FROM FERMI-PASTA-ULAM PROBLEM TO GALAXIES: THE
QUEST FOR RELAXATION

A.E.ALLAHVERDYAN^1;2 AND V.G.GURZADYAN^2;3

1. SPhT, CEA Saclay, 91191 Gif-sur-Yvette cedex, France;
2.Yerevan PhysicsInstitute and Garni Space Asronomy Institute, Armenia;
3.ICRA, Department ofPhysics, University of Rome La Sapienza, Rome, Italy

The major problem posed by the Fermi-Pasta-Ulam work was the relaxation (ther-
malization) of a many-body system. We review two approaches to this problem, the
ergodic theory and Langevin (stochastic) equation ones, which have been applied
for the description of statistical mechanics of stellar systems. Among the particular
problems that we consider, are 1-dimensional long-range interacting systems and
iterated maps and 3-dimensional N-body gravitating systems.

COMMENTS ON FERMI'S ORIGINAL PAPERS ON COSMIC RAY
ACCELERATION

SUSAN AMES

Radioastronomy Institute, Auf dem Hugel 71, D-53121 Bonn, Germany
Email: sames@astro.uni-bonn.de

In his two 1949 papers on cosmic rays, Fermi introduced the concepts which formthe basis of most theories of cosmic ray acceleration today: magnetic trapping;
repeated, small stochastic gains; energy derived fron the large scale bulk kinetic
energy of interstellar plasmas. I consider the historical context in which these
concepts were proposed, and compare the questions which Fermi regarded as un-
resolved with those which we now regard as unresolved.

CIRCULAR HOLONOMY, CLOCK EFFECTS AND
GRAVITOELECTROMAGNETISM: STILL GOING AROUND IN
CIRCLES AFTER ALL THESE YEARS . . .

DONATO BINI
Istituto per le Applicazioni del Calcolo, ”M. Picone”, C.N.R., I– 00161 Rome, Italy
and I.C.R.A., Universit`a di Roma, I–00185 Roma, Italy.
e-mail: binid@icra.it

ROBERT T. JANTZEN
Dept.of Math. Sciences, Villanova University, Villanova, PA 19085, USA
and I.C.R.A., Universit`a di Roma, I–00185 Roma, Italy.
e-mail: robert.jantzen@villanova.edu

The historical origins of Fermi-Walker transport and Fermi coordinates and theconstruction of Fermi-Walker transported frames in black hole spacetimes are reviewed.

For geodesics this transport reduces to parallel transport and these framescan be explicitly constructed using Killing-Yano tensors as shown by Marck. For
accelerated or geodesic circular orbits in such spacetimes, both parallel and Fermi-
Walker transported frames can be given, and allow one to study circular holonomy
and related clock and spin transport effects. In particular the total angle of rotation
that a spin vector undergoes around a closed loop can be expressed in a
factored form, where each factor is due to a different relativistic effect, in contrast
with the usual sum of terms decomposition. Finally the Thomas precession frequency
is shown to be a special case of the simple relationship between the parallel
transport and Fermi-Walker transport frequencies for stationary circular orbits.

FROM MAGNETOHYDRODYNAMICS TO MAGNETARSCOMMENTS ON PAPERS:S. CHANDRASEKHAR AND E. FERMI ”MAGNETIC FIELDS IN
SPIRAL ARMS” (Ap. J. 118, 113-115 (1953)); AND ”PROBLEMS
OF GRAVITATIONAL STABILITY IN THE PRESENCE OF A
MAGNETIC FIELD” (Ap. J. 118, 116-141 (1953))

DINO BOCCALETTI
Department of Mathematics, University of Rome ”La Sapienza”, Italy
E-mail: boccaletti@uniroma1.it

