Transitions from low-density state towards high-density state in stochastic bistable plasma-condensate systems
In this article we study transitions from low-density states towards high-density states in bistable plasmacondensate systems. We take into account an anisotropy in transference of adatoms between neighbour layers induced by the electric field near substrate. We derive the generalized one-layer mod...
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| Cite this: | Transitions from low-density state towards high-density state in stochastic bistable plasma-condensate systems / A.V. Dvornichenko, V.O. Kharchenko, D.O. Kharchenko // Condensed Matter Physics. — 2018. — Т. 21, № 4. — С. 43001: 1–8 . — Бібліогр.: 32 назв. — англ. |
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| author | Dvornichenko, A.V. Kharchenko, V.O. Kharchenko, D.O. |
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| citation_txt | Transitions from low-density state towards high-density state in stochastic bistable plasma-condensate systems / A.V. Dvornichenko, V.O. Kharchenko, D.O. Kharchenko // Condensed Matter Physics. — 2018. — Т. 21, № 4. — С. 43001: 1–8 . — Бібліогр.: 32 назв. — англ. |
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| description | In this article we study transitions from low-density states towards high-density states in bistable plasmacondensate systems. We take into account an anisotropy in transference of adatoms between neighbour layers
induced by the electric field near substrate. We derive the generalized one-layer model by assuming that the
strength of the electric field is subjected to both periodic oscillations and multiplicative fluctuations. By studying
the homogeneous system we discuss the corresponding mean passage time. In the limit of weak fluctuations,
we show the optimization of the mean passage time with variation in the frequency of periodic driving in the
non-adiabatic limit. Noise induced effects corresponding to asynchronization and acceleration in the transition
dynamics are studied in detail.
У цiй статтi нами дослiджено переходи вiд стану з низькою густиною адсорбату до стану з його високою
концентрацiєю в бiстабiльних системах плазма-конденсат. При цьому враховується анiзотропiя у переходах адатомiв мiж сусiднiми шарами, що спричинена дiєю електричного поля поблизу поверхнi. В рамках узагальненої одношарової моделi дослiджуються ефекти, пов’язанi з перiодичними коливаннями та
флуктуацiями напруженостi електричного поля. При дослiдженнi однорiдної системи встановлено особливостi зовнiшнього впливу на середнiй час переходу вiд стану з низькою густиною адсорбату до стану
з високою його концентрацiєю. В границi слабких флуктуацiй продемонстровано процес оптимiзацiй середнього часу переходу при змiнi частоти перiодичного керуючого поля. Детально вивчаються ефекти,
пов’язанi з процесами асинхронiзацiї та прискорення в динамiцi переходiв.
|
| first_indexed | 2025-12-07T13:21:37Z |
| format | Article |
| fulltext |
Condensed Matter Physics, 2018, Vol. 21, No 4, 43001: 1–8
DOI: 10.5488/CMP.21.43001
http://www.icmp.lviv.ua/journal
Transitions from low-density state towards
high-density state in stochastic bistable
plasma-condensate systems
A.V. Dvornichenko1, V.O. Kharchenko1,2, D.O. Kharchenko2
1 Sumy State University, 2 Rymskyi-Korsakov St., 40007 Sumy, Ukraine
2 Institute of Applied Physics of the National Academy of Sciences of Ukraine,
58 Petropavlivska St., 40000 Sumy, Ukraine
Received August 13, 2018, in final form October 29, 2018
In this article we study transitions from low-density states towards high-density states in bistable plasma-
condensate systems. We take into account an anisotropy in transference of adatoms between neighbour layers
induced by the electric field near substrate. We derive the generalized one-layer model by assuming that the
strength of the electric field is subjected to both periodic oscillations and multiplicative fluctuations. By studying
the homogeneous system we discuss the corresponding mean passage time. In the limit of weak fluctuations,
we show the optimization of the mean passage time with variation in the frequency of periodic driving in the
non-adiabatic limit. Noise induced effects corresponding to asynchronization and acceleration in the transition
dynamics are studied in detail.
