## Abstract

This article overviews the contributions to the special Christmas Issues of *Phil. Trans. R. Soc. A* published in Decembers 2004–2006, which together cover most of the physical sciences. It also plays the role of a *Preface* for the 2006 issue, which is devoted to the work of young scientists in mathematics and physics.

## 1. Introduction

The Triennial Series of Christmas Issues of *Phil. Trans. R. Soc. A* was started in 2002 as a natural follow-up to the successful Millennium Issues. Devoted to visions of the future by leading young scientists, the series rolls through the physical sciences in a 3-year cycle as described in appendix A. A similar series of Christmas Issues has now been started in *Phil. Trans. R. Soc. B*, which covers the biological sciences.

In these Triennial Issues, the authors present cutting-edge research in a wider context and look forward to new developments. The articles are intended for a general scientific audience and reflect the Royal Society's wish to promote communications between scientific disciplines. This attribute is particularly important in addressing the need to better connect today's highly specialized scientific areas.

In the same spirit, here we shall overview articles not only in this year's issue but also in the preceding 2 years’ issues. This way, we are able to provide a snapshot of current progress in a wide spectrum of physical sciences. To get a good feel of the advancement of modern physical sciences as viewed by young researchers, think of James Clerk Maxwell who launched a professorial career at Marischal College in Aberdeen at the age of 25 exactly 150 years ago. Remarkable examples of Maxwell's multidisciplinary works include: (i) the study of colours linking human visual perception with numbers and photography, (ii) the analysis of dynamical stability applied to engineering control and planetary science, (iii) the geometrical methods in continuum mechanics and theoretical physics, (iv) the kinetic theory that transforms thermal and statistical physics as well as physical chemistry, and (v) Maxwell's most celebrated theory of electromagnetism impacting profoundly on the subsequent developments of physics, mathematics, and engineering, and beyond.

Since Maxwell's time, the physical sciences have further advanced and have been well enriched with new concepts, methodologies and applicability, not least with the advent of quantum mechanics, relativity, atomic scale technologies and computer sciences. Some of their ongoing and future developments have been reported and speculated on, over the last 3 years, in the most recent complete circle of the Triennial Issues. They provide a unique opportunity to see how different thrusts of science influence the research topics taken up by some of today's young scientists in the physical sciences. We feel that the subjects covered provide a good guide to the future perspectives in these areas.

## 2. Christmas 2006, mathematics and physics

This year's Christmas Issue consists of 22 papers in the broad and overlapping areas of mathematics and physics. These papers are organized into themed groups as follows.

Mathematics

Pure mathematics.

Coding and cryptography.

Applied mathematics.

Mathematical biology.

Physics

Particles and gravity.

Quantum computing and control.

General physics.

Nanoscience.

As indicated above, four fields of mathematics are covered. In group (i) for pure mathematics, the paper by Džamonja (2006) discusses the problem of finding the right ‘measure’ for a given Boolean algebra. She shows how this problem influences other mathematical disciplines and vice versa, and outlines the long-term goal of the related research. The paper by Hone (2006) reviews Dodgson condensation, an intriguing problem from algebraic combinatorics, and explains its interplay with number theory and mathematical physics.

In group (ii) for coding and cryptography, Huczynska (2006) explores the interactions between mathematics and engineering inspired by the reliability issues in coding for data transmission along powerlines, and discusses the future developments. The security of cryptography is addressed by Dent (2006) with emphasis on certain fundamental problems to be solved. A new approach is presented in terms of the random oracle model.

There are four papers in group (iii) for applied mathematics. Pelloni (2006) overviews a transformation method for solving linear and integrable nonlinear partial differential equations. Due originally to Fokas, the new transformation is shown to provide a unified mathematical technique and in particular a generalization to the Fourier transform. Thiffeault & Finn (2006) present an interesting application of topological chaos to fluid stirring and mixing with moving rods. They introduce a novel design for a mixing device based on their mathematical approach. The simulation of complex fluids is addressed by Wilson (2006). The author identifies the constitutive modelling for given materials as the most pressing issue for the stability analysis of such fluids used in the plastics industry. The paper by Zimmer (2006) is devoted to challenges from the mathematical modelling of shape-memory materials whose complex dynamics occur at multiple scales. The author sees the ability better to model micro–macro transition as one of the most important future directions in this area.

