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  • 1980-1984  (6)
  • iteration  (4)
  • Contractility  (1)
  • Striated muscle  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 27 (1982), S. 441-456 
    ISSN: 1572-9613
    Keywords: Ising model ; Cayley tree ; phase transition ; iteration ; fixed point ; bifurcation ; ferromagnetic ; antiferromagnetic.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Ising model on a Cayley tree displays a peculiar (continuous order) phase transition with zero long-range order at all finite temperatures. When one studies expection values of spins far removed from the surface (which contains a finite fraction of the total number of spins in the thermodynamic limit), however, one obtains the so-called Bethe approximation. Here we study such a local description by setting up a simple recurrence relation for successive shell magnetizations far removed from the surface. In the ferromagnetic case the local magnetization is a fixed point of the iterative transformation, while in the antiferromagnetic case the fixed point bifurcates to a two-cycle of the transformation (for low temperatures and fields) giving rise to local sublattice magnetizations. In both cases, local thermodynamical properties are obtained by integration.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 27 (1982), S. 457-472 
    ISSN: 1572-9613
    Keywords: Cayley tree ; iteration ; fixed point ; spin glass ; Gaussian distribution ; local mean-field theory ; SK equations ; TAP equations.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper we study rigorously the random Ising model on a Cayley tree in the limit of infinite coordination numberz → 8. An iterative scheme is developed relating mean magnetizations and mean square magnetizations of successive shells far removed from the surface of the lattice. In this way we obtain local properties of the model in the (thermodynamic) limit of an infinite number of shells. When the coupling constants are independent Gaussian random variables the SK expressions emerge as stable fixed points of our scheme and provide a valid local mean-field theory of spin glasses in which negative local entropy (at low temperatures) while perfectly possible mathematically may still perhaps be physically undesirable. Finally we examine the TAP equations and show that if the average over bond disorder and the limitz → 8 are actually performed, one recovers our iterative scheme and hence the SK equations also in the thermodynamic limit.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 27 (1982), S. 183-200 
    ISSN: 1572-9613
    Keywords: Maps on an interval ; iteration ; conjugacy ; universal ; fixed point function ; functional equation ; doubling transformation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract By considering functions defined on the unit interval with a single zero minimum and a single unit maximum we are led to a version of the doubling or universal transformation. The fixed point functions of this doubling transformation have certain invariance properties under conjugacy. These invariance properties lead to a widening of the concept of universality to power law conjugacy classes in which the Feigenbaum divergence parameter δ is a function only of the product of the powers with which iterating functions approach unity at the maximum and zero at the minimum. We also construct an effective method for computing the divergence parameter from iterates, and derivatives of iterates, generated by the appropriate fixed point function.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 33 (1983), S. 419-436 
    ISSN: 1572-9613
    Keywords: Cayley tree ; iteration ; fixed points ; cycles ; attractors ; chaos ; spin glass ; frequency locking ; devil's staircase
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An iterative scheme is developed for a renormalized effective nearest-neighbor couplingK r and effective field per siteK r for spins in therth shell of a Cayley tree with nearest neighborJ, and next nearest neighborJ′, interactions between Ising spins on the lattice. In addition to the expected paramagnetic, ferromagnetic, and antiferromagnetic phases, we find an intermediate range ofJ'/J 〈 0 values whereX r, and Kr iterate to a continuous or quasicontinuous attractor in theX-K plane. In this range the local magnetization is mainly chaotic with oscillatory glasslike behavior. Embedded in the chaos, however, are regions of periodic and commensurate phases.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 1432-2013
    Keywords: Skeletal muscle ; Hyperthyroidism ; Contractility ; Fibre types
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract Male Wistar rats were made hyperthyroid by intraperitoneal injections on alternate days for 1–6 weeks, of 200 μg/kg triiodothyronine (T3). The effects of this treatment on the contractile properties of the soleus, a slow twitch and the extensor digitorum longus (EDL), a fast twitch skeletal muscle, were studied in vivo in the anaesthetized animal. Post mortem, serial frozen sections of both muscles were stained histochemically for myosin ATPase, succinic dehydrogenase and phosphorylase. Muscle fibres were classified as either slow twitch (SO), fast twitch oxidative glycolytic (FOG) or fast twitch glycolytic (FG). Elevation of plasma T3 levels is associated with progressive alterations in the muscle fibre populations of both muscles. In the soleus there is conversion of SO to FOG fibres while in the EDL the main effect is FG to FOG conversion. There are also marked changes, mainly confined to the soleus muscle, in contractile properties; progressive increases in isometric twitch and tetanic tension and in the rates of contraction and relaxation during both twitch and tetanus. The effect of T3 on slow muscle contractility may be related to its effect on muscle phenotype. However, changes in the former precede detectable fibre population changes. T3 may influence properties such as the Ca2+ binding activity of sarcoplasmic reticulum of existing slow twitch fibres before the later changes associated with the interconversion of fibre types occur.
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 1432-0878
    Keywords: Striated muscle ; Lizard ; Capillaries ; Mitochondria ; Endplates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Notes: Summary The white and red regions of the iliofibularis muscle of the lizard Dipsosaurus dorsalis were analyzed using histologic and morphometric analysis. These regions are composed of fast glycolytic (FG) and both fast oxidative, glycolytic (FOG) and tonic fibers, respectively. Endplate morphology and number of endplates per fiber were estimated from fibers from both areas. Capillary volume densities of the red and white regions were quantified from transverse sections. Mitochondrial volume of fibers from the red and white regions were estimated from electron micrographs. All fibers from the white region of the iliofibularis possessed a single, well defined endplate, as did most red region fibers. The remaining red fibers (28±5%) possessed an average of 14.7±3 endplates each, distributed along the entire length of the fiber at intervals of approximately 1124 μm. Red fibers possessed twice the mitochondrial volume of white fibers (7.6±0.4%, red; 3.8±0.3%, white). Mitochondria were distributed uniformly through the fibers from both regions. Capillary anisotropy was low (γ = 1.018) in both regions. Capillary densities of the red region (629±35 mm-2) were much greater than those of the corresponding White region (73±8 mm-2). The data indicate that capillary densities, mitochondrial volumes and theoretical diffusion distances correlate well with the oxidative capacity of lizard muscle fibers. Tonic fibrs of this species appear oxidative and therefore metabolically capable of functioning during locomotion. The similar mitochondrial volumes and capillary densities of reptilian and mammalian muscles suggest that the greater oxidative capacity of mammalian muscle is due in part to possession of more oxidatively active mitochondria rather than to possession of more mitochondria per se.
    Type of Medium: Electronic Resource
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