Further tests of universality assumption for liquid-gas critical points

New evaluations of data taken from ³He, ⁴He, CO₂, SF₆, and CCIF₃ seem to corroborate the universality assumption for critical amplitudes.     

Spherically symmetric free fall collapse

The general dynamical equations for spherical gravitational collapse are derived by introducing the eigenvalue of the conformal Weyl tensor in the 2-2 component of the Einstein tensor and assuming the material content of the models to be a perfect fluid. Since this eigenvalue is coupled always with the material energy density, it has been interpreted as theenergy density of the free gravitational field whose presence is related with anisotropy and inhomogeneity. As a particular case, the collapse of a spherically symmetric dust (zero pressure) with vanishing radial acceleration (free fall collapse) is discussed. It is shown that the model is inhomogeneous with non-vanishing shear of the congruence of world lines of the dust particles. The model contains gravitational radiation by Szekere’s criterion since both shear invariant and the spatial gradient of density are non-vanishing. This is in contrast to the Oppenheimer-Synder model for which both the above mentioned characteristics are absent. A particular solution which is anisotropic and inhomogeneous has been given to prove the emission of gravitational radiation by the freely falling dust and in this case the energy density of the free gravitational field contains a typeN term superposed on the coulombian field.     

New critical matrix models and generalized universality

We study a class of one-matrix models with an action containing nonpolynomial terms. By tuning the coupling constants in the action to criticality we obtain that the eigenvalue density vanishes as an arbitrary real power at the origin, thus defining a new class of multicritical matrix models. The corresponding microscopic scaling law is given and possible applications to the chiral phase transition in QCD are discussed. For generic coupling constants off-criticality we prove that all microscopic correlation functions at the origin of the spectrum remain in the known Bessel universality class. An arbitrary number of Dirac mass terms can be included and the corresponding massive universality is maintained as well. We also investigate the critical behavior at the edge of the spectrum: there, in contrast to the behavior at the origin, we find the same critical exponents as derived from matrix models with a polynomial action.     

New spin-orbit-induced universality class in the integer quantum Hall regime

Using heuristic arguments and numerical simulations it is argued that the critical exponent nu describing the localization length divergence at the integer quantum-Hall transition is modified in the presence of spin-orbit scattering with short-range correlations. The exponent is very close to nu=4/3, the percolation correlation length exponent, consistent with the prediction of a semiclassical argument. In addition, a band of weakly localized states is conjectured.     

Remarks concerning the notion of free fall in axiomatic space-time theory

The notion of free fall plays a central role in EPS axiomatics. A constructive procedure for the detection of freely falling gravitational monopoles has been elaborated by Coleman and Korté. This was done in order to eliminate the vagueness of the primitive notion of free fall from spacetime theory. In this paper it is shown that neither the gravitational monopoles nor their free fall can be detected by the proposed procedure alone, without using physical laws beyond the mentioned spacetime theories. For this purpose, two examples of geodesic directing fields in a Schwarzschild space time are presented, one for particles obeying a special Lorentz-force equation and one for objects obeying Papapetrou's spinning particle equation. Two possibilities are discussed to overcome the difficulties of the constructive procedure.     

Rapid solidification of Al-Cu-Ag ternary alloy under the free fall condition

The rapid solidification of Al-30%Cu-18%Ag ternary alloy is investigated by using the free fall method. Its solidified microstructure is composed of θ(Al₂Cu), α(Al) and ξ(Ag₂Al) phases. The liquidus temperature and solidus temperature are determined as 778 and 827 K, respectively. The alloy melt undercooled amounts up to ΔT _Max=171 K (0.20T _L). Its microstructural evolution is investigated based on the theoretical analysis of undercooling behavior and nucleation mechanics. It is found that the undercooling increases with the decrease of the diameter of the alloy droplet. When ΔT<78 K, the primary θ(Al₂Cu) phase of the alloy grows into coarse dendrite. When 78 K⩽ΔT⩽171 K, its refined θ(Al₂Cu) phase grows alternatively with α(Al) phase. Once ΔT⩾171 K, its microstructure is characterized by the anomalous (θ+α+ξ) ternary eutectic. Supported by the National Natural Science Foundation of China (Grant Nos. 50121101 and 50395105)     

New universality classes in “Percolative” dynamics

We study a site analogue of directed percolation. Random trajectories are generated and their critical behavior is studied. The critical behavior corresponds to that of simple percolation in some of the parameter space, but elsewhere the exponents reveal new universality classes. As a byproduct, we use the model to make an improved estimate of the percolation hull exponents and to calculate the site percolation probability for the square lattice.     

