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.

Thermal Conductivity Of Composites With Nanoscale Inclusions And Size-Dependent Percolation

An analytical model for thermal conductivity of composites with nanoparticles in a matrix is developed based on the effective medium theory by introducing the intrinsic size effect of thermal conductivity of nanoparticles and the interface thermal resistance effect between two phases. The model predicts the percolation of thermal conductivity with the volume fraction change of the second phase, and the percolation threshold depends on the size and the shape of the nanoparticles. The theoretical predictions are in agreement with the experimental results.

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.

Range-wide Yangtze freshwater dolphin expedition: The last chance to see Baiji?

Background, Aim and Scope. There are two species of fresh water cetaceans surviving in the Yangtze River system in China: Baiji (Lipotes vexillifer) and Yangtze finless porpoise (Neophocaena phocaenoides asiaeorientalis). As a result of the expansion of human activities on the river, their distribution ranges appear to be decreasing and in the case of the Baiji, are even being restricted to several sections. The Baiji is the world's most critically endangered cetacean species with a population estimated at only a few tens of individuals. The Yangtze finless porpoise is the world's only freshwater-adapted population of the species, and it has been estimated that only around 1,000 individuals remain in the river system. In order to prevent the extinction of Baiji and a sharp decline in the abundance of the porpoise, in situ conservation (i.e. in the river) and two ex situ conservation (i.e. in semi-natural reserves and in captivity) strategies were proposed and have been implemented since the early 1990s. In view of both the severely endangered status of the animals and the severely degraded conditions of their habitats, the feasibility and actual status of these two strategies are raised for discussion. Main Features. The threats faced by the cetaceans are mainly from the unfettered exploitation of the river's resources. In the past 20 years, five nature reserves have been established along the river. Imposing maximum prohibition of harmful and illegal fishing methods in the reserves might prolong the process of extinction of these cetaceans in the wild, but so far, the administrative measures taken in the reserves have not yet kept the abundance from sharply declining. As human use of the river and its resources is expected to intensify for many decades into the future, the ability of the river to continue to support these species is certainly undecided. Therefore, rescuing animals from the river and establishing viable breeding populations in semi-natural reserves, in which the environment is similar to the main stream of the river, and in captivity, has to be considered urgently as the short-term goal of ex situ strategies. Since the abundance of porpoises is higher than that of the Baiji, we have first established breeding populations of them in the semi-natural reserves and in captivity. But, considering the extremely low density of Baiji in the river, an immediate range-wide Yangtze Baiji survey is an urgent need for locating and capturing sufficient Baiji for successfully establishing a breeding population of them in semi-natural reserves. Results. Two semi-natural reserves (in Shishou, Hubei Province, and Tongling, Anhui Province) have been set up along the river in order to establish breeding populations of the Baiji and the porpoises. So far, several small groups of porpoises that were caught in the main stream of the river have successively been introduced into the semi-natural reserves. Under careful management, these animals in both of the semi-natural reserves not only survive, but can also reproduce naturally and successfully. At least one or three calves were born in each reserve each year. Additionally, a breeding group of porpoises is being established at the Baiji Dolphinarium at the Institute of Hydrobiology, Chinese Academy of Sciences, Wuhan. There are presently four adults and one calf living in the Dolphinarium. The calf, born in July, 2005, is the first captive bred Yangtze Finless Porpoise in the world. In preparation for the range-wide Yangtze cetacean survey, a 9-day pilot expedition on the river near Wuhan was conducted in March, 2006, in order to develop methods for locating the Baiji. No Baiji were expected to be seen in such a short period but about 40 porpoise sightings were observed. Results of the pilot survey indicated that traditional visual and acoustical survey methods for cetaceans should be adapted to find the elusive Baiji in the river. Currently, the range-wide Yangtze cetacean survey is in preparation. The survey will cover over 1,700 km of the Yangtze River from Yichang to Shanghai, and is expected to provide detailed information on Baiji and porpoise numbers and distribution patterns in the river. Discussion. Although the short-term goal of ex situ conservation is to rescue cetaceans from the river and to establish viable breeding populations in semi-natural reserves and in captivity, the long-term goal of releasing the animals back into the river when the threats have decreased and the natural environment has been improved, should not be neglected. Moreover, the in situ conservation efforts in the natural reserves, and even in the entire Yangtze River system, including the lakes, should not be ignored or abandoned at any time. The activities contributing to the conservation of the Baiji and the porpoise in the wild have the incidental effect of benefiting the entire Yangtze ecosystem and other rare threatened species. The dynamics of the groups of porpoises in semi-natural reserves should be monitored continually, in order to guide the establishment of breeding groups of Baiji in these semi-natural reserves in the near future. Conclusions. Under the existing severely degraded conditions of the Yangtze system, the sharply fall populations of Baiji and porpoises will not be suspended in the foreseeable future. Therefore, ex situ conservation should be emphasized, and the severely threatened Baiji in the river should be removed and translocated to semi-natural reserves for establishing viable breeding populations. The successful program of capturing, translocating and maintaining finless porpoises in the Shishou semi-natural reserve has demonstrated its adequacy as an ex situ environment for cetaceans. Following the successful pilot survey in the river, the immediate range-wide Yangtze cetacean survey is proposed and is in preparation. The range-wide survey is expected to ensure that any remaining Baiji can be found reliably and captured successfully after the survey. Recommendations and Perspectives. During the range-wide survey, not only the Baiji but also the porpoise as well as their habitats should be investigated based on visual and acoustical methods that adapted to the river and the animals. Meanwhile, the current risk levels to the Baiji and porpoises should be evaluated at each area where Baiji or porpoises can be reliably sighted. Any capture efforts should be targeted on the most threatened areas, or where there is maximum risk of injury or death. The immediate track of the Baiji should be carried out once a Baiji is sighted during the range-wide survey in order to obtain the movement route of the animals, which is crucial information for the successful capture operation. Additionally, the need to establish new semi-natural reserves for the porpoises should be placed on the agenda of local and central governments in the near future.

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.

Geomagnetic paleointensity dating of South China Sea sediments for the last 130 kyr

Relative paleointensity records from the northern South China Sea, northwest Pacific Ocean were studied in two gravity piston cores. Continuous mineral magnetic and paleomagnetic measurements were made using discrete sediment samples. Detailed rock magnetic parameters, such as thermomagnetic and high-field hysteresis data, indicate that pseudo-single domain magnetite in a narrow range of grain-size and concentration is the main contributor to the remanent magnetization. The uniform magnetic mineralogy meets the commonly accepted criteria for establishing relative paleointensity records. The relative paleointensity (RPI) curves were constructed by normalizing the natural remanent magnetization (NRM) with isothermal remanent magnetization (IRM), both in the 20-60 mT demagnetization state. Dating constraints have been provided by radiocarbon ages in the upper 400 cm of both cores. Furthermore, we have correlated our paleointensity records with NAPIS-75, S.Atlantic-1089, Sint-200 and NOPAPIS-250 to determine the chronological RPI framework for the South China Sea (SCS-PIS). Although some temporal offsets of paleointensity features between the different records have been recognized, their similar shape suggests that relative paleointensity on the 10(3)-10(4) year scale is globally coherent and can provide an age framework for sediments independent of delta O-18 ages.