3,643 research outputs found
Methods of spatial statistics for the characterization of dislocation systems
Gegenstand der Arbeit ist die Entwicklung statistischer Verfahren zur SchĂ€tzung der Anzahl der Versetzungen in multikristallinem Silizium. Die erste Methode benutzt Ideen aus der Theorie der Keim-Korn-Modelle, speziell die sphĂ€rische Kontaktverteilungsfunktion. Die zweite Methode geht von einer summarischen Modellierung der IntensitĂ€tsfunktion aus. Beide Verfahren liefern, wie erwartet, gröĂere Werte als die bisherigen, von Physikern entwickelten, SchĂ€tzer. Der Wachstumsprozess der Versetzungen im Siliziumblock wĂ€hrend der Kristallisation wird durch deterministische Wachstumsprozesse mit zufĂ€lligen Stoppzeiten modelliert. Sie fĂŒhren zu Pareto- und Weibullverteilungen fĂŒr die Anzahl der Versetzungen in Gebieten fester GröĂe. Diese Modelle wurden auch erfolgreich in der statistischen Analyse der GröĂe von WaldbrĂ€nden, der Anzahlen von Galaxien in kubischen Zellen des Universums und der TeilchengröĂenverteilungen in einem verfahrenstechnischen Prozess benutzt
Analogue Hawking Radiation and Sine-Gordon Soliton in a Superconducting Circuit
We propose the use of a waveguide-like transmission line based on
direct-current superconducting quantum interference devices (dc-SQUID) and
study the sine-Gordon (SG) equation which characterises the dynamical behavior
of the superconducting phase in this transmission line. Guided by the duality
between black holes in Jackiw-Teitelboim (JT) dilaton gravity and solitons in
sine-Gordon field theory, we show how to, in our setup, realize 1 + 1
dimensional black holes as solitons of the sine-Gordon equation. We also study
the analogue Hawking radiation in terms of the quantum soliton evaporation, and
analyze its feasibility within current circuit quantum electrodynamics (cQED)
technology. Our results may not only facilitate experimentally understanding
the relation between Jackiw-Teitelboim dilaton gravity and sine-Gordon field
theory, but also pave a new way, in principle, for the exploration of analogue
quantum gravitational effects.Comment: 6 pages, 2 figure
Exact Solutions to the Sine-Gordon Equation
A systematic method is presented to provide various equivalent solution
formulas for exact solutions to the sine-Gordon equation. Such solutions are
analytic in the spatial variable and the temporal variable and they
are exponentially asymptotic to integer multiples of as
The solution formulas are expressed explicitly in terms of a real triplet of
constant matrices. The method presented is generalizable to other integrable
evolution equations where the inverse scattering transform is applied via the
use of a Marchenko integral equation. By expressing the kernel of that
Marchenko equation as a matrix exponential in terms of the matrix triplet and
by exploiting the separability of that kernel, an exact solution formula to the
Marchenko equation is derived, yielding various equivalent exact solution
formulas for the sine-Gordon equation.Comment: 43 page
Plastic dislocation and incompatibility density as indicators for residual stresses
Residual stresses in forming simulations are typically investigated by analyzing the remaining stress state after removing all external loadings. However, the generation of the stress state during forming remains unknown. As a remedy, we use the plastic and elastic dislocation and incompatibility densities - derived from continuum mechanical and differential geometrical considerations - as indicators to track the generation of residual stresses through out a forming operation. Theoretical backgrounds for small and large strain plasticity are highlighted and practical aspects regarding implementation are provided. Two examples demonstrate the functionality of the approach, whereby the plastic incompatibility density in phenomenological, multiplicative large strain plasticity serves as indicator
On the non-uniform motion of dislocations: The retarded elastic fields, the retarded dislocation tensor potentials and the Li\'enard-Wiechert tensor potentials
The purpose of this paper is the fundamental theory of the non-uniform motion
of dislocations in two and three space-dimensions. We investigate the
non-uniform motion of an arbitrary distribution of dislocations, a dislocation
loop and straight dislocations in infinite media using the theory of
incompatible elastodynamics. The equations of motion are derived for
non-uniformly moving dislocations. The retarded elastic fields produced by a
distribution of dislocations and the retarded dislocation tensor potentials are
determined. New fundamental key-formulae for the dynamics of dislocations are
derived (Jefimenko type and Heaviside-Feynman type equations of dislocations).
In addition, exact closed-form solutions of the elastic fields produced by a
dislocation loop are calculated as retarded line integral expressions for
subsonic motion. The fields of the elastic velocity and elastic distortion
surrounding the arbitrarily moving dislocation loop are given explicitly in
terms of the so-called three-dimensional elastodynamic Li\'enard-Wiechert
tensor potentials. The two-dimensional elastodynamic Li\'enard-Wiechert tensor
potentials and the near-field approximation of the elastic fields for straight
dislocations are calculated. The singularities of the near-fields of
accelerating screw and edge dislocations are determined.Comment: 31 pages, to appear in: Philosophical Magazin
On the fundamentals of the three-dimensional translation gauge theory of dislocations
We propose a dynamic version of the three-dimensional translation gauge
theory of dislocations. In our approach, we use the notions of the dislocation
density and dislocation current tensors as translational field strengths and
the corresponding response quantities (pseudomoment stress, dislocation
momentum flux). We derive a closed system of field equations in a very elegant
quasi-Maxwellian form as equations of motion for dislocations. In this
framework, the dynamical Peach-Koehler force density is derived as well.
Finally, the similarities and the differences between the Maxwell field theory
and the dislocation gauge theory are presented.Comment: 17 pages, to appear in: Mathematics and Mechanics of Solid
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