1,724 research outputs found
A tree of linearisable second-order evolution equations by generalised hodograph transformations
We present a list of (1+1)-dimensional second-order evolution equations all
connected via a proposed generalised hodograph transformation, resulting in a
tree of equations transformable to the linear second-order autonomous evolution
equation. The list includes autonomous and nonautonomous equations.Comment: arXiv version is already officia
On integration of the Kowalevski gyrostat and the Clebsch problems
For the Kowalevski gyrostat change of variables similar to that of the
Kowalevski top is done. We establish one to one correspondence between the
Kowalevski gyrostat and the Clebsch system and demonstrate that Kowalevski
variables for the gyrostat practically coincide with elliptic coordinates on
sphere for the Clebsch case. Equivalence of considered integrable systems
allows to construct two Lax matrices for the gyrostat using known rational and
elliptic Lax matrices for the Clebsch model. Associated with these matrices
solutions of the Clebsch system and, therefore, of the Kowalevski gyrostat
problem are discussed. The Kotter solution of the Clebsch system in modern
notation is presented in detail.Comment: LaTeX, 24 page
Effective action for Einstein-Maxwell theory at order RF**4
We use a recently derived integral representation of the one-loop effective
action in Einstein-Maxwell theory for an explicit calculation of the part of
the effective action containing the information on the low energy limit of the
five-point amplitudes involving one graviton, four photons and either a scalar
or spinor loop. All available identities are used to get the result into a
relatively compact form.Comment: 13 pages, no figure
On nonlocal symmetries, nonlocal conservation laws and nonlocal transformations of evolution equations
We discuss nonlocal symmetries and nonlocal conservation laws that follow
from the systematic potentialisation of evolution equations. Those are the Lie
point symmetries of the auxiliary systems, also known as potential symmetries.
We define higher-degree potential symmetries which then lead to nonlocal
conservation laws and nonlocal transformations for the equations. We
demonstrate our approach by the Burgers' hierarchy and the
Calogero-Degasperis-Ibragimov-Shabat hierarchy
Mechanism of Deep-focus Earthquakes Anomalous Statistics
Analyzing the NEIC-data we have shown that the spatial deep-focus earthquake
distribution in the Earth interior over the 1993-2006 is characterized by the
clearly defined periodical fine discrete structure with period L=50 km, which
is solely generated by earthquakes with magnitude M 3.9 to 5.3 and only on the
convergent boundary of plates. To describe the formation of this structure we
used the model of complex systems by A. Volynskii and S. Bazhenov. The key
property of this model consists in the presence of a rigid coating on a soft
substratum. It is shown that in subduction processes the role of a rigid
coating plays the slab substance (lithosphere) and the upper mantle acts as a
soft substratum. Within the framework of this model we have obtained the
estimation of average values of stress in the upper mantle and Young's modulus
for the oceanic slab (lithosphere) and upper mantle.Comment: 9 pages, 7 figure
Construction of the Pauli-Villars-regulated Dirac vacuum in electromagnetic fields
Using the Pauli-Villars regularization and arguments from convex analysis, we
construct solutions to the classical time-independent Maxwell equations in
Dirac's vacuum, in the presence of small external electromagnetic sources. The
vacuum is not an empty space, but rather a quantum fluctuating medium which
behaves as a nonlinear polarizable material. Its behavior is described by a
Dirac equation involving infinitely many particles. The quantum corrections to
the usual Maxwell equations are nonlinear and nonlocal. Even if photons are
described by a purely classical electromagnetic field, the resulting vacuum
polarization coincides to first order with that of full Quantum
Electrodynamics.Comment: Final version to appear in Arch. Rat. Mech. Analysi
Chiral perturbation theory
The main elements and methods of chiral perturbation theory, the effective
field theory of the Standard Model below the scale of spontaneous chiral
symmetry breaking, are summarized. Applications to the interactions of mesons
and baryons at low energies are reviewed, with special emphasis on developments
of the last three years. Among the topics covered are the strong,
electromagnetic and semileptonic weak interactions of mesons at and beyond
next--to--leading order in the chiral expansion, nonleptonic weak interactions
of mesons, virtual photon corrections and the meson--baryon system. The
discussion is limited to processes at zero temperature, for infinite volume and
with at most one baryon.Comment: 84 pages, Latex, 11 PostScript figures (in separate file) embedded
with epsfig.sty, complete ps file (compressed, uuencoded, 0.6 MB) available
via email on request; to appear in Progr. Part. Nucl. Phys., vol. 3
Quantum effects in the evolution of vortices in the electromagnetic field
We analyze the influence of electron-positron pairs creation on the motion of
vortex lines in electromagnetic field. In our approach the electric and
magnetic fields satisfy nonlinear equations derived from the Euler-Heisenberg
effective Lagrangian. We show that these nonlinearities may change the
evolution of vortices.Comment: REVTEX4 and 5 EPS figure
Espécies florestais nativas prioritárias para produção de sementes e mudas no estado do Amapá.
O Brasil assumiu compromisso internacional de restaurar e reflorestar 12 milhões de hectares de florestas até 2030, nas suas Contribuições Nacionalmente Determinadas firmadas no Acordo de Paris. Embora o desmatamento ainda não seja um grande problema para o Amapá, sementes e mudas de espécies nativas possuem grande potencial como produto regional capaz de contribuir para geração de renda complementar das comunidades e agricultores que detém florestas e utilizam esses recursos como meio de vida. Por isso é necessário conhecer a importância ecológica e comercial de espécies nativas, para auxiliar a cadeia de produção de sementes e mudas na região. O objetivo do estudo foi realizar um levantamento de espécies nativas prioritárias no estado do Amapá, avaliando o grau de importância econômica e ambiental dessas espécies
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