New universality class in spin-one-half Fibonacci Heisenberg chains

Low energy properties of the S=1/2 antiferromagnetic Heisenberg chains with Fibonacci exchange modulation are studied using the real space renormalization group method for strong exchange modulation. Using the analytical solution of the recursion equation, the true asymptotic behavoir is revealed, which was veiled by the finite size effect in the previous numerical works. It is found that the ground state of this model belongs to a new universality class with a logarithmically divergent dynamical exponent which is neither like Fibonacci XY chains nor like XY chains with relevant aperiodicity.     

New universality type in chaotic synchronization of dynamic systems

A quite universal mechanism of establishing chaotic synchronization regime in coupled dynamic systems is found. It is shown that the synchronous regime arises due to the phase coupling between the Fourier-spectrum components of the interacting chaotic oscillators.     

Gravitational collapse in free fall of a slowly rotating star

The Oppenheimer-Snyder model of a spherically symmetric collapse in free fall is generalized to the case in which the star possesses a small rotation. The exterior geometry is chosen to be the Kerr metric in synchronous coordinates, discarding terms of the order (a/r)². The interior geometry is constructed by adding to the exact metric of the nonrotating case an off-diagonal first-order term in the parametera. This term is determined in part by requiring the validity of the junction conditions at the star's surface and, also, by demanding the conserved angular momentum of the source be equal toMa, in agreement with the value measured by a distant observer. The resulting stress-energy tensor describes a homogeneous, pressureless, ideal fluid (dust) nonuniformly rotating relative to the synchronous frame, which is no longer comoving with the stellar matter. The dynamics of collapse is qualitatively the same as in the spherically symmetric case. Again the star's surface crosses the event horizon when the mass density is finite everywhere, and space-time has not developed any singularity as viewed by freely falling observers at rest in the synchronous frame.Based on a dissertation submitted (by J. C. F.) to the Facultad de Ciencias Fisicas y Matemáticas, Universidad de Chile. in partial fulfilment of the requirements of the Magister degree.     

Deformation of a water shell during free fall in air

The basic regularities of the change in the shape and sizes (the initial volume is 0.05–0.5 L) of a water shell are singled out in its deformation during free fall in air from a height of 3 m. The 3D recording of the basic stages of deformation (flattening of the shell, nucleation, growth, and destruction of bubbles, formation of the droplet cloud) is carried out using high-speed (up to 10⁵ frames per second) Phantom V411 and Phantom Miro M310 video cameras and the program complex Tema Automotive (with the function of continuous tracking). The physical model of destruction of large water bodies is formulated at free fall with the formation of the droplet cloud.     

Republication of: The geometry of free fall and light propagation

This is a reprinting of the paper by Jürgen Ehlers, Felix Pirani and Alfred Schild, first published in 1972 in a separate volume containing articles written in hounour of J. L. Synge. The original book is long out of print and almost forgotten by today. The authors present a method of deriving the Lorentzian geometry from compatible conformal and projective structures on a four dimensional manifold. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Andrzej Trautman.     

Density functional theory for nonuniform polymer melts: Based on the universality of the free energy density functional

A density functional theory is proposed for nonuniform freely jointed tangential hard sphere polymer melts in which the bonding interaction is treated on the basis of the properties of the Dirac δ-function, thus avoiding the use of the single chain simulation in the theory. The excess free energy is treated by making use of the universality of the free energy density functional and the Verlet-modified (VM) bridge function. To proceed numerically, one of the input parameters, the second-order direct correlation function of a uniform polymer melt is obtained by solving numerically the Polymer-RISM integral equation with the Percus-Yevick (PY) closure. The predictions of the present theory for the site density distribution, the partition coefficient and the adsorption isotherm, near a hard wall or between two hard walls are compared with computer simulation results and with those of previous theories. Comparison indicates that the present approach is more accurate than the previous integral equation theory and the most accurate Monte Carlo density functional theories. The predicted oscillations of the medium-induced force between two hard walls immersed in polymer melts are consistent with the experimental results available in the literature. Received 18 April 2000