Dwa lata później: uwagi o reformach w szkolnictwie wyższym i w nauce

The Author discusses dilemmas, difficulties and effects of the higher education and scientific institutions reform, that was launched two years ago. First, he points out the differences of solutions accepted by higher education and scientific institutions in Poland after the Second World War, as compared to the Soviet model. Having outlined the basic assumptions of the reform, the Author discusses the controversial issue of the scope of the state interventionism in both areas. He pays attention to the external obstacles, i.e., obstacles localized outside the system of scientific and higher education institutions, which influence formulation of policy toward such institutions. Also, he examines internal constrains of structural, organizational, societal and financial character. Next, the Author presents the genuine function of various financial mechanisms, their methods of application and coherence ratios. Also, dilemmas concerning applicability of competition rules in case of scientific activities and the question of research evaluation are discussed. He discusses the issue of transformation of scientific and educational institutions, examines factors hampering or keeping back the transformation process. The last paragraph of the paper presents issues concerning research and teaching staff - limits to the personnel management, selection procedures, barriers to young employees flow and aging of academicians.Autor omawia dylematy, trudności i konsekwencje reform zapoczątkowanych przed dwoma laty w Polsce w sferze nauki i szkolnictwa wyższego. Na wstępie pokazuje, w jakim stopniu kształtowane przez 40 lat po wojnie polskie rozwiązania w dziedzinie szkolnictwa i nauki różniły się od radzieckiego pierwowzoru. Po zarysowaniu podstawowych założeń reform autor przechodzi do omówienia kontrowersyjnego problemu - zakresu interwencji państwa w obu sferach. Zwraca uwagę na trudności zewnętrzne - tkwiące poza samą nauką - tworzenia polityki naukowej, a także na ograniczenia strukturalno-organizacyjne, społeczne i finansowe zawarte w systemie nauki. W dalszej części artykułu autor ukazuje rzeczywistą rolę mechanizmów finansowania nauki i szkolnictwa wyższego, sposób ich stosowania, stopień spójności, a także kłopoty związane z realizacją zasad konkurencji i oceny badań naukowych. Omawia problemy przebudowy instytucji badawczych i edukacyjnych oraz czynniki utrudniające lub opóźniające proces restrukturyzacji. W końcowej części artykułu przedstawia zagadnienia dotyczące personelu badawczego i nauczającego - ograniczenia polityki kadrowej, mechanizmów selekcji, bariery dopływu młodej kadry i starzenie się personelu

Singularities of Green functions of the products of the Laplace type operators

The structure of diagonal singularities of Green functions of partial differential operators of even order acting on smooth sections of a vector bundle over a Riemannian man ifold is studied. A special class of operators formed by the products of second-order operators of Laplace type defined with the help of a unique Riemannian metric and a unique bundle connection but with different potential terms is investigated. Explicit simple formulas for singularities of Green functions of such operators in terms of the usual heat kernel coefficients are obtained.Comment: 12 Pages, LaTeX, 30 KB, No Figures, submitted to Physics Letters B, Discussion of the Huygence principle is remove

Brownian motion meets Riemann curvature

The general covariance of the diffusion equation is exploited in order to explore the curvature effects appearing on brownian motion over a d-dimensional curved manifold. We use the local frame defined by the so called Riemann normal coordinates to derive a general formula for the mean-square geodesic distance (MSD) at the short-time regime. This formula is written in terms of $O(d)$ invariants that depend on the Riemann curvature tensor. We study the n-dimensional sphere case to validate these results. We also show that the diffusion for positive constant curvature is slower than the diffusion in a plane space, while the diffusion for negative constant curvature turns out to be faster. Finally the two-dimensional case is emphasized, as it is relevant for the single particle diffusion on biomembranes.Comment: 16 pages and 3 figure

Epicyclic frequencies derived from the effective potential: simple and practical formulae

We present and discuss a short and simple derivation of orbital epicyclic frequencies for circular geodesic orbits in stationary and axially symmetric spacetimes. Such spacetimes include as special cases analytically known black hole Kerr and Schwarzschild spacetimes, as well as the analytic Hartle-Thorne spacetime and all numerically constructed spacetimes relevant for rotating neutron stars. Our derivation follows directly from energy and angular momentum conservation and it uses the concept of the effective potential. It has never been published, except for a few special cases, but it has already become a part of the common knowledge in the field.Comment: Invited lecture at the conference "From X-ray Binaries to Quasars: Black Hole Accretion on All Mass Scales", 13-15 July, 2004, Amsterda

