3,278 research outputs found
TiGL - An Open Source Computational Geometry Library for Parametric Aircraft Design
This paper introduces the software TiGL: TiGL is an open source high-fidelity
geometry modeler that is used in the conceptual and preliminary aircraft and
helicopter design phase. It creates full three-dimensional models of aircraft
from their parametric CPACS description. Due to its parametric nature, it is
typically used for aircraft design analysis and optimization. First, we present
the use-case and architecture of TiGL. Then, we discuss it's geometry module,
which is used to generate the B-spline based surfaces of the aircraft. The
backbone of TiGL is its surface generator for curve network interpolation,
based on Gordon surfaces. One major part of this paper explains the
mathematical foundation of Gordon surfaces on B-splines and how we achieve the
required curve network compatibility. Finally, TiGL's aircraft component module
is introduced, which is used to create the external and internal parts of
aircraft, such as wings, flaps, fuselages, engines or structural elements
Fluctuations in glassy systems
We summarize a theoretical framework based on global time-reparametrization
invariance that explains the origin of dynamic fluctuations in glassy systems.
We introduce the main ideas without getting into much technical details. We
describe a number of consequences arising from this scenario that can be tested
numerically and experimentally distinguishing those that can also be explained
by other mechanisms from the ones that we believe, are special to our proposal.
We support our claims by presenting some numerical checks performed on the 3d
Edwards-Anderson spin-glass. Finally, we discuss up to which extent these ideas
apply to super-cooled liquids that have been studied in much more detail up to
present.Comment: 33 pages, 7 figs, contribution to JSTAT special issue `Principles of
Dynamical Systems' work-shop at Newton Institute, Univ. of Cambridge, U
Geometrical aspects and connections of the energy-temperature fluctuation relation
Recently, we have derived a generalization of the known canonical fluctuation
relation between heat capacity and
energy fluctuations, which can account for the existence of macrostates with
negative heat capacities . In this work, we presented a panoramic overview
of direct implications and connections of this fluctuation theorem with other
developments of statistical mechanics, such as the extension of canonical Monte
Carlo methods, the geometric formulations of fluctuation theory and the
relevance of a geometric extension of the Gibbs canonical ensemble that has
been recently proposed in the literature.Comment: Version accepted for publication in J. Phys. A: Math and The
General two-order-parameter Ginzburg-Landau model with quadratic and quartic interactions
Ginzburg-Landau model with two order parameters appears in many
condensed-matter problems. However, even for scalar order parameters, the most
general U(1)-symmetric Landau potential with all quadratic and quartic terms
contains 13 independent coefficients and cannot be minimized with
straightforward algebra. Here, we develop a geometric approach that circumvents
this computational difficulty and allows one to study properties of the model
without knowing the exact position of the minimum. In particular, we find the
number of minima of the potential, classify explicit symmetries possible in
this model, establish conditions when and how these symmetries are
spontaneously broken, and explicitly describe the phase diagram.Comment: 36 pages, 7 figures; v2: added additional clarifications and a
discussion on how this method differs from the MIB-approac
On Approximations of the Curve Shortening Flow and of the Mean Curvature Flow based on the DeTurck trick
In this paper we discuss novel numerical schemes for the computation of the
curve shortening and mean curvature flows that are based on special
reparametrizations. The main idea is to use special solutions to the harmonic
map heat flow in order to reparametrize the equations of motion. This idea is
widely known from the Ricci flow as the DeTurck trick. By introducing a
variable time scale for the harmonic map heat flow, we obtain families of
numerical schemes for the reparametrized flows. For the curve shortening flow
this family unveils a surprising geometric connection between the numerical
schemes in [5] and [9]. For the mean curvature flow we obtain families of
schemes with good mesh properties similar to those in [3]. We prove error
estimates for the semi-discrete scheme of the curve shortening flow. The
behaviour of the fully-discrete schemes with respect to the redistribution of
mesh points is studied in numerical experiments. We also discuss possible
generalizations of our ideas to other extrinsic flows
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