Size effect of the subharmonic Shapiro steps on the interference phenomena in the Frenkel-Kontorova model with realistic substrate potentials

2013 ◽  
Vol 114 (17) ◽  
pp. 174504 ◽  
Author(s):  
J. Tekić ◽  
P. Mali ◽  
Z. Ivić ◽  
M. Pantić
Keyword(s):  
Size Effect ◽  
Shapiro Steps ◽  
Kontorova Model

scholarly journals Description of Shapiro steps on the potential energy surface of a Frenkel–Kontorova model, Part II: free boundaries of the chain

2021 ◽  
Vol 94 (3) ◽  
Author(s):  
W. Quapp ◽  
J. M. Bofill
Keyword(s):  
Free Boundary ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Free Boundaries ◽  
Shapiro Steps ◽  
Free Boundary Conditions ◽  
The Past ◽  
1D Chain ◽  
Kontorova Model

Abstract We explain Shapiro steps in a Frenkel–Kontorova (FK) model for a 1D chain of particles with free boundaries. The action of an external alternating force for the oscillating structure of the chain is important here. The different ’floors’ of the potential energy surface (PES) of this model play an important role. They are regions of kinks, double kinks, and so on. We will find out that the preferable movements are the sliding of kinks or antikinks through the chain. The more kinks / antikinks are included the higher is the ’floor’ through the PES. We find the Shapiro steps moving and oscillating anywhere between the floors. They start with a single jump over the highest SP in the global valley through the PES, like in part I of this series. They finish with complicated oscillations in the PES, for excitations directly over the critical depinning force. We use an FK model with free boundary conditions. In contrast to other results in the past, for this model, we obtain Shapiro steps in an unexpected, inverse sequence. We demonstrate Shapiro steps for a case with soft ’springs’ between an 8-particle FK chain. Graphic abstract

AMPLITUDE DEPENDENCE OF THE SHAPIRO STEPS

2007 ◽  
Vol 21 (23n24) ◽  
pp. 4234-4238 ◽  
Author(s):  
JASMINA TEKIĆ
Keyword(s):  
Amplitude Dependence ◽  
Step Width ◽  
Shapiro Steps ◽  
Existence And Stability ◽  
Kontorova Model

The existence and stability of the Shapiro steps in the ac driven dissipative Frenkel-Kontorova model are studied. The particular attention has been focused on, the variations of the step width and critical depinning force with the ac amplitude. The amplitude dependence is strongly influenced by the frequency of ac force where at the higher frequencies, the oscillations have the Bessel like form.

Influence of the deformable substrate potential on Shapiro steps in the incommensurate structure

2014 ◽  
Vol 28 (28) ◽  
pp. 1450225
Author(s):  
Zhi-Gang Shao ◽  
Jia-Yu Li ◽  
Cang-Long Wang ◽  
Lei Yang
Keyword(s):  
Shape Parameter ◽  
Amplitude Dependence ◽  
Standard Potential ◽  
Shapiro Steps ◽  
Substrate Potential ◽  
Threshold Force ◽  
Incommensurate Structure ◽  
Kontorova Model

Influence of the deformable substrate potential on Shapiro steps is investigated in the overdamped Frenkel–Kontorova model with incommensurate structure. Both the number and size of Shapiro steps are strongly affected by the deformation of substrate potential. As substrate potential gets deformed, the oscillation of Shapiro steps reduces and the periodicity of oscillation significantly changes. For some value of shape parameter r, the odd and even maxima oscillation forms of harmonic steps still maintain the Bessel-like form. Compared with those in standard potential, the amplitude dependence of harmonic step exhibits obvious difference. The dynamical DC threshold force correspondingly increases with rising the value of r.

scholarly journals Description of Shapiro steps on the potential energy surface of a Frenkel–Kontorova model Part I: The chain in a variable box

2021 ◽  
Vol 94 (3) ◽  
Author(s):  
W. Quapp ◽  
J. M. Bofill
Keyword(s):  
Potential Energy ◽  
Boundary Conditions ◽  
Potential Energy Surface ◽  
Periodic Boundary ◽  
Energy Surface ◽  
Periodic Boundary Conditions ◽  
Shapiro Steps ◽  
Kontorova Model

AbstractWe explain the vibrations of a Frenkel–Kontorova (FK) model under Shapiro steps by the action of an external alternating force. We demonstrate Shapiro steps for a case with soft ‘springs’ between an 8-particles FK chain. Shapiro steps start with a single jump over the highest $$\hbox {SP}_4$$ SP 4 in the global valley through the PES. They finish with doubled, and again doubled oscillations. We study in this part I a traditional FK model with periodic boundary conditions.

scholarly journals Shapiro steps in the commensurate structures with integer value of the winding number

2015 ◽  
Vol 38-39 (1) ◽  
pp. 1-10
Author(s):  
Petar Mali ◽  
Jasmina Tekić
Keyword(s):  
Degrees Of Freedom ◽  
Analytical Form ◽  
Mode Locking ◽  
Winding Number ◽  
Single Particles ◽  
Step Size ◽  
Standard Case ◽  
Shapiro Steps ◽  
The One ◽  
Kontorova Model

Abstract Dynamical mode locking phenomena and the appearance of Shapiro steps are studied in commensurate structures with integer values of winding number in the dc- and ac-driven overdamped Frenkel-Kontorova model. While in the standard case with sinusoidal substrate potential, the system reduces to the single particles model in which only harmonic steps exist and analytical form for the step size can be revealed, in the case of deformable potential, the presence of many degrees of freedom strongly influences the Shapiro steps. Whole series of subharmonic steps appear, and the two types of response functions, the one for the commensurate structures with odd and the one for the commensurate structures with even winding number have been observed.

Subharmonic Shapiro Steps in the Frenkel-Kontorova Model

2007 ◽  
Vol 50 (91) ◽  
pp. 229 ◽  
Author(s):  
Bambi Bambi ◽  
Jasmina Jasmina
Keyword(s):  
Shapiro Steps ◽  
Kontorova Model

The observation of solutions in Ni3Nb

1988 ◽  
Vol 46 ◽  
pp. 540-541
Author(s):  
Z.M. Wang ◽  
J.P. Zhang
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Phase Modulation ◽  
High Resolution Electron Microscopy ◽  
Antiphase Domain ◽  
Boundary Area ◽  
Matrix Type ◽  
Resolution Electron ◽  
Domain Boundaries ◽  
Kontorova Model

High resolution electron microscopy reveals that antiphase domain boundaries in β-Ni3Nb have a hexagonal unit cell with lattice parameters ah=aβ and ch=bβ, where aβ and bβ are of the orthogonal β matrix. (See Figure 1.) Some of these boundaries can creep “upstairs” leaving an incoherent area, as shown in region P. When the stepped boundaries meet each other, they do not lose their own character. Our consideration in this work is to estimate the influnce of the natural misfit δ{(ab-aβ)/aβ≠0}. Defining the displacement field at the boundary as a phase modulation Φ(x), following the Frenkel-Kontorova model [2], we consider the boundary area to be made up of a two unit chain, the upper portion of which can move and the lower portion of the β matrix type, assumed to be fixed. (See the schematic pattern in Figure 2(a)).

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