Cosmic rays are an ever present aspect of nature. The birth of the field of elementary-particle physics can be traced to studies of cosmic rays. Now advances in technology and new instrumentation are changing the nature of cosmic-ray research. New forms of astronomy are being created. Ground-based instruments, spawned by cosmic-ray techniques, permit the observation of astrophysical objects emitting radiation in very-high-energy gamma rays, $(>~100\mathrm{GeV}),$ high-energy neutrinos (⩾1 TeV), and the most energetic particles found in the cosmic radiation $(>~5\times {10}^{19}\mathrm{eV}).\mathrm{}$ At these energies the galactic and intergalactic magnetic fields deflect the cosmic-ray protons by only a few degrees. The interaction of these cosmic rays with the cosmic background radiation limits the possible sources to redshifts far less than unity. The origin of these highest-energy cosmic rays is not understood. The present status of knowledge of these cosmic rays and the prospects for solving the mystery concerning their origin are the subjects of this brief article.

One hundred years ago we did not know how stars generate energy, the age of the Universe was thought to be only millions of years, and our Milky Way galaxy was the only galaxy known. Today, we know that we live in an evolving and expanding universe comprising billions of galaxies, all held together by dark matter. With the hot big-bang model we can trace the evolution of the Universe from the hot soup of quarks and leptons that existed a fraction of a second after the beginning, to the formation of galaxies a few billion years later, and finally to the Universe we see today 13 billion years after the big bang, with its clusters of galaxies, superclusters, voids, and great walls. The attractive force of gravity acting on tiny primeval inhomogeneities in the distribution of matter gave rise to all the structure seen today. A paradigm based upon deep connections between cosmology and elementary particle physics—inflation+cold dark matter—holds the promise of extending our understanding to an even more fundamental level and much earlier times, as well as shedding light on the unification of the forces and particles of Nature. As we enter the 21st century, a flood of observations is testing this paradigm.

The neutrino was the first elementary particle proposed that was not a constituent of ordinary matter. Because neutrinos interact only weakly, they play a unique role in particle physics, astrophysics, and cosmology. The possibility that neutrinos have a mass and oscillate from one form to another has led to a great variety of ongoing experiments.

Recent advances in theory and experiment for the anomalous magnetic moments of the electron and muon are reviewed. Implications of these developments for fundamental physics are discussed.

String theory and supersymmetry are theoretical ideas that go beyond the standard model of particle physics and show promise for unifying all forces. After a brief introduction to supersymmetry, the authors discuss the prospects for its experimental discovery in the near future. They then show how the magic of supersymmetry allows us to solve certain quantum field theories exactly, thus leading to new insights about field theory dynamics related to electric-magnetic duality. The discussion of superstring theory starts with its perturbation expansion, which exhibits new features including “stringy geometry.” The authors then turn to more recent nonperturbative developments. Using new dualities, all known superstring theories are unified, and their strong-coupling behavior is clarified. A central ingredient is the existence of extended objects called branes.

Plasmas consisting exclusively of particles with a single sign of charge (e.g., pure electron plasmas and pure ion plasmas) can be confined by static electric and magnetic fields (in a Penning trap) and also be in a state of global thermal equilibrium. This important property distinguishes these totally unneutralized plasmas from neutral and quasineutral plasmas. This paper reviews the conditions for, and the structure of, the thermal equilibrium states. Both theory and experiment are discussed, but the emphasis is decidedly on theory. It is a huge advantage to be able to use thermal equilibrium statistical mechanics to describe the plasma state. Such a description is easily obtained and complete, including for example the details of the plasma shape and microscopic order. Pure electron and pure ion plasmas are routinely confined for hours and even days, and thermal equilibrium states are observed. These plasmas can be cooled to the cryogenic temperature range, where liquid and crystal-like states are realized. The authors discuss the structure of the correlated states separately for three plasma sizes: large plasmas, in which the free energy is dominated by the bulk plasma; mesoscale plasmas, in which the free energy is strongly influenced by the surface; and Coulomb clusters, in which the number of particles is so small that the canonical ensemble is not a good approximation for the microcanonical ensemble. All three cases have been studied through numerical simulations, analytic theory, and experiment. In addition to describing the structure of the thermal equilibrium states, the authors develop a thermodynamic theory of the trapped plasma system. Thermodynamic inequalities and Maxwell relations provide useful bounds on and general relationships between partial derivatives of the various thermodynamic variables.