Key words: stochastic systems, bistable systems, mean passage time
PACS: 05.10.Gg, 05.40.-a, 05.45.-a
1. Introduction
Plasma-condensate systems serve a useful technique to produce well structured thin films with
separatedmulti-layer adsorbate islands of nano-meter size of semiconductors andmetals [1, 2]. Nowadays,
such nano-structured thin films attract an increased interest due to their technological applications in
modern nano-electronic devices possessing exceptional functionality [3–6]. Adsorptive bistable systems
manifest a stochastic resonance phenomenon under conditions of periodically varying pressure of gaseous
atmosphere (see, for example, [7]), or chemical potential [8]. In the technological applications, this
stochastic resonance effect is used to optimize the output signal-to-noise ratio, when fluctuations (noise)
play a constructive role and enhance a response of a nonlinear dynamical system subjected to a weak
external periodic signal [9–15].
Previously, it was shown that one can control the adsorbate concentration on the substrate and
the corresponding first-order phase transitions between low-density and high-density states by varying
temperature, adsorption and desorption rates in adsorptive systems [16–23]. At the same time, it was
shown that multi-layer systems manifest a cascade of first-order phase transitions when a new additional
layer of adsorbate is formed [24, 25]. Such systems were mainly studied under the assumption of
the equiprobable transference of adatoms between neighbour layers according to the standard vertical
diffusion mechanism [26, 27].
A fabrication of nanostructured thin films with the help of plasma-condensate devices is governed
by the following mechanism. Ions, sputtered by magnetron, attain a growing surface located in a hollow
cathode due to the presence of the electric field near it and become adatoms. Being exposed under the
action of an electric field near the substrate, the main part of adatoms are re-evaporated to be later
This work is licensed under a Creative Commons Attribution 4.0 International License . Further distribution
of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
43001-1
https://doi.org/10.5488/CMP.21.43001
http://www.icmp.lviv.ua/journal
http://creativecommons.org/licenses/by/4.0/
A.V. Dvornichenko, V.O. Kharchenko, D.O. Kharchenko
ionized again and to return back onto the upper layers of the growing surface [28]. Hence, plasma-
condensate systems are characterized by the anisotropy in the transitions of adatoms between neighbour
layers induced by the electric field, with preferential motion from bottom layers towards top layers. We
have shown earlier that in such a bistable system, the anisotropy strength related to the strength of the
static electric field near the substrate controls the dynamics and morphology of the growing adsorbate
structures [29]. In [30], we have derived a reduced one-layer model describing the pattern formation on
the intermediate layer of a multi-layer system.
In the present study, we focus on the transitions from low-density states towards high-density states
in the effective reduced model of plasma-condensate system derived in [30], by taking into account both
periodic oscillations and fluctuations of the strength of the electric field. The main aim of the work
is to define such an external impact onto the mean passage time from low- to high-density state in a
homogeneous model of multi-layer plasma-condensate systems.
We organize our work in the following manner. In the next section we discuss the stochastic model of
a plasma-condensate system. In section 3 we analyze an influence of the periodic driving and stochastic
force onto the mean passage time. Main conclusions are collected in the last section.