As it is known, Fermi was one of the first scientists to draw the attention of the astrophysicists to the possible existence of a galactic magnetic field. The first
occasion (1949) was that of the famous theory on the origins of cosmic rays. In the
succeeding years (’52-’53) Fermi had regular discussions with Chandrasekhar on a
variety of astrophysical problems bearing on hydromagnetics. The two papers here
commented were the outcome of those discussions. The element of novelty in these
papers lies in the introduction of a magnetic field as a fundamental ingredient
in the study of of the behaviour of cosmic masses. In the first paper, from the
study of the plane of polarization of light one arrives at estimating the magnitude
of the ordered component of the galactic magnetic field in the spiral arms. In
the second paper the gravitational stability is studied in presence of a magnetic
field, by extending the virial theorem in order to take the forces due to a magnetic
field into consideration. The prediction that a gravitating fluid sphere under the
influence of a strong magnetic field tends to become unstable and highly oblate
by contracting along the axis of symmetry of the field assumes great interest with
relation to present problems inherent to neutron stars with strong magnetic fields
and emission of gravitational waves. Today it may be also interesting to extend
the scheme of Fermi and Chandrasekhar to consider an electric field instead of a
magnetic field and then to state for this case the necessary condition for stability.
Possible connections with a Reissner-Nordstrom black hole are suggested.

THE FERMI-PASTA-ULAM PROBLEM

A. CARATI, L. GALGANI, A. PONNO
Università di Milano, Dipartimento di Matematica,Via Saldini 50, 20133-Milano, Italy
E-mail: carati@mat.unimi.it, galgani@mat.unimi.it, ponno@mat.unimi.it

A. GIORGILLI
Università di Milano Bicocca, Dipartimento di Matematica e Applicazioni, Via degli Arcimboldi 8, 20126-Milano, Italy
E-mail: antonio@matapp.unimib.it

A review is given of the Fermi{Pasta{Ulam problem. Its foundational relevance in con-
nection with the relations between classical and quantum mechanics is pointed out, and the status of the numerical and analytical results is discussed.

Numerical simulation of large-scale convection in type-II supernovae explosion

V. M. Chechetkin, M. V. Popov and S. D. UstyugovKeldysh
Institute of Applied Mathematics, Russian Academy of Sciences
Miusskaya 4, 125047, Russia

Summary. — In the last decades, scientifics have tried to understand the explosionmechanism of stars that is responsible for the simultaneous formation of neutron star and supernova outburst.The main problem is the determination of a source of energyin the ejection of a supernova envelope. The gravitation energy as a source of energy in supernova is placed first. However, subsequent studies led to certain problemsin using gravitation energy if the assumption of neutrino diffusion was adopted.

Situation is changed if one takes into consideration large-scale convective instabilityowing to the neutronization of matter in a protoneutron star during the collapse ofstar with low initial entropy. The three-dimensional hydrodinamic calculation for 75×75×75 grid with step 0.015R(R = 2×107 cm)sho ws that large-scale bubbleswith 106 cm emerge. When the bubble reaches low density, the neutrinos containedin matter freely escape from it in the regime of volume radiation. The characteristic time of this process is equalled to 0.02 s. The shock from the initial bounce whenthe collapse in the stellar core stops will then be supported by the neutrino emission, resulting in the ejection of an envelope. In rotating protoneutron star the large-scalebubbles come to the surface of the stellar core along the axis of rotation. Neutrinoswith energy 50–100 MeV are contained in the bubbles. Our calculations show that time of neutrino emission from such bubble is equal near 0.01 second with meanenergy of neutrino 60–70 MeV.

PACS 97.60.Bw – Supernovae.
PACS 01.30.Cc – Conference proceedings.

Enrico Fermi’s excursions through the fields of classical physics:
Watching the landscapes of phase space and the nature of
dynamical paths, looking for ergodicity

-
INOA - Largo E. Fermi, 6, 50125 Firenze, Italy
ICRA - P.le Repubblica, 10, 65122 Pescara, Italy

Summary. — The (relatively few) works of Fermi within the fields of classical physics had, and still have, a deep impact on our understanding of the structure of phase space of generic nonlinear systems, along with the relative implicationson the justification of a statistical description of macroscopic systems and the approachtowards equilibrium. One of those milestones along the path to reconcilemicroscopic dynamics with macroscopic description is the first inverse experiment,performed by Fermi, Pasta, Ulam and Tsingou on an one-dimensional anharmonicchain (FPU model). After a brief historical introduction whose aim is mainly to show how that revolutionary experiment frames perfectly into Fermi’s personality, Idiscuss how this model, and particularly the philosophy beyond it, can be considered,still today, a valid conceptual paradigm. I show how to obtain analytical estimates of dynamic and geometric quantities through which it is possible to generalize theexisting definitions of chaoticity indicators and of the threshold marking the onset ofstrong chaos. Nevertheless, as far as some of the most recent successful approaches to FPU problem are concerned, I outline how these cannot be generalized painlessly.Discussing in some details why they work for FPU-like models, we meet with thedifficulties and troubles emerging when trying to applying them to peculiar Hamiltonian systems, for which these methodologies can give, at most, just some hints ontheir macroscopic behaviour. In particular, I review some conceptual and technicalaspects of the combined use of the geometrical transcription of dynamics and the theory of stochastic differential equations, pointing out the issues preventing a directextension to more general systems.

