Extension of the firefly algorithm and preference rules for solving MINLP problems
Costa, M. Fernanda P.; Francisco, Rogério B.; Rocha, Ana Maria A. C.; Fernandes, Edite M. G. P.
2017-07-01
An extension of the firefly algorithm (FA) for solving mixed-integer nonlinear programming (MINLP) problems is presented. Although penalty functions are nowadays frequently used to handle integrality conditions and inequality and equality constraints, this paper proposes the implementation within the FA of a simple rounded-based heuristic and four preference rules to find and converge to MINLP feasible solutions. Preliminary numerical experiments are carried out to validate the proposed methodology.
Multi-objective Evolutionary Algorithms for MILP and MINLP in Process Synthesis
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Steady-state non-dominated sorting genetic algorithm (SNSGA), a new form of multi-objective genetic algorithm, is implemented by combining the steady-state idea in steady-state genetic algorithms (SSGA) and the fitness assignment strategy of non-dominated sorting genetic algorithm (NSGA). The fitness assignment strategy is improved and a new self-adjustment scheme of σshare is proposed. This algorithm is proved to be very efficient both computationally and in terms of the quality of the Pareto fronts produced with five test problems including GA difficult problem and GA deceptive one. Finally, SNSGA is introduced to solve multi-objective mixed integer linear programming (MILP) and mixed integer non-linear programming (MINLP) problems in process synthesis.
Uilhoorn, F. E.
2016-10-01
In this article, the stochastic modelling approach proposed by Box and Jenkins is treated as a mixed-integer nonlinear programming (MINLP) problem solved with a mesh adaptive direct search and a real-coded genetic class of algorithms. The aim is to estimate the real-valued parameters and non-negative integer, correlated structure of stationary autoregressive moving average (ARMA) processes. The maximum likelihood function of the stationary ARMA process is embedded in Akaike's information criterion and the Bayesian information criterion, whereas the estimation procedure is based on Kalman filter recursions. The constraints imposed on the objective function enforce stability and invertibility. The best ARMA model is regarded as the global minimum of the non-convex MINLP problem. The robustness and computational performance of the MINLP solvers are compared with brute-force enumeration. Numerical experiments are done for existing time series and one new data set.
A Novel Interactive MINLP Solver for CAPE Applications
DEFF Research Database (Denmark)
Henriksen, Jens Peter; Støy, S.; Russel, Boris Mariboe;
2000-01-01
This paper presents an interactive MINLP solver that is particularly suitable for solution of process synthesis, design and analysis problems. The interactive MINLP solver is based on the decomposition based MINLP algorithms, where a NLP sub-problem is solved in the innerloop and a MILP master...
Yin, Sisi; Nishi, Tatsushi
2014-11-01
Quantity discount policy is decision-making for trade-off prices between suppliers and manufacturers while production is changeable due to demand fluctuations in a real market. In this paper, quantity discount models which consider selection of contract suppliers, production quantity and inventory simultaneously are addressed. The supply chain planning problem with quantity discounts under demand uncertainty is formulated as a mixed-integer nonlinear programming problem (MINLP) with integral terms. We apply an outer-approximation method to solve MINLP problems. In order to improve the efficiency of the proposed method, the problem is reformulated as a stochastic model replacing the integral terms by using a normalisation technique. We present numerical examples to demonstrate the efficiency of the proposed method.
MINLP model for simultaneous scheduling and retrofit of refinery preheat train
Directory of Open Access Journals (Sweden)
Zulkafli N. Izyan, M. Noryani, Abdul H. Dayanasari, M. Shuhaimi
2014-01-01
Full Text Available There is greater awareness today on the depleting fossil energy resources and the growing problem of atmospheric pollution. Engineers are developing practical techniques to ensure energy processes are designed and operated efficiently. Inefficient heat exchangers lead to higher fuel demand and higher carbon emission. This paper presents mixed-integer nonlinear programming (MINLP model for simultaneous cleaning and retrofit of crude preheat train (CPT in oil refinery plant. The formulation of the model is generated and coded in General Algebraic Modeling System (GAMS. The model minimizes the cost of energy and the cost of cleaning. The model takes into account the changes in fouling rates throughout time. There are two cases for this study. The cases are online cleaning (Case 1 and simultaneous online cleaning and retrofit (Case 2. The largest energy saving are found in Case 2. The installation of high efficiency heat exchangers improves furnace inlet temperature (FIT from 215oC to 227oC. Furthermore, Case 2 results in the highest percentage of cost saving by about 59%. The payback period for investment in high efficiency heat exchangers is 5 months. Thus, Case 2 is the most cost effective option for reductions of energy consumption in Crude Distillation Unit (CDU.
Energy Technology Data Exchange (ETDEWEB)
Linderoth, Jeff T. [University of Wisconsin-Madison; Luedtke, James R. [University of Wisconsin-Madison
2013-05-30
The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Problems involving both discrete and nonlinear components are known as mixed-integer nonlinear programs (MINLPs) and are among the most challenging computational optimization problems. This research project added to the understanding of this area by making a number of fundamental advances. First, the work demonstrated many novel, strong, tractable relaxations designed to deal with non-convexities arising in mathematical formulation. Second, the research implemented the ideas in software that is available to the public. Finally, the work demonstrated the importance of these ideas on practical applications and disseminated the work through scholarly journals, survey publications, and conference presentations.
Institute of Scientific and Technical Information of China (English)
Meysam Kamalinejad; Majid Amidpour; S.M. Mousavi Naeynian
2015-01-01
Liquefied natural gas (LNG) is the most economical way of transporting natural gas (NG) over long distances. Liq-uefaction of NG using vapor compression refrigeration system requires high operating and capital cost. Due to lack of systematic design methods for multistage refrigeration cycles, conventional approaches to determine op-timal cycle are largely trial-and-error. In this paper a novel mixed integer non-linear programming (MINLP) model is introduced to select optimal synthesis of refrigeration systems to reduce both operating and capital costs of an LNG plant. Better conceptual understanding of design improvement is illustrated on composite curve (CC) and exergetic grand composite curve (EGCC) of pinch analysis diagrams. In this method a superstruc-ture representation of complex refrigeration system is developed to select and optimize key decision variables in refrigeration cycles (i.e. partition temperature, compression configuration, refrigeration features, refrigerant flow rate and economic trade-off). Based on this method a program (LNG-Pro) is developed which integrates VBA, Refprop and Excel MINLP Solver to automate the methodology. Design procedure is applied on a sample LNG plant to illustrate advantages of using this method which shows a 3.3% reduction in total shaft work consumption.
Institute of Scientific and Technical Information of China (English)
陈理; 王克峰; 徐霄羽; 姚平经
2004-01-01
In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant. The overall mixed integer nonlinear programming (MINLP) problem is hierarchically structured into a mixed integer linear programming (MILP) problem first and then a reduced dimensional MINLP problem, which are optimized by mathematical programming (MP) and genetic algorithm (GA) respectively. The basis idea relies on combining MP with GA to exploit their complementary capacity. The key features of the hierarchical model are explained and illustrated with some real world cases from the multiproduct batch plants.
Nonlinear programming analysis and methods
Avriel, Mordecai
2012-01-01
This text provides an excellent bridge between principal theories and concepts and their practical implementation. Topics include convex programming, duality, generalized convexity, analysis of selected nonlinear programs, techniques for numerical solutions, and unconstrained optimization methods.
Nonlinear programming analysis and methods
Avriel, Mordecai
2003-01-01
Comprehensive and complete, this overview provides a single-volume treatment of key algorithms and theories. The author provides clear explanations of all theoretical aspects, with rigorous proof of most results. The two-part treatment begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs. The second part concerns techniques for numerical solutions and unconstrained optimization methods, and it presents commonly used algorithms for constrained nonlinear optimization problems. This g
Institute of Scientific and Technical Information of China (English)
陈理; 王克峰; 徐霄羽; 姚平经
2004-01-01
In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant.The overall mixed integer nonlinear programming (MINLP) problem is hierarchically structured into a mixed integer linear programming (MILP) problem first and then a reduced dimensional MINLP problem, which are optimized by mathematical programming (MP) and genetic algorithm (GA) respectively. The basis idea relies on combining MP with GA to exploit their complementary capacity. The key features of the hierarchical model are explained and illustrated with some real world cases from the multiproduct batch plants.
LINEAR AND NONLINEAR SEMIDEFINITE PROGRAMMING
Directory of Open Access Journals (Sweden)
Walter Gómez Bofill
2014-12-01
Full Text Available This paper provides a short introduction to optimization problems with semidefinite constraints. Basic duality and optimality conditions are presented. For linear semidefinite programming some advances by dealing with degeneracy and the semidefinite facial reduction are discussed. Two relatively recent areas of application are presented. Finally a short overview of relevant literature on algorithmic approaches for efficiently solving linear and nonlinear semidefinite programming is provided.
Automatic design of synthetic gene circuits through mixed integer non-linear programming.
Huynh, Linh; Kececioglu, John; Köppe, Matthias; Tagkopoulos, Ilias
2012-01-01
Automatic design of synthetic gene circuits poses a significant challenge to synthetic biology, primarily due to the complexity of biological systems, and the lack of rigorous optimization methods that can cope with the combinatorial explosion as the number of biological parts increases. Current optimization methods for synthetic gene design rely on heuristic algorithms that are usually not deterministic, deliver sub-optimal solutions, and provide no guaranties on convergence or error bounds. Here, we introduce an optimization framework for the problem of part selection in synthetic gene circuits that is based on mixed integer non-linear programming (MINLP), which is a deterministic method that finds the globally optimal solution and guarantees convergence in finite time. Given a synthetic gene circuit, a library of characterized parts, and user-defined constraints, our method can find the optimal selection of parts that satisfy the constraints and best approximates the objective function given by the user. We evaluated the proposed method in the design of three synthetic circuits (a toggle switch, a transcriptional cascade, and a band detector), with both experimentally constructed and synthetic promoter libraries. Scalability and robustness analysis shows that the proposed framework scales well with the library size and the solution space. The work described here is a step towards a unifying, realistic framework for the automated design of biological circuits.
Recent advances in multiparametric nonlinear programming
Domínguez, Luis F.
2010-05-01
In this paper, we present recent developments in multiparametric nonlinear programming. For the case of convex problems, we highlight key issues regarding the full characterization of the parametric solution space and we discuss, through an illustrative example problem, four alternative state-of-the-art multiparametric nonlinear programming algorithms. We also identify a number of main challenges for the non-convex case and highlight future research directions. © 2009 Elsevier Ltd. All rights reserved.
Non-Iterative Rigid 2D/3D Point-Set Registration Using Semidefinite Programming.
Khoo, Yuehaw; Kapoor, Ankur
2016-07-01
We describe a convex programming framework for pose estimation in 2D/3D point-set registration with unknown point correspondences. We give two mixed-integer nonlinear program (MINLP) formulations of the 2D/3D registration problem when there are multiple 2D images, and propose convex relaxations for both the MINLPs to semidefinite programs that can be solved efficiently by interior point methods. Our approach to the 2D/3D registration problem is non-iterative in nature as we jointly solve for pose and correspondence. Furthermore, these convex programs can readily incorporate feature descriptors of points to enhance registration results. We prove that the convex programs exactly recover the solution to the MINLPs under certain noiseless condition. We apply these formulations to the registration of 3D models of coronary vessels to their 2D projections obtained from multiple intra-operative fluoroscopic images. For this application, we experimentally corroborate the exact recovery property in the absence of noise and further demonstrate robustness of the convex programs in the presence of noise.
Directory of Open Access Journals (Sweden)
Samira Salahi
2016-08-01
Full Text Available Reduction of fossil resources, increasing the production of greenhouse gas emissions and demand growth lead to greater use of distributed energy resources in power system especially in distribution networks. Integrating these resources in order to supply local loads creates a new concept called micro-grid. Optimal operation of micro-grid in the specific time period is one of the most important problems of them. In this paper, the operation problem of micro-grids is modeled considering the economical, technical and environmental issues, as well as uncertainties related to loads, wind speed and solar radiation. The resulting model is a Mixed-Integer Non-Linear Programming (MINLP. To demonstrate the effectiveness of the proposed model, Bisheh village in Iran is considered as a case study. The results showed that considering load curtailment costs, the power losses of the main grid, the penalties of pollutant gasses emissions and the elimination of energy subsides will tremendous impacts on the operation of microgrids. Article History: Received March 12, 2016; Received in revised form June 20, 2016; Accepted July 2nd 2016; Available online How to Cite This Article: Salahi, S., and Bahramara, S. (2016 Modeling Operation Problem of Micro-grids Considering Economical, Technical and Environmental issues as Mixed-Integer Non-Linear Programming. Int. Journal of Renewable Energy Development, 5(2, 139-149. http://dx.doi.org/10.14710/ijred.5.2.139-149
Solutions manual to accompany Nonlinear programming
Bazaraa, Mokhtar S; Shetty, C M
2014-01-01
As the Solutions Manual, this book is meant to accompany the main title, Nonlinear Programming: Theory and Algorithms, Third Edition. This book presents recent developments of key topics in nonlinear programming (NLP) using a logical and self-contained format. The volume is divided into three sections: convex analysis, optimality conditions, and dual computational techniques. Precise statements of algortihms are given along with convergence analysis. Each chapter contains detailed numerical examples, graphical illustrations, and numerous exercises to aid readers in understanding the concepts a
A Stability Theory in Nonlinear Programming
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
We propose a new method for finding the local optimal points ofthe constrained nonlinear programming by Ordinary Differential Equations (ODE), and prove asymptotic stability of the singular points of partial variables in this paper. The condition of overall uniform, asymptotic stability is also given.
Optimality conditions in smooth nonlinear programming
Still, G.; Streng, M.
1996-01-01
This survey is concerned with necessary and sufficient optimality conditions for smooth nonlinear programming problems with inequality and equality constraints. These conditions deal with strict local minimizers of order one and two and with isolated minimizers. In most results, no constraint qualif
Some Duality Results for Fuzzy Nonlinear Programming Problem
Sangeeta Jaiswal; Geetanjali Panda
2012-01-01
The concept of duality plays an important role in optimization theory. This paper discusses some relations between primal and dual nonlinear programming problems in fuzzy environment. Here, fuzzy feasible region for a general fuzzy nonlinear programming is formed and the concept of fuzzy feasible solution is defined. First order dual relation for fuzzy nonlinear programming problem is studied.
Nonlinear programming with feedforward neural networks.
Energy Technology Data Exchange (ETDEWEB)
Reifman, J.
1999-06-02
We provide a practical and effective method for solving constrained optimization problems by successively training a multilayer feedforward neural network in a coupled neural-network/objective-function representation. Nonlinear programming problems are easily mapped into this representation which has a simpler and more transparent method of solution than optimization performed with Hopfield-like networks and poses very mild requirements on the functions appearing in the problem. Simulation results are illustrated and compared with an off-the-shelf optimization tool.
96 International Conference on Nonlinear Programming
1998-01-01
About 60 scientists and students attended the 96' International Conference on Nonlinear Programming, which was held September 2-5 at Institute of Compu tational Mathematics and Scientific/Engineering Computing (ICMSEC), Chi nese Academy of Sciences, Beijing, China. 25 participants were from outside China and 35 from China. The conference was to celebrate the 60's birthday of Professor M.J.D. Powell (Fellow of Royal Society, University of Cambridge) for his many contributions to nonlinear optimization. On behalf of the Chinese Academy of Sciences, vice president Professor Zhi hong Xu attended the opening ceremony of the conference to express his warm welcome to all the participants. After the opening ceremony, Professor M.J.D. Powell gave the keynote lecture "The use of band matrices for second derivative approximations in trust region methods". 13 other invited lectures on recent advances of nonlinear programming were given during the four day meeting: "Primal-dual methods for nonconvex optimization" by...
STEW A Nonlinear Data Modeling Computer Program
Chen, H
2000-01-01
A nonlinear data modeling computer program, STEW, employing the Levenberg-Marquardt algorithm, has been developed to model the experimental sup 2 sup 3 sup 9 Pu(n,f) and sup 2 sup 3 sup 5 U(n,f) cross sections. This report presents results of the modeling of the sup 2 sup 3 sup 9 Pu(n,f) and sup 2 sup 3 sup 5 U(n,f) cross-section data. The calculation of the fission transmission coefficient is based on the double-humped-fission-barrier model of Bjornholm and Lynn. Incident neutron energies of up to 5 MeV are considered.
A New Approach to Solving Nonlinear Programming
Institute of Scientific and Technical Information of China (English)
SHEN Jie; CHEN Ling
2002-01-01
A method for solving nonlinear programming using genetic algorithm is presented. In the operations of crossover and mutation in each generation, to ensure the new solutions are all feasible, we present a method in which the bounds of every variable in the solution are estimated beforehand according to the constrained conditions. For the operation of mutation, we present two methods of cube bounding and variable bounding. The experimental results are given and analyzed. They show that the method is efficient and can obtain the results in less generation.
STEW: A Nonlinear Data Modeling Computer Program
Energy Technology Data Exchange (ETDEWEB)
Chen, H.
2000-03-04
A nonlinear data modeling computer program, STEW, employing the Levenberg-Marquardt algorithm, has been developed to model the experimental {sup 239}Pu(n,f) and {sup 235}U(n,f) cross sections. This report presents results of the modeling of the {sup 239}Pu(n,f) and {sup 235}U(n,f) cross-section data. The calculation of the fission transmission coefficient is based on the double-humped-fission-barrier model of Bjornholm and Lynn. Incident neutron energies of up to 5 MeV are considered.
Bifurcations and sensitivity in parametric nonlinear programming
Lundberg, Bruce N.; Poore, Aubrey B.