2. Model of adsorptive system
By considering the adsorbate concentration xn ∈ [0, 1] on the selected n layer of a multi-layer
system (where x0 = 1 corresponds to the substrate) we follow [24, 29] and describe an evolution of
the adsorbate on each n-th layer by the reaction force f (xn) which includes adsorption, desorption and
transference reactions between neighbour layers. Adsorption processes on any n-th layer are governed by
the term fa = kapxn−1(1 − xn)(1 − xn+1), where the adsorption rate ka is defined through the adsorption
energy Ea, temperature T measured in energetic units and frequency factor ν as ka = νe−Ea/T ; p is
the density of the plasma. Adsorption is possible on free sites on the current n-th layer if both non-
zero adsorbate concentration on the precursor (n − 1)-th layer and free space on the next (n + 1)-th
layer exist. Desorption processes are described by the term fd = −kdnxnxn−1(1 − xn+1), where the
desorption rate kdn = k0
d exp[Un(r)/T] is defined through the desorption rate for non-interacting particles
k0
d , and interaction potential of adsorbed particles Un(r) giving contribution due to a strong local
bond (substratum-mediated interactions). Desorption rate k0
d = νe−Ed/T relates to the life time scale
of adatoms τd = (k0
d)
−1, where Ed is the desorption energy. Desorption processes on n layer require a
non-zero adsorbate concentration on both n-th and (n − 1)-th layers and free space on the (n + 1)-th
layer. Transference of adatoms between neighbour layers is described by the ordinary vertical diffusion
fv = D0 (xn−1 + xn+1 − 2xn) with diffusion coefficient D0. As far as in plasma-condensate devices, the
electrical field presence near the substrate leads to the process of desorption — additional ionization —
adsorption onto upper layers, we take into account such an electrical field induced motion from lower to
upper layers in the form of additional transference of adsorbed particles from lower towards upper layers:
kr [(1 − xn)xn−1 − xn(1 − xn+1)], where the rate constant kr defines the anisotropy strength proportional
to the strength of the electric field near the substrate. Formally, the electrical field should go into the
exponent within the discrete state model. In our consideration, we use a weak field approximation (in the
lowest order expansion).
For the functional form of Un(x), we assume an attractive (as indicated earlier, substratum-mediated)
potential among particles separated by a distance r . In the framework of self-consistent approximation,
the potential Un(r) on any n-th layer can be represented as [24, 25, 29, 30]:
Un(r) = xn−1
[
−
∫
u(r − r ′)xn(r ′)dr′
]
, (1)
where the integration is provided over the whole surface. For the attractive potential u(r − r ′), we assume
that it is the same in any n-th layer. Following [22, 23] for u(r), we choose a Gaussian profile
u(r) =
2ε√
4πr2
0
exp
(
−
r
4r2
0
)
, (2)
43001-2
Low-high density state transitions in plasma-condensate systems
where ε is the interaction strength and r0 is the interaction radius. If the interaction radius is small
compared to the diffusion length, and the coverage is not much affected by variations in this radius, we
can use an approximation∫
u(r − r ′)xn(r ′)dr ′ '
∫
u(r − r ′) ×
∑
n
(r − r ′)n
n!
∇nxn(r)dr ′, (3)
which in the homogeneous case gives U(r) ' −2ε xnxn−1.
To define the adsorbate concentration on both (n − 1)-th and (n + 1)-th layers through xn, we exploit
the recipe proposed in [30] where the adsorbate concentration on the n-th layer, xn, can be defined as the
ratio between square occupied by the adsorbate on the n-th layer and on the substrate as xn ' Sn/S0. In
accordance with the principle of surface energy minimization, the adsorbate concentration on each next
layer of a multi-layer system is less than one on the previous layer. By considering a multi-layer adsorbate
island as a pyramidal structure with the terrace width d, the linear size of the multi-layer adsorbate
structure Rn ∝
√
Sn on each n-th layer decreases with the layer number n growth, Rn = R0 − nd. Hence,
for the adsorbate concentration on each n layer, we get xn = [1 − n(d/R0)]
2. By defining xn−1 and xn+1
in the same manner and introducing a small parameter β0 = 2d/R0 we get xn∓1 =
(√
xn ± 1/2β0
)2. Next,
we measure time in units kd, introduce dimensionless quantities α ≡ ka/kd, u ≡ kr/kd, D ≡ D0/kd,
ε = ε/T and fix β0 = 0.1, D = 1. By combining all the terms and dropping the index n, we finally get the
evolution equation of adsorbate concentration on the selected level of a multi-layer plasma-condensate
system in the following form [30]:
dt x = α(1 − x)ν(x) − xν(x)eλ(x) + uγ(x) +
β2
0
2
, (4)
where the following notations ν(x) = (
√
x + 1/2β0)
2[1 − (
√
x − 1/2β0)
2], λ(x) = −2εx(
√
x + β0/2)2,
γ(x) = β0[(1 − 2x)
√
x + β0/4] are used. The third term in the derived one-layer model (4) corresponds
to the electrical field influence onto the system dynamics.
