First-order depinning transition of a driven interface in disordered media

Park, Kwangho; Kwak, Sungbok; Kim, In-mook

doi:10.1103/physreve.65.035102

Cited by 3 publications

(3 citation statements)

References 18 publications

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“…Interestingly, the roughness exponent obtained from the QKPZ type of growth with inertia effect is the same as that obtained in the interface growth without inertia effect. 29) In the growth, inertia effect does not change the roughness of the interface. Therefore, it is very interesting to study the QEW type of growth with inertia effect because inertia effect might make the growing interface rougher according to our results.…”

Section: áð0þ 1=ð4þ2àdþmentioning

confidence: 99%

“…(29). To calculate the dynamical exponent z, the scale dependence of and must be known, which can be obtained by integrating eqs.…”

Section: áð0þ 1=ð4þ2àdþmentioning

confidence: 99%

“…[27][28][29] In the QKPZ type of growth without inertia effect, successive growth of the interface can occur at a site a bit far from the newly updated site near the depinning threshold. In the QKPZ type of growth with inertia effect, however, successive growth of the interface occurs more and more at very adjacent sites of the newly updated one as the inertia effect increases.…”

Section: áð0þ 1=ð4þ2àdþmentioning

confidence: 99%

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Dynamics of an Interface Driven through Random Media: The Effect of a Spatially Correlated Noise

Park

Kim

2003

J. Phys. Soc. Jpn.

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We studied the quenched Edwards-Wilkinson (QEW) equation with power-law type of a correlated noise near the depinning threshold. We solved analytically the QEW equation by using a functional renormalization group method. We obtained the critical exponents characterizing the depinning transition. We found that the value of the roughness exponent increases from 1 to 1.46341 in one spatial dimension as does from 0 to 0.5, where is a constant characterizing the degree of the correlation.Interface motion in random media has been a popular research topic in the field of nonequilibrium statistical physics 1) because it is related to many physical phenomena such as fluid invasion in porous media, 2,3) depinning of charge density waves, 4) fluid imbibition in paper, 5) driven flux motion in type-II superconductors, 6,7) etc. Interface motion driven through random media can be explained by the quenched Kardar-Parisi-Zhang (QKPZ) equation, 8) @Hðx; tÞ @twhere Hðx; tÞ is the interface height of a site x on the substrate at time t. ðx; HÞ denotes a quenched noise with the following properties:ÁðzÞ is assumed to be a monotonically decreasing function of z for z > 0, and to decay exponentially to zero over a finite distance a ? . f ðx À x 0 Þ is usually assumed to be a delta function d ðx À x 0 Þ, where d is a substrate dimension. It is known that in eq. (1) is nonzero for the interface driven in anisotropic random media but zero for the interface driven in isotropic random media when the velocity of a driven interface is almost 0. 9,10) Equation (1) is called the quenched Edwards-Wilkinson (QEW) equation in case of ¼ 0. 11) The interface in eq. (1) is pinned when the driving force F is smaller than F c . However, the interface moves with a constant velocity when F > F c . This phenomenon is called the pinning-depinning (PD) transition. The velocity of the interface follows v $ ðF À F c Þ close to the transition point, where is called the velocity exponent. When F ) F c , the dynamics of the driven interface show the same scaling behavior as in the case ðx; HÞ $ ðx; tÞ. 12) Then, if there do not exist spatial and temporal correlation in the noise, the noise ðx; tÞ has the following properties:Equation (1) is called the Kardar-Parisi-Zhang (KPZ) equation if 6 ¼ 0 and ðx; HÞ can be described as ðx; tÞ because of F ) F c . The width of the interface driven through random media shows a nontrivial dynamical scaling behavior near the depinning threshold,where h i ðtÞ is the height of a site i on the substrate at time t. " h h and L denote the mean height and system size, respectively. The symbol hÁ Á Ái stands for the statistical average. The scaling function gðxÞ approaches a constant for x ) 1, and gðxÞ $ x for x ( 1 with z ¼ =. The exponents , , z are called the roughness, growth, and dynamic exponent, respectively. The scaling exponents for the QKPZ equation are ¼ 0:63 and ¼ 0:63 in d ¼ 1. 13,14) The exponents for the QEW equation are ¼ 1 and ¼ 0:75 in d ¼ 1. 15,16) When one considers the continuum equation for a driven interface...

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Section: áð0þ 1=ð4þ2àdþmentioning

confidence: 99%

“…(29). To calculate the dynamical exponent z, the scale dependence of and must be known, which can be obtained by integrating eqs.…”

Section: áð0þ 1=ð4þ2àdþmentioning

confidence: 99%

Section: áð0þ 1=ð4þ2àdþmentioning

confidence: 99%

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Dynamics of an Interface Driven through Random Media: The Effect of a Spatially Correlated Noise

Park

Kim

2003

J. Phys. Soc. Jpn.

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Coherent electron transport in bent cylindrical surfaces

et al. 2005

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Transition from stable to unstable growth by an inertial force

2003

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We introduce a simple growth model where the growth of the interface is affected by an inertial force and a white noise. The magnitude of the inertial force is controlled by a constant p between 0 and 1. An inertial force increases continuously from 0, as p does from 0 to 1. In our model, the interface starts growing from a flat state. When pp(c), however, the interface width increases continuously without saturation as time elapses. We explain via simple calculation how this interesting phenomenon occurs in our model. We find p(c)=0.5 from the calculation. This critical value is in excellent agreement with the critical value p(c)=0.50(1) found from the simulations of our model.

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First-order depinning transition of a driven interface in disordered media

Cited by 3 publications

References 18 publications

Dynamics of an Interface Driven through Random Media: The Effect of a Spatially Correlated Noise

Dynamics of an Interface Driven through Random Media: The Effect of a Spatially Correlated Noise

Coherent electron transport in bent cylindrical surfaces

Transition from stable to unstable growth by an inertial force

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