Physics Reports

Published by Elsevier BV

Print ISSN: 0370-1573


Fig. 7. Scaling analyses of heartbeat time series in health, ageing and disease. Here, log F (n) is plotted as a function of log(n) for a healthy young subject, a
Correlations of absolute energy with age for ACh in intervals (a) VI, (c) V and for SNP in intervals (b) VI, (d) V. The filled circles represent males, and the crosses represent females.
FFT power spectra for simple sine waves (see the text) plotted (a) on a linear scale and (b) as the time-averaged wavelet amplitude plotted on a semi-log scale, from the same HRV signal.
Correlations of relative energy with age for ACh in intervals (a) VI, (c) V and for SNP in intervals (b) VI, (d) V. The filled circles represent males, and the crosses represent females.
Age-related changes in average flow and total energy. Correlations between age and (a) average flow with ACh, (b) average flow with SNP, (c) total energy with ACh and (d) total energy with SNP. The filled circles represent males, and the crosses represent females.


Nonlinear dynamics of cardiovascular aging
  • Article
  • Full-text available

March 2010


1,196 Reads

Yuri Shiogai



The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time-frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in dynamical terms. Clear evidence is found for dynamical ageing.

Spallation processes and nuclear interaction products of cosmic rays

September 1990


88 Reads

Most cosmic-ray nuclei heavier than helium have suffered nuclear collisions in the interstellar gas, with transformation of nuclear composition. The isotopic and elemental composition at the sources has to be inferred from the observed composition near the Earth. The source composition permits tests of current ideas on sites of origin, nucleosynthesis in stars, evolution of stars, the mixing and composition of the interstellar medium and injection processes prior to acceleration. The effects of nuclear spallation, production of radioactive nuclides and the time dependence of their decay provide valuable information on the acceleration and propagation of cosmic rays, their nuclear transformations, and their confinement time in the Galaxy. The formation of spallation products that only decay by electron capture and are relatively long-lived permits an investigation of the nature and density fluctuations (like clouds) of the interstellar medium. Since nuclear collisions yield positrons, antiprotons, gamma rays and neutrinos, we shall discuss these topics briefly.

MCnet-11-01 General-purpose event generators for LHC physics

January 2011


167 Reads


Jonathan Butterworth


Stefan Gieseke




We review the physics basis, main features and use of general-purpose Monte Carlo event generators for the simulation of proton-proton collisions at the Large Hadron Collider. Topics included are: the generation of hard-scattering matrix elements for processes of interest, at both leading and next-to-leading QCD perturbative order; their matching to approximate treatments of higher orders based on the showering approximation; the parton and dipole shower formulations; parton distribution functions for event generators; non-perturbative aspects such as soft QCD collisions, the underlying event and diffractive processes; the string and cluster models for hadron formation; the treatment of hadron and tau decays; the inclusion of QED radiation and beyond-Standard-Model processes. We describe the principal features of the ARIADNE, Herwig++, PYTHIA 8 and SHERPA generators, together with the Rivet and Professor validation and tuning tools, and discuss the physics philosophy behind the proper use of these generators and tools. This review is aimed at phenomenologists wishing to understand better how parton-level predictions are translated into hadron-level events as well as experimentalists wanting a deeper insight into the tools available for signal and background simulation at the LHC.

Hadronic interactions and cosmic radiation at energies above 105 GeV

September 1975


8 Reads

A selection of results in particle physics is given from experiments with the cosmic radiation from about 1960 to December 1974. Mostly, the results are from interactions of energy greater than 105 GeV. The topics covered are: a) variation of charged particle multiplicity with energy, b) rise in the p-p cross section with energy, c) rise in the NN production cross section with energy, d) the mean pT and its distribution at energies from 105 to 108 GeV, e) the mass spectrum of ‘fireballs” and the transverse momenta of decay products in the fireball CMS, f) other emulsion chamber results including the event ‘Centauro’, g) the search and evidence for very massive, comparatively stable particles, h) interactions between 1017 and 1021 eV.

