1,294,968 research outputs found
Symmetries and degrees of freedom in 2-dimensional dual models
The 2-dimensional version of the Schwarz and Sen duality model (Tseytlin
model) is analyzed at the classical and quantum levels. The solutions are
obtained after removing the gauge dependent sector using the Dirac method. The
Poincar\`e invariance is verified at both levels. An extension with global
supersymmetry is also proposed.Comment: 3 pages, revtex, minor correction
Populations with interaction and environmental dependence: from few, (almost) independent, members into deterministic evolution of high densities
Many populations, e.g. of cells, bacteria, viruses, or replicating DNA
molecules, start small, from a few individuals, and grow large into a
noticeable fraction of the environmental carrying capacity . Typically, the
elements of the initiating, sparse set will not be hampering each other and
their number will grow from in a branching process or Malthusian
like, roughly exponential fashion, , where is the size at
discrete time , is the offspring mean per individual (at the
low starting density of elements, and large ), and a sum of i.i.d.
random variables. It will, thus, become detectable (i.e. of the same order as
) only after around generations, when its density will
tend to be strictly positive. Typically, this entity will be random, even if
the very beginning was not at all stochastic, as indicated by lower case ,
due to variations during the early development. However, from that time
onwards, law of large numbers effects will render the process deterministic,
though initiated by the random density at time log , expressed through the
variable . Thus, acts both as a random veil concealing the start and a
stochastic initial value for later, deterministic population density
development. We make such arguments precise, studying general density and also
system-size dependent, processes, as . As an intrinsic size
parameter, may also be chosen to be the time unit. The fundamental ideas
are to couple the initial system to a branching process and to show that late
densities develop very much like iterates of a conditional expectation
operator.Comment: presented at IV Workshop on Branching Processes and their
Applications at Badajoz, Spain, 10-13 April, 201
Effective medium approach for stiff polymer networks with flexible cross-links
Recent experiments have demonstrated that the nonlinear elasticity of in
vitro networks of the biopolymer actin is dramatically altered in the presence
of a flexible cross-linker such as the abundant cytoskeletal protein filamin.
The basic principles of such networks remain poorly understood. Here we
describe an effective medium theory of flexibly cross-linked stiff polymer
networks. We argue that the response of the cross-links can be fully attributed
to entropic stiffening, while softening due to domain unfolding can be ignored.
The network is modeled as a collection of randomly oriented rods connected by
flexible cross-links to an elastic continuum. This effective medium is treated
in a linear elastic limit as well as in a more general framework, in which the
medium self-consistently represents the nonlinear network behavior. This model
predicts that the nonlinear elastic response sets in at strains proportional to
cross-linker length and inversely proportional to filament length. Furthermore,
we find that the differential modulus scales linearly with the stress in the
stiffening regime. These results are in excellent agreement with bulk rheology
data.Comment: 12 pages, 8 figure
Symbolic reduction of block diagrams using FORMAC
Two computer programs - one written in FORMAC to generate the desired symbolic expressions, the other in FORTRAN 4 to numerically evaluate the expressions are announced. The FORTRAN program accepts the symbolic punched output from the FORMAC program in either unexpanded or expanded form. It numerically evaluates the expressions
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