Showing papers in "Advances in Physics in 2002"

Evolution of networks

Abstract: We review the recent rapid progress in the statistical physics of evolving networks. Interest has focused mainly on the structural properties of complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of this kind have recently been created, which opens a wide field for the study of their topology, evolution, and the complex processes which occur in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of the large sizes of these networks, the distances between most of their vertices are short - a feature known as the 'small-world' effect. We discuss how growing networks self-organize into scale-free structures, and investigate the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation and disease spread on these networks. We present a number of models demonstrat...

The Fluctuation Theorem

Abstract: The question of how reversible microscopic equations of motion can lead to irreversible macroscopic behaviour has been one of the central issues in statistical mechanics for more than a century. The basic issues were known to Gibbs. Boltzmann conducted a very public debate with Loschmidt and others without a satisfactory resolution. In recent decades there has been no real change in the situation. In1993 we discovered a relation, subsequently known as the Fluctuation Theorem (FT), which gives an analytical expression for the probability of observing Second Law violating dynamicaluctuations in thermostatted dissipa- tive non-equilibrium systems. The relation was derived heuristically and applied to the special case of dissipative non-equilibrium systems subject to constant energy `thermostatting'. These restrictions meant that the full importance of the Theorem was not immediately apparent. Within a few years, derivations of the Theorem were improved but it has only been inthe last few of years that the generality ofthe Theorem has been appreciated. We now know that the Second Law of Thermo- dynamics can be derived assuming ergodicity at equilibrium, and causality. We take the assumption of causality to be axiomatic. It is causality which ultimately is responsible for breaking time reversal symmetry and which leads to the possibility of irreversible macroscopic behaviour. The Fluctuation Theorem does much more than merely prove that in large systems observed for long periods of time, the Second Law is overwhelmingly likely to be valid. The Fluctuation Theorem quanti®es the probability of observing Second Law violations in small systems observed for a short time. Unlike the Boltzmann equation, the FT is completely consistent with Loschmidt's observa- tion that for time reversible dynamics, every dynamical phase space trajectory and its conjugate time reversedanti-trajectory', are both solutions of the underlying equations of motion. Indeed the standard proofs of the FT explicitly consider conjugate pairs of phase space trajectories. Quantitative predictions made by the Fluctuation Theorem regarding the probability of Second Law violations have been con®rmed experimentally, both using molecular dynamics computer simula- tion and very recently in laboratory experiments.

Tube theory of entangled polymer dynamics

Abstract: The dynamics of entangled flexible polymers is dominated by physics general to many chemical systems. It is an appealing interdisciplinary field where experimental and theoretical physics can work closely with chemistry and chemical engineering. The role of topological interactions is particularly important, and has given rise to a successful theoretical framework: the 'tube model'. Progress over the last 30 years is reviewed in the light of specially-synthesized model materials, an increasing palette of experimental techniques, simulation and both linear and nonlinear rheological response. Our current understanding of a series of processes in entangled dynamics: 'reptation', 'contour length fluctuation' and 'constraint-release' are set in the context of remaining serious challenges. Especial attention is paid to the phenomena associated with polymers of complex topology or 'long chain branching'.

Collective and single particle diffusion on surfaces

Abstract: We review in this article the current theoretical understanding of collective and single particle diffusion on surfaces and how it relates to the existing experimental data. We begin with a brief survey of the experimental techniques that have been employed for the measurement of the surface diffusion coefficients. This is followed by a section on the basic concepts involved in this field. In particular, we wish to clarify the relation between jump or exchange motion on microscopic length scales, and the diffusion coefficients which can be defined properly only in the long length and time scales. The central role in this is played by the memory effects. We also discuss the concept of diffusion under nonequilibrium conditions. In the third section, a variety of different theoretical approaches that have been employed in studying surface diffusion such as first principles calculations, transition state theory, the Langevin equation, Monte Carlo and molecular dynamics simulations, and path integral formalism...

Intersonic shear cracks and fault ruptures

Abstract: Recent experimental observations of intersonic shear rupture events that occur in a variety of material systems have rekindled interest in the intersonic failure phenomenon. Since the early 1990s, engineers and scientists working in all length scales, from the atomistic, the structural, all the way up to the scale of the earth's deformation processes, have undertaken joint efforts to study this unexplored area of fracture mechanics. The analysis in the present article emphasizes the cooperative and complementary manner in which experimental observations and analytical and numerical developments have proceeded. The article first reviews early contributions to the theoretical literature of dynamic subsonic and intersonic fracture and highlights the significant differences between tensile and shear cracks. The article then uses direct laboratory observations as a framework for discussing the physics of intersonic shear rupture occurring in constitutively homogeneous (isotropic and anisotropic) as well as in ...

