Optimal bounded control of first-passage failure of quasi-integrable Hamiltonian systems with wide-band random excitation

The optimal bounded control of quasi-integrable Hamiltonian systems with wide-band random excitation for minimizing their first-passage failure is investigated. First, a stochastic averaging method for multi-degrees-of-freedom (MDOF) strongly nonlinear quasi-integrable Hamiltonian systems with wide-band stationary random excitations using generalized harmonic functions is proposed. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximizinig reliability and maximizing mean first-passage time are formulated based on the averaged It$\ddot{\rm o}$ equations by applying the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraints. The relationship between the dynamical programming equations and the backward Kolmogorov equation for the conditional reliability function and the Pontryagin equation for the conditional mean first-passage time of optimally controlled system is discussed. Finally, the conditional reliability function, the conditional probability density and mean of first-passage time of an optimally controlled system are obtained by solving the backward Kolmogorov equation and Pontryagin equation. The application of the proposed procedure and effectiveness of control strategy are illustrated with an example.

First-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems

An n degree-of-freedom Hamiltonian system with r (1¡r¡n) independent 0rst integrals which are in involution is calledpartially integrable Hamiltonian system. A partially integrable Hamiltonian system subject to light dampings andweak stochastic excitations is called quasi-partially integrable Hamiltonian system. In the present paper, the procedures for studying the 0rst-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems are proposed. First, the stochastic averaging methodfor quasi-partially integrable Hamiltonian systems is brie4y reviewed. Then, basedon the averagedIt ˆo equations, a backwardKolmogorov equation governing the conditional reliability function, a set of generalized Pontryagin equations governing the conditional moments of 0rst-passage time and their boundary and initial conditions are established. After that, the dynamical programming equations and their associated boundary and 0nal time conditions for the control problems of maximization of reliability andof maximization of mean 0rst-passage time are formulated. The relationship between the backwardKolmogorov equation andthe dynamical programming equation for reliability maximization, andthat between the Pontryagin equation andthe dynamical programming equation for maximization of mean 0rst-passage time are discussed. Finally, an example is worked out to illustrate the proposed procedures and the e9ectiveness of feedback control in reducing 0rst-passage failure.

First-passage failure of quasi-integrable Hamiltonian systems

The first-passage failure of quasi-integrable Hamiltonian si-stems (multidegree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations) is investigated. The motion equations of such a system are first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving these equations with suitable initial and boundary conditions. Two examples are given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the procedure.

First-passage time of Duffing oscillator under combined harmonic and white-noise excitations

The first-passage time of Duffing oscillator under combined harmonic and white-noise excitations is studied. The equation of motion of the system is first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. Numerical results for two resonant cases with several sets of parameter values are obtained and the analytical results are verified by using those from digital simulation.

Optimal bounded control of first-passage failure of strongly non-linear oscillators under combined harmonic and white-noise excitations

A procedure for designing the optimal bounded control of strongly non-linear oscillators under combined harmonic and white-noise excitations for minimizing their first-passage failure is proposed. First, a stochastic averaging method for strongly non-linear oscillators under combined harmonic and white-noise excitations using generalized harmonic functions is introduced. Then, the dynamical programming equations and their boundary and final time conditions for the control problems of maximizing reliability and of maximizing mean first-passage time are formulated from the averaged Ito equations by using the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraint. Finally, the conditional reliability function, the conditional probability density and mean of the first-passage time of the optimally controlled system are obtained from solving the backward Kolmogorov equation and Pontryagin equation. An example is given to illustrate the proposed procedure and the results obtained are verified by using those from digital simulation. (C) 2003 Elsevier Ltd. All rights reserved.

Universal quantum computation with trapped ions in thermal motion by adiabatic passage

We propose a universal quantum computation scheme for trapped ions in thermal motion via the technique of adiabatic passage, which incorporates the advantages of both the adiabatic passage and the model of trapped ions in thermal motion. Our scheme is immune from the decoherence due to spontaneous emission from excited states as the system in our scheme evolves along a dark state. In our scheme the vibrational degrees of freedom are not required to be cooled to their ground states because they are only virtually excited. It is shown that the fidelity of the resultant gate operation is still high even when the magnitude of the effective Rabi frequency moderately deviates from the desired value.

Stimulated Raman adiabatic passage from atomic to molecular Bose-Einstein condensates: Feedback laser-detuning control and suppression of dynamical instability

We present a feedback control scheme that designs time-dependent laser-detuning frequency to suppress possible dynamical instability in coupled free-quasibound-bound atom-molecule condensate systems. The proposed adaptive frequency chirp with feedback is shown to be highly robust and very efficient in the passage from an atomic to a stable molecular Bose-Einstein condensate.

Gut contents of silver carp, Hypophthalmichthys molitrix, and the disruption of a centric diatom, Cyclotella, on passage through the esophagus and intestine

The digestibility of algae by stomachless filter-feeding fish has been debated for decades. Results from gut contents and digestive enzyme analysis suggest poor utilization, while the measurement of food assimilation using radiolabeled isotope techniques indicate reasonable assimilation efficiency. Phytoplankton in the gut contents of the planktivorous filter-feeding silver carp were studied during March-May. The fish were cultured in a large net cage in a shallow, hypertrophic subtropical Chinese lake, Lake Donghu. In terms of biomass, the dominant phytoplankton in the fore-gut contents were Cyclotella (average 77.8%, range 69.7-93.5%) and Cryptomonas (average 9.57%, range 0-20.4%). The Ivlev's electivity index E of silver carp was much higher for Cyclotella (1.54) than for Cryptomonas (0.56). The majority of the phytoplankton found in the intestines of silver carp were 8-20 mu m, but they were also able to collect particles as small as 4.5-10 mu m, smaller than their filtering net meshes, suggesting that the secretion of mucus may play an important role in collecting such small particles. We conclude that disruption of cell walls is principally by the pharyngeal teeth, explaining previous contradictory conclusions. (C) 1999 Elsevier Science B.V. All rights reserved.

