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From random to self avoiding walks
300
Nonlinear Science Abstracts
that case. The entropy production sign is estimated to be positive. Some possible consequences of the results obtained as those on the lying problem of statistical physics are briefly mentioned and some conjectures are made on the possible relevance of results to the possibility of new insights into quantummechanics principles. JOURNAL: Nuovo Cim. 69B (1982) 136. 147
(MI,T4) CHAOTIC BAND STRUCTURE OF ALMOST PERIODIC POTENTIALS, Asher Peres, Department of Physics, Technion - Israel Institute of Technology 32 000 Raifa, ISRAEL. It has been conjectured that the band structure of an almost periodic potential is a Cantor set. Numerical calculations are presented which lend support to this conjecture. JOURNAL: none given 148
(M4,T6) INVARIANT MANIFOLDS FOR SMOOTH MAPS WITH SINGULARITIES, I. EXISTENCE, II. ABSOLUTE CONTINUITY., Anatole Katok and Jean-Marie Strelcyn, Fascicule n ° 32, Department de Mathematlques, Avenue LB Clement, 93430, Villetaneuse, FRANCE. In this paper we generalize the part of Pesln invarlant manifold theory concerning the existence of invarlant manifolds to a class of smooth transformation with singularities. The absolute continuity of families of invariant manifolds in our framework is the subject of Part II of this paper. The motivation for such a generalization lles in the fact that some important dynamical systems occurring in classical mechanics (for example, the motion of the system of rigid balls with elastic collisions) do have singularities. Some of these systems (including the example mentioned) can be reduced to so-called billiard systems. JOURNAL: none given 149 (P3,Tg) FROM RANDOM TO SELF AVOIDING WALKS, Cyril Domb, Physics Department, Bar-llan University, Ramat-Gan, ISRAEL. A brief review will be given of the current situation in the theory of self-avoiding walks (SAW's). The Domb-Joyce model first introduced in 1972 consists of a random walk on a lattice in which each N step configuration has a weighting factor
Here i and j are the lattice sites occupied by the i-th and J-th points of the walk.--When ~ = 0 the model reduces to a standard random walk, and when w ffi I it is a self avoiding walk. The universality hypothesis of critical phenomena will be used to conjecture the behaviour of the model as a function of ~ for large N. The implications for the theory of dilute polymer solutions will be indicated. JOURNAL: J. Stat. Phys.
Nonlinear Science Abstracts
that case. The entropy production sign is estimated to be positive. Some possible consequences of the results obtained as those on the lying problem of statistical physics are briefly mentioned and some conjectures are made on the possible relevance of results to the possibility of new insights into quantummechanics principles. JOURNAL: Nuovo Cim. 69B (1982) 136. 147
(MI,T4) CHAOTIC BAND STRUCTURE OF ALMOST PERIODIC POTENTIALS, Asher Peres, Department of Physics, Technion - Israel Institute of Technology 32 000 Raifa, ISRAEL. It has been conjectured that the band structure of an almost periodic potential is a Cantor set. Numerical calculations are presented which lend support to this conjecture. JOURNAL: none given 148
(M4,T6) INVARIANT MANIFOLDS FOR SMOOTH MAPS WITH SINGULARITIES, I. EXISTENCE, II. ABSOLUTE CONTINUITY., Anatole Katok and Jean-Marie Strelcyn, Fascicule n ° 32, Department de Mathematlques, Avenue LB Clement, 93430, Villetaneuse, FRANCE. In this paper we generalize the part of Pesln invarlant manifold theory concerning the existence of invarlant manifolds to a class of smooth transformation with singularities. The absolute continuity of families of invariant manifolds in our framework is the subject of Part II of this paper. The motivation for such a generalization lles in the fact that some important dynamical systems occurring in classical mechanics (for example, the motion of the system of rigid balls with elastic collisions) do have singularities. Some of these systems (including the example mentioned) can be reduced to so-called billiard systems. JOURNAL: none given 149 (P3,Tg) FROM RANDOM TO SELF AVOIDING WALKS, Cyril Domb, Physics Department, Bar-llan University, Ramat-Gan, ISRAEL. A brief review will be given of the current situation in the theory of self-avoiding walks (SAW's). The Domb-Joyce model first introduced in 1972 consists of a random walk on a lattice in which each N step configuration has a weighting factor
Here i and j are the lattice sites occupied by the i-th and J-th points of the walk.--When ~ = 0 the model reduces to a standard random walk, and when w ffi I it is a self avoiding walk. The universality hypothesis of critical phenomena will be used to conjecture the behaviour of the model as a function of ~ for large N. The implications for the theory of dilute polymer solutions will be indicated. JOURNAL: J. Stat. Phys.