740 research outputs found
Distinguished rheological models in the framework of a thermodynamical internal variable theory
We present and analyze a thermodynamical theory of rheology with single
internal variable. The universality of the model is ensured as long as the
mesoscopic and/or microscopic background processes satisfy the applied
thermodynamical principles, which are the second law, the basic balances and
the existence of an additional-tensorial-state variable. The resulting model,
which we suggest to call the Kluitenberg-Verh\'as body, is the
Poynting-Thomson-Zener body with an additional inertial element, or, in other
words, is the extension of Jeffreys model to solids. We argue that this
Kluitenberg-Verh\'as body is the natural thermodynamical building block of
rheology. An important feature of the presented methodology is that nontrivial
inequality-type restrictions arise for the four parameters of the model. We
compare these conditions and other aspects to those of other known
thermodynamical approaches, like Extended Irreversible Thermodynamics or the
original theory of Kluitenberg.Comment: 16 pages, 1 figure, revise
Impurity flows and plateau-regime poloidal density variation in a tokamak pedestal
In the pedestal of a tokamak, the sharp radial gradients of density and
temperature can give rise to poloidal variation in the density of impurities.
At the same time, the flow of the impurity species is modified relative to the
conventional neoclassical result. In this paper, these changes to the density
and flow of a collisional impurity species are calculated for the case when the
main ions are in the plateau regime. In this regime it is found that the
impurity density can be higher at either the inboard or outboard side. This
finding differs from earlier results for banana- or Pfirsch-Schl\"uter-regime
main ions, in which case the impurity density is always higher at the inboard
side in the absence of rotation. Finally, the modifications to the impurity
flow are also given for the other regimes of main-ion collisionality.Comment: 15 pages, 5 figures, submitted to Physics of Plasma
Moebius Structure of the Spectral Space of Schroedinger Operators with Point Interaction
The Schroedinger operator with point interaction in one dimension has a U(2)
family of self-adjoint extensions. We study the spectrum of the operator and
show that (i) the spectrum is uniquely determined by the eigenvalues of the
matrix U belonging to U(2) that characterizes the extension, and that (ii) the
space of distinct spectra is given by the orbifold T^2/Z_2 which is a Moebius
strip with boundary. We employ a parametrization of U(2) that admits a direct
physical interpretation and furnishes a coherent framework to realize the
spectral duality and anholonomy recently found. This allows us to find that
(iii) physically distinct point interactions form a three-parameter quotient
space of the U(2) family.Comment: 16 pages, 2 figure
s-wave scattering and the zero-range limit of the finite square well in arbitrary dimensions
We examine the zero-range limit of the finite square well in arbitrary
dimensions through a systematic analysis of the reduced, s-wave two-body
time-independent Schr\"odinger equation. A natural consequence of our
investigation is the requirement of a delta-function multiplied by a
regularization operator to model the zero-range limit of the finite-square well
when the dimensionality is greater than one. The case of two dimensions turns
out to be surprisingly subtle, and needs to be treated separately from all
other dimensions
Thermodynamic hierarchies of evolution equations
Non-equilibrium thermodynamics with internal variables introduces a natural
hierarchical arrangement of evolution equations. Three examples are shown: a
hierarchy of linear constitutive equations in thermodynamic rhelogy with a
single internal variable, a hierarchy of wave equations in the theory of
generalized continua with dual internal variables and a hierarchical
arrangement of the Fourier equation in the theory of heat conduction with
current multipliers.Comment: 7 pages, 1 figur
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