Analysis of the stationary states of the deterministic system (4), defined from the condition dt x = 0,
allows us to obtain the phase diagram shown in figure 1 that illustrates the influence of the anisotropy
strength u onto the system states. Here, in the cusp (domain II), the system is bistable. The bifurcation
diagram x(α), representing first-order low-high density states transitions, is shown in the bottom inset
at u = 0.3, ε = 4.0. It follows that an increase in the anisotropy strength shrinks the bistability domain
in adsorption coefficient α and requires elevated values of the interaction strength ε for its realization.
The potential U(x) = −
∫
f (x)dx shown in the top inset corresponds to the spinodal and is plotted at
α = 0.064, ε = 4.0 and u = 0.7 (black dot inside the cusp in figure 1).
The control parameter u defines the external conditions for the growth of the layers. Generally, it can
be a function of time and/or can be changed in a stochastic manner. Next, we assume that the anisotropy
0.0 0.1 0.2 0.3
2
3
4
5
III
u = 0.3
u = 0.7
x
0.2 0.4 0.6
U
x
0.10 0.15 0.20
0.0
0.5
1.0
Figure 1. Phase diagram for the plasma-condensate system: (I) indicates the monostability domain, (II)
is the bistability domain.
43001-3
A.V. Dvornichenko, V.O. Kharchenko, D.O. Kharchenko
strength u is subjected to both periodic oscillations and fluctuations: u = u0+ A sin(ωt)+ξ(t), where u0 =
〈u〉 and ξ(t) is the Gaussian noise with zero mean, 〈ξ(t)〉 = 0 and correlation 〈ξ(t)ξ(t ′)〉 = 2σ2δ(|t − t ′ |);
σ2 is the intensity of fluctuations. In such a case, the deterministic evolution equation (4) attains the form
of the Langevin equation of the form
dt x = f (x) + Aγ(x) sin(ωt) + γ(x)ξ(t), (5)
where f (x) corresponds to the right-hand side of equation (4). It follows that if x = x0, where γ(x0) = 0,
then an influence of the electric field near the substrate onto adsorbate concentration disappears leading
to the isotropic deterministic system described only by adsorption, desorption and ordinary vertical
diffusion. At the same time, x0 is not an absorbing state as far as f (x0) , 0.
3. Mean passage time
Usually, the combined effect of periodic and stochastic driving forces in bistable potentials leads to a
stochastic resonance phenomenon. According to this scenario, a slow periodic force moves the “Brownian
particle”, located in one minimum of the bistable potential, towards its maximum. If the periodic driving
synchronizes with the fluctuation force, then the last one throws the “Brownian particle” over the potential
barrier and there takes place a switch between the two stable states. Let us provide a detailed description
of transitions from low- to high-density state by studying the passage time. To this end, we fix α = 0.064,
ε = 4.0 and u0 = 0.7, corresponding to the black point on the phase diagram in figure 1 on the spinodal
and perform numerical simulations of the Langevin equation (5) with the time step ∆t = 0.001 on the
graphical processor units (GPUs) with double precision. This technique provides an effective acceleration
of numerics by a factor of about 500 over the standard CPUs computing for this special problem.
In figure 2, we present the time dependence of the concentration of the adsorbate (one realization
shown by grey colour) and mean adsorbate concentration, averaged by 104 realizations (black curve).
In all simulations, the initial condition for the adsorbate concentration was selected in the minimum of
the potential U(x) corresponding to the low-density state. It follows that during the system evolution,
the combined influence of periodic and stochastic driving leads to the transition towards a high-density
state that in average occurs at time instant tp, when the dispersion 〈(δx)2〉, averaged over an ensemble,
falls to zero after its maximum (see inset in figure 2). Next, we study the influence of the periodic
driving (amplitude A and frequency ω) and the stochastic force (intensity of fluctuations σ2) onto the
mean passage time (mpt) from the low-density state, corresponding to minimum of the bistable potential
U(x) with small x, towards the high-density state [the minimum of U(x) with large x], defined as:
mpt = N−1 ∑N
i=1 tp, where sum is taken over N = 104 realizations.
