Fuzzy sets: A topos-logical point of view

Bénabou deduction-categories are defined, with a set of additional assumptions that define categories with formal finite limits (resp. formal regular categories, formal logoi, formal topoi). They are shown to be generalized structures in which higher-order many-sorted languages can be realized. The corresponding Gentzen-type higher-order calculus of sequents is explicited and the soundness theorem is formulated. A construction is given, which associates to each deduction category with formal properties a real category with the corresponding real properties, in a universal way. The corresponding sounddess and completeness properties are formulated for the real categories thus obtained. Fuzzy sets, as generalized by Goguen are introduced, considered as the objects of a category Fuz(H), which turns out to be the real category associated to a very simple formal topos, and thus to be itself a topos: furthermore this is proved to be a Grothendieck topos which is a strictly full epireflective subcategory of Higgs' category of ‘H-valued sets’. Topoi are proposed as generalized fuzzy sets, and deductio0-categories as generalized² fuzzy sets. Some related topics such as Arbib-Manes fuzzy theories, probability, many-valued and fuzzy logics, intensional logic are very briefly touched upon.     

Damage Spreading in a 2D Ising Model with Swendsen–Wang Dynamics

Damage spreading for Ising cluster dynamics is investigated numerically by using random numbers in a way that conforms with the notion of submitting the two evolving replicas to the same thermal noise. Two damage spreading transitions are found; damage does not spread either at low or high temperatures. We determine some critical exponents at the high-temperature transition point, which seem consistent with directed percolation.     

Rigorous derivation of domain growth kinetics without conservation laws

The time evolution of the Ising model that describes shrinking domains is studied. A singly connected domain of Ising spins, embedded in a sea of the opposite phase, develops atT=0 according to a dynamic rule that does not allow its perimeter to increase. At long enough times the domain disappears; we show that the average lifetime of such a domain is proportional to its area. We also consider theT=0 dynamics of a single infinite quadrant. The area of the quadrant decreases during the time evolution, and we show that the area lost grows linearly with time. We solve a first passage time problem as well. That is, we calculate the average time it takes for the area lost to reach a given value for the first time. Lastly, we map the infinite quadrant model onto a diffusion problem with exclusion in one dimension. This latter problem is mapped onto a critical six-vertex model.     

Phase transitions in an exactly soluble one-dimensional exclusion process

We consider an exclusion process with particles injected with rate at the origin and removed with rate at the right boundary of a one-dimensional chain of sites. The particles are allowed to hop onto unoccupied sites, to the right only. For the special case of = = 1 the model was solved previously by Derridaet al. Here we extend the solution to general , . The phase diagram obtained from our exact solution differs from the one predicted by the mean-field approximation.     

Flowing Sand—A Possible Physical Realization of Directed Percolation

A simple model for flowing sand on an inclined plane is introduced. The model is related to recent experiments by Douady and Daerr and reproduces some of the experimentally observed features. Avalanches of intermediate size appear to be compact, placing the critical behavior of the model into the universality class of compact directed percolation. On very large scales, however, the avalanches break up into several branches, leading to a crossover from compact to ordinary directed percolation. Thus, systems of flowing granular matter on an inclined plane could serve as a first physical realization of directed percolation.     

Effect of gamma‐irradiation sterilization on the physical and mechanical properties of a hybrid wound dressing

A wound dressing should ideally provide an optimal healing environment which enables rapid healing. It should maintain a moist environment at the wound surface, allow gas exchange, act as a barrier to microorganisms, remove excess exudates and afford mechanical protection to the wound. A new bioresorbable hybrid wound dressing which combines a poly(DL‐lactic‐co‐glycolic acid) porous top layer with a spongy collagen sublayer was developed and studied. The top layer contained the antibiotic drug gentamicin for controlled release to the wound site. It is of very high importance to use an appropriate sterilization process for this special new wound dressing, which will not have a deleterious effect on its function. Our investigation therefore focused on the effects of gamma‐irradiation sterilization (10, 25, 35 and 50 kGy) on the structure properties of this wound dressing. The physical and mechanical properties were of the wound dressings were affected by the gamma irradiation because of a combination of chain scission and crosslinking of the collagen layer mainly. The weight loss and water vapor transmission rate were increased, while the water uptake was decreased with the increase in the irradiation dose. The changes were small when doses of 10 or 25 kGy were applied at room temperature. The gamma‐irradiation resulted in stronger but more brittle wound dressings. These trends were smaller when the sterilization process was carried out in liquid nitrogen. Our research shows that gamma‐sterilization process is feasible for our new concept of hybrid wound dressings and optimal conditions can be chosen. Copyright © 2016 John Wiley & Sons, Ltd.     

Impurity Dynamics of the XY-Model

The time dependent expectation value of a magnetic perturbation of the XY-Hamiltonian is computed exactly. Thermalization information is obtained.