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Nucleation-Initiated Solidification of Thin Si Films

MRS Online Proceedings Library 2011年第1期979卷 1-6页

作者： S. Hazair P. C. van der Wilt Y. Deng U. J. Chung A. B. Limanov James S. Im Program of Materials Science Department of Applied Physics and Applied Mathematics Columbia University New York USA

Thin Si films on SiO2 that are completely melted by pulsed laser irradiation cool rapidly and eventually solidify via nucleation and growth of solids. It has been observed that a variety of solidified microstructures can be obtained, depending primarily (but not exclusively) on the degree of supercooling achieved prior to the onset of nucleation. This paper focuses on investigating one particular and unusual polycrystalline microstructure that consists of “flowerlike” grains, the interiors of which can be described as being made up of two distinct regions: (1) an extremely defective core region consisting of fine-grained material, and (2) an outer region consisting of relatively defect-free crystal “petals” that radiate outwards. After considering the microstructural details and experimental behavior of the microstructure, we have formulated a growth-based physical model to account for the formation of the microstructure. The model is found to be also capable of accounting for other complex and unusual microstructures obtained via nucleation and growth in the complete melting regime.

关键词： Si nucleation & growth thin film

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Efficient tracking for hybrid systems with a bounded number of mode switches

Efficient tracking for hybrid systems with a bounded number ...

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50th Israel Annual Conference on Aerospace Sciences 2010

作者： Sigalov, Daniel Oshman, Yaakov Interdepartmental Program for Applied Mathematics Technion - Israel Institute of Technology Haifa 32000 Israel Department of Aerospace Engineering Technion - Israel Institute of Technology Haifa 32000 Israel

ISBN: (纸本)9781617380839

We consider the problem of tracking the state of a hybrid system capable of performing a bounded number of mode switches. The system is assumed to either follow a nominal model standing for, e.g., the non-maneuvering motion regime of a target, or the fault-free operation mode of a sensor, or obey an anomalous model representing, e.g., the abrupt evasive maneuvers of a target or the faulty operation of a sensor. The optimal tracking algorithm requires the implementation of a polynomially growing number of primitive Kalman filters. On the other hand, the system's switching dynamics is not Markov because of the a priori limited number of model switches, thus ruling out the use of popular estimation schemes such as the IMM and GPB algorithms. We derive an efficient estimation scheme that uses a number of primitive Kalman filters that is linear in the number of possible maneuvers. The scheme resembles the IMM algorithm in that it uses interaction between some of the primitive filters before every estimation cycle, thus reducing the number of such filters. The algorithm is fully derived, tested in simulation, and shown to outperform the state-of-the-art IMM filter in a typical example.

关键词： Kalman filters

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Sequential Lateral Solidification of Ultra-Thin a-Si Films

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MRS Online Proceedings Library 2011年第1期621卷 991-996页

作者： Hans S. Cho Dongbyum Kim Alexander B. Limanov Mark A. Crowder James S. Im Program in Materials Science and Engineering Department of Applied Physics and Applied Mathematics School of Engineering and Applied Science Columbia University New York USA

This paper demonstrates that Sequential Lateral Solidification (SLS) of Si can be carried out on films as thin as–and potentially much thinner than–250 Å. When compared to thicker Si films, however, the SLS-processed ultra-thin films contain more twins, and successful processing requires irradiation within a narrower laser energy density range and a smaller per-pulse translation distance. The physical interpretation of these findings is formulated by analyzing the details of the microstructures observed in single-pulse-irradiation-induced Controlled Super-Lateral Growth (C-SLG) experiments. SEM and TEM analyses reveal complicated microstructural details that we interpret as originating from breakdown of epitaxial growth during lateral solidification, an effect that is detrimental to the SLS process. Based on considerations of far-from- equilibrium solidification behavior of Si, it is argued that undercooling of the solidification interface below a threshold value at which solidification no longer proceeds epitaxially–arising from reduction in interfacial recalescence during lateral solidification of ultra-thin Si films, relative to that of thicker films–is responsible for the breakdown. Based on this model, we discuss how external parameters may be adjusted so as to permit optimal crystallization of ultra-thin Si films using SLS.