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
0.2
0.3
0.4
0.5
0.6
tp
tp
x
(t
),
<
x
(t
)>
time
x(t)
<x(t)>
x10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
0.2
0.4
0.6
0.8
1.0
<
(
x
)2
>
time
Figure 2. Time dependencies of the concentration of the adsorbate (one realization shown by grey colour)
and mean adsorbate concentration, averaged by 104 realizations (black curve). Inset represents time
dependence of the dispersion. Results were obtained at A = 0.06 and ω = 10−3, σ2 = 0.05.
43001-4
Low-high density state transitions in plasma-condensate systems
3.1. Limit of quasi-deterministic driving
First, we focus our attention onto the influence of the periodic driving in the limit of weak fluctuations
with σ2 = 10−5. Dependencies of the mean passage time mpt from the low-density state to the high-
density state on the amplitude of the periodic driving A at different values of the frequency ω and on the
frequency ω at different values of the amplitude of the periodic driving A are shown in figures 3 (a), (b),
respectively. From figure 3 (a) it follows that at small values of the amplitude A, the transition becomes
impossible due to log(mpt) → ∞ independent of the frequency ω. With an increase in the amplitude A,
the value of the mpt abruptly decreases and remains constant at large values of A. An increase in the
periodic driving frequency ω requires elevated values of the driving amplitude A for the transition, on
the one hand, and results in a decrease in the transition time at large A, on the other hand.
The dependence mpt(ω), shown in figure 3 (b) is of a more complicated structure. Here, we have
a special kind of synchronization: at a fixed value of the periodic force amplitude A, an increase in
the frequency leads to a decrease in the transition time, until the minimal value mptmin is reached; at a
further growth in ω, the mpt increases. This minimal value of the transition time mptmin decreases with
the growth of the amplitude A. Hence, the mpt optimizes with the frequency of the periodic driving at
non-adiabatic limit.
a)
-4 -3 -2 -1 0
5
6
7
8
9
10
lo
g
(m
p
t)
log(A)
= 10
-3
= 5x10
-3
= 10
-2
b)
-9 -8 -7 -6 -5 -4 -3
5
6
7
8
9
10
lo
g
(m
p
t)
log( )
A=0.0436
A=0.06
A=0.1
mptmin
Figure 3. Dependencies of the mean passage time from low-density state to high-density state on a)
amplitude of the periodic driving A at different values on the frequency ω and b) frequency ω at different
values of amplitude of the periodic driving A at σ2 = 10−5.
3.2. Noise-induced effects
Next, we analyze a change in the transition time mpt by varying the intensity of fluctuations σ2
for different values of amplitude A and frequency ω of periodic driving. The dependencies mpt(σ2)
at A = 0.06 and different values of ω are shown in figure 4 (a). It is seen that at small values of
the driving frequency ω, an increase in the noise intensity weakly decreases the transition time [see
curve with filled squares at ω = 0.001 in figure 4 (a)]. If σ2 becomes large enough, σ2 > σ2
max, then the
stochastic force starts to play a dominant role in the system dynamics and a further increase in its intensity
significantly decreases the transition time from low- to high-density state. An increase in the periodic
driving frequency at small σ2 acts in the manner presented in figure 3 (b):mpt decreases, attains the value
mptmin and then increases. At σ2 < σ2
max, the value mptmin weakly increases with σ2. At large values
of the periodic force frequency, the transition from low- to high-density state occurs only at elevated
values of the intensity of fluctuations. At narrow interval of frequency values, the mean transition time
manifests a non-monotonous dependence on the noise intensity (see curves with filled and empty circles
at ω = 0.005 and 0.007 and curve with filled triangles at ω = 0.0074). Here, with an increase in the
intensity of fluctuations, the transition time increases, attains maximal value and then decreases. Hence,
at small values of the noise intensity, its increase leads to the delay in the transition dynamics. It means
43001-5
A.V. Dvornichenko, V.O. Kharchenko, D.O. Kharchenko
a)
-12 -10 -8 -6 -4 -2 0
5
6
7
8
9
10
= 0.001
= 0.002
= 0.005
= 0.007
= 0.0074
= 0.01
= 0.05
lo
g
(m
p
t)
log(
2
)
2
max
b)
-12 -10 -8 -6 -4 -2 0
5
6
7
8
9
10
lo
g
(m
p
t)
log(
2
)
A = 0.01
A = 0.05
A = 0.0675
A = 0.068
A = 0.0685
A = 0.07
A = 0.1
Figure 4.Dependencies of the mean passage time from low-density state to high-density state on intensity
of fluctuations σ2 at: a) A = 0.06 and different values of the frequencyω of periodic driving; b)ω = 0.01
and different values of the amplitude of the periodic driving A.