Four papers are presented in group (iv) for mathematical biology. The paper by Coombes *et al*. (2006) reviews the mathematical aspects of systems neuroscience. The authors’ future vision of neural blueprints lies on more complete mathematical tools that support new experimental discoveries in neurobiology. The state-of-the-art in computer simulation of DNA is overviewed by Harris (2006). The author remarks in particular that a better understanding of certain thermal processes in cells will be invaluable for the future design of ‘nanoengines’. The study of the flow of energy and information across cells is discussed by Liverpool (2006). Attention is drawn to future theoretical and experimental works on the novel behaviour of active living soft matter in cells as opposed to the conventional soft matter. Finally, the paper by Twarock (2006) on mathematical virology addresses the structure and life cycle of viruses. It is hoped that new mathematical tools will enable new insights in virology and the design of anti-viral therapeutics.

Papers in physics appear in four themed groups as follows. In group (v) for particles and gravity, the paper by Wang (2006) introduces the rapidly growing new approach to quantum gravity, loop quantum gravity. A novel canonical framework is presented that promises to resolve a major quantum ambiguity inherent in the present formulation and to hasten progress towards unifying general relativity and quantum mechanics. The ongoing effort to detect the postulated Higg's particle giving rise to the origin of mass, and its importance, is reported by Shears *et al*. (2006). They are hoping that this will be realized with the completion and operation of the Large Hadron Collider in the next few years.

Two papers are in group (vi) for quantum computing and control. Kendon (2006) explains the fundamental difference between the classical and the quantum random walks applicable to computational algorithms, and points to possible major progress on the latter. Schirmer (2006) gives an overview of the present achievements in controlling quantum phenomena and offers an outlook on overcoming the challenges in realizing quantum technology.

Three papers fall in group (vii) for general physics. The paper by Benabid (2006) reviews a new light-guiding method using hollow-core photonic fibres, and shows future prospects opened by these fibres in new science and technology. Pachos & Carollo (2006) present an analysis of Berry (geometric) phase related to certain critical phenomena of quantum spin systems. They highlight challenges in future generalizations to a wide variety of critical phenomena with arbitrary spins. The paper by Patanè & Fromhold (2006) reviews the recently discovered chaotic behaviour of electrons in superlattices. This rare chaos is speculated to provide a new mechanism for controlling extremely sensitive electronic devices.

Three more papers are in group (viii) for nanoscience. The paper by Catchpole (2006) describes the application of nanostructures to photo-voltaic devices that may lead to major improvement of solar cells as an important future source of energy. Dankowicz (2006) gives an overview on the tapping-mode atomic-force microscopy and its use for non-intrusive characterization of nanostructures. Attention is drawn to its associated nonlinear phenomena that may provide important tools for micro- and nanoscale applications. Finally, the optical trapping and manipulation of micro- and nanoscale particles using ‘optical tweezers’ are described by McGloin (2006). He predicts that, following 20 years development, the technology is already maturing and in the next 20 years it will lead to novel developments and wide applications.

## 3. Christmas 2005, astronomy and earth science

The 2005 Triennial Issue is devoted to astronomy and the Earth sciences and contains an introductory article (Thompson & Wang 2005) and 16 contributed papers organized into themed groups as follows.

Cosmology and beyond the Solar System.

The Solar System.

Earth's interior and oceans.

Earth's surface, atmosphere and climate.

In group (i), the paper by Munshi & Valageas (2005) describes ongoing and future research into the gravitational lensing survey, which promises to reveal new knowledge about the distribution of material in the Universe. It is followed by Read & Trentham (2005) on the survey of baryonic mass within different types of galaxies. The survey will yield knowledge about the actual distribution of baryons and may serve to confirm our understanding of the Big Bang theory. The third paper in this group by Hardcastle (2005) presents an interesting discussion on some striking energetic astronomical sources observable through X-rays.