1990-01-01
The parametric nonlinear programming problem is that of determining the behavior of solution(s) as a parameter or vector of parameters alpha belonging to R(sup r) varies over a region of interest for the problem: Minimize over x the set f(x, alpha):h(x, alpha) = 0, g(x, alpha) is greater than or equal to 0, where f:R(sup (n+r)) approaches R, h:R(sup (n+r)) approaches R(sup q) and g:R(sup (n+r)) approaches R(sup p) are assumed to be at least twice continuously differentiable. Some of these parameters may be fixed but not known precisely and others may be varied to enhance the performance of the system. In both cases a fundamentally important problem in the investigation of global sensitivity of the system is to determine the stability boundaries of the regions in parameter space which define regions of qualitatively similar solutions. The objective is to explain how numerical continuation and bifurcation techniques can be used to investigate the parametric nonlinear programming problem in a global sense. Thus, first the problem is converted to a closed system of parameterized nonlinear equations whose solution set contains all local minimizers of the original problem. This system, which will be represented as F(z,alpha) = O, will include all Karush-Kuhn-Tucker and Fritz John points, both feasible and infeasible solutions, and relative minima, maxima, and saddle points of the problem. The local existence and uniqueness of a solution path (z(alpha), alpha) of this system as well as the solution type persist as long as a singularity in the Jacobian D(sub z)F(z,alpha) is not encountered. Thus the nonsingularity of this Jacobian is characterized in terms of conditions on the problem itself. Then, a class of efficient predictor-corrector continuation procedures for tracing solution paths of the system F(z,alpha) = O which are tailored specifically to the parametric programming problem are described. Finally, these procedures and the obtained information are illustrated
An SQP Algorithm for Recourse-based Stochastic Nonlinear Programming
Directory of Open Access Journals (Sweden)
Xinshun Ma
2016-05-01
Full Text Available The stochastic nonlinear programming problem with completed recourse and nonlinear constraints is studied in this paper. We present a sequential quadratic programming method for solving the problem based on the certainty extended nonlinear model. This algorithm is obtained by combing the active set method and filter method. The convergence of the method is established under some standard assumptions. Moreover, a practical design is presented and numerical results are provided.
An Algorithm for Linearly Constrained Nonlinear Programming Programming Problems.
1980-01-01
ALGORITHM FOR LINEARLY CONSTRAINED NONLINEAR PROGRAMMING PROBLEMS Mokhtar S. Bazaraa and Jamie J. Goode In this paper an algorithm for solving a linearly...distance pro- gramr.ing, as in the works of Bazaraa and Goode 12], and Wolfe [16 can be used for solving this problem. Special methods that take advantage of...34 Pacific Journal of Mathematics, Volume 16, pp. 1-3, 1966. 2. M. S. Bazaraa and J. j. Goode, "An Algorithm for Finding the Shortest Element of a
A Four-Type Decision-Variable MINLP Model for a Supply Chain Network Design
Directory of Open Access Journals (Sweden)
M. M. Monteiro
2010-01-01
Full Text Available We propose a mixed integer nonlinear programming model for the design of a one-period planning horizon supply chain with integrated and flexible decisions on location of plants and of warehouses, on levels of production and of inventory, and on transportation models, considering stochastic demand and the ABC classification for finished goods, which is an NP-hard industrial engineering optimization problem. Furthermore, computational implementation of the proposed model is presented through the direct application of the outer approximation algorithm on some randomly generated supply chain data.
Constrained optimization for image restoration using nonlinear programming
Yeh, C.-L.; Chin, R. T.
1985-01-01
The constrained optimization problem for image restoration, utilizing incomplete information and partial constraints, is formulated using nonlinear proramming techniques. This method restores a distorted image by optimizing a chosen object function subject to available constraints. The penalty function method of nonlinear programming is used. Both linear or nonlinear object function, and linear or nonlinear constraint functions can be incorporated in the formulation. This formulation provides a generalized approach to solve constrained optimization problems for image restoration. Experiments using this scheme have been performed. The results are compared with those obtained from other restoration methods and the comparative study is presented.
On filter-successive linearization methods for nonlinear semidefinite programming
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially effcient.
On filter-successive linearization methods for nonlinear semidefinite programming
Institute of Scientific and Technical Information of China (English)
LI ChengJin; SUN WenYui
2009-01-01
In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially efficient.
Energy Technology Data Exchange (ETDEWEB)
Tveit, T.M.; Fogelholm, C.J. (Helsinki Univ. of Technology, Dept. of Energy Technology, P.O.Box 4400, FI-02015 TKK (Finland)); Sangsu, K. (Korea District Heating Corp., R and D Dept., 186 Bundang-dong, Bundang-gu, Seongnam-si, Gyeonggi-do, 463-908 (Korea))
2008-09-15
In this paper a multi-period MINLP model for optimising operation and structural changes to CHP plants in district heating networks with long-term thermal storage is applied to an existing district heating network. The best result found shows an annual profit of approximately 22.9 million USD. The best solution found without the thermal storage shows an annual profit of 18.1 million USD. This gives an estimate of the value of the long-term thermal storage of 4.8 million USD/a
An Adaptive Neural Network Model for Nonlinear Programming Problems
Institute of Scientific and Technical Information of China (English)
Xiang-sun Zhang; Xin-jian Zhuo; Zhu-jun Jing
2002-01-01
In this paper a canonical neural network with adaptively changing synaptic weights and activation function parameters is presented to solve general nonlinear programming problems. The basic part of the model is a sub-network used to find a solution of quadratic programming problems with simple upper and lower bounds. By sequentially activating the sub-network under the control of an external computer or a special analog or digital processor that adjusts the weights and parameters, one then solves general nonlinear programming problems. Convergence proof and numerical results are given.
Using genetic programming to discover nonlinear variable interactions.
Westbury, Chris; Buchanan, Lori; Sanderson, Michael; Rhemtulla, Mijke; Phillips, Leah
2003-05-01
Psychology has to deal with many interacting variables. The analyses usually used to uncover such relationships have many constraints that limit their utility. We briefly discuss these and describe recent work that uses genetic programming to evolve equations to combine variables in nonlinear ways in a number of different domains. We focus on four studies of interactions from lexical access experiments and psychometric problems. In all cases, genetic programming described nonlinear combinations of items in a manner that was subsequently independently verified. We discuss the general implications of genetic programming and related computational methods for multivariate problems in psychology.
Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.
Jiang, Yu; Jiang, Zhong-Ping
2014-05-01
This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system.
An Evaluation and Comparison of Three Nonlinear Programming Codes
1976-03-01
sixth problem was selected from the Himmelblau collection [Ref. 11] and the remaining two were adaptations cf an inventory model and an entropy model...both require utilization of the main nonlinear codes with their high core and corresponding time requirements. Himmelblau estimated preparation times...Nonlinear Program mincf Moclel for "Determining a Huni/Eions ITix, By R*.J. CTasen, E.¥.Graves ana J.Y7 Iu, 3arch 1974. 11. Himmelblau . D.M., Applied
Modified Filled Function to Solve NonlinearProgramming Problem
Institute of Scientific and Technical Information of China (English)
2015-01-01
Filled function method is an approach to find the global minimum of nonlinear functions. Many Problems, such as computing,communication control, and management, in real applications naturally result in global optimization formulations in a form ofnonlinear global integer programming. This paper gives a modified filled function method to solve the nonlinear global integerprogramming problem. The properties of the proposed modified filled function are also discussed in this paper. The results ofpreliminary numerical experiments are also reported.
Generic Mathematical Programming Formulation and Solution for Computer-Aided Molecular Design
2015-01-01
This short communication presents a generic mathematical programming formulation for Computer-Aided Molecular Design (CAMD). A given CAMD problem, based on target properties, is formulated as a Mixed Integer Linear/Non-Linear Program (MILP/MINLP). The mathematical programming model presented here, which is formulated as an MILP/MINLP problem, considers first-order and second-order molecular groups for molecular structure representation and property estimation. It is shown that various CAMD pr...
Energy Technology Data Exchange (ETDEWEB)
Shamloo, H.; Haghighi, A. [K.N. Toosi Univ. of Technology, Tehran (Iran, Islamic Republic of). Dept. of Civil Engineering
2009-07-01
The flow properties of pipes are affected by leaks. Leak detection methods based on hydraulic modelling and real data records aim to find a pipe's leak parameters including their number, location and size. Inverse Transient Analysis (ITA), generally in time domain, is a powerful approach to develop leak detection methods with considerable benefits. This paper introduced an ITA based leak detection method along with a numerical model developed for direct transient analysis of leaks in pipes using method of characteristics (MOC). Transient state flow was generated in pipe and the pressure fluctuations were sampled only at the end valve location. To minimize the effects of unsteadiness and uncertainties due to the numerical modeling and also practical problems caused by water hammer, the downstream end valve was considered to be closed gradually within a long enough time. Then, using the sampled data and a direct transient analysis model, a mixed integer nonlinear program was developed. A mixed genetic algorithm was used in which the binary chromosomes were decoded as mixed integer leak locations and real leak areas. In order to find unknown leak parameters in a pipe, an objective function was defined using the least squares criterion of differences between observed and calculated pressure heads at the valve location. The genetic algorithm was found to be a powerful and easy to use optimization tool to solve complicated mixed integer nonlinear program (MINLP) problems in leak detection. 24 refs., 1 tab., 7 figs.
A ROBUST TRUST REGION ALGORITHM FOR SOLVING GENERAL NONLINEAR PROGRAMMING
Institute of Scientific and Technical Information of China (English)
Xin-wei Liu; Ya-xiang Yuan
2001-01-01
The trust region approach has been extended to solving nonlinear constrained optimization. Most of these extensions consider only equality constraints and require strong global regularity assumptions. In this paper, a trust region algorithm for solving general nonlinear programming is presented, which solves an unconstrained piecewise quadratic trust region subproblem and a quadratic programming trust region subproblem at each iteration. A new technique for updating the penalty parameter is introduced. Under very mild conditions, the global convergence results are proved. Some local convergence results are also proved. Preliminary numerical results are also reported.
Incremental approximate dynamic programming for nonlinear flight control design
Zhou, Y.; Van Kampen, E.J.; Chu, Q.P.
2015-01-01
A self-learning adaptive flight control design for non-linear systems allows reliable and effective operation of flight vehicles in a dynamic environment. Approximate dynamic programming (ADP) provides a model-free and computationally effective process for designing adaptive linear optimal
A Novel Nonlinear Programming Model for Distribution Protection Optimization
Zambon, Eduardo; Bossois, Débora Z.; Garcia, Berilhes B.; Azeredo, Elias F.
2009-01-01
This paper presents a novel nonlinear binary programming model designed to improve the reliability indices of a distribution network. This model identifies the type and location of protection devices that should be installed in a distribution feeder and is a generalization of the classical optimizat
An SQP algorithm for mathematical programs with nonlinear complementarity constraints
Institute of Scientific and Technical Information of China (English)
Zhi-bin ZHU; Jin-bao JIAN; Cong ZHANG
2009-01-01
In this paper,we describe a successive approximation and smooth sequential quadratic programming (SQP) method for mathematical programs with nonlinear complementarity constraints (MPCC). We introduce a class of smooth programs to approximate the MPCC. Using an l1 penalty function,the line search assures global convergence,while the superlinear convergence rate is shown under the strictly complementary and second-order sufficient conditions. Moreover,we prove that the current iterated point is an exact stationary point of the mathematical programs with equilibrium constraints (MPEC) when the algorithm terminates finitely.
A Filter Method for Nonlinear Semidefinite Programming with Global Convergence
Institute of Scientific and Technical Information of China (English)
Zhi Bin ZHU; Hua Li ZHU
2014-01-01
In this study, a new filter algorithm is presented for solving the nonlinear semidefinite programming. This algorithm is inspired by the classical sequential quadratic programming method. Unlike the traditional filter methods, the suffi cient descent is ensured by changing the step size instead of the trust region radius. Under some suitable conditions, the global convergence is obtained. In the end, some numerical experiments are given to show that the algorithm is eff ective.
Lee, Chang Jun
2015-01-01
In the fields of researches associated with plant layout optimization, the main goal is to minimize the costs of pipelines and pumping between connecting equipment under various constraints. However, what is the lacking of considerations in previous researches is to transform various heuristics or safety regulations into mathematical equations. For example, proper safety distances between equipments have to be complied for preventing dangerous accidents on a complex plant. Moreover, most researches have handled single-floor plant. However, many multi-floor plants have been constructed for the last decade. Therefore, the proper algorithm handling various regulations and multi-floor plant should be developed. In this study, the Mixed Integer Non-Linear Programming (MINLP) problem including safety distances, maintenance spaces, etc. is suggested based on mathematical equations. The objective function is a summation of pipeline and pumping costs. Also, various safety and maintenance issues are transformed into inequality or equality constraints. However, it is really hard to solve this problem due to complex nonlinear constraints. Thus, it is impossible to use conventional MINLP solvers using derivatives of equations. In this study, the Particle Swarm Optimization (PSO) technique is employed. The ethylene oxide plant is illustrated to verify the efficacy of this study.
A FORTRAN program for calculating nonlinear seismic ground response
Joyner, William B.
1977-01-01
The program described here was designed for calculating the nonlinear seismic response of a system of horizontal soil layers underlain by a semi-infinite elastic medium representing bedrock. Excitation is a vertically incident shear wave in the underlying medium. The nonlinear hysteretic behavior of the soil is represented by a model consisting of simple linear springs and Coulomb friction elements arranged as shown. A boundary condition is used which takes account of finite rigidity in the elastic substratum. The computations are performed by an explicit finite-difference scheme that proceeds step by step in space and time. A brief program description is provided here with instructions for preparing the input and a source listing. A more detailed discussion of the method is presented elsewhere as is the description of a different program employing implicit integration.
A novel neural network for nonlinear convex programming.
Gao, Xing-Bao
2004-05-01
In this paper, we present a neural network for solving the nonlinear convex programming problem in real time by means of the projection method. The main idea is to convert the convex programming problem into a variational inequality problem. Then a dynamical system and a convex energy function are constructed for resulting variational inequality problem. It is shown that the proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem. Compared with the existing neural networks for solving the nonlinear convex programming problem, the proposed neural network has no Lipschitz condition, no adjustable parameter, and its structure is simple. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results.
Approximate Augmented Lagrangian Functions and Nonlinear Semidefinite Programs
Institute of Scientific and Technical Information of China (English)
X. X. HUANG; K. L. TEO; X. Q. YANG
2006-01-01
In this paper, an approximate augmented Lagrangian function for nonlinear semidefinite programs is introduced. Some basic properties of the approximate augmented Lagrange function such as monotonicity and convexity are discussed. Necessary and sufficient conditions for approximate strong duality results are derived. Conditions for an approximate exact penalty representation in the framework of augmented Lagrangian are given. Under certain conditions, it is shown that any limit point of a sequence of stationary points of approximate augmented Lagrangian problems is a KKT point of the original semidefinite program and that a sequence of optimal solutions to augmented Lagrangian problems converges to a solution of the original semidefinite program.
Bonus algorithm for large scale stochastic nonlinear programming problems
Diwekar, Urmila
2015-01-01
This book presents the details of the BONUS algorithm and its real world applications in areas like sensor placement in large scale drinking water networks, sensor placement in advanced power systems, water management in power systems, and capacity expansion of energy systems. A generalized method for stochastic nonlinear programming based on a sampling based approach for uncertainty analysis and statistical reweighting to obtain probability information is demonstrated in this book. Stochastic optimization problems are difficult to solve since they involve dealing with optimization and uncertainty loops. There are two fundamental approaches used to solve such problems. The first being the decomposition techniques and the second method identifies problem specific structures and transforms the problem into a deterministic nonlinear programming problem. These techniques have significant limitations on either the objective function type or the underlying distributions for the uncertain variables. Moreover, these ...
Relaxation and decomposition methods for mixed integer nonlinear programming
Nowak, Ivo; Bank, RE
2005-01-01
This book presents a comprehensive description of efficient methods for solving nonconvex mixed integer nonlinear programs, including several numerical and theoretical results, which are presented here for the first time. It contains many illustrations and an up-to-date bibliography. Because on the emphasis on practical methods, as well as the introduction into the basic theory, the book is accessible to a wide audience. It can be used both as a research and as a graduate text.
An application of Matlab c on Dimensional Nonlinear Programming
Fernando Giménez Palomares; María José Marín Fernández
2014-01-01
[EN] Nonlinear Programming (NLP) is a widely applicable tool in modeling real life problems applied to business, economics and engineering. Is to maximize or minimize a scalar field whose domain is given as a set of constraints given by equalities and/or inequalities not necessarily linear. In this paper we present a virtual laboratory to study the PNL graphically and numerically in the case of two variables [EN] La Programación No Lineal (PNL) constituye una herramienta de amp...
A Recurrent Neural Network for Nonlinear Fractional Programming
Directory of Open Access Journals (Sweden)
Quan-Ju Zhang
2012-01-01
Full Text Available This paper presents a novel recurrent time continuous neural network model which performs nonlinear fractional optimization subject to interval constraints on each of the optimization variables. The network is proved to be complete in the sense that the set of optima of the objective function to be minimized with interval constraints coincides with the set of equilibria of the neural network. It is also shown that the network is primal and globally convergent in the sense that its trajectory cannot escape from the feasible region and will converge to an exact optimal solution for any initial point being chosen in the feasible interval region. Simulation results are given to demonstrate further the global convergence and good performance of the proposing neural network for nonlinear fractional programming problems with interval constraints.
A hybrid nonlinear programming method for design optimization
Rajan, S. D.
1986-01-01
Solutions to engineering design problems formulated as nonlinear programming (NLP) problems usually require the use of more than one optimization technique. Moreover, the interaction between the user (analysis/synthesis) program and the NLP system can lead to interface, scaling, or convergence problems. An NLP solution system is presented that seeks to solve these problems by providing a programming system to ease the user-system interface. A simple set of rules is used to select an optimization technique or to switch from one technique to another in an attempt to detect, diagnose, and solve some potential problems. Numerical examples involving finite element based optimal design of space trusses and rotor bearing systems are used to illustrate the applicability of the proposed methodology.
Structural Optimization for Reliability Using Nonlinear Goal Programming
El-Sayed, Mohamed E.
1999-01-01
This report details the development of a reliability based multi-objective design tool for solving structural optimization problems. Based on two different optimization techniques, namely sequential unconstrained minimization and nonlinear goal programming, the developed design method has the capability to take into account the effects of variability on the proposed design through a user specified reliability design criterion. In its sequential unconstrained minimization mode, the developed design tool uses a composite objective function, in conjunction with weight ordered design objectives, in order to take into account conflicting and multiple design criteria. Multiple design criteria of interest including structural weight, load induced stress and deflection, and mechanical reliability. The nonlinear goal programming mode, on the other hand, provides for a design method that eliminates the difficulty of having to define an objective function and constraints, while at the same time has the capability of handling rank ordered design objectives or goals. For simulation purposes the design of a pressure vessel cover plate was undertaken as a test bed for the newly developed design tool. The formulation of this structural optimization problem into sequential unconstrained minimization and goal programming form is presented. The resulting optimization problem was solved using: (i) the linear extended interior penalty function method algorithm; and (ii) Powell's conjugate directions method. Both single and multi-objective numerical test cases are included demonstrating the design tool's capabilities as it applies to this design problem.
