Relaxation and transport contrast

The observation that a specific chemical species existing in a given physicochemical environment is characterized by specific values of and 7 2 is important both in the implementation of imaging pulse sequences to obtain quantitative information and in the modification of the pulse sequences to image selectively one species and/or phase within the sample. 

To perform a quantitative imaging or spectroscopy experiment, the relaxation time characteristics of all species (and relevant physical states of those species) must be fully characterized so that the pulse angles and delays between pulses are optimized for that particular system. In particular, if successive repetitions of a pulse sequence are applied at time scales ( recycle delays ) of the order of or 

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The majority of the early MRI studies specific to catalysis addressed the heterogeneity in structure and transport within catalyst pellets. In-plane spatial resolution achieved in these investigations was approximately 30 pm, and the pellets themselves were of typical dimension 1-5 mm. In the majority of cases, investigations addressed the pure (usually oxide) support so that the quantitative nature of the data obtained was not lost because of the presence of metal (which introduces an unknown degree of nuclear spin relaxation time contrast into the images). 

To account for this phenomenon of spinless conductivity, physicists have introduced the concept of transport via structural defects in the polymer chain. In a conventional semiconductor, an electron can be removed from the valence band and placed in the conduction band, and the structure can be assumed to remain rigid. In contrast, an electronic excitation in polymeric materials is accompanied by a distortion or relaxation of the lattice around the excitation, which minimizes the local lattice strain energy. The combined... 

In contrast to hyperbolic systems, the phase space structure in the mixed system is quite intricate and inhomogeneous, which brings about transport phenomena and relaxation processes essentially different from uniformly hyperbolic cases [3]. A remarkable fact is that qualitatively different classes of motions such as quasi-periodic motions on invariant tori and stochastic motions in chaotic seas coexist in a single phase space. The ordered motions associated with invariant tori are embedded in disordered motions in a self-similar way. The geometry of phase space then reflects the dynamics. 

The spectrum of Lyapunov exponents provides fundamental and quantitative characterization of a dynamical system. Lyapunov exponents of a reference trajectory measure the exponential rates of principal divergences of the initially neighboring trajectories [1], Motion with at least one positive Lyapunov exponent has strong sensitivity to small perturbations of the initial conditions, and is said to be chaotic. In contrast, the principal divergences in regular motion, such as quasi-periodic motion, are at most linear in time, and then all the Lyapunov exponents are vanishing. The Lyapunov exponents have been studied both theoretically and experimentally in a wide range of systems [2-5], to elucidate the connections to the physical phenomena of importance, such as transports in phase spaces and nonequilibrium relaxation [6,7]. 

The contrasting structure of the plates and the separators is also relevant to the functioning of the battery. For example, the capillary pressures dictate that electrolyte fills the plates preferentially. This preferential filling appears to be the ideal situation since it can best support the electrochemical reaction, i.e., it leaves the separator partially saturated so that movement of electrolyte can provide pathways for gas transport. If, however, the overall saturation is too low or there is excessive loss of water, the separator will dry out and give rise to an increase in the internal resistance of the battery and the possibility of thermal runaway. An increase in internal resistance, and consequent low service-life, can also result if the compression between separators and battery plates relaxes over a period of time. Overcompression may cause fibres to fracture with a loss of resilience, i.e., the separators lose the ability to return to original thickness after a high pressure is applied and... 

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