Wartell, R. M. & Benight, A. S. Thermal denaturation of DNA molecules: a comparison of theory with experiment. Phys. Rep. 126, 67-107

September 1985


318 Reads

Experimental and theoretical results on the helix-coil transition of DNA are reviewed. The theoretical model of the transition is described, and the influence of heterogeneous base pair stacking, and strand dissociation on the predicted melting transition is examined. New experimental transition data on seven DNAs, 154–587 base pairs (bp) long, are reported and compared with theoretical calculations. We review and evaluate previous studies on long DNAs (≥1000 bp) as well as previous and recent results on short DNAs. The comparison of theory with equilibrium melting curves of short DNAs indicates that base pair sequence has a relatively small influence on the stacking free energy. Excellent agreement is obtained between theory and equilibrium transitions of 14 out of 15 fragments 80–587 pb. The deviation between theory and experiment for a 516 bp DNA can be attributed to the formation of stem-loop structures. This may provide the explanation for inconsistent results observed with long DNAs. The effect of single base pair changes on DNA transitions is discussed. Current views on fluctuational opening of base pairs at temperatures below the transition are described.

Bound state properties of Borromean halo nuclei: 6He and 11Li

August 1993


337 Reads

The nuclei 6He and 11Li which exhibit pronounced halo-structures with two loosely bound valence neutrons, are currently being explored as secondary-beam projectiles. These nuclei are Borromean, i.e. while they are bound (only one bound state) they have, considered as three-body systems, no bound states in the binary subsystems. We argue that a three-body description is the natural one for central properties of such exotic loosely bound nuclei, and give the state of the art by comparing fully blown three-body calculations for 6He (and neighboring A=6 nuclei) with a range of measured observables. We restrict this review to bound state properties, with emphasis on genuine three-body features. The bound state is the initial stage of the various reaction scenarios that now are being studied experimentally and a main objective of these studies. Currently used procedures for solving the three-body bound state problem are outlined, with emphasis on expansions on hyperspherical harmonics and also the coordinate space Faddeev approach. Although strict calculations can also be carried out for 11Li, they are inconclusive concerning the details of the structure since the available information on the binary neutron-9Li(core) channel is insufficient. Calculations for a number of plausible model interactions, including treatments of the Pauli principle, are presented. They all reproduce the binding energy and halo characteristics such as valence one-particle density and give about the same internal r.m.s. geometry for 11Li. In spite of this, the wave functions have pronounced differences in their spatial correlations. The same ambiguity is also present in other inclusive observables, such as momentum distributions. We also demonstrate that candidates for the nuclear structure can be explored within an approximate scheme COSMA. Predictions of exclusive observables are discussed, and quantities such as momentum correlations in complete measurements are found to be more sensitive to the detailed features of the nuclear structure of the bound state.

Photonuclear reaction cross sections for 12C, 14N and 16O

October 1985


49 Reads

The results of an evaluation of the available photonuclear-reaction data for 12C, 14N and 16O are presented. While some reaction-yield data are given for energies up to 50 MeV, the primary emphasis is on the excitation-energy range extending from the proton separation energies up to 30 MeV. In addition to photodisintegration measurements, cross-section data derived from inverse particle-capture and electrodisintegration experiments are considered. Data are presented in graphical as well as tabular form. Included in the tables are: energy-weighted moments of the cross sections, bremsstrahlung induced reaction-yield data, radioactive-properties of reaction products, and reaction separation energies.

Nucleosynthesis in massive stars and the 12C(α, γ)16O reaction rate

May 1993


38 Reads

The evolution of a grid massive stars ranging from 12 to 40 M⊙ has been followed through all stages of nuclear burning up to the point of iron core collapse. The critical and highly uncertain rate for the reaction 12C(α, γ)16O has been varied over a range from 0.5 to 3.0 times that given by Caughlan and Fowler and two different prescriptions for semiconvection have been explored. The nucleosynthesis resulting from integrating the yields of these models over plausible initial stellar mass distributions is found to be in excellent agreement with the observed solar abundances of virtually all the intermediate mass isotopes (16 ≤ A ≤ 32) if, and only if, the rate of the 12C(α, γ)16O reaction is taken to be 1.7 ± 0.5 times that given by Caughlan and Fowler. This range is a small subset of what is allowed by current experimental measurements and can be taken as a nucleosynthetic “prediction” of the value that this rate needs to have in order to prevent 5- to 100-fold deviations from the observed relative abundances of key isotopes. These results are insensitive to the assumed slope of the initial stellar mass distribution within observational limits, and relatively insensitive to the theory of semiconvection (except for the apparent excessive production of 18O when semiconvective mixing is suppressed). Three of the stars have been followed through simulated explosions to obtain the explosive modifications to their nucleosynthesis (including the “neutrino process”), which for most isotopes is relatively small. Isotopic yields of both stable radioactive products are tabulated as are the calculated iron core masses of the presupernova stars.