that in such conditions, one gets asynchronization in periodic and stochastic driving: while periodic force
moves the “Brownian particle” towards the maximum of the bistable potential, fluctuations return it back
to the low-density state. With a further increase in σ2, the noise starts to play the dominant role in the
system dynamics which leads to the transition through the potential barrier.
In figure 4 (b), we present dependencies of the mean transition time on the noise intensity at a fixed
value of the periodic driving frequency ω = 0.01 and different values of the driving amplitude A. It
follows that with an increase in A, the transition from low- to high-density state occurs faster. An increase
in the noise intensity leads to (i) a decrease in the transition time at small values of the periodic driving
amplitude; (ii) a delay in the transition dynamics at intermediate values of A; (iii) at elevated values of
the periodic driving amplitude, the noise influences the system dynamics only at large values.
4. Conclusions
In this article, we have provided a detailed study of the transitions from low-density state to high-
density state in multi-layer plasma-condensate systems in a reduced one-layer model. By taking into
account the anisotropy in transference between layers, induced by the electric field near the substrate, we
assume periodic oscillations and fluctuations of the electric field strength. We discussed the influence
of both periodic driving and stochastic force onto the mean passage time needed for transition from the
low-density state towards the high-density state. It is shown that in the case of a weak fluctuating force,
the mean passage time decreases with the periodic driving amplitude growth and optimizes with the
frequency of periodic driving. An increase in the intensity of the electrical field fluctuations at small σ2
delays the transition towards the high-density state due to asynchronization in periodic and stochastic
driving; a growth in the intensity of fluctuations at large σ2, leads to a decrease in the time needed to
pass from low-density state towards high-density state.
We expect that this investigation could be also useful for a source of hydrogen negative ions with
a metal-hydride electrode [31] and while using the metal-hydride as a plasma-facing material in fusion
reactors [32].
Acknowledgements
Support of this research by the Ministry of Education and Science of Ukraine, project
No. 0117U003927, is gratefully acknowledged.
43001-6
Low-high density state transitions in plasma-condensate systems
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A.V. Dvornichenko, V.O. Kharchenko, D.O. Kharchenko
Переходи вiд стану з низькою концентрацiєю до стану з
високою концентрацiєю у стохастичнiй бiстабiльнiй системi
плазма-конденсат
А.В. Дворниченко1, В.О. Харченко1,2, Д.О. Харченко2
1 Сумський державний унiверситет, вул. Римського-Корсакова, 2, 40007 Суми, Україна
2 Iнститут прикладної фiзики НАН України, вул. Петропавлiвська, 58, 40000 Суми, Україна
У цiй статтi нами дослiджено переходи вiд стану з низькою густиною адсорбату до стану з його високою
концентрацiєю в бiстабiльних системах плазма-конденсат. При цьому враховується анiзотропiя у пере-
ходах адатомiв мiж сусiднiми шарами, що спричинена дiєю електричного поля поблизу поверхнi. В рам-
ках узагальненої одношарової моделi дослiджуються ефекти, пов’язанi з перiодичними коливаннями та
флуктуацiями напруженостi електричного поля. При дослiдженнi однорiдної системи встановлено осо-
бливостi зовнiшнього впливу на середнiй час переходу вiд стану з низькою густиною адсорбату до стану
з високою його концентрацiєю. В границi слабких флуктуацiй продемонстровано процес оптимiзацiй се-
реднього часу переходу при змiнi частоти перiодичного керуючого поля. Детально вивчаються ефекти,
пов’язанi з процесами асинхронiзацiї та прискорення в динамiцi переходiв.