Parity violation in the compound nucleus is reviewed as an example of a wider class of phenomena: The breaking of a discrete symmetry by a weak interaction in a stochastic or chaotic quantum system. Generically, enhancement factors amplify the signal for symmetry breaking, and the stochastic properties allow the strength of the symmetry-breaking interaction to be inferred from that signal without the need to know the wave functions of individual states. We describe recent experiments on parity violation that have been undertaken in this spirit. The scattering of spin-polarized neutrons by medium-weight and heavy nuclei provides signals for parity violation at the percent level. The statistical analysis of the data yields values for the spreading width around ${10}^{-6}\mathrm{eV},$ in keeping with theoretical expectations. We discuss open problems and possible future directions.

Granulated materials, like sand and sugar and salt, are composed of many pieces that can move independently. The study of collisions and flow in these materials requires new theoretical ideas beyond those in the standard statistical mechanics or hydrodynamics or traditional solid mechanics. Granular materials differ from standard molecular materials in that frictional forces among grains can dissipate energy and drive the system toward frozen or glassy configurations. In experimental studies of these materials, one sees complex flow patterns similar to those of ordinary liquids, but also freezing, plasticity, and hysteresis. To explain these results, theorists have looked at models based upon inelastic collisions among particles. With the aid of computer simulations of these models they have tried to build a “statistical dynamics” of inelastic collisions. One effect seen, called inelastic collapse, is a freezing of some of the degrees of freedom induced by an infinity of inelastic collisions. More often some degrees of freedom are partially frozen, so that there can be a rather cold clump of material in correlated motion. Conversely, thin layers of material may be mobile, while all the material around them is frozen. In these and other ways, granular motion looks different from movement in other kinds of materials. Simulations in simple geometries may also be used to ask questions like When does the usual Boltzmann-Gibbs-Maxwell statistical mechanics arise?, What are the nature of the probability distributions for forces between the grains?, and Might the system possibly be described by uniform partial differential equations? One might even say that the study of granular materials gives one a chance to reinvent statistical mechanics in a new context.

There is abundant evidence that the mass of the Universe is dominated by dark matter of unknown form. The MACHO project is one of several teams searching for the dark matter around our Galaxy in the form of massive compact halo objects (MACHOs). If a compact object passes very close to the line of sight to a background star, the gravitational deflection of light causes an apparent brightening of the star, i.e., a gravitational “microlensing” event. Such events will be very rare, so millions of stars must be monitored for many years. We describe our search for microlensing using a very large CCD camera on the dedicated 1.27 m telescope at Mt. Stromlo, Australia: currently some 14 events have been discovered towards the Large Magellanic Cloud. The lack of short-timescale events excludes planetary mass MACHOs as a major contributor to the dark matter, but the observed long events (durations 1–6 months) suggest that a major fraction may be in fairly massive objects $\sim 0.5{\mathrm{M}}_{\odot }.$ It is currently difficult but not impossible to explain these events by other lens populations; we discuss some prospects for clarifying the nature of the lenses.

The discovery of the antiproton some 40 years ago and the almost synchronous fall of parity $\mathrm{}\left(P\right)\mathrm{}$ and charge conjugation $\mathrm{}\left(C\right)\mathrm{}$ symmetries were soon followed by the realization that $\mathrm{CPT}$ rather than $C$ invariance is the fundamental symmetry connecting matter and antimatter, and that consequently any measurement of the antiproton’s properties can be interpreted as a test of that symmetry. It is the latter view of the antiproton, as an object of study in its own right, rather than as a means to such other ends as the production of gauge bosons and meson resonances, that is presented here. The authors review the technical steps that have led from the handful of antiprotons observed by Chamberlain, Segrè, Wiegand, and Ypsilantis to the intense, high-quality beams available today and show how the state of rest and isolation required for high precision measurements of their properties can be achieved by confining them in electromagnetic traps or in their microscopic counterparts, exotic atoms. The test bench role of antiprotons and antihydrogen atoms for both $\mathrm{CPT}$ symmetry and the gravitational weak equivalence principle is discussed, and the body of experimental results obtained since 1955 critically reviewed from this standpoint. Future experiments are then discussed in the light of the closure of the CERN Low Energy Antiproton Ring (LEAR), its replacement in 1999 by the Antiproton Decelerator (AD), and the likely antiproton source at the Japan Hadron Facility.