Camporesi, R.: Harmonic analysis and propagators on homogeneous spaces. Phys. Rep. 196, 1-134

November 1990


1,103 Reads

The techniques of harmonic analysis of homogeneous spaces are reviewed, and applied to the theory of propagators. The spectral geometry of homogeneous and, in particular, of symmetric spaces is considered, with explicit calculations of the heat kernel and the zeta function. Several topics relevant to physical applications are discussed, including the Schwinger-DeWitt expansion, the exactness of the WKB approximation in curved spaces, the connection between free motion on symmetric spaces and quantum integrable systems, and finite-temperature quantum field theories in higher dimensions. The paper contains some new results of both mathematical and physical interest; e.g., explicit formulas for the scalar degeneracies of the Laplacian on a compact symmetric space, exact forms of the zeta function on the symmetric spaces of rank one, extension of the finite-temperature formalism to spinor fields in higher-dimensional static spacetimes, and Casimir energy calculations in even dimensions.

Vulpiani, A.: Anomalous scaling laws in multifractal objects. Phys. Rep. 156, 147

December 1987


348 Reads

Anomalous scaling laws appear in a wide class of phenomena where global dilation invariance fails. In this case, the description of scaling properties requires the introduction of an infinite set of exponents.Numerical and experimental evidence indicates that this description is relevant in the theory of dynamical systems, of fully developed turbulence, in the statistical mechanics of disordered systems, and in some condensed matter problems.We describe anomalous scaling in terms of multifractal objects. They are defined by a measure whose scaling properties are characterized by a family of singularities, which are identified by a scaling exponent. Singularities corresponding to the same exponent are distributed on fractal set. The multifractal object arises as the superposition of these sets, whose fractal dimensions are related to the anomalous scaling exponents via a Legendre transformation. It is thus possible to reconstruct the probability distribution of the singularity exponents.We review the application of this formalism to the description of chaotic attractors in dissipative systems, of the energy dissipating set in fully developed turbulence, of some probability distributions in condensed matter problems. Moreover, a simple extension of the method allows us to treat from the same point of view temporal intermittency in chaotic systems and sample to sample fluctuations in disordered systems.We stress the phenomenological nature of the approach and discuss the few cases in which it was possible to reach a more fundamental understanding of anomalous scaling. We point out the need of a theory which should explain its origin and pave the way to a microscopic calculation of the probability distribution of the singularities.

The Magnus expansion and some of its applications. Physics Reports, 470(5-6), 151-238

November 2008


601 Reads

Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem, shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to build up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of preserving, at any order, certain symmetries of the exact solution.The goal of this review is threefold. First, to collect a number of developments scattered through half a century of scientific literature on Magnus expansion. They concern the methods for the generation of terms in the expansion, estimates of the radius of convergence of the series, generalizations and related non-perturbative expansions. Second, to provide a bridge with its implementation as generator of especial purpose numerical integration methods, a field of intense activity during the last decade. Third, to illustrate with examples the kind of results one can expect from Magnus expansion, in comparison with those from both perturbative schemes and standard numerical integrators. We buttress this issue with a revision of the wide range of physical applications found by Magnus expansion in the literature.

Blandford, R. & Eichler, D. Particle acceleration at astrophysical shocks: a theory of cosmic ray origin. Phys. Rep. 154, 1-75

October 1987


140 Reads

The theory of first order Fermi acceleration at collisionless astrophysical shock fronts is reviewed. Observations suggest that shock waves in different astrophysical environments accelerate cosmic rays efficiently. In the first order process, high energy particles diffuse through Alfvén waves that scatter them and couple them to the background plasma. These particles gain energy, on the average, every time they cross the schock front and bounce off approaching scattering centers. Calculations demonstrate that the distribution function transmitted by a plane shock is roughly a power law in momentum with slope similar to that inferred in galactic cosmic ray sources. The generation of the scattering Alfvén waves by the streaming cosmic rays is described and it is argued that the wave amplitude is probably non-linear within sufficiently strong astrophysical shocks. Hydromagnetic scattering can operate on the thermal particles as well, possibly establishing the shock structure. This suggests a model of strong collisionless shocks in which high energy particles are inevitably produced very efficiently. Observable consequences of this model, together with its limitations and some alternatives, are described. Cosmic ray origin and astrophysical shocks can no longer be considered separately.

