Painleve equations from Darboux chains - Part 1: P3-P5

We show that the Painleve equations P3-P5 can be derived (in a unified way) from a periodic sequence of Darboux transformations for a Schrodinger problem with quadratic eigenvalue dependency. The general problem naturally divides into three different branches, each described by an infinite chain of equations. The Painleve equations are obtained by closing the chain periodically at the lowest nontrivial level(s). The chains provide ``symmetric forms'' for the Painleve equations, from which Hirota bilinear forms and Lax pairs are derived. In this paper (Part 1) we analyze in detail the cases P3-P5, while P6 will be studied in Part 2.Comment: 23 pages, 1 reference added + minor change

Magnetized Accretion Inside the Marginally Stable Orbit around a Black Hole

Qualitative arguments are presented to demonstrate that the energy density of magnetic fields in matter accreting onto a black hole inside the marginally stable orbit is automatically comparable to the rest-mass energy density of the accretion flow. Several consequences follow: magnetic effects must be dynamically significant, but cannot be so strong as to dominate; outward energy transport in Alfven waves may alter the effective efficiency of energy liberation; and vertical magnetic stresses in this region may contribute to "coronal" activity.Comment: to appear in Ap. J. Letter

Approximate Treatment of Hermitian Effective Interactions and a Bound on the Error

The Hermitian effective interaction can be well-approximated by (R+R^dagger)/2 if the eigenvalues of omega^dagger omega are small or state-independent(degenerate), where R is the standard non-Hermitian effective interaction and omega maps the model-space states onto the excluded space. An error bound on this approximation is given.Comment: 13 page

f_K/f_pi in Full QCD with Domain Wall Valence Quarks

We compute the ratio of pseudoscalar decay constants f_K/f_pi using domain-wall valence quarks and rooted improved Kogut-Susskind sea quarks. By employing continuum chiral perturbation theory, we extract the Gasser-Leutwyler low-energy constant L_5, and extrapolate f_K/f_pi to the physical point. We find: f_K/f_pi = 1.218 (+- 0.002) (+0.011 -0.024) where the first error is statistical and the second error is an estimate of the systematic due to chiral extrapolation and fitting procedures. This value agrees within the uncertainties with the determination by the MILC collaboration, calculated using Kogut-Susskind valence quarks, indicating that systematic errors arising from the choice of lattice valence quark are small.Comment: 14 pages, 9 figure

Random Matrix Theory and the Sixth Painlev\'e Equation

A feature of certain ensembles of random matrices is that the corresponding measure is invariant under conjugation by unitary matrices. Study of such ensembles realised by matrices with Gaussian entries leads to statistical quantities related to the eigenspectrum, such as the distribution of the largest eigenvalue, which can be expressed as multidimensional integrals or equivalently as determinants. These distributions are well known to be $\tau$-functions for Painlev\'e systems, allowing for the former to be characterised as the solution of certain nonlinear equations. We consider the random matrix ensembles for which the nonlinear equation is the $\sigma$ form of \PVI. Known results are reviewed, as is their implication by way of series expansions for the distributions. New results are given for the boundary conditions in the neighbourhood of the fixed singularities at $t=0,1,\infty$ of $\sigma$\PVI displayed by a generalisation of the generating function for the distributions. The structure of these expansions is related to Jimbo's general expansions for the $\tau$-function of $\sigma$\PVI in the neighbourhood of its fixed singularities, and this theory is itself put in its context of the linear isomonodromy problem relating to \PVI.Comment: Dedicated to the centenary of the publication of the Painlev\'e VI equation in the Comptes Rendus de l'Academie des Sciences de Paris by Richard Fuchs in 190

Strong mass effect on ion beam mixing in metal bilayers

Molecular dynamics simulations have been used to study the mechanism of ion beam mixing in metal bilayers. We are able to explain the ion induced low-temperature phase stability and melting behavior of bilayers using only a simple ballistic picture up to 10 keV ion energies. The atomic mass ratio of the overlayer and the substrate constituents seems to be a key quantity in understanding atomic mixing. The critical bilayer mass ratio of $\delta < 0.33$ is required for the occurrence of a thermal spike (local melting) with a lifetime of $\tau > 0.3$ ps at low-energy ion irradiation (1 keV) due to a ballistic mechanism. The existing experimental data follow the same trend as the simulated values.Comment: 4 pages, 4 figures, preprin

A small sealed Ta crucible for thermal analysis of volatile metallic samples

Differential thermal analysis on metallic alloys containing volatile elements can be highly problematic. Here we show how measurements can be performed in commercial, small-sample, equipment without modification. This is achieved by using a sealed Ta crucible, easily fabricated from Ta tubing and sealed in a standard arc furnace. The crucible performance is demonstrated by measurements on a mixture of Mg and MgB$_2$, after heating up to 1470$^{\circ}{\rm C}$. We also show data, measured on an alloy with composition Gd$_{40}$Mg$_{60}$, that clearly shows both the liquidus and a peritectic, and is consistent with published phase diagram data

Nucleon-deuteron scattering with the JISP16 potential

The nucleon-nucleon J-matrix Inverse Scattering Potential JISP16 is applied to elastic nucleon-deuteron (Nd) scattering and the deuteron breakup process at the lab. nucleon energies up to 135 MeV. The formalism of the Faddeev equations is used to obtain 3N scattering states. We compare predictions based on the JISP16 force with data and with results based on various NN interactions: the CD Bonn, the AV18, the chiral force with the semi-local regularization at the 5th order of the chiral expansion and with low-momentum interactions obtained from the CD Bonn force as well as with the predictions from the combination of the AV18 NN interaction and the Urbana IX 3N force. JISP16 provides a satisfactory description of some observables at low energies but strong deviations from data as well as from standard and chiral potential predictions with increasing energy. However, there are also polarization observables at low energies for which the JISP16 predictions differ from those based on the other forces by a factor of two. The reason for such a behavior can be traced back to the P-wave components of the JISP16 force. At higher energies the deviations can be enhanced by an interference with higher partial waves and by the properties of the JISP16 deuteron wave function. In addition, we compare the energy and angular dependence of predictions based on the JISP16 force with the results of the low-momentum forces obtained with different values of the momentum cutoff parameter. We found that such low-momentum forces can be employed to interpret the Nd elastic scattering data only below some specific energy which depends on the cutoff parameter. Since JISP16 is defined in a finite oscillator basis, it has properties similar to low momentum interactions and its application to the description of Nd scattering data is limited to a low momentum transfer region.Comment: 26 pages, 12 eps figures; Version accepted to Phys. Rev. C: text is shortened, few figures regarding the nucleon-deuteron elastic scattering observables are removed but a short discussion of the nucleon induced deuteron breakup cross section is added. Conclusions remain unchange