Experimental tests of quantum nonlinear dynamics in atom optics

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose-Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 out of phase with the initial state.

Gelatinization of starch in mixed sugar systems

Sugars affect the gelatinization of starch, with the effect varying significantly between sugars. Since many food products contain a mixture of sugar sources, it is important to understand how their mixtures affect starch gelatinization. In a Rapid Visco Analyser study of maize starch gelatinization, changing proportions in binary mixtures of refined sugars saw a largely proportionate change in starch gelatinization properties. However, binary mixture of pure sugars and honey, or a model honey system (the main sugars in honey) and honey responded differently. Generally, replacing 25% or 50% of the refined sugar or model honey system with honey gave a large change in starch gelatinization properties, while further increases in honey level had little further effect. Differences between honey and buffered model honey system (either gluconic acid, or a mixture of citric acid and di-sodium phosphate) showed the sensitivity of starch gelatinization to the composition of the nonsaccharide component. (c) 2004 Swiss Society of Food Science and Technology. Published by Elsevier Ltd. All rights reserved.

Modelling predicts positive and negative interactions between three Australian tropical tree species in monoculture and binary mixture

Computer modelling promises to. be an important tool for analysing and predicting interactions between trees within mixed species forest plantations. This study explored the use of an individual-based mechanistic model as a predictive tool for designing mixed species plantations of Australian tropical trees. The 'spatially explicit individually based-forest simulator' (SeXI-FS) modelling system was used to describe the spatial interaction of individual tree crowns within a binary mixed-species experiment. The three-dimensional model was developed and verified with field data from three forest tree species grown in tropical Australia. The model predicted the interactions within monocultures and binary mixtures of Flindersia brayleyana, Eucalyptus pellita and Elaeocarpus grandis, accounting for an average of 42% of the growth variation exhibited by species in different treatments. The model requires only structural dimensions and shade tolerance as species parameters. By modelling interactions in existing tree mixtures, the model predicted both increases and reductions in the growth of mixtures (up to +/- 50% of stem volume at 7 years) compared to monocultures. This modelling approach may be useful for designing mixed tree plantations. (c) 2006 Published by Elsevier B.V.

Probability distribution modelling to improve stability in nonlinear MIMO control

We consider the direct adaptive inverse control of nonlinear multivariable systems with different delays between every input-output pair. In direct adaptive inverse control, the inverse mapping is learned from examples of input-output pairs. This makes the obtained controller sub optimal, since the network may have to learn the response of the plant over a larger operational range than necessary. Moreover, in certain applications, the control problem can be redundant, implying that the inverse problem is ill posed. In this paper we propose a new algorithm which allows estimating and exploiting uncertainty in nonlinear multivariable control systems. This approach allows us to model strongly non-Gaussian distribution of control signals as well as processes with hysteresis. The proposed algorithm circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider.

Identification of nonlinear systems by correlation using pseudorandom signals

This thesis is concerned with the measurement of the characteristics of nonlinear systems by crosscorrelation, using pseudorandom input signals based on m sequences. The systems are characterised by Volterra series, and analytical expressions relating the rth order Volterra kernel to r-dimensional crosscorrelation measurements are derived. It is shown that the two-dimensional crosscorrelation measurements are related to the corresponding second order kernel values by a set of equations which may be structured into a number of independent subsets. The m sequence properties determine how the maximum order of the subsets for off-diagonal values is related to the upper bound of the arguments for nonzero kernel values. The upper bound of the arguments is used as a performance index, and the performance of antisymmetric pseudorandom binary, ternary and quinary signals is investigated. The performance indices obtained above are small in relation to the periods of the corresponding signals. To achieve higher performance with ternary signals, a method is proposed for combining the estimates of the second order kernel values so that the effects of some of the undesirable nonzero values in the fourth order autocorrelation function of the input signal are removed. The identification of the dynamics of two-input, single-output systems with multiplicative nonlinearity is investigated. It is shown that the characteristics of such a system may be determined by crosscorrelation experiments using phase-shifted versions of a common signal as inputs. The effects of nonlinearities on the estimates of system weighting functions obtained by crosscorrelation are also investigated. Results obtained by correlation testing of an industrial process are presented, and the differences between theoretical and experimental results discussed for this case;

