Anomalous diffusion in interstellar medium
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Vladimir V. Uchaikin
Abstract
Interstellar medium (ISM) consists of few components being in chaotic motion of turbulent kind. They interact with each other, exchange with energy, and some of them emit and absorb electromagnetic radiation and elementary particles. Neutral gas under the influence of gravity is crammed into molecular clouds with magnetic fields, charged particles born in supernova explosions and accelerated on their remnants fly in the magnetic fields and magnetized clouds and scattered on them, continuing their motion around wriggling magnetic lines. How far away this picture is from the slender motion of the planets in our solar system along the Keplerian orbits! On these giant scales, the Newton calm motion laws are replaced by the Kolmogorov stormy turbulence laws, molecular diffusion is replaced by turbulent diffusion, and integer-order differential equations are replaced by the fractional one. Some details of this change of paradigms are discussed in this chapter. In its conclusion, the authors dare to state a hypothesis that the deep reason for the appearance of fractional orders operators instead of the integer ones, is a transition from a closed mechanical system to an open system.
Abstract
Interstellar medium (ISM) consists of few components being in chaotic motion of turbulent kind. They interact with each other, exchange with energy, and some of them emit and absorb electromagnetic radiation and elementary particles. Neutral gas under the influence of gravity is crammed into molecular clouds with magnetic fields, charged particles born in supernova explosions and accelerated on their remnants fly in the magnetic fields and magnetized clouds and scattered on them, continuing their motion around wriggling magnetic lines. How far away this picture is from the slender motion of the planets in our solar system along the Keplerian orbits! On these giant scales, the Newton calm motion laws are replaced by the Kolmogorov stormy turbulence laws, molecular diffusion is replaced by turbulent diffusion, and integer-order differential equations are replaced by the fractional one. Some details of this change of paradigms are discussed in this chapter. In its conclusion, the authors dare to state a hypothesis that the deep reason for the appearance of fractional orders operators instead of the integer ones, is a transition from a closed mechanical system to an open system.
Kapitel in diesem Buch
- Frontmatter I
- Preface V
- Contents VII
- Fractional electromagnetics 1
- Fractional electrodynamics with spatial dispersion 25
- Fractional-calculus tools applied to study the nonexponential relaxation in dielectrics 53
- Fractional diffusion-wave phenomena 71
- Fractional diffusion and parametric subordination 99
- The fractional advection-dispersion equation for contaminant transport 129
- Anomalous diffusion in interstellar medium 151
- Fractional kinetics in random/complex media 183
- Nonlocal quantum mechanics: fractional calculus approach 207
- Fractional quantum fields 237
- Fractional quantum mechanics of open quantum systems 257
- Fractional quantum mechanics with topological constraint 279
- Fractional time quantum mechanics 299
- Index 317
Kapitel in diesem Buch
- Frontmatter I
- Preface V
- Contents VII
- Fractional electromagnetics 1
- Fractional electrodynamics with spatial dispersion 25
- Fractional-calculus tools applied to study the nonexponential relaxation in dielectrics 53
- Fractional diffusion-wave phenomena 71
- Fractional diffusion and parametric subordination 99
- The fractional advection-dispersion equation for contaminant transport 129
- Anomalous diffusion in interstellar medium 151
- Fractional kinetics in random/complex media 183
- Nonlocal quantum mechanics: fractional calculus approach 207
- Fractional quantum fields 237
- Fractional quantum mechanics of open quantum systems 257
- Fractional quantum mechanics with topological constraint 279
- Fractional time quantum mechanics 299
- Index 317
