16,479 research outputs found
Folds in 2D String Theories
We study maps from a 2D world-sheet to a 2D target space which include folds.
The geometry of folds is discussed and a metric on the space of folded maps is
written down. We show that the latter is not invariant under area preserving
diffeomorphisms of the target space. The contribution to the partition function
of maps associated with a given fold configuration is computed. We derive a
description of folds in terms of Feynman diagrams. A scheme to sum up the
contributions of folds to the partition function in a special case is suggested
and is shown to be related to the Baxter-Wu lattice model. An interpretation of
folds as trajectories of particles in the adjoint representation of
gauge group in the large limit which interact in an unusual way with the
gauge fields is discussed.Comment: 56 pages, latex, followed by epsf, 13 uuencoded epsf figure
The String Theory Approach to Generalized 2D Yang-Mills Theory
We calculate the partition function of the ( and ) generalized
theory defined on an arbitrary Riemann surface. The result which is
expressed as a sum over irreducible representations generalizes the Rusakov
formula for ordinary YM_2 theory. A diagrammatic expansion of the formula
enables us to derive a Gross-Taylor like stringy description of the model. A
sum of 2D string maps is shown to reproduce the gauge theory results. Maps with
branch points of degree higher than one, as well as ``microscopic surfaces''
play an important role in the sum. We discuss the underlying string theory.Comment: TAUP-2182-94, 53 pages of LaTeX and 5 uuencoded eps figure
Fragmentation phase transition in atomic clusters I --- Microcanonical thermodynamics
Here we first develop the thermodynamics of microcanonical phase transitions
of first and second order in systems which are thermodynamically stable in the
sense of van Hove. We show how both kinds of phase transitions can
unambiguously be identified in relatively small isolated systems of
atoms by the shape of the microcanonical caloric equation of state
I.e. within microcanonical thermodynamics one does not need to go to the
thermodynamic limit in order to identify phase transitions. In contrast to
ordinary (canonical) thermodynamics of the bulk microcanonical thermodynamics
(MT) gives an insight into the coexistence region. The essential three
parameters which identify the transition to be of first order, the transition
temperature , the latent heat , and the interphase surface
entropy can very well be determined in relatively small
systems like clusters by MT. The phase transition towards fragmentation is
introduced. The general features of MT as applied to the fragmentation of
atomic clusters are discussed. The similarities and differences to the boiling
of macrosystems are pointed out.Comment: Same as before, abstract shortened my e-mail address: [email protected]
Experimental and Theoretical Search for a Phase Transition in Nuclear Fragmentation
Phase transitions of small isolated systems are signaled by the shape of the
caloric equation of state e^*(T), the relationship between the excitation
energy per nucleon e^* and temperature. In this work we compare the
experimentally deduced e^*(T) to the theoretical predictions. The
experimentally accessible temperature was extracted from evaporation spectra
from incomplete fusion reactions leading to residue nuclei. The experimental
e^*(T) dependence exhibits the characteristic S-shape at e^* = 2-3 MeV/A. Such
behavior is expected for a finite system at a phase transition. The observed
dependence agrees with predictions of the MMMC-model, which simulates the total
accessible phase-space of fragmentation
Twisted Link Theory
We introduce stable equivalence classes of oriented links in orientable
three-manifolds that are orientation -bundles over closed but not
necessarily orientable surfaces. We call these twisted links, and show that
they subsume the virtual knots introduced by L. Kauffman, and the projective
links introduced by Yu. Drobotukhina. We show that these links have unique
minimal genus three-manifolds. We use link diagrams to define an extension of
the Jones polynomial for these links, and show that this polynomial fails to
distinguish two-colorable links over non-orientable surfaces from
non-two-colorable virtual links.Comment: 33 pages and 35 figure
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The effect of treatment on pathogen virulence.
The optimal virulence of a pathogen is determined by a trade-off between maximizing the rate of transmission and maximizing the duration of infectivity. Treatment measures such as curative therapy and case isolation exert selective pressure by reducing the duration of infectivity, reducing the value of duration-increasing strategies to the pathogen and favoring pathogen strategies that maximize the rate of transmission. We extend the trade-off models of previous authors, and represents the reproduction number of the pathogen as a function of the transmissibility, host contact rate, disease-induced mortality, recovery rate, and treatment rate, each of which may be influenced by the virulence. We find that when virulence is subject to a transmissibility-mortality trade-off, treatment can lead to an increase in optimal virulence, but that in other scenarios (such as the activity-recovery trade-off) treatment decreases the optimal virulence. Paradoxically, when levels of treatment rise with pathogen virulence, increasing control efforts may raise predicted levels of optimal virulence. Thus we show that conflict can arise between the epidemiological benefits of treatment and the evolutionary risks of heightened virulence
Theoretical investigation of finite size effects at DNA melting
We investigated how the finiteness of the length of the sequence affects the
phase transition that takes place at DNA melting temperature. For this purpose,
we modified the Transfer Integral method to adapt it to the calculation of both
extensive (partition function, entropy, specific heat, etc) and non-extensive
(order parameter and correlation length) thermodynamic quantities of finite
sequences with open boundary conditions, and applied the modified procedure to
two different dynamical models. We showed that rounding of the transition
clearly takes place when the length of the sequence is decreased. We also
performed a finite-size scaling analysis of the two models and showed that the
singular part of the free energy can indeed be expressed in terms of an
homogeneous function. However, both the correlation length and the average
separation between paired bases diverge at the melting transition, so that it
is no longer clear to which of these two quantities the length of the system
should be compared. Moreover, Josephson's identity is satisfied for none of the
investigated models, so that the derivation of the characteristic exponents
which appear, for example, in the expression of the specific heat, requires
some care
Invariant Connections with Torsion on Group Manifolds and Their Application in Kaluza-Klein Theories
Invariant connections with torsion on simple group manifolds are studied
and an explicit formula describing them is presented. This result is used for
the dimensional reduction in a theory of multidimensional gravity with
curvature squared terms on . We calculate the potential of
scalar fields, emerging from extra components of the metric and torsion, and
analyze the role of the torsion for the stability of spontaneous
compactification.Comment: 13 pages, LATEX, UB-ECM-PF 93/1
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