Notwithstanding, this analysis gives noteworthy hints even on the much more controversialissue of a statistical description of gravitationally interacting N-body systems, furthermore allowing to understand some seemingly inconsistent results existing inthe literature.

PACS 01.65.+g – History of science.
PACS 05.20.-y – Classical statistical mechanics.
PACS 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems.
PACS 01.30.Cc – Conference proceedings.

THE LATEST VIEW OF THE EARLY UNIVERSE

PAOLO DE BERNARDIS AND SILVIA MASI
Università di Roma La Sapienza

The Big Bang Nucleosynthesis (so beautifully pioneered by Enrico Fermi) and theCosmic Microwave Background (CMB) are closely linked and other complementary tools to investigate the Early Universe. We shortly review this topic and focuson the latest results on the CMB. Resolved images of the CMB produced by theBOOMERanG, MAXIMA and DASI experiments allow a detailed study of the
physical processes taking place before recombination, depicting a consistent new
cosmology. We present the experimental evidence, the current interpretation of
the data, the problems still open, and the future activity in this field.

NEUTRINOS AND BIG BANG NUCLEOSYNTHESIS

A. D. DOLGOV
INFN, sezione di Ferrara, Via Paradiso, 12 - 44100, Ferrara, Italy
ITEP, Bol. Cheremushkinskaya 25, 117218, Moscow, Russia
E-mail: dolgov@fe.infn.it

The role of neutrinos in big bang nucleosynthesis is discussed. The bounds on the number of neutrino families, neutrino degeneracy, parameters of neutrino oscillations are presented. A model of chemically inhomogeneous, while energetically smooth, universe created by inhomogeneous cosmological neutrino asymmetry is described. Nucleosynthesis limits on production of right-handed neutrinos are considered.

ON THE EVOLUTION OF NONLINEAR N-BODY SYSTEMS:
SUBSTRUCTURE OF A DISTANT GALAXY CLUSTER

V.G.GURZADYAN (1) AND A.MAZURE (2)
(1) ICRA, Department of Physics, University of Rome "La Sapienza", Rome, Italy
and Yerevan Physics Institute, Yerevan, Armenia;
(2) Laboratoire d'Astrophysiquede Marseille, Marseille, France

The graph-theoretical S-tree technique developed for the study of the nonlinear N-
body systems, is used for the study for the first time of the substructure of a highredshift cluster of galaxies, namely of MS 1054-03, z≈0,8. Nearby galaxy clustersstudied via the same S-tree code reveal several clearly distinguished subgroups withsigni cant bulk velocities. Therefore the study of distant clusters can enable totrace the evolution of their dynamics over cosmological time scales. The study ofthe MS 1054-03 showed a di erent structure, i.e. no evidence of merging subgroupsbut only of a core of galaxies with velocity dispersion about 700 km
s��1 while thevelocity dispersion of the main cluster 1870 km
s��1. Further study of samples
of high redshift clusters will enable to conclude whether this discrepancy in the
structure and dynamics between nearby and distant galaxy clusters is a genuine
evolutionary effect.

Kolmogorov Complexity, String Information, Panspermia andthe Fermi Paradox

V.G.Gurzadyan
Dipartimento di Fisica, Università "La Sapienza", Rome
and Yerevan Physics Institute

Abstract - Bit strings rather than byte files can be a mode of transmission both for intelligent signals and for travels of extraterrestrial life. Kolmogorov complexity, i.e. the minimal length of a binary coded string completely defining a system, can then, due to its universality, become akey concept in the strategy of the search of extraterrestrials. Evaluating, forillustration, the Kolmogorov complexity of the human genome, one comes toan unexpected conclusion that a low complexity compressed string - analogof Noah's ark - will enable the recovery of the totality of terrestrial life. The recognition of bit strings of various complexity up to incompressible Martin-Löf random sequences, will require a different strategy for the analysis of the cosmic signals. The Fermi paradox "Where is Everybody?" can be viewed under in the light of such information panspermia, i.e. a Universe full oftraveling life streams.

