Scale invariance and dynamical correlations in growth models of molecular beam epitaxy

Sarma, S. Das; Lanczycki, C. J.; Kotlyar, R.; Ghaisas, S. V.

doi:10.1103/physreve.53.359

Cited by 141 publications

(170 citation statements)

References 69 publications

Supporting

Mentioning

152

Contrasting

Order By: Relevance

“…The important consequence of scaling, expressed by Eq. (10), is the existence of the upper bound for the memory request for any finite number L of processors and for any finite load N per processor. As it is stated by Eq.…”

Section: Application To Pdesmentioning

confidence: 99%

See 1 more Smart Citation

Roughening of the interfaces in(1+1)-dimensional two-component surface growth with an admixture of random deposition

2004

View full text Add to dashboard Cite

We simulate competitive two-component growth on a one dimensional substrate of L sites. One component is a Poisson-type deposition that generates Kardar-Parisi-Zhang (KPZ) correlations. The other is random deposition (RD). We derive the universal scaling function of the interface width for this model and show that the RD admixture acts as a dilatation mechanism to the fundamental time and height scales, but leaves the KPZ correlations intact. This observation is generalized to other growth models. It is shown that the flat-substrate initial condition is responsible for the existence of an early non-scaling phase in the interface evolution. The length of this initial phase is a nonuniversal parameter, but its presence is universal. We introduce a method to measure the length of this initial non-scaling phase. In application to parallel and distributed computations, the important consequence of the derived scaling is the existence of the upper bound for the desynchronization in a conservative update algorithm for parallel discrete-event simulations. It is shown that such algorithms are generally scalable in a ring communication topology.

show abstract

Section: Application To Pdesmentioning

confidence: 99%

“…One group of examples is the anomalous roughening in epitaxial growth models [5,10,11], fractures [12,13] and in models with subdiffusive behavior or quenched disorder [14]. These systems exhibit different dynamic scaling on local and global scales, characterized by different values of roughness exponents.…”

Section: Introductionmentioning

confidence: 99%

Roughening of the interfaces in(1+1)-dimensional two-component surface growth with an admixture of random deposition

2004

View full text Add to dashboard Cite

show abstract

“…Two important examples are fluid flow in porous media [1] and deposition of atoms during molecular beam epitaxy (MBE) [1,2]. It is expected that at times much later than typical aggregation times and on macroscopic length scales these interfaces develop a characteristic scaling behavior, where the scaling exponents fall into certain dynamic universality classes [1,2,3].…”

Section: Introductionmentioning

confidence: 99%

“…(1.1) gives access to the exponents α and z both experimentally by reflection high energy electron diffraction (RHEED) (see, e.g., chaper 16 of Ref. [1]) and by direct imaging using a surface tunneling microscope [6] and theoretically by continuum models [1,2] and Monte-Carlo simulations [2,5].…”

Section: Introductionmentioning

confidence: 99%

Erratum: Short-time scaling behavior of growing interfaces [Phys. Rev. E55, 668 (1997)]

Krech¹

1997

Phys. Rev. E

View full text Add to dashboard Cite

The short-time evolution of a growing interface is studied analytically and numerically for the Kadar-Parisi-Zhang (KPZ) universality class. The scaling behavior of response and correlation functions is reminiscent of the "initial slip" behavior found in purely dissipative critical relaxation (model A). Unlike model A the initial slip exponent for the KPZ equation can be expressed by the dynamical exponent z. In 2+1 dimensions z is estimated from the short-time evolution of the correlation function for ballistic deposition and for the RSOS model.

show abstract

“…On the theoretical side, considerable effort has been focused on developing suitable evolution equations for the growing layer. 10 While many different versions 8,9,[26][27][28][29][30][31] of such equations exist, depending on the details of deposition processes and molecular interactions and kinetics, all of them share certain fundamental characteristics: they are noisy, nonlinear partial differential equations in space and time, and describe an important class of generic nonequilibrium phenomena.…”

mentioning

confidence: 99%

Controlling surface morphologies by time-delayed feedback

2007

View full text Add to dashboard Cite

We propose a method to control the roughness of a growing surface via a time-delayed feedback scheme. The method is very general and can be applied to a wide range of nonequilibrium growth phenomena, from solid-state epitaxy to tumor growth. Possible experimental realizations are suggested. As an illustration, we consider the Kardar-Parisi-Zhang equation ͓Phys. Rev. Lett. 56, 889 ͑1986͔͒ in 1 + 1 dimensions and show that the effective growth exponent of the surface width can be stabilized at any desired value in the interval ͓0.25, 0.33͔, for a significant length of time. DOI: 10.1103/PhysRevB.75.233414 PACS number͑s͒: 68.35.Rh, 05.10.Gg, 02.30.Ks, 02.60.Cb The control of unstable states in chaotic or patternforming nonlinear dynamical systems has attracted much interest recently. 1,2 Time-delayed feedback control 3 has been especially successful in stabilizing a variety of dynamic and spatial structures, including noise-induced oscillations and patterns found, e.g., in semiconductor nanostructures. [4][5][6][7] Here, we propose to apply these control techniques to a completely new class of dynamical phenomena, namely, farfrom-equilibrium surface growth. [8][9][10] The goal is to stabilize desired surface characteristics, such as spatiotemporal height-height correlations or the surface roughness, during the growth process. Even if such control can only be sustained in a finite window of time, its experimental potential is undiminished since the growth process can simply be terminated when the desired characteristics have been achieved, thanks to today's precise in situ characterization capabilities. Moreover, paradigmatic growth models, such as the KardarParisi-Zhang ͑KPZ͒ equation, 11 find applications in many diverse areas of science, e.g., thin film growth, 12-15 fluctuating hydrodynamics, 16 driven diffusive systems, [17][18][19] tumor growth in biophysics, [20][21][22] propagating fire fronts, 23 and econophysics. 24 Therefore, broad implications can be expected if methods from control theory can be successfully implemented in this vast context.In this Brief Report, we provide an exploration of these ideas. We choose the most promising type of control, timedelayed feedback, and study its effects on the KPZ equation. 11 Specifically, we attempt to control the effective dynamic growth exponent ␤ associated with the roughness of the growing surface. By implementing two realizations of the control scheme, we will see below that we can, indeed, stabilize ␤ in a range of values between the two universal limits, 1 / 4 and 1 / 3, over at least one to two decades in time. In the following, we will use the language of surface growth, but our findings are just as relevant in the context of all other applications of the KPZ equation. For instance, in recent work on tumor growth, 20 it has been shown that an efficient method to influence the proliferation of tumor cells at the border is coupled to the growth exponents and the universality class of growth. The authors suggest and establish a therapy which rests on th...

show abstract

Scale invariance and dynamical correlations in growth models of molecular beam epitaxy

Cited by 141 publications

References 69 publications

Roughening of the interfaces in(1+1)-dimensional two-component surface growth with an admixture of random deposition

Roughening of the interfaces in(1+1)-dimensional two-component surface growth with an admixture of random deposition

Erratum: Short-time scaling behavior of growing interfaces [Phys. Rev. E55, 668 (1997)]

Controlling surface morphologies by time-delayed feedback

Contact Info

Product

Resources

About