Solid friction from stick–slip down to pinning and aging

We review the present state of understanding of solid friction at low velocities and for systems with negligibly small wear effects. We first analyze in detail the behavior of friction at interfaces between macroscopic hard rough solids, whose main dynamical features are well described by the Rice–Ruina rate and state-dependent constitutive law. We show that it results from two combined effects: (i) the threshold rheology of nanometer-thick junctions jammed under confinement into a soft glassy structure and (ii) the geometric aging, i.e. slow growth of the real area of contact via asperity creep interrupted by sliding. Closer analysis leads to identifying a second aging-rejuvenation process, at work within the junctions themselves. We compare the effects of structural aging at such multicontact, very highly confined, interfaces with those met under different confinement levels, namely boundary lubricated contacts and extended adhesive interfaces involving soft materials (hydrogels, elastomers). This leads us to propose a classification of frictional junctions in terms of the relative importance of jamming and adsorption-induced metastability.

Solid friction from stick–slip down to pinning and aging

All authors

Tristan Baumberger &; Christiane Caroli

https://doi.org/10.1080/00018730600732186

Published online:

28 November 2010

Table     

The relationship between attractive interparticle forces and bulk behaviour in dry and uncharged fine powders

Memento, homo, qui pulvis est et pulverem reverteris.

Genesis 3

Polvos serán, mas polvo enamorado.

Francisco de Quevedo

The physics of granular materials in ambient gases is governed by interparticle forces, gas–particle interaction, geometry of particle positions and geometry of particle contacts. At low consolidations these are strongly dependent on the external forces, boundary conditions and on the assembling procedure. For dry fine powders of micron and sub-micron particle size interparticle attractive forces are typically much higher than particle weight, and particles tend to aggregate. Because of this, cohesive powders fracture before breaking, flow and avalanche in coherent blocks much larger than the particle size. Similarly the drag force for micron sized particles is large compared to their weight for velocities as low as 1?mm/s. Due to this extreme sensitivity to interstitial gas flow, powders transit directly from plastic dense flows to fluidization without passing through collisional regimes with negligible gas interaction. These two features, strong attractive forces and strong gas interaction make powder behaviour differ qualitatively from the behaviour of large, noncohesive grains. In this paper we investigate the implications of these two features on the bulk powder behaviour. More in particular, the aim of this paper is to examine the relationship between attractive interparticle forces at grain level, with solid bulk properties at low consolidations (solid fraction, stresses), fluidization (aggregation, settling) and flow regime boundaries (plastic flow, inertial flow, fluidization and suspension). Many of the experimental results reported here are for dry and uncharged fine powders made of polymer particles of the order of 10 microns in diameter. However, the basic concepts and methodology are of general applicability.

The relationship between attractive interparticle forces and bulk behaviour in dry and uncharged fine powders

All authors

A. Castellanos

https://doi.org/10.1080/17461390500402657

Published online:

19 February 2007

Table     

Spin-polarised currents and magnetic domain walls

Electrical currents flowing in ferromagnetic materials are spin-polarised as a result of the spin-dependent band structure. When the spatial direction of the polarisation changes, in a domain structure, the electrons must somehow accommodate the necessary change in direction of their spin angular momentum as they pass through the wall. Reflection, scattering, or a transfer of angular momentum onto the lattice are all possible outcomes, depending on the circumstances. This gives rise to a variety of different physical effects, most importantly a contribution to the electrical resistance caused by the wall, and a motion of the wall driven by the spin-polarised current.

Historical and recent research on these topics is reviewed.

Spin-polarised currents and magnetic domain walls

All authors

C. H. Marrows

https://doi.org/10.1080/00018730500442209

Published online:

19 February 2007

Table     

Scale invariance in plastic flow of crystalline solids

From the traditional viewpoint of continuum plasticity, plastic deformation of crystalline solids is, at least in the absence of so-called plastic instabilities, envisaged as a smooth and quasi-laminar flow process. Recent theoretical and experimental investigations, however, demonstrate that crystal plasticity is characterized by large intrinsic spatio-temporal fluctuations with scale-invariant characteristics: In time, deformation proceeds through intermittent bursts with power-law size distributions; in space, deformation patterns and deformation-induced surface morphology are characterized by long-range correlations, self-similarity and/or self-affine roughness. We discuss this scale-invariant behaviour in terms of robust scaling associated with a non-equilibrium critical point (‘yielding transition’).

