12,803 research outputs found
Stochastic Eulerian Lagrangian Methods for Fluid-Structure Interactions with Thermal Fluctuations
We present approaches for the study of fluid-structure interactions subject
to thermal fluctuations. A mixed mechanical description is utilized combining
Eulerian and Lagrangian reference frames. We establish general conditions for
operators coupling these descriptions. Stochastic driving fields for the
formalism are derived using principles from statistical mechanics. The
stochastic differential equations of the formalism are found to exhibit
significant stiffness in some physical regimes. To cope with this issue, we
derive reduced stochastic differential equations for several physical regimes.
We also present stochastic numerical methods for each regime to approximate the
fluid-structure dynamics and to generate efficiently the required stochastic
driving fields. To validate the methodology in each regime, we perform analysis
of the invariant probability distribution of the stochastic dynamics of the
fluid-structure formalism. We compare this analysis with results from
statistical mechanics. To further demonstrate the applicability of the
methodology, we perform computational studies for spherical particles having
translational and rotational degrees of freedom. We compare these studies with
results from fluid mechanics. The presented approach provides for
fluid-structure systems a set of rather general computational methods for
treating consistently structure mechanics, hydrodynamic coupling, and thermal
fluctuations.Comment: 24 pages, 3 figure
A survey on fractional order control techniques for unmanned aerial and ground vehicles
In recent years, numerous applications of science and engineering for modeling and control of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) systems based on fractional calculus have been realized. The extra fractional order derivative terms allow to optimizing the performance of the systems. The review presented in this paper focuses on the control problems of the UAVs and UGVs that have been addressed by the fractional order techniques over the last decade
``String'' formulation of the Dynamics of the Forward Interest Rate Curve
We propose a formulation of the term structure of interest rates in which the
forward curve is seen as the deformation of a string. We derive the general
condition that the partial differential equations governing the motion of such
string must obey in order to account for the condition of absence of arbitrage
opportunities. This condition takes a form similar to a fluctuation-dissipation
theorem, albeit on the same quantity (the forward rate), linking the bias to
the covariance of variation fluctuations. We provide the general structure of
the models that obey this constraint in the framework of stochastic partial
(possibly non-linear) differential equations. We derive the general solution
for the pricing and hedging of interest rate derivatives within this framework,
albeit for the linear case (we also provide in the appendix a simple and
intuitive derivation of the standard European option problem). We also show how
the ``string'' formulation simplifies into a standard N-factor model under a
Galerkin approximation.Comment: 24 pages, European Physical Journal B (in press
Combinatorial Continuous Maximal Flows
Maximum flow (and minimum cut) algorithms have had a strong impact on
computer vision. In particular, graph cuts algorithms provide a mechanism for
the discrete optimization of an energy functional which has been used in a
variety of applications such as image segmentation, stereo, image stitching and
texture synthesis. Algorithms based on the classical formulation of max-flow
defined on a graph are known to exhibit metrication artefacts in the solution.
Therefore, a recent trend has been to instead employ a spatially continuous
maximum flow (or the dual min-cut problem) in these same applications to
produce solutions with no metrication errors. However, known fast continuous
max-flow algorithms have no stopping criteria or have not been proved to
converge. In this work, we revisit the continuous max-flow problem and show
that the analogous discrete formulation is different from the classical
max-flow problem. We then apply an appropriate combinatorial optimization
technique to this combinatorial continuous max-flow CCMF problem to find a
null-divergence solution that exhibits no metrication artefacts and may be
solved exactly by a fast, efficient algorithm with provable convergence.
Finally, by exhibiting the dual problem of our CCMF formulation, we clarify the
fact, already proved by Nozawa in the continuous setting, that the max-flow and
the total variation problems are not always equivalent.Comment: 26 page
Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium
This paper investigates the reconstruction of elastic Green's function from
the cross-correlation of waves excited by random noise in the context of
scattering theory. Using a general operator equation, -the resolvent formula-,
Green's function reconstruction is established when the noise sources satisfy
an equipartition condition. In an inhomogeneous medium, the operator formalism
leads to generalized forms of optical theorem involving the off-shell
-matrix of elastic waves, which describes scattering in the near-field. The
role of temporal absorption in the formulation of the theorem is discussed.
Previously established symmetry and reciprocity relations involving the
on-shell -matrix are recovered in the usual far-field and infinitesimal
absorption limits. The theory is applied to a point scattering model for
elastic waves. The -matrix of the point scatterer incorporating all
recurrent scattering loops is obtained by a regularization procedure. The
physical significance of the point scatterer is discussed. In particular this
model satisfies the off-shell version of the generalized optical theorem. The
link between equipartition and Green's function reconstruction in a scattering
medium is discussed
Euler's variational approach to the elastica
The history of the elastica is examined through the works of various
contributors, including those of Jacob and Daniel Bernoulli, since its first
appearance in a 1690 contest on finding the profile of a hanging flexible cord.
Emphasis will be given to Leonhard Euler's variational approach to the
elastica, laid out in his landmark 1744 book on variational techniques. Euler's
variational approach based on the concept of differential value is highlighted,
including the derivation of the general equation for the elastica from the
differential value of the first kind, from which nine shapes adopted by a
flexed lamina under different end conditions are obtained. To show the
potential of Euler's variational method, the development of the unequal
curvature of elastic bands based on the differential value of the second kind
is also examined. We also revisited some of Euler's examples of application,
including the derivation of the Euler-Bernoulli equation for the bending of a
beam from the Euler-Poisson equation, the pillar critical load before buckling,
and the vibration of elastic laminas, including the derivation of the equations
for the mode shapes and the corresponding natural frequencies. Finally, the
pervasiveness of Euler's elastica solution found in various studies over the
years as given on recent reviews by third parties is highlighted, which also
includes its major role in the development of the theory of elliptic functions.Comment: 18 pages, 7 figure
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