A convergence theory for a class of nonlinear programming problems.
Rauch, S. W.
1973-01-01
A recent convergence theory of Elkin concerning methods for unconstrained minimization is extended to a certain class of nonlinear programming problems. As in Elkin's original approach, the analysis of a variety of step-length algorithms is treated entirely separately from that of several direction algorithms. This allows for their combination into many different methods for solving the constrained problem. These include some of the methods of Rosen and Zoutendijk. We also extend the results of Topkis and Veinott to nonconvex sets and drop their requirement of the uniform feasibility of a subsequence of the search directions.
Penalized interior point approach for constrained nonlinear programming
Institute of Scientific and Technical Information of China (English)
LU Wen-ting; YAO Yi-rong; ZHANG Lian-sheng
2009-01-01
A penalized interior point approach for constrained nonlinear programming is examined in this work. To overcome the difficulty of initialization for the interior point method, a problem equivalent to the primal problem via incorporating an auxiliary variable is constructed. A combined approach of logarithm barrier and quadratic penalty function is proposed to solve the problem. Based on Newton's method, the global convergence of interior point and line search algorithm is proven.Only a finite number of iterations is required to reach an approximate optimal solution. Numerical tests are given to show the effectiveness of the method.
Directory of Open Access Journals (Sweden)
Arturo Jiménez-Gutiérrez
2014-08-01
Full Text Available The synthesis of water networks based on properties has commonly ignored the effect of temperature on the property balances that are part of the formulation. When wide differences of temperatures are observed within the process, such an effect might yield significant errors in the application of conventional property balances. In this work, a framework for the development of water networks that include temperature effects on property balances is presented. The approach is based on the inclusion of constants in the property operators that are commonly used to carry out the property balances. An additional term to take care of composition effects is also included. The resulting approach is embedded into a formulation based on a mixed-integer nonlinear programming model for the design of water networks. A case study is presented that shows that the proposed approach yields an improvement in the prediction of the resulting properties for the integrated network, thus affecting the optimal solution.
Lu, Bao-Liang; Ito, Koji
2003-09-01
In this paper we present a method for converting general nonlinear programming (NLP) problems into separable programming (SP) problems by using feedforward neural networks (FNNs). The basic idea behind the method is to use two useful features of FNNs: their ability to approximate arbitrary continuous nonlinear functions with a desired degree of accuracy and their ability to express nonlinear functions in terms of parameterized compositions of functions of single variables. According to these two features, any nonseparable objective functions and/or constraints in NLP problems can be approximately expressed as separable functions with FNNs. Therefore, any NLP problems can be converted into SP problems. The proposed method has three prominent features. (a) It is more general than existing transformation techniques; (b) it can be used to formulate optimization problems as SP problems even when their precise analytic objective function and/or constraints are unknown; (c) the SP problems obtained by the proposed method may highly facilitate the selection of grid points for piecewise linear approximation of nonlinear functions. We analyze the computational complexity of the proposed method and compare it with an existing transformation approach. We also present several examples to demonstrate the method and the performance of the simplex method with the restricted basis entry rule for solving SP problems.
A New Kind of Simple Smooth Exact Penalty Function of Constrained Nonlinear Programming
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The penalty function method is one basic method for solving constrained nonlinear programming, in which simple smooth exact penalty functions draw much attention for their simpleness and smoothness. This article offers a new kind of simple smooth approximative exact penalty function of general constrained nonlinear programmings and analyzes its properties.
Approximating electrical distribution networks via mixed-integer nonlinear programming
Energy Technology Data Exchange (ETDEWEB)
Lakhera, Sanyogita [Citibank, New York City, NY (United States); Shanbhag, Uday V. [Department of Industrial and Enterprise Systems Engineering at the University of Illinois at Urbana-Champaign, 117 Transportation Building, 104 S. Mathews Ave., Urbana, IL 61801 (United States); McInerney, Michael K. [Construction Engineering Research Laboratory (CERL) (United States)
2011-02-15
Given urban data derived from a geographical information system (GIS), we consider the problem of constructing an estimate of the electrical distribution system of an urban area. We employ the image data to obtain an approximate electrical load distribution over a network of a prespecificed discretization. Together with partial information about existing substations, we determine the optimal placement of electrical substations to sustain such a load that minimizes the cost of capital and losses. This requires solving large-scale quadratic programs with discrete variables for which we present a novel penalization-smoothing scheme. The choice of locations allows one to determine the optimal flows in this network, as required by physical requirements which provide us with an approximation of the distribution network. Furthermore, the scheme allows for approximating systems in the presence of no-go areas, such as lakes and fields. We examine the performance of our algorithm on the solution of a set of location problems and observe that the scheme is capable of solving large-scale instances, well beyond the realm of existing mixed-integer nonlinear programming solvers. We conclude with a case study in which a stage-wise extension of this scheme is developed to reflect the temporal evolution of load. (author)
Nonlinear programming strategies for source detection of municipal water networks.
Energy Technology Data Exchange (ETDEWEB)
van Bloemen Waanders, Bart Gustaaf; Biegler, Lorenz T. (Carnegie Mellon University, Pittsburgh, PA); Bartlett, Roscoe Ainsworth; Laird, Carl Damon (Carnegie Mellon University, Pittsburgh, PA)
2003-01-01
Increasing concerns for the security of the national infrastructure have led to a growing need for improved management and control of municipal water networks. To deal with this issue, optimization offers a general and extremely effective method to identify (possibly harmful) disturbances, assess the current state of the network, and determine operating decisions that meet network requirements and lead to optimal performance. This paper details an optimization strategy for the identification of source disturbances in the network. Here we consider the source inversion problem modeled as a nonlinear programming problem. Dynamic behavior of municipal water networks is simulated using EPANET. This approach allows for a widely accepted, general purpose user interface. For the source inversion problem, flows and concentrations of the network will be reconciled and unknown sources will be determined at network nodes. Moreover, intrusive optimization and sensitivity analysis techniques are identified to assess the influence of various parameters and models in the network in a computational efficient manner. A number of numerical comparisons are made to demonstrate the effectiveness of various optimization approaches.
Nonlinear programming technique for analyzing flocculent settling data.
Rashid, Md Mamunur; Hayes, Donald F
2014-04-01
The traditional graphical approach for drawing iso-concentration curves to analyze flocculent settling data and design sedimentation basins poses difficulties for computer-based design methods. Thus, researchers have developed empirical approaches to analyze settling data. In this study, the ability of five empirical approaches to fit flocculent settling test data is compared. Particular emphasis is given to compare rule-based SETTLE and rule-based nonlinear programming (NLP) techniques as a viable alternative to the modeling methods of Berthouex and Stevens (1982), San (1989), and Ozer (1994). Published flocculent settling data are used to test the suitability of these empirical approaches. The primary objective, however, is to determine if the results of a NLP optimization technique are more reliable than those of other approaches. For this, mathematical curve fitting is conducted and the modeled concentration data are graphically compared to the observed data. The design results in terms of average solid removal efficiency as a function of detention times are also compared. Finally, the sum of squared errors values from these approaches are compared. The results indicate a strong correlation between observed and NLP modeled concentration data. The SETTLE and NLP approaches tend to be more conservative at lower retention times and less conservative at longer retention times. The SETTLE approach appears to be the most conservative. In terms of sum of squared errors values, NLP appears to be rank number one (i.e., best model) for eight data sets and number two for six data sets among 15 data sets. Therefore, NLP is recommended for analyzing flocculent settling data as a logical extension of other approaches. The NLP approach is further recommended as it is an optimization technique and uses conventional mathematical algorithms that can be solved using widely available software such as EXCEL and LINGO.
Generic Mathematical Programming Formulation and Solution for Computer-Aided Molecular Design
DEFF Research Database (Denmark)
Zhang, Lei; Cignitti, Stefano; Gani, Rafiqul
2015-01-01
This short communication presents a generic mathematical programming formulation for Computer-Aided Molecular Design (CAMD). A given CAMD problem, based on target properties, is formulated as a Mixed Integer Linear/Non-Linear Program (MILP/MINLP). The mathematical programming model presented here......, which is formulated as an MILP/MINLP problem, considers first-order and second-order molecular groups for molecular structure representation and property estimation. It is shown that various CAMD problems can be formulated and solved through this model....
Generic Mathematical Programming Formulation and Solution for Computer-Aided Molecular Design
DEFF Research Database (Denmark)
Zhang, Lei; Cignitti, Stefano; Gani, Rafiqul
2015-01-01
This short communication presents a generic mathematical programming formulation for Computer-Aided Molecular Design (CAMD). A given CAMD problem, based on target properties, is formulated as a Mixed Integer Linear/Non-Linear Program (MILP/MINLP). The mathematical programming model presented here......, which is formulated as an MILP/MINLP problem, considers first-order and second-order molecular groups for molecular structure representation and property estimation. It is shown that various CAMD problems can be formulated and solved through this model....
Directory of Open Access Journals (Sweden)
Norhuda Abdul Manaf
2017-03-01
Full Text Available This paper presents an algorithm that combines model predictive control (MPC with MINLP optimization and demonstrates its application for coal-fired power plants retrofitted with solvent based post-combustion CO2 capture (PCC plant. The objective function of the optimization algorithm works at a primary level to maximize plant economic revenue while considering an optimal carbon capture profile. At a secondary level, the MPC algorithm is used to control the performance of the PCC plant. Two techno-economic scenarios based on fixed (capture rate is constant and flexible (capture rate is variable operation modes are developed using actual electricity prices (2011 with fixed carbon prices ($AUD 5, 25, 50/tonne-CO2 for 24 h periods. Results show that fixed operation mode can bring about a ratio of net operating revenue deficit at an average of 6% against the superior flexible operation mode.
An Approximate Algorithm for a Class of Nonlinear Bilevel Integer Programming
Institute of Scientific and Technical Information of China (English)
LI Lei; TENG Chun-xian; TIAN Guang-yue
2002-01-01
The algorithm for a class of nonlinear bilevel integer programming is discussed in this paper. It is based on the theory and algorithm for nonlinear integer programming. The continuity methods for integer programming are studied in this paper. After simulated annealing algorithm is applied to the upper-level programming problem and the thought of filled function method for continuous global optimization is applied to the corresponding lower-level programming, an approximate algorithm is established. The satisfactory algorithm is elaborated in the following example.
Nonlinear programming extensions to rational function approximations of unsteady aerodynamics
Tiffany, Sherwood H.; Adams, William M., Jr.
1987-01-01
This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.
The Expansion of Dynamic Solving Process About a Class of Non-linear Programming Problems
Institute of Scientific and Technical Information of China (English)
ZANG Zhen-chun
2001-01-01
In this paper, we research non-linear programming problems which have a given specialstructure, some simple forms of this kind structure have been solved in some papers, here we focus on othercomplex ones.
COYOTE: a finite-element computer program for nonlinear heat-conduction problems
Energy Technology Data Exchange (ETDEWEB)
Gartling, D.K.
1982-10-01
COYOTE is a finite element computer program designed for the solution of two-dimensional, nonlinear heat conduction problems. The theoretical and mathematical basis used to develop the code is described. Program capabilities and complete user instructions are presented. Several example problems are described in detail to demonstrate the use of the program.
A One-parameter Filled Function Method for Nonlinear Integer Programming
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
This paper gives a new definition of the filled function for nonlinear integer programming problem. A filled function satisfying our definition is presented. This function contains only one parameter. The properties of the proposed filled function and the method using this filled function to solve nonlinear integer programming problem are also discussed. Numerical results indicate the efficiency and reliability of the proposed filled function algorithm.
One-parameter quasi-filled function algorithm for nonlinear integer programming
Institute of Scientific and Technical Information of China (English)
SHANG You-lin; HAN Bo-shun
2005-01-01
A definition of the quasi-filled function for nonlinear integer programming problem is given in this paper. A quasi-filled function satisfying our definition is presented. This function contains only one parameter. The properties of the proposed quasi-filled function and the method using this quasi-filled function to solve nonlinear integer programming problem are also discussed in this paper. Numerical results indicated the efficiency and reliability of the proposed quasi-filled function algorithm.
Optimality Condition and Wolfe Duality for Invex Interval-Valued Nonlinear Programming Problems
Directory of Open Access Journals (Sweden)
Jianke Zhang
2013-01-01
Full Text Available The concepts of preinvex and invex are extended to the interval-valued functions. Under the assumption of invexity, the Karush-Kuhn-Tucker optimality sufficient and necessary conditions for interval-valued nonlinear programming problems are derived. Based on the concepts of having no duality gap in weak and strong sense, the Wolfe duality theorems for the invex interval-valued nonlinear programming problems are proposed in this paper.
Nonlinear Multidimensional Assignment Problems Efficient Conic Optimization Methods and Applications
2015-06-24
CONTRACT NUMBER 5b. GRANT NUMBER FA9550-12-1-0153 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Mittelmann, Hans D 5d. PROJECT NUMBER 5e. TASK NUMBER 5f...problems. The size 16 three-dimensional quadratic assignment problem Q3AP from wireless communications was solved using a sophisticated approach...placement of the sensors. However, available MINLP solvers are not sufficiently effective, even in the convex case, and a hybrid Benders
AN ALGORITHM FOR FINDING GLOBAL MINIMUM OF NONLINEAR INTEGER PROGRAMMING
Institute of Scientific and Technical Information of China (English)
Wei-wenTian; Lian-shengZhang
2004-01-01
A filled function is proposed by R.Ge[2] for finding a global minimizer of a function of several continuous variables. In [4], an approach for finding a global integer minimizer of nonlinear flmction using the above filled function is given. Meanwhile a major obstacle is met: if ρ > 0 is small, and ‖xI- xI* is large, where xI - an integer point, xI* - a current local integer minimizer, then the value of the filled function almost equals zero. Thus it is difficult to recognize the size of the value of the filled flmction and can not to find the global integer minimizer of nonlinear function. In this paper, two new filled functions are proposed for finding global integer minimizer of nonlinear flmction, the new filled function improves some properties of the filled function proposed by R. Ge [2]. Some numerical results are given, which indicate the new filled function (4.1) to find global integer minimizer of nonlinear function is efficient.
Domínguez, Luis F.
2010-12-01
This work introduces two algorithms for the solution of pure integer and mixed-integer bilevel programming problems by multiparametric programming techniques. The first algorithm addresses the integer case of the bilevel programming problem where integer variables of the outer optimization problem appear in linear or polynomial form in the inner problem. The algorithm employs global optimization techniques to convexify nonlinear terms generated by a reformulation linearization technique (RLT). A continuous multiparametric programming algorithm is then used to solve the reformulated convex inner problem. The second algorithm addresses the mixed-integer case of the bilevel programming problem where integer and continuous variables of the outer problem appear in linear or polynomial forms in the inner problem. The algorithm relies on the use of global multiparametric mixed-integer programming techniques at the inner optimization level. In both algorithms, the multiparametric solutions obtained are embedded in the outer problem to form a set of single-level (M)(I)(N)LP problems - which are then solved to global optimality using standard fixed-point (global) optimization methods. Numerical examples drawn from the open literature are presented to illustrate the proposed algorithms. © 2010 Elsevier Ltd.
Nonlinear programming for classification problems in machine learning
Astorino, Annabella; Fuduli, Antonio; Gaudioso, Manlio
2016-10-01
We survey some nonlinear models for classification problems arising in machine learning. In the last years this field has become more and more relevant due to a lot of practical applications, such as text and web classification, object recognition in machine vision, gene expression profile analysis, DNA and protein analysis, medical diagnosis, customer profiling etc. Classification deals with separation of sets by means of appropriate separation surfaces, which is generally obtained by solving a numerical optimization model. While linear separability is the basis of the most popular approach to classification, the Support Vector Machine (SVM), in the recent years using nonlinear separating surfaces has received some attention. The objective of this work is to recall some of such proposals, mainly in terms of the numerical optimization models. In particular we tackle the polyhedral, ellipsoidal, spherical and conical separation approaches and, for some of them, we also consider the semisupervised versions.
DEFF Research Database (Denmark)
Ommen, Torben Schmidt; Markussen, Wiebke Brix; Elmegaard, Brian
2014-01-01
differences and differences between the solution found by each optimisation method. One of the investigated approaches utilises LP (linear programming) for optimisation, one uses LP with binary operation constraints, while the third approach uses NLP (non-linear programming). The LP model is used...... of selected units by 23%, while for a non-linear approach the increase can be higher than 39%. The results indicate a higher coherence between the two latter approaches, and that the MLP (mixed integer programming) optimisation is most appropriate from a viewpoint of accuracy and runtime. © 2014 Elsevier Ltd...
Guevara, V R
2004-02-01
A nonlinear programming optimization model was developed to maximize margin over feed cost in broiler feed formulation and is described in this paper. The model identifies the optimal feed mix that maximizes profit margin. Optimum metabolizable energy level and performance were found by using Excel Solver nonlinear programming. Data from an energy density study with broilers were fitted to quadratic equations to express weight gain, feed consumption, and the objective function income over feed cost in terms of energy density. Nutrient:energy ratio constraints were transformed into equivalent linear constraints. National Research Council nutrient requirements and feeding program were used for examining changes in variables. The nonlinear programming feed formulation method was used to illustrate the effects of changes in different variables on the optimum energy density, performance, and profitability and was compared with conventional linear programming. To demonstrate the capabilities of the model, I determined the impact of variation in prices. Prices for broiler, corn, fish meal, and soybean meal were increased and decreased by 25%. Formulations were identical in all other respects. Energy density, margin, and diet cost changed compared with conventional linear programming formulation. This study suggests that nonlinear programming can be more useful than conventional linear programming to optimize performance response to energy density in broiler feed formulation because an energy level does not need to be set.
Dynamic Simulations of Nonlinear Multi-Domain Systems Based on Genetic Programming and Bond Graphs
Institute of Scientific and Technical Information of China (English)
DI Wenhui; SUN Bo; XU Lixin
2009-01-01
A dynamic simulation method for non-linear systems based on genetic programming (GP) and bond graphs (BG) was developed to improve the design of nonlinear multi-domain energy conversion sys-tems. The genetic operators enable the embryo bond graph to evolve towards the target graph according to the fitness function. Better simulation requires analysis of the optimization of the eigenvalue and the filter circuit evolution. The open topological design and space search ability of this method not only gives a more optimized convergence for the operation, but also reduces the generation time for the new circuit graph for the design of nonlinear multi-domain systems.
