Single-particle spectra and two-particle Bose-Einstein correlation functions
are determined analytically utilizing a self-similar solution of
non-relativistic hydrodynamics for ellipsoidally-symmetric, expanding
fireballs, by assuming that the symmetry axes of the ellipsoids are tilted in
the frame of the observation. The directed, elliptic and third flows are
calculated analytically. The mass dependences of the slope parameters in the
principal directions of the expansion, together with the mass and angular
dependences of the HBT radius parameters, reflect directly the ellipsoidal
properties of the flow.Comment: 4 pages, 3 figure
New solutions are found for the non-relativistic hydrodynamical equations. These solutions describe expanding matter with a Gaussian density profile. In the simplest case, thermal equilibrium is maintained without any interaction, the energy is conserved, and the process is isentropic. More general solutions are also obtained that describe explosions driven by heat production, or contraction of the matter caused by energy loss.Introduction. The equations of hydrodynamics correspond to local conservation of some charges as well as energy and momentum. The equations are scale-invariant, hence can be applied to phenomenological description of physical phenomena from collisions of heavy nuclei to collisions of galaxies. Recently, a lot of experimental and theoretical effort went into the exploration of hydrodynamical behaviour of strongly interacting hadronic matter in non-relativistic as well as in relativistic heavy ion collisions, see for example refs.[1]- [7]. Due to the non-linear nature of the equations of hydrodynamics, exact solutions of these equations are rarely found. In ref.[2] an exact solution of hydrodynamics of expanding fireballs was found 20 years ago. The purpose of this Letter is to present and analyze a new, exact solution of the non-relativistic hydrodynamical equations, with a generalization to heat production or loss (e.g. due to radiation). We hope that the results presented herewith may be utilized to access analytically the time-evolution of the hydrodynamically behaving strongly interacting matter as probed by non-relativistic heavy ion collisions [4,5]. The results are, however, rather general in nature and they can be applied to any physical phenomena where the non-relativistic hydrodynamical description is valid.Adiabatic expansion. Consider a hydrodynamical system described by the continuity equation, the Euler equation and the local energy conservation:
Simple, self-similar, elliptic solutions of non-relativistic fireball hydrodynamics are presented, generalizing earlier results for spherically symmetric fireballs with Hubble flows and homogeneous temperature profiles. The transition from one dimensional to three dimensional expansions is investigated in an efficient manner.
A b s t r a c t . We list arguments for creating n unified theory of Kewtonian Gravity and QuantumMechanics. This nonrelativistic level has been historically bypassed, however even here one is confronted with conceptional problems anticipating some features of Relativistic Quantum Gravity. Bearing in mind Wigner's famous analysis on measurability in the relativistic case here a genuine uncertainty of the Newton potential is verified, leading to the breakdown of the Schrodinger equation when leaving microscopic regions.
Fur eine Newtonsche qusntisierte GravitationI n h a l t s i i b e r s i c h t . Wir geben eine Reihe von Argumenten fur eine Vereinigung von Pl'ewtonscher Gravitationstheorie und Quantenmechanik. Dieser Schritt im Nichtrelativistischen wurde historisch umgangen. Man wird jedoch anch hier mit konzeptionellen Problemen konfrontiert, dieZuge der relativistischen Quantengravitation tragen. Unter Beachtung von Wigners beriihmter Analyse der Meabarkeit im relativistischen Fall wird hier eine allgemeine Unbestimmtheit des Newtonschen Potentials verifiziert, die ZII einem Zusammenbruch der Schrijdingergleichung fiihrt, wenn mikroskopische Regionen verlassen werden.
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