Ditza Auerbach - Academia.edu (original) (raw)
Papers by Ditza Auerbach
Proceedings of SPIE, Mar 11, 2010
Photomask degradation via haze defect formation is an increasing troublesome yield problem in the... more Photomask degradation via haze defect formation is an increasing troublesome yield problem in the semiconductor fab. Wafer inspection is often utilized to detect haze defects due to the fact that it can be a bi-product of process control wafer inspection; furthermore, the detection of the haze on the wafer is effectively enhanced due to the multitude of distinct fields being
Ditza Auerbach, ' Celso Grebogi, '1 Edward Ott, ' and James A. Yorke ' Laboratory... more Ditza Auerbach, ' Celso Grebogi, '1 Edward Ott, ' and James A. Yorke ' Laboratory for Plasma Research, University of Maryland, College Park, Maryland 20742 '2~institute for Physical Sciences and Technology and Department ofMathematics, University of Maryland, College Park, Maryland 20742 t 1Department of Physics and Department of Electrical Engineering, University of Maryland, College Park, Maryland 20742 (Received 29 June 1992)
NATO ASI Series, 1989
Systems governed by deterministic dynamics may exhibit unpredictable time evolution, thus appeari... more Systems governed by deterministic dynamics may exhibit unpredictable time evolution, thus appearing chaotic. Such phenomena are ubiquitous in nature, ranging from turbulent fluid flows to heart arrythmia. The unpredictability of chaotic systems arises from the abundancy of trajectories that exist for slight changes of the initial conditions. The entropy provides a measure of the multitude of possible time evolutions a system may exhibit, but does not provide a quantification of the ease or difficulty with which the set of all possible motions can be organized and encoded. Many of the proposed definitions [1] for dynamical complexity reduce to entropy related quantities such as the Kolmogorov entropy, and as such are measures of randomness. In this communication a measure of complexity unrelated to the entropy is introduced in order to quantify the difficulty in organizing the possible motions of a chaotic system. Other proposed topological definitions of complexity [2], such as the algorithmic complexity usually diverge for a generic chaotic system.
Proteins: Structure, Function, and Genetics, 1997
Physical Review Letters, 1994
Physical Review Letters, 1996
Proteins: Structure, Function, and Genetics, 1997
MD simulations, currently the most detailed description of the dynamic evolution of proteins, are... more MD simulations, currently the most detailed description of the dynamic evolution of proteins, are based on the repeated solution of a set of differential equations implementing Newton's second law. Many such systems are known to exhibit chaotic behavior, i.e., very small changes in initial conditions are amplified exponentially and lead to vastly different, inherently unpredictable behavior. We have investigated the response of a protein fragment in an explicit solvent environment to very small perturbations of the atomic positions (10(-3)-10(-9) A). Independent of the starting conformation (native-like, compact, extended), perturbed dynamics trajectories deviated rapidly, leading to conformations that differ by approximately 1 A RMSD within 1-2 ps. Furthermore, introducing the perturbation more than 1-2 ps before a significant conformational transition leads to a loss of the transition in the perturbed trajectories. We present evidence that the observed chaotic behavior reflects physical properties of the system rather than numerical instabilities of the calculation and discuss the implications for models of protein folding and the use of MD as a tool to analyze protein folding pathways.
Journal of The Optical Society of America B-optical Physics, 1996
A control scheme for eliminating the chaotic fluctuations observed in coupled arrays of semicondu... more A control scheme for eliminating the chaotic fluctuations observed in coupled arrays of semiconductor lasers driven high above threshold is introduced. Using the model equations, we show that the output field of the array can be stabilized to a steady in-phase state characterized by a narrow far-field optical beam. Only small local perturbations to the ambient drive current are involved in the control procedure. We carry out a linear stability analysis of the desired synchronized state and find that the number of active unstable modes that are controlled scales with the number of elements in the array. Numerical support for the effectiveness of our proposed control technique in both ring arrays and linear arrays is presented.
Physical Review Letters, 1992
... REVIEW LETTERS and used to extract the periodic orbit along with its un-stable eigenvalue acc... more ... REVIEW LETTERS and used to extract the periodic orbit along with its un-stable eigenvalue according ... This is accomplished by choosing the parame-ter perturbations 8Pi+l, . . . 6Pi+k-1 according to the (k - 1 ... (3) (neglecting the term involving 57(k)). In gen-eral, estimation of the ...
Physical Review Letters, 1987
2388 7, 1, 15, 29, 63, 55, 103, respectively. The Lyapunov numbers of all these cycles were calcu... more 2388 7, 1, 15, 29, 63, 55, 103, respectively. The Lyapunov numbers of all these cycles were calculated. To check the validity and accuracy of our algorithms we compared the results with" exact" calculations which use the explicit knowledge of the map.(In extracting the data from the chaotic signal as above no knowledge of the underlying map is assumed.) In this calculation one first lays a grid of points covering the attractor. Typically the num-ber of grid points is at least 5 timeslarger than the num-ber of periodic points that one expects to find. ...