Directory of Open Access Journals (Sweden)
Paras Bhatnagar
2012-10-01
Full Text Available Kaul and Kaur [7] obtained necessary optimality conditions for a non-linear programming problem by taking the objective and constraint functions to be semilocally convex and their right differentials at a point to be lower semi-continuous. Suneja and Gupta [12] established the necessary optimality conditions without assuming the semilocal convexity of the objective and constraint functions but their right differentials at the optimal point to be convex. Suneja and Gupta [13] established necessary optimality conditions for an efficient solution of a multiobjective non-linear programming problem by taking the right differentials of the objective functions and constraintfunctions at the efficient point to be convex. In this paper we obtain some results for a properly efficient solution of a multiobjective non-linear fractional programming problem involving semilocally convex and related functions by assuming generalized Slater type constraint qualification.
Two-parameters quasi-filled function algorithm for nonlinear integer programming
Institute of Scientific and Technical Information of China (English)
WANG Wei-xiang; SHANG You-lin; ZHANG Lian-sheng
2006-01-01
A quasi-filled function for nonlinear integer programming problem is given in this paper. This function contains two parameters which are easily to be chosen. Theoretical properties of the proposed quasi-filled function are investigated. Moreover,we also propose a new solution algorithm using this quasi-filled function to solve nonlinear integer programming problem in this paper. The examples with 2 to 6 variables are tested and computational results indicated the efficiency and reliability of the proposed quasi-filled function algorithm.
Energy Technology Data Exchange (ETDEWEB)
Kim, D.; Ghanem, R. [State Univ. of New York, Buffalo, NY (United States)
1994-12-31
Multigrid solution technique to solve a material nonlinear problem in a visual programming environment using the finite element method is discussed. The nonlinear equation of equilibrium is linearized to incremental form using Newton-Rapson technique, then multigrid solution technique is used to solve linear equations at each Newton-Rapson step. In the process, adaptive mesh refinement, which is based on the bisection of a pair of triangles, is used to form grid hierarchy for multigrid iteration. The solution process is implemented in a visual programming environment with distributed computing capability, which enables more intuitive understanding of solution process, and more effective use of resources.
Zhong, Xiangnan; He, Haibo; Zhang, Huaguang; Wang, Zhanshan
2014-12-01
In this paper, we develop and analyze an optimal control method for a class of discrete-time nonlinear Markov jump systems (MJSs) with unknown system dynamics. Specifically, an identifier is established for the unknown systems to approximate system states, and an optimal control approach for nonlinear MJSs is developed to solve the Hamilton-Jacobi-Bellman equation based on the adaptive dynamic programming technique. We also develop detailed stability analysis of the control approach, including the convergence of the performance index function for nonlinear MJSs and the existence of the corresponding admissible control. Neural network techniques are used to approximate the proposed performance index function and the control law. To demonstrate the effectiveness of our approach, three simulation studies, one linear case, one nonlinear case, and one single link robot arm case, are used to validate the performance of the proposed optimal control method.
Nonlinear Programming Approach to Optimal Scaling of Partially Ordered Categories
Nishisato, Shizuhiko; Arri, P. S.
1975-01-01
A modified technique of separable programming was used to maximize the squared correlation ratio of weighted responses to partially ordered categories. The technique employs a polygonal approximation to each single-variable function by choosing mesh points around the initial approximation supplied by Nishisato's method. Numerical examples were…
A computer program for predicting nonlinear uniaxial material responses using viscoplastic models
Chang, T. Y.; Thompson, R. L.
1984-01-01
A computer program was developed for predicting nonlinear uniaxial material responses using viscoplastic constitutive models. Four specific models, i.e., those due to Miller, Walker, Krieg-Swearengen-Rhode, and Robinson, are included. Any other unified model is easily implemented into the program in the form of subroutines. Analysis features include stress-strain cycling, creep response, stress relaxation, thermomechanical fatigue loop, or any combination of these responses. An outline is given on the theoretical background of uniaxial constitutive models, analysis procedure, and numerical integration methods for solving the nonlinear constitutive equations. In addition, a discussion on the computer program implementation is also given. Finally, seven numerical examples are included to demonstrate the versatility of the computer program developed.
A high-performance feedback neural network for solving convex nonlinear programming problems.
Leung, Yee; Chen, Kai-Zhou; Gao, Xing-Bao
2003-01-01
Based on a new idea of successive approximation, this paper proposes a high-performance feedback neural network model for solving convex nonlinear programming problems. Differing from existing neural network optimization models, no dual variables, penalty parameters, or Lagrange multipliers are involved in the proposed network. It has the least number of state variables and is very simple in structure. In particular, the proposed network has better asymptotic stability. For an arbitrarily given initial point, the trajectory of the network converges to an optimal solution of the convex nonlinear programming problem under no more than the standard assumptions. In addition, the network can also solve linear programming and convex quadratic programming problems, and the new idea of a feedback network may be used to solve other optimization problems. Feasibility and efficiency are also substantiated by simulation examples.
Ultimate limit state design of sheet pile walls by finite elements and nonlinear programming
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven
2005-01-01
as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe....
A Smooth Newton Method for Nonlinear Programming Problems with Inequality Constraints
Directory of Open Access Journals (Sweden)
Vasile Moraru
2012-02-01
Full Text Available The paper presents a reformulation of the Karush-Kuhn-Tucker (KKT system associated nonlinear programming problem into an equivalent system of smooth equations. Classical Newton method is applied to solve the system of equations. The superlinear convergence of the primal sequence, generated by proposed method, is proved. The preliminary numerical results with a problems test set are presented.
Teren, F.
1977-01-01
Minimum time accelerations of aircraft turbofan engines are presented. The calculation of these accelerations was made by using a piecewise linear engine model, and an algorithm based on nonlinear programming. Use of this model and algorithm allows such trajectories to be readily calculated on a digital computer with a minimal expenditure of computer time.
Ultimate Limit State Design Of Sheet Pile Walls By Finite Elements And Nonlinear Programming
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven
2005-01-01
as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe...
Optimum sensitivity derivatives of objective functions in nonlinear programming
Barthelemy, J.-F. M.; Sobieszczanski-Sobieski, J.
1983-01-01
The feasibility of eliminating second derivatives from the input of optimum sensitivity analyses of optimization problems is demonstrated. This elimination restricts the sensitivity analysis to the first-order sensitivity derivatives of the objective function. It is also shown that when a complete first-order sensitivity analysis is performed, second-order sensitivity derivatives of the objective function are available at little additional cost. An expression is derived whose application to linear programming is presented.
A new method of thermal network modeling - A nonlinear programming approach
Adachi, M.; Miyaoka, S.; Muramatsu, A.; Funabashi, M.; Nakajima, T.
A new method for correcting thermal network model coefficients is described. This method sharply reduces discrepancies obtained by the nonlinear programming approach in the conductance coefficients and radiation coefficients for determining the heat balance of a spacecraft. The method consists of an experimental design and a nonlinear parameter identification. An experimental design for obtaining useful data for the thermal network model correction is discussed. A simulation study has shown that the standard deviation of the estimated temperature and estimation error of the parameters are reduced by 50 percent and 70 percent respectively.
Giles, G. L.; Wallas, M.
1981-01-01
User documentation is presented for a computer program which considers the nonlinear properties of the strain isolator pad (SIP) in the static stress analysis of the shuttle thermal protection system. This program is generalized to handle an arbitrary SIP footprint including cutouts for instrumentation and filler bar. Multiple SIP surfaces are defined to model tiles in unique locations such as leading edges, intersections, and penetrations. The nonlinearity of the SIP is characterized by experimental stress displacement data for both normal and shear behavior. Stresses in the SIP are calculated using a Newton iteration procedure to determine the six rigid body displacements of the tile which develop reaction forces in the SIP to equilibrate the externally applied loads. This user documentation gives an overview of the analysis capabilities, a detailed description of required input data and an example to illustrate use of the program.
Design of asymptotic estimators: an approach based on neural networks and nonlinear programming.
Alessandri, Angelo; Cervellera, Cristiano; Sanguineti, Marcello
2007-01-01
A methodology to design state estimators for a class of nonlinear continuous-time dynamic systems that is based on neural networks and nonlinear programming is proposed. The estimator has the structure of a Luenberger observer with a linear gain and a parameterized (in general, nonlinear) function, whose argument is an innovation term representing the difference between the current measurement and its prediction. The problem of the estimator design consists in finding the values of the gain and of the parameters that guarantee the asymptotic stability of the estimation error. Toward this end, if a neural network is used to take on this function, the parameters (i.e., the neural weights) are chosen, together with the gain, by constraining the derivative of a quadratic Lyapunov function for the estimation error to be negative definite on a given compact set. It is proved that it is sufficient to impose the negative definiteness of such a derivative only on a suitably dense grid of sampling points. The gain is determined by solving a Lyapunov equation. The neural weights are searched for via nonlinear programming by minimizing a cost penalizing grid-point constraints that are not satisfied. Techniques based on low-discrepancy sequences are applied to deal with a small number of sampling points, and, hence, to reduce the computational burden required to optimize the parameters. Numerical results are reported and comparisons with those obtained by the extended Kalman filter are made.
Nonlinear programming in design of control systems with specified handling qualities.
Schy, A. A.
1972-01-01
A method is described for using nonlinear programing in the computer-aided design of aircraft control systems. It is assumed that the quality of such systems depends on many criteria. These criteria are included in the constraints vector, and the design proceeds through a sequence of nonlinear programing solutions in which the designer varies the specification of sets of requirements levels. The method is applied to design of a lateral stability augmentation system (SAS) for a fighter aircraft, in which the requirements vector is chosen from the official handling-qualities specifications. Results are shown for several simple SAS configurations designed to obtain desirable handling qualities over all design flight conditions with minimum feedback gains.
Direct heuristic dynamic programming for nonlinear tracking control with filtered tracking error.
Yang, Lei; Si, Jennie; Tsakalis, Konstantinos S; Rodriguez, Armando A
2009-12-01
This paper makes use of the direct heuristic dynamic programming design in a nonlinear tracking control setting with filtered tracking error. A Lyapunov stability approach is used for the stability analysis of the tracking system. It is shown that the closed-loop tracking error and the approximating neural network weight estimates retain the property of uniformly ultimate boundedness under the presence of neural network approximation error and bounded unknown disturbances under certain conditions.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Nonlinear time series prediction is studied by using an improved least squares support vector machine (LSSVM) regression based on chaotic mutation evolutionary programming (CMEP) approach for parameter optimization.We analyze how the prediction error varies with different parameters (σ, γ) in LS-SVM. In order to select appropriate parameters for the prediction model, we employ CMEP algorithm. Finally, Nasdaq stock data are predicted by using this LS-SVM regression based on CMEP, and satisfactory results are obtained.
A nonlinear programming method for system design with results that have been implemented
Hauser, F.
1984-01-01
A general nonlinear programming algorithm (NICO) is discussed. An academic optimization example is given. The NICO multi-input, multi-output control system design is discussed. NICO applications relative to launch vehicle autopilot design, space shuttle static balance, transient response criteria in the design of a reentry vehicle control system, and waterjet propulsion and lift system components sized to a large surface effect ship are noted.
Nonlinear program based optimization of boost and buck-boost converter designs
Rahman, S.; Lee, F. C.
1981-01-01
The facility of an Augmented Lagrangian (ALAG) multiplier based nonlinear programming technique is demonstrated for minimum-weight design optimizations of boost and buck-boost power converters. Certain important features of ALAG are presented in the framework of a comprehensive design example for buck-boost power converter design optimization. The study provides refreshing design insight of power converters and presents such information as weight and loss profiles of various semiconductor components and magnetics as a function of the switching frequency.
Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification
Mordukhovich, B. S.; Outrata, J. (Jiří)
2013-01-01
The paper concerns the study of tilt stability of local minimizers in standard problems of nonlinear programming. This notion plays an important role in both theoretical and numerical aspects of optimization and has drawn a lot of attention in optimization theory and its applications, especially in recent years. Under the classical Mangasarian–Fromovitz Constraint Qualification, we establish relationships between tilt stability and some other stability notions in constrained optimization. I...
Trajectory optimization for vehicles using control vector parameterization and nonlinear programming
Energy Technology Data Exchange (ETDEWEB)
Spangelo, I.
1994-12-31
This thesis contains a study of optimal trajectories for vehicles. Highly constrained nonlinear optimal control problems have been solved numerically using control vector parameterization and nonlinear programming. Control vector parameterization with shooting has been described in detail to provide the reader with the theoretical background for the methods which have been implemented, and which are not available in standard text books. Theoretical contributions on accuracy analysis and gradient computations have also been presented. Optimal trajectories have been computed for underwater vehicles controlled in all six degrees of freedom by DC-motor driven thrusters. A class of nonlinear optimal control problems including energy-minimization, possibly combined with time minimization and obstacle avoidance, has been developed. A program system has been specially designed and written in the C language to solve this class of optimal control problems. Control vector parameterization with single shooting was used. This special implementation has made it possible to perform a detailed analysis, and to investigate numerical details of this class of optimization methods which would have been difficult using a general purpose CVP program system. The results show that this method for solving general optimal control problems is well suited for use in guidance and control of marine vehicles. Results from rocket trajectory optimization has been studied in this work to bring knowledge from this area into the new area of trajectory optimization of marine vehicles. 116 refs., 24 figs., 23 tabs.
Directory of Open Access Journals (Sweden)
Olav Slupphaug
2001-01-01
Full Text Available We present a mathematical programming approach to robust control of nonlinear systems with uncertain, possibly time-varying, parameters. The uncertain system is given by different local affine parameter dependent models in different parts of the state space. It is shown how this representation can be obtained from a nonlinear uncertain system by solving a set of continuous linear semi-infinite programming problems, and how each of these problems can be solved as a (finite series of ordinary linear programs. Additionally, the system representation includes control- and state constraints. The controller design method is derived from Lyapunov stability arguments and utilizes an affine parameter dependent quadratic Lyapunov function. The controller has a piecewise affine output feedback structure, and the design amounts to finding a feasible solution to a set of linear matrix inequalities combined with one spectral radius constraint on the product of two positive definite matrices. A local solution approach to this nonconvex feasibility problem is proposed. Complexity of the design method and some special cases such as state- feedback are discussed. Finally, an application of the results is given by proposing an on-line computationally feasible algorithm for constrained nonlinear state- feedback model predictive control with robust stability.
Energy Technology Data Exchange (ETDEWEB)
Raju, P. P.
1980-05-01
This report summarizes the results of the study program to assess the benefits of nonlinear analysis methods in Light Water Reactor (LWR) component designs. The current study reveals that despite its increased cost and other complexities, nonlinear analysis is a practical and valuable tool for the design of LWR components, especially under ASME Level D service conditions (faulted conditions) and it will greatly assist in the evaluation of ductile fracture potential of pressure boundary components. Since the nonlinear behavior is generally a local phenomenon, the design of complex components can be accomplished through substructuring isolated localized regions and evaluating them in detail using nonlinear analysis methods.
Gas network optimization by MINLP
Humpola, Jesco
2014-01-01
Ein Viertel des europäischen Energiebedarfs wird durch Gas gedeckt, das durch ein europaweites Pipelinesystem verteilt wird. Aufgrund von Ausbaukosten von 1 Mio. Euro pro Kilometer ist der Netzausbau ein Milliardenunterfangen. Die größte Herausforderung besteht darin zu entscheiden, wie das Netzwerk kostengünstig ausgebaut und genutzt werden kann, um notwendige Gasmengen zu transportieren. Diese Aufgabe kann mit Hilfe eines mathematischen Optimierungsproblems formuliert werden, wobei anwendun...
A mathematical programming approach for sequential clustering of dynamic networks
Silva, Jonathan C.; Bennett, Laura; Papageorgiou, Lazaros G.; Tsoka, Sophia
2016-02-01
A common analysis performed on dynamic networks is community structure detection, a challenging problem that aims to track the temporal evolution of network modules. An emerging area in this field is evolutionary clustering, where the community structure of a network snapshot is identified by taking into account both its current state as well as previous time points. Based on this concept, we have developed a mixed integer non-linear programming (MINLP) model, SeqMod, that sequentially clusters each snapshot of a dynamic network. The modularity metric is used to determine the quality of community structure of the current snapshot and the historical cost is accounted for by optimising the number of node pairs co-clustered at the previous time point that remain so in the current snapshot partition. Our method is tested on social networks of interactions among high school students, college students and members of the Brazilian Congress. We show that, for an adequate parameter setting, our algorithm detects the classes that these students belong more accurately than partitioning each time step individually or by partitioning the aggregated snapshots. Our method also detects drastic discontinuities in interaction patterns across network snapshots. Finally, we present comparative results with similar community detection methods for time-dependent networks from the literature. Overall, we illustrate the applicability of mathematical programming as a flexible, adaptable and systematic approach for these community detection problems. Contribution to the Topical Issue "Temporal Network Theory and Applications", edited by Petter Holme.
Model-based optimal design of experiments - semidefinite and nonlinear programming formulations.
Duarte, Belmiro P M; Wong, Weng Kee; Oliveira, Nuno M C
2016-02-15
We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for finding D-, A- and E-optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficient D-optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice.
1979-01-01
A nonlinear, maximum likelihood, parameter identification computer program (NLSCIDNT) is described which evaluates rotorcraft stability and control coefficients from flight test data. The optimal estimates of the parameters (stability and control coefficients) are determined (identified) by minimizing the negative log likelihood cost function. The minimization technique is the Levenberg-Marquardt method, which behaves like the steepest descent method when it is far from the minimum and behaves like the modified Newton-Raphson method when it is nearer the minimum. Twenty-one states and 40 measurement variables are modeled, and any subset may be selected. States which are not integrated may be fixed at an input value, or time history data may be substituted for the state in the equations of motion. Any aerodynamic coefficient may be expressed as a nonlinear polynomial function of selected 'expansion variables'.