A techno-economic study of the recycling of mixed plastics to useful products

The techno-economic implications of recycling the components of mixed plastics waste have been studied in a two-part investigation: (a) An economic survey of the prospects for plastics recycling, the plastics waste arisings from retailing, building, automotive, light engineering and chemical industries have been surveyed by mans of questionnaires and interviews. This was partially successful and indicated that very considerable quantities of relatively clean plastics packaging was available in major department chains and household stores. The possibility of devising collection systems for such sources, which do not lead to any extra cost, have been suggested. However, the household collection of plastics waste has been found to be uneconomic due to high cost of collection, transportation and lack of markets for the end products. (b) In a technical study of blends of PE/PP and PE/PS which are found in admixture in waste plastics, it has been shown that they exhibit poor mechanical properties due to incompatibility. Consequently reprocessing of such unsegregated blends results in products of little technological value. The inclusion of some commercial block and graft copolymers which behave as solid phase dispersants (SPES) increase the toughness of the blends (e.g. EPDM in PE/PP blend and SBS in PE/PS blend). Also, EPDM is found to be very effective for improving the toughness of single component polypropylene. However, the improved Technical properties of such blends have been accompanied by a fast rate of photo-oxidation and loss of toughness due to the presence of unsaturation in SPD's. The change in mechanical properties occurring during oven ageing and ultra-violet light accelerated weathering of these binary and ternary blends was followed by a viscoelastonetric technique (Rheovibron) over 9,, wide range of temperatures, impact resistance at room temperature (20-41'G) and changes in functional groups (i.e. carbonyl and trans-1,4-polybutadiene). Also the heat and light stability of single and mixed plastics to which thiol antioxidants were bound to SPE1 segment have been studied and compared with conventional antioxidants. The long-term performance of the mixed plastics containing SPE1 have been improved significantly by the use of conventional and bound antioxidants. It is concluded that an estimated amount of 30000 tonnes/year of plastics waste is available from department chains and household stores which can be converted to useful end products. This justifies pilot-experiments in collaboration with supermarkets, recyclers and converters by use of low cost SPD's and additives designed to make the materials more compatible.

Exploiting uncertainty in nonlinear stochastic control problem

This work introduces a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. Convergence of the output error for the proposed control method is verified by using a Lyapunov function. Several simulation examples are provided to demonstrate the efficiency of the developed control method. The manner in which such a method is extended to nonlinear multi-variable systems with different delays between the input-output pairs is considered and demonstrated through simulation examples.

Comparison of frequency symmetric signal generation from a BPSK input using fiber and semiconductor-based nonlinear elements

This letter compares two nonlinear media for simultaneous carrier recovery and generation of frequency symmetric signals from a 42.7-Gb/s nonreturn-to-zero binary phase-shift-keyed input by exploiting four-wave mixing in a semiconductor optical amplifier and a highly nonlinear optical fiber for use in a phase-sensitive amplifier.

Molecular dynamics simulations of the adsorption and diffusion behavior of pure and mixed alkanes in silicalite

The adsorption and diffusion of mixed hydrocarbon components in silicalite have been studied using molecular dynamic simulation methods. We have investigated the effect of molecular loadings and temperature on the diffusional behavior of both pure and mixed alkane components. For binary mixtures with components of similar sizes, molecular diffusional behavior in the channels was noticed to be reversed as loading is increased. This behavior was noticeably absent for components of different sizes in the mixture. Methane molecules in the methane/propane mixture have the highest diffusion coefficients across the entire loading range. Binary mixtures containing ethane molecules prove more difficult to separate compared to other binary components. In the ternary mixture, however, ethane molecules diffuse much faster at 400 K in the channel with a tendency to separate out quickly from other components. © 2005 Elsevier Inc. All rights reserved.

Fully probabilistic control for stochastic nonlinear control systems with input dependent noise

Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained.

Probabilistic DHP adaptive critic for nonlinear stochastic control systems

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Kárnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained.

A mixture density network approach to modelling and exploiting uncertainty in nonlinear control problems

In nonlinear and stochastic control problems, learning an efficient feed-forward controller is not amenable to conventional neurocontrol methods. For these approaches, estimating and then incorporating uncertainty in the controller and feed-forward models can produce more robust control results. Here, we introduce a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. A nonlinear multi-variable system with different delays between the input-output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non-Gaussian distributions of control signal as well as processes with hysteresis. © 2004 Elsevier Ltd. All rights reserved.

Integer Programming Approach to HP Folding

One of the most widely studied protein structure prediction models is the hydrophobic-hydrophilic (HP) model, which explains the hydrophobic interaction and tries to maximize the number of contacts among hydrophobic amino-acids. In order to find a lower bound for the number of contacts, a number of heuristics have been proposed, but finding the optimal solution is still a challenge. In this research, we focus on creating a new integer programming model which is capable to provide tractable input for mixed-integer programming solvers, is general enough and allows relaxation with provable good upper bounds. Computational experiments using benchmark problems show that our formulation achieves these goals.

A Representation of Binary Matrices

Христина Костадинова, Красимир Йорджев - В статията се обсъжда представянето на произволна бинарна матрица с помощта на последователност от цели неотрицателни числа. Разгледани са някои предимства и недостатъци на това представяне като алтернатива на стандартното, общоприето представяне чрез двумерен масив. Показано е, че представянето на бинарните матрици с помощта на наредени n-торки от естествени числа води до по-бързи алгоритми и до съществена икономия на оперативна памет. Използуван е апарата на обектно-ориентираното програмиране със синтаксиса и семантиката на езика C++.