Time-dependent Schr\"odinger equations having isomorphic symmetry algebras. I. Classes of interrelated equations

In this paper, we focus on a general class of Schr\"odinger equations that are time-dependent and quadratic in X and P. We transform Schr\"odinger equations in this class, via a class of time-dependent mass equations, to a class of solvable time-dependent oscillator equations. This transformation consists of a unitary transformation and a change in the ``time'' variable. We derive mathematical constraints forthe transformation and introduce two examples.Comment: LaTeX, 18 pages, new format, edite

Polymorphism of the tumor necrosis factor beta gene in systemic lupus erythematosus

We investigated the Nco I restriction fragment length polymorphism (RFLP) of the tumor necrosis factor beta (TNFB) gene in 173 patients with systemic lupus erythematosus (SLE), 192 unrelated healthy controls, and eleven panel families, all of German origin. The phenotype frequency of the TNFB*I allele was significantly increased in patients compared to controls (63.6% vs 47.1%, RR = 1.96, p <0.002). The results of a two-point haplotype statistical analysis between TNFB and HLA alleles show that there is linkage disequilibrium between TNFB*I and HLA-A1, Cw7, B8, DR3, DQ2, and C4A DE. The frequency of TNFB*I was compared in SLE patients and controls in the presence or absence of each of these alleles. TNFB*I is increased in patients over controls only in the presence of the mentioned alleles. Therefore, the whole haplotypeA1, Cw7, B8, TNFB* I, C4A DE, DR3, DQ2 is increased in patients and it cannot be determined which of the genes carried by this haplotype is responsible for the susceptibility to SLE. In addition, two-locus associations were analyzed in 192 unrelated healthy controls for TNFB and class I alleles typed by serology, and for TNFB and class II alleles typed by polymerase chain reaction/oligonucleotide probes. We found positive linkage disequilibrium between TNFB*I and the following alleles: HLA-A24, HLA-B8, DRBI*0301, DRBI*ll04, DRBI*1302, DQAI*0501, DQBI*0201, DQBI*0604, and DPBI*OIO1. TNFB*2 is associated with HLA-B7, DRBI*1501, and DQB I *0602

A Finite Difference Representation of Neutrino Radiation Hydrodynamics in Spherically Symmetric General Relativistic Space-Time

We present an implicit finite difference representation for general relativistic radiation hydrodynamics in spherical symmetry. Our code, Agile-Boltztran, solves the Boltzmann transport equation for the angular and spectral neutrino distribution functions in self-consistent simulations of stellar core collapse and postbounce evolution. It implements a dynamically adaptive grid in comoving coordinates. Most macroscopically interesting physical quantities are defined by expectation values of the distribution function. We optimize the finite differencing of the microscopic transport equation for a consistent evolution of important expectation values. We test our code in simulations launched from progenitor stars with 13 solar masses and 40 solar masses. ~0.5 s after core collapse and bounce, the protoneutron star in the latter case reaches its maximum mass and collapses further to form a black hole. When the hydrostatic gravitational contraction sets in, we find a transient increase in electron flavor neutrino luminosities due to a change in the accretion rate. The muon- and tauon-neutrino luminosities and rms energies, however, continue to rise because previously shock-heated material with a non-degenerate electron gas starts to replace the cool degenerate material at their production site. We demonstrate this by supplementing the concept of neutrinospheres with a more detailed statistical description of the origin of escaping neutrinos. We compare the evolution of the 13 solar mass progenitor star to simulations with the MGFLD approximation, based on a recently developed flux limiter. We find similar results in the postbounce phase and validate this MGFLD approach for the spherically symmetric case with standard input physics.Comment: reformatted to 63 pages, 24 figures, to be published in ApJ

Modeling core collapse supernovae in 2 and 3 dimensions with spectral neutrino transport

The overwhelming evidence that the core collapse supernova mechanism is inherently multidimensional, the complexity of the physical processes involved, and the increasing evidence from simulations that the explosion is marginal presents great computational challenges for the realistic modeling of this event, particularly in 3 spatial dimensions. We have developed a code which is scalable to computations in 3 dimensions which couples PPM Lagrangian with remap hydrodynamics [1], multigroup, flux-limited diffusion neutrino transport [2], with many improvements), and a nuclear network [3]. The neutrino transport is performed in a ray-by-ray plus approximation wherein all the lateral effects of neutrinos are included (e.g., pressure, velocity corrections, advection) except the transport. A moving radial grid option permits the evolution to be carried out from initial core collapse with only modest demands on the number of radial zones. The inner part of the core is evolved after collapse along with the rest of the core and mantle by subcycling the lateral evolution near the center as demanded by the small Courant times. We present results of 2-D simulations of a symmetric and an asymmetric collapse of both a 15 and an 11 M progenitor. In each of these simulations we have discovered that once the oxygen rich material reaches the shock there is a synergistic interplay between the reduced ram pressure, the energy released by the burning of the shock heated oxygen rich material, and the neutrino energy deposition which leads to a revival of the shock and an explosion.Comment: 10 pages, 3 figure