The heat kernel for deformed spheres

We derive the asymptotic expansion of the heat kernel for a Laplace operator acting on deformed spheres. We calculate the coefficients of the heat kernel expansion on two- and three-dimensional deformed spheres as functions of deformation parameters. We find that under some deformation the conformal anomaly for free scalar fields on $R^4\times \tilde S^2$ and $R^6\times \tilde S^2$ is canceled.Comment: 10 pages, latex, no figure

Generalized Sums over Histories for Quantum Gravity I. Smooth Conifolds

This paper proposes to generalize the histories included in Euclidean functional integrals from manifolds to a more general set of compact topological spaces. This new set of spaces, called conifolds, includes nonmanifold stationary points that arise naturally in a semiclasssical evaluation of such integrals; additionally, it can be proven that sequences of approximately Einstein manifolds and sequences of approximately Einstein conifolds both converge to Einstein conifolds. Consequently, generalized Euclidean functional integrals based on these conifold histories yield semiclassical amplitudes for sequences of both manifold and conifold histories that approach a stationary point of the Einstein action. Therefore sums over conifold histories provide a useful and self-consistent starting point for further study of topological effects in quantum gravity. Postscript figures available via anonymous ftp at black-hole.physics.ubc.ca (137.82.43.40) in file gen1.ps.Comment: 81pp., plain TeX, To appear in Nucl. Phys.

Exotic spacetimes, superconducting strings with linear momentum, and (not quite) all that

We derive the general exact vacuum metrics associated with a stationary (non static), non rotating, cylindrically symmetric source. An analysis of the geometry described by these vacuum metrics shows that they contain a subfamily of metrics that, although admitting a consistent time orientation, display "exotic" properties, such as "trapping" of geodesics and closed causal curves through every point. The possibility that such spacetimes could be generated by a superconducting string, endowed with a neutral current and momentum, has recently been considered by Thatcher and Morgan. Our results, however, differ from those found by Thatcher and Morgan, and the discrepancy is explained. We also analyze the general possibility of constructing physical sources for the exotic metrics, and find that, under certain restrictions, they must always violate the dominant energy condition (DEC). We illustrate our results by explicitly analyzing the case of concentric shells, where we find that in all cases the external vacuum metric is non exotic if the matter in the shells satisfies the DEC.Comment: 13 pages with no figures. Accepted in PR

Twisted Superconducting Semilocal Strings

A new class of twisted, current carrying, stationary, straight string solutions having finite energy per unit length is constructed numerically in an extended Abelian Higgs model with global SU(2) symmetry. The new solutions correspond to deformations of the embedded Abrikosov-Nielsen-Olesen (ANO) vortices by a twist -- a relative coordinate dependent phase between the two Higgs fields. The twist induces a global current flowing through the string, and the deformed solutions bifurcate with the ANO vortices in the limit of vanishing current. For each value of the winding number $n=1,2...$ (determining the magnetic flux through the plane orthogonal to the string) there are $n$ distinct, two-parametric families of solutions. One of the continuously varying parameters is the twist, or the corresponding current, the other one can be chosen to be the momentum of the string. For fixed values of the momentum and twist, the $n$ distinct solutions have different energies and can be viewed as a lowest energy ``fundamental'' string and its $n-1$ ``excitations'' characterized by different values of their ``polarization''. The latter is defined as the ratio of the angular momentum of the vortex and its momentum. In their rest frame the twisted vortices have lower energy than the embedded ANO vortices and could be of considerable importance in various physical systems (from condensed matter to cosmic strings).Comment: 39 pages, 20 figure

Spectral Action for Robertson-Walker metrics

We use the Euler-Maclaurin formula and the Feynman-Kac formula to extend our previous method of computation of the spectral action based on the Poisson summation formula. We show how to compute directly the spectral action for the general case of Robertson-Walker metrics. We check the terms of the expansion up to a_6 against the known universal formulas of Gilkey and compute the expansion up to a_{10} using our direct method

Heat-kernel coefficients of the Laplace operator on the D-dimensional ball

We present a very quick and powerful method for the calculation of heat-kernel coefficients. It makes use of rather common ideas, as integral representations of the spectral sum, Mellin transforms, non-trivial commutation of series and integrals and skilful analytic continuation of zeta functions on the complex plane. We apply our method to the case of the heat-kernel expansion of the Laplace operator on a $D$-dimensional ball with either Dirichlet, Neumann or, in general, Robin boundary conditions. The final formulas are quite simple. Using this case as an example, we illustrate in detail our scheme ---which serves for the calculation of an (in principle) arbitrary number of heat-kernel coefficients in any situation when the basis functions are known. We provide a complete list of new results for the coefficients $B_3,...,B_{10}$, corresponding to the $D$-dimensional ball with all the mentioned boundary conditions and $D=3,4,5$.Comment: 29 pages, LaTex, lines had been cut in the previous version by transmission, no further change