649 research outputs found
Satellite applications to marine geodesy
Potential use of satellites for enhancing positioning capabilities and for marine geodetic contro
Fuzzy Surfaces of Genus Zero
A fuzzy version of the ordinary round 2-sphere has been constructed with an
invariant curvature. We here consider linear connections on arbitrary fuzzy
surfaces of genus zero. We shall find as before that they are more or less
rigidly dependent on the differential calculus used but that a large number of
the latter can be constructed which are not covariant under the action of the
rotation group. For technical reasons we have been forced to limit our
considerations to fuzzy surfaces which are small perturbations of the fuzzy
sphere.Comment: 11 pages, Late
The Relativistic N-body Problem in a Separable Two-Body Basis
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the
relativistic N-body problem in a separable two-body basis in which the
particles interact pair-wise through scalar and vector interactions. The
resultant N-body Hamiltonian is relativistically covariant. It can be easily
separated in terms of the center-of-mass and the relative motion of any
two-body subsystem. It can also be separated into an unperturbed Hamiltonian
with a residual interaction. In a system of two-body composite particles, the
solutions of the unperturbed Hamiltonian are relativistic two-body internal
states, each of which can be obtained by solving a relativistic
Schr\"odinger-like equation. The resultant two-body wave functions can be used
as basis states to evaluate reaction matrix elements in the general N-body
problem. We prove a relativistic version of the post-prior equivalence which
guarantees a unique evaluation of the reaction matrix element, independent of
the ways of separating the Hamiltonian into unperturbed and residual
interactions. Since an arbitrary reaction matrix element involves composite
particles in motion, we show explicitly how such matrix elements can be
evaluated in terms of the wave functions of the composite particles and the
relevant Lorentz transformations.Comment: 42 pages, 2 figures, in LaTe
Noncommutative Geometry of Finite Groups
A finite set can be supplied with a group structure which can then be used to
select (classes of) differential calculi on it via the notions of left-, right-
and bicovariance. A corresponding framework has been developed by Woronowicz,
more generally for Hopf algebras including quantum groups. A differential
calculus is regarded as the most basic structure needed for the introduction of
further geometric notions like linear connections and, moreover, for the
formulation of field theories and dynamics on finite sets. Associated with each
bicovariant first order differential calculus on a finite group is a braid
operator which plays an important role for the construction of distinguished
geometric structures. For a covariant calculus, there are notions of invariance
for linear connections and tensors. All these concepts are explored for finite
groups and illustrated with examples. Some results are formulated more
generally for arbitrary associative (Hopf) algebras. In particular, the problem
of extension of a connection on a bimodule (over an associative algebra) to
tensor products is investigated, leading to the class of `extensible
connections'. It is shown that invariance properties of an extensible
connection on a bimodule over a Hopf algebra are carried over to the extension.
Furthermore, an invariance property of a connection is also shared by a `dual
connection' which exists on the dual bimodule (as defined in this work).Comment: 34 pages, Late
Propagating modes of non-Abelian tensor gauge field of second rank
In the recently proposed extension of the YM theory, non-Abelian tensor gauge
field of the second rank is represented by a general tensor whose symmetric
part describes the propagation of charged gauge boson of helicity two and its
antisymmetric part - the helicity zero charged gauge boson. On the
non-interacting level these polarizations are similar to the polarizations of
the graviton and of the Abelian antisymmetric B field, but the interaction of
these gauge bosons carrying non-commutative internal charges cannot be directly
identified with the interaction of gravitons or B field. Our intention here is
to illustrate this result from different perspectives which would include
Bianchi identity for the corresponding field strength tensor and the analysis
of the second-order partial differential equation which describes in this
theory the propagation of non-Abelian tensor gauge field of the second rank.Comment: 22 pages, Latex fil
Automorphisms of associative algebras and noncommutative geometry
A class of differential calculi is explored which is determined by a set of
automorphisms of the underlying associative algebra. Several examples are
presented. In particular, differential calculi on the quantum plane, the
-deformed plane and the quantum group GLpq(2) are recovered in this way.
Geometric structures like metrics and compatible linear connections are
introduced.Comment: 28 pages, some references added, several amendments of minor
importance, remark on modular group in section 8 omitted, to appear in J.
Phys.
CO2 capture and ions removal through reaction with potassium hydroxide in desalination reject brine: Statistical optimization
Previous studies have investigated the overall performance of the modified Solvay process based on a new alkaline compound, namely, KOH. Preliminary results have confirmed its high reactivity and effectiveness in capturing CO2 and managing reject brine. In this study, parametric sensitivity analysis has been carried out to optimize the operating conditions and thereby maximize CO2 capture and ions removal from high-salinity brines. Response surface methodology (RSM) analysis using the central composite design (CCD) approach was implemented to statistically determine the impact of important operating conditions, including KOH concentration (30–110 g/l), CO2 gas flow rate (400–1600 ml/min), gauge pressure (1–3 barg), and temperature (10–50 °C) on key response process output variables, such as CO2 uptake and ions reduction. The importance of these parameters and their interactions were confirmed by employing analysis of variance (ANOVA) approach at a confidence level of 95% (p < 0.05). These analyses demonstrated that under the optimized conditions of a temperature of 10 °C, gauge pressure of 2.1 barg, CO2 gas flow rate of 848.5 ml/min, KOH concentration of 110 g/l, and an inert mixing particle volume fraction of 15%, a maximum CO2 uptake value of 0.58 g/g KOH, maximum sodium (Na+) removal of 44.1%, chloride (Cl−) removal of 40.1%, calcium (Ca2+) removal of 100%, and magnesium (Mg2+) removal of 99.8% were achieved. The characterization of the collected solid products at optimum conditions revealed the production of valuable and useful products, particularly sodium and potassium bicarbonates, in addition to KCl.Open Access funding is provided by the Qatar National Library.Scopu
Relativistic Calculation of the Meson Spectrum: a Fully Covariant Treatment Versus Standard Treatments
A large number of treatments of the meson spectrum have been tried that
consider mesons as quark - anti quark bound states. Recently, we used
relativistic quantum "constraint" mechanics to introduce a fully covariant
treatment defined by two coupled Dirac equations. For field-theoretic
interactions, this procedure functions as a "quantum mechanical transform of
Bethe-Salpeter equation". Here, we test its spectral fits against those
provided by an assortment of models: Wisconsin model, Iowa State model,
Brayshaw model, and the popular semi-relativistic treatment of Godfrey and
Isgur. We find that the fit provided by the two-body Dirac model for the entire
meson spectrum competes with the best fits to partial spectra provided by the
others and does so with the smallest number of interaction functions without
additional cutoff parameters necessary to make other approaches numerically
tractable. We discuss the distinguishing features of our model that may account
for the relative overall success of its fits. Note especially that in our
approach for QCD, the resulting pion mass and associated Goldstone behavior
depend sensitively on the preservation of relativistic couplings that are
crucial for its success when solved nonperturbatively for the analogous
two-body bound-states of QED.Comment: 75 pages, 6 figures, revised content
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