228,766 research outputs found
Conformal Mapping on Rough Boundaries I: Applications to harmonic problems
The aim of this study is to analyze the properties of harmonic fields in the
vicinity of rough boundaries where either a constant potential or a zero flux
is imposed, while a constant field is prescribed at an infinite distance from
this boundary. We introduce a conformal mapping technique that is tailored to
this problem in two dimensions. An efficient algorithm is introduced to compute
the conformal map for arbitrarily chosen boundaries. Harmonic fields can then
simply be read from the conformal map. We discuss applications to "equivalent"
smooth interfaces. We study the correlations between the topography and the
field at the surface. Finally we apply the conformal map to the computation of
inhomogeneous harmonic fields such as the derivation of Green function for
localized flux on the surface of a rough boundary
Scaling and universality in coupled driven diffusive models
Inspired by the physics of magnetohydrodynamics (MHD) a simplified coupled
Burgers-like model in one dimension (1d), a generalization of the Burgers model
to coupled degrees of freedom, is proposed to describe 1dMHD. In addition to
MHD, this model serves as a 1d reduced model for driven binary fluid mixtures.
Here we have performed a comprehensive study of the universal properties of the
generalized d-dimensional version of the reduced model. We employ both
analytical and numerical approaches. In particular, we determine the scaling
exponents and the amplitude-ratios of the relevant two-point time-dependent
correlation functions in the model. We demonstrate that these quantities vary
continuously with the amplitude of the noise cross-correlation. Further our
numerical studies corroborate the continuous dependence of long wavelength and
long time-scale physics of the model on the amplitude of the noise
cross-correlations, as found in our analytical studies. We construct and
simulate lattice-gas models of coupled degrees of freedom in 1d, belonging to
the universality class of our coupled Burgers-like model, which display similar
behavior. We use a variety of numerical (Monte-Carlo and Pseudospectral
methods) and analytical (Dynamic Renormalization Group, Self-Consistent
Mode-Coupling Theory and Functional Renormalization Group) approaches for our
work. The results from our different approaches complement one another.
Possible realizations of our results in various nonequilibrium models are
discussed.Comment: To appear in JSTAT (2009); 52 pages in JSTAT format. Some figure
files have been replace
High-level signatures and initial semantics
We present a device for specifying and reasoning about syntax for datatypes,
programming languages, and logic calculi. More precisely, we study a notion of
signature for specifying syntactic constructions.
In the spirit of Initial Semantics, we define the syntax generated by a
signature to be the initial object---if it exists---in a suitable category of
models. In our framework, the existence of an associated syntax to a signature
is not automatically guaranteed. We identify, via the notion of presentation of
a signature, a large class of signatures that do generate a syntax.
Our (presentable) signatures subsume classical algebraic signatures (i.e.,
signatures for languages with variable binding, such as the pure lambda
calculus) and extend them to include several other significant examples of
syntactic constructions.
One key feature of our notions of signature, syntax, and presentation is that
they are highly compositional, in the sense that complex examples can be
obtained by assembling simpler ones. Moreover, through the Initial Semantics
approach, our framework provides, beyond the desired algebra of terms, a
well-behaved substitution and the induction and recursion principles associated
to the syntax.
This paper builds upon ideas from a previous attempt by Hirschowitz-Maggesi,
which, in turn, was directly inspired by some earlier work of
Ghani-Uustalu-Hamana and Matthes-Uustalu.
The main results presented in the paper are computer-checked within the
UniMath system.Comment: v2: extended version of the article as published in CSL 2018
(http://dx.doi.org/10.4230/LIPIcs.CSL.2018.4); list of changes given in
Section 1.5 of the paper; v3: small corrections throughout the paper, no
major change
Extended Universality of the Surface Curvature in Equilibrium Crystal Shapes
We investigate the universal property of curvatures in surface models which
display a flat phase and a rough phase whose criticality is described by the
Gaussian model. Earlier we derived a relation between the Hessian of the free
energy and the Gaussian coupling constant in the six-vertex model. Here we show
its validity in a general setting using renormalization group arguments. The
general validity of the relation is confirmed numerically in the RSOS model by
comparing the Hessian of the free energy and the Gaussian coupling constant in
a transfer matrix finite-size-scaling study. The Hessian relation gives clear
understanding of the universal curvature jump at roughening transitions and
facet edges and also provides an efficient way of locating the phase
boundaries.Comment: 19 pages, RevTex, 3 Postscript Figures, To appear in Phys. Rev.
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