Thermal expansion of polycrystalline aggregates: II. Self consistent approximation

The Self Consistent Scheme approximation method is applied to evaluate the thermal expansion coefficient of statistically isotropic polycrystalline aggregates, in terms of single crystal thermoelastic properties and polycrystal elastic properties. The case of orthorhombic crystals is considered in detail.     

Theoretical and Numerical Studies of Transonic Flow of Moist Air Around a Thin Airfoil

Numerical studies of a two-dimensional and steady transonic flow of moist air around a thin airfoil with condensation are presented. The computations are guided by a recent transonic small-disturbance (TSD) theory of Rusak and Lee (2000) on this topic. The asymptotic model provides a simplified framework to investigate the changes in the flow field caused by the heat addition from a nonequilibrium process of condensation of water vapor in the air by homogeneous nucleation. An iterative method which is based on a type-sensitive difference scheme is applied to solve the governing equations. The results demonstrate the similarity rules for transonic flow of moist air and the effects of energy supply by condensation on the flow behavior. They provide a method to formulate various cases with different flow properties that have a sufficiently close behavior and that can be used in future computations, experiments, and design of flow systems operating with moist air. Also, the computations show that the TSD solutions of moist air flows represent the essence of the flow character computed from the inviscid fluid flow equations. Received 5 October 2000 and accepted 21 March 2002     

Isomeric solid enols on ring- and amide-carbonyls of substituted 2-carbanilido-1,3-indandiones

Both isomeric enols on ring carbonyl (5b) and on amide carbonyl (6b) derived from N-p-methoxyphenyl-2-carbamido-1,3-indandione (4b) were isolated, and their X-ray structures were determined. X-ray diffraction of the N-o,p-dimethoxy analogue indicated a disorder ascribed to the presence of a 6:4 mixture of 5c and 6c. Calculation (B3LYP/6-31+G*) gave good agreement with observed geometries. The calculated energies indicated that enols 6 are more stable by <1 kcal/mol than enols 5 and much more stable than amides 4.     

Observable Enols of Anhydrides: Claimed Literature Systems,Calculations, and Predictions

The literature describing the observation of enols of carboxylic anhydrides and mixed carboxylic‐sulfuric anhydrides was examined. In the phenylbutyric anhydride system, the alleged enol was shown to be ethylphenylketene, and the monoenol EtC(Ph)=C(OH)OC(=O)CH(Ph)Et ( 5 ) and the dienol ( 6 ) should not be observed according to calculations. Calculations also show that the claimed enols H₂C=C(OH)OSO₂Y, Y=SO, Ac ( 15 ) and the enol of 2H‐pyran‐2,6(3H)‐dione ( 7 ) are too unstable to be observed. The bulky enols of β,β‐ditipylacetic formic ( 35a ) or trifluoroacetic ( 35b ) anhydride were calculated to be unstable with pK_Enol=7.7 (6.2). The suggestion that compounds with the 3‐acyl or 3‐aroyl‐2H‐pyran‐2,6(3H)‐dione skeleton are enolic was examined. In the solid state, all the known structures show that enolization takes place on C(5)=O. However, B3LYP/6‐31G** calculations show that, for 3‐acetyl‐4‐methyl‐2H‐pyran‐2,6(3H)‐dione ( 10 , R¹=Me, R²=H), which is completely enolic, the enol on the acetyl group (cf. 12 ) is only 0.9 kcal/mol more stable than the enol on the anhydride (cf. 11 ). Calculations also revealed that 3‐(trifluoroacetyl)‐2H‐pyran‐2,6(3H)‐dione ( 28 ) should exist in nearly equal amounts of the enol of anhydride (cf. 30 ) and the enol of the acyl group (cf. 29 ), whereas the enol of anhydride (cf. 32 ) is the only stable species for 3‐(methoxycarbonyl)‐2H‐pyran‐2,6(3H)‐dione ( 31 ). Furan‐2,5‐diol ( 27 ) and 5‐hydroxyfuran‐2‐one ( 26 ) are calculated not to give observable isomers of succinic anhydride ( 25 ) (pK_Enol=30 and 18, resp.) in spite of the expected aromatic stabilization of 27 . Surprisingly, the calculations reveal that the enol (NC)₂C=C(OH)OCHO ( 38 ) is less stable than its tautomeric anhydride ( 37 ) (pK_Enol=1.6). Comparison of calculated pK_Enol values for (NC)₂CHC(=O)X ( 41 ) and MeC(=O)X indicates that the assumption that substitution by two β‐CN groups affects similarly all the systems regardless of X is incorrect. A pK_Enol((NC)₂CHC(=O)X) vs. pK_Enol(MeC(=O)X) plot is linear for most substituents with severe and mild negative deviations, respectively, for X=NH₂ and MeO. Appropriate isodesmic reactions have shown that the β,β‐(CN)₂ substitution increases the stabilization of the enol of amide (X=NH₂) by 14.6 kcal/mol over that for the anhydride (X=OCHO), whereas the amide form is 7.1 kcal/mol less destabilized than for the anhydride. The pK_Enol value for (MeOCO)₂CHCOOCHO ( 43 ) is 3.6, i.e., stabilization by these β‐electron‐withdrawing groups is insufficient to make the enols observable.     