The 17 keV neutrino

August 1996


14 Reads

A controversy over the possible existence of a 17 keV mass state coupled to the electron neutrino occurred during the period 1985–1993. A number of independent experiments found evidence for this state in nuclear decay spectra, while others did not. Ultimately a consensus that the 17 keV neutrino does not exist was reached. We review and evaluate the experiments that reported evidence for and against the 17 keV neutrino, and discuss the various issues of experimental systematics that contributed to the development and resolution of the controversy. We attempt to distill the lessons learned from this experience and draw some general conclusions that are relevant to future research.

Zurek, W. H. Cosmological experiments in condensed matter systems. Phys. Rep. 276, 177-221

July 1996


91 Reads

Topological defects are thought to be left behind by the cosmological phase transitions which occur as the universe expands and cools. Similar processes can be studied in the phase transitions which take place in the laboratory: “Cosmological” experiments in superfluid helium and in liquid crystals were carried out within the past few years, and their results shed a new light on the dynamics of the defect-formation process. The aim of this paper is to review the key ideas behind this cosmology-condensed matter connection and to propose new experiments which could probe heretofore unaddressed aspects of the topological defects formation process.

Acoustical characteristics of porous materials. Physics Reports, 82(3) 179-227

February 1982


146 Reads

The diversity of porous materials is noted. However, this study is particularly relevant to the use of sound absorbent materials in architectural acoustics. The theory of sound propagation within an idealised porous material consisting of a rigid matrix through which run parallel cylindrical pores normal to the surface is reviewed. Extensions to pores of arbitrary orientation and cross-section are achieved by introducing physically-measura ble microstructural constants rather than phenomenological bulk parameters that might be frequency dependent. By comparison of several theories that account for sound propagation within an elastically-framed porous material a basis is laid for an improved formulation, that takes into account both viscosity and heat conduction.The application of various propagation theories to model the reflection and transmission of sound at porous boundaries is considered. Particular attention is paid to the common assumption of local reaction and to the adequacy of modelling the porous interface as that of a quasi-homogeneous fluid. Finally the most widely used methods of measuring acoustical characteristics of porous materials at normal and oblique incidence and of obtaining their values by empirical means are surveyed.

From bubble chambers to electronic systems: 25 years of evolution in particle detectors at CERN (1979–2004)

December 2004


42 Reads

The European Organization for nuclear research (CERN) celebrates in October 2004 its 50th anniversary. A centre of excellence for elementary particle physics research, the laboratory has contributed to the development of advanced technologies for the construction of powerful accelerators and experiments. As a follow-up of the article published by this journal in 1980, on the occasion of CERN's 25th anniversary, this contribution describes the developments of particle detectors and experimental set-ups that took place in the laboratory during the last 25 years.

Axisymmetrical Structures of Planetary Nebulae and SN 1987A

April 1998


14 Reads

I summarize some recent models and ideas for the formation of axisymmetrical structures of planetary nebulae and the three rings of SN 1987A, as follows. (a) I review the general role of binary companions, including brown dwarfs and planets. (b) I propose a mechanism for axisymmetrical mass loss on the AGB that may account for the axially symmetric structures of elliptical planetary nebulae and that operates for slowly rotating AGB stars. (c) I propose a model for the formation of the two outer rings of SN 1987A, which is based on the numerical simulation of Soker (1989), and discuss a mechanism for their displacement from the exploding star. Comment: In the proceedings of the conference Physical Processes in Astrophysical Fluids. Will be published as a special volume of Physics Reports. LATEX, 9 pages,1 figure

Parallel computing in the 1990's: Attacking the software problem

July 1992


42 Reads

It is today's general wisdom that the productive use of parallel architectures depends crucially on the availability of powerful development tools and run-time environments. In this paper, we systematically discuss the fundamental software problems encountered in programming parallel architectures, in particular those with distributed resources. All these problems need to be solved, if efficient and convenient use of parallel machines is to be guaranteed. We present a five phases model of parallel application program development, which describes the required efforts in parallel programming by means of four transformation steps: problem analysis, algorithmdesign, implementation, and mapping. The major part of the paper is dedicated to the description of three research projects which focus on the last three transformation steps: SKELETON, a tool for providing improved algorithmic support for the application-oriented programmer, SPADE, an integrated development and run-time environment, and MARC, a tool for automatic mapping of parallel programs.