Scale invariance in plastic flow of crystalline solids

All authors

Michael Zaiser

https://doi.org/10.1080/00018730600583514

Published online:

01 February 2007

Table     

Wet granular materials

Most studies on granular physics have focused on dry granular media, with no liquids between the grains. However, in geology and many real world applications (e.g. food processing, pharmaceuticals, ceramics, civil engineering, construction, and many industrial applications), liquid is present between the grains. This produces inter-grain cohesion and drastically modifies the mechanical properties of the granular media (e.g. the surface angle can be larger than 90 degrees). Here we present a review of the mechanical properties of wet granular media, with particular emphasis on the effect of cohesion. We also list several open problems that might motivate future studies in this exciting but mostly unexplored field.

Wet granular materials

All authors

Namiko Mitarai &; Franco Nori

https://doi.org/10.1080/00018730600626065

Published online:

01 February 2007

Table     

Glassy colloidal systems

This review focuses on recent developments in the theoretical, numerical and experimental study of slow dynamics in colloidal systems, with a particular emphasis on the glass transition phenomenon. Colloidal systems appear to be particularly suited for tackling the general problem of dynamic arrest, since they show a larger flexibility compared to atomic and molecular glasses because of their size and the possibility of manipulating the physical and chemical properties of the samples. Indeed, a wealth of new effects, not easily observable in molecular liquids, have been predicted and measured in colloidal systems. The slow dynamic behavior of three classes of colloidal suspension is reviewed – hard colloids, short-range attractive colloids and soft colloidal systems – selecting the model systems among the most prominent candidates for grasping the essential features of dynamic arrest. Emphasis is on the possibility of performing a detailed comparison between experimental data and theoretical predictions based on the mode coupling theory of the glass transition. Finally, the importance of understanding the system's kinetic arrest phase diagram, i.e. the regions in phase space where disordered arrested states can be expected, is stressed. When and how these states are kinetically stabilized with respect to the ordered lowest free energy phases is then examined in order to provide a framework for interpreting and developing new ideas in the study of new materials.

Glassy colloidal systems

All authors

F. Sciortino &; P. Tartaglia

https://doi.org/10.1080/00018730500414570

Published online:

19 February 2007

Table     

Statistical models of brittle fragmentation

Recent developments in statistical models for fragmentation of brittle material are reviewed. The generic objective of these models is understanding the origin of the fragment size distributions (FSDs) that result from fracturing brittle material. Brittle fragmentation can be divided into two categories: (1) Instantaneous fragmentation for which breakup generations are not distinguishable and (2) continuous fragmentation for which generations of chronological fragment breakups can be identified. This categorization becomes obvious in mining industry applications where instantaneous fragmentation refers to blasting of rock and continuous fragmentation to the consequent crushing and grinding of the blasted rock fragments. A model of unstable cracks and crack-branch merging contains both of the FSDs usually related to instantaneous fragmentation: the scale invariant FSD with the power exponent (2?1/D) and the double exponential FSD which relates to Poisson process fragmentation. The FSDs commonly related to continuous fragmentation are: the lognormal FSD originating from uncorrelated breakup and the power-law FSD which can be modeled as a cascade of breakups. Various solutions to the generic rate equation of continuous fragmentation are briefly listed. Simulations of crushing experiments reveal that both cascade and uncorrelated fragmentations are possible, but that also a mechanism of maximizing packing density related to Apollonian packing may be relevant for slow compressive crushing.

Statistical models of brittle fragmentation

All authors

J. A. Åström

https://doi.org/10.1080/00018730600731907

Published online:

28 November 2010

Table     

Measurement of momentum distribution of lightatoms and molecules in condensed matter systems using inelastic neutron scattering