Ключовi слова: стохастичнi системи, бiстабiльнi системи, середнiй час переходу мiж станами
43001-8
Introduction
Model of adsorptive system
Mean passage time
Limit of quasi-deterministic driving
Noise-induced effects
Conclusions
|
| id | nasplib_isofts_kiev_ua-123456789-157463 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-12-07T13:21:37Z |
| publishDate | 2018 |
| publisher | Інститут фізики конденсованих систем НАН України |
| record_format | dspace |
| spelling | Dvornichenko, A.V. Kharchenko, V.O. Kharchenko, D.O. 2019-06-20T03:41:39Z 2019-06-20T03:41:39Z 2018 Transitions from low-density state towards high-density state in stochastic bistable plasma-condensate systems / A.V. Dvornichenko, V.O. Kharchenko, D.O. Kharchenko // Condensed Matter Physics. — 2018. — Т. 21, № 4. — С. 43001: 1–8 . — Бібліогр.: 32 назв. — англ. 1607-324X PACS: 05.10.Gg, 05.40.-a, 05.45.-a DOI:10.5488/CMP.21.43001 arXiv:1806.08526 https://nasplib.isofts.kiev.ua/handle/123456789/157463 In this article we study transitions from low-density states towards high-density states in bistable plasmacondensate systems. We take into account an anisotropy in transference of adatoms between neighbour layers induced by the electric field near substrate. We derive the generalized one-layer model by assuming that the strength of the electric field is subjected to both periodic oscillations and multiplicative fluctuations. By studying the homogeneous system we discuss the corresponding mean passage time. In the limit of weak fluctuations, we show the optimization of the mean passage time with variation in the frequency of periodic driving in the non-adiabatic limit. Noise induced effects corresponding to asynchronization and acceleration in the transition dynamics are studied in detail. У цiй статтi нами дослiджено переходи вiд стану з низькою густиною адсорбату до стану з його високою концентрацiєю в бiстабiльних системах плазма-конденсат. При цьому враховується анiзотропiя у переходах адатомiв мiж сусiднiми шарами, що спричинена дiєю електричного поля поблизу поверхнi. В рамках узагальненої одношарової моделi дослiджуються ефекти, пов’язанi з перiодичними коливаннями та флуктуацiями напруженостi електричного поля. При дослiдженнi однорiдної системи встановлено особливостi зовнiшнього впливу на середнiй час переходу вiд стану з низькою густиною адсорбату до стану з високою його концентрацiєю. В границi слабких флуктуацiй продемонстровано процес оптимiзацiй середнього часу переходу при змiнi частоти перiодичного керуючого поля. Детально вивчаються ефекти, пов’язанi з процесами асинхронiзацiї та прискорення в динамiцi переходiв. Support of this research by the Ministry of Education and Science of Ukraine, project No. 0117U003927, is gratefully acknowledged. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Transitions from low-density state towards high-density state in stochastic bistable plasma-condensate systems Переходи вiд стану з низькою концентрацiєю до стану з високою концентрацiєю у стохастичнiй бiстабiльнiй системi плазма-конденсат Article published earlier |
| spellingShingle | Transitions from low-density state towards high-density state in stochastic bistable plasma-condensate systems Dvornichenko, A.V. Kharchenko, V.O. Kharchenko, D.O. |
| title | Transitions from low-density state towards high-density state in stochastic bistable plasma-condensate systems |
| title_alt | Переходи вiд стану з низькою концентрацiєю до стану з високою концентрацiєю у стохастичнiй бiстабiльнiй системi плазма-конденсат |
| title_full | Transitions from low-density state towards high-density state in stochastic bistable plasma-condensate systems |
| title_fullStr | Transitions from low-density state towards high-density state in stochastic bistable plasma-condensate systems |
| title_full_unstemmed | Transitions from low-density state towards high-density state in stochastic bistable plasma-condensate systems |
| title_short | Transitions from low-density state towards high-density state in stochastic bistable plasma-condensate systems |
| title_sort | transitions from low-density state towards high-density state in stochastic bistable plasma-condensate systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/157463 |
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