A GENERAL THEORY OF SELF GRAVITATING SYSTEMS AND THE VIRIAL THEOREM

SIMONETTA FILIPPI
Faculty of Engineering, University Campus Biomed., via Longoni, 83, 00155 Rome, Italy
ICRA (International Center for Relativistic Astrophysics) P.le A. Moro, 2, 00185 Rome,
ITALY
E-mail: s.filippi@unicampus.it

The paper of Fermi and Chandrasekhar "Problems of Gravitational Stability in thePresence of a Magnetic field", among others, considers the scalar virial theorem for a self gravitating magnetized object. The problems which are considered in that paper were largely at Fermi s suggestion. The generalization of the virial theorem, the existence of an upper limit to the magnetic energy of a configuration in equilibrium under its own gravitation, the distortion of the spherical shape of a body in gravitational equilibrium, form the basis on which a wide number of
physical problems on self-gravitating objects are focused by our work group from
several years. We present step by step the progresses on the generalization of the
problem of the equilibrium figures for self gravitating bodies.

Nonthermal radiation of Kerr black holes

I. B. Khriplovich
Budker Institute of Nuclear Physics - 630090 Novosibirsk, Russia
Novosibirsk University - 630090 Novosibirsk, Russia

Summary. — Nonthermal radiation of a Kerr black hole is considered as tunneling of created particles through an effective Dirac gap. In the leading semiclassical approximationthis approach is applicable to bosons as well. Our semiclassical results for photons and gravitons do not contradict those obtained previously. For neutrinos the result of our accurate quantum-mechanical calculation is about two times larger than the previous one.

PACS 97.60.Lf – Black holes.
PACS 01.30.Cc – Conference proceedings.

 PARTICLE ACCELERATION AT ASTROPHYSICAL SHOCK FRONTS: FROM SUPERNOVA REMNANTS TO GAMMA-RAY BURSTS

J.G. KIRK
Max-Planck-Institut fur Kernphysik, Postfach 10 39 80, 69029 Heidelberg, Germany
E-mail: John.Kirk@mpi-hd.mpg.de

In two seminal papers, Fermi outlined the stochastic theory of particle acceleration in astrophysical environments. Fifty years later, a direct descendant of this theory is still the favoured explanation for the problem which motivated Fermi - the acceleration of cosmic rays in our galaxy. More recently, the same basic ideas have been generalised to apply to situations involving relativistic motion, such as active galaxies and gamma-ray bursts. This paper presents Fermi's characteristically simple and powerful ideas, describes their generalisation and assesses their impact on the current status of our ideas concerning the origins of galactic cosmic rays and gamma-ray bursts.

Weak interaction processes and core collapse supernova

K. Langanke⁽¹⁾ and G. Martìnez-Pinedo⁽²⁾
(1) Institute for Physics and Astronomy, University of Aarhus DK-8000 Aarhus C, Denmark
(2) Departement für Physik und Astronomie der Universität Basel- Basel, Schweiz

Summary. — The paper reviews the weak interaction processes which are essential during core collapse supernovae. These include electron capture and β decay of nuclei in the iron mass range. Modern shell model developments are now capable to describe the involved nuclear structure problem adequately. The stellar weak interaction rates based on these shell model calculations are noticeably different than the empirical rates conventionally adopted in presupernova models. In particular, electron capture is significantly slower than believed leading to presupernova models with larger electron-to-baryon ratios, smaller iron core masses and smaller entropy. Current interest on improving the microphysics input in collapse simulations focusses on electron capture on heavier nuclei and on neutrino-nucleus reactions. Modern nuclear structure models promise to reduce uncertainties related to these processes in the near future.

PACS 98.65.Cw – Galaxy clusters.
PACS 01.30.Cc – Conference proceedings.

FROM NEUTRON STARS TO EXTREMAL BLACK HOLES. THE OPTICAL GEOMETRY APPROACH.

