On the Reductions and Classical Solutions of the Schlesinger equations

The Schlesinger equations $S_{(n,m)}$ describe monodromy preserving deformations of order $m$ Fuchsian systems with $n+1$ poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of $n$ copies of $m\times m$ matrix algebras equipped with the standard linear Poisson bracket. In this paper we address the problem of reduction of particular solutions of ``more complicated'' Schlesinger equations $S_{(n,m)}$ to ``simpler'' $S_{(n',m')}$ having $n'< n$ or $m' < m$.Comment: 32 pages. To the memory of our friend Andrei Bolibruc

Shear coordinate description of the quantised versal unfolding of D_4 singularity

In this paper by using Teichmuller theory of a sphere with four holes/orbifold points, we obtain a system of flat coordinates on the general affine cubic surface having a D_4 singularity at the origin. We show that the Goldman bracket on the geodesic functions on the four-holed/orbifold sphere coincides with the Etingof-Ginzburg Poisson bracket on the affine D_4 cubic. We prove that this bracket is the image under the Riemann-Hilbert map of the Poisson Lie bracket on the direct sum of three copies of sl_2. We realise the action of the mapping class group by the action of the braid group on the geodesic functions . This action coincides with the procedure of analytic continuation of solutions of the sixth Painlev\'e equation. Finally, we produce the explicit quantisation of the Goldman bracket on the geodesic functions on the four-holed/orbifold sphere and of the braid group action.Comment: 14 pages, 2 picture

Double scaling limits of random matrices and minimal (2m,1) models: the merging of two cuts in a degenerate case

In this article, we show that the double scaling limit correlation functions of a random matrix model when two cuts merge with degeneracy $2m$ (i.e. when $y\sim x^{2m}$ for arbitrary values of the integer $m$) are the same as the determinantal formulae defined by conformal $(2m,1)$ models. Our approach follows the one developed by Berg\`{e}re and Eynard in \cite{BergereEynard} and uses a Lax pair representation of the conformal $(2m,1)$ models (giving Painlev\'e II integrable hierarchy) as suggested by Bleher and Eynard in \cite{BleherEynard}. In particular we define Baker-Akhiezer functions associated to the Lax pair to construct a kernel which is then used to compute determinantal formulae giving the correlation functions of the double scaling limit of a matrix model near the merging of two cuts.Comment: 37 pages, 4 figures. Presentation improved, typos corrected. Published in Journal Of Statistical Mechanic

Rational Solutions of the Painleve' VI Equation

In this paper, we classify all values of the parameters $\alpha$, $\beta$, $\gamma$ and $\delta$ of the Painlev\'e VI equation such that there are rational solutions. We give a formula for them up to the birational canonical transformations and the symmetries of the Painlev\'e VI equation.Comment: 13 pages, 1 Postscript figure Typos fixe

Experimental study of fusion neutron and proton yields produced by petawatt-laser-irradiated D2-3He or CD4-3He clustering gases

We report on experiments in which the Texas Petawatt laser irradiated a mixture of deuterium or deuterated methane clusters and helium-3 gas, generating three types of nuclear fusion reactions: D(d, 3He)n, D(d, t)p and 3He(d, p)4He. We measured the yields of fusion neutrons and protons from these reactions and found them to agree with yields based on a simple cylindrical plasma model using known cross sections and measured plasma parameters. Within our measurement errors, the fusion products were isotropically distributed. Plasma temperatures, important for the cross sections, were determined by two independent methods: (1) deuterium ion time-of-flight, and (2) utilizing the ratio of neutron yield to proton yield from D(d, 3He)n and 3He(d, p)4He reactions, respectively. This experiment produced the highest ion temperature ever achieved with laser-irradiated deuterium clusters.Comment: 16 pages, 6 figure

Temperature measurements of fusion plasmas produced by petawatt laser-irradiated D2-3He or CD4-3He clustering gases

Two different methods have been employed to determine the plasma temperature in a laser-cluster fusion experiment on the Texas Petawatt laser. In the first, the temperature was derived from time-of-flight data of deuterium ions ejected from exploding D2 or CD4 clusters. In the second, the temperature was measured from the ratio of the rates of two different nuclear fusion reactions occurring in the plasma at the same time: D(d, 3He)n and 3He(d, p)4He. The temperatures determined by these two methods agree well, which indicates that: i) The ion energy distribution is not significantly distorted when ions travel in the disassembling plasma; ii) The kinetic energy of deuterium ions, especially the hottest part responsible for nuclear fusion, is well described by a near-Maxwellian distribution.Comment: 13 pages, 4 figure

Measurement of the plasma astrophysical S factor for the 3He(D, p)4He reaction in exploding molecular clusters

The plasma astrophysical S factor for the 3He(D, p)4He fusion reaction was measured for the first time at temperatures of few keV, using the interaction of intense ultrafast laser pulses with molecular deuterium clusters mixed with 3He atoms. Different proportions of D2 and 3He or CD4 and 3He were mixed in the gas jet target in order to allow the measurement of the cross-section for the 3He(D, p)4He reaction. The yield of 14.7 MeV protons from the 3He(D, p)4He reaction was measured in order to extract the astrophysical S factor at low energies. Our result is in agreement with other S factor parameterizations found in the literature

Mass measurements of very neutron-deficient Mo and Tc isotopes and their impact on rp process nucleosynthesis

The masses of ten proton-rich nuclides, including the N=Z+1 nuclides 85-Mo and 87-Tc, were measured with the Penning trap mass spectrometer SHIPTRAP. Compared to the Atomic Mass Evaluation 2003 a systematic shift of the mass surface by up to 1.6 MeV is observed causing significant abundance changes of the ashes of astrophysical X-ray bursts. Surprisingly low alpha-separation energies for neutron-deficient Mo and Tc are found, making the formation of a ZrNb cycle in the rp process possible. Such a cycle would impose an upper temperature limit for the synthesis of elements beyond Nb in the rp process.Comment: Link to online abstract: http://link.aps.org/doi/10.1103/PhysRevLett.106.12250