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Selforganized pore formation and openloopcontrol in semiconductor etching, to appear
 Computational Physics of Transport and Interface dynamics
, 2003
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The invariant density of a chaotic dynamical system with small noise Contents
, 1998
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OpenLoopControl of Pore Formation in Semiconductor Etching
"... Electrochemical etching of semiconductors gives rise to a wide variety of selforganized structures including fractal structures, regular and branching pores. The CurrentBurst Model and the Aging Concept are considered to describe the dynamical behavior governing the structure formation. Here the s ..."
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Electrochemical etching of semiconductors gives rise to a wide variety of selforganized structures including fractal structures, regular and branching pores. The CurrentBurst Model and the Aging Concept are considered to describe the dynamical behavior governing the structure formation. Here the suppression of sidebranching during pore growth is demonstrated by an openloopcontrol method, resulting in pores with oscillating diameter. 1
Timescales and lengthscales from noise
"... Noise and nonlinearity can combine to produce surprising and counterintuitive effects. One such is noisecontrolled dynamics, where very small amplitude additive noise dramatically changes the dynamics. The phenomenon has been reported in a onedimensional map [16], and in ordinary differential equa ..."
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Noise and nonlinearity can combine to produce surprising and counterintuitive effects. One such is noisecontrolled dynamics, where very small amplitude additive noise dramatically changes the dynamics. The phenomenon has been reported in a onedimensional map [16], and in ordinary differential equations describing the resonant interaction of wave modes [4, 14], the intermittent destabilisation of convection by shear [3, 7], pulsating laser oscillations [8] and plane Poiseuille flow [5]. Noisecontrolled dynamics has also been found in a set of stochastic partial differential equations describing the shear instability of thermohaline convection [18, 14]. Experimental results exhibit the phenomenon in a YAG:ND3+ laser subject to a periodically modulated pump: oscillations of the laser output intensity are sensitive to noise during long intervals separating intensity pulses [2]. We shall describe the latter example in a little more detail below, but first we shall begin with a fairly simple and general set of equations. In many systems exhibiting invariance under translation and reflection, it is useful to understand the parameter space with reference to the HopfHopf codimension2 normal form. After rescaling, the differential equations for the coupled evolution of two (positive) mode amplitudes are x ̇ = µx(1 − δx2) − xr2 r ̇ = r(x2 − 1 + γr2). (1) Let us take 0 < µ 1 fixed and describe the dynamics as a function of δ and γ. There are fixed points of (1) at the origin, at (x, r) = (0, γ−