دانلود کتاب آرامش غیرعادی در سیستم های کلوئیدی

When a system is perturbed, it tends to relax back to equilibrium. The simplest theoretical description of relaxation as a function of time t after a perturbation is an exponential law ∝exp(−t/τ ) with a characteristic time τ . Indeed, the decaying motion of damped harmonic oscillators, thermal relaxation of a typical body to its ambient temperature, and discharging of a capacitor all exhibit exponential relaxation, with decay rates independent of the time at which the systems are perturbed from equilibrium. However, in many cases, the relaxation of systems is far from exponential and may depend on their history of perturbation [1]. The dynamics of disordered systems, starting from an initial perturbed state towards its equilibrium, can often be slow and involve a number of different relaxation mechanisms in parallel. For example, logarithmic relaxation has been experimentally observed in compaction of sand in a tube [2], the current decay in superconductors [3], volume relaxation in crumpling paper [4], mechanical relaxation of plant roots [5], and frictional strength [6]. In solid-state physics, glassy systems show extremely slow dynamics below and just above the glass transition. In a variety of systems, at short times (less than the time tw during which an external force has been applied), the relaxation dynamics are logarithmic (∝ln(tw/t)), whereas a power-law (∝tw/t) is observed at long times [7]. These relaxations are much slower than exponential or stretched exponential decay, and their equilibration times are often experimentally unreachable. Similar to glasses, proteins display a slow relaxation process best described by a stretched exponential when perturbed by temperature and pressure [8]. Stretched exponential behaviors are also observed in systems such as molecular and electronic glasses [9], metallic glass-forming melts [10], and granular systems [11]. The relaxation dynamics governed by these laws are anomalously slow and can take longer than usual to relax. Generally, when such systems are perturbed, relaxation to equilibrium involves the relaxation of a spectrum of modes. Each of the modes relaxes independently and exponentially to its equilibrium, but with a different relaxation rate. In some cases, some of these modes may get trapped in metastable states and relax with long equilibration times. Although the best-known relaxation anomalies involve very slow relaxations, there is another class where relaxation can be much faster than expected. The best-known of these investigations concerns an anomalous cooling effect in water, known as the Mpemba effect [12]. Under certain conditions, an initially hot sample of water can freeze faster than an initially warm sample of water. The effect may appear counterintuitive, as our intuitions are set by systems that remain at or near equilibrium; in that case, a system starting at a higher temperature cannot reach equilibrium without passing through all the intermediate temperatures. However, in a thermal quench, systems do not remain in equilibrium. Thus, the state of the system at any instant is not described by a single temperature. A large temperature gradient can be set up by convective currents within the volume and may be represented by a temperature field T (x, t). One can calculate the spatial average of T (x, t) as the water cools, but the average temperature does not represent the water that had been initially prepared at the same temperature. Thus, the system does not necessarily have to pass through all the intermediate states to reach equilibrium and can sometimes cool faster. After their discovery in water, these anomalous cooling effects were observed in other physical systems, suggesting that such behavior may be a general phenomenon in nature