Chemical Trends in the Ice Springs Basalt, Black Rock Desert, Utah

The Holocene Ice Springs volcanic field of west-central Utah consists of 0.53 km3 of tholeitic basalts erupted as a sequence of nested cinder cones and associated lava flows. Whole rock x-ray fluorescence and atomic absorption analysis of ninety-six samples of known relative age document statistically significant inter- and intra- eruption chemical variations. Elemental trends include increases in Ti, Fe, Ca, P, and Sr and decreases in Si, K, Rb, Ni, Cr, and Zr with decreasing age. Microprobe analyses of microphenocrysts of olivine, plagioclase, and Fe-Ti oxides and of groundmass olivine, plagioclase, and clinopyroxene indicate limited chemical variation between mineral assemblages of the eruptive events. Petrographic analyses have identified the presence of minor amounts of silicic xenoliths, orthopyroxene megacrysts, and plagioclase xenocrysts. Potassium-argon determinations establish the existence of excess argon in the basaltic cinder (30.05 x 10 -12 moles/gm) and in distal lava flows (8.29 x 10 -12 moles/gm) which suggest apparent ages of 16 and 4.3 million years respectively. Strontium isotopic data (Puskar and Condie, 1973) show systematic variations from oldest eruptions (87Sr/86Sr=0.7052) to youngest eruptions (87Sr/86Sr=0.7059). Theoretical evaluation of observed major element, trace element, isotopic, and thermophysical properties of the lavas and cinders limits the importance of proposed magmatic differentation processes. The data are compatible with model involving crystal fractionation, crustal assimilation, and magma mixing. Initial modification of mantle derived melts resulted from olivine fractionation at depth. Subsequent combination of 6 to 8% fractionation of plagioclase, minor olivine, and magnetite at shallow depths, less than one percent assimilation of silicic crustal basement rocks, and interaction of compositionally similar magma pulses explains the overall inter-eruption chemical trends. The intra-eruption variations follow the overall trends and a similar combination of processes of lesser magnitude accounts for the intra-eruption variations

NS Fivebrane and Tachyon Condensation

We argue that a semi-infinite D6-brane ending on an NS5-brane can be obtained from the condensation of the tachyon on the unstable D9-brane of type IIA theory. The construction uses a combination of the descriptions of these branes as solitons of the worldvolume theory of the D9-brane. The NS5-brane, in particular, involves a gauge bundle which is operator valued, and hence is better thought of as a gerbe.Comment: 20 pages, harvma

Multi-particle Correlations in Quaternionic Quantum Systems

We investigate the outcomes of measurements on correlated, few-body quantum systems described by a quaternionic quantum mechanics that allows for regions of quaternionic curvature. We find that a multi-particle interferometry experiment using a correlated system of four nonrelativistic, spin-half particles has the potential to detect the presence of quaternionic curvature. Two-body systems, however, are shown to give predictions identical to those of standard quantum mechanics when relative angles are used in the construction of the operators corresponding to measurements of particle spin components.Comment: REVTeX 3.0, 16 pages, no figures, UM-P-94/54, RCHEP-94/1

Braess's Paradox in Wireless Networks: The Danger of Improved Technology

When comparing new wireless technologies, it is common to consider the effect that they have on the capacity of the network (defined as the maximum number of simultaneously satisfiable links). For example, it has been shown that giving receivers the ability to do interference cancellation, or allowing transmitters to use power control, never decreases the capacity and can in certain cases increase it by $\Omega(\log (\Delta \cdot P_{\max}))$, where $\Delta$ is the ratio of the longest link length to the smallest transmitter-receiver distance and $P_{\max}$ is the maximum transmission power. But there is no reason to expect the optimal capacity to be realized in practice, particularly since maximizing the capacity is known to be NP-hard. In reality, we would expect links to behave as self-interested agents, and thus when introducing a new technology it makes more sense to compare the values reached at game-theoretic equilibria than the optimum values. In this paper we initiate this line of work by comparing various notions of equilibria (particularly Nash equilibria and no-regret behavior) when using a supposedly "better" technology. We show a version of Braess's Paradox for all of them: in certain networks, upgrading technology can actually make the equilibria \emph{worse}, despite an increase in the capacity. We construct instances where this decrease is a constant factor for power control, interference cancellation, and improvements in the SINR threshold ($\beta$), and is $\Omega(\log \Delta)$ when power control is combined with interference cancellation. However, we show that these examples are basically tight: the decrease is at most O(1) for power control, interference cancellation, and improved $\beta$, and is at most $O(\log \Delta)$ when power control is combined with interference cancellation

Spontaneous Symmetry Breaking in Presence of Electric and Magnetic Charges

Starting with the definition of quaternion gauge theory, we have undertaken the study of SU(2)_{e}\times SU(2)_{m}\times U(1)_{e}\times U(1)_{m} in terms of the simultaneous existence of electric and magnetic charges along with their Yang - Mills counterparts. As such, we have developed the gauge theory in terms of four coupling constants associated with four - gauge symmetry SU(2)_{e}\times SU(2)_{m}\times U(1)_{e}\times U(1)_{m}. Accordingly, we have made an attempt to obtain the abelian and non - Abelian gauge structures for the particles carrying simultaneously the electric and magnetic charges (namely dyons). Starting from the Lagrangian density of two SU(2)\times U(1) gauge theories responsible for the existence of electric and magnetic charges, we have discussed the consistent theory of spontaneous symmetry breaking and Higgs mechanism in order to generate the masses. From the symmetry breaking, we have generated the two electromagnetic fields, the two massive vector W^{\pm} and Z^{0} bosons fields and the Higgs scalar fields

The Standard Model Fermion Spectrum From Complex Projective spaces

It is shown that the quarks and leptons of the standard model, including a right-handed neutrino, can be obtained by gauging the holonomy groups of complex projective spaces of complex dimensions two and three. The spectrum emerges as chiral zero modes of the Dirac operator coupled to gauge fields and the demonstration involves an index theorem analysis on a general complex projective space in the presence of topologically non-trivial SU(n)xU(1) gauge fields. The construction may have applications in type IIA string theory and non-commutative geometry.Comment: 13 pages. Typset using LaTeX and JHEP3 style files. Minor typos correcte

Singular forces and point-like colloids in lattice Boltzmann hydrodynamics

We present a second-order accurate method to include arbitrary distributions of force densities in the lattice Boltzmann formulation of hydrodynamics. Our method may be used to represent singular force densities arising either from momentum-conserving internal forces or from external forces which do not conserve momentum. We validate our method with several examples involving point forces and find excellent agreement with analytical results. A minimal model for dilute sedimenting particles is presented using the method which promises a substantial gain in computational efficiency.Comment: 22 pages, 9 figures. Submitted to Phys. Rev.

Spectroscopy of drums and quantum billiards: perturbative and non-perturbative results

We develop powerful numerical and analytical techniques for the solution of the Helmholtz equation on general domains. We prove two theorems: the first theorem provides an exact formula for the ground state of an arbirtrary membrane, while the second theorem generalizes this result to any excited state of the membrane. We also develop a systematic perturbative scheme which can be used to study the small deformations of a membrane of circular or square shapes. We discuss several applications, obtaining numerical and analytical results.Comment: 29 pages, 12 figures, 7 tabl