1,098 research outputs found
Fractional Fokker-Planck Equation for Fractal Media
We consider the fractional generalizations of equation that defines the
medium mass. We prove that the fractional integrals can be used to describe the
media with noninteger mass dimensions. Using fractional integrals, we derive
the fractional generalization of the Chapman-Kolmogorov equation (Smolukhovski
equation). In this paper fractional Fokker-Planck equation for fractal media is
derived from the fractional Chapman-Kolmogorov equation. Using the Fourier
transform, we get the Fokker-Planck-Zaslavsky equations that have fractional
coordinate derivatives. The Fokker-Planck equation for the fractal media is an
equation with fractional derivatives in the dual space.Comment: 17 page
Electroproduction of Charmonia off Protons and Nuclei
Elastic virtual photoproduction of charmonia on nucleons is calculated in a
parameter free way with the light-cone dipole formalism and the same input:
factorization in impact parameters, light-cone wave functions for the photons
and the charmonia, and the universal phenomenological dipole cross section
which is fitted to other data. The charmonium wave functions are calculated
with four known realistic potentials, and two models for the dipole cross
section are tested. Very good agreement with data for the cross section of
charmonium electroproduction is found in a wide range of and . Using
the ingredients from those calculations we calculate also exclusive
electroproduction of charmonia off nuclei. Here new effects become important,
(i) color filtering of the pair on its trajectory through nuclear
matter, (ii) dependence on the finite lifetime of the fluctuation
(coherence length) and (iii) gluon shadowing in a nucleus compared to the one
in a nucleon. Total coherent and incoherent cross sections for C, Cu and Pb as
functions of are presented. The results can be tested with future
electron-nucleus colliders or in the peripheral collisions of relativistic
heavy ions.Comment: Talk at 2-nd International Workshop on Hadron Physics, 25-29
September 2002, Coimbra, Portugal. To appear in the Workshop Proceedings
(will be published by the American Institute of Physics
Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches
Fractional generalization of an exterior derivative for calculus of
variations is defined. The Hamilton and Lagrange approaches are considered.
Fractional Hamilton and Euler-Lagrange equations are derived. Fractional
equations of motion are obtained by fractional variation of Lagrangian and
Hamiltonian that have only integer derivatives.Comment: 21 pages, LaTe
Path Integral for Quantum Operations
In this paper we consider a phase space path integral for general
time-dependent quantum operations, not necessarily unitary. We obtain the path
integral for a completely positive quantum operation satisfied Lindblad
equation (quantum Markovian master equation). We consider the path integral for
quantum operation with a simple infinitesimal generator.Comment: 24 pages, LaTe
Fractional Liouville and BBGKI Equations
We consider the fractional generalizations of Liouville equation. The
normalization condition, phase volume, and average values are generalized for
fractional case.The interpretation of fractional analog of phase space as a
space with fractal dimension and as a space with fractional measure are
discussed. The fractional analogs of the Hamiltonian systems are considered as
a special class of non-Hamiltonian systems. The fractional generalization of
the reduced distribution functions are suggested. The fractional analogs of the
BBGKI equations are derived from the fractional Liouville equation.Comment: 20 page
Fractional Systems and Fractional Bogoliubov Hierarchy Equations
We consider the fractional generalizations of the phase volume, volume
element and Poisson brackets. These generalizations lead us to the fractional
analog of the phase space. We consider systems on this fractional phase space
and fractional analogs of the Hamilton equations. The fractional generalization
of the average value is suggested. The fractional analogs of the Bogoliubov
hierarchy equations are derived from the fractional Liouville equation. We
define the fractional reduced distribution functions. The fractional analog of
the Vlasov equation and the Debye radius are considered.Comment: 12 page
Transport Equations from Liouville Equations for Fractional Systems
We consider dynamical systems that are described by fractional power of
coordinates and momenta. The fractional powers can be considered as a
convenient way to describe systems in the fractional dimension space. For the
usual space the fractional systems are non-Hamiltonian. Generalized transport
equation is derived from Liouville and Bogoliubov equations for fractional
systems. Fractional generalization of average values and reduced distribution
functions are defined. Hydrodynamic equations for fractional systems are
derived from the generalized transport equation.Comment: 11 pages, LaTe
Fractional Derivative as Fractional Power of Derivative
Definitions of fractional derivatives as fractional powers of derivative
operators are suggested. The Taylor series and Fourier series are used to
define fractional power of self-adjoint derivative operator. The Fourier
integrals and Weyl quantization procedure are applied to derive the definition
of fractional derivative operator. Fractional generalization of concept of
stability is considered.Comment: 20 pages, LaTe
Corrosion Resistance of Fe-Cr-Al-Si Alloys with Low Chromium Content
Within the framework of this work, alloys with a chromium content of 5 to14 wt%, aluminum from 0 to 4 wt% and silicon from 0 to 4 wt%. The samples were tested for resistance to oxidation with calm dry air (800 ∘C, 0.1 MPa) for 60 hours; in high parameter water (350 ∘C, 16 MPa), for 300 hours; in steam (400 ∘C, 10 MPa), for 72hours and superheated steam (1100 ∘C, 0.1 MPa) for 1 hour.The compositions most resistant to corrosion under the specified conditions were determined, and the existence of a synergistic effect of silicon and aluminum asalloying elements of iron alloys was confirmed.
Keywords: fuel cladding; PWR; tolerant fuel, ferrite steel; corrosive resistance steel
"Unusual" metals in two dimensions: one-particle model of the metal-insulator transition at T=0
The conductance of disordered nano-wires at T=0 is calculated in one-particle
approximation by reducing the original multi-dimensional problem for an open
bounded system to a set of exactly one-dimensional non-Hermitian problems for
mode propagators. Regarding two-dimensional conductor as a limiting case of
three-dimensional disordered quantum waveguide, the metallic ground state is
shown to result from its multi-modeness. On thinning the waveguide (in
practice, e. g., by means of the ``pressing'' external electric field) the
electron system undergoes a continuous phase transition from metallic to
insulating state. The result predicted conform qualitatively to the observed
anomalies of the resistance of different planar electron and hole systems.Comment: 7 pages, LATEX-2
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