Studies of single-particle momentum distributions in light atoms and molecules are reviewed with specific emphasis on experimental measurements using the deep inelastic neutron scattering technique at eV energies. The technique has undergone a remarkable development since the mid-1980s, when intense fluxes of epithermal neutrons were made available from pulsed neutron sources. These types of measurements provide a probe of the short-time dynamics of the recoiling atoms or molecules as well as information on the local structure of the materials. The paper introduces both the theoretical framework for the interpretation of deep inelastic neutron scattering experiments and thoroughly illustrates the physical principles underlying the impulse approximation from light atoms and molecules. The most relevant experimental studies performed on a variety of condensed matter systems in the last 20 years are reviewed. The experimental technique is critically presented in the context of a full list of published work. It is shown how, in some cases, these measurements can be used to extract directly the effective Born–Oppenheimer potential. A summary of the progress made to date in instrument development is also provided. Current data analysis and the interpretation of the results for a variety of physical systems is chosen to illustrate the scope and power of the method. The review ends with a brief consideration of likely developments in the foreseeable future. Particular discussion is given to the use of the VESUVIO spectrometer at ISIS.

Measurement of momentum distribution of lightatoms and molecules in condensed matter systems using inelastic neutron scattering

All authors

C. Andreani, D. Colognesi, J. Mayers, G. F. Reiter &; R. Senesi

https://doi.org/10.1080/00018730500403136

Published online:

19 February 2007

Table     

STABILITY-INDICATING METHODS FOR DETERMINATION OF MELOXICAM AND TENOXICAM IN THE PRESENCE OF THEIR DEGRADATION PRODUCTS

ABSTRACT

A spectrophotometric and a spectrofluorimetric methods are developed for the determination of two nonsteroidal anti-inflammatory drugs meloxicam I and tenoxicam II in the presence of their degradation products, namely 5-methyl-2-aminothiazole (III), benzothiazine carboxylic acid (IV), for meloxicam, pyridine-2-amine (V) and methyl 4-hydroxy-2-methyl-2H-thienol[2,3-e]1,2-thiazine-3-carboxylate-1, 1-dioxide (VI) for tenoxicam, Fig. 1.

STABILITY-INDICATING METHODS FOR DETERMINATION OF MELOXICAM AND TENOXICAM IN THE PRESENCE OF THEIR DEGRADATION PRODUCTS

All authors

Elham A. Taha, Nahla N. Salama & Laila S. Abdel Fattah

https://doi.org/10.1081/SL-120013886

Published online:

01 September 2006

Figure 1. The structure of the studied drugs and their degradation products.     

13.

Quantum dynamics in strong fluctuating fields     

Igor Goychuk  Peter Hänggi 《物理学进展》2013,62(6-7):525-584

A large number of multifaceted quantum transport processes in molecular systems and physical nanosystems, such as e.g. nonadiabatic electron transfer in proteins, can be treated in terms of quantum relaxation processes which couple to one or several fluctuating environments. A thermal equilibrium environment can conveniently be modelled by a thermal bath of harmonic oscillators. An archetype situation provides a two-state dissipative quantum dynamics, commonly known under the label of a spin-boson dynamics. An interesting and nontrivial physical situation emerges, however, when the quantum dynamics evolves far away from thermal equilibrium. This occurs, for example, when a charge transferring medium possesses nonequilibrium degrees of freedom, or when a strong time-dependent control field is applied externally. Accordingly, certain parameters of underlying quantum subsystem acquire stochastic character. This may occur, for example, for the tunnelling coupling between the donor and acceptor states of the transferring electron, or for the corresponding energy difference between electronic states which assume via the coupling to the fluctuating environment an explicit stochastic or deterministic time-dependence. Here, we review the general theoretical framework which is based on the method of projector operators, yielding the quantum master equations for systems that are exposed to strong external fields. This allows one to investigate on a common basis, the influence of nonequilibrium fluctuations and periodic electrical fields on those already mentioned dynamics and related quantum transport processes. Most importantly, such strong fluctuating fields induce a whole variety of nonlinear and nonequilibrium phenomena. A characteristic feature of such dynamics is the absence of thermal (quantum) detailed balance.

Quantum dynamics in strong fluctuating fields

All authors

Igor Goychuk &; Peter Hänggi

https://doi.org/10.1080/00018730500429701

Published online:

19 February 2007

Table     

14.