Adiabatic plasma buncher

In this paper, we present a new scheme of injection into a plasma accelerator, aimed at producing a high-quality beam while relaxing the demands on the bunch length of the injected beam. The beam dynamics in the injector, consisting of a high-voltage pulsed photodiode, is analyzed and optimized to produce a λ_p/20 long electron bunch at 2.5 MeV. This bunch is injected into a plasma wave in which it compresses down to λ_p/100, while accelerating up to 250 MeV. This simultaneous bunching and acceleration of a high-quality beam requires a proper combination of injection energy and injection phase. Preliminary results from simulations are shown to assess the potentials of the scheme     

On Quantum Entropy

Quantum physics, despite its intrinsically probabilistic nature, lacks a definition of entropy fully accounting for the randomness of a quantum state. For example, von Neumann entropy quantifies only the incomplete specification of a quantum state and does not quantify the probabilistic distribution of its observables; it trivially vanishes for pure quantum states. We propose a quantum entropy that quantifies the randomness of a pure quantum state via a conjugate pair of observables/operators forming the quantum phase space. The entropy is dimensionless, it is a relativistic scalar, it is invariant under canonical transformations and under CPT transformations, and its minimum has been established by the entropic uncertainty principle. We expand the entropy to also include mixed states. We show that the entropy is monotonically increasing during a time evolution of coherent states under a Dirac Hamiltonian. However, in a mathematical scenario, when two fermions come closer to each other, each evolving as a coherent state, the total system’s entropy oscillates due to the increasing spatial entanglement. We hypothesize an entropy law governing physical systems whereby the entropy of a closed system never decreases, implying a time arrow for particle physics. We then explore the possibility that as the oscillations of the entropy must by the law be barred in quantum physics, potential entropy oscillations trigger annihilation and creation of particles.     

The minimum equitable radius location problem with continuous demand

We analyze the location of p facilities satisfying continuous area demand. Three objectives are considered: (i) the p-center objective (to minimize the maximum distance between all points in the area and their closest facility), (ii) equalizing the load service by the facilities, and (iii) the minimum equitable radius – minimizing the maximum radius from each point to its closest facility subject to the constraint that each facility services the same load. The paper offers three contributions: (i) a new problem – the minimum equitable radius is presented and solved by an efficient algorithm, (ii) an improved and efficient algorithm is developed for the solution of the p-center problem, and (iii) an improved algorithm for the equitable load problem is developed. Extensive computational experiments demonstrated the superiority of the new solution algorithms.