771 research outputs found
On the harmonic Boltzmannian waves in laser-plasma interaction
We study the permanent regimes of the reduced Vlasov-Maxwell system for
laser-plasma interaction. A non-relativistic and two different relativistic
models are investigated. We prove the existence of solutions where the
distribution function is Boltzmannian and the electromagnetic variables are
time-harmonic and circularly polarized
Impact of strong magnetic fields on collision mechanism for transport of charged particles
One of the main applications in plasma physics concerns the energy production
through thermo-nuclear fusion. The controlled fusion is achieved by magnetic
confinement i.e., the plasma is confined into a toroidal domain (tokamak) under
the action of huge magnetic fields. Several models exist for describing the
evolution of strongly magnetized plasmas, most of them by neglecting the
collisions between particles. The subject matter of this paper is to
investigate the effect of large magnetic fields with respect to a collision
mechanism. We consider here linear collision Boltzmann operators and derive, by
averaging with respect to the fast cyclotronic motion due to strong magnetic
forces, their effective collision kernels
A Fast Algorithm for Computing the p-Curvature
We design an algorithm for computing the -curvature of a differential
system in positive characteristic . For a system of dimension with
coefficients of degree at most , its complexity is \softO (p d r^\omega)
operations in the ground field (where denotes the exponent of matrix
multiplication), whereas the size of the output is about . Our
algorithm is then quasi-optimal assuming that matrix multiplication is
(\emph{i.e.} ). The main theoretical input we are using is the
existence of a well-suited ring of series with divided powers for which an
analogue of the Cauchy--Lipschitz Theorem holds.Comment: ISSAC 2015, Jul 2015, Bath, United Kingdo
Design of waveguides, bends and splitters in photonic crystal slabs with hexagonal holes in a triangular lattice
Waveguides in photonic crystal slabs (PCS) can be obtained by omitting a row of holes (W1-waveguides). In general the propagation properties in such waveguides suffer from the unavoidable periodic sidewall corrugation caused by the remaining parts of the crystal. The corrugation acts as a Bragg reflector, causing the occurrence of so-called mini stopbands in the transmission of the waveguide. The effect is quite strong in PCS with circular holes, but it can be significantly reduced if correctly oriented hexagonal holes are used. This so-called hexagon-type PCS allows the design of waveguides, bends and splitters having a relatively high group velocity and a wide transmission window in the PCS stopband for modes having their magnetic field oriented mainly perpendicular to the slab
The Ising model and Special Geometries
We show that the globally nilpotent G-operators corresponding to the factors
of the linear differential operators annihilating the multifold integrals
of the magnetic susceptibility of the Ising model () are
homomorphic to their adjoint. This property of being self-adjoint up to
operator homomorphisms, is equivalent to the fact that their symmetric square,
or their exterior square, have rational solutions. The differential Galois
groups are in the special orthogonal, or symplectic, groups. This self-adjoint
(up to operator equivalence) property means that the factor operators we
already know to be Derived from Geometry, are special globally nilpotent
operators: they correspond to "Special Geometries".