KJELL ROSQUIST
Department of Physics, SCFAB, Stockholm University, 106 91 Stockholm, Sweden

The optical geometries of black holes and relativistic stellar objects are discussed and compared. Gravitational trapping of relativistic particles in compact objects is treated in terms of the appearance of necks in the optical geometry. Indications are given for essentially two mechanisms which are responsible for the existence of necks and hence trapping. The two mechanisms correspond to properties of the equation of state of matter at high pressure. Phase transitions in the stellar interior can lead to trapping via one of the mechanisms which is due to a softening of the equation of state in some pressure region. It is also pointed out that there are similarities between the optical geometries of high pressure uniform density stars and extremal Reissner-Nordstrom black holes. 

 ON THE INSTANTANEOUS SPECTRUM OF GAMMA-RAY BURSTS

REMO RUFFINI, CARLO LUCIANO BIANCO and SHE-SHENG XUE
ICRA - International Center for Relativistic Astrophysics and Dipartimento di Fisica, Università di Roma "La Sapienza", Piazzale Aldo Moro 5, I-00185 Roma, Italy

PASCAL CHARDONNET
ICRA - International Center for Relativistic Astrophysics
and Université de Savoie, LAPTH | LAPP, BP 110, F74941 Annecy-le-Vieux Cedex, France

FEDERICO FRASCHETTI
ICRA - International Center for Relativistic Astrophysics
and Università di Trento, Via Sommarive 14, I-38050 Povo (Trento), Italy

VAHE GURZADYAN
ICRA - International Center for Relativistic Astrophysics
and Yerevan Physics Institute, Alikhanian Brothers Street 2, 375036, Yerevan-36, Armenia

A theoretical attempt to identify the physical process responsible for the afterglow emission of Gamma-Ray Bursts (GRBs) is presented, leading to the occurrence of thermal emission in the comoving frame of the shock wave which gives rise to the bursts. The determination of the luminosities and spectra involves integration over an infinite number of Planckian spectra, weighted by appropriate relativistic transformations, each one corresponding to a different viewing angle in the past light cone of the observer. The relativistic transformations have been computed using the equations of motion of GRBs within our theory, giving special attention to the determination of the equitemporal surfaces. The only free parameter of the present theory is the "effective emitting area" in the shock wave front. A self-consistent model for the observed hard-to-soft transition in GRBs is also presented. When applied to GRB 991216 a precise fit (χ ≈ 1.078) of the observed luminosity in the 2-10 keV band is obtained. Similarly, detailed estimates of the observed luminosity in the 50-300 keV and in the 10-50 keV bands are obtained.

Charges in gravitational fields: from Fermi, via Hanni-Ruffini-Wheeler, to the “electric Meissner effect”

R. Ruffini⁽¹⁾⁽²⁾
(1) Dipartimento di Fisica, Universit`a “La Sapienza” di Roma, I–00185, Italy
(2) International Center for Relativistic Astrophysics - I.C.R.A., University of Rome “La Sapienza”, I–00185 Rome, Italy

Summary. — Recent developments in obtaining a detailed model for gamma ray bursts have shown the need for a deeper understanding of phenomena described by solutions of the Einstein-Maxwell equations, reviving interest in the behavior of charges close to a black hole. In particular a drastic difference has been found between the lines of force of a charged test particle in the fields of Schwarzschild and Reissner-Nordström black holes. This difference characterizes a general relativistic effect for the electric field of a charged test particle around a (charged) Reissner- Nordstr¨om black hole similar to the “Meissner effect” for a magnetic field around a superconductor. These new results are related to earlier work by Fermi and Hanni-Ruffini-Wheeler.

PACS 04.20 – .
PACS 04.20 – .

 THE FERMI-PASTA-ULAM-TSINGOU NUMERICAL EXPERIMENT: TIME-SCALES FOR THE RELAXATION TO THERMODYNAMICAL EQUILIBRIUM

STEFANO RUFFO
Dipartimento di Energetica "S. Stecco", Università di Firenze, via S. Marta 3, INFN
and INFN I-50139 Firenze Italy
and ENS-Lyon, Laboratoire de Physique, 46 Allee d'Italie 69364 Lyon Cedex 07 France E-mail: ruffo@avanzi.de.unifi.it

The approach to equilibrium of an isolated system is the basic principle of thermo- dynamics: the so-called zero-principle. Fermi, Pasta and Ulam (FPU) performed the first numerical study of this process for a chain of anharmonically coupled oscillators. The FPU "experiment" has been an amazingly rich source of problems in modern dynamical system theory. Recent results have shown the presence of increasingly long time-scales of the relaxation process as the energy is decreased. States previously classified as "frozen" have been instead discovered to approach very slowly the equipartition state. The dependence of the diffusive time-scale D on energy E and number of degrees of freedom N has been found both analytically and numerically for some classes of initial conditions. An interesting extension of the FPU experiment concerns systems with long-range interactions that simulate gravity. Here unconventional thermal behaviors have been found to persist for times which increase with system size.

