First- and Second-order Crossover of the Escape Rate for the Biaxial Spin Model with the Field Applied along the Hard Axis at Resonance

2011 ◽  
Vol 59 (1) ◽  
pp. 93-97
Author(s):  
Doo Hyung Kang ◽  
Mincheol Shin ◽  
Gwang-Hee Kim
Keyword(s):  
Spin Model ◽  
Second Order ◽  
Escape Rate ◽  
Hard Axis ◽  
At Resonance

scholarly journals On second order nonlocal boundary value problem at resonance

2016 ◽  
Vol 56 (1) ◽  
pp. 143-153 ◽  
Author(s):  
Katarzyna Szymańska-Dębowska
Keyword(s):  
Boundary Value Problem ◽  
Bounded Variation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Second Order ◽  
Function Of Bounded Variation ◽  
Nonlocal Boundary Value Problem ◽  
At Resonance ◽  
Problem At Resonance

Abstract This work is devoted to the existence of solutions for a system of nonlocal resonant boundary value problem $$\matrix{{x'' = f(t,x),} \hfill & {x'(0) = 0,} \hfill & {x'(1) = {\int_0^1 {x(s)dg(s)},} }} $$ where f : [0, 1] × ℝk → ℝk is continuous and g : [0, 1] → ℝk is a function of bounded variation.

Stability and resonance conditions of second-order fractional systems

2016 ◽  
Vol 24 (4) ◽  
pp. 659-672 ◽  
Author(s):  
Elena Ivanova ◽  
Xavier Moreau ◽  
Rachid Malti
Keyword(s):  
Second Order ◽  
Damping Factor ◽  
Fractional Differentiation ◽  
Resonance Amplitude ◽  
Fractional Systems ◽  
Integral Number ◽  
At Resonance ◽  
Fractional System ◽  
The Stability ◽  
Normalized Gain

The interest of studying fractional systems of second order in electrical and mechanical engineering is first illustrated in this paper. Then, the stability and resonance conditions are established for such systems in terms of a pseudo-damping factor and a fractional differentiation order. It is shown that a second-order fractional system might have a resonance amplitude either greater or less than one. Moreover, three abaci are given allowing the pseudo-damping factor and the differentiation order to be determined for, respectively, a desired normalized gain at resonance, a desired phase at resonance, and a desired normalized resonant frequency. Furthermore, it is shown numerically that the system root locus presents a discontinuity when the fractional differentiation order is an integral number.

scholarly journals Escape rate of a biaxial nanospin system in a magnetic field: First- and second-order transitions between quantum and classical regimes

1999 ◽  
Vol 59 (21) ◽  
pp. 13581-13583 ◽  
Author(s):  
Chang Soo Park ◽  
Sahng-Kyoon Yoo ◽  
D. K. Park ◽  
Dal-Ho Yoon
Keyword(s):  
Magnetic Field ◽  
Second Order ◽  
Escape Rate
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