2,592 research outputs found
The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions
We show that for two dimensional manifolds M with negative Euler
characteristic there exists subsets of the space of smooth Riemannian metrics
which are invariant and either parabolic or backwards-parabolic for the 2nd
order RG flow. We also show that solutions exists globally on these sets.
Finally, we establish the existence of an eternal solution that has both a UV
and IR limit, and passes through regions where the flow is parabolic and
backwards-parabolic
Evidence for contact delocalization in atomic scale friction
We analyze an advanced two-spring model with an ultra-low effective tip mass
to predict nontrivial and physically rich 'fine structure' in the atomic
stick-slip motion in Friction Force Microscopy (FFM) experiments. We
demonstrate that this fine structure is present in recent, puzzling
experiments. This shows that the tip apex can be completely or partially
delocalized, thus shedding new light on what is measured in FFM and, possibly,
what can happen with the asperities that establish the contact between
macroscopic sliding bodies.Comment: 4 pages text and 3 figure
On the L_p-solvability of higher order parabolic and elliptic systems with BMO coefficients
We prove the solvability in Sobolev spaces for both divergence and
non-divergence form higher order parabolic and elliptic systems in the whole
space, on a half space, and on a bounded domain. The leading coefficients are
assumed to be merely measurable in the time variable and have small mean
oscillations with respect to the spatial variables in small balls or cylinders.
For the proof, we develop a set of new techniques to produce mean oscillation
estimates for systems on a half space.Comment: 44 pages, introduction revised, references expanded. To appear in
Arch. Rational Mech. Ana
Dynamical heat channels
We consider heat conduction in a 1D dynamical channel. The channel consists
of a group of noninteracting particles, which move between two heat baths
according to some dynamical process. We show that the essential thermodynamic
properties of the heat channel can be evaluated from the diffusion properties
of the underlying particles. Emphasis is put on the conduction under anomalous
diffusion conditions. \\{\bf PACS number}: 05.40.+j, 05.45.ac, 05.60.cdComment: 4 figure
Partial Schauder estimates for second-order elliptic and parabolic equations
We establish Schauder estimates for both divergence and non-divergence form
second-order elliptic and parabolic equations involving H\"older semi-norms not
with respect to all, but only with respect to some of the independent
variables.Comment: CVPDE, accepted (2010)
To the modification of methods of nuclear chronometry in astrophysics and geophysics
In practically all known till now methods of nuclear chronometry there were
usually taken into account the life-times of only fundamental states of
-radioactive nuclei. But in the processes of nuclear synthesis in stars
and under the influence of the constant cosmic radiation on surfaces of planets
the excitations of the -radioactive nuclei are going on. Between them
there are the states with the excited -particles inside the parent
nuclei and so with much smaller life-times. And inside the large masses of
stellar, terrestrial and meteoric substances the transitions between different
internal conditions of radioactive nuclei are accompanied by infinite chains of
the -radiations with the subsequent -absorptions, the further
-radiations etc. For the description of the -decay evolution
with considering of such excited states and multiple -radiations and
-absorptions inside stars and under the influence of the cosmic
radiation on the earth surface we present the quantum-mechanical approach,
which is based on the generalized Krylov-Fock theorem.
Some simple estimations are also presented. They bring to the conclusion that
the usual (non-corrected) "nuclear clocks" do really indicate not to realistic
values but to the \emph{upper limits} of the durations of the -decay
stellar and planet processes.Comment: 6 pages, Standard LaTeX v.2
Unitarity of the tree approximation to the Glauber AA amplitude for large A
The nucleus-nucleus Glauber amplitude in the tree approximation is studied
for heavy participant nuclei. It is shown that, contrary to previous published
results, it is not unitary for realistic values of nucleon-nucleon
cross-sections.Comment: 15 pages, 1 figure, 1 table. Submitted to Yad. Fi
Non-affine geometrization can lead to nonphysical instabilities
Geometrization of dynamics consists of representing trajectories by geodesics
on a configuration space with a suitably defined metric. Previously, efforts
were made to show that the analysis of dynamical stability can also be carried
out within geometrical frameworks, by measuring the broadening rate of a bundle
of geodesics. Two known formalisms are via Jacobi and Eisenhart metrics. We
find that this geometrical analysis measures the actual stability when the
length of any geodesic is proportional to the corresponding time interval. We
prove that the Jacobi metric is not always an appropriate parametrization by
showing that it predicts chaotic behavior for a system of harmonic oscillators.
Furthermore, we show, by explicit calculation, that the correspondence between
dynamical- and geometrical-spread is ill-defined for the Jacobi metric. We find
that the Eisenhart dynamics corresponds to the actual tangent dynamics and is
therefore an appropriate geometrization scheme.Comment: Featured on the Cover of the Journal. 9 pages, 6 figures:
http://iopscience.iop.org/1751-8121/48/7/07510
A Design of a Material Assembly in Space-Time Generating and Storing Energy
The paper introduces a theoretical background of the mechanism of electromagnetic energy and power accumulation and its focusing in narrow pulses travelling along a transmission line with material parameters variable in 1D-space and time. This mechanism may be implemented due to a special material geometry- a distribution of two different dielectrics in a spatio-temporal checkerboard. We concentrate on the practically reasonable means to bring this mechanism into action in a device that may work both as energy generator and energy storage. The basic ideas discussed below appear to be fairly general; we have chosen their electromagnetic implementation as an excellent framework for the entire concept
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