Supernova 1993J: One year later

May 1995


15 Reads

Supernova 1993J, a Type IIpec supernova, was discovered on March 28 in the nearby galaxy M81. The spectra displayed strong Balmer lines establishing its classification as a Type II supernova. About 26 days after explosion the Hα profile became anomalous, signaling the presence of significant amounts of helium. Additionally, the light curve displayed an anomalous double peak. We review the observations and interpretation of Supernova 1993J through the use of light curve fitting and synthetic spectra.

The Confrontation between General Relativity and Experiment: A 1998 Update

November 1984


13 Reads

The status of experimental tests of general relativity to the end of 1983 is reviewed. The experimental support for the Einstein equivalence principle is summarized. If this principle is valid, gravitation must be described by a curved space-time, “metric” theory of gravity. General properties of metric theories are described and the parametrized post-Newtonian (PPN) formalism for treating the weak-field, slow-motion limit of such theories is set up. A zoo of selected metric theories of gravity is presented. Experimental tests of metric theories are then described, including the “classical” tests, tests of the strong equivalence principle, and others. The possibility of using gravitational-wave observations to test metric theories is discussed. A review is presented of the binary pulsar, in which the first evidence for gravitational radiation has been found. Finally cosmological tests of alternative theories are briefly described.

Static quadrupole moments of first 2+ states in the 2s1d shell: A review of experiment and theory

July 1981


10 Reads

Available experimental information on the static electric quadrupole moments Q2+ of the 2+ first excited states of even-mass nuclei in the 2s1d shell is tabulated and critically reviewed, and “adopted values” are presented. The results reveal a well defined pattern for the variation of Q2+ through the shell. Predictions of Q2+ made from various nuclear models are tabulated and compared with experiment. For each nucleus the qua ty and quality of the existing data for Q2+, together with the current theoretical significance of the result, are used as criteria to determi whether new experimental work is desirable.

Cosmology at Low Frequencies: The 21 cm Transition and the High-Redshift Universe

August 2006


221 Reads

Observations of the high-redshift Universe with the 21 cm hyperfine line of neutral hydrogen promise to open an entirely new window onto the early phases of cosmic structure formation. Here we review the physics of the 21 cm transition, focusing on processes relevant at high redshifts, and describe the insights to be gained from such observations. These include measuring the matter power spectrum at z~50, observing the formation of the cosmic web and the first luminous sources, and mapping the reionization of the intergalactic medium. The epoch of reionization is of particular interest, because large HII regions will seed substantial fluctuations in the 21 cm background. We also discuss the experimental challenges involved in detecting this signal, with an emphasis on the Galactic and extragalactic foregrounds. These increase rapidly toward low frequencies and are especially severe for the highest redshift applications. Assuming that these difficulties can be overcome, the redshifted 21 cm line will offer unique insight into the high-redshift Universe, complementing other probes but providing the only direct, three-dimensional view of structure formation from z~200 to z~6. Comment: extended review accepted by Physics Reports, 207 pages, 44 figures (some low resolution); version with high resolution figures available at; minor changes to match published version

Zinn-Justin, J.: Quantum field theory in the large N limit: a review. Phys. Rep. 385, 69-228

October 2003


344 Reads

We review the solutions of O(N) and U(N) quantum field theories in the large N limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large N, the method relies on constructing effective field theories for composite fields after integration over the original degrees of freedom. We first solve a general scalar U(φ2) field theory for N large and discuss various non-perturbative physical issues such as critical behaviour. We show how large N results can also be obtained from variational calculations. We illustrate these ideas by showing that the large N expansion allows to relate the (φ2)2 theory and the non-linear σ-model, models which are renormalizable in different dimensions. Similarly, a relation between CP(N−1) and abelian Higgs models is exhibited. Large N techniques also allow solving self-interacting fermion models. A relation between the Gross–Neveu, a theory with a four-fermi self-interaction, and a Yukawa-type theory renormalizable in four dimensions then follows. We discuss dissipative dynamics, which is relevant to the approach to equilibrium, and which in some formulation exhibits quantum mechanics supersymmetry. This also serves as an introduction to the study of the 3D supersymmetric quantum field theory. Large N methods are useful in problems that involve a crossover between different dimensions. We thus briefly discuss finite size effects, finite temperature scalar and supersymmetric field theories. We also use large N methods to investigate the weakly interacting Bose gas. The solution of the general scalar U(φ2) field theory is then applied to other issues like tricritical behaviour and double scaling limit.

Top-cited authors