A theoretical perspective is provided on the glass transition in molecular liquids at thermal equilibrium, on the spatially heterogeneous and aging dynamics of disordered materials, and on the rheology of soft glassy materials. We start with a broad introduction to the field and emphasize its connections with other subjects and its relevance. The important role played by computer simulations in studying and understanding the dynamics of systems close to the glass transition at the molecular level is given. The recent progress on the subject of the spatially heterogeneous dynamics that characterizes structural relaxation in materials with slow dynamics is reviewed. The main theoretical approaches are presented describing the glass transition in supercooled liquids, focusing on theories that have a microscopic, statistical mechanics basis. We describe both successes and failures and critically assess the current status of each of these approaches. The physics of aging dynamics in disordered materials and the rheology of soft glassy materials are then discussed, and recent theoretical progress is described. For each section, an extensive overview is given of the most recent advances, but we also describe in some detail the important open problems that will occupy a central place in this field in the coming years.

Theoretical perspective on the glass transition and amorphous materials

Mammalian skeletal muscle shows an enormous variability in its functional features such as rate of force production, resistance to fatigue, and energy metabolism, with a wide spectrum from slow aer...

Calcium Ion in Skeletal Muscle: Its Crucial Role for Muscle Function, Plasticity, and Disease

Magnetic Relaxation in Fine‐Particle Systems

The physics of the photorefractive effect is briefly discussed. A coupled-mode theory is then developed to analyze the coupling of two coherent electromagnetic waves inside a photorefractive medium. Both codirectional and contradirectional coupling are considered. The coupled-mode theory is then extended to consider the case of nondegenerate two-wave mixing. A discussion of the fundamental limit of the speed of photorefractive effect is then introduced. The coupling of two polarized beams inside photorefractive cubic crystals is considered. The formulation is focused on the cross-polarization two-beam coupling in semiconductors such as GaAs. The coupling of two electromagnetic waves inside a Kerr medium and the electrostrictive Kerr effect are discussed. A new concept of nonlinear Bragg scattering is introduced. The similarity among various kinds of two-wave mixing, including stimulated Brillouin scattering and stimulated Raman scattering are pointed out. Several applications of two-wave mixing are discussed. These include photorefractive resonators, optical nonreciprocity, resonator model of self-pumped phase conjugators, real-time holography, and nonlinear optical information processing. >

Two-wave mixing in nonlinear media

This review reports on the research done during past years on violations of the fluctuation–dissipation theorem (FDT) in glassy systems. It is focused on the existence of a quasi-fluctuation–dissipation theorem (QFDT) in glassy systems and the current supporting knowledge gained from numerical simulation studies. It covers a broad range of non-stationary aging and stationary driven systems such as structural glasses, spin glasses, coarsening systems, ferromagnetic models at criticality, trap models, models with entropy barriers, kinetically constrained models, sheared systems and granular media. The review is divided into four main parts: (1) an introductory section explaining basic notions related to the existence of the FDT in equilibrium and its possible extension to the glassy regime (QFDT), (2) a description of the basic analytical tools and results derived in the framework of some exactly solvable models, (3) a detailed report of the current evidence in favour of the QFDT and (4) a brief digression on the experimental evidence in its favour. This review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the QFDT as well as for the more expert readers who may be interested in more specific results.

http://iopscience.iop.org/article/10.1088/0305-4470/36/21/201/pdf

Violation of the fluctuation–dissipation theorem in glassy systems: basic notions and the numerical evidence

Large values of the exponential gain coefficient Γ are obtained (Γ≂8–12 cm−1) when recording with a moving grating in photorefractive BSO crystals (nearly degenerate two‐wave mixing; drift recording mode). The resolution of the Kukhtarev’s equations with a moving grating shows a resonance effect which at the optimum velocity makes the modulation of the photoinduced space charge field Esc higher. An optimum of the grating spacing also exists: Λopt:2π(E0/NA)(μe/eγR)1/2. In such conditions, the space charge field is phase shifted by π/2 with respect to the incident fringe pattern; this allows an efficient beam coupling between the two recording beams. The dependence of the gain Γ versus the incident beam ratio β of the two interfering waves is interpreted by including the second‐order term in the Fourier development of Esc. The conditions allowing one to obtain a reasonable agreement between the theory and experiments are presented and discussed, as well as the adopted values of the crystals’ parameters.

