Inclusive inelastic scattering of heavy ions and nuclear correlations

Calculations of inclusive inelastic scattering distributions for heavy ion collisions are considered within the high energy optical model. Using ground state sum rules, the inclusive projectile and complete projectile-target inelastic angular distributions are treated in both independent particle and correlated nuclear models. Comparisons between the models introduced are made for alpha particles colliding with He-4, C-12, and O-16 targets and protons colliding with O-16. Results indicate that correlations contribute significantly, at small momentum transfers, to the inelastic sum. Correlation effects are hidden, however, when total scattering distributions are considered because of the dominance of elastic scattering at small momentum transfers

Schwinger-Dyson operator of Yang-Mills matrix models with ghosts and derivations of the graded shuffle algebra

We consider large-N multi-matrix models whose action closely mimics that of Yang-Mills theory, including gauge-fixing and ghost terms. We show that the factorized Schwinger-Dyson loop equations, expressed in terms of the generating series of gluon and ghost correlations G(xi), are quadratic equations S^i G = G xi^i G in concatenation of correlations. The Schwinger-Dyson operator S^i is built from the left annihilation operator, which does not satisfy the Leibnitz rule with respect to concatenation. So the loop equations are not differential equations. We show that left annihilation is a derivation of the graded shuffle product of gluon and ghost correlations. The shuffle product is the point-wise product of Wilson loops, expressed in terms of correlations. So in the limit where concatenation is approximated by shuffle products, the loop equations become differential equations. Remarkably, the Schwinger-Dyson operator as a whole is also a derivation of the graded shuffle product. This allows us to turn the loop equations into linear equations for the shuffle reciprocal, which might serve as a starting point for an approximation scheme.Comment: 13 pages, added discussion & references, title changed, minor corrections, published versio

Three-Dimensional Numerical Study of Conjugate Heat Transfer in Diverging Microchannel

Increase in applications of varying cross sectional area microchannels in microdevices has provided the need to understand fluid flow and heat transfer through such flow passages. This study focuses on conjugate heat transfer study through a diverging microchannel. Three-dimensional numerical simulations are performed using commercially available package. Diverging microchannels with different geometrical configurations (i.e. varying angle: 1-8°, depth: 86-200 μm, solid-to- fluid thickness ratio: 1.5-4) are employed for this purpose. Simulations are carried out for varying mass flow rate (3.3 x 10 –5 -8.3 x 10 –5 kg/s) and heat flux (2.4-9.6 W/cm 2 ) conditions. Heat distribution along the flow direction is studied to understand the effect of wall conduction. Wall conduction number ( M ) varies from 0.006 to 0.024 for the range of parameters selected in the study. Wall conduction is observed to be a direct function of depth and solid-to-fluid thickness ratio, and varies inversely with angle of diverging microchannel. It is observed that the area variation and wall conduction contribute separately towards redistribution of the supplied heat flux. This leads to reduced temperature gradients in diverging microchannel. The results presented in this work will be useful for designing future microdevices involving heating or coolin

Eikonal solutions to optical model coupled-channel equations

Methods of solution are presented for the Eikonal form of the nucleus-nucleus coupled-channel scattering amplitudes. Analytic solutions are obtained for the second-order optical potential for elastic scattering. A numerical comparison is made between the first and second order optical model solutions for elastic and inelastic scattering of H-1 and He-4 on C-12. The effects of bound-state excitations on total and reaction cross sections are also estimated

Nonlinear dispersive regularization of inviscid gas dynamics

Ideal gas dynamics can develop shock-like singularities with discontinuous density. Viscosity typically regularizes such singularities and leads to a shock structure. On the other hand, in 1d, singularities in the Hopf equation can be non-dissipatively smoothed via KdV dispersion. Here, we develop a minimal conservative regularization of 3d ideal adiabatic flow of a gas with polytropic exponent $\gamma$. It is achieved by augmenting the Hamiltonian by a capillarity energy $\beta(\rho) (\nabla \rho)^2$. The simplest capillarity coefficient leading to local conservation laws for mass, momentum, energy and entropy using the standard Poisson brackets is $\beta(\rho) = \beta_*/\rho$ for constant $\beta_*$. This leads to a Korteweg-like stress and nonlinear terms in the momentum equation with third derivatives of $\rho$, which are related to the Bohm potential and Gross quantum pressure. Just like KdV, our equations admit sound waves with a leading cubic dispersion relation, solitary and periodic traveling waves. As with KdV, there are no steady continuous shock-like solutions satisfying the Rankine-Hugoniot conditions. Nevertheless, in 1d, for $\gamma = 2$, numerical solutions show that the gradient catastrophe is averted through the formation of pairs of solitary waves which can display approximate phase-shift scattering. Numerics also indicate recurrent behavior in periodic domains. These observations are related to an equivalence between our regularized equations (in the special case of constant specific entropy potential flow in any dimension) and the defocussing nonlinear Schrodinger equation (cubically nonlinear for $\gamma = 2$), with $\beta_*$ playing the role of $\hbar^2$. Thus, our regularization of gas dynamics may be viewed as a generalization of both the single field KdV & NLS equations to include the adiabatic dynamics of density, velocity, pressure & entropy in any dimension.Comment: 19 pages, 20 figure file

Targeted cooling with CVD diamond and micro-channel to meet 3-D IC heat dissipation challenge

Thermal simulation of a stack consists of three IC layers bonded “face up” is performed. It is shown that by inserting electrically isolated thermal through silicon via (TTSV) having Cu core and CVD diamond as a liner shell that extends across the layers to substrate, significant temperature reduction up to (103K) 62% can be achieved which also reflected through almost 60% reduction in thermal resistivity. Additionally simple microchannel integration with IC 3 layer and allowed fluid flow through the channel show transient temperature reduction. TTSV is also shown to be effective in mitigating severe heat dissipation issue facing 3-D IC bonded “face down” and logic layer stacked on memory substrate

Simplified model for solar cosmic ray exposure in manned Earth orbital flights

A simple calculational model is derived for use in estimating solar cosmic ray exposure to critical body organs in low-Earth orbit at the center of a large spherical shield of fixed thickness. The effects of the Earth's geomagnetic field, including storm conditions and the astronauts' self-shielding, are evaluated explicitly. The magnetic storm model is keyed to the planetary index K(sub p)