Directory of Open Access Journals (Sweden)
Samir Dey
2015-07-01
Full Text Available This paper proposes a new multi-objective intuitionistic fuzzy goal programming approach to solve a multi-objective nonlinear programming problem in context of a structural design. Here we describe some basic properties of intuitionistic fuzzy optimization. We have considered a multi-objective structural optimization problem with several mutually conflicting objectives. The design objective is to minimize weight of the structure and minimize the vertical deflection at loading point of a statistically loaded three-bar planar truss subjected to stress constraints on each of the truss members. This approach is used to solve the above structural optimization model based on arithmetic mean and compare with the solution by intuitionistic fuzzy goal programming approach. A numerical solution is given to illustrate our approach.
2016-07-01
Advanced Research Projects Agency (DARPA) Dynamics-Enabled Frequency Sources (DEFYS) program is focused on the convergence of nonlinear dynamics and...Early work in this program has shown that nonlinear dynamics can provide performance advantages. However, the pathway from initial results to...dependent nonlinear stiffness observed in these devices. This work is ongoing, and will continue through the final period of this program . Reference 9
Chen, Zhi; Yuan, Yuan; Zhang, Shu-Shen; Chen, Yu; Yang, Feng-Lin
2013-03-26
Critical environmental and human health concerns are associated with the rapidly growing fields of nanotechnology and manufactured nanomaterials (MNMs). The main risk arises from occupational exposure via chronic inhalation of nanoparticles. This research presents a chance-constrained nonlinear programming (CCNLP) optimization approach, which is developed to maximize the nanaomaterial production and minimize the risks of workplace exposure to MNMs. The CCNLP method integrates nonlinear programming (NLP) and chance-constrained programming (CCP), and handles uncertainties associated with both the nanomaterial production and workplace exposure control. The CCNLP method was examined through a single-walled carbon nanotube (SWNT) manufacturing process. The study results provide optimal production strategies and alternatives. It reveal that a high control measure guarantees that environmental health and safety (EHS) standards regulations are met, while a lower control level leads to increased risk of violating EHS regulations. The CCNLP optimization approach is a decision support tool for the optimization of the increasing MNMS manufacturing with workplace safety constraints under uncertainties.
The solution of singular optimal control problems using direct collocation and nonlinear programming
Downey, James R.; Conway, Bruce A.
1992-08-01
This paper describes work on the determination of optimal rocket trajectories which may include singular arcs. In recent years direct collocation and nonlinear programming has proven to be a powerful method for solving optimal control problems. Difficulties in the application of this method can occur if the problem is singular. Techniques exist for solving singular problems indirectly using the associated adjoint formulation. Unfortunately, the adjoints are not a part of the direct formulation. It is shown how adjoint information can be obtained from the direct method to allow the solution of singular problems.
A Class of Semilocal E-Preinvex Functions and Its Applications in Nonlinear Programming
Directory of Open Access Journals (Sweden)
Hehua Jiao
2012-01-01
Full Text Available A kind of generalized convex set, called as local star-shaped E-invex set with respect to η, is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal E-preinvex functions, which is a generalization of semi-E-preinvex functions and semilocal E-convex functions, is introduced. Simultaneously, some of its basic properties are discussed. Furthermore, as its applications, some optimality conditions and duality results are established for a nonlinear programming.
Designing A Nonlinear Integer Programming Model For A Cross-Dock By A Genetic Algorithm
Bahareh Vaisi; Reza Tavakkoli-Moghaddam
2015-01-01
Abstract This paper presents a non-linear integer programming model for a cross-dock problem that considers the total transportation cost of inbound and outbound trucks from an origin to a destination and the total cost of assigning strip and stack doors to trucks based on their number of trips and the distance between doors in cross-dock. In previous studies these two cost-based problems are modeled separately however it is more realistic and practical to use both of them as an integrated cr...
Fleming, P.
1983-01-01
A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.
A NEW SQP-FILTER METHOD FOR SOLVING NONLINEAR PROGRAMMING PROBLEMS
Institute of Scientific and Technical Information of China (English)
Duoquan Li
2006-01-01
In [4],Fletcher and Leyffer present a new method that solves nonlinear programming problems without a penalty function by SQP-Filter algorithm. It has attracted much attention due to its good numerical results. In this paper we propose a new SQP-Filter method which can overcome Maratos effect more effectively. We give stricter acceptant criteria when the iterative points are far from the optimal points and looser ones vice-versa. About this new method,the proof of global convergence is also presented under standard assumptions. Numerical results show that our method is efficient.
Linear combination of forecasts with numerical adjustment via MINIMAX non-linear programming
Directory of Open Access Journals (Sweden)
Jairo Marlon Corrêa
2016-03-01
Full Text Available This paper proposes a linear combination of forecasts obtained from three forecasting methods (namely, ARIMA, Exponential Smoothing and Artificial Neural Networks whose adaptive weights are determined via a multi-objective non-linear programming problem, which seeks to minimize, simultaneously, the statistics: MAE, MAPE and MSE. The results achieved by the proposed combination are compared with the traditional approach of linear combinations of forecasts, where the optimum adaptive weights are determined only by minimizing the MSE; with the combination method by arithmetic mean; and with individual methods
CAD of control systems: Application of nonlinear programming to a linear quadratic formulation
Fleming, P.
1983-01-01
The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a Computer Aided Design (CAD) package where both design objective and constraints are quadratic cost functions. This formulation permits the separate consideration of, for example, model following errors, sensitivity measures and control energy as objectives to be minimized or limits to be observed. Efficient techniques for computing the interrelated cost functions and their gradients are utilized in conjunction with a nonlinear programming algorithm. The effectiveness of the approach and the degree of insight into the problem which it affords is illustrated in a helicopter regulation design example.
Institute of Scientific and Technical Information of China (English)
Qin Ni
2001-01-01
An NGTN method was proposed for solving large-scale sparse nonlinear programming (NLP) problems. This is a hybrid method of a truncated Newton direction and a modified negative gradient direction, which is suitable for handling sparse data structure and possesses Q-quadratic convergence rate. The global convergence of this new method is proved,the convergence rate is further analysed, and the detailed implementation is discussed in this paper. Some numerical tests for solving truss optimization and large sparse problems are reported. The theoretical and numerical results show that the new method is efficient for solving large-scale sparse NLP problems.
Nonsingularity Conditions for FB System of Reformulating Nonlinear Second-Order Cone Programming
Directory of Open Access Journals (Sweden)
Shaohua Pan
2013-01-01
Full Text Available This paper is a counterpart of Bi et al., 2011. For a locally optimal solution to the nonlinear second-order cone programming (SOCP, specifically, under Robinson’s constraint qualification, we establish the equivalence among the following three conditions: the nonsingularity of Clarke’s Jacobian of Fischer-Burmeister (FB nonsmooth system for the Karush-Kuhn-Tucker conditions, the strong second-order sufficient condition and constraint nondegeneracy, and the strong regularity of the Karush-Kuhn-Tucker point.
Luo, Biao; Wu, Huai-Ning; Li, Han-Xiong
2015-04-01
Highly dissipative nonlinear partial differential equations (PDEs) are widely employed to describe the system dynamics of industrial spatially distributed processes (SDPs). In this paper, we consider the optimal control problem of the general highly dissipative SDPs, and propose an adaptive optimal control approach based on neuro-dynamic programming (NDP). Initially, Karhunen-Loève decomposition is employed to compute empirical eigenfunctions (EEFs) of the SDP based on the method of snapshots. These EEFs together with singular perturbation technique are then used to obtain a finite-dimensional slow subsystem of ordinary differential equations that accurately describes the dominant dynamics of the PDE system. Subsequently, the optimal control problem is reformulated on the basis of the slow subsystem, which is further converted to solve a Hamilton-Jacobi-Bellman (HJB) equation. HJB equation is a nonlinear PDE that has proven to be impossible to solve analytically. Thus, an adaptive optimal control method is developed via NDP that solves the HJB equation online using neural network (NN) for approximating the value function; and an online NN weight tuning law is proposed without requiring an initial stabilizing control policy. Moreover, by involving the NN estimation error, we prove that the original closed-loop PDE system with the adaptive optimal control policy is semiglobally uniformly ultimately bounded. Finally, the developed method is tested on a nonlinear diffusion-convection-reaction process and applied to a temperature cooling fin of high-speed aerospace vehicle, and the achieved results show its effectiveness.
Sahoo, Avimanyu; Xu, Hao; Jagannathan, Sarangapani
2017-03-01
This paper presents an approximate optimal control of nonlinear continuous-time systems in affine form by using the adaptive dynamic programming (ADP) with event-sampled state and input vectors. The knowledge of the system dynamics is relaxed by using a neural network (NN) identifier with event-sampled inputs. The value function, which becomes an approximate solution to the Hamilton-Jacobi-Bellman equation, is generated by using event-sampled NN approximator. Subsequently, the NN identifier and the approximated value function are utilized to obtain the optimal control policy. Both the identifier and value function approximator weights are tuned only at the event-sampled instants leading to an aperiodic update scheme. A novel adaptive event sampling condition is designed to determine the sampling instants, such that the approximation accuracy and the stability are maintained. A positive lower bound on the minimum inter-sample time is guaranteed to avoid accumulation point, and the dependence of inter-sample time upon the NN weight estimates is analyzed. A local ultimate boundedness of the resulting nonlinear impulsive dynamical closed-loop system is shown. Finally, a numerical example is utilized to evaluate the performance of the near-optimal design. The net result is the design of an event-sampled ADP-based controller for nonlinear continuous-time systems.
Lu, Zhao; Sun, Jing; Butts, Kenneth
2014-05-01
Support vector regression for approximating nonlinear dynamic systems is more delicate than the approximation of indicator functions in support vector classification, particularly for systems that involve multitudes of time scales in their sampled data. The kernel used for support vector learning determines the class of functions from which a support vector machine can draw its solution, and the choice of kernel significantly influences the performance of a support vector machine. In this paper, to bridge the gap between wavelet multiresolution analysis and kernel learning, the closed-form orthogonal wavelet is exploited to construct new multiscale asymmetric orthogonal wavelet kernels for linear programming support vector learning. The closed-form multiscale orthogonal wavelet kernel provides a systematic framework to implement multiscale kernel learning via dyadic dilations and also enables us to represent complex nonlinear dynamics effectively. To demonstrate the superiority of the proposed multiscale wavelet kernel in identifying complex nonlinear dynamic systems, two case studies are presented that aim at building parallel models on benchmark datasets. The development of parallel models that address the long-term/mid-term prediction issue is more intricate and challenging than the identification of series-parallel models where only one-step ahead prediction is required. Simulation results illustrate the effectiveness of the proposed multiscale kernel learning.
Policy iteration adaptive dynamic programming algorithm for discrete-time nonlinear systems.
Liu, Derong; Wei, Qinglai
2014-03-01
This paper is concerned with a new discrete-time policy iteration adaptive dynamic programming (ADP) method for solving the infinite horizon optimal control problem of nonlinear systems. The idea is to use an iterative ADP technique to obtain the iterative control law, which optimizes the iterative performance index function. The main contribution of this paper is to analyze the convergence and stability properties of policy iteration method for discrete-time nonlinear systems for the first time. It shows that the iterative performance index function is nonincreasingly convergent to the optimal solution of the Hamilton-Jacobi-Bellman equation. It is also proven that any of the iterative control laws can stabilize the nonlinear systems. Neural networks are used to approximate the performance index function and compute the optimal control law, respectively, for facilitating the implementation of the iterative ADP algorithm, where the convergence of the weight matrices is analyzed. Finally, the numerical results and analysis are presented to illustrate the performance of the developed method.
Discrete-time nonlinear HJB solution using approximate dynamic programming: convergence proof.
Al-Tamimi, Asma; Lewis, Frank L; Abu-Khalaf, Murad
2008-08-01
Convergence of the value-iteration-based heuristic dynamic programming (HDP) algorithm is proven in the case of general nonlinear systems. That is, it is shown that HDP converges to the optimal control and the optimal value function that solves the Hamilton-Jacobi-Bellman equation appearing in infinite-horizon discrete-time (DT) nonlinear optimal control. It is assumed that, at each iteration, the value and action update equations can be exactly solved. The following two standard neural networks (NN) are used: a critic NN is used to approximate the value function, whereas an action network is used to approximate the optimal control policy. It is stressed that this approach allows the implementation of HDP without knowing the internal dynamics of the system. The exact solution assumption holds for some classes of nonlinear systems and, specifically, in the specific case of the DT linear quadratic regulator (LQR), where the action is linear and the value quadratic in the states and NNs have zero approximation error. It is stressed that, for the LQR, HDP may be implemented without knowing the system A matrix by using two NNs. This fact is not generally appreciated in the folklore of HDP for the DT LQR, where only one critic NN is generally used.
On the solution of mixed-integer nonlinear programming models for computer aided molecular design.
Ostrovsky, Guennadi M; Achenie, Luke E K; Sinha, Manish
2002-11-01
This paper addresses the efficient solution of computer aided molecular design (CAMD) problems, which have been posed as mixed-integer nonlinear programming models. The models of interest are those in which the number of linear constraints far exceeds the number of nonlinear constraints, and with most variables participating in the nonconvex terms. As a result global optimization methods are needed. A branch-and-bound algorithm (BB) is proposed that is specifically tailored to solving such problems. In a conventional BB algorithm, branching is performed on all the search variables that appear in the nonlinear terms. This translates to a large number of node traversals. To overcome this problem, we have proposed a new strategy for branching on a set of linear branchingfunctions, which depend linearly on the search variables. This leads to a significant reduction in the dimensionality of the search space. The construction of linear underestimators for a class of functions is also presented. The CAMD problem that is considered is the design of optimal solvents to be used as cleaning agents in lithographic printing.
Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo
2016-04-08
This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.
Zhu, Yuanheng; Zhao, Dongbin; Yang, Xiong; Zhang, Qichao
2017-01-10
Sum of squares (SOS) polynomials have provided a computationally tractable way to deal with inequality constraints appearing in many control problems. It can also act as an approximator in the framework of adaptive dynamic programming. In this paper, an approximate solution to the H∞ optimal control of polynomial nonlinear systems is proposed. Under a given attenuation coefficient, the Hamilton-Jacobi-Isaacs equation is relaxed to an optimization problem with a set of inequalities. After applying the policy iteration technique and constraining inequalities to SOS, the optimization problem is divided into a sequence of feasible semidefinite programming problems. With the converged solution, the attenuation coefficient is further minimized to a lower value. After iterations, approximate solutions to the smallest L₂-gain and the associated H∞ optimal controller are obtained. Four examples are employed to verify the effectiveness of the proposed algorithm.
A high performance neural network for solving nonlinear programming problems with hybrid constraints
Tao, Qing; Cao, Jinde; Xue, Meisheng; Qiao, Hong
2001-09-01
A continuous neural network is proposed in this Letter for solving optimization problems. It not only can solve nonlinear programming problems with the constraints of equality and inequality, but also has a higher performance. The main advantage of the network is that it is an extension of Newton's gradient method for constrained problems, the dynamic behavior of the network under special constraints and the convergence rate can be investigated. Furthermore, the proposed network is simpler than the existing networks even for solving positive definite quadratic programming problems. The network considered is constrained by a projection operator on a convex set. The advanced performance of the proposed network is demonstrated by means of simulation of several numerical examples.
A nonlinear bi-level programming approach for product portfolio management.
Ma, Shuang
2016-01-01
Product portfolio management (PPM) is a critical decision-making for companies across various industries in today's competitive environment. Traditional studies on PPM problem have been motivated toward engineering feasibilities and marketing which relatively pay less attention to other competitors' actions and the competitive relations, especially in mathematical optimization domain. The key challenge lies in that how to construct a mathematical optimization model to describe this Stackelberg game-based leader-follower PPM problem and the competitive relations between them. The primary work of this paper is the representation of a decision framework and the optimization model to leverage the PPM problem of leader and follower. A nonlinear, integer bi-level programming model is developed based on the decision framework. Furthermore, a bi-level nested genetic algorithm is put forward to solve this nonlinear bi-level programming model for leader-follower PPM problem. A case study of notebook computer product portfolio optimization is reported. Results and analyses reveal that the leader-follower bi-level optimization model is robust and can empower product portfolio optimization.
Park, Y. C.; Chang, M. H.; Lee, T.-Y.
2007-06-01
A deterministic global optimization method that is applicable to general nonlinear programming problems composed of twice-differentiable objective and constraint functions is proposed. The method hybridizes the branch-and-bound algorithm and a convex cut function (CCF). For a given subregion, the difference of a convex underestimator that does not need an iterative local optimizer to determine the lower bound of the objective function is generated. If the obtained lower bound is located in an infeasible region, then the CCF is generated for constraints to cut this region. The cutting region generated by the CCF forms a hyperellipsoid and serves as the basis of a discarding rule for the selected subregion. However, the convergence rate decreases as the number of cutting regions increases. To accelerate the convergence rate, an inclusion relation between two hyperellipsoids should be applied in order to reduce the number of cutting regions. It is shown that the two-hyperellipsoid inclusion relation is determined by maximizing a quadratic function over a sphere, which is a special case of a trust region subproblem. The proposed method is applied to twelve nonlinear programming test problems and five engineering design problems. Numerical results show that the proposed method converges in a finite calculation time and produces accurate solutions.
FORTRAN programs for calculating nonlinear seismic ground response in two dimensions
Joyner, W.B.
1978-01-01
The programs described here were designed for calculating the nonlinear seismic response of a two-dimensional configuration of soil underlain by a semi-infinite elastic medium representing bedrock. There are two programs. One is for plane strain motions, that is, motions in the plane perpendicular to the long axis of the structure, and the other is for antiplane strain motions, that is motions parallel to the axis. The seismic input is provided by specifying what the motion of the rock-soil boundary would be if the soil were absent and the boundary were a free surface. This may be done by supplying a magnetic tape containing the values of particle velocity for every boundary point at every instant of time. Alternatively, a punch card deck may be supplied giving acceleration values at every instant of time. In the plane strain program it is assumed that the acceleration values apply simultaneously to every point on the boundary; in the antiplane strain program it is assumed that the acceleration values characterize a plane shear wave propagating upward in the underlying elastic medium at a specified angle with the vertical. The nonlinear hysteretic behavior of the soil is represented by a three-dimensional rheological model. A boundary condition is used which takes account of finite rigidity in the elastic substratum. The computations are performed by an explicit finite-difference scheme that proceeds step by step in space and time. Computations are done in terms of stress departures from an unspecified initial state. Source listings are provided here along with instructions for preparing the input. A more detailed discussion of the method is presented elsewhere.
