FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3100617757> ?p ?o ?g. }

• W3100617757 endingPage "485" @default.
• W3100617757 startingPage "485" @default.
• W3100617757 abstract "view Abstract Citations (8) References (55) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Phase-Transition Theory of Instabilities. II. Fourth-Harmonic Bifurcations and lambda -Transitions Christodoulou, Dimitris M. ; Kazanas, Demosthenes ; Shlosman, Isaac ; Tohline, Joel E. Abstract We use a free-energy minimization approach to describe in simple and clear physical terms the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Our approach is fully nonlinear and stems from the Ginzburg-Landau theory of phase transitions. In this paper, we examine fourth-harmonic axisymmetric disturbances in Maclaurin spheroids and fourth-harmonic nonaxisymmetric disturbances in Jacobi ellipsoids. These two cases are very similar in the framework of phase transitions. It has been conjectured (Hachisu & Eriguchi 1983) that third-order phase transitions, manifested as smooth bifurcations in the angular momentum-rotation frequency plane, may occur on the Maclaurin sequence at the bifurcation point of the axisymmetric one-ring sequence and on the Jacobi sequence at the bifurcation point of the dumbbell-binary sequence. We show that these transitions are forbidden when viscosity maintains uniform rotation. The uniformly rotating one-ring/dumbbell equilibria close to each bifurcation point and their neighboring uniformly rotating nonequilibrium states have higher free energies than the Maclaurin/Jacobi equilibria of the same mass and angular momentum. These high-energy states act as free-energy barriers preventing the transition of spheroids/ellipsoids from their local minima to the free-energy minima that exist on the low rotation frequency branch of the one-ring/binary sequence. At a critical point, the two minima of the free-energy function are equal, signaling the appearance of a first-order phase transition. This transition can take place beyond the critical point only nonlinearly if the applied perturbations contribute enough energy to send the system over the top of the barrier (and if, in addition, viscosity maintains uniform rotation). In the angular momentum-rotation frequency plane, the one-ring and dumbbell-binary sequences have the shape of an inverted S and two corresponding turning points each. Because of this shape, the free-energy barrier disappears suddenly past the higher turning point, leaving the spheroid/ellipsoid on a saddle point but also causing a catastrophe by permitting a secular transition toward a one-ring/binary minimum energy state. This transition appears as a typical second-order phase transition, although there is no associated sequence bifurcating at the transition point (cf. Christodoulou et al. 1995a). Irrespective of whether a nonlinear first-order phase transition occurs between the critical point and the higher turning point or an apparent second-order phase transition occurs beyond the higher turning point, the result is fission (i.e., spontaneous breaking of the topology) of the original object on a secular timescale: the Maclaurin spheroid becomes a uniformly rotating axisymmetric torus, and the Jacobi ellipsoid becomes a binary. The presence of viscosity is crucial since angular momentum needs to be redistributed for uniform rotation to be maintained. We strongly suspect that the secular catastrophe is the dynamical analog of the notorious λ-transition of liquid 4He because it appears as a second-order phase transition with infinite specific heat at the point where the free-energy barrier disappears suddenly. This transition is not an elementary catastrophe. In contrast to this case, a dynamical catastrophe takes place from the bifurcation point to the lower branch of the Maclaurin toroid sequence because all conservation laws are automatically satisfied between the two equilibrium states. Furthermore, the free-energy barrier disappears gradually, and this transition is part of the elementary cusp catastrophe. This type of λ-transition is the dynamical analog of the Bose-Einstein condensation of an ideal Bose gas. The phase transitions of the dynamical systems are briefly discussed in relation to previous numerical simulations of the formation and evolution of protostellar systems. Some technical discussions concerning related results obtained from linear stability analyses, the breaking of topology, and the nonlinear theories of structural stability and catastrophic morphogenesis are included in an appendix. Publication: The Astrophysical Journal Pub Date: June 1995 DOI: 10.1086/175807 arXiv: arXiv:astro-ph/9504062 Bibcode: 1995ApJ...446..485C Keywords: GALAXIES: KINEMATICS AND DYNAMICS; GALAXIES: STRUCTURE; INSTABILITIES; STARS: FORMATION; STARS: ROTATION; Astrophysics E-Print: 34 pages, postscript, compressed,uuencoded. 7 figures available in postscript, compressed form by anonymous ftp from asta.pa.uky.edu (cd /shlosman/paper2 mget *.ps.Z). To appear in ApJ full text sources arXiv | ADS | Related Materials (3) Part 1: 1995ApJ...446..472C Part 3: 1995ApJ...446..500C Part 4: 1995ApJ...446..510C" @default.