A tutorial discussion of the propagation of waves in random media is presented. To a first approximation the transport of the multiple scattered waves is given by diffusion theory, but important corrections are presented. These corrections are calculated with the radiative transfer or Schwarzschild-Milne equation, which describes intensity transport at the “mesoscopic” level and is derived from the “microscopic” wave equation. A precise treatment of the diffuse intensity is derived which automatically includes the effects of boundary layers. Effects such as the enhanced backscatter cone and imaging of objects in opaque media are also discussed within this framework. This approach is extended to mesoscopic correlations between multiple scattered intensities that arise when scattering is strong. These correlations arise from the underlying wave character. The derivation of correlation functions and intensity distribution functions is given and experimental data are discussed. Although the focus is on light scattering, the theory is also applicable to microwaves, sound waves, and noninteracting electrons.

This article reviews recent developments in multiresolution analysis that make it a powerful tool for the systematic treatment of the multiple length scales inherent in the electroniic structure of matter. While the focus is on electronic structure, the advances described herein are useful for nonlinear problems in the physical sciences in general. Among the reviewed developments is the exact construction of multiresolution representations from extremely limited samples of physical fields in real space. This new and profound result is the critical advance in finally allowing systematic, all electron calculations to compete in efficiency with state-of-the-art electronic structure calculations that depend for their celerity upon freezing the core electronic degrees of freedom. This review presents the theory of wavelets from a physical perspective, provides a unified and self-contained treatment of nonlinear couplings and physical operators, and introduces a modern framework for effective single-particle theories of quantum mechanics.

Ab initio methods for calculating the adiabatic electronic properties of a single isolated molecule interacting with a metal surface are reviewed. First the fundamental approaches of Anderson, Grimley, and Newns for chemisorption, as well as of Zaremba and Kohn, for physisorption, are outlined. Then the density-functional theory and its approximations are considered. The different models for the adsorbate system are described. They comprise those in which the system has a finite volume—i.e., the cluster, the slab, and the supercell models—and those which take into account the semi-infinite nature of the substrate—i.e., the embedding approach based either on the Dyson equation or on Green’s-function matching. Those definitions are also introduced that we deem important for the understanding of the physical properties of systems to be presented in this article. The lack of full screening in a localized region around the adsorbate, and hence the existence of long-range Friedel’s oscillations induced by the adsorbate in the metal, are discussed. The way in which the lack of full screening influences the calculated adsorption energies is estimated by the grand-canonical functional. Recent ab initio results on physisorption of a noble-gas atom on metals deal mainly with the limits of validity of the simpler effective-medium theory and with the anticorrugating effect of He. Atomic chemisorption is considered in order to deal with the concept of bonding at a metal. Dissociative chemisorption calculations mainly treat the ${\mathrm{H}}_2$ metal system. Here both the adiabatic electronic properties and the sticking probabilities recently obtained using the ab initio potential-energy surfaces are analyzed. Carbon monoxide chemisorption, lateral interactions between adsorbates, adatom diffusion, and chemisorption on stepped surfaces are presented as prototypes of the large variety of ab initio results currently available. Finally, the conclusions are devoted to the respective merits of the different theoretical approaches and to some future directions.