In group (ii) for the Solar System, attention is turned to phenomena in our immediate space environment. The main interests here lie in the origin of life and (related to life) the behaviours of the Sun and the planets. Sephton (2005) reviews present studies, and offers future visions, on the role of organic matter, especially carbon-rich meteorites, within the Solar System. The dynamics of the Sun and the stability of the solar phenomena can obviously affect life on Earth, and De Moortel (2005) presents an overview of coronal seismology and explores its viability to determine the physical conditions of the coronal plasma. Seismic methods applied to the solar surface are described by Tong (2005), who outlines how these methods are contributing to new research into the imaging of sunspots. Hagermann (2005) explains why planets are themselves heat engines, with internal heat flows. Impacts of asteroids on Earth remain a significant natural hazard. Research into the impact rate and how we may predict and avoid any consequent catastrophes are reported by Bland (2005).

Group (iii) is devoted to the Earth's interior and oceans. The paper by Bovolo (2005) explains how recent seismic tomography yields three-dimensional models of the seismic wave velocities, by making use of the thermodynamic properties of the minerals. Issues on the possible mixing of upper and lower mantles are also addressed. Rippeth (2005) examines the mixing in seasonally stratified shelf seas. Berndt (2005) looks at the flow in passive continental margins in terms of sustainable ecosystems for the commercial fish stock. The ocean's plant life is discussed by Martin (2005) with a focus on phytoplankton at macro- to mesoscales and their response to climate change. Striking images of the resulting ‘kaleidoscope ocean’ are displayed.

In group (iv) for the Earth's surface, atmosphere and climate, the paper by Holden (2005) is dedicated to environmental processes operating in peatlands. Volcanic activities form a threat to life and the environment. Their remote sensing with ground-based spectroscopy is reviewed in the paper by McGonigle (2005). The author then speculates on possible breakthroughs in this field. Williams (2005) addresses a very ambitious subject for future research, the modelling of climate change. An account of its difficulties in terms of uncertainty in the physical processes involved is given. Finally, the paper by Belcher (2005) presents the modelling of air mixing, in the context of urban air quality. This issue is also relevant for estimating the transport of any harmful material by air in the event of a terrorist attack.

## 4. Christmas 2004, chemistry and life science

This Triennial Issue, devoted to chemistry and life science, contains a preface by Thompson (2004) and 16 contributed papers by young scientists, which are organized into themed groups as follows.

Chemistry.

Biochemistry.

Genetics and evolution.

Bioengineering and medicine.

Group (i) for chemistry contains four papers. Timmel & Henbest (2004) study spin chemistry in magnetic fields and its implication on magnetoreception in birds. Vallance (2004) reviews recent developments in molecular photography of chemical events. The paper by Marken (2004) is devoted to electrifying interfaces. Edler (2004) reviews a bottom-up approach to nanotechnology using surfactant templating techniques.

There are six papers in themed group (ii) for biochemistry. Weissman (2004) reviews progress on biosynthesis and highlights some key information from recent experiments. Applications of quantum chemistry (van Mourik 2004) and powder diffraction (Tremayne 2004) to the life sciences are covered by two papers. One subsection, devoted to studies of colour and vision, covers natural animal colours (Parker 2004), binocular vision (Harris 2004) and the design of visual interfaces (Davis 2004).

In group (iii) for genetics and evolution, papers are devoted to developments in chemical genetics (Westwood 2004), the use of microscopic movements in the mammalian nucleus to help understand our genes (Sleeman 2004) and the effect of environmental change on biotic evolution (van Tuinen *et al*. 2004).

Finally, three papers in group (iv) for bioengineering and medicine cover bone repair (Hing 2004), the tracking of intracellular ion migration (Sastry & Lastoskie 2004) and the chemistry of the adaptive mind (Cools & Robbins 2004). The last of these papers addresses treatments for abnormalities such as Parkinson's disease, attention-deficit hyperactivity disorder and drug addiction.

## Footnotes

One contribution of 23 to a Triennial Issue ’Mathematics and physics’.

- © 2006 The Royal Society