Artificial time integration

Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be “close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process can be improved to better reflect the actual properties sought. In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling approach may possibly lead to algorithms with improved efficiency. AMS subject classification (2000)  65L05, 65M32, 65N21, 65N22, 65D18     

空位在金刚石近(001)表面扩散的分子动力学模拟

用分子动力学方法模拟了空位在金刚石近(001)表面的扩散过程,研究了温度对空位扩散的影响.结果表明,当温度为1000K左右时,位于近表面第二层上的空位开始向表面运动;当温度在1400—2000K时,空位完全扩散到表面.这与实验结果和其他计算结果符合得很好.同时发现,温度为1400—1800K时,空位的扩散经历了两次迁移运动,其分别对应了均方位移图中的两个极大值.在不施加任何约束的条件下得到了空位的动态扩散路径,空位在金刚石近(001)表面的扩散势垒约为042eV.并探讨了一定温度下空位数目增多及其不同排列 关键词： 金刚石 空位 扩散 分子动力学     

Structure and magnetism of bcc(1 1 0)-like Fe films grown on Cu(0 0 1) via ion beam triangulation and spin-polarized electron capture

The structure and magnetism of thin epitaxial Fe layers grown on Cu(0 0 1) is investigated by grazing scattering of fast H and He atoms. Information on the atomic structure of the film and substrate surfaces is obtained by making use of ion beam triangulation with protons. The magnetic behavior is studied via the polarization of light emitted after capture of spin-polarized electrons into excited atomic terms during scattering of He atoms. For the formation of bcc(1 1 0)-like Fe films at higher coverages, we detect differences in structural and magnetic properties for room and low temperature growth. We suggest that the crystalline structure depends on the film morphology and that Cu impurities affect the magnetic properties.     

Estimating Invariant Probability Densities for Dynamical Systems

Knowing a probability density (ideally, an invariant density) for the trajectories of a dynamical system allows many significant estimates to be made, from the well-known dynamical invariants such as Lyapunov exponents and mutual information to conditional probabilities which are potentially more suitable for prediction than the single number produced by most predictors. Densities on typical attractors have properties, such as singularity with respect to Lebesgue measure, which make standard density estimators less useful than one would hope. In this paper we present a new method of estimating densities which can smooth in a way that tends to preserve fractal structure down to some level, and that also maintains invariance. We demonstrate with applications to real and artificial data.     

Single chain force spectroscopy - Reading the sequence of HP protein models

We study the elastic properties of single A/B random copolymer chains, with a specific sequence and use them as theoretical model for so called HP proteins. HP proteins carry hydrophilic (P) and hydrophobic (H) monomers. We predict a rich structure in the force-extension relations which can be attributed to the information in the sequence. The variational method is used to probe local minima on the path of stretching and releasing for the chain molecules. At a given force, we find multiple configurations which are separated by energy barriers. A collapsed globular configuration consists of several domains which unravel cooperatively. Upon stretching, the unfolding path shows a stepwise pattern corresponding to the unfolding of each domain. While releasing, several cores can be created simultaneously in the middle of the chain, resulting in a different path of collapse. The long-range interactions and stiffness of the chain simplify the potential landscape given by the disorder in sequence. Received 5 March 2002 / Received in final form 16 May 2002 Published online 13 August 2002     

Controlling global stochasticity of Hamiltonian systems by nonlinear perturbation

A method of controlling global stochasticity in Hamiltonian systems by applying nonlinear perturbation is proposed. With the well-known standard map we demonstrate that this control method can convert global stochasticity into regular motion in a wide chaotic region for arbitrary initial condition, in which the control signal remains very weak after a few kicks. The system in which chaos has been controlled approximates to the original Hamiltonian system, and this approach appears robust against small external noise. The mechanism underlying this high control efficiency is intuitively explained. Received 15 January 2002 Published online 6 June 2002     