Statistical models of fracture     

Mikko J. Alava  Phani K. V. V. Nukala  Stefano Zapperi 《物理学进展》2013,62(3-4):349-476

Disorder and long-range interactions are two of the key components that make material failure an interesting playfield for the application of statistical mechanics. The cornerstone in this respect has been lattice models of the fracture in which a network of elastic beams, bonds, or electrical fuses with random failure thresholds are subject to an increasing external load. These models describe on a qualitative level the failure processes of real, brittle, or quasi-brittle materials. This has been particularly important in solving the classical engineering problems of material strength: the size dependence of maximum stress and its sample-to-sample statistical fluctuations. At the same time, lattice models pose many new fundamental questions in statistical physics, such as the relation between fracture and phase transitions. Experimental results point out to the existence of an intriguing crackling noise in the acoustic emission and of self-affine fractals in the crack surface morphology. Recent advances in computer power have enabled considerable progress in the understanding of such models. Among these partly still controversial issues, are the scaling and size-effects in material strength and accumulated damage, the statistics of avalanches or bursts of microfailures, and the morphology of the crack surface. Here we present an overview of the results obtained with lattice models for fracture, highlighting the relations with statistical physics theories and more conventional fracture mechanics approaches.

Statistical models of fracture

All authors

Mikko J. Alava, Phani K. V. V. Nukala &; Stefano Zapperi

https://doi.org/10.1080/00018730300741518

Published online:

28 November 2010

Table     

15.

Energetics of naphthalene derivatives,IV+: a calorimetric and calculational thermochemical study of the isomeric naphthalenemethanols     

M. A. R. Matos  V. M. F. Morais  C. C. S. Sousa  M. V. Roux  R. Notario 《Molecular physics》2013,111(13-14):1789-1796

The standard (p°?=?0.1?MPa) molar energies of combustion in oxygen, at T?=?298.15?K, of 1-naphthalenemethanol and 2-naphthalenemethanol were measured by static bomb calorimetry. The values of the standard molar enthalpies of sublimation, at T?=?298.15?K, were obtained by Calvet microcalorimetry. Combining these results the standard molar enthalpies of formation of the compounds, in the gas phase, at T?=?298.15?K, have been calculated.

Energetics of naphthalene derivatives, IV+ ⁺Paper III: Roux, M.V., Temprado, M., Notario, R., Verevkin, S.P., Emel’yanenko, V.N., DeMasters, D.E., Liebman, J.F. Mol. Phys., 102, 1909 (2004). : a calorimetric and calculational thermochemical study of the isomeric naphthalenemethanols

All authors

M. A. R. Matos, V. M. F. Morais, C. C. S. Sousa, M. V. Roux, R. Notario &; J. F. Liebman

https://doi.org/10.1080/00268970701413891

Published online:

04 December 2010

Table     

16.

Magnetic fluctuations and itinerant ferromagnetism in two-dimensional systems with Van Hove singularities     

P. A. Igoshev  A. A. Katanin  V. Yu. Irkhin 《Journal of Experimental and Theoretical Physics》2007,105(5):1043-1056

A criterion for ferromagnetism in two-dimensional systems with the Fermi level near Van Hove singularities (VHSs) is analyzed. In the quasistatic approximation applied to a spin-fermion model, it is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction I between the electronic and spin degrees of freedom is sufficiently large (I > I _c). The critical interaction I _c is much greater than its value determined from the Stoner criterion; hence, the latter criterion is not an adequate criterion for ferromagnetism in the presence of Van Hove singularities in the electronic spectrum. By combining the quasistatic approximation with the method of equations of motion, the electronic self-energy is obtained in the first order in the inverse number of spin components.     

17.

Phase diagram and transport properties of Sb-doped Ca0.88La0.12Fe2As2 single crystals     

Xiang-Zhuo Xing  Wei Zhou  Chun-Qiang Xu  Nan Zhou  Fei-Fei Yuan  Yu-Feng Zhang  Xiao-Feng Xu  Zhi-Xiang Shi 《Frontiers of Physics》2017,12(4):127401

The effects of isovalent Sb substitution on the superconducting properties of the Ca_0.88La_0.12Fe₂(As_1-ySb_y)₂ system have been studied through electrical resistivity measurements. It is seen that the antiferromagnetic or structural transition is suppressed with Sb content, and a high-T_c superconducting phase, accompanied by a low-T_c phase, emerges at 0.02 ≤ y ≤ 0.06. In this intermediate-doping regime, normal-state transport shows non-Fermi-liquid-like behaviors with nearly T-linear resistivity above the high-T_c phase. With further Sb doping, this high-T_c phase abruptly vanishes for y > 0.06 and the conventional Fermi liquid is restored, while the low-T_c phase remains robust against Sb impurities. The coincidence of the high-T_c phase and non-Fermi liquid transport behaviors in the intermediate Sb-doping regime suggests that AFM fluctuations play an important role in the observed non-Fermi liquid behaviors, which may be intimately related to the unusual nonbulk high-T_c phase in this system.     

