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Geometric effects of a quarter of corrugated torus
In the spirit of the thin-layer quantization scheme, we give the effective
Shr\"{o}dinger equation for a particle confined to a corrugated torus, in which
the geometric potential is substantially changed by corrugation. We find the
attractive wells reconstructed by the corrugation not being at identical
depths, which is strikingly different from that of a corrugated nanotube,
especially in the inner side of the torus. By numerically calculating the
transmission probability, we find that the resonant tunneling peaks and the
transmission gaps are merged and broadened by the corrugation of the inner side
of torus. These results show that the quarter corrugated torus can be used not
only to connect two tubes with different radiuses in different directions, but
also to filter the particles with particular incident~energies.Comment: 7 pages, 8 figure
The subordinated processes controlled by a family of subordinators and corresponding Fokker-Planck type equations
In this work, we consider subordinated processes controlled by a family of
subordinators which consist of a power function of time variable and a negative
power function of stable random variable. The effect of parameters in
the subordinators on the subordinated process is discussed. By suitable
variable substitutions and Laplace transform technique, the corresponding
fractional Fokker-Planck-type equations are derived. We also compute their mean
square displacements in a free force field. By choosing suitable ranges of
parameters, the resulting subordinated processes may be subdiffusive, normal
diffusive or superdiffusive.Comment: 11 pages, accepted by J. Stat. Mech.: Theor. Ex
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