43,454 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
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
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
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
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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
Fully gapped superconducting state in Au2Pb: a natural candidate for topological superconductor
We measured the ultra-low-temperature specific heat and thermal conductivity
of AuPb single crystal, a possible three-dimensional Dirac semimetal with a
superconducting transition temperature 1.05 K. The electronic
specific heat can be fitted by a two-band s-wave model, which gives the gap
amplitudes (0)/ = 1.38 and (0)/ = 5.25.
From the thermal conductivity measurements, a negligible residual linear term
in zero field and a slow field dependence of at low
field are obtained. These results suggest that AuPb has a fully gapped
superconducting state in the bulk, which is a necessary condition for
topological superconductor if AuPb is indeed one.Comment: 6 pages, 4 figure
Superfluid pairing in a mixture of a spin-polarized Fermi gas and a dipolar condensate
We consider a mixture of a spin-polarized Fermi gas and a dipolar
Bose-Einstein condensate in which s-wave scattering between fermions and the
quasiparticles of the dipolar condensate can result in an effective attractive
Fermi-Fermi interaction anisotropic in nature and tunable by the dipolar
interaction. We show that such an interaction can significantly increase the
prospect of realizing a superfluid with a gap parameter characterized with a
coherent superposition of all odd partial waves. We formulate, in the spirit of
the Hartree-Fock-Bogoliubov mean-field approach, a theory which allows us to
estimate the critical temperature when the anisotropic Fock potential is taken
into consideration and to determine the system parameters that optimize the
critical temperature at which such a superfluid emerges before the system
begins to phase separate.Comment: 10 pages, 3 figure
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