9,852 research outputs found
Critical dynamics of nonconserved -vector model with anisotropic nonequilibrium perturbations
We study dynamic field theories for nonconserving -vector models that are
subject to spatial-anisotropic bias perturbations. We first investigate the
conditions under which these field theories can have a single length scale.
When N=2 or , it turns out that there are no such field theories, and,
hence, the corresponding models are pushed by the bias into the Ising class. We
further construct nontrivial field theories for N=3 case with certain bias
perturbations and analyze the renormalization-group flow equations. We find
that the three-component systems can exhibit rich critical behavior belonging
to two different universality classes.Comment: Included RG analysis and discussion on new universality classe
NIP omega-categorical structures: the rank 1 case
We classify primitive, rank 1, omega-categorical structures having
polynomially many types over finite sets. For a fixed number of 4-types, we
show that there are only finitely many such structures and that all are built
out of finitely many linear orders interacting in a restricted number of ways.
As an example of application, we deduce the classification of primitive
structures homogeneous in a language consisting of n linear orders as well as
all reducts of such structures.Comment: Substantial changes made to the presentation, especially in sections
3 and
The non-isothermal spreading of a thin drop on a heated or cooled horizontal substrate
We revisit the spreading of a thin drop of incompressible Newtonian fluid on a uniformly heated or cooled smooth planar surface. The dynamics of the moving contact line are modelled by a Tanner Law relating the contact angle to the speed of the contact line. The present work builds on an earlier theoretical investigation by Ehrhard and Davis (JFM, 229,365{388 (1991)) who derived the non-linear partial differential equation governing the evolution of the drop. The (implicit) exact solution to the two-dimensional version of this equation in the limit of quasi-steady motion is obtained. Numerically calculated and asymptotic solutions are presented and compared. In particular, multiple solutions are found for a drop hanging beneath a suffciently cooled substrate. If time permits, some basic models for evaporative spreading will be considered
Permutation-twisted modules for even order cycles acting on tensor product vertex operator superalgebras
We construct and classify -twisted -modules for even and a vertex operator superalgebra. In particular,
we show that the category of weak -twisted -modules for even is isomorphic to the category of weak parity-twisted
-modules. This result shows that in the case of a cyclic permutation of even
order, the construction and classification of permutation-twisted modules for
tensor product vertex operator superalgebras is fundamentally different than in
the case of a cyclic permutation of odd order, as previously constructed and
classified by the first author. In particular, in the even order case it is the
parity-twisted -modules that play the significant role in place of the
untwisted -modules that play the significant role in the odd order case.Comment: arXiv admin note: text overlap with arXiv:math/9803118,
arXiv:1310.1956. Constant term in Corollary 6.5 corrected; other minor typos
corrected; reference to arXiv:1401.4635 added; minor clarifications in
exposition made. To appear in the International Journal of Mathematic
Instanton Expansion of Noncommutative Gauge Theory in Two Dimensions
We show that noncommutative gauge theory in two dimensions is an exactly
solvable model. A cohomological formulation of gauge theory defined on the
noncommutative torus is used to show that its quantum partition function can be
written as a sum over contributions from classical solutions. We derive an
explicit formula for the partition function of Yang-Mills theory defined on a
projective module for arbitrary noncommutativity parameter \theta which is
manifestly invariant under gauge Morita equivalence. The energy observables are
shown to be smooth functions of \theta. The construction of noncommutative
instanton contributions to the path integral is described in some detail. In
general, there are infinitely many gauge inequivalent contributions of fixed
topological charge, along with a finite number of quantum fluctuations about
each instanton. The associated moduli spaces are combinations of symmetric
products of an ordinary two-torus whose orbifold singularities are not resolved
by noncommutativity. In particular, the weak coupling limit of the gauge theory
is independent of \theta and computes the symplectic volume of the moduli space
of constant curvature connections on the noncommutative torus.Comment: 52 pages LaTeX, 1 eps figure, uses espf. V2: References added and
repaired; V3: Typos corrected, some clarifying explanations added; version to
be published in Communications in Mathematical Physic
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