4,716 research outputs found
Towards tensor-based methods for the numerical approximation of the Perron-Frobenius and Koopman operator
The global behavior of dynamical systems can be studied by analyzing the
eigenvalues and corresponding eigenfunctions of linear operators associated
with the system. Two important operators which are frequently used to gain
insight into the system's behavior are the Perron-Frobenius operator and the
Koopman operator. Due to the curse of dimensionality, computing the
eigenfunctions of high-dimensional systems is in general infeasible. We will
propose a tensor-based reformulation of two numerical methods for computing
finite-dimensional approximations of the aforementioned infinite-dimensional
operators, namely Ulam's method and Extended Dynamic Mode Decomposition (EDMD).
The aim of the tensor formulation is to approximate the eigenfunctions by
low-rank tensors, potentially resulting in a significant reduction of the time
and memory required to solve the resulting eigenvalue problems, provided that
such a low-rank tensor decomposition exists. Typically, not all variables of a
high-dimensional dynamical system contribute equally to the system's behavior,
often the dynamics can be decomposed into slow and fast processes, which is
also reflected in the eigenfunctions. Thus, the weak coupling between different
variables might be approximated by low-rank tensor cores. We will illustrate
the efficiency of the tensor-based formulation of Ulam's method and EDMD using
simple stochastic differential equations
Dynamics and energetics of emergent magnetic monopoles in chiral magnets
The formation and destruction of topologically quantized magnetic whirls,
so-called skyrmions, in chiral magnets is driven by the creation and motion of
singular hedgehog defects. These can be identified with emergent magnetic
monopoles and antimonopoles. We investigate how the energetics of and forces
between monopoles and antimonopoles influence their creation rate and dynamics.
We study a single skyrmion line defect in the helical phase using both
micromagnetic simulations and a Ginzburg-Landau analysis. Monopole-antimonople
pairs are created in a thermally activated process, largely controlled by the
(core) energy of the monopole. The force between monopoles and antimonopoles is
linear in distance and described by a string tension. The sign and size of the
string tension determines the stability of the phases and the velocity of the
monopoles.Comment: 4 pages, 5 figure
Improving the Lattice QCD Hamiltonian
Improvement of the Hamiltonian in lattice gauge theory is considered. We give
explicit expressions for classical improvement and discuss also quantum
corrections.Comment: 3 pages, Latex. Presented at Lattice 97: 15th International Symposium
on Lattice Field Theory, Edinburgh, Scotland, 22-26 Jul 1997, to appear in
Nucl. Phys. B(Proc. Suppl.
Numerical Investigation of the Aerodynamic Properties of a Flying Wing Configuration
The numerical investigations of a generic UCAV configuration are presented. These investigations are part of the DLR internal project UCAV-2010. Compressible speed conditions are considered and presented. The DLR-F17E UCAV configuration is a flying lambda delta wing with sweep angle of 53° and varying leading edge radius. The flow field of
this UCAV configuration is dominated by vortex structures and vortex-to-vortex interaction. The paper aims to give a comparison between numerical- and experimental investigations in order to gain a deeper understanding of the complex flow physics. Furthermore, it will highlight the influence of Mach- and Reynolds number change on the flow and the overall aerodynamic behavior of the configuration. The DLR TAU-Code is used to simulate the flow field, using an unstructured grid and the turbulence model of Spalart-Allmaras. Forces and moment measurements taken in the DNW-TWG, Göttingen, on the DLR-F17E configuration serve as the experimental basis to validate the numerical findings. Findings on the SACCON configuration serve as a comparison case aiming to show possible portability between different model scales but also to find analogies between low speed (M=0.15) and compressible speed (M=0.5) scenarios. This paper builds up upon the finding within the NATO/RTO AVT-161 Research Task Group on “Assessment and Control Predictions for NATO Air and Sea Vehicles” and its findings shall serve as a basis for further experimental investigations of medium to high speed wind tunnel experiments. Furthermore, this paper addresses the importance of understanding and the ability to predict controlled- and
uncontrolled flow separation and the interaction of vortex systems in order to estimate the aerodynamic behavior within the entire flight envelope and to meet Stability- and Control
needs
Tensor-based dynamic mode decomposition
Dynamic mode decomposition (DMD) is a recently developed tool for the
analysis of the behavior of complex dynamical systems. In this paper, we will
propose an extension of DMD that exploits low-rank tensor decompositions of
potentially high-dimensional data sets to compute the corresponding DMD modes
and eigenvalues. The goal is to reduce the computational complexity and also
the amount of memory required to store the data in order to mitigate the curse
of dimensionality. The efficiency of these tensor-based methods will be
illustrated with the aid of several different fluid dynamics problems such as
the von K\'arm\'an vortex street and the simulation of two merging vortices
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