Xu, Hao; Jagannathan, Sarangapani
2013-03-01
The stochastic optimal controller design for the nonlinear networked control system (NNCS) with uncertain system dynamics is a challenging problem due to the presence of both system nonlinearities and communication network imperfections, such as random delays and packet losses, which are not unknown a priori. In the recent literature, neuro dynamic programming (NDP) techniques, based on value and policy iterations, have been widely reported to solve the optimal control of general affine nonlinear systems. However, for realtime control, value and policy iterations-based methodology are not suitable and time-based NDP techniques are preferred. In addition, output feedback-based controller designs are preferred for implementation. Therefore, in this paper, a novel NNCS representation incorporating the system uncertainties and network imperfections is introduced first by using input and output measurements for facilitating output feedback. Then, an online neural network (NN) identifier is introduced to estimate the control coefficient matrix, which is subsequently utilized for the controller design. Subsequently, the critic and action NNs are employed along with the NN identifier to determine the forward-in-time, time-based stochastic optimal control of NNCS without using value and policy iterations. Here, the value function and control inputs are updated once a sampling instant. By using novel NN weight update laws, Lyapunov theory is used to show that all the closed-loop signals and NN weights are uniformly ultimately bounded in the mean while the approximated control input converges close to its target value with time. Simulation results are included to show the effectiveness of the proposed scheme.
On large-scale nonlinear programming techniques for solving optimal control problems
Energy Technology Data Exchange (ETDEWEB)
Faco, J.L.D.
1994-12-31
The formulation of decision problems by Optimal Control Theory allows the consideration of their dynamic structure and parameters estimation. This paper deals with techniques for choosing directions in the iterative solution of discrete-time optimal control problems. A unified formulation incorporates nonlinear performance criteria and dynamic equations, time delays, bounded state and control variables, free planning horizon and variable initial state vector. In general they are characterized by a large number of variables, mostly when arising from discretization of continuous-time optimal control or calculus of variations problems. In a GRG context the staircase structure of the jacobian matrix of the dynamic equations is exploited in the choice of basic and super basic variables and when changes of basis occur along the process. The search directions of the bound constrained nonlinear programming problem in the reduced space of the super basic variables are computed by large-scale NLP techniques. A modified Polak-Ribiere conjugate gradient method and a limited storage quasi-Newton BFGS method are analyzed and modifications to deal with the bounds on the variables are suggested based on projected gradient devices with specific linesearches. Some practical models are presented for electric generation planning and fishery management, and the application of the code GRECO - Gradient REduit pour la Commande Optimale - is discussed.
Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach.
Duarte, Belmiro P M; Wong, Weng Kee
2015-08-01
This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted.
Zhu, Yuanheng; Zhao, Dongbin; Li, Xiangjun
2017-03-01
H∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces errors that are detrimental to the control performance. To overcome this problem, an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous-time, unknown nonlinear ZSG with only online data. A model-free approach to the Hamilton-Jacobi-Isaacs equation is developed based on the policy iteration method. Control and disturbance policies and value are approximated by neural networks (NNs) under the critic-actor-disturber structure. The NN weights are solved by the least-squares method. According to the theoretical analysis, our algorithm is equivalent to a Gauss-Newton method solving an optimization problem, and it converges uniformly to the optimal solution. The online data can also be used repeatedly, which is highly efficient. Simulation results demonstrate its feasibility to solve the unknown nonlinear ZSG. When compared with other algorithms, it saves a significant amount of online measurement time.
Pavarini, C.
1974-01-01
Work in two somewhat distinct areas is presented. First, the optimal system design problem for a Mars-roving vehicle is attacked by creating static system models and a system evaluation function and optimizing via nonlinear programming techniques. The second area concerns the problem of perturbed-optimal solutions. Given an initial perturbation in an element of the solution to a nonlinear programming problem, a linear method is determined to approximate the optimal readjustments of the other elements of the solution. Then, the sensitivity of the Mars rover designs is described by application of this method.
Institute of Scientific and Technical Information of China (English)
Wan Zhongping; Wang Guangrain; Lv Yibing
2011-01-01
The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.
Robust Optimization Using Supremum of the Objective Function for Nonlinear Programming Problems
Energy Technology Data Exchange (ETDEWEB)
Lee, Se Jung; Park, Gyung Jin [Hanyang University, Seoul (Korea, Republic of)
2014-05-15
In the robust optimization field, the robustness of the objective function emphasizes an insensitive design. In general, the robustness of the objective function can be achieved by reducing the change of the objective function with respect to the variation of the design variables and parameters. However, in conventional methods, when an insensitive design is emphasized, the performance of the objective function can be deteriorated. Besides, if the numbers of the design variables are increased, the numerical cost is quite high in robust optimization for nonlinear programming problems. In this research, the robustness index for the objective function and a process of robust optimization are proposed. Moreover, a method using the supremum of linearized functions is also proposed to reduce the computational cost. Mathematical examples are solved for the verification of the proposed method and the results are compared with those from the conventional methods. The proposed approach improves the performance of the objective function and its efficiency.
Hamiltonian-Driven Adaptive Dynamic Programming for Continuous Nonlinear Dynamical Systems.
Yang, Yongliang; Wunsch, Donald; Yin, Yixin
2017-02-01
This paper presents a Hamiltonian-driven framework of adaptive dynamic programming (ADP) for continuous time nonlinear systems, which consists of evaluation of an admissible control, comparison between two different admissible policies with respect to the corresponding the performance function, and the performance improvement of an admissible control. It is showed that the Hamiltonian can serve as the temporal difference for continuous-time systems. In the Hamiltonian-driven ADP, the critic network is trained to output the value gradient. Then, the inner product between the critic and the system dynamics produces the value derivative. Under some conditions, the minimization of the Hamiltonian functional is equivalent to the value function approximation. An iterative algorithm starting from an arbitrary admissible control is presented for the optimal control approximation with its convergence proof. The implementation is accomplished by a neural network approximation. Two simulation studies demonstrate the effectiveness of Hamiltonian-driven ADP.
Lewis, Robert Michael
1997-01-01
This paper discusses the calculation of sensitivities. or derivatives, for optimization problems involving systems governed by differential equations and other state relations. The subject is examined from the point of view of nonlinear programming, beginning with the analytical structure of the first and second derivatives associated with such problems and the relation of these derivatives to implicit differentiation and equality constrained optimization. We also outline an error analysis of the analytical formulae and compare the results with similar results for finite-difference estimates of derivatives. We then attend to an investigation of the nature of the adjoint method and the adjoint equations and their relation to directions of steepest descent. We illustrate the points discussed with an optimization problem in which the variables are the coefficients in a differential operator.
Assimilation of ERBE data with a nonlinear programming technique to improve cloud-cover diagnosis
Wu, Xiangqian; Smith, William L.
1992-01-01
A method is developed to assimilate satellite data for the purpose of improving the diagnosis of fractional cloud cover within a numerical weather prediction model. The method makes use of a nonlinear programming technique to find a set of parameters for the cloud diagnosis that minimizes the difference between the observed and model-produced outgoing longwave radiation (OLR). The algorithm and theoretical basis of the method are presented. The method has been applied in two forecast experiments using a numerical weather prediction model. The results from a winter case demonstrate that the root-mean-square (rms) difference between the observed and forecasted OLR can be reduced by 50 percent when the optimized cloud diagnosis is used, with the remaining rms difference within the background noise.
An inner-outer nonlinear programming approach for constrained quadratic matrix model updating
Andretta, M.; Birgin, E. G.; Raydan, M.
2016-01-01
The Quadratic Finite Element Model Updating Problem (QFEMUP) concerns with updating a symmetric second-order finite element model so that it remains symmetric and the updated model reproduces a given set of desired eigenvalues and eigenvectors by replacing the corresponding ones from the original model. Taking advantage of the special structure of the constraint set, it is first shown that the QFEMUP can be formulated as a suitable constrained nonlinear programming problem. Using this formulation, a method based on successive optimizations is then proposed and analyzed. To avoid that spurious modes (eigenvectors) appear in the frequency range of interest (eigenvalues) after the model has been updated, additional constraints based on a quadratic Rayleigh quotient are dynamically included in the constraint set. A distinct practical feature of the proposed method is that it can be implemented by computing only a few eigenvalues and eigenvectors of the associated quadratic matrix pencil.
EXACT AUGMENTED LAGRANGIAN FUNCTION FOR NONLINEAR PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS
Institute of Scientific and Technical Information of China (English)
DU Xue-wu; ZHANG Lian-sheng; SHANG You-lin; LI Ming-ming
2005-01-01
An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions,the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, from the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented.
User's guide to the Fault Inferring Nonlinear Detection System (FINDS) computer program
Caglayan, A. K.; Godiwala, P. M.; Satz, H. S.
1988-01-01
Described are the operation and internal structure of the computer program FINDS (Fault Inferring Nonlinear Detection System). The FINDS algorithm is designed to provide reliable estimates for aircraft position, velocity, attitude, and horizontal winds to be used for guidance and control laws in the presence of possible failures in the avionics sensors. The FINDS algorithm was developed with the use of a digital simulation of a commercial transport aircraft and tested with flight recorded data. The algorithm was then modified to meet the size constraints and real-time execution requirements on a flight computer. For the real-time operation, a multi-rate implementation of the FINDS algorithm has been partitioned to execute on a dual parallel processor configuration: one based on the translational dynamics and the other on the rotational kinematics. The report presents an overview of the FINDS algorithm, the implemented equations, the flow charts for the key subprograms, the input and output files, program variable indexing convention, subprogram descriptions, and the common block descriptions used in the program.
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
A universal numerical approach for nonlinear mathematic programming problems is presented with an application of ratios of first-order differentials/differences of objective functions to constraint functions with respect to design variables. This approach can be efficiently used to solve continuous and, in particular, discrete programmings with arbitrary design variables and constraints. As a search method, this approach requires only computations of the functions and their partial derivatives or differences with respect to design variables, rather than any solution of mathematic equations. The present approach has been applied on many numerical examples as well as on some classical operational problems such as one-dimensional and two-dimensional knap-sack problems, one-dimensional and two-dimensional resource-distribution problems, problems of working reliability of composite systems and loading problems of machine, and more efficient and reliable solutions are obtained than traditional methods. The present approach can be used without limitation of modeling scales of the problem. Optimum solutions can be guaranteed as long as the objective function,constraint functions and their first-order derivatives/differences exist in the feasible domain or feasible set. There are no failures of convergence and instability when this approach is adopted.
Energy Technology Data Exchange (ETDEWEB)
Glass, Micheal W.; Hogan, Roy E., Jr.; Gartling, David K.
2010-03-01
The need for the engineering analysis of systems in which the transport of thermal energy occurs primarily through a conduction process is a common situation. For all but the simplest geometries and boundary conditions, analytic solutions to heat conduction problems are unavailable, thus forcing the analyst to call upon some type of approximate numerical procedure. A wide variety of numerical packages currently exist for such applications, ranging in sophistication from the large, general purpose, commercial codes, such as COMSOL, COSMOSWorks, ABAQUS and TSS to codes written by individuals for specific problem applications. The original purpose for developing the finite element code described here, COYOTE, was to bridge the gap between the complex commercial codes and the more simplistic, individual application programs. COYOTE was designed to treat most of the standard conduction problems of interest with a user-oriented input structure and format that was easily learned and remembered. Because of its architecture, the code has also proved useful for research in numerical algorithms and development of thermal analysis capabilities. This general philosophy has been retained in the current version of the program, COYOTE, Version 5.0, though the capabilities of the code have been significantly expanded. A major change in the code is its availability on parallel computer architectures and the increase in problem complexity and size that this implies. The present document describes the theoretical and numerical background for the COYOTE program. This volume is intended as a background document for the user's manual. Potential users of COYOTE are encouraged to become familiar with the present report and the simple example analyses reported in before using the program. The theoretical and numerical background for the finite element computer program, COYOTE, is presented in detail. COYOTE is designed for the multi-dimensional analysis of nonlinear heat conduction
Optimal in silico target gene deletion through nonlinear programming for genetic engineering.
Hong, Chung-Chien; Song, Mingzhou
2010-02-24
Optimal selection of multiple regulatory genes, known as targets, for deletion to enhance or suppress the activities of downstream genes or metabolites is an important problem in genetic engineering. Such problems become more feasible to address in silico due to the availability of more realistic dynamical system models of gene regulatory and metabolic networks. The goal of the computational problem is to search for a subset of genes to knock out so that the activity of a downstream gene or a metabolite is optimized. Based on discrete dynamical system modeling of gene regulatory networks, an integer programming problem is formulated for the optimal in silico target gene deletion problem. In the first result, the integer programming problem is proved to be NP-hard and equivalent to a nonlinear programming problem. In the second result, a heuristic algorithm, called GKONP, is designed to approximate the optimal solution, involving an approach to prune insignificant terms in the objective function, and the parallel differential evolution algorithm. In the third result, the effectiveness of the GKONP algorithm is demonstrated by applying it to a discrete dynamical system model of the yeast pheromone pathways. The empirical accuracy and time efficiency are assessed in comparison to an optimal, but exhaustive search strategy. Although the in silico target gene deletion problem has enormous potential applications in genetic engineering, one must overcome the computational challenge due to its NP-hardness. The presented solution, which has been demonstrated to approximate the optimal solution in a practical amount of time, is among the few that address the computational challenge. In the experiment on the yeast pheromone pathways, the identified best subset of genes for deletion showed advantage over genes that were selected empirically. Once validated in vivo, the optimal target genes are expected to achieve higher genetic engineering effectiveness than a trial
Optimal in silico target gene deletion through nonlinear programming for genetic engineering.
Directory of Open Access Journals (Sweden)
Chung-Chien Hong
Full Text Available BACKGROUND: Optimal selection of multiple regulatory genes, known as targets, for deletion to enhance or suppress the activities of downstream genes or metabolites is an important problem in genetic engineering. Such problems become more feasible to address in silico due to the availability of more realistic dynamical system models of gene regulatory and metabolic networks. The goal of the computational problem is to search for a subset of genes to knock out so that the activity of a downstream gene or a metabolite is optimized. METHODOLOGY/PRINCIPAL FINDINGS: Based on discrete dynamical system modeling of gene regulatory networks, an integer programming problem is formulated for the optimal in silico target gene deletion problem. In the first result, the integer programming problem is proved to be NP-hard and equivalent to a nonlinear programming problem. In the second result, a heuristic algorithm, called GKONP, is designed to approximate the optimal solution, involving an approach to prune insignificant terms in the objective function, and the parallel differential evolution algorithm. In the third result, the effectiveness of the GKONP algorithm is demonstrated by applying it to a discrete dynamical system model of the yeast pheromone pathways. The empirical accuracy and time efficiency are assessed in comparison to an optimal, but exhaustive search strategy. SIGNIFICANCE: Although the in silico target gene deletion problem has enormous potential applications in genetic engineering, one must overcome the computational challenge due to its NP-hardness. The presented solution, which has been demonstrated to approximate the optimal solution in a practical amount of time, is among the few that address the computational challenge. In the experiment on the yeast pheromone pathways, the identified best subset of genes for deletion showed advantage over genes that were selected empirically. Once validated in vivo, the optimal target genes are
Gorelick, S.M.; Voss, C.I.; Gill, P.E.; Murray, W.; Saunders, M.A.; Wright, M.H.
1984-01-01
A simulation-management methodology is demonstrated for the rehabilitation of aquifers that have been subjected to chemical contamination. Finite element groundwater flow and contaminant transport simulation are combined with nonlinear optimization. The model is capable of determining well locations plus pumping and injection rates for groundwater quality control. Examples demonstrate linear or nonlinear objective functions subject to linear and nonlinear simulation and water management constraints. -from Authors
Optimal bipedal interactions with dynamic terrain: synthesis and analysis via nonlinear programming
Hubicki, Christian; Goldman, Daniel; Ames, Aaron
In terrestrial locomotion, gait dynamics and motor control behaviors are tuned to interact efficiently and stably with the dynamics of the terrain (i.e. terradynamics). This controlled interaction must be particularly thoughtful in bipeds, as their reduced contact points render them highly susceptible to falls. While bipedalism under rigid terrain assumptions is well-studied, insights for two-legged locomotion on soft terrain, such as sand and dirt, are comparatively sparse. We seek an understanding of how biological bipeds stably and economically negotiate granular media, with an eye toward imbuing those abilities in bipedal robots. We present a trajectory optimization method for controlled systems subject to granular intrusion. By formulating a large-scale nonlinear program (NLP) with reduced-order resistive force theory (RFT) models and jamming cone dynamics, the optimized motions are informed and shaped by the dynamics of the terrain. Using a variant of direct collocation methods, we can express all optimization objectives and constraints in closed-form, resulting in rapid solving by standard NLP solvers, such as IPOPT. We employ this tool to analyze emergent features of bipedal locomotion in granular media, with an eye toward robotic implementation.
Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.
Wei, Qinglai; Liu, Derong; Lin, Hanquan
2016-03-01
In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.
Event-Based Robust Control for Uncertain Nonlinear Systems Using Adaptive Dynamic Programming.
Zhang, Qichao; Zhao, Dongbin; Wang, Ding
2016-10-18
In this paper, the robust control problem for a class of continuous-time nonlinear system with unmatched uncertainties is investigated using an event-based control method. First, the robust control problem is transformed into a corresponding optimal control problem with an augmented control and an appropriate cost function. Under the event-based mechanism, we prove that the solution of the optimal control problem can asymptotically stabilize the uncertain system with an adaptive triggering condition. That is, the designed event-based controller is robust to the original uncertain system. Note that the event-based controller is updated only when the triggering condition is satisfied, which can save the communication resources between the plant and the controller. Then, a single network adaptive dynamic programming structure with experience replay technique is constructed to approach the optimal control policies. The stability of the closed-loop system with the event-based control policy and the augmented control policy is analyzed using the Lyapunov approach. Furthermore, we prove that the minimal intersample time is bounded by a nonzero positive constant, which excludes Zeno behavior during the learning process. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed control scheme.
Sahoo, Avimanyu; Xu, Hao; Jagannathan, Sarangapani
2016-09-01
This paper presents an event-triggered near optimal control of uncertain nonlinear discrete-time systems. Event-driven neurodynamic programming (NDP) is utilized to design the control policy. A neural network (NN)-based identifier, with event-based state and input vectors, is utilized to learn the system dynamics. An actor-critic framework is used to learn the cost function and the optimal control input. The NN weights of the identifier, the critic, and the actor NNs are tuned aperiodically once every triggered instant. An adaptive event-trigger condition to decide the trigger instants is derived. Thus, a suitable number of events are generated to ensure a desired accuracy of approximation. A near optimal performance is achieved without using value and/or policy iterations. A detailed analysis of nontrivial inter-event times with an explicit formula to show the reduction in computation is also derived. The Lyapunov technique is used in conjunction with the event-trigger condition to guarantee the ultimate boundedness of the closed-loop system. The simulation results are included to verify the performance of the controller. The net result is the development of event-driven NDP.
