Disordered media physics

Percolation phenomena deal with the effect of clustering and coimectivity of microscopic elements in a disordered medium [129], Percolation theory represents a random composite material as a network or lattice structure of two or more distinct types of microscopic elements or phase domains, the so-called percolation sites. These elements represent mutually exclusive physical properties, e.g., electrically conducting vs. isolating phase domains, pore space vs. solid matrix, atoms with spin up vs. spin down states. Here, we will refer to black and white elements for definiteness. The network onto which black and white elements of the composite medium are distributed could be continuous (continuum percolation) or discrete (discrete or lattice percolation) it could be a disordered or regular network. With a probability p a randomly chosen percolation site will be... 

Druger, S.D., Ratner, M.A., Nitzan, A. (1985) Generalized hopping model for frequency-dependent transport in a dynamically disordered medium, with applications to polymer solid electrolytes. Physical Review B, 31, 3939. 

We are not going to deal with all these examples of application of percolation theory to catalysis in this paper. Although the physics of these problems are different the basic numerical and mathematical techniques are very similar. For the deactivation problem discussed here, for example, one starts with a three-dimensional network representation of the catalyst porous structure. Systematic procedures of how to map any disordered porous medium onto an equivalent random network of pore bodies and throats have been developed and detailed accounts can be found in a number of publications ( 8). For the purposes of this discussion it suffices to say that the success of the mapping techniques strongly depends on the availability of quality structural data, such as mercury porosimetry, BET and direct microscopic observations. Of equal importance, however, is the correct interpretation of this data. It serves no purpose to perform careful mercury porosimetry and BET experiments and then use the wrong model (like the bundle of pores) for data analysis and interpretation. 

A fully microscopic interpretation of the temperature dependence of the absorption maximum, even well above any order-disorder transition temperature, is a formidable task because of the potential importance of many complicated physical factors (27-30). As a first attack on this problem, we have adopted a simple mean-field (or effective-medium) approach (28-30) with the assumption that the absorption peak (to) is linearly perturbed from its limiting dl -trans value ((Orod) by the presence of bond rotational defects (free energy of formation, e)... 

Schirmacher, W., Anomalous diffusion in disordered systems an effective medium description. Berichte der Bunsengesellschaft fur Physical Chemie, 1991. 95 pp. 368-376 Gefen, Y., A. Aharony, and S. Alexander, Anomalous diffusion on percolating clusters. Physical Review Letters, 1983. 50 pp. 77-80... 

In future work, we wiU extend and validate the different models to other class of diseases. Approximately 1-1.5 % of the French population suffer from dementia and the causes of dementia are neurological disorders such as Alzheimer s disease (which causes 50 %-70 % of aU dementia), blood flow-related (vascular) disorders such as multi-infarct diseases, inherited disorders such as Huntington s disease, and infections such as HIV [15]. In fact, we would like to simulate the patient s progress in order to forecast and to analyze the need for long, medium and short-term care. This allows us to evaluate human, financial and physical resources in the future. 

In condensed matter physics, the effects of disorder, defects, and impurities are relevant for many materials properties hence their understanding is of utmost importance. The effects of randomness and disorder can be dramatic and have been investigated for a variety of systems covering a wide field of complex phenomena [109]. Examples include the pinning of an Abrikosov flux vortex lattice by impurities in superconductors [110], disorder in Ising magnets [111], superfluid transitions of He in a porous medium [112], and phase transitions in randomly confined smectic liquid crystals [113, 114]. 

Within the CPA, the real disordered material is replaced by a uniform effective medium that is determined in a self-consistent way through the requirement that the additional scattering resulting from embedding a real atom of the alloy into this medium vanishes when averaged over the components of the alloy. This eminently physical requirement is attended to by a great number of further desirable properties. 

Demonstration of an intra-articular effusion is a major step in the investigation of musculoskeletal disorders, as it points the clinician s attention toward a joint problem and excludes other extra-articular sources of pain and disability. A joint effusion can derive from traumatic or mechanical causes as well as from inflammatory or infectious synovitis more rarely, it can be related to neoplastic conditions. At physical examination, detection of synovial effusion depends on the overall amount of fluid and the type of joint is involved. Accurate palpation allows detection of medium to large effu-... 

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