Beyond the small order factor operators (occurring in the linear differential
operators associated with and ), and, in particular,
those associated with modular forms, we focus on the quite large order-twelve
and order-23 operators. We show that the order-twelve operator has an exterior
square which annihilates a rational solution. Then, its differential Galois
group is in the symplectic group . The order-23 operator
is shown to factorize in an order-two operator and an order-21 operator. The
symmetric square of this order-21 operator has a rational solution. Its
differential Galois group is, thus, in the orthogonal group
.Comment: 33 page
Ising n-fold integrals as diagonals of rational functions and integrality of series expansions: integrality versus modularity
We show that the n-fold integrals of the magnetic susceptibility
of the Ising model, as well as various other n-fold integrals of the "Ising
class", or n-fold integrals from enumerative combinatorics, like lattice Green
functions, are actually diagonals of rational functions. As a consequence, the
power series expansions of these solutions of linear differential equations
"Derived From Geometry" are globally bounded, which means that, after just one
rescaling of the expansion variable, they can be cast into series expansions
with integer coefficients. Besides, in a more enumerative combinatorics
context, we show that generating functions whose coefficients are expressed in
terms of nested sums of products of binomial terms can also be shown to be
diagonals of rational functions. We give a large set of results illustrating
the fact that the unique analytical solution of Calabi-Yau ODEs, and more
generally of MUM ODEs, is, almost always, diagonal of rational functions. We
revisit Christol's conjecture that globally bounded series of G-operators are
necessarily diagonals of rational functions. We provide a large set of examples
of globally bounded series, or series with integer coefficients, associated
with modular forms, or Hadamard product of modular forms, or associated with
Calabi-Yau ODEs, underlying the concept of modularity. We finally address the
question of the relations between the notion of integrality (series with
integer coefficients, or, more generally, globally bounded series) and the
modularity (in particular integrality of the Taylor coefficients of mirror
map), introducing new representations of Yukawa couplings.Comment: 100 page
Ekonomska analiza razvoja rumunjske crne metalurgije
The ferrous metallurgy represents a traditional occupation, being extremely important for the national economy. Romania has gone through all the stages foreseen for the restructuring of this industry in compliance with the provisions of the European Councilâs Decision (1999/582/EC) concerning the partnership for the EU adherence, which included a special chapter on ferrous metallurgy, the provisions of the Protocol no. 2 (ECSC), as well as with other significant normative acts subsequently enacted. Following the performed restructuring â privatizations, state allowances, liquidations, re-technologization â the activity of this sector has developed, still being under the potential of the Romanian metallurgic industry. Nowadays, the disadvantages relating to energy intensity and the increased need for imported raw materials are doubled by the difficulties generated by the global crisis.Crna metalurgija je tradicionalna djelatnost i veoma je znaÄajna za nacionalno gospodarstvo. Rumunjska je proĆĄla kroz sve faze predviÄene za preustroj te industrije sukladno odredbama Odluke Europskog vijeÄa (1999/582/EZ) u svezi s partnerstvom za zajedniĆĄtvo EU, ĆĄto je obuhvaÄalo i posebno poglavlje o crnoj metalurgiji, te sukladno odredbama Protokola br. 2 (EZUÄ â Europska zajednica za ugljen i Äelik) kao i drugim znaÄajnim naknadno donesenim normativnim aktima, Nakon obavljena preustroja â privatizacije, drĆŸavnih subvencija, likvidacija, retehnologizacije, razvila se djelatnost ove grane, ali joĆĄ uvijek ispod moguÄnosti rumunjske metalurĆĄke industrije. Danas su se zbog teĆĄkoÄa generiranih od globalne krize udvostruÄile nepovoljne okolnosti koje se odnose na energijski intenzivne djelatnosti i poveÄanu potrebu za sirovinama
Waveguides, bends and Y-junctions with improved transmission and bandwidth in hexagon-type SOI photonic crystal slabs
This paper presents novel ways of implementing waveguide components in photonic crystal slabs based on silicon-on-insulator (SOI). The integration platform we consider consists of hexaÂŹgonal holes arranged in a triangular lattice (âhexagon-typeâ photonic crystal). The waveguides are made of one missing row of holes (W1) with triangular air inclusions symmetrically added on each side of the waveguide. \ud
Size and position of these inclusions are tuning parameters for the band diagram and can be used for minimizing the distributed Bragg reflection (DBR) effect. The waveguides show single-mode behavior with reasonably high group velocity and large transmission window, inside the gap between H-like modes**. These waveguides, closely resembling conventional ridge waveguides, can be combined to form efficient bends and Y-junctions. The bends and Y-junctions include intermediate short waveguide sections at half the bend angle playing the role of corner âmirrorsâ. Qualitative design rules were obtained from 2D calculations based on effective index approximation.\u
- âŠ