Hard and Soft - Core Equations of State for Simple Fluids: VI. General Theory of Termination Temperatures,and a Validity Criterion for the Second Virial Coefficient

Abstract

A general proof is given that the classical second virial coefficient satisfies the requirement for the non-existence of a termination point of any locus of C_v extrema. This validity criterion is applied to some proposed forms for the second virial coefficient. The order of the termination temperatures is verified for a fairly general intermolecular potential. In particular a proof is given that T_F lies between T_C and T_A. Also the hard-core limit of the ratio T_D/T_A(～2) is examined briefly.     

Thermal Decomposition Kinetics of Some Metal Complexes of 2,3-Hydroxyimino-4-phenyl-6-phenyazo-1-thia-4,5-diazacyclohexa-5-diene

The Ni(II), Cu(II) Co(II) and Zn(II) complexes of 2,3‐hydroxyimino‐4‐phenyl‐6‐phenyazo‐1‐thia‐4,5‐diaza‐ cyclohexa‐5‐diene (H₂L) were synthesized. Thermal behavior of these complexes was studied in dynamic nitrogen atmosphere by TA (thermogravimetric analysis), DTA (differential thermal analysis) and DTG (differential thermal gravimetry) techniques. The reaction order, the activation energies, the entropies, the enthalpies, the free energies, and the pre‐exponential factors of the thermal decomposition reactions were calculated from the thermogravimetric curves. The kinetic analysis of the thermogravimetric data was performed by using several methods such as MacCallum‐Tanner (MT), van Krevelen (vK), Madhusudanan‐Krishnan‐Ninan (MKN), Wanjun‐Yuwen‐Hen‐Cunxin (WYHC), Horowitz‐Metzger (HM) and Coats‐Redfern method (CR) based on the single heating rate. Most appropriate methods were determined for each decomposition step according to the least‐square linear regression. The Ni(II), Cu(II) Co(II) and Zn(II) complexes displayed one‐ or two‐stage decomposition pattern when heating in a dynamic nitrogen atmosphere and metal oxides remained as end products of the complexes. The characterization of the end products of the decomposition was performed by X‐ray diffraction.     

Beta–neutrino correlation experiments on laser trapped 38mK, 37K

Laser trapping and cooling techniques are now being applied to the study of nuclear β-decay at several labs. A magneto-optical trap (MOT) provides a localized source of atoms suspended in space, so the low-energy recoiling nuclei can freely escape and be detected in coincidence with the β. This allows reconstruction of the neutrino momentum, and the deduction of the β-v correlation in a more direct fashion than previously possible. In addition, the nuclei can be polarized by atomic techniques, opening a new class of spin correlation measurements to test the degree to which parity is maximally violated in the weak interaction. Our present experiment has detected several hundred thousand recoil-β⁺ coincidences from the 0⁺ → 0⁺ pure Fermi decay of ^38mK, produced at the on-line isotope separators TISOL and ISAC at TRIUMF. Our goal is to set constraints on non-Standard Model scalar bosons competitive with high-energy colliders and more conventional β-v correlation experiments. This revised version was published online in August 2006 with corrections to the Cover Date.     

Accuracies and conservation errors of various ghost fluid methods for multi-medium Riemann problem

Since the (original) ghost fluid method (OGFM) was proposed by Fedkiw et al. in 1999 [5], a series of other GFM-based methods such as the gas–water version GFM (GWGFM), the modified GFM (MGFM) and the real GFM (RGFM) have been developed subsequently. Systematic analysis, however, has yet to be carried out for the various GFMs on their accuracies and conservation errors. In this paper, we develop a technique to rigorously analyze the accuracies and conservation errors of these different GFMs when applied to the multi-medium Riemann problem with a general equation of state (EOS). By analyzing and comparing the interfacial state provided by each GFM to the exact one of the original multi-medium Riemann problem, we show that the accuracy of interfacial treatment can achieve “third-order accuracy” in the sense of comparing to the exact solution of the original mutli-medium Riemann problem for the MGFM and the RGFM, while it is of at most “first-order accuracy” for the OGFM and the GWGFM when the interface approach is actually near in balance. Similar conclusions are also obtained in association with the local conservation errors. A special test method is exploited to validate these theoretical conclusions from the numerical viewpoint.     

Hydraulic analysis of free-surface flows with solidification

Summary The paper is concerned with a one-dimensional analysis of plane open-channel flow with continuous solidification. The process is of relevance for recent developments in the casting of steel and other metals. The bottom of the channel consists of a rotating casting roll and a horizontal cooling table, where the solidified material is withdrawn with given velocity. The study is restricted to the region downstream of the top of the casting roll. Surface tension is neglected. In the main part of the analysis inviscid fluid flow is considered since the Reynolds number is very large in the applications. It is found that the steady-state solutions are nonunique in a certain parameter range. In addition to a continuous solution, there are two solutions including hydraulic jumps, with one hydraulic jump being located on the casting roll, the other one on the cooling table. Regarding the stability of the non unique solutions, the evolution of disturbances is investigated numerically as an initial-value problem. It is concluded that the hydraulic jump on the cooling table is unstable, while the other discontinuous solution as well as the continuous solution are stable for sufficiently small disturbances. Which stable solution is attained in the steady state, depends on the history of the process. Friction at the liquid/solid interface is taken into account in the last part of the analysis. A constant friction coefficient is assumed. It is found that the history of the process determines the steady-state solution if, and only if, the friction coefficient is sufficiently small. For larger values of the friction coefficient, the steady-state solution is unique and independent of the history of the transient process. Furthermore, for sufficiently large friction coefficients, stable hydraulic jumps are found, in contrast to the inviscid case, also on the cooling table. Received 19 March 1999; accepted for publication 3 May 1999     

探讨稳态法实验中的绝热问题

本文利用付立叶导热方程式 ,分析了导热系数测定仪在绝热问题上出现的漏洞与在制造上存在的缺陷 ,由此提出被测样品的侧面必须经过绝热处理 ,才能提高测量精确度的结论     

An invariant set in energy space for supercritical NLS in 1D

We consider radial solutions of a mass supercritical monic NLS and we prove the existence of a set, which looks like a hypersurface, in the space of finite energy functions, invariant for the flow and formed by solutions which converge to ground states.