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91.
We study a model for the gel degradation by an enzyme, where the gel is schematized as a cubic lattice, and the enzyme as a random walker, that cuts the bonds over which it passes. The model undergoes a (reverse) percolation transition, which for low density of enzymes falls in a universality class different from random percolation. In particular, we have measured a gel fraction critical exponent beta=1.0+/-0.1, in excellent agreement with experiments made on the real system.  相似文献   
92.
In order to study analytically the nature of the size segregation in granular mixtures, we introduce a mean field theory in the framework of a statistical mechanics approach, based on Edwards' original ideas. For simplicity we apply the theory to a lattice model for a hard sphere binary mixture under gravity, and we find a new purely thermodynamic mechanism that gives rise to the size segregation phenomenon. By varying the number of small grains and the mass ratio, we find a crossover from the Brazil nut to the reverse Brazil nut effect, which becomes a true phase transition when the number of small grains is larger then a critical value. We suggest that this transition is induced by the effective attraction between large grains due to the presence of small ones (depletion force). Finally the theoretical results are confirmed by numerical simulations of the 3d system under taps.  相似文献   
93.
To understand the origin of the dynamical transition, between high-temperature exponential relaxation and low-temperature nonexponential relaxation, that occurs well above the static transition in glassy systems, a frustrated spin model, with and without disorder, is considered. The model has two phase transitions, the lower being a standard spin glass transition (in the presence of disorder) or fully frustrated Ising (in the absence of disorder), and the higher being a Potts transition. Monte Carlo results clarify that in the model with (or without) disorder the precursor phenomena are related to the Griffiths (or Potts) transition. The Griffiths transition is a vanishing transition which occurs above the Potts transition and is present only when disorder is present, while the Potts transition which signals the effect due to frustration is always present. These results suggest that precursor phenomena in frustrated systems are due either to disorder and/or to frustration, giving a consistent interpretation also for the limiting cases of Ising spin glass and of Ising fully frustrated model, where also the Potts transition is vanishing. This interpretation could play a relevant role in glassy systems beyond the spin systems case.  相似文献   
94.
Z4-Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets   总被引:3,自引:0,他引:3  
When m is odd, spreads in an orthogonal vector space of type+(2m + 2,2) are related to binary Kerdock codes and extremalline-sets in 2m + 1 with prescribed angles. Spreads in a 2m-dimensionalbinary symplectic vector space are related to Kerdock codesover Z4 and extremal line-sets in with prescribed angles. These connections involve binary, realand complex geometry associated with extraspecial 2-groups.A geometric map from symplectic to orthogonal spreads is shownto induce the Gray map from a corresponding Z4-Kerdock codeto its binary image. These geometric considerations lead tothe construction, for any odd composite m, of large numbersof Z4-Kerdock codes. They also produce new Z4-linear Kerdockand Preparata codes. 1991 Mathematics Subject Classification:primary 94B60; secondary 51M15, 20C99.  相似文献   
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