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  • dimensional crossover  (2)
  • effective fitness  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 74 (1994), S. 219-238 
    ISSN: 1572-9613
    Keywords: Equation of state ; renormalization group ; effective exponents ; crossover scaling laws ; finite size scaling ; dimensional crossover
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Using the formalism developed in earlier work, dimensional crossover on ad-dimensional layered Ising-type system satisfying periodic boundary conditions and of sizeL is considered belowT c (L), T c (L) being the critical temperature of the finite-size system. Effective critical exponents δeff and βeff are shown explicitly to crossover between theird- and (d−1)-dimensional values for ξ L →∞ in the limitsL/ξ L →∞ andL/ξ L →0, respectively, ξ L , being the correlation length in the layers. Using anL-dependent renormalization group, the effective exponents are shown to satisfy natural generalizations of the standard scaling laws. In addition,L-dependent global scaling fields which span the entire crossover are defined and a scaling form of the equation of state in terms of them derived. All the above assertions are verified explicitly to one loop in perturbation theory, in particular effective exponents and a universal crossover equation of state are obtained and shown in the above asymptotic limits to be in good agreement with known results.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 87 (1997), S. 273-291 
    ISSN: 1572-9613
    Keywords: Renormalization group ; finite size scaling ; dimensional crossover ; scaling functions ; effective exponents
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider dimensional crossover for anO(N) Landau-Ginzburg-Wilson model on ad-dimensional film geometry of thicknessL in the large-N limit. We calculate the full universal crossover scaling forms for the free energy and the equation of state. We compare the results obtained using “environmentally friendly” renormalization with those found using a direct, non-renormalization-group approach. A set of effective critical exponents are calculated and scaling laws for these exponents are shown to hold exactly, thereby yielding nontrivial relations between the various thermodynamic scaling functions.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Genetic programming and evolvable machines 1 (2000), S. 363-378 
    ISSN: 1573-7632
    Keywords: effective fitness ; fitness landscape ; evolution equations ; genotype–phenotype map ; induced symmetry breaking
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In evolutionary computation the concept of a fitness landscape has played an important role, evolution itself being portrayed as a hill-climbing process on a rugged landscape. In this article we review the recent development of an alternative paradigm for evolution on a fitness landscape—effective fitness. It is shown that in general, in the presence of other genetic operators such as mutation and recombination, hill-climbing is the exception rather than the rule; a discrepancy that has its origin in the different ways in which the concept of fitness appears—as a measure of the number of fit offspring, or as a measure of the probability to reach reproductive age. Effective fitness models the former not the latter and gives an intuitive way to understand population dynamics as flows on an effective fitness landscape when genetic operators other than reproductive selection play an important role. Additionally, we will show that when the genotype-phenotype map is degenerate, i.e. there exists a synonym symmetry, it can be used to quantify the degree of symmetry breaking of the map, thus allowing for a quantitative explanation of phenomena such as self-adaptation, bloat and evolutionary robustness.
    Type of Medium: Electronic Resource
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