Nodal and periastron precession of inclined orbits in the field of a rotating black hole and a rapidly rotating neutron star

N. Sibgatullin
Moscow State University - Vorob’evy gory, Moscow, 119899 Russia

Summary. — The inclination of low-eccentricity orbits is shown to significantly affect the orbital parameters, in particular, the Keplerian, nodal precession, and periastron rotation frequencies, which are interpreted in terms of observable quantities. For the nodal precession and periastron rotation frequencies of low-eccentricity orbits in a Kerr field, we derive a Taylor expansion in terms of the Kerr parameter at arbitrary orbital inclinations to the black-hole spin axis and at arbitrary radial coordinates. The particle radius, energy, and angular momentum in the marginally stable circular orbits are calculated as functions of the Kerr parameter j and parameter s (a minimum latitudinal angle reached at the orbit)in the form of Taylor expansions in terms of j to within O[j6]. By analyzing our numerical results, we give compact approximation formulas for the nodal precession frequency of the marginally stable circular orbits at various s in the entire range of variation of Kerr parameter. We derive a formula for the nodal precession frequency and the Keplerian period of a particle at an arbitrarily inclined orbit in the post-Newtonian approximation in the external field of an oblate rotating neutron star (NS). We also derive formulas for the nodal precession and periastron rotation frequencies of slightly inclined low-eccentricity orbits in the field of a rapidly rotating NS in the form of asymptotic expansions whose first terms are given by the Okazaki-Kato formulas. The NS gravitational field is described by the exact solution of the Einstein equation that includes the NS quadrupole moment induced by rapid rotation. Convenient asymptotic formulas are given for the metric coefficients of the corresponding space-time in the form of Kerr metric perturbations in Boyer-Lindquist coordinates.

PACS 95.30.Cq – Elementary particle processes (astrophysics).
PACS 01.30.Cc – Conference proceedings. 

ENRICO FERMI AND THE STATISTICS OF COMETS

COSTANTINO SIGISMONDI
Department of Physics, University of Rome "La Sapienza"
and ICRA, International Center for Relativistic Astrophysics,
Piazzale Aldo Moro, 5, 00185 Rome
and Piazza della Repubblica 10, 65122 Pescara, Italy
sigismondi@icra.it

FRANCESCA MAIOLINO
Biology Department, University of Rome "La Sapienza",
Piazzale Aldo Moro, 5, 00185 Rome, Italy
francesca@videor.it

For his abilitation thesis at the "Scuola Normale Superiore" of Pisa, Enrico Fermi presented in 1922 a theorem of statistics with an application to the case of comets. He studied comets with coplanar orbit to that one of Jupiter, and neglected the influence of other planets. The probability of ejection of the comets from the solar system after interacting with Jupiter is calculated, as well as the probability of impact on Jupiter. We discuss those results comparing them with modern issues in solar system comogony (Oort cloud, Kuiper belt). We apply the calculation of Fermi to the case of the Earth, in order to recover the time rate of comets collision with our planet, which reliably produced the extinction of the dinosaurs.

Enrico Fermi and X-ray imaging: An overview from his thesis work (1922) to astronomical applications

C. Sigismondi⁽¹⁾⁽²⁾ and A. Mastroianni⁽¹⁾
(1) Dipartimento di Fisica, Università di Roma “La Sapienza” - P.le A. Moro 5, 00185 Rome
(2) ICRA, International Center for Relativistic Astrophysics P.zza della Repubblica 10, 65100 Pescara, Italy

Summary. — Enrico Fermi studied the formation of images with X-rays and presented his first experimental work as dissertation at University of Pisa in the spring of 1922 (Nuovo Cimento, 24 (1922) 133 and 25 (1923) 63). Although those seminal ideas are not present in the sources investigated by Riccardo Giacconi and Bruno Rossi (J. Geophys. Res., 65 (1960) 773) when they firstly proposed a telescope for imaging with X-rays, the thesis of Fermi was the most complete on X-rays physics at his time. Fermi used the technique of “mandrels” to form optical surfaces. He was a forerunner to the technique used for the mirrors of Exosat, Beppo-SAX, Jet-X and XMM-Newton telescopes, and this technique is now a mainstay of many optical manufacturing techniques.