18.

Decay of B_c (3S) → B D     

V. V. Kiselev   《Physics letters. [Part B]》1997,390(1-4)

The decay constant for the vector state of 3S-level in the heavy (

Full-size image

c)-quarkonium is evaluated in the framework of sum rules for the mesonic currents. A scaling relation for the constants of vector quarkonia with different quark contents is derived. The numerical estime gives Γ (B^*+_c(3S) → B⁺ D⁰) = 90 ± 35 MeV.     

19.

Semileptonic decays B → (π, )eν in relativistic quark model     

D. Melikhov 《Physics letters. [Part B]》1996,380(3-4)

Quark model results for the B → π, decays are analysed, making use of the dispersion formulation of the model: The form factors at q² > 0 are expressed as relativistic invariant double spectral representation over invariant masses of the initial and final mesons through their light-cone wave functions. The dependence of the results on the quark model parameters is studied. For various versions of the quark model the ranges

Full-size image

,

Full-size image

, and Γ_L/Γ_T = 0.7 ± 0.08 are found. The effects of the constituent quark transition form factor are briefly discussed.     

20.

Frequency and amplitude stabilization device for a cw CO₂ laser     

D. Courtois  C. Thiebeaux  A. Delahaigue  E. Merienne  P. Jouve 《Optics & Laser Technology》1981,13(3):155-159

     

Quantum dynamics in strong fluctuating fields

A large number of multifaceted quantum transport processes in molecular systems and physical nanosystems, such as e.g. nonadiabatic electron transfer in proteins, can be treated in terms of quantum relaxation processes which couple to one or several fluctuating environments. A thermal equilibrium environment can conveniently be modelled by a thermal bath of harmonic oscillators. An archetype situation provides a two-state dissipative quantum dynamics, commonly known under the label of a spin-boson dynamics. An interesting and nontrivial physical situation emerges, however, when the quantum dynamics evolves far away from thermal equilibrium. This occurs, for example, when a charge transferring medium possesses nonequilibrium degrees of freedom, or when a strong time-dependent control field is applied externally. Accordingly, certain parameters of underlying quantum subsystem acquire stochastic character. This may occur, for example, for the tunnelling coupling between the donor and acceptor states of the transferring electron, or for the corresponding energy difference between electronic states which assume via the coupling to the fluctuating environment an explicit stochastic or deterministic time-dependence. Here, we review the general theoretical framework which is based on the method of projector operators, yielding the quantum master equations for systems that are exposed to strong external fields. This allows one to investigate on a common basis, the influence of nonequilibrium fluctuations and periodic electrical fields on those already mentioned dynamics and related quantum transport processes. Most importantly, such strong fluctuating fields induce a whole variety of nonlinear and nonequilibrium phenomena. A characteristic feature of such dynamics is the absence of thermal (quantum) detailed balance.

Quantum dynamics in strong fluctuating fields

All authors

Igor Goychuk &; Peter Hänggi

https://doi.org/10.1080/00018730500429701

Published online:

19 February 2007

Table     

Statistical models of fracture

Disorder and long-range interactions are two of the key components that make material failure an interesting playfield for the application of statistical mechanics. The cornerstone in this respect has been lattice models of the fracture in which a network of elastic beams, bonds, or electrical fuses with random failure thresholds are subject to an increasing external load. These models describe on a qualitative level the failure processes of real, brittle, or quasi-brittle materials. This has been particularly important in solving the classical engineering problems of material strength: the size dependence of maximum stress and its sample-to-sample statistical fluctuations. At the same time, lattice models pose many new fundamental questions in statistical physics, such as the relation between fracture and phase transitions. Experimental results point out to the existence of an intriguing crackling noise in the acoustic emission and of self-affine fractals in the crack surface morphology. Recent advances in computer power have enabled considerable progress in the understanding of such models. Among these partly still controversial issues, are the scaling and size-effects in material strength and accumulated damage, the statistics of avalanches or bursts of microfailures, and the morphology of the crack surface. Here we present an overview of the results obtained with lattice models for fracture, highlighting the relations with statistical physics theories and more conventional fracture mechanics approaches.

