5,127 research outputs found
Quantum criticality in disordered bosonic optical lattices
Using the exact Bose-Fermi mapping, we study universal properties of
ground-state density distributions and finite-temperature quantum critical
behavior of one-dimensional hard-core bosons in trapped incommensurate optical
lattices. Through the analysis of universal scaling relations in the quantum
critical regime, we demonstrate that the superfluid to Bose glass transition
and the general phase diagram of disordered hard-core bosons can be uniquely
determined from finite-temperature density distributions of the trapped
disordered system.Comment: 4 pages, 5 figure
On one-sided filters for spectral Fourier approximations of discontinuous functions
The existence of one-sided filters, for spectral Fourier approximations of discontinuous functions, which can recover spectral accuracy up to discontinuity from one side, was proved. A least square procedure was also used to construct such a filter and test it on several discontinuous functions numerically
Non-oscillatory spectral Fourier methods for shock wave calculations
A non-oscillatory spectral Fourier method is presented for the solution of hyperbolic partial differential equations. The method is based on adding a nonsmooth function to the trigonometric polynomials which are the usual basis functions for the Fourier method. The high accuracy away from the shock is enhanced by using filters. Numerical results confirm that no oscillations develop in the solution. Also, the accuracy of the spectral solution of the inviscid Burgers equation is shown to be higher than a fixed order
Gravitational collapse of magnetized clouds II. The role of Ohmic dissipation
We formulate the problem of magnetic field dissipation during the accretion
phase of low-mass star formation, and we carry out the first step of an
iterative solution procedure by assuming that the gas is in free-fall along
radial field lines. This so-called ``kinematic approximation'' ignores the back
reaction of the Lorentz force on the accretion flow. In quasi steady-state, and
assuming the resistivity coefficient to be spatially uniform, the problem is
analytically soluble in terms of Legendre's polynomials and confluent
hypergeometric functions. The dissipation of the magnetic field occurs inside a
region of radius inversely proportional to the mass of the central star (the
``Ohm radius''), where the magnetic field becomes asymptotically straight and
uniform. In our solution, the magnetic flux problem of star formation is
avoided because the magnetic flux dragged in the accreting protostar is always
zero. Our results imply that the effective resistivity of the infalling gas
must be higher by several orders of magnitude than the microscopic electric
resistivity, to avoid conflict with measurements of paleomagnetism in
meteorites and with the observed luminosity of regions of low-mass star
formation.Comment: 20 pages, 4 figures, The Astrophysical Journal, in pres
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