1,606 research outputs found
Spectral Representation for the Effective Macroscopic Response of a Polycrystal: Application to Third-Order Nonlinear Susceptibility
Erratum:
In our paper, we show that the spectral representation for isotropic
two-component composites also applies to uniaxial polycrystals. We have learned
that this result was, in fact, first conjectured by G.W. Milton. While our
derivation is more detailed, our result for the spectral function is the same
as Milton's. We very much regret not having been aware of this work at the time
of writing our paper.
Original abstract:
We extend the spectral theory used for the calculation of the effective
linear response functions of composites to the case of a polycrystalline
material with uniaxially anisotropic microscopic symmetry. As an application,
we combine these results with a nonlinear decoupling approximation as modified
by Ma et al., to calculate the third-order nonlinear optical susceptibility of
a uniaxial polycrystal, assuming that the effective dielectric function of the
polycrystal can be calculated within the effective-medium approximation.Comment: v2 includes erratum and the original preprin
Dynamics of An Underdamped Josephson Junction Ladder
We show analytically that the dynamical equations for an underdamped ladder
of coupled small Josephson junctions can be approximately reduced to the
discrete sine-Gordon equation. As numerical confirmation, we solve the coupled
Josephson equations for such a ladder in a magnetic field. We obtain
discrete-sine-Gordon-like IV characteristics, including a flux flow and a
``whirling'' regime at low and high currents, and voltage steps which represent
a lock-in between the vortex motion and linear ``phasons'', and which are
quantitatively predicted by a simple formula. At sufficiently high anisotropy,
the fluxons on the steps propagate ballistically.Comment: 11pages, latex, no figure
Synchronization in disordered Josephson junction arrays: Small-world connections and the Kuramoto model
We study synchronization in disordered arrays of Josephson junctions. In the
first half of the paper, we consider the relation between the coupled
resistively- and capacitively shunted junction (RCSJ) equations for such arrays
and effective phase models of the Winfree type. We describe a multiple-time
scale analysis of the RCSJ equations for a ladder array of junctions
\textit{with non-negligible capacitance} in which we arrive at a second order
phase model that captures well the synchronization physics of the RCSJ
equations for that geometry. In the second half of the paper, motivated by
recent work on small world networks, we study the effect on synchronization of
random, long-range connections between pairs of junctions. We consider the
effects of such shortcuts on ladder arrays, finding that the shortcuts make it
easier for the array of junctions in the nonzero voltage state to synchronize.
In 2D arrays we find that the additional shortcut junctions are only marginally
effective at inducing synchronization of the active junctions. The differences
in the effects of shortcut junctions in 1D and 2D can be partly understood in
terms of an effective phase model.Comment: 31 pages, 21 figure
Effective conductivity of 2D isotropic two-phase systems in magnetic field
Using the linear fractional transformation, connecting effective
conductivities sigma_{e} of isotropic two-phase systems with and without
magnetic field, explicit approximate expressions for sigma_{e} in a magnetic
field are obtained. They allow to describe sigma_{e} of various inhomogeneous
media at arbitrary phase concentrations x and magnetic fields. the x-dependence
plots of sigma_e at some values of inhomogeneity and magnetic field are
constructed. Their behaviour is qualitatively compatible with the existing
experimental data. The obtained results are applicable for different two-phase
systems (regular and nonregular as well as random), satisfying the symmetry and
self-duality conditions, and admit a direct experimental checking.Comment: 9 pages, 2 figures, Latex2e, small corrections and new figure
Exact results and scaling properties of small-world networks
We study the distribution function for minimal paths in small-world networks.
Using properties of this distribution function, we derive analytic results
which greatly simplify the numerical calculation of the average minimal
distance, , and its variance, . We also discuss the
scaling properties of the distribution function. Finally, we study the limit of
large system sizes and obtain some analytic results.Comment: RevTeX, 4 pages, 5 figures included. Minor corrections and addition
Eigenstates of a Small Josephson Junction Coupled to a Resonant Cavity
We carry out a quantum-mechanical analysis of a small Josephson junction
coupled to a single-mode resonant cavity. We find that the eigenstates of the
combined junction-cavity system are strongly entangled only when the gate
voltage applied at one of the superconducting islands is tuned to certain
special values. One such value corresponds to the resonant absorption of a
single photon by Cooper pairs in the junction. Another special value
corresponds to a {\em two-photon} absorption process. Near the single-photon
resonant absorption, the system is accurately described by a simplified model
in which only the lowest two levels of the Josephson junction are retained in
the Hamiltonian matrix. We noticed that this approximation does not work very
well as the number of photons in the resonator increases. Our system shows also
the phenomenon of ``collapse and revival'' under suitable initial conditions,
and our full numerical solution agrees with the two level approximation result.Comment: 7 pages, and 6 figures. To be published in Phys. Rev.
Dynamical Mass Constraints on Low-Mass Pre-Main-Sequence Stellar Evolutionary Tracks: An Eclipsing Binary in Orion with a 1.0 Msun Primary and an 0.7 Msun Secondary
We report the discovery of a double-lined, spectroscopic, eclipsing binary in
the Orion star-forming region. We analyze the system spectroscopically and
photometrically to empirically determine precise, distance-independent masses,
radii, effective temperatures, and luminosities for both components. The
measured masses for the primary and secondary, accurate to ~1%, are 1.01 Msun
and 0.73 Msun, respectively; thus the primary is a definitive pre-main-sequence
solar analog, and the secondary is the lowest-mass star yet discovered among
pre-main-sequence eclipsing binary systems. We use these fundamental
measurements to test the predictions of pre-main-sequence stellar evolutionary
tracks. None of the models we examined correctly predict the masses of the two
components simultaneously, and we implicate differences between the theoretical
and empirical effective temperature scales for this failing. All of the models
predict the observed slope of the mass-radius relationship reasonably well,
though the observations tend to favor models with low convection efficiencies.
Indeed, considering our newly determined mass measurements together with other
dynamical mass measurements of pre-main-sequence stars in the literature, as
well as measurements of Li abundances in these stars, we show that the data
strongly favor evolutionary models with inefficient convection in the stellar
interior, even though such models cannot reproduce the properties of the
present-day Sun.Comment: Accepted by Ap
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