There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black Hole Explosions

Femtosecond filamentation in transparent media

Dust -acoustic waves in dusty plasmas

The book Introduction to Plasma Physics by Shukla and Mamun deals with various aspects of collective processes in dusty plasmas. The first introductory chapters review dust charging and the forces on dust grains in the plasma. The next two chapters give an elaborate description of the various waves and instabilities present in plasmas. In our opinion this makes the book a must for scientists involved in dusty plasma research as for the first time these phenomena are clearly explained and catalogued in a single work. Magnetic as well as non-magnetic plasmas are treated and where applicable examples from laboratory or space plasmas are given. The text is suitable for graduate level teaching as well as referencing purposes. The authors state in the preface: `This book has grown out of research work on topics on which the authors have spent a considerable amount of time and thought.' This explains the final chapters of the book, where `hot topics' on respectively elongated grains, non-linear waves and dust crystals are discussed. Since these chapters deal with state-of-the-art research, the results are inevitably not presented in a systematic way, but rather as a compilation of recent papers. Throughout the book the subject is treated using a theoretical approach. This makes it complementary to the book Dusty Plasmas: Physics, Chemistry and Technological Impacts in Plasma Processing edited by A Bouchoule which takes an applied approach. The research on dusty plasmas is a relatively new and rapidly expanding area of science. This book will serve as a handbook on waves and instabilities dusty plasmas in the coming years. But the character of the last chapters shows that more is to come in this exciting field of research. E Stoffels and W W Stoffels

Introduction to Dusty Plasma Physics

The existence of a new low-frequency electrostatic wave in an unmagnetized collisionless dusty plasma is pointed out.

https://iopscience.iop.org/article/10.1088/0031-8949/45/5/015/pdf

Dust ion-acoustic wave

Strong-field effects in laboratory and astrophysical plasmas and high intensity laser and cavity systems are considered, related to quantum electrodynamical (QED) photon-photon scattering. Current state-of-the-art laser facilities are close to reaching energy scales at which laboratory astrophysics will become possible. In such high energy density laboratory astrophysical systems, quantum electrodynamics will play a crucial role in the dynamics of plasmas and indeed the vacuum itself. Developments such as the free-electron laser may also give a means for exploring remote violent events such as supernovae in a laboratory environment. At the same time, superconducting cavities have steadily increased their quality factors, and quantum nondemolition measurements are capable of retrieving information from systems consisting of a few photons. Thus, not only will QED effects such as elastic photon-photon scattering be important in laboratory experiments, it may also be directly measurable in cavity experiments. Here implications of collective interactions between photons and photon-plasma systems are described. An overview of strong field vacuum effects is given, as formulated through the Heisenberg-Euler Lagrangian. Based on the dispersion relation for a single test photon traveling in a slowly varying background electromagnetic field, a set of equations describing the nonlinear propagation of an electromagnetic pulse on a radiation plasma is derived. The stability of the governing equations is discussed, and it is shown using numerical methods that electromagnetic pulses may collapse and split into pulse trains, as well as be trapped in a relativistic electron hole. Effects, such as the generation of novel electromagnetic modes, introduced by QED in pair plasmas is described. Applications to laser-plasma systems and astrophysical environments are also discussed.

Nonlinear collective effects in photon-photon and photon-plasma interactions

Solitary electrostatic structures involving density depletions have been observed in the upper ionosphere by the Freja satellite [Dovner et al., 1994]. If these are interpreted as ion sound solitons, the difficulty arises that the standard Korteweg-de Vries description predicts structures with enhanced rather than depleted density. Here we show that the presence of non-thermal electrons may change the nature of ion sound solitary structures and allow the existence of structures very like those observed.

Padma Kant Shukla

Papers

Dust -acoustic waves in dusty plasmas

Introduction to Dusty Plasma Physics

Dust ion-acoustic wave

Nonlinear collective effects in photon-photon and photon-plasma interactions

Electrostatic solitary structures in non‐thermal plasmas