Improving the cold quark-matter pressure via soft interactions at N3LO

The propagation of long-wavelength gluons through a dense QCD medium at high baryon chemical potential μB is qualitatively modified by the effects of screening, arising from scatterings off the high-momentum quarks in the medium. This same screening phenomenon also impacts gluons occurring in loop corrections to the pressure of cold quark matter, leading to contributions from the parametric scale αs1/2μB, starting at next-to-next-to-leading order (N2LO) in the strong coupling constant αs. At next-to-next-to-next-to-leading order (N3LO), interactions between these long-wavelength gluonic modes contribute to the pressure. These interaction corrections have recently been computed in Ref [1, 2], and the inclusion of these interactions slightly improves the convergence of the equation of state of cold quark matter. In these proceedings, we present these results and provide details summarizing how this lengthy calculation was performed.

Reduced Life Cycles Cost and Improved Analysis Accuracy Utilizing WESTEMS™ Integrated Modeling Methods

Traditional methods of qualifying pressure vessel components to ASME stress and fatigue requirements often involve complex and lengthy calculation processes. The costs of individually analyzing every specified transient can be prohibitive if large numbers of transients are considered, with each one having varied loading conditions acting on the components. In addition, the time dependent nature of real transient loads results in a significant computational and bookkeeping problem. In most cases the analyst uses a number of simplifying and enveloping assumptions to develop stresses to represent all transient conditions. He relies on his experience and judgment to make simplifications with respect to the timing of applied mechanical loads, as well as the relationship between the applied mechanical loads and the timing of the thermal loads. The analyst’s skill governs the length and complexity of the qualification process. The WESTEMS™ Integrated Modeling approach dramatically simplifies this effort and improves analysis accuracy, while reducing the overall time necessary to perform the analysis. WESTEMS™ Integrated Models can reduce the process of analyzing a list of transients defined by global parameter time histories and reporting final design stress and fatigue to a few steps. This paper discusses how WESTEMS™ overcomes the technical difficulties encountered in automating such tasks, and shows the technical superiority of WESTEMS™ over the current traditional methods. It also demonstrates how applying the WESTEMS™ technology to NSSS equipment can reduce engineering life cycle costs.

Nonlinear Regenerative Machine Tool Vibrations

The existence and the nature of the Hopf bifurcation is presented in the delay-differential equation model of the so-called regenerative machine tool vibration. The relevant nonlinearity is considered at the cutting force dependence on the chip thickness. The delayed terms show a special algebraic structure in the nonlinear part of the equation of motion. This results in a surprisingly simple and useful analytical formula in the end of the lengthy calculation based on center manifold reduction in the corresponding infinite dimensional phase space. The result gives a simple way to estimate the domain of attraction of the stable stationary cutting as well as an estimation of that technological parameter domain, where the cutting is globally stable.

Examples of the Zeeman effect at intermediate strengths of magnetic field

In a recent paper called “The Zeeman Effect and Spherical Harmonics,” Prof. Darwin gives a set of formulæ from which can be determined the frequencies and intensities of the lines in the standard Zeeman Effect. Except for s — p doublets these quantities could previously only be calculated for strong or weak magnetic fields, and the interest of the new formulæ lies in the fact that from them we can also calculate the frequency and intensity at any intermediate field. Approximate algebraic solutions are available for strong or weak fields, but the new method makes numerical solutions for all strengths easily practicable. The present work gives the application of the new formulæ to three cases which involve simple but lengthy calculation. These are the s — p and p — d doublets and the s — p triplets, but we describe first the case of the s — p triplets as this illustrates most fully the method under consideration. As these cases involve respectively 10, 34 and 19 lines, it will be readily seen that the discussion of any more complicated systems would lead to a large amount of work. The simplest case of all, that of the s — p doublets, is already known from the work of Voigt (by entirely different methods). As, however, so much of the material for working out the s — p doublets by the new method is the same as we require for the p — d doublets, we have included in a brief form the results for the simpler case. The theory and procedure is, of course, similar for all the three examples considered, so we now give an outline of the calculations and results before entering into the detail for the several cases separately. Referring to 5 of the previous paper, we find the following rules for forming the “chains of equations” on which the whole calculation is based.