5,899 research outputs found
Global-in-time solutions for the isothermal Matovich-Pearson equations
In this paper we study the Matovich-Pearson equations describing the process
of glass fiber drawing. These equations may be viewed as a 1D-reduction of the
incompressible Navier-Stokes equations including free boundary, valid for the
drawing of a long and thin glass fiber. We concentrate on the isothermal case
without surface tension. Then the Matovich-Pearson equations represent a
nonlinearly coupled system of an elliptic equation for the axial velocity and a
hyperbolic transport equation for the fluid cross-sectional area. We first
prove existence of a local solution, and, after constructing appropriate
barrier functions, we deduce that the fluid radius is always strictly positive
and that the local solution remains in the same regularity class. To the best
of our knowledge, this is the first global existence and uniqueness result for
this important system of equations
Theory of Drop Formation
We consider the motion of an axisymmetric column of Navier-Stokes fluid with
a free surface. Due to surface tension, the thickness of the fluid neck goes to
zero in finite time. After the singularity, the fluid consists of two halves,
which constitute a unique continuation of the Navier-Stokes equation through
the singular point. We calculate the asymptotic solutions of the Navier-Stokes
equation, both before and after the singularity. The solutions have scaling
form, characterized by universal exponents as well as universal scaling
functions, which we compute without adjustable parameters
Quantification of finite-temperature effects on adsorption geometries of -conjugated molecules
The adsorption structure of the molecular switch azobenzene on Ag(111) is
investigated by a combination of normal incidence x-ray standing waves and
dispersion-corrected density functional theory. The inclusion of non-local
collective substrate response (screening) in the dispersion correction improves
the description of dense monolayers of azobenzene, which exhibit a substantial
torsion of the molecule. Nevertheless, for a quantitative agreement with
experiment explicit consideration of the effect of vibrational mode
anharmonicity on the adsorption geometry is crucial.Comment: 12 pages, 3 figure
Supersymmetry and the Chiral Schwinger Model
We have constructed the N=1/2 supersymmetric general Abelian model with
asymmetric chiral couplings. This leads to a N=1/2 supersymmetrization of the
Schwinger model. We show that the supersymmetric general model is plagued with
problems of infrared divergence. Only the supersymmetric chiral Schwinger model
is free from such problems and is dynamically equivalent to the chiral
Schwinger model because of the peculiar structure of the N=1/2 multiplets.Comment: one 9 pages Latex file, one ps file with one figur
Operator Ordering Problem of the Nonrelativistic Chern-Simons Theory
The operator ordering problem due to the quantization or regularization
ambiguity in the Chern-Simons theory exists. However, we show that this can be
avoided if we require Galilei covariance of the nonrelativistic Abelian
Chern-Simons theory even at the quantum level for the extended sources. The
covariance can be recovered only by choosing some particular operator orderings
for the generators of the Galilei group depending on the quantization
ambiguities of the commutation relation. We show that the
desired ordering for the unusual prescription is not the same as the well-known
normal ordering but still satisfies all the necessary conditions. Furthermore,
we show that the equations of motion can be expressed in a similar form
regardless of the regularization ambiguity. This suggests that the different
regularization prescriptions do not change the physics. On the other hand, for
the case of point sources the regularization prescription is uniquely
determined, and only the orderings, which are equivalent to the usual one, are
allowed.Comment: 18 page
Charged Particle with Magnetic Moment in the Aharonov-Bohm Potential
We considered a charged quantum mechanical particle with spin
and gyromagnetic ratio in the field af a magnetic string. Whereas the
interaction of the charge with the string is the well kown Aharonov-Bohm effect
and the contribution of magnetic moment associated with the spin in the case
is known to yield an additional scattering and zero modes (one for each
flux quantum), an anomaly of the magnetic moment (i.e. ) leads to bound
states. We considered two methods for treating the case . \\ The first is
the method of self adjoint extension of the corresponding Hamilton operator. It
yields one bound state as well as additional scattering. In the second we
consider three exactly solvable models for finite flux tubes and take the limit
of shrinking its radius to zero. For finite radius, there are bound
states ( is the number of flux quanta in the tube).\\ For the bound
state energies tend to infinity so that this limit is not physical unless along with . Thereby only for fluxes less than unity the results of
the method of self adjoint extension are reproduced whereas for larger fluxes
bound states exist and we conclude that this method is not applicable.\\ We
discuss the physically interesting case of small but finite radius whereby the
natural scale is given by the anomaly of the magnetic moment of the electron
.Comment: 16 pages, Latex, NTZ-93-0
Planar Two-particle Coulomb Interaction: Classical and Quantum Aspects
The classical and quantum aspects of planar Coulomb interactions have been
studied in detail. In the classical scenario, Action Angle Variables are
introduced to handle relativistic corrections, in the scheme of
time-independent perturbation theory. Complications arising due to the
logarithmic nature of the potential are pointed out. In the quantum case,
harmonic oscillator approximations are considered and effects of the
perturbations on the excited (oscillator) states have been analysed. In both
the above cases, the known 3+1-dimensional analysis is carried through side by
side, for a comparison with the 2+1-dimensional (planar) results.Comment: LaTex, Figures on request, e-mail:<[email protected]
Local and Global Analytic Solutions for a Class of Characteristic Problems of the Einstein Vacuum Equations in the "Double Null Foliation Gauge"
The main goal of this work consists in showing that the analytic solutions
for a class of characteristic problems for the Einstein vacuum equations have
an existence region larger than the one provided by the Cauchy-Kowalevski
theorem due to the intrinsic hyperbolicity of the Einstein equations. To prove
this result we first describe a geometric way of writing the vacuum Einstein
equations for the characteristic problems we are considering, in a gauge
characterized by the introduction of a double null cone foliation of the
spacetime. Then we prove that the existence region for the analytic solutions
can be extended to a larger region which depends only on the validity of the
apriori estimates for the Weyl equations, associated to the "Bel-Robinson
norms". In particular if the initial data are sufficiently small we show that
the analytic solution is global. Before showing how to extend the existence
region we describe the same result in the case of the Burger equation, which,
even if much simpler, nevertheless requires analogous logical steps required
for the general proof. Due to length of this work, in this paper we mainly
concentrate on the definition of the gauge we use and on writing in a
"geometric" way the Einstein equations, then we show how the Cauchy-Kowalevski
theorem is adapted to the characteristic problem for the Einstein equations and
we describe how the existence region can be extended in the case of the Burger
equation. Finally we describe the structure of the extension proof in the case
of the Einstein equations. The technical parts of this last result is the
content of a second paper.Comment: 68 page
Finite-size anyons and perturbation theory
We address the problem of finite-size anyons, i.e., composites of charges and
finite radius magnetic flux tubes. Making perturbative calculations in this
problem meets certain difficulties reminiscent of those in the problem of
pointlike anyons. We show how to circumvent these difficulties for anyons of
arbitrary spin. The case of spin 1/2 is special because it allows for a direct
application of perturbation theory, while for any other spin, a redefinition of
the wave function is necessary. We apply the perturbative algorithm to the
N-body problem, derive the first-order equation of state and discuss some
examples.Comment: 18 pages (RevTex) + 4 PS figures (all included); a new section on
equation of state adde
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