Phase diagram and equations of state of BaSO4

Abstract

The phase diagram and equations of state of BaSO₄, were determined up to 29 GPa and 1000 K in a resistance-heating type diamond anvil cell. At room temperature, barite is the stable form of BaSO₄ which undergoes a reversible phase transition at 10 GPa. The high-pressure form is tentatively determined to be triclinic. At high temperature, a similar phase transition takes place in BaSO₄, but at a pressure higher than that at room temperature. Our results indicate that the phase boundary of the two polymorphs in BasO₄ has a positive slope (dT/dP) of 90 K/GPa. The equations of state for both barite and its high-pressure phase are reported.     

Newton's method and periodic solutions of nonlinear wave equations

We prove the existence of periodic solutions of the nonlinear wave equation satisfying either Dirichlet or periodic boundary conditions on the interval [O, π]. The coefficients of the eigenfunction expansion of this equation satisfy a nonlinear functional equation. Using a version of Newton's method, we show that this equation has solutions provided the nonlinearity g(x, u) satisfies certain generic conditions of nonresonance and genuine nonlinearity. © 1993 John Wiley & Sons, Inc.     

Affine diffeomorphisms of translation surfaces: Periodic points, Fuchsian groups, and arithmeticity

We study translation surfaces with rich groups of affine diffeomorphisms—“prelattice” surfaces. These include the lattice translation surfaces studied by W. Veech. We show that there exist prelattice but nonlattice translation surfaces. We characterize arithmetic surfaces among prelattice surfaces by the infinite cardinality of their set of points periodic under affine diffeomorphisms. We give examples of translation surfaces whose periodic points and Weierstrass points coincide.     

Image of the Spectral Measure of a Jacobi Field and the Corresponding Operators

By definition, a Jacobi field is a family of commuting selfadjoint three-diagonal operators in the Fock space The operators J(ϕ) are indexed by the vectors of a real Hilbert space H₊. The spectral measure ρ of the field J is defined on the space H₋ of functionals over H₊. The image of the measure ρ under a mapping is a probability measure ρ_K on T₋. We obtain a family J_K of operators whose spectral measure is equal to ρ_K. We also obtain the chaotic decomposition for the space L²(T₋, d_{ρ K}).     

An intelligent decomposition of pairwise comparison matrices for large-scale decisions

A Pairwise Comparison Matrix (PCM) has been used to compute for relative priorities of elements and are integral components in widely applied decision making tools: the Analytic Hierarchy Process (AHP) and its generalized form, the Analytic Network Process (ANP). However, PCMs suffer from several issues limiting their applications to large-scale decision problems. These limitations can be attributed to the curse of dimensionality, that is, a large number of pairwise comparisons need to be elicited from a decision maker. This issue results to inconsistent preferences due to the limited cognitive powers of decision makers. To address these limitations, this research proposes a PCM decomposition methodology that reduces the elicited pairwise comparisons. A binary integer program is proposed to intelligently decompose a PCM into several smaller subsets using interdependence scores among elements. Since the subsets are disjoint, the most independent pivot element is identified to connect all subsets to derive the global weights of the elements from the original PCM. As a result, the number of pairwise comparison is reduced and consistency is of the comparisons is improved. The proposed decomposition methodology is applied to both AHP and ANP to demonstrate its advantages.     

Computerized Developments in Design,Generation, Simulation of Meshing,and Stress Analysis of Gear Drives

The paper represents new computerized developments in design, generation, simulation of meshing, and stress analysis of gear drives. The main contents of the paper are: (i) application of a predesigned parabolic function of transmission errors for reduction of noise, (ii) computerized simulation of noise caused by transmission errors, (iii) modification of the basic algorithm of tooth contact analysis, and (iv) application of approaches developed for enhanced design and simulation of meshing of the following gear drives: (a) spiral bevel gear drives, (b) face-gear drives (including an approach for grinding), and (c) modified helical gear drives. The developed theory is illustrated with numerical examples.     

How Fear of Future Outcomes Affects Social Dynamics

Journal of Statistical Physics - Mutualistic relationships among the different species are ubiquitous in nature. To prevent mutualism from slipping into antagonism, a host often invokes a...