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Optimizing cooperative cognitive radio networks with opportunistic access

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Journal of Computer Networks and Communications 2012年

作者： Zafar, Ammar Alouini, Mohamed-Slim Chen, Yunfei Radaydeh, Redha M. Electrical Engineering Program KAUST Al Khawarizmi Applied Mathematics Building 1 Mail Box 2675 Makkah Province Thuwal 23955-6900 Saudi Arabia School of Engineering University of Warwick Coventry CV4 7AL United Kingdom Electrical Engineering Department KAUST Thuwal 23955-6900 Saudi Arabia Department of Electrical and Computer Engineering Texas AandM University Texas AandM Engineering Building Education City Doha Qatar

Optimal resource allocation for cooperative cognitive radio networks with opportunistic access to the licensed spectrum is studied. Resource allocation is based on minimizing the symbol error rate at the receiver. Both the cases of all-participate relaying and selective relaying are considered. The objective function is derived and the constraints are detailed for both scenarios. It is then shown that the objective functions and the constraints are nonlinear and nonconvex functions of the parameters of interest, that is, source and relay powers, symbol time, and sensing time. Therefore, it is difficult to obtain closed-form solutions for the optimal resource allocation. The optimization problem is then solved using numerical techniques. Numerical results show that the all-participate system provides better performance than its selection counterpart, at the cost of greater resources. © 2012 Ammar Zafar et al.

关键词： Resource allocation

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Fast wavelet-based single-particle reconstruction in Cryo-EM

Fast wavelet-based single-particle reconstruction in Cryo-EM

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IEEE International Symposium on Biomedical Imaging

作者： Cédric Vonesch Lanhui Wang Yoel Shkolnisky Amit Singer Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Applied Mathematics Tel-Aviv University Tel-Aviv Israel

This paper presents a novel algorithm for the 3D tomographic inversion problem that arises in single-particle electron cryomicroscopy (Cryo-EM). It is based on two key components: 1) a variational formulation that promotes sparsity in the wavelet domain and 2) the Toeplitz structure of the combined projection/back-projection operator. The first idea has proven to be very effective for the recovery of piecewise-smooth signals, which is confirmed by our numerical experiments. The second idea allows for a computationally efficient implementation of the reconstruction procedure, using only one circulant convolution per iteration.

关键词： Image reconstruction Signal to noise ratio Three dimensional displays Fourier transforms Kernel Tomography

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Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients

Strong and weak divergence in finite time of Euler's method ...

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作者： Hutzenthaler, Martin Jentzen, Arnulf Kloeden, Peter E. LMU Biozentrum Department Biologie II University of Munich 82152 Planegg-Martinsried Germany Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544-1000 United States Institute for Mathematics Goethe University Frankfurt am Main 60054 Frankfurt am Main Germany

The stochastic Euler scheme is known to converge to the exact solution of a stochastic differential equation (SDE) with globally Lipschitz continuous drift and diffusion coefficients. Recent results extend this convergence to coefficients that grow, at most, linearly. For superlinearly growing coefficients, finite-time convergence in the strong mean-square sense remains. In this article, we answer this question to the negative and prove, for a large class of SDEs with non-globally Lipschitz continuous coefficients, that Euler's approximation converges neither in the strong mean-square sense nor in the numerically weak sense to the exact solution at a finite time point. Even worse, the difference of the exact solution and of the numerical approximation at a finite time point diverges to infinity in the strong mean-square sense and in the numerically weak sense. © 2010 The Royal Society.

关键词： Stochastic systems

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Linear optimal estimation problems in systems with actuator faults

Linear optimal estimation problems in systems with actuator ...

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作者： Sigalov, Daniel Oshman, Yaakov Technion - Israel Institute of Technology Program for Applied Mathematics Haifa 32000 Israel Technion - Israel Institute of Technology Department of Aerospace Engineering Haifa 32000 Israel

ISBN: (纸本)9781457702679

We consider estimating the state of a dynamic system subject to actuator faults. The discretely-valued fault mechanism renders the system hybrid, and results in anomalous changes in the dynamics equation that may be interpreted as random accelerations. Two closely related problem formulations are considered. In the first formulation multiple models are used to describe the system's behavior: one model stands for the nominal, fault-free actuator condition, all other models correspond to various actuator fault conditions, and the system can freely assume any model at any time. In the second formulation the abnormal mode is described by a single dynamical model, and the system can switch between the nominal and anomalous conditions a bounded number of times, with the bound assumed known. In both formulations, the minimum mean squared error (MMSE) optimal state estimator requires a polynomially growing number of primitive Kalman filters, and is, thus, computationally infeasible. We derive sequential, linear MMSE-optimal state estimation algorithms for both problem formulations. Depending only on the first two moments of the random quantities of the problem, linear optimal filters are robust with respect to the actual driving noise distributions, in the sense that they achieve the smallest worst-case estimation error of all other (nonlinear) filters. Although derived assuming seemingly different problem formulations, both filters share essentially the same structure, thus exposing a certain duality between the underlying problems. The performance of both estimators is demonstrated in a simulation study, where they are compared to the interacting multiple model filter. © 2011 IEEE.