Ferromagnetism and electron-phonon coupling in the manganites

Abstract: The physics of ferromagnetic doped manganites, such as La 1-x Ca x MnO 3 with x ≈ 0.2-0.4, is reviewed. The concept of double exchange is discussed within the general framework of itinerant electron magnetism. The new feature in this context is the coupling of electrons to local phonon modes. Emphasis is placed on the quantum nature of the phonons and the link with polaron physics. However it is stressed that the manganites fall into an intermediate coupling regime where standard small-polaron theory does not apply. The recently-developed many-body coherent potential approximation is able to deal with this situation and Green's recent application to the Holstein double-exchange model is described. Issues addressed include the nature of the basic electronic structure, the metal-insulator transition, a unification of colossal magnetoresistance, pressure effects and the isotope effect, pseudogaps in spectroscopy and the effect of electron-phonon coupling on spin waves.

Low-energy quasiparticles in high-Tc cuprates

Abstract: The aim of this review is to summarize existing experimental investigations on the nature of the low-energy quasiparticle excitations in high- T c cuprates, and to examine critically recent claims of consistency between the experimentally determined low-temperature thermodynamic and transport properties in certain cuprates and theoretical predictions based on standard perturbation theory for a BCS d-wave superconductor. Measurements of the low-temperature specific heat, thermal conductivity, microwave conductivity, penetration depth and scanning tunnelling microscopy are described, both in the Meissner state and in the mixed state. These results are then compared with the predictions of quasi-classical theory of a d-wave BCS superconductor and the self-consistent T-matrix approximation for both a single impurity and a finite impurity concentration. Detailed inspection reveals that significant discrepancies still exist between experiment and theory, with important implications for the development of a cohe...

dx2 - y2 superconductivity and the Hubbard model

Abstract: The numerical studies of d x 2 - y 2 -wave pairing in the two-dimensional (2D) and the 2-leg Hubbard models are reviewed. For this purpose, the results obtained from the determinantal Quantum Monte Carlo and the Density-Matrix Renormalization-Group calculations are presented. These are calculations which were motivated by the discovery of the high- T c cuprates. In this review, the emphasis is placed on the microscopic many-body processes which are responsible for the d x 2 - y 2 -wave pairing correlations observed in the 2D and the 2-leg Hubbard models. In order to gain insight into these processes, the results on the effective pairing interaction as well as the magnetic, density and the single-particle excitations will be reviewed. In addition, comparisons will be made with the other numerical approaches to the Hubbard model and the numerical results on the t - J model. The results reviewed here indicate that an effective pairing interaction which is repulsive at ( ~ , ~ ) momentum transfer, and enhance...

Wavefunction methods in electronic-structure theory of solids

Abstract: The electronic-structure theory of solids is presently dominated by density-functional methods which avoid calculations of the many-body wavefunction, and instead compute directly properties of the ground state. We argue that methods which determine the many-electron wavefunctions should receive particular attention in the future. A survey is given of our present knowledge of how to calculate these wavefunctions for a solid. The accuracy we envisage compares with the one obtainable for small molecules when applying quantum-chemical methods.

Structure and dynamics of cellular systems

Abstract: This review addresses recent progress in the analysis and modelling of disordered cell structures. It focuses on planar systems, for which most research has been performed. The subject is approached from a general viewpoint rather than focusing on the specific evolution of certain systems. To this end, results of studies performed in completely different disciplines, ranging from applied sciences, biology and physics to mathematics, are gathered and discussed systematically. Special emphasis is laid on common properties of the different structures, including a critical discussion of the information contained in typically measured quantities. Efficient techniques for the simulation of typical disordered cell structures are summarized, and novel theoretical approaches to the modelling of dynamical cell structures are presented. Here, special attention is paid to the application of the methods of statistical mechanics and the resulting implications. In several systems, a breakdown of order induced by variati...

Granular materials: Towards the statistical mechanics of jammed configurations

Abstract: The properties of granular materials can be well defined, that is be a branch of physics, but conventional statistical mechanics is inadequate to handle what amounts to the physics of disordered packings of hard-core particles, either static or driven by external forces. A new approach that employs statistical-mechanical concepts is offered for the description of such systems. An analysis of the stress field in static granular packings is given within the framework of this approach. There are more conventional systems such as polymer glasses which have a rather similar statistical physics to granular media, and some speculative ideas are offered which are a real departure from conventional glass theories.