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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Vladimirov, S.V. Ivanov, A.V. Robinson, P.A. |
| Copyright Year | 2003 |
| Description | Author affiliation: Sch. of Phys., Sydney Univ., NSW, Australia (Vladimirov, S.V.; Ivanov, A.V.; Robinson, P.A.) |
| Abstract | The remarkable property of critical phenomena is the universal scaling appearing in vast variety of systems, e.g., magnets and gases follow simple power laws for the order parameter, specific heat capacity, susceptibility, compressibility, etc. In thermodynamic systems, phase transitions take place at a critical temperature when the coefficients, characterizing the linear response of the system to external perturbations, diverge and long-range order appears, causing a transition to a new phase due to collective behavior of an entire system. Thus, irrespective of the amplitude of perturbations, the system behaves nonlinearly at the critical point. Nonlinearity, inherent to criticality, leads to scalings that are universal for the thermodynamic systems as well as for plasmas and gravitating systems. However, analysis based on the partition function (as in thermodynamics) is generally not applicable to the kinetic systems governed by coupled Vlasov and Poisson equations which, under certain conditions, lose their stability in a manner analogous to a second-order phase transition. Unlike second-order phase transitions, studied as nonlinear phenomena from the very beginning, analysis of Vlasov-Poisson systems is largely based on dispersion relations obtained by linearization of initially nonlinear equations. This allows one to predict criticality, but, similar to linear thermodynamics, cannot describe all properties of the critical state. Thus nonlinear analysis is important for plasmas where critical states are common because of the wealth of instabilities. Another example can be found far from plasmas: the dynamics of a normal brain are revealed to be close to marginal stability, apparently a vital condition for successful adaptability. Here, a model Vlasov-Poisson gravitating system is simulated near the point of marginal stability and the critical exponents are calculated. These exponents obey the Widom, Rushbrooke, and Griffith laws at the formal dimensionality d=5 and are not the Landau-Weiss exponents contrary to the expectation for the equivalent mean field model. |
| Sponsorship | Plasma Sci. & Applications Committee of the IEEE Nucl. & Plasma Sci. Soc. Hanyang Univ. Japan Soc. Plasma Res. Assoc. Korea Atomic Energy Res. Inst. Korea Basic Sci. Inst. Korea Vacuum Soc |
| File Size | 83826 |
| File Format | |
| ISBN | 078037911X |
| ISSN | 07309244 |
| DOI | 10.1109/PLASMA.2003.1228967 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2003-06-05 |
| Publisher Place | South Korea |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Thermodynamics Plasma stability Plasma properties Plasma simulation Power system modeling Magnetic properties Magnets Gases Magnetic susceptibility Plasma temperature |
| Content Type | Text |
| Resource Type | Article |
| Subject | Atomic and Molecular Physics, and Optics Condensed Matter Physics Electrical and Electronic Engineering |
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