Growth and characterization of model oxide catalysts

Oxide catalysts are frequently used to convert toxic species to environmentally benign molecules, and to prevent the formation of toxic species in the first place. In this paper, growth and characterization of model oxide systems employed in both approaches is discussed. An example of the former approach is the selective catalytic reduction (SCR) of NO emitted from power plants by NH₃, which employs tungsten and vanadium oxides supported on the anatase polymorph of TiO₂. To model SCR catalysts, epitaxial titanium, vanadium and tungsten oxide films were grown using molecular beam epitaxy and magnetron sputtering. Two different anatase orientations were grown on LaAlO₃ substrates and their interactions with vanadia were characterized. On LaAlO₃ (0 0 1), anatase exposed a (4 × 1) reconstructed (0 0 1) surface. Vanadia lifted the reconstruction and at 1 ML a (1 × 1) surface with mostly V⁵⁺ was observed. Continued V₂O₅ growth led to loss of order, but at high temperatures epitaxial VO₂ could be grown; vanadia behaved similarly on anatase films on LaAlO₃ (1 1 0). Results suggested that the monolayer is pseudomorphic with O adsorption oxidizing the surface V to 5+, since the anatase structure cannot accommodate more bulk oxygen, only a monolayer can be pseudomorphic and have only V⁵⁺. Thus the vanadia monolayer has unique structural and chemical properties that can help explain why vanadia monolayers on TiO₂ are much more active than bulk V₂O₅. For WO₃, a series of added row reconstructions were observed as the epitaxial films were reduced. The effect of these structures on surface chemistry was characterized by studying 1-propanol adsorption. The results indicated that the structure of the WO₃ surface did not alter its catalytic function but had a strong effect on reaction kinetics. As an example of a system where catalysts prevent the formation of toxic species, the reactivity of oxidized Pd surfaces used in CH₄ catalytic combustion were studied. An ordered PdO-like monolayer was found to be less reactive towards CO than adsorbed O on Pd. On the other hand, the PdO layer favored a lower activation energy C₃H₆ oxidation pathway. The results indicated that Pd oxidation reduces the sticking coefficient of reactive species but once molecules adsorb, the oxide surface can reduce the activation energy for subsequent reaction.     

Numerical simulation of the spatiotemporal evolution of a nanoparticle–plasma system

A one-dimensional nanodusty plasma was modeled by self-consistently coupling a plasma model with nanoparticle growth, charging, and transport models. As nanoparticles grow from subnanometer to tens of nm in diameter, the numerical results predict a rich spatiotemporal structure, including four distinct temporal phases: a charge-limited phase, a charge accumulation phase, an early ion drag phase, and a sheath interaction phase.     

Molecular dynamics simulations on the structures and properties of ε-CL-20-based PBXs ——Primary theoretical studies on HEDM formulation design

Five polymer bonded explosives (PBXs) with the base explosive ε-CL-20 (hexanitrohexaazaisowurtzi- tane), the most important high energy density compound (HEDC), and five polymer binders (Estane 5703, GAP, HTPB, PEG, and F2314) were constructed. Molecular dynamics (MD) method was employed to investigate their binding energies (Ebind), compatibility, safety, mechanical properties, and energetic properties. The information and rules were reported for choosing better binders and guiding formula- tion design of high energy density material (HEDM). According to the calculated binding energies, the ordering of compatibility and stability of the five PBXs was predicted as ε-CL-20/PEG > ε-CL-20/ Estane5703 ≈ε-CL-20/GAP > ε-CL-20/HTPB > ε-CL-20/F2314. By pair correlation function g(r) analyses, hydrogen bonds and vdw are found to be the main interactions between the two components. The elasticity and isotropy of PBXs based ε-CL-20 can be obviously improved more than pure ε-CL-20 crystal. It is not by changing the molecular structures of ε-CL-20 for each binder to affect the sensitivity. The safety and energetic properties of these PBXs are mainly influenced by the thermal capability (C°p) and density (ρ) of binders, respectively.     

Biham–Middleton–Levine model with four-directional traffic

We study the four-directional traffic flow on a two-dimensional lattice. In the case of discrete densities, we assume equal number of vehicles in each lane. Except for the minimum density, the gridlock emerges swiftly. Two kinds of gridlock have been observed. The global gridlock dominates the system when the density is twice the minimum value. At higher densities, the system is pervaded by local gridlocks. We also analyze the time evolution of average speed. In the case of continuous densities, the vehicle numbers vary from lane to lane. The global gridlock is then destroyed by the fluctuations; while the local gridlock can still be observed.