Semi-Hard Scattering Unraveled from Collective Dynamics by Two-Pion Azimuthal Correlations in 158 A GeV/c Pb + Au Collisions

Elliptic flow and two-particle azimuthal correlations of charged hadrons and high-$p_T$ pions ($p_T>$ 1 GeV/$c$) have been measured close to mid-rapidity in 158A GeV/$c$ Pb+Au collisions by the CERES experiment. Elliptic flow ($v_2$) rises linearly with $p_T$ to a value of about 10% at 2 GeV/$c$. Beyond $p_T\approx$ 1.5 GeV/$c$, the slope decreases considerably, possibly indicating a saturation of $v_2$ at high $p_T$. Two-pion azimuthal anisotropies for $p_T>$ 1.2 GeV/$c$ exceed the elliptic flow values by about 60% in mid-central collisions. These non-flow contributions are attributed to near-side and back-to-back jet-like correlations, the latter exhibiting centrality dependent broadening.Comment: Submitted to Phys. Rev. Letters, 4 pages, 5 figure

The consequences of nuclear electron capture in core collapse supernovae

The most important weak nuclear interaction to the dynamics of stellar core collapse is electron capture, primarily on nuclei with masses larger than 60. In prior simulations of core collapse, electron capture on these nuclei has been treated in a highly parameterized fashion, if not ignored. With realistic treatment of electron capture on heavy nuclei come significant changes in the hydrodynamics of core collapse and bounce. We discuss these as well as the ramifications for the post-bounce evolution in core collapse supernovae.Comment: Accepted by PRL, 5 pages, 2 figure

Positive Surgical Margins in the 10 Most Common Solid Cancers.

A positive surgical margin (PSM) following cancer resection oftentimes necessitates adjuvant treatments and carries significant financial and prognostic implications. We sought to compare PSM rates for the ten most common solid cancers in the United States, and to assess trends over time. Over 10 million patients were identified in the National Cancer Data Base from 1998-2012, and 6.5 million had surgical margin data. PSM rates were compared between two time periods, 1998-2002 and 2008-2012. PSM was positively correlated with tumor category and grade. Ovarian and prostate cancers had the highest PSM prevalence in women and men, respectively. The highest PSM rates for cancers affecting both genders were seen for oral cavity tumors. PSM rates for breast cancer and lung and bronchus cancer in both men and women declined over the study period. PSM increases were seen for bladder, colon and rectum, and kidney and renal pelvis cancers. This large-scale analysis appraises the magnitude of PSM in the United States in order to focus future efforts on improving oncologic surgical care with the goal of optimizing value and improving patient outcomes

General-Relativistic Thomas-Fermi model

A system of self-gravitating massive fermions is studied in the framework of the general-relativistic Thomas-Fermi model. We study the properties of the free energy functional and its relation to Einstein's field equations. A self-gravitating fermion gas we then describe by a set of Thomas-Fermi type self-consistency equations.Comment: 7 pages, LaTex, to appear in Gen. Rel. Gra

Large deviation techniques applied to systems with long-range interactions

We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by Ellis, Physica D 133, 106 (1999), which uses large deviation techniques. We show how it can be adapted to obtain the solution of a large class of simple models, which can show ensemble inequivalence. The model Hamiltonian can have both discrete (Ising, Potts) and continuous (HMF, Free Electron Laser) state variables. This latter extension gives access to the comparison with dynamics and to the study of non-equilibri um effects. We treat both infinite range and slowly decreasing interactions and, in particular, we present the solution of the alpha-Ising model in one-dimension with $0\leq\alpha<1$

Classification of phase transitions and ensemble inequivalence, in systems with long range interactions

Systems with long range interactions in general are not additive, which can lead to an inequivalence of the microcanonical and canonical ensembles. The microcanonical ensemble may show richer behavior than the canonical one, including negative specific heats and other non-common behaviors. We propose a classification of microcanonical phase transitions, of their link to canonical ones, and of the possible situations of ensemble inequivalence. We discuss previously observed phase transitions and inequivalence in self-gravitating, two-dimensional fluid dynamics and non-neutral plasmas. We note a number of generic situations that have not yet been observed in such systems.Comment: 42 pages, 11 figures. Accepted in Journal of Statistical Physics. Final versio