Proceedings of SPIE, Mar 11, 2010
Photomask degradation via haze defect formation is an increasing troublesome yield problem in the... more Photomask degradation via haze defect formation is an increasing troublesome yield problem in the semiconductor fab. Wafer inspection is often utilized to detect haze defects due to the fact that it can be a bi-product of process control wafer inspection; furthermore, the detection of the haze on the wafer is effectively enhanced due to the multitude of distinct fields being
Ditza Auerbach, ' Celso Grebogi, '1 Edward Ott, ' and James A. Yorke ' Laboratory... more Ditza Auerbach, ' Celso Grebogi, '1 Edward Ott, ' and James A. Yorke ' Laboratory for Plasma Research, University of Maryland, College Park, Maryland 20742 '2~institute for Physical Sciences and Technology and Department ofMathematics, University of Maryland, College Park, Maryland 20742 t 1Department of Physics and Department of Electrical Engineering, University of Maryland, College Park, Maryland 20742 (Received 29 June 1992)
NATO ASI Series, 1989
Systems governed by deterministic dynamics may exhibit unpredictable time evolution, thus appeari... more Systems governed by deterministic dynamics may exhibit unpredictable time evolution, thus appearing chaotic. Such phenomena are ubiquitous in nature, ranging from turbulent fluid flows to heart arrythmia. The unpredictability of chaotic systems arises from the abundancy of trajectories that exist for slight changes of the initial conditions. The entropy provides a measure of the multitude of possible time evolutions a system may exhibit, but does not provide a quantification of the ease or difficulty with which the set of all possible motions can be organized and encoded. Many of the proposed definitions [1] for dynamical complexity reduce to entropy related quantities such as the Kolmogorov entropy, and as such are measures of randomness. In this communication a measure of complexity unrelated to the entropy is introduced in order to quantify the difficulty in organizing the possible motions of a chaotic system. Other proposed topological definitions of complexity [2], such as the algorithmic complexity usually diverge for a generic chaotic system.
Proteins: Structure, Function, and Genetics, 1997
Physical Review Letters, 1994
Physical Review Letters, 1996
Proteins: Structure, Function, and Genetics, 1997
MD simulations, currently the most detailed description of the dynamic evolution of proteins, are... more MD simulations, currently the most detailed description of the dynamic evolution of proteins, are based on the repeated solution of a set of differential equations implementing Newton's second law. Many such systems are known to exhibit chaotic behavior, i.e., very small changes in initial conditions are amplified exponentially and lead to vastly different, inherently unpredictable behavior. We have investigated the response of a protein fragment in an explicit solvent environment to very small perturbations of the atomic positions (10(-3)-10(-9) A). Independent of the starting conformation (native-like, compact, extended), perturbed dynamics trajectories deviated rapidly, leading to conformations that differ by approximately 1 A RMSD within 1-2 ps. Furthermore, introducing the perturbation more than 1-2 ps before a significant conformational transition leads to a loss of the transition in the perturbed trajectories. We present evidence that the observed chaotic behavior reflects physical properties of the system rather than numerical instabilities of the calculation and discuss the implications for models of protein folding and the use of MD as a tool to analyze protein folding pathways.
Journal of The Optical Society of America B-optical Physics, 1996
A control scheme for eliminating the chaotic fluctuations observed in coupled arrays of semicondu... more A control scheme for eliminating the chaotic fluctuations observed in coupled arrays of semiconductor lasers driven high above threshold is introduced. Using the model equations, we show that the output field of the array can be stabilized to a steady in-phase state characterized by a narrow far-field optical beam. Only small local perturbations to the ambient drive current are involved in the control procedure. We carry out a linear stability analysis of the desired synchronized state and find that the number of active unstable modes that are controlled scales with the number of elements in the array. Numerical support for the effectiveness of our proposed control technique in both ring arrays and linear arrays is presented.
Physical Review Letters, 1992
... REVIEW LETTERS and used to extract the periodic orbit along with its un-stable eigenvalue acc... more ... REVIEW LETTERS and used to extract the periodic orbit along with its un-stable eigenvalue according ... This is accomplished by choosing the parame-ter perturbations 8Pi+l, . . . 6Pi+k-1 according to the (k - 1 ... (3) (neglecting the term involving 57(k)). In gen-eral, estimation of the ...
Physical Review Letters, 1987
2388 7, 1, 15, 29, 63, 55, 103, respectively. The Lyapunov numbers of all these cycles were calcu... more 2388 7, 1, 15, 29, 63, 55, 103, respectively. The Lyapunov numbers of all these cycles were calculated. To check the validity and accuracy of our algorithms we compared the results with" exact" calculations which use the explicit knowledge of the map.(In extracting the data from the chaotic signal as above no knowledge of the underlying map is assumed.) In this calculation one first lays a grid of points covering the attractor. Typically the num-ber of grid points is at least 5 timeslarger than the num-ber of periodic points that one expects to find. ...