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Contents Ann. Phys. 12009

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Ann. Phys. (Berlin) 18, No. 1, 1 – 3 (2009) / DOI 10.1002/andp.200918001
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Page 4 – 12
Christine Borchers, Jan Schroers, and Ralf Busch
Prediction of spinodal wavelength in continuously cooled
metallic liquid
The spinodal decomposition of a deeply
undercooled metallic liquid Zr41.2
Ti13.8 Cu12.5 Ni10 Be22.5 between 800 and 700 K
is analysed in the framework of the theory of Cahn
and Hilliard for continuous cooling, and the wavelength with maximum amplification is predicted,
using as input parameters thermodynamic values
gained in experiments. Electron microscopical
studies show the microstructure of glass forming alloys Zr41.2 Ti13.8 Cu12.5 Ni10 Be22.5 . The
as-cast material exhibits a two phase mixture of
amorphous regions with different compositions.
Evidence for spinodal decomposition is given, and the computed maximumamplitude wavelength corresponds well with the one found in the experiments.
Page 13 – 32
Mariusz P. Da̧browski, Janusz Garecki, and David B. Blaschke
Conformal transformations and conformal invariance in
Conformal transformations are frequently used tools in order to study relations between various theories of gravity and Einstein’s general relativity theory. In this paper we discuss the rules of these transformations for geometric quantities as well as for the matter energy-momentum tensor. We show
the subtlety of the matter energy-momentum conservation law which refers
to the fact that the conformal transformation “creates” an extra matter term
composed of the conformal factor which enters the conservation law. In an
extreme case of the flat original spacetime the matter is “created” due to work
done by the conformal transformation to bend the spacetime which was originally flat. We discuss how to construct the conformally invariant gravity theories and also find the conformal transformation rules for the curvature invariants R2 , Rab Rab , Rabcd Rabcd and the Gauss-Bonnet invariant in a spacetime
of an arbitrary dimension. Finally, we present the conformal transformation
rules in the fashion of the duality transformations of the superstring theory.
In such a case the transitions between conformal frames reduce to a simple
change of the sign of a redefined conformal factor.
© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Page 33 – 44
Hiromu Ishio and Emmanuel Haven
Information in asset pricing: a wave function approach
This paper introduces a quantum-like wave function as an information wave
function. We show how the option pricing partial differential equation can be
re-written when we account for such information wave function. We use two
stochastic differential equations, one of which relates to Nelson’s hypothesis
of Universal Brownian motion. We also provide for two examples which further highlight the proposed theory.
Page 45 – 56
D. H. Delphenich
Integrability and the variational formulation of non-conservative
mechanical systems
It is shown that one can obtain canonically-defined dynamical equations for
non-conservative mechanical systems by starting with a first variation functional, instead of an action functional, and finding their zeroes. The kernel
of the first variation functional, as an integral functional, is a 1-form on the
manifold of kinematical states, which then represents the dynamical state of
the system. If the 1-form is exact then the first variation functional is associated with the first variation of an action functional in the usual manner. The
dynamical equations then follow from the vanishing of the dual of the Spencer
operator that acts on the dynamical state. This operator, in turn, relates to the
integrability of the kinematical states. The method is applied to the modeling
of damped oscillators.
Page 57 – 70
Alexander Unzicker
A look at the abandoned contributions to cosmology of Dirac,
Sciama, and Dicke
The separate contributions to cosmology of the above researchers are revisited and a cosmology encompassing their basic ideas is proposed. We study
Dirac’s article (1938) on the large number hypothesis, Sciama’s proposal
(1953) of realizing Mach’s principle, and Dicke’s considerations (1957) on
a flat-space representation of general relativity with a variable speed of light
(VSL). Dicke’s tentative theory can be formulated in a way which is compatible with Sciama’s hypothesis on the gravitational constant G. Additionally,
such a cosmological model is shown to satisfy Dirac’s second ‘large number’
hypothesis on the total number of particles in the universe being proportional
to the square of the epoch. In the same context, Dirac’s first hypothesis on an
epoch-dependent G – contrary to his prediction – does not necessarily produce a visible time dependence of G. While Dicke’s proposal reproduces the
classical tests of GR in first approximation, the cosmological redshift is described by a shortening of measuring rods rather than an expansion of space.
Since the temporal evolution of the horizon R is governed by Ṙ(t) = c(t), the
flatness and horizon problems do not arise in the common form.
© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Ann. Phys. (Berlin) 18, No. 1 (2009)
Page 71 – 72
Dieter Hoffmann and Mark Walker (eds.), “Physicists between Autonomy and
Adaptation. The German Physical Society in the Third Reich” (in German)
Reviewer: Hubert Goenner
Page 73 – 76
A closer look into the grand history of
Annalen der Physik: themes which occupied
the minds of physicists one century ago.
Annalen der Physik is indexed in Chemical Abstracts Service/SciFinder, COMPENDEX, Current
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Recognized by the European Physical Socity
© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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