485,499 research outputs found
Extracting information from S-curves of language change
It is well accepted that adoption of innovations are described by S-curves
(slow start, accelerating period, and slow end). In this paper, we analyze how
much information on the dynamics of innovation spreading can be obtained from a
quantitative description of S-curves. We focus on the adoption of linguistic
innovations for which detailed databases of written texts from the last 200
years allow for an unprecedented statistical precision. Combining data analysis
with simulations of simple models (e.g., the Bass dynamics on complex networks)
we identify signatures of endogenous and exogenous factors in the S-curves of
adoption. We propose a measure to quantify the strength of these factors and
three different methods to estimate it from S-curves. We obtain cases in which
the exogenous factors are dominant (in the adoption of German orthographic
reforms and of one irregular verb) and cases in which endogenous factors are
dominant (in the adoption of conventions for romanization of Russian names and
in the regularization of most studied verbs). These results show that the shape
of S-curve is not universal and contains information on the adoption mechanism.
(published at "J. R. Soc. Interface, vol. 11, no. 101, (2014) 1044"; DOI:
http://dx.doi.org/10.1098/rsif.2014.1044)Comment: 9 pages, 5 figures, Supplementary Material is available at
http://dx.doi.org/10.6084/m9.figshare.122178
Phase field modeling of electrochemistry I: Equilibrium
A diffuse interface (phase field) model for an electrochemical system is
developed. We describe the minimal set of components needed to model an
electrochemical interface and present a variational derivation of the governing
equations. With a simple set of assumptions: mass and volume constraints,
Poisson's equation, ideal solution thermodynamics in the bulk, and a simple
description of the competing energies in the interface, the model captures the
charge separation associated with the equilibrium double layer at the
electrochemical interface. The decay of the electrostatic potential in the
electrolyte agrees with the classical Gouy-Chapman and Debye-H\"uckel theories.
We calculate the surface energy, surface charge, and differential capacitance
as functions of potential and find qualitative agreement between the model and
existing theories and experiments. In particular, the differential capacitance
curves exhibit complex shapes with multiple extrema, as exhibited in many
electrochemical systems.Comment: v3: To be published in Phys. Rev. E v2: Added link to
cond-mat/0308179 in References 13 pages, 6 figures in 15 files, REVTeX 4,
SIUnits.sty. Precedes cond-mat/030817
Universal Dynamics of Damped-Driven Systems: The Logistic Map as a Normal Form for Energy Balance
Damped-driven systems are ubiquitous in engineering and science. Despite the
diversity of physical processes observed in a broad range of applications, the
underlying instabilities observed in practice have a universal characterization
which is determined by the overall gain and loss curves of a given system. The
universal behavior of damped-driven systems can be understood from a
geometrical description of the energy balance with a minimal number of
assumptions. The assumptions on the energy dynamics are as follows: the energy
increases monotonically as a function of increasing gain, and the losses become
increasingly larger with increasing energy, i.e. there are many routes for
dissipation in the system for large input energy. The intersection of the gain
and loss curves define an energy balanced solution. By constructing an
iterative map between the loss and gain curves, the dynamics can be shown to be
homeomorphic to the logistic map, which exhibits a period doubling cascade to
chaos. Indeed, the loss and gain curves allow for a geometrical description of
the dynamics through a simple Verhulst diagram (cobweb plot). Thus irrespective
of the physics and its complexities, this simple geometrical description
dictates the universal set of logistic map instabilities that arise in complex
damped-driven systems. More broadly, damped-driven systems are a class of
non-equilibrium pattern forming systems which have a canonical set of
instabilities that are manifest in practice.Comment: 26 pages, 31 figure
Ideal free streamline flow over a curved obstacle
AbstractIn the classical two-dimensional model the description of Helmholtz's (Kirchhoff) flow is a problem of complex analysis which can be solved analytically only for a few simple bodies or polygonal contours, using the Schwarz-Christoffel map. This paper presents a practical method for computing flows over arbitrary obstacles whose boundaries may be piecewise smooth curves, while the impinging flow may be an unbounded flow, a jet, or a semi-infinite stream, i.e. the ocean
Central extensions of current groups in two dimensions
In this paper we generalize some of these results for loop algebras and
groups as well as for the Virasoro algebra to the two-dimensional case. We
define and study a class of infinite dimensional complex Lie groups which are
central extensions of the group of smooth maps from a two dimensional
orientable surface without boundary to a simple complex Lie group G. These
extensions naturally correspond to complex curves. The kernel of such an
extension is the Jacobian of the curve. The study of the coadjoint action shows
that its orbits are labelled by moduli of holomorphic principal G-bundles over
the curve and can be described in the language of partial differential
equations. In genus one it is also possible to describe the orbits as conjugacy
classes of the twisted loop group, which leads to consideration of difference
equations for holomorphic functions. This gives rise to a hope that the
described groups should possess a counterpart of the rich representation theory
that has been developed for loop groups. We also define a two-dimensional
analogue of the Virasoro algebra associated with a complex curve. In genus one,
a study of a complex analogue of Hill's operator yields a description of
invariants of the coadjoint action of this Lie algebra. The answer turns out to
be the same as in dimension one: the invariants coincide with those for the
extended algebra of currents in sl(2).Comment: 17 page
Query processing of geometric objects with free form boundarie sin spatial databases
The increasing demand for the use of database systems as an integrating
factor in CAD/CAM applications has necessitated the development of database
systems with appropriate modelling and retrieval capabilities. One essential
problem is the treatment of geometric data which has led to the development of
spatial databases. Unfortunately, most proposals only deal with simple geometric
objects like multidimensional points and rectangles. On the other hand, there has
been a rapid development in the field of representing geometric objects with free
form curves or surfaces, initiated by engineering applications such as mechanical
engineering, aviation or astronautics. Therefore, we propose a concept for the realization
of spatial retrieval operations on geometric objects with free form
boundaries, such as B-spline or Bezier curves, which can easily be integrated in
a database management system. The key concept is the encapsulation of geometric
operations in a so-called query processor. First, this enables the definition of
an interface allowing the integration into the data model and the definition of the
query language of a database system for complex objects. Second, the approach
allows the use of an arbitrary representation of the geometric objects. After a
short description of the query processor, we propose some representations for free
form objects determined by B-spline or Bezier curves. The goal of efficient query
processing in a database environment is achieved using a combination of decomposition
techniques and spatial access methods. Finally, we present some experimental
results indicating that the performance of decomposition techniques is
clearly superior to traditional query processing strategies for geometric objects
with free form boundaries
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