163 research outputs found
Adaptive Fitness Landscape for Replicator Systems: To Maximize or not to Maximize
Sewall Wright's adaptive landscape metaphor penetrates a significant part of
evolutionary thinking. Supplemented with Fisher's fundamental theorem of
natural selection and Kimura's maximum principle, it provides a unifying and
intuitive representation of the evolutionary process under the influence of
natural selection as the hill climbing on the surface of mean population
fitness. On the other hand, it is also well known that for many more or less
realistic mathematical models this picture is a sever misrepresentation of what
actually occurs. Therefore, we are faced with two questions. First, it is
important to identify the cases in which adaptive landscape metaphor actually
holds exactly in the models, that is, to identify the conditions under which
system's dynamics coincides with the process of searching for a (local) fitness
maximum. Second, even if the mean fitness is not maximized in the process of
evolution, it is still important to understand the structure of the mean
fitness manifold and see the implications of this structure on the system's
dynamics. Using as a basic model the classical replicator equation, in this
note we attempt to answer these two questions and illustrate our results with
simple well studied systems.Comment: 13 pages, 4 figure
Replicator equations and space
A reaction--diffusion replicator equation is studied. A novel method to apply
the principle of global regulation is used to write down the model with
explicit spatial structure. Properties of stationary solutions together with
their stability are analyzed analytically, and relationships between stability
of the rest points of the non-distributed replicator equation and distributed
system are shown. A numerical example is given to show that the spatial
variable in this particular model promotes the system's permanence.Comment: 24 page
Scattering theory of superconductive tunneling in quantum junctions
We present a consistent theory of superconductive tunneling in single-mode
junctions within a scattering formulation of Bogoliubov-de Gennes quantum
mechanics. Both dc Josephson effect and dc quasiparticle transport in voltage
biased junctions are considered. Elastic quasiparticle scattering by the
junction determines equilibrium Josephson current. We discuss the origin of
Andreev bound states in tunnel junctions and their role in equilibrium
Josephson transport. In contrast, quasiparticle tunneling in voltage biased
junctions is determined by inelastic scattering. We derive a general expression
for inelastic scattering amplitudes and calculate the quasiparticle current at
all voltages with emphasis on a discussion of the properties of subgap tunnel
current and the nature of subharmonic gap structure.Comment: 47 pages, 9 figures, [preprint,eqsecnum,aps]{revtex
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