关键词： Hybrid systems

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Tracking maneuvering targets with a soft bound on the number of maneuvers

Tracking maneuvering targets with a soft bound on the number...

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ISBN: (纸本)9781457702679

We revisit the problem of tracking the state of a hybrid system capable of performing a bounded number of mode switches. In a previous paper we have addressed a version of the problem where we have assumed the existence of a deterministic, known hard bound on the number of mode transitions. In addition, it was assumed that the system can possess only two modes, e.g., the maneuvering and non-maneuvering regimes of a tracked target. In the present paper we relax both assumptions: we assume a soft, stochastic bound on the number of mode transitions, and altogether remove the restriction on the number of modes of the system (thus, e.g., the target can have multiple different maneuvering modes, in addition to the non-maneuvering one). Similarly to the case where the number of transition was deterministically hard-bounded, the existence of the bound renders the mode switching mechanism non-Markov. Thus, the two formulations address similar, though not identical, problems, that cannot be solved by direct application of standard algorithms for hybrid systems. The novel solution approach is based on transforming the non-Markovian mode switching mechanism to an equivalent Markovian one, at the price of augmenting the mode definition. A standard interacting multiple model (IMM) filter is then applied to the transformed problem in a straightforward manner. The performance of the new method is demonstrated via a simulation study comprising three examples, in which the new method is compared with 1) the filter for hard-bounded mode transitions, and 2) a standard IMM filter directly applied to the original problem. The study shows that even when working outside its operating envelope, the new filter closely approximates the best filter for the scenario. © 2011 IEEE.

关键词： Hybrid systems

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Linear Optimal State Estimation in Systems with Independent Mode Transitions

Linear Optimal State Estimation in Systems with Independent ...

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IEEE Conference on Decision and Control

作者： Daniel Sigalov Tomer Michaeli Yaakov Oshman Interdepartmental Program for Applied Mathematics Department of Electrical Engineering Department of Aerospace Engineering

ISBN: (纸本)9781612848006

A generalized state space representation of a dynamical system with random modes is presented. The dynamics equation includes the effect of the state's linear minimum mean squared error (LMMSE) optimal estimate, representing the behavior of a closed loop control system featuring a state estimator. The measurement equation is allowed to depend on past LMMSE estimate of the state, which can be used to represent the fact that measurements are obtained from a validation window centered at the predicted measurement position and not from the entire surveillance region. The matrices comprising the system's mode constitute an independent stochastic process. It is shown that the proposed formulation generalizes several important problems considered in the past, and allows a unified modeling of new ones. The LMMSE optimal filter is derived for the considered general problem and is shown to reduce, in some special cases, to some well known classical algorithms. The new concept, as well as the derived algorithm, are demonstrated for the problem of target tracking in clutter, and are shown to attain performance that is competitive to that of several popular nonlinear methods.

关键词： State estimation State-space Representation Closed loop control systems Target tracking clutter Mean square error DYNAMICAL SYSTEMS random fashion UNIFIED MODEL

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Graph sparsification by effective resistances

Graph sparsification by effective resistances

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作者： Spielman, Daniel A. Srivastava, Nikhil Program in Applied Mathematics Department of Computer Science Yale University New Haven CT 06520 United States Department of Computer Science Yale University New Haven CT 06520 United States

We present a nearly linear time algorithm that produces high-quality spectral sparsifiers of weighted graphs. Given as input a weighted graph G = (V, E, w) and a parameter ∈ > 0, we produce a weighted subgraph H = (V, E˜, w˜) of G such that |E˜| = O(n logn/∈2) and all x ∈ RV satisfy (1 - ∈) Σuv∈E (x(u) - x(v))2wuv ≤ Σuv∈E˜ (x(u) - x(v))2w˜uv ≤ (1 + ∈) Σuv∈E (x(u) - x(v))2wuv· This improves upon the spectral sparsifiers constructed by Spielman and Teng, which had O(nlogcn) edges for some large constant c, and upon the cut sparsifiers of Benczúr and Karger, which only satisfied these inequalities for x ∈ {0, 1}V. A key ingredient in our algorithm is a subroutine of independent interest: a nearly linear time algorithm that builds a data structure from which we can query the approximate effective resistance between any two vertices in a graph in O(logn) time. © 2011 Society for Industrial and applied mathematics.

关键词： Clustering algorithms

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