Quantitative Description of V2O3V_2O_3 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 $V_2O_3$. The form of the optical conductivity shows $\omega^{3/2}$ rising and is quite similar to the experimental data, and the density of states shows $\omega^{1/2}$ 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 $D_{M}=1.33$. We also found that the stiffness exponent $\alpha =-0.25$ is universal, but varies with the plasticity parameters $s$ and $\theta_{p}$. 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 $P(k)\sim k^{-\gamma}$ at large $k$, we found that the finite size exponent $\bar{\nu}$ takes on the value 5/2 when $\gamma>5$, the same as in the globally coupled Kuramoto model. For highly heterogeneous networks ($3<\gamma <5$), $\bar{\nu}$ and the order parameter exponent $\beta$ depend on $\gamma$. 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

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 Au$_2$Pb single crystal, a possible three-dimensional Dirac semimetal with a superconducting transition temperature $T_c \approx$ 1.05 K. The electronic specific heat can be fitted by a two-band s-wave model, which gives the gap amplitudes $\Delta_1$(0)/$k_BT_c$ = 1.38 and $\Delta_2$(0)/$k_BT_c$ = 5.25. From the thermal conductivity measurements, a negligible residual linear term $\kappa_0/T$ in zero field and a slow field dependence of $\kappa_0/T$ at low field are obtained. These results suggest that Au$_2$Pb has a fully gapped superconducting state in the bulk, which is a necessary condition for topological superconductor if Au$_2$Pb 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