PACS 95.55.-n – Astronomical and space-research instrumentation.
PACS 01.30.Cc – Conference proceedings.

First results from SNO

J. J. Simpson
for the SNO Collaboration
Department of Physics, University of Guelph - Guelph, ON N1G 2W1, Canada

Summary. — The Sudbury Neutrino Observatory (SNO) is a water imaging Cherenkov detector which contains 1000 tonnes of D₂O as the principal target for solar neutrinos. The use of deuterium permits the simultaneous measurement of both the ν_e flux and the total flux of all active neutrino types from the decay of ⁸B in the sun. In this paper recent results from SNO are presented. It is found that the ν_e flux as measured by the charged-current reaction on deuterium is significantly smaller than the total ν-flux as determined by elastic scattering from electrons in the D₂O. The results imply that the active ν-flux from the sun is consistent with present solar models of the ⁸B ν-flux, and that only about one-third of this flux consists of ν_e.

PACS 98.65.Cw – Galaxy clusters.
PACS 01.30.Cc – Conference proceedings.

NEUTRINO MASS SPECTRUM AND NEUTRINO ASTROPHYSICS

A. YU. SMIRNOV
The Abdus Salam ICTP, Strada Costiera 11, 34100 Trieste, Italy,
Institute for Nuclear Research, RAS, Moscow, Russia
E-mail: smirnov@ictp.trieste.it

Neutrino astrophysics, and in particular study of solar and supernova neutrinos, plays important role in reconstruction of the neutrino mass and mixing spectrum. Observable effects of neutrino mass and mixing are based on neutrino transformations in matter. The Fermi coupling constant determines immediately the scale of phenomena and applications of the effects. We consider the status the solar neutrino problem. The MSW LMA solution with Δm² = (6 − 7) · 10⁻⁵ eV² and tan²θ = 0.35 − 0.4 gives the best fit of the data. In the case of LMA solution the Earth matter effects allow to explain some features of signals from SN1987A. Future studies of neutrino signals from supernova, and in particular the Earth matter effects on these neutrinos will allow to select or confirm the solution of the solar neutrino problem, identify the type of mass hierarchy (ordering) of the neutrino spectrum and measure or restrict the mixing parameter U_e3.

 CLOSE NEUTRON STARS BINARIES

J. R. WILSON
Lawrence Livermore National Laboratory, Livermore, CA 94550
E-mail: jimwilson@llnl.gov

G. J. MATHEWS
University of Notre Dame, Notre Dame, IN 46556

J. D. SALMONSON
Lawrence Livermore national Laboratory, Livermore, CA 94550

We present numerical hydrodynamic calculations of neutron star binaries. First we give results for binary stars in circular orbits and second we give results for stars in head-on collision. In both cases the stars undergo compression as they become closer together. In the first case of circular motion, the compression leads to a possible mechanism for gamma-ray bursts.

THE DYADOSPHERE OF ELECTROMAGNETIC BLACK HOLE AND ITS HYDRODYNAMIC EXPANSION

REMO RUFFINI and SHE-SHENG XUE
ICRANet and Physics Department, University of Rome “La Sapienza”, I-00185 Rome, Italy
E-mail: ruffini@icra.it and xue@icra.it

The dyadosphere of electromagnetic black hole and its hydrodynamic expansion are briefly reviewed.

FROM THE FPU-PROBLEM (LA-1940 REPORT) TO CHAOS

G.M. ZASLAVSKY
Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012,
Department of Physics, New York University, 2-4 Washington Place, New York, NY 10003, USA

We discuss the FPU problem in the context of an attempt to find a transition from regular dynamics to the chaotic one. The Fermi mechanism of acceleration was a precursor of the FPU problem. The FPU problem has inspired scienti c activities in Hamiltonian integrability, chaos, and the validity of discretization of differential equations. We discuss brie y the latter two issues as well as some new achievements in the theory of chaos.