Sahoo, Avimanyu; Jagannathan, Sarangapani
2017-02-01
In this paper, an event-driven stochastic adaptive dynamic programming (ADP)-based technique is introduced for nonlinear systems with a communication network within its feedback loop. A near optimal control policy is designed using an actor-critic framework and ADP with event sampled state vector. First, the system dynamics are approximated by using a novel neural network (NN) identifier with event sampled state vector. The optimal control policy is generated via an actor NN by using the NN identifier and value function approximated by a critic NN through ADP. The stochastic NN identifier, actor, and critic NN weights are tuned at the event sampled instants leading to aperiodic weight tuning laws. Above all, an adaptive event sampling condition based on estimated NN weights is designed by using the Lyapunov technique to ensure ultimate boundedness of all the closed-loop signals along with the approximation accuracy. The net result is event-driven stochastic ADP technique that can significantly reduce the computation and network transmissions. Finally, the analytical design is substantiated with simulation results.
The nurse scheduling problem: a goal programming and nonlinear optimization approaches
Hakim, L.; Bakhtiar, T.; Jaharuddin
2017-01-01
Nurses scheduling is an activity of allocating nurses to conduct a set of tasks at certain room at a hospital or health centre within a certain period. One of obstacles in the nurse scheduling is the lack of resources in order to fulfil the needs of the hospital. Nurse scheduling which is undertaken manually will be at risk of not fulfilling some nursing rules set by the hospital. Therefore, this study aimed to perform scheduling models that satisfy all the specific rules set by the management of Bogor State Hospital. We have developed three models to overcome the scheduling needs. Model 1 is designed to schedule nurses who are solely assigned to a certain inpatient unit and Model 2 is constructed to manage nurses who are assigned to an inpatient room as well as at Polyclinic room as conjunct nurses. As the assignment of nurses on each shift is uneven, then we propose Model 3 to minimize the variance of the workload in order to achieve equitable assignment on every shift. The first two models are formulated in goal programming framework, while the last model is in nonlinear optimization form.
Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming
Shi, Yun. Y.; Nelson, R. L.; Young, D. H.
1990-01-01
The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.
Optimal Reservoir Operation for Hydropower Generation using Non-linear Programming Model
Arunkumar, R.; Jothiprakash, V.
2012-05-01
Hydropower generation is one of the vital components of reservoir operation, especially for a large multi-purpose reservoir. Deriving optimal operational rules for such a large multi-purpose reservoir serving various purposes like irrigation, hydropower and flood control are complex, because of the large dimension of the problem and the complexity is more if the hydropower production is not an incidental. Thus optimizing the operations of a reservoir serving various purposes requires a systematic study. In the present study such a large multi-purpose reservoir, namely, Koyna reservoir operations are optimized for maximizing the hydropower production subject to the condition of satisfying the irrigation demands using a non-linear programming model. The hydropower production from the reservoir is analysed for three different dependable inflow conditions, representing wet, normal and dry years. For each dependable inflow conditions, various scenarios have been analyzed based on the constraints on the releases and the results are compared. The annual power production, combined monthly power production from all the powerhouses, end of month storage levels, evaporation losses and surplus are discussed. From different scenarios, it is observed that more hydropower can be generated for various dependable inflow conditions, if the restrictions on releases are slightly relaxed. The study shows that Koyna dam is having potential to generate more hydropower.
Designing A Nonlinear Integer Programming Model For A Cross-Dock By A Genetic Algorithm
Directory of Open Access Journals (Sweden)
Bahareh Vaisi
2015-03-01
Full Text Available Abstract This paper presents a non-linear integer programming model for a cross-dock problem that considers the total transportation cost of inbound and outbound trucks from an origin to a destination and the total cost of assigning strip and stack doors to trucks based on their number of trips and the distance between doors in cross-dock. In previous studies these two cost-based problems are modeled separately however it is more realistic and practical to use both of them as an integrated cross-docking model. Additionally this model is solved for a randomly generated numerical example with three suppliers and two customers by the use of a genetic algorithm. By comparing two different parameter levels i.e. low and high numbers of populations the optimum solution is obtained considering a high level population size. A number of strip and stack doors are equal to a number of inbound and outbound trucks in the same sequence as 4 and 6 respectively. Finally the conclusion is presented.
Domínguez, Luis F.
2012-06-25
An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear programming subproblem and a mixed-integer nonlinear programming subproblem to provide a series of parametric upper and lower bounds. The primal subproblem is formulated by fixing the integer variables and solved through a series of multiparametric quadratic programming (mp-QP) problems based on quadratic approximations of the objective function, while the deterministic master subproblem is formulated so as to provide feasible integer solutions for the next primal subproblem. To reduce the computational effort when infeasibilities are encountered at the vertices of the critical regions (CRs) generated by the primal subproblem, a simplicial approximation approach is used to obtain CRs that are feasible at each of their vertices. The algorithm terminates when there does not exist an integer solution that is better than the one previously used by the primal problem. Through a series of examples, the proposed algorithm is compared with a multiparametric mixed-integer outer approximation (mp-MIOA) algorithm to demonstrate its computational advantages. © 2012 American Institute of Chemical Engineers (AIChE).
Sumin, M. I.
2015-06-01
A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiability properties in the sense of nonlinear (nonsmooth) analysis. Such subdifferentiability can be understood as the existence of a proximal subgradient or a Fréchet subdifferential. In other words, an individual problem has a corresponding generalized Kuhn-Tucker vector. Under this assumption, a stable sequential Kuhn-Tucker theorem in nondifferential iterative form is proved and discussed in terms of minimizing sequences on the basis of the dual regularization method. This theorem provides necessary and sufficient conditions for the stable construction of a minimizing approximate solution in the sense of Warga in the considered problem, whose initial data can be approximately specified. A substantial difference of the proved theorem from its classical same-named analogue is that the former takes into account the possible instability of the problem in the case of perturbed initial data and, as a consequence, allows for the inherited instability of classical optimality conditions. This theorem can be treated as a regularized generalization of the classical Uzawa algorithm to nonlinear programming problems. Finally, the theorem is applied to the "simplest" nonlinear optimal control problem, namely, to a time-optimal control problem.
Exact Penalty Function and Asymptotic Strong Nonlinear Duality in Integer Programming
Institute of Scientific and Technical Information of China (English)
Fu-sheng Bai; Z.Y.Wu; L.S. Zhang
2004-01-01
In this paper, a logarithmic-exponential penalty function with two parameters for integer programmingis discussed. We obtain the exact penalty properties and then establish the asymptotic strong nonlinear duality in the corresponding logarithmic-exponential dual formulation by using the obtained exact penalty properties.The discussion is based on the logarithmic-exponential nonlinear dual formulation proposed in [6].
Directory of Open Access Journals (Sweden)
Zhong Wan
2013-01-01
Full Text Available In accord with the practical engineering design conditions, a nonlinear programming model is constructed for maximizing the fatigue life of V-belt drive in which some polymorphic uncertainties are incorporated. For a given satisfaction level and a confidence level, an equivalent formulation of this uncertain optimization model is obtained where only interval parameters are involved. Based on the concepts of maximal and minimal range inequalities for describing interval inequality, the interval parameter model is decomposed into two standard nonlinear programming problems, and an algorithm, called two-step based sampling algorithm, is developed to find an interval optimal solution for the original problem. Case study is employed to demonstrate the validity and practicability of the constructed model and the algorithm.
Directory of Open Access Journals (Sweden)
Yonghwan Kim
2011-03-01
Full Text Available The present paper introduced a computer program, called WISH, which is based on a time-domain Rankine panel method. The WISH has been developed for practical use to predict the linear and nonlinear ship motion and structural loads in waves. The WISH adopts three different levels of seakeeping analysis: linear, weakly-nonlinear and weak-scatterer approaches. Later, WISH-FLEX has been developed to consider hydroelasticity effects on hull-girder structure. This program can solve the springing and whipping problems by coupling between the hydrodynamic and structural problems. More recently this development has been continued to more diverse problems, including the motion responses of multiple adjacent bodies, the effects of seakeeping in ship maneuvering, and the floating-body motion in finite-depth domain with varying bathymetry. This paper introduces a brief theoretical and numerical background of the WISH package, and some validation results. Also several applications to real ships and offshore structures are shown.
Poole, L. R.
1972-01-01
A computer program is presented by which the effects of nonlinear suspension-system elastic characteristics on parachute inflation loads and motions can be investigated. A mathematical elastic model of suspension-system geometry is coupled to the planar equations of motion of a general vehicle and canopy. Canopy geometry and aerodynamic drag characteristics and suspension-system elastic properties are tabular inputs. The equations of motion are numerically integrated by use of an equivalent fifth-order Runge-Kutta technique.
A nonlinear programming optimization model to maximize net revenue in cheese manufacture.
Papadatos, A; Berger, A M; Pratt, J E; Barbano, D M
2002-11-01
A nonlinear programming optimization model was developed to maximize net revenue in cheese manufacture and is described in this paper. The model identifies the optimal mix of milk resources together with the types of cheeses and co-products that maximize net revenue. It works in Excel while it takes the data specified by the user from a user-friendly interface created in Access. The user can specify any number of resources, cheese types, and co-products. To demonstrate the capabilities of the model, we determined the impact of variation in milk price and composition in the period 1998 to 2000 on the optimal mix of resources and optimal type of co-product for Cheddar and low-moisture, part-skim Mozzarella. It was also desired to determine the impact of variation in protein content of nonfat dry milk (NDM) on net revenue, and examine the effect of reconstitution of NDM with water versus milk on net revenue. The optimal mix of resources and the net revenue markedly varied as milk resource prices and composition varied. The net revenue for Mozzarella was much higher than for Cheddar when the price of cream was high. Cheese plants that did not optimize the use of resources in response to variations in prices and composition missed a significant profit opportunity. Whey powder was more profitable than 34% whey protein concentrate and lactose in most months. The use of high-protein NDM led to an appreciable increase in net revenue. When the value of the nonfat portion of raw milk was high, reconstitution of NDM with water rather than milk markedly raised net revenue.
Research on an augmented Lagrangian penalty function algorithm for nonlinear programming
Frair, L.
1978-01-01
The augmented Lagrangian (ALAG) Penalty Function Algorithm for optimizing nonlinear mathematical models is discussed. The mathematical models of interest are deterministic in nature and finite dimensional optimization is assumed. A detailed review of penalty function techniques in general and the ALAG technique in particular is presented. Numerical experiments are conducted utilizing a number of nonlinear optimization problems to identify an efficient ALAG Penalty Function Technique for computer implementation.
Abrashkevich, Alexander; Puzynin, I. V.
2004-01-01
A FORTRAN program is presented which solves a system of nonlinear simultaneous equations using the continuous analog of Newton's method (CANM). The user has the option of either to provide a subroutine which calculates the Jacobian matrix or allow the program to calculate it by a forward-difference approximation. Five iterative schemes using different algorithms of determining adaptive step size of the CANM process are implemented in the program. Program summaryTitle of program: CANM Catalogue number: ADSN Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSN Program available from: CPC Program Library, Queen's University of Belfast, Northern Ireland Licensing provisions: none Computer for which the program is designed and others on which it has been tested: Computers: IBM RS/6000 Model 320H, SGI Origin2000, SGI Octane, HP 9000/755, Intel Pentium IV PC Installation: Department of Chemistry, University of Toronto, Toronto, Canada Operating systems under which the program has been tested: IRIX64 6.1, 6.4 and 6.5, AIX 3.4, HP-UX 9.01, Linux 2.4.7 Programming language used: FORTRAN 90 Memory required to execute with typical data: depends on the number of nonlinear equations in a system. Test run requires 80 KB No. of bits in distributed program including test data, etc.: 15283 Distribution format: tar gz format No. of lines in distributed program, including test data, etc.: 1794 Peripherals used: line printer, scratch disc store External subprograms used: DGECO and DGESL [1] Keywords: nonlinear equations, Newton's method, continuous analog of Newton's method, continuous parameter, evolutionary differential equation, Euler's method Nature of physical problem: System of nonlinear simultaneous equations F i(x 1,x 2,…,x n)=0,1⩽i⩽n, is numerically solved. It can be written in vector form as F( X)= 0, X∈ Rn, where F : Rn→ Rn is a twice continuously differentiable function with domain and range in n-dimensional Euclidean space. The solutions of such systems of
Wang, Fei-Yue; Jin, Ning; Liu, Derong; Wei, Qinglai
2011-01-01
In this paper, we study the finite-horizon optimal control problem for discrete-time nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an ε-error bound. The optimal number of control steps can also be obtained by the proposed ADP algorithms. A convergence analysis of the proposed ADP algorithms in terms of performance index function and control policy is made. In order to facilitate the implementation of the iterative ADP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. Finally, two simulation examples are employed to illustrate the applicability of the proposed method.
Minimum fuel coplanar aeroassisted orbital transfer using collocation and nonlinear programming
Shi, Yun Yuan; Young, D. H.
1991-01-01
The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem
Tiffany, Sherwood H.; Adams, William M., Jr.
1988-01-01
The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.
Solution of transient optimization problems by using an algorithm based on nonlinear programming
Teren, F.
1977-01-01
A new algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
Solution of transient optimization problems by using an algorithm based on nonlinear programming
Teren, F.
1977-01-01
A new algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
Directory of Open Access Journals (Sweden)
Toly Chen
2013-01-01
Full Text Available This study proposes a multiobjective fuzzy nonlinear programming (MOFNP approach to enhance the long-term yield competitiveness of a semiconductor manufacturing factory. By modeling the long-term competitiveness of every product in a semiconductor manufacturing plant with the fuzzy correlation coefficient (FCC between time and instantaneous competitiveness, the proposed model considers the various viewpoints when interpreting the overall competitiveness of the semiconductor manufacturing plant in the long-term. All noninferior solutions of the MOFNP solutions are then derived using a systematic procedure. A real example is employed to illustrate the applicability of the proposed methodology.
Zhang, Huaguang; Song, Ruizhuo; Wei, Qinglai; Zhang, Tieyan
2011-12-01
In this paper, a novel heuristic dynamic programming (HDP) iteration algorithm is proposed to solve the optimal tracking control problem for a class of nonlinear discrete-time systems with time delays. The novel algorithm contains state updating, control policy iteration, and performance index iteration. To get the optimal states, the states are also updated. Furthermore, the "backward iteration" is applied to state updating. Two neural networks are used to approximate the performance index function and compute the optimal control policy for facilitating the implementation of HDP iteration algorithm. At last, we present two examples to demonstrate the effectiveness of the proposed HDP iteration algorithm.
Institute of Scientific and Technical Information of China (English)
2013-01-01
In this paper, a numerical method based on a coupling between a mathematical model of nonlinear transient ship manoeu-vring motion in the horizontal plane and Mathematical Programming (MP) techniques is proposed. The aim of the proposed proce-dure is an efficient estimation of optimal ship hydrodynamic parameters in a dynamic model at the early design stage. The proposed procedure has been validated through turning circle and zigzag manoeuvres based on experimental data of sea trials of the 190 000-dwt oil tanker. Comparisons between experimental and computed data show a good agreement of overall tendency in manoeuvring trajectories.
Generalized Equations and Their Solutions. Part 2. Applications to Nonlinear Programming
1980-03-01
Bolivar, Caracas, Venezuela, with support from the United Nations Educational, Scientific and Cultural Organization under Proyecto UNESCO VEN-77-002. The...tional, Scientific and Cultural Crganization under Proyecto UNESCO VEN-77-0 02. Vhe author greatly appreciates the hospitality and support extended...condition is satisfied by the linearizations of the nonlinear problem, then the latter has, at least locally, an upper Lipschitzian inverse (which, of
Sharqawy, Mostafa H.
2016-12-01
Pore network models (PNM) of Berea and Fontainebleau sandstones were constructed using nonlinear programming (NLP) and optimization methods. The constructed PNMs are considered as a digital representation of the rock samples which were based on matching the macroscopic properties of the porous media and used to conduct fluid transport simulations including single and two-phase flow. The PNMs consisted of cubic networks of randomly distributed pores and throats sizes and with various connectivity levels. The networks were optimized such that the upper and lower bounds of the pore sizes are determined using the capillary tube bundle model and the Nelder-Mead method instead of guessing them, which reduces the optimization computational time significantly. An open-source PNM framework was employed to conduct transport and percolation simulations such as invasion percolation and Darcian flow. The PNM model was subsequently used to compute the macroscopic properties; porosity, absolute permeability, specific surface area, breakthrough capillary pressure, and primary drainage curve. The pore networks were optimized to allow for the simulation results of the macroscopic properties to be in excellent agreement with the experimental measurements. This study demonstrates that non-linear programming and optimization methods provide a promising method for pore network modeling when computed tomography imaging may not be readily available.
Institute of Scientific and Technical Information of China (English)
杨轶华; 吕显瑞; 刘庆怀
2006-01-01
In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method (CHIIP)for convex nonlinear programming problems. For any convex nonlinear programming,without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.
An introduction to nonlinear programming. IV - Numerical methods for constrained minimization
Sorenson, H. W.; Koble, H. M.
1976-01-01
An overview is presented of the numerical solution of constrained minimization problems. Attention is given to both primal and indirect (linear programs and unconstrained minimizations) methods of solution.
Final Report---Optimization Under Nonconvexity and Uncertainty: Algorithms and Software
Energy Technology Data Exchange (ETDEWEB)
Jeff Linderoth
2011-11-06
the goal of this work was to develop new algorithmic techniques for solving large-scale numerical optimization problems, focusing on problems classes that have proven to be among the most challenging for practitioners: those involving uncertainty and those involving nonconvexity. This research advanced the state-of-the-art in solving mixed integer linear programs containing symmetry, mixed integer nonlinear programs, and stochastic optimization problems. The focus of the work done in the continuation was on Mixed Integer Nonlinear Programs (MINLP)s and Mixed Integer Linear Programs (MILP)s, especially those containing a great deal of symmetry.