First-passage time distribution and non-Markovian diffusion dynamics of protein folding

We study the kinetics of protein folding via statistical energy landscape theory. We concentrate on the local-connectivity case, where the configurational changes can only occur among neighboring states, with the folding progress described in terms of an order parameter given by the fraction of native conformations. The non-Markovian diffusion dynamics is analyzed in detail and an expression for the mean first-passage time (MFPT) from non-native unfolded states to native folded state is obtained. It was found that the MFPT has a V-shaped dependence on the temperature. We also find that the MFPT is shortened as one increases the gap between the energy of the native and average non-native folded states relative to the fluctuations of the energy landscape. The second- and higher-order moments are studied to infer the first-passage time distribution. At high temperature, the distribution becomes close to a Poisson distribution, while at low temperatures the distribution becomes a Levy-type distribution with power-law tails, indicating a nonself-averaging intermittent behavior of folding dynamics. We note the likely relevance of this result to single-molecule dynamics experiments, where a power law (Levy) distribution of the relaxation time of the underlined protein energy landscape is observed.

Diffusion dynamics, moments, and distribution of first-passage time on the protein-folding energy landscape, with applications to single molecules

We study the dynamics of protein folding via statistical energy-landscape theory. In particular, we concentrate on the local-connectivity case with the folding progress described by the fraction of native conformations. We found that the first passage-time (FPT) distribution undergoes a dynamic transition at a temperature below which the FPT distribution develops a power-law tail, a signature of the intermittent nonexponential kinetic phenomena for the folding dynamics. Possible applications to single-molecule dynamics experiments are discussed.

Temperature dependence of the distribution of the first passage time: Results from discontinuous molecular dynamics simulations of an all-atom model of the second beta-hairpin fragment of protein G

More than 22 000 folding kinetic simulations were performed to study the temperature dependence of the distribution of first passage time (FPT) for the folding of an all-atom Go-like model of the second beta-hairpin fragment of protein G. We find that the mean FPT (MFPT) for folding has a U (or V)-shaped dependence on the temperature with a minimum at a characteristic optimal folding temperature T-opt*. The optimal folding temperature T-opt* is located between the thermodynamic folding transition temperature and the solidification temperature based on the Lindemann criterion for the solid. Both the T-opt* and the MFPT decrease when the energy bias gap against nonnative contacts increases. The high-order moments are nearly constant when the temperature is higher than T-opt* and start to diverge when the temperature is lower than T-opt*. The distribution of FPT is close to a log-normal-like distribution at T* greater than or equal to T-opt*. At even lower temperatures, the distribution starts to develop long power-law-like tails, indicating the non-self-averaging intermittent behavior of the folding dynamics. It is demonstrated that the distribution of FPT can also be calculated reliably from the derivative of the fraction not folded (or fraction folded), a measurable quantity by routine ensemble-averaged experimental techniques at dilute protein concentrations.

带电胶体粒子结晶过程的实验研究

利用带电单分散聚苯乙烯胶体粒子,通过自组装机理,制备了体积百分比为4·8%的具有多晶结构的胶体晶体,并用Kossel衍射技术和紫外可见分光光度计分别对晶体的生长过程进行了监测.通过对Kossel的图像分析检测不同阶段相应的晶格结构,发现胶体结晶过程晶体结构演变顺序为由液态—随机层结构—堆无序结构—面心立方孪晶结构到面心立方结构.定量地确定了结晶过程中晶体不同晶面的晶面间距和晶体的晶格常数,通过紫外可见分光光度计测量的晶体透射谱图,计算得到111晶面的晶面间距和晶体的晶格常数,与用Kossel衍射技术得到的结果相一致,还发现随样品放置时间的延长,衰减峰变窄和加深,并向短波方向移动,对应着晶体的晶格常数减小的现象.

在激波波面中氧分子的非平衡离解

对强激波作用下双原子分子振动与离解耦合的非平衡离解过程进行了理论计算.本工作的特点是将计算起点建立在分子基本参数上,采用主方程理论处理振动与离解的耦合,振动跃迁几率用SSH理论计算,在离解限附近考虑多量子数跃迁并计及原子复合的影响.对O2-Ar体系,计算给出了在正激波后O2分子振动能级分布、振动弛豫时间、离解孕育时间、离解产物浓度、离解速率系数等物理量随时间的演化.计算结果分别与Camac和Wray的实验相符.计算显示,在激波作用的后期,有准稳态的振动能级布居分布.计算结果显示,Park模型低估了非平衡离解速率系数,Hansen模型则高估了非平衡离解速率系数.

Coherent quantum control of atomic and molecular processes by using the technique of laser pulses

Several schemes for coherent quantum control of atomic and molecular processes have been proposed and investigated by using the techniques of adiabatic passage and ultrashort pulses, respectively. Some interesting results have been found.

Creation of arbitrary coherent superposition states in four-level systems

Using the technique of stimulated Raman adiabatic passage, we propose schemes for creating arbi- trary coherent superposition states of atoms in four-level systems: a A-type system with twofold final states and a four-level ladder system. With the use of a control field, arbitrary coherent superposition states are created without the condition of multiphoton resonance. Suitable manipulation of detunings and the control field can create either a single state or any superposition states desired. (c) 2005 Pleiades Publishing, Inc.