Statistical models of fracture

All authors

Mikko J. Alava, Phani K. V. V. Nukala &; Stefano Zapperi

https://doi.org/10.1080/00018730300741518

Published online:

28 November 2010

Table     

Energetics of naphthalene derivatives,IV+: a calorimetric and calculational thermochemical study of the isomeric naphthalenemethanols

The standard (p°?=?0.1?MPa) molar energies of combustion in oxygen, at T?=?298.15?K, of 1-naphthalenemethanol and 2-naphthalenemethanol were measured by static bomb calorimetry. The values of the standard molar enthalpies of sublimation, at T?=?298.15?K, were obtained by Calvet microcalorimetry. Combining these results the standard molar enthalpies of formation of the compounds, in the gas phase, at T?=?298.15?K, have been calculated.

Energetics of naphthalene derivatives, IV+ ⁺Paper III: Roux, M.V., Temprado, M., Notario, R., Verevkin, S.P., Emel’yanenko, V.N., DeMasters, D.E., Liebman, J.F. Mol. Phys., 102, 1909 (2004). : a calorimetric and calculational thermochemical study of the isomeric naphthalenemethanols

All authors

M. A. R. Matos, V. M. F. Morais, C. C. S. Sousa, M. V. Roux, R. Notario &; J. F. Liebman

https://doi.org/10.1080/00268970701413891

Published online:

04 December 2010

Table     

Magnetic fluctuations and itinerant ferromagnetism in two-dimensional systems with Van Hove singularities

A criterion for ferromagnetism in two-dimensional systems with the Fermi level near Van Hove singularities (VHSs) is analyzed. In the quasistatic approximation applied to a spin-fermion model, it is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction I between the electronic and spin degrees of freedom is sufficiently large (I > I _c). The critical interaction I _c is much greater than its value determined from the Stoner criterion; hence, the latter criterion is not an adequate criterion for ferromagnetism in the presence of Van Hove singularities in the electronic spectrum. By combining the quasistatic approximation with the method of equations of motion, the electronic self-energy is obtained in the first order in the inverse number of spin components.     

Phase diagram and transport properties of Sb-doped Ca0.88La0.12Fe2As2 single crystals

The effects of isovalent Sb substitution on the superconducting properties of the Ca_0.88La_0.12Fe₂(As_1-ySb_y)₂ system have been studied through electrical resistivity measurements. It is seen that the antiferromagnetic or structural transition is suppressed with Sb content, and a high-T_c superconducting phase, accompanied by a low-T_c phase, emerges at 0.02 ≤ y ≤ 0.06. In this intermediate-doping regime, normal-state transport shows non-Fermi-liquid-like behaviors with nearly T-linear resistivity above the high-T_c phase. With further Sb doping, this high-T_c phase abruptly vanishes for y > 0.06 and the conventional Fermi liquid is restored, while the low-T_c phase remains robust against Sb impurities. The coincidence of the high-T_c phase and non-Fermi liquid transport behaviors in the intermediate Sb-doping regime suggests that AFM fluctuations play an important role in the observed non-Fermi liquid behaviors, which may be intimately related to the unusual nonbulk high-T_c phase in this system.     

Decay of Bc (3S) → B D

The decay constant for the vector state of 3S-level in the heavy (

Full-size image

c)-quarkonium is evaluated in the framework of sum rules for the mesonic currents. A scaling relation for the constants of vector quarkonia with different quark contents is derived. The numerical estime gives Γ (B^*+_c(3S) → B⁺ D⁰) = 90 ± 35 MeV.     

Semileptonic decays B → (π, )eν in relativistic quark model

Quark model results for the B → π, decays are analysed, making use of the dispersion formulation of the model: The form factors at q² > 0 are expressed as relativistic invariant double spectral representation over invariant masses of the initial and final mesons through their light-cone wave functions. The dependence of the results on the quark model parameters is studied. For various versions of the quark model the ranges

Full-size image

,

Full-size image

, and Γ_L/Γ_T = 0.7 ± 0.08 are found. The effects of the constituent quark transition form factor are briefly discussed.