The interstellar medium of galaxies is the reservoir out of which stars are born and into which stars inject newly created elements as they age. The physical properties of the interstellar medium are governed in part by the radiation emitted by these stars. Far-ultraviolet $(6\mathrm{}\mathrm{eV}<h\nu <13.6\mathrm{}\mathrm{eV})$ photons from massive stars dominate the heating and influence the chemistry of the neutral atomic gas and much of the molecular gas in galaxies. Predominantly neutral regions of the interstellar medium in which the heating and chemistry are regulated by far ultraviolet photons are termed Photo- Dissociation Regions (PDRs). These regions are the origin of most of the non-stellar infrared (IR) and the millimeter and submillimeter CO emission from galaxies. The importance of PDRs has become increasingly apparent with advances in IR and submillimeter astronomy. The IR emission from PDRs includes fine structure lines of C, ${\mathrm{C}}^{+},$ and O; rovibrational lines of ${\mathrm{H}}_2;$ rotational lines of CO; broad mid-IR features of polycyclic aromatic hydrocarbons; and a luminous underlying IR continuum from interstellar dust. The transition of H to ${\mathrm{H}}_2$ and ${\mathrm{C}}^{+}$ to CO occurs within PDRs. Comparison of observations with theoretical models of PDRs enables one to determine the density and temperature structure, the elemental abundances, the level of ionization, and the radiation field. PDR models have been applied to interstellar clouds near massive stars, planetary nebulae, red giant outflows, photoevaporating planetary disks around newly formed stars, diffuse clouds, the neutral intercloud medium, and molecular clouds in the interstellar radiation field—in summary, much of the interstellar medium in galaxies. Theoretical PDR models explain the observed correlations of the [CII] 158 μm with the CO $J=1\mathrm{}–0$ emission, the CO $J=1\mathrm{}–0$ luminosity with the interstellar molecular mass, and the [CII] 158 μm plus [OI] 63 μm luminosity with the IR continuum luminosity. On a more global scale, PDR models predict the existence of two stable neutral phases of the interstellar medium, elucidate the formation and destruction of star-forming molecular clouds, and suggest radiation-induced feedback mechanisms that may regulate star formation rates and the column density of gas through giant molecular clouds.

The authors review progress in understanding the nature of atomic collisions occurring at temperatures ranging from the millidegrees Kelvin to the nanodegrees Kelvin regime. The review includes advances in experiments with atom beams, light traps, and purely magnetic traps. Semiclassical and fully quantal theories are described and their appropriate applicability assessed. The review divides the subject into two principal categories: collisions in the presence of one or more light fields and ground-state collisions in the dark.

An open system is not conservative because energy can escape to the outside. As a result, the time-evolution operator is not Hermitian in the usual sense and the eigenfunctions (factorized solutions in space and time) are no longer normal modes but quasinormal modes (QNMs) whose frequencies $\omega$ are complex. Qausinormal-mode analysis has been a powerful tool for investigating open systems. Previous studies have been mostly system specific, and use a few QNMs to provide approximate descriptions. Here the authors review developments that lead to a unifying treatment. The formulation leads to a mathematical structure in close analogy to that in conservative, Hermitian systems. Hence many of the mathematical tools for the latter can be transcribed. Emphasis is placed on those cases in which the QNMs form a complete set and thus give an exact description of the dynamics. In situations where the QNMs are not complete, the “remainder” is characterized. Applications to optics in microspheres and to gravitational waves from black holes are given as examples. The second-quantized theory is sketched. Directions for further development are outlined.

Long hydrocarbon chain polymers dissolved in a liquid qualitatively alter the way the liquid moves and transmits forces. The basic origins of this behavior can be understood geometrically by recognizing that a polymer chain resembles a random walk. The spatial distribution of atoms may be described by scaling properties and quantified using the notion of fractal dimension and dilation invariance. The strong thermodynamic and hydrodynamic interactions of polymers may be accounted for in terms of the intersection properties of fractal objects. These intersection properties show why polymers exclude flow as well as one another from their interiors, despite their arbitrarily small interior concentration. Self avoidance decreases the fractal dimension of a polymer. The origin of this decrease and conditions for its occurrence are explained. From these geometric properties, scaling laws describing how osmotic pressure, diffusion, and stress relaxation depend on molecular weight and concentration are explained.