Compound Perpendicular Diffusion of Cosmic Rays and Field Line Random Walk, with Drift

2008 ◽  
Author(s):  
G. M. Webb ◽  
J. A. le Roux ◽  
G. P. Zank ◽  
E. Kh. Kaghashvili ◽  
G. Li ◽  
...  
Keyword(s):  
Random Walk ◽  
Cosmic Rays ◽  
Field Line ◽  
Random Walk With Drift ◽  
Perpendicular Diffusion

scholarly journals Optimal Strategies for Prudent Investors

1998 ◽  
Vol 01 (04) ◽  
pp. 473-486 ◽  
Author(s):  
Roberto Baviera ◽  
Michele Pasquini ◽  
Maurizio Serva ◽  
Angelo Vulpiani
Keyword(s):  
Growth Rate ◽  
Random Walk ◽  
Exponential Growth ◽  
Optimal Strategies ◽  
Maximum Amount ◽  
Exponential Growth Rate ◽  
One Dimensional ◽  
Economic Level ◽  
Random Walk With Drift ◽  
Analytical Expressions

We consider a stochastic model of investment on an asset in a stock market for a prudent investor. she decides to buy permanent goods with a fraction α of the maximum amount of money owned in her life in order that her economic level never decreases. The optimal strategy is obtained by maximizing the exponential growth rate for a fixed α. We derive analytical expressions for the typical exponential growth rate of the capital and its fluctuations by solving an one-dimensional random walk with drift.

scholarly journals Random Walk and Trapping of Interplanetary Magnetic Field Lines: Global Simulation, Magnetic Connectivity, and Implications for Solar Energetic Particles

2021 ◽  
Author(s):  
David Ruffolo ◽  
Rohit Chhiber ◽  
William H. Matthaeus ◽  
Arcadi V. Usmanov ◽  
Paisan Tooprakai ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Random Walk ◽  
Field Line ◽  
Large Scale ◽  
Transport Model ◽  
Source Region ◽  
Science Research ◽  
Energetic Particles ◽  
Solar Energetic Particles ◽  
Field Lines

<p>The random walk of magnetic field lines is an important ingredient in understanding how the connectivity of the magnetic field affects the spatial transport and diffusion of charged particles. As solar energetic particles (SEPs) propagate away from near-solar sources, they interact with the fluctuating magnetic field, which modifies their distributions. We develop a formalism in which the differential equation describing the field line random walk contains both effects due to localized magnetic displacements and a non-stochastic contribution from the large-scale expansion. We use this formalism together with a global magnetohydrodynamic simulation of the inner-heliospheric solar wind, which includes a turbulence transport model, to estimate the diffusive spreading of magnetic field lines that originate in different regions of the solar atmosphere. We first use this model to quantify field line spreading at 1 au, starting from a localized solar source region, and find rms angular spreads of about 20 – 60 degrees. In the second instance, we use the model to estimate the size of the source regions from which field lines observed at 1 au may have originated, thus quantifying the uncertainty in calculations of magnetic connectivity; the angular uncertainty is estimated to be about 20 degrees. Finally, we estimate the filamentation distance, i.e., the heliocentric distance up to which field lines originating in magnetic islands can remain strongly trapped in filamentary structures. We emphasize the key role of slab-like fluctuations in the transition from filamentary to more diffusive transport at greater heliocentric distances. This research has been supported in part by grant RTA6280002 from Thailand Science Research and Innovation and the Parker Solar Probe mission under the ISOIS project (contract NNN06AA01C) and a subcontract to University of Delaware from Princeton University (SUB0000165).  MLG acknowledges support from the Parker Solar Probe FIELDS MAG team.  Additional support is acknowledged from the  NASA LWS program  (NNX17AB79G) and the HSR program (80NSSC18K1210 & 80NSSC18K1648).</p>

scholarly journals A MODELIZACIÓN DOS CAMBIOS NA LONXEVIDADE DA POBLACIÓN DO PAÍS BASCO E A SÚA ESTIMACIÓN FUTURA

2015 ◽  
Vol 24 (2) ◽  
pp. 45-54
Author(s):  
Amaia Jone BETZUEN ÁLVAREZ ◽  
Amancio BETZUEN ZALBIDEGOITIA
Keyword(s):  
Random Walk ◽  
Random Walk With Drift

O obxectivo deste traballo é estimar a tendencia futura da mortaldade da poboación doPaís Basco a través da mellora da mortaldade para o período 1991-2013, para o cal oestudo é validable. A investigación realízase a través dun modelo estocástico bietápico aoque realizamos dúas achegas. Por unha banda, unha información inicial supervisada queposibilitará prognosticar mellor o avellentamento da poboación do País Basco baixo oscriterios de Solvencia II. E por outra, na estimación inclúese unha variante na extensión doparámetro do tempo de calendario mediante unha regresión logarítmica lineal no canto dacoñecida “random walk with drift”. 

Detailed analytical investigation of magnetic field line random walk in turbulent plasmas: II. Isotropic turbulence

2009 ◽  
Vol 75 (2) ◽  
pp. 183-192 ◽  
Author(s):  
I. KOURAKIS ◽  
R. C. TAUTZ ◽  
A. SHALCHI
Keyword(s):  
Magnetic Field ◽  
Random Walk ◽  
Field Line ◽  
Isotropic Turbulence ◽  
Mean Square Displacement ◽  
Analytical Investigation ◽  
Turbulence Spectrum ◽  
Quasilinear Theory ◽  
Magnetic Turbulence ◽  
Field Lines

AbstractThe random walk of magnetic field lines in the presence of magnetic turbulence in plasmas is investigated from first principles. An isotropic model is employed for the magnetic turbulence spectrum. An analytical investigation of the asymptotic behavior of the field-line mean-square displacement 〈(Δx)2〉 is carried out, in terms of the position variable z. It is shown that 〈(Δx)2〉 varies as ~z ln z for large distance z. This result corresponds to a superdiffusive behavior of field line wandering. This investigation complements previous work, which relied on a two-component model for the turbulence spectrum. Contrary to that model, quasilinear theory appears to provide an adequate description of the field-line random walk for isotropic turbulence.

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