• W3100617757 created "2020-11-23" @default.
• W3100617757 creator A5045312816 @default.
• W3100617757 creator A5073553250 @default.
• W3100617757 creator A5078610888 @default.
• W3100617757 creator A5083097422 @default.
• W3100617757 date "1995-06-01" @default.
• W3100617757 modified "2023-09-23" @default.
• W3100617757 title "Phase-Transition Theory of Instabilities. II. Fourth-Harmonic Bifurcations and lambda -Transitions" @default.
• W3100617757 doi "https://doi.org/10.1086/175807" @default.
• W3100617757 hasPublicationYear "1995" @default.
• W3100617757 type Work @default.
• W3100617757 sameAs 3100617757 @default.
• W3100617757 citedByCount "3" @default.
• W3100617757 countsByYear W31006177572019 @default.
• W3100617757 crossrefType "journal-article" @default.
• W3100617757 hasAuthorship W3100617757A5045312816 @default.
• W3100617757 hasAuthorship W3100617757A5073553250 @default.
• W3100617757 hasAuthorship W3100617757A5078610888 @default.
• W3100617757 hasAuthorship W3100617757A5083097422 @default.
• W3100617757 hasBestOaLocation W31006177571 @default.
• W3100617757 hasConcept C121332964 @default.
• W3100617757 hasConcept C149288129 @default.
• W3100617757 hasConcept C155675718 @default.
• W3100617757 hasConcept C158622935 @default.
• W3100617757 hasConcept C2781349735 @default.
• W3100617757 hasConcept C62520636 @default.
• W3100617757 hasConcept C74650414 @default.
• W3100617757 hasConcept C85075877 @default.
• W3100617757 hasConceptScore W3100617757C121332964 @default.
• W3100617757 hasConceptScore W3100617757C149288129 @default.
• W3100617757 hasConceptScore W3100617757C155675718 @default.
• W3100617757 hasConceptScore W3100617757C158622935 @default.
• W3100617757 hasConceptScore W3100617757C2781349735 @default.
• W3100617757 hasConceptScore W3100617757C62520636 @default.
• W3100617757 hasConceptScore W3100617757C74650414 @default.
• W3100617757 hasConceptScore W3100617757C85075877 @default.
• W3100617757 hasLocation W31006177571 @default.
• W3100617757 hasLocation W31006177572 @default.
• W3100617757 hasOpenAccess W3100617757 @default.
• W3100617757 hasPrimaryLocation W31006177571 @default.
• W3100617757 hasRelatedWork W126288685 @default.
• W3100617757 hasRelatedWork W2016910425 @default.
• W3100617757 hasRelatedWork W2063188179 @default.
• W3100617757 hasRelatedWork W2068878082 @default.
• W3100617757 hasRelatedWork W2093923179 @default.
• W3100617757 hasRelatedWork W2108346646 @default.
• W3100617757 hasRelatedWork W2611892599 @default.
• W3100617757 hasRelatedWork W2810568372 @default.
• W3100617757 hasRelatedWork W2949915041 @default.
• W3100617757 hasRelatedWork W34174254 @default.
• W3100617757 hasVolume "446" @default.
• W3100617757 isParatext "false" @default.
• W3100617757 isRetracted "false" @default.
• W3100617757 magId "3100617757" @default.
• W3100617757 workType "article" @default.