Cristina Stoica

Bio: Cristina Stoica is an academic researcher from Wilfrid Laurier University. The author has contributed to research in topics: Phase space & n-body problem. The author has an hindex of 13, co-authored 44 publications receiving 630 citations. Previous affiliations of Cristina Stoica include Space Sciences Laboratory & Imperial College London.

Geometric Mechanics and Symmetry: From Finite to Infinite Dimensions

Abstract: ,by Darryl D. Holm, Tanya Schmah and Cristina Stoica, Oxford University Press,Oxford, 2009, xi + 515 pp., ISBN: 978-0-19-921290-3The purpose of the book is to provide the unifying viewpoint of Lagrangian andHamiltonian mechanics in the coordinate-free language of differential geometryin the spirit of the Marsden-Ratiu school. The book is similar in content - althoughless formal - to the book by J. Marsden and T. Ratiu [7]. One can also mentionthe companion two-volumes book by Holm [4,5] written at a more basic level,and that one can recommend as an introductory reading. The classical treatises onthe subject are the books by Abraham-Marsden [1], Arnold [2] and Libermann-Marle [6].Typical applications are N-particle systems, rigid bodies, continua such as u-ids and electromagnetic systems that illustrate the powerfulness of the adoptedpoint of view. The geometrical structure allows the covering of both the nite-dimensional conservative case (rst part of the book) and the innite dimensionalsituation in the second part. The notion of symmetry here is central, as it allowsa reduction of the number of dimensions of the mechanical systems, and furtherexploits the conserved quantities (momentum map) associated to symmetry. Liegroup symmetries, Poisson reduction and momentum maps are rst discussed.The concepts are introduced in a progressive and clear manner in the rst part ofthe book. The second part devoted to innite dimensional systems is motivatedby the identication of Euler’s ideal uid motion with the geodesic o w on thegroup of volume-preserving diffeomorphism. The Euler-PoincarO (EP) variationalprinciple for the Euler uid equations is exposed in the framework of geometricmechanics, in association with Lie-Poisson Hamiltonian structure of Noether’stheorem and momentum maps. Original applications of the Euler-PoincarO equa-tions to solitons, computational anatomy, image matching, or geophysical uiddynamics are given at the end of the second part of the book.Here the rst chapter recapitulates the Newtonian, Lagrangian and Hamiltonian117

Phase-space structure and regularization of Manev-type problems

Abstract: Phase-space structure and regularization of Manev-type problems Florin Diacu a;∗, Vasile Mioc b, Cristina Stoica c a Department of Mathematics and Statistics, University of Victoria, Victoria, Canada V8W 3P4 b Astronomical Institute of the Romanian Academy, Astronomical Observatory Cluj-Napoca, Str. Cire silor 19, 3400 Cluj-Napoca, Romania c Institute for Gravitation and Space Sciences, Laboratory for Gravitation, Str. Mendeleev 21-25, Bucharest, Romania

The global flow of the Manev problem

Abstract: The Manev problem (a two‐body problem given by a potential of the form A/r+B/r2, where r is the distance between particles and A,B are positive constants) comprises several important physical models, having its roots in research done by Isaac Newton. We provide its analytic solution, then completely describe its global flow using McGehee coordinates and topological methods, and offer the physical interpretation of all solutions. We prove that if the energy constant is negative, the orbits are, generically, precessional ellipses, except for a zero‐measure set of initial data, for which they are ellipses. For zero energy, the orbits are precessional parabolas, and for positive energy they are precessional hyperbolas. In all these cases, the set of initial data leading to collisions has positive measure.

On the restricted three body problem with oblate primaries

Abstract: We present a study of the Lagrangian triangular equilibria in the planar restricted three body problem where the primaries are oblate homogeneous spheroids steadily rotating around their axis of symmetry and whose equatorial planes coincide throughout their motion.

The Schwarzschild Problem in Astrophysics

Abstract: The Schwarzschild problem (the two-body problem associated to apotential of the form A/r + B/r3 has been qualitativelyinvestigated in an astrophysical framework, exemplified by two likelysituations: motion of a particle in the photogravitational field ofan oblate, rotating star, or in that of a star which generates aSchwarzschild field Using McGehee-type transformations, regularizedequations of motion are obtained, and the collision singularity isblown up and replaced by the collision manifold λ (a torus)pasted on the phase space The flow on λ is fullycharacterized Then, reducing the 4D phase space to dimension 2, theglobal flow in the phase plane is depicted for all possible values ofthe energy and for all combinations of nonzero A and B Eachphase trajectory is interpreted in terms of physical motion,obtaining in this way a telling geometric and physical picture of themodel

The New York Review of Books

Abstract: It comes as something ofa surprise to reflect that the New York Review ofBooks is now over twenty years old. Even people of my generation (that is, old enough to remember the revolutionary 196os but not young enough to have taken a very exciting part in them) think of the paper as eternally youthful. In fact, it has gone through years of relatively quiet life, yet, as always in a competitive journalistic market, it is the controversies that attract the interest of the reader and to which the history (especially an admittedly impressionistic survey that tries to include something of the intellectual context in which a journal has operated) must give some attention. Not all the attacks which the New York Review has attracted, both early in its career and more recently, are worth more than a brief summary. What do we now make, for example, of Richard Kostelanetz's forthright accusation that 'The New York Review was from its origins destined to publicize Random House's (and especially [Jason] Epstein's) books and writers'?1 Well, simply that, even if the statistics bear out the charge (and Kostelanetz provides some suggestive evidence to support it, at least with respect to some early issues), there is nothing surprising in a market economy about a publisher trying to push his books through the pages of a journal edited by his friends. True, the New York Review has not had room to review more than around fifteen books in each issue and there could be a bias in the selection of

Geophysical fluid dynamics.

Abstract: The potential for sea ice-albedo feedback to give rise to nonlinear climate change in the Arctic Ocean – defined as a nonlinear relationship between polar and global temperature change or, equivalently, a time-varying polar amplification – is explored in IPCC AR4 climate models. Five models supplying SRES A1B ensembles for the 21 st century are examined and very linear relationships are found between polar and global temperatures (indicating linear Arctic Ocean climate change), and between polar temperature and albedo (the potential source of nonlinearity). Two of the climate models have Arctic Ocean simulations that become annually sea ice-free under the stronger CO 2 increase to quadrupling forcing. Both of these runs show increases in polar amplification at polar temperatures above-5 o C and one exhibits heat budget changes that are consistent with the small ice cap instability of simple energy balance models. Both models show linear warming up to a polar temperature of-5 o C, well above the disappearance of their September ice covers at about-9 o C. Below-5 o C, surface albedo decreases smoothly as reductions move, progressively, to earlier parts of the sunlit period. Atmospheric heat transport exerts a strong cooling effect during the transition to annually ice-free conditions. Specialized experiments with atmosphere and coupled models show that the main damping mechanism for sea ice region surface temperature is reduced upward heat flux through the adjacent ice-free oceans resulting in reduced atmospheric heat transport into the region.

Simulating Hamiltonian dynamics.

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