Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem

The reversibility of sea ice loss in a state-of-the-art climate model

Rapid Arctic sea ice retreat has fueled speculation about the possibility of threshold (or ‘tipping point’) behavior and irreversible loss of the sea ice cover. We test sea ice reversibility within a state-of-the-art atmosphere–ocean global climate model by increasing atmospheric carbon dioxide until the Arctic Ocean becomes ice-free throughout the year and subsequently decreasing it until the initial ice cover returns. Evidence for irreversibility in the form of hysteresis outside the envelope of natural variability is explored for the loss of summer and winter ice in both hemispheres. We find no evidence of irreversibility or multiple ice-cover states over the full range of simulated sea ice conditions between the modern climate and that with an annually ice-free Arctic Ocean. Summer sea ice area recovers as hemispheric temperature cools along a trajectory that is indistinguishable from the trajectory of summer sea ice loss, while the recovery of winter ice area appears to be slowed due to the long response times of the ocean near the modern winter ice edge. The results are discussed in the context of previous studies that assess the plausibility of sea ice tipping points by other methods. The findings serve as evidence against the existence of threshold behavior in the summer or winter ice cover in either hemisphere

Pauli's Theorem and Quantum Canonical Pairs: The Consistency Of a Bounded, Self-Adjoint Time Operator Canonically Conjugate to a Hamiltonian with Non-empty Point Spectrum

In single Hilbert space, Pauli's well-known theorem implies that the existence of a self-adjoint time operator canonically conjugate to a given Hamiltonian signifies that the time operator and the Hamiltonian possess completely continuous spectra spanning the entire real line. Thus the conclusion that there exists no self-adjoint time operator conjugate to a semibounded or discrete Hamiltonian despite some well-known illustrative counterexamples. In this paper we evaluate Pauli's theorem against the single Hilbert space formulation of quantum mechanics, and consequently show the consistency of assuming a bounded, self-adjoint time operator canonically conjugate to a Hamiltonian with an unbounded, or semibounded, or finite point spectrum. We point out Pauli's implicit assumptions and show that they are not consistent in a single Hilbert space. We demonstrate our analysis by giving two explicit examples. Moreover, we clarify issues sorrounding the different solutions to the canonical commutation relations, and, consequently, expand the class of acceptable canonical pairs beyond the solutions required by Pauli's theorem.Comment: contains corrections to minor typographical errors of the published versio

How Events Come Into Being: EEQT, Particle Tracks, Quantum Chaos, and Tunneling Time

In sections 1 and 2 we review Event Enhanced Quantum Theory (EEQT). In section 3 we discuss applications of EEQT to tunneling time, and compare its quantitative predictions with other approaches, in particular with B\"uttiker-Larmor and Bohm trajectory approach. In section 4 we discuss quantum chaos and quantum fractals resulting from simultaneous continuous monitoring of several non-commuting observables. In particular we show self-similar, non-linear, iterated function system-type, patterns arising from quantum jumps and from the associated Markov operator. Concluding remarks pointing to possible future development of EEQT are given in section 5.Comment: latex, 27 pages, 7 postscript figures. Paper submitted to Proc. Conference "Mysteries, Puzzles And Paradoxes In Quantum Mechanics, Workshop on Entanglement And Decoherence, Palazzo Feltrinelli, Gargnano, Garda Lake, Italy, 20-25 September, 199

A Goldstone Theorem in Thermal Relativistic Quantum Field Theory

We prove a Goldstone Theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of space-like decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed

Mutual information between geomagnetic indices and the solar wind as seen by WIND : implications for propagation time estimates

The determination of delay times of solar wind conditions at the sunward libration point to effects on Earth is investigated using mutual information. This measures the amount of information shared between two timeseries. We consider the mutual information content of solar wind observations, from WIND, and the geomagnetic indices. The success of five commonly used schemes for estimating interplanetary propagation times is examined. Propagation assuming a fixed plane normal at 45 degrees to the GSE x-axis (i.e. the Parker Spiral estimate) is found to give optimal mutual information. The mutual information depends on the point in space chosen as the target for the propagation estimate, and we find that it is maximized by choosing a point in the nightside rather than dayside magnetosphere. In addition, we employ recurrence plot analysis to visualize contributions to the mutual information, this suggests that it appears on timescales of hours rather than minutes

Completeness in Photometric and Spectroscopic Searches for Clusters

We investigate, using simulated galaxy catalogues, the completeness of searches for massive clusters of galaxies in redshift surveys or imaging surveys with photometric redshift estimates, i.e. what fraction of clusters (M>10^14/h Msun) are found in such surveys. We demonstrate that the matched filter method provides an efficient and reliable means of identifying massive clusters even when the redshift estimates are crude. In true redshift surveys the method works extremely well. We demonstrate that it is possible to construct catalogues with high completeness, low contamination and both varying little with redshift.Comment: ApJ in press, 15 pages, 10 figure

The XMM-Newton Ω\Omega Project

The abundance of high-redshift galaxy clusters depends sensitively on the matter density \OmM and, to a lesser extent, on the cosmological constant $\Lambda$. Measurements of this abundance therefore constrain these fundamental cosmological parameters, and in a manner independent and complementary to other methods, such as observations of the cosmic microwave background and distance measurements. Cluster abundance is best measured by the X-ray temperature function, as opposed to luminosity, because temperature and mass are tightly correlated, as demonstrated by numerical simulations. Taking advantage of the sensitivity of XMM-Newton, our Guaranteed Time program aims at measuring the temperature of the highest redshift (z>0.4) SHARC clusters, with the ultimate goal of constraining both \OmM and $\Lambda$.Comment: To appear in the Proceedings of the XXI Moriond Conference: Galaxy Clusters and the High Redshift Universe Observed in X-rays, edited by D. Neumann, F. Durret, & J. Tran Thanh Va

The Binary Neutron Star event LIGO/VIRGO GW170817 a hundred and sixty days after merger: synchrotron emission across the electromagnetic spectrum

We report deep Chandra, HST and VLA observations of the binary neutron star event GW170817 at $t<160$ d after merger. These observations show that GW170817 has been steadily brightening with time and might have now reached its peak, and constrain the emission process as non-thermal synchrotron emission where the cooling frequency $\nu_c$ is above the X-ray band and the synchrotron frequency $\nu_m$ is below the radio band. The very simple power-law spectrum extending for eight orders of magnitude in frequency enables the most precise measurement of the index $p$ of the distribution of non-thermal relativistic electrons $N(\gamma)\propto \gamma^{-p}$ accelerated by a shock launched by a NS-NS merger to date. We find $p=2.17\pm0.01$, which indicates that radiation from ejecta with $\Gamma\sim3-10$ dominates the observed emission. While constraining the nature of the emission process, these observations do \emph{not} constrain the nature of the relativistic ejecta. We employ simulations of explosive outflows launched in NS ejecta clouds to show that the spectral and temporal evolution of the non-thermal emission from GW170817 is consistent with both emission from radially stratified quasi-spherical ejecta traveling at mildly relativistic speeds, \emph{and} emission from off-axis collimated ejecta characterized by a narrow cone of ultra-relativistic material with slower wings extending to larger angles. In the latter scenario, GW170817 harbored a normal SGRB directed away from our line of sight. Observations at $t\le 200$ days are unlikely to settle the debate as in both scenarios the observed emission is effectively dominated by radiation from mildly relativistic material.Comment: Updated with the latest VLA and Chandra dat