870 research outputs found
The adjoint problem in the presence of a deformed surface: the example of the Rosensweig instability on magnetic fluids
The Rosensweig instability is the phenomenon that above a certain threshold
of a vertical magnetic field peaks appear on the free surface of a horizontal
layer of magnetic fluid. In contrast to almost all classical hydrodynamical
systems, the nonlinearities of the Rosensweig instability are entirely
triggered by the properties of a deformed and a priori unknown surface. The
resulting problems in defining an adjoint operator for such nonlinearities are
illustrated. The implications concerning amplitude equations for pattern
forming systems with a deformed surface are discussed.Comment: 11 pages, 1 figur
On the Theory of Superfluidity in Two Dimensions
The superfluid phase transition of the general vortex gas, in which the
circulations may be any non-zero integer, is studied. When the net circulation
of the system is not zero the absence of a superfluid phase is shown. When the
net circulation of the vortices vanishes, the presence of off-diagonal long
range order is demonstrated and the existence of an order parameter is
proposed. The transition temperature for the general vortex gas is shown to be
the Kosterlitz---Thouless temperature. An upper bound for the average vortex
number density is established for the general vortex gas and an exact
expression is derived for the Kosterlitz---Thouless ensemble.Comment: 22 pages, one figure, written in plain TeX, published in J. Phys. A24
(1991) 502
Bosonization method for second super quantization
A bosonic-fermionic correspondence allows an analytic definition of
functional super derivative, in particular, and a bosonic functional calculus,
in general, on Bargmann- Gelfand triples for the second super quantization. A
Feynman integral for the super transformation matrix elements in terms of
bosonic anti-normal Berezin symbols is rigorously constructed.Comment: In memoriam of F. A. Berezin, accepted in Journal of Nonlinear
Mathematical Physics, 15 page
Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images
We present an efficient algorithm to compute Euler characteristic curves of
gray scale images of arbitrary dimension. In various applications the Euler
characteristic curve is used as a descriptor of an image.
Our algorithm is the first streaming algorithm for Euler characteristic
curves. The usage of streaming removes the necessity to store the entire image
in RAM. Experiments show that our implementation handles terabyte scale images
on commodity hardware. Due to lock-free parallelism, it scales well with the
number of processor cores. Our software---CHUNKYEuler---is available as open
source on Bitbucket.
Additionally, we put the concept of the Euler characteristic curve in the
wider context of computational topology. In particular, we explain the
connection with persistence diagrams
On the Meaning of the Principle of General Covariance
We present a definite formulation of the Principle of General Covariance
(GCP) as a Principle of General Relativity with physical content and thus
susceptible of verification or contradiction. To that end it is useful to
introduce a kind of coordinates, that we call quasi-Minkowskian coordinates
(QMC), as an empirical extension of the Minkowskian coordinates employed by the
inertial observers in flat space-time to general observers in the curved
situations in presence of gravitation. The QMC are operationally defined by
some of the operational protocols through which the inertial observers
determine their Minkowskian coordinates and may be mathematically characterized
in a neighbourhood of the world-line of the corresponding observer. It is taken
care of the fact that the set of all the operational protocols which are
equivalent to measure a quantity in flat space-time split into inequivalent
subsets of operational prescriptions under the presence of a gravitational
field or when the observer is not inertial. We deal with the Hole Argument by
resorting to de idea of the QMC and show how it is the metric field that
supplies the physical meaning of coordinates and individuates point-events in
regions of space-time where no other fields exist. Because of that the GCP has
also value as a guiding principle supporting Einstein's appreciation of its
heuristic worth in his reply to Kretschmann in 1918
Smooth adiabatic evolutions with leaky power tails
Adiabatic evolutions with a gap condition have, under a range of
circumstances, exponentially small tails that describe the leaking out of the
spectral subspace. Adiabatic evolutions without a gap condition do not seem to
have this feature in general. This is a known fact for eigenvalue crossing. We
show that this is also the case for eigenvalues at the threshold of the
continuous spectrum by considering the Friedrichs model.Comment: Final form, to appear in J. Phys. A; 11 pages, no figure
One-Dimensional Discrete Stark Hamiltonian and Resonance Scattering by Impurities
A one-dimensional discrete Stark Hamiltonian with a continuous electric field
is constructed by extension theory methods. In absence of the impurities the
model is proved to be exactly solvable, the spectrum is shown to be simple,
continuous, filling the real axis; the eigenfunctions, the resolvent and the
spectral measure are constructed explicitly. For this (unperturbed) system the
resonance spectrum is shown to be empty. The model considering impurity in a
single node is also constructed using the operator extension theory methods.
The spectral analysis is performed and the dispersion equation for the
resolvent singularities is obtained. The resonance spectrum is shown to contain
infinite discrete set of resonances. One-to-one correspondence of the
constructed Hamiltonian to some Lee-Friedrichs model is established.Comment: 20 pages, Latex, no figure
Korn's second inequality and geometric rigidity with mixed growth conditions
Geometric rigidity states that a gradient field which is -close to the
set of proper rotations is necessarily -close to a fixed rotation, and is
one key estimate in nonlinear elasticity. In several applications, as for
example in the theory of plasticity, energy densities with mixed growth appear.
We show here that geometric rigidity holds also in and in
interpolation spaces. As a first step we prove the corresponding linear
inequality, which generalizes Korn's inequality to these spaces
Three-periodic nets and tilings: natural tilings for nets
Rules for determining a unique natural tiling that carries a given three-periodic
net as its 1-skeleton are presented and justified. A computer implementation of
the rules and their application to tilings for zeolite nets and for the nets of the
RCSR database are described
Uniqueness in MHD in divergence form: right nullvectors and well-posedness
Magnetohydrodynamics in divergence form describes a hyperbolic system of
covariant and constraint-free equations. It comprises a linear combination of
an algebraic constraint and Faraday's equations. Here, we study the problem of
well-posedness, and identify a preferred linear combination in this divergence
formulation. The limit of weak magnetic fields shows the slow magnetosonic and
Alfven waves to bifurcate from the contact discontinuity (entropy waves), while
the fast magnetosonic wave is a regular perturbation of the hydrodynamical
sound speed. These results are further reported as a starting point for
characteristic based shock capturing schemes for simulations with
ultra-relativistic shocks in magnetized relativistic fluids.Comment: To appear in J Math Phy
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