Two‐beam coupling in photorefractive Bi12SiO20 crystals with moving grating: Theory and experiments

The magnetic properties of a spin-glass depend on the time spent in the low-temperature phase: this is the so-called ageing phenomenon. We present measurements of the low-frequency a.c. susceptibility (0.01 to 0.1 Hz) and of the relaxation of the thermo-remanent magnetization in the CdCr 1.7 In 0.3 S 4 insulating spin-glass; we investigate the influence of temperature variations on the ageing processes in the spin-glass phase, in order to get a better insight into their mechanism. The wide spectrum of relaxation times observed in spin-glass dynamics reflects the existence of many energy valleys in the phase space; a hierarchical organization of these valleys, whose bifurcations appear as the temperature is decreased, is the simplest picture which accounts for our results Mesures de la susceptibilite magnetique (0,01-0,1 Hz) et de la relaxation de l'aimantation thermoremanente dans CdCr 1,7 In 0,3 S 4 ; analyse de l'influence des variations de temperature sur le vieillissement dans la phase verre de spin. Un schema d'organisation hierarchique des vallees d'energies dans l'espace des phases permet de rendre compte de l'ensemble des resultats experimentaux

Ageing phenomena in a spin-glass : effect of temperature changes below Tg

We present a quantitative comparison between dynamic measurements on spin glasses. The case of CdIn0.3Cr1.7S4 is discussed in detail and references are made to CsNiFeF6 and Ag:Mn (2.6%). The measured quantities are the relaxation of the thermoremanent magnetization MTRM(t) in the range of observation times 1–105 s, the out‐of‐phase susceptibility χ‘(ω) in the range 10−3–5×104 Hz, and the magnetic noise power spectrum M2(ω) between 10−2 and 103 Hz. The aging of the thermoremanent magnetization relaxation is analyzed on the basis of a phenomenological theory of time scaling which allows to derive the form of the equilibrium relaxation. It is shown that the measured values of χ‘ and ∼(M2(ω)) are related according to the fluctuation dissipation theorem (FDT). The consequences of the applicability of the FDT in the frequency domain are discussed, with reference to the expected violation of the theorem in the spin‐glass phase at ω=0. An important modification of the frequency dependence of χ‘(ω) is observed at ...

Spin‐glass dynamics from magnetic noise, relaxation, and susceptibility measurements (invited)

Filters with binary amplitude (i.e., 0 and 1) that provide optimal trade-offs among three important criteria (i.e., noise robustness, correlation-peak sharpness, and Horner efficiency) are presented. A method for optimizing the discrimination capabilities is also presented.

Multicriteria optimal binary amplitude phase-only filters

The application of a regularization technique to filter synthesis in pattern recognition with synthetic discriminant function filters is presented. The proposed technique uses the stabilizing functional approach for two-dimensional ill-posed problems. Filter synthesis is thus formulated as the minimization of some relevant criteria with specified correlation values for some training input images and limited maximum value of a stabilizing functional. The choice of a particular stabilizing functional to be minimized is related to a priori knowledge regarding the pattern-recognition problem. The analogy between the regularization methods and optimal trade-off filters is also presented and is illustrated with numerical experiments.

Ph. Refregier

Papers

Two‐beam coupling in photorefractive Bi12SiO20 crystals with moving grating: Theory and experiments

Ageing phenomena in a spin-glass : effect of temperature changes below Tg

Spin‐glass dynamics from magnetic noise, relaxation, and susceptibility measurements (invited)

Multicriteria optimal binary amplitude phase-only filters

Application of the stabilizing functional approach to pattern-recognition filters