C,D corresponds to classical optical Fresnel
transformation, these parameters are the solution to a set of partial
differential equations set up in the above mentioned converting process. In
this way the exact wavefunction solution of the Schr\"odinger equation governed
by the Caldirola-Kanai Hamiltonian is obtained, which represents a squeezed
number state. The corresponding Wigner function is derived by virtue of the
Weyl ordered form of the Wigner operator and the order-invariance of Weyl
ordered operators under similar transformations. The method used here can be
suitable for solving Schr\"odinger equation of other time-dependent
oscillators.Comment: 6 pages, 2 figure
Finite-size scaling of synchronized oscillation on complex networks
The onset of synchronization in a system of random frequency oscillators
coupled through a random network is investigated. Using a mean-field
approximation, we characterize sample-to-sample fluctuations for networks of
finite size, and derive the corresponding scaling properties in the critical
region. For scale-free networks with the degree distribution at large , we found that the finite size exponent
takes on the value 5/2 when , the same as in the globally coupled
Kuramoto model. For highly heterogeneous networks (),
and the order parameter exponent depend on . The analytic
expressions for these exponents obtained from the mean field theory are shown
to be in excellent agreement with data from extensive numerical simulations.Comment: 7 page
Hybrid Chaplygin gas and phantom divide crossing
Hybrid Chaplygin gas model is put forward, in which the gases play the role
of dark energy. For this model the coincidence problem is greatly alleviated.
The effective equation of state of the dark energy may cross the phantom divide
. Furthermore, the crossing behaviour is decoupled from any gravity
theories. In the present model, is only a transient behaviour. There is
a de Sitter attractor in the future infinity. Hence, the big rip singularity,
which often afflicts the models with matter whose effective equation of state
less than -1, is naturally disappear. There exist stable scaling solutions,
both at the early universe and the late universe. We discuss the perturbation
growth of this model. We find that the index is consistent with observations.Comment: 11 pages, 4 figures, V3: discussions on the perturbation growth
added, V4: minor corrections, to match the published versio
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An experimental study of dynamic flow of nanofluid with different concentrations
This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.Current reported data of nanofluid concentration is almost all based on TEM observation, which is in a static situation. No data of dynamic concentration during flow is reported. In the present study, an experimental measurement based on nuclear magnetic resonance (NMR) of monitoring the dynamic concentrations of nanofluid flow is carried out. It is demonstrated that the ferrofluid with Fe3O4 as its nanoparticles coated with surfactant as a special type of nanofluid can be used as T2 contrast agent in NMR scanning as well as a magnetic and thermal sensitive nanoparticle solution that would enhance heat transfer
Chiral symmetry breaking in a uniform external magnetic field II. Symmetry restoration at high temperatures and chemical potentials
Chiral symmetry is dynamically broken in quenched, ladder QED at weak gauge
couplings when an external magnetic field is present. In this paper, we show
that chiral symmetry is restored above a critical chemical potential and the
corresponding phase transition is of first order. In contrast, the chiral
symmetry restoration at high temperatures (and at zero chemical potential) is a
second order phase transition.Comment: Latex; 12 pages; 8 postscript figures include
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