Word, Daniel P; Cummings, Derek A T; Burke, Donald S; Iamsirithaworn, Sopon; Laird, Carl D
2012-08-07
Mathematical models can enhance our understanding of childhood infectious disease dynamics, but these models depend on appropriate parameter values that are often unknown and must be estimated from disease case data. In this paper, we develop a framework for efficient estimation of childhood infectious disease models with seasonal transmission parameters using continuous differential equations containing model and measurement noise. The problem is formulated using the simultaneous approach where all state variables are discretized, and the discretized differential equations are included as constraints, giving a large-scale algebraic nonlinear programming problem that is solved using a nonlinear primal-dual interior-point solver. The technique is demonstrated using measles case data from three different locations having different school holiday schedules, and our estimates of the seasonality of the transmission parameter show strong correlation to school term holidays. Our approach gives dramatic efficiency gains, showing a 40-400-fold reduction in solution time over other published methods. While our approach has an increased susceptibility to bias over techniques that integrate over the entire unknown state-space, a detailed simulation study shows no evidence of bias. Furthermore, the computational efficiency of our approach allows for investigation of a large model space compared with more computationally intensive approaches.
Jamali, A.; Khaleghi, E.; Gholaminezhad, I.; Nariman-zadeh, N.
2016-05-01
In this paper, a new multi-objective genetic programming (GP) with a diversity preserving mechanism and a real number alteration operator is presented and successfully used for Pareto optimal modelling of some complex non-linear systems using some input-output data. In this study, two different input-output data-sets of a non-linear mathematical model and of an explosive cutting process are considered separately in three-objective optimisation processes. The pertinent conflicting objective functions that have been considered for such Pareto optimisations are namely, training error (TE), prediction error (PE), and the length of tree (complexity of the network) (TL) of the GP models. Such three-objective optimisation implementations leads to some non-dominated choices of GP-type models for both cases representing the trade-offs among those objective functions. Therefore, optimal Pareto fronts of such GP models exhibit the trade-off among the corresponding conflicting objectives and, thus, provide different non-dominated optimal choices of GP-type models. Moreover, the results show that no significant optimality in TE and PE may occur when the TL of the corresponding GP model exceeds some values.
Designing a Fresh Food Supply Chain Network: An Application of Nonlinear Programming
Directory of Open Access Journals (Sweden)
Yu-Chung Tsao
2013-01-01
Full Text Available In today’s business environment, many fresh food companies have complex supply networks to distribute their products. For example, agricultural products are distributed through a multiechelon supply chain which includes agricultural association, agricultural produce marketing corporations (APMCs, markets, and so forth. In this paper a fresh produce supply network model is designed to determine the optimal service area for APMCs, the replenishment cycle time of APMCs, and the freshness-keeping effort, while maximizing the total profit. The objective is to address the integrated facility location, inventory allocation, and freshness-keeping effort problems. This paper develops an algorithm to solve the nonlinear problem, provides numerical analysis to illustrate the proposed solution procedure, and discusses the effects of various system parameters on the decisions and total profits. A real case of an agricultural product supply chain in Taiwan is used to verify the model. Results of this study can serve as a reference for business managers and administrators.
An inertia-free filter line-search algorithm for large-scale nonlinear programming
Energy Technology Data Exchange (ETDEWEB)
Chiang, Nai-Yuan; Zavala, Victor M.
2016-02-15
We present a filter line-search algorithm that does not require inertia information of the linear system. This feature enables the use of a wide range of linear algebra strategies and libraries, which is essential to tackle large-scale problems on modern computing architectures. The proposed approach performs curvature tests along the search step to detect negative curvature and to trigger convexification. We prove that the approach is globally convergent and we implement the approach within a parallel interior-point framework to solve large-scale and highly nonlinear problems. Our numerical tests demonstrate that the inertia-free approach is as efficient as inertia detection via symmetric indefinite factorizations. We also demonstrate that the inertia-free approach can lead to reductions in solution time because it reduces the amount of convexification needed.
Directory of Open Access Journals (Sweden)
Zhi-yuan Li
2014-01-01
Full Text Available As the core of the effective financial crisis prevention, enterprise finance crisis prediction has been the focal attention of both theorists and businessmen. Financial crisis predictions need to apply a variety of financial and operating indicators for its analysis. Therefore, a new evaluation model based on nonlinear programming is established, the nature of the model is proved, the detailed solution steps of the model are given, and the significance and algorithm of the model are thoroughly discussed in this study. The proposed model can deal with the case of missing data, and has the good isotonic property and profound theoretical background. In the empirical analysis to predict the financial crisis and through the comparison of the analysis of historical data and the real enterprises with financial crisis, we find that the results are in accordance with the real enterprise financial conditions and the proposed model has a good predictive ability.
Directory of Open Access Journals (Sweden)
Seyed Abolghasem Mortazavi
2014-03-01
Full Text Available Water resources sustainability is one of the major issues in the agricultural sustainability. In this study sustainability of water resources has been investigated by use of linear and non-linear models in six models based on optimal utilization of water resources in the north parts farms of Iran because of incorrect use of agricultural water resources, from 2011 to 2012. Also “gross margin per a unit of water consumption” and “employment per a unit of water consumption” are used as indicators for assessing the sustainability of cropping patterns. The results show that cropping pattern of fractional goal programming (FGP model has been near to current situation and has shown realistic conditions according to expertise and advantage of this area in cultivation of certain crops. So the FGP model has desirability in each of indicators than other five models.
Huang, Y L; Huang, G H; Liu, D F; Zhu, H; Sun, W
2012-10-15
Although integrated simulation and optimization approaches under stochastic uncertainty have been applied to eutrophication management problems, few studies are reported in eutrophication control planning where multiple formats of uncertainties and nonlinearities are addressed in forms of intervals and probabilistic distributions within an integrated framework. Since the impounding of Three Gorges Reservoir (TGR), China in 2003, the hydraulic conditions and aquatic environment of the Xiangxi Bay (XXB) have changed significantly. The resulting emergence of eutrophication and algal blooms leads to its deteriorated water quality. The XXB becomes an ideal case study area. Thus, a simulation-based inexact chance-constrained nonlinear programming (SICNP) model is developed and applied to eutrophication control planning in the XXB of the TGR under uncertainties. In the SICNP, the wastewater treatment costs for removing total phosphorus (TP) are set as the objective function; effluent discharge standards, stream water quality standards and eutrophication control standards are considered in the constraints; a steady-state simulation model for phosphorus transport and fate is embedded in the environmental standards constraints; the interval programming and chance-constrained approaches are integrated to provide interval decision variables but also the associated risk levels in violating the system constraints. The model results indicate that changes in the violating level (q) will result in different strategy distributions at spatial and temporal scales; the optimal value of cost objective is from [2.74, 13.41] million RMB to [2.25, 13.08] million RMB when q equals from 0.01 to 0.25; the required TP treatment efficiency for the Baisha plant is the most stringent, which is followed by the Xiakou Town and the Zhaojun Town, while the requirement for the Pingyikou cement plant is the least stringent. The model results are useful for making optimal policies on eutrophication
Zhang, Jilie; Zhang, Huaguang; Liu, Zhenwei; Wang, Yingchun
2015-07-01
In this paper, we consider the problem of developing a controller for continuous-time nonlinear systems where the equations governing the system are unknown. Using the measurements, two new online schemes are presented for synthesizing a controller without building or assuming a model for the system, by two new implementation schemes based on adaptive dynamic programming (ADP). To circumvent the requirement of the prior knowledge for systems, a precompensator is introduced to construct an augmented system. The corresponding Hamilton-Jacobi-Bellman (HJB) equation is solved by adaptive dynamic programming, which consists of the least-squared technique, neural network approximator and policy iteration (PI) algorithm. The main idea of our method is to sample the information of state, state derivative and input to update the weighs of neural network by least-squared technique. The update process is implemented in the framework of PI. In this paper, two new implementation schemes are presented. Finally, several examples are given to illustrate the effectiveness of our schemes.
Mu, Chaoxu; Ni, Zhen; Sun, Changyin; He, Haibo
2016-04-22
A data-driven adaptive tracking control approach is proposed for a class of continuous-time nonlinear systems using a recent developed goal representation heuristic dynamic programming (GrHDP) architecture. The major focus of this paper is on designing a multivariable tracking scheme, including the filter-based action network (FAN) architecture, and the stability analysis in continuous-time fashion. In this design, the FAN is used to observe the system function, and then generates the corresponding control action together with the reference signals. The goal network will provide an internal reward signal adaptively based on the current system states and the control action. This internal reward signal is assigned as the input for the critic network, which approximates the cost function over time. We demonstrate its improved tracking performance in comparison with the existing heuristic dynamic programming (HDP) approach under the same parameter and environment settings. The simulation results of the multivariable tracking control on two examples have been presented to show that the proposed scheme can achieve better control in terms of learning speed and overall performance.
Tavakoli, Ali; Nikoo, Mohammad Reza; Kerachian, Reza; Soltani, Maryam
2015-04-01
In this paper, a new fuzzy methodology is developed to optimize water and waste load allocation (WWLA) in rivers under uncertainty. An interactive two-stage stochastic fuzzy programming (ITSFP) method is utilized to handle parameter uncertainties, which are expressed as fuzzy boundary intervals. An iterative linear programming (ILP) is also used for solving the nonlinear optimization model. To accurately consider the impacts of the water and waste load allocation strategies on the river water quality, a calibrated QUAL2Kw model is linked with the WWLA optimization model. The soil, water, atmosphere, and plant (SWAP) simulation model is utilized to determine the quantity and quality of each agricultural return flow. To control pollution loads of agricultural networks, it is assumed that a part of each agricultural return flow can be diverted to an evaporation pond and also another part of it can be stored in a detention pond. In detention ponds, contaminated water is exposed to solar radiation for disinfecting pathogens. Results of applying the proposed methodology to the Dez River system in the southwestern region of Iran illustrate its effectiveness and applicability for water and waste load allocation in rivers. In the planning phase, this methodology can be used for estimating the capacities of return flow diversion system and evaporation and detention ponds.
1980-01-01
thickness of the foil which was used for the plano -convex foil case in the previous project [1] is now a dummy input in these programs. 8 3.1 INPUT DATA...the plano -convex foil (dummy variable). XXDD End of the normalized foil =1. YYDD Y coordinate of upper end of the normalized foil. 16 R Specifies the...6)’CAVLEN’( 1.-UU22).C1.-CAVLEN) 00 25 LG:1,LPM CI~NO CPC?.SIP) NEXT* FOR THE FIRST wETTE3 ARC PORTION Sl-- CP IS BASED ON Ul AND Pie 140 LP:1 IS
2015-08-17
our best knowledge , this is the first study of using a “predictive” approach through a model network to design the event-triggered ADP. This is the...investigated in the com- munity before, to our best knowledge , this is the first study of using a “predictive” approach through a model network to...programming has been used to solve the optimal control for many years. However, due to the ” curse of di- mensionality” [9], [10], the adaptive dynamic
Stenvall, A.; Tarhasaari, T.
2010-07-01
Due to the rapid development of personal computers from the beginning of the 1990s, it has become a reality to simulate current penetration, and thus hysteresis losses, in superconductors with other than very simple one-dimensional (1D) Bean model computations or Norris formulae. Even though these older approaches are still usable, they do not consider, for example, multifilamentary conductors, local critical current dependency on magnetic field or varying n-values. Currently, many numerical methods employing different formulations are available. The problem of hysteresis losses can be scrutinized via an eddy current formulation of the classical theory of electromagnetism. The difficulty of the problem lies in the non-linear resistivity of the superconducting region. The steep transition between the superconducting and the normal states often causes convergence problems for the most common finite element method based programs. The integration methods suffer from full system matrices and, thus, restrict the number of elements to a few thousands at most. The so-called T - phiv formulation and the use of edge elements, or more precisely Whitney 1-forms, within the finite element method have proved to be a very suitable method for hysteresis loss simulations of different geometries. In this paper we consider making such finite element method software from first steps, employing differential geometry and forms.
Directory of Open Access Journals (Sweden)
Mohammad Ali Afshari
2012-10-01
Full Text Available The aim of this paper is to present mathematical models optimizing all materials flows in supply chain. In this research a fuzzy multi-objective nonlinear mixed- integer programming model with piecewise linear membership function is applied to design a multi echelon supply chain network (SCN by considering total transportation costs and capacities of all echelons with fuzzy objectives. The model that is proposed in this study has 4 fuzzy functions. The first function is minimizing the total transportation costs between all echelons (suppliers, factories, distribution centers (DCs and customers. The second one is minimizing holding and ordering cost on DCs. The third objective is minimizing the unnecessary and unused capacity of factories and DCs via decreasing variance of transported amounts between echelons. The forth is minimizing the number of total vehicles that ship the materials and products along with SCN. For solving such a problem, as nodes increases in SCN, the traditional method does not have ability to solve large scale problem. So, we applied a Meta heuristic method called Genetic Algorithm. The numerical example is real world applied and compared the results with each other demonstrate the feasibility of applying the proposed model to given problem, and also its advantages are discussed.
Directory of Open Access Journals (Sweden)
M. Pattnaik
2013-08-01
Full Text Available In this paper the concept of fuzzy Non-Linear Programming Technique is applied to solve an economic order quantity (EOQ model under restricted space. Since various types of uncertainties and imprecision are inherent in real inventory problems they are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by usual probabilistic models. The questions how to define inventory optimization tasks in such environment how to interpret optimal solutions arise. This paper allows the modification of the Single item EOQ model in presence of fuzzy decision making process where demand is related to the unit price and the setup cost varies with the quantity produced/Purchased. This paper considers the modification of objective function and storage area in the presence of imprecisely estimated parameters. The model is developed for the problem by employing different modeling approaches over an infinite planning horizon. It incorporates all concepts of a fuzzy arithmetic approach, the quantity ordered and the demand per unit compares both fuzzy non linear and other models. Investigation of the properties of an optimal solution allows developing an algorithm whose validity is illustrated through an example problem and ugh MATLAB (R2009a version software, the two and three dimensional diagrams are represented to the application. Sensitivity analysis of the optimal solution is also studied with respect to changes in different parameter values and to draw managerial insights of the decision problem.
Zhang, Huaguang; Cui, Lili; Zhang, Xin; Luo, Yanhong
2011-12-01
In this paper, a novel data-driven robust approximate optimal tracking control scheme is proposed for unknown general nonlinear systems by using the adaptive dynamic programming (ADP) method. In the design of the controller, only available input-output data is required instead of known system dynamics. A data-driven model is established by a recurrent neural network (NN) to reconstruct the unknown system dynamics using available input-output data. By adding a novel adjustable term related to the modeling error, the resultant modeling error is first guaranteed to converge to zero. Then, based on the obtained data-driven model, the ADP method is utilized to design the approximate optimal tracking controller, which consists of the steady-state controller and the optimal feedback controller. Further, a robustifying term is developed to compensate for the NN approximation errors introduced by implementing the ADP method. Based on Lyapunov approach, stability analysis of the closed-loop system is performed to show that the proposed controller guarantees the system state asymptotically tracking the desired trajectory. Additionally, the obtained control input is proven to be close to the optimal control input within a small bound. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed control scheme.
Cao, Ning; Zhang, Huaguang; Luo, Yanhong; Feng, Dezhi
2012-09-01
In this article, a novel iteration algorithm named two-stage approximate dynamic programming (TSADP) is proposed to seek the solution of nonlinear switched optimal control problem. At each iteration of TSADP, a multivariate optimal control problem is transformed to be a certain number of univariate optimal control problems. It is shown that the value function at each iteration can be characterised pointwisely by a set of smooth functions recursively obtained from TSADP, and the associated control policy, continuous control and switching control law included, is explicitly provided in a state-feedback form. Moreover, the convergence and optimality of TSADP is strictly proven. To implement this algorithm efficiently, neural networks, critic and action networks, are utilised to approximate the value function and continuous control law, respectively. Thus, the value function is expressed by the weights of critic networks pointwise. Besides, redundant weights are ruled out at each iteration to simplify the exponentially increasing computation burden. Finally, a simulation example is provided to demonstrate its effectiveness.
Energy Technology Data Exchange (ETDEWEB)
Stenvall, A; Tarhasaari, T, E-mail: antti.stenvall@tut.f [Electromagnetics, Tampere University of Technology, PO Box 692, 33101 Tampere (Finland)
2010-07-15
Due to the rapid development of personal computers from the beginning of the 1990s, it has become a reality to simulate current penetration, and thus hysteresis losses, in superconductors with other than very simple one-dimensional (1D) Bean model computations or Norris formulae. Even though these older approaches are still usable, they do not consider, for example, multifilamentary conductors, local critical current dependency on magnetic field or varying n-values. Currently, many numerical methods employing different formulations are available. The problem of hysteresis losses can be scrutinized via an eddy current formulation of the classical theory of electromagnetism. The difficulty of the problem lies in the non-linear resistivity of the superconducting region. The steep transition between the superconducting and the normal states often causes convergence problems for the most common finite element method based programs. The integration methods suffer from full system matrices and, thus, restrict the number of elements to a few thousands at most. The so-called T - {psi} formulation and the use of edge elements, or more precisely Whitney 1-forms, within the finite element method have proved to be a very suitable method for hysteresis loss simulations of different geometries. In this paper we consider making such finite element method software from first steps, employing differential geometry and forms.
Directory of Open Access Journals (Sweden)
Pattnaik Monalisha
2015-01-01
Full Text Available In this paper, the concept of fuzzy Non-Linear Programming Technique is applied to solve an economic order quantity (EOQ model for restricted budget and space. Since various types of uncertainties and imprecision are inherent in real inventory problems, they are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by the usual probabilistic models. The questions are how to define inventory optimization tasks in such environment and how to interpret the optimal solutions. This paper allow the modification of the Single item EOQ model in presence of fuzzy decision making process where demand is related to the unit price, and the setup cost varies with the quantity produced/Purchased. The modification of objective function, budget, and storage area in the presence of imprecisely estimated parameters are considered. The model is developed by employing different approaches over an infinite planning horizon. It incorporates all the concepts of a fuzzy arithmetic approach and comparative analysis with other non linear models. Investigation of the properties of an optimal solution allows developing an algorithm whose validity is illustrated by an example problem, and two and three dimensional diagrams are represented to this application through MATL(R2009a software. Sensitivity analysis of the optimal solution is studied with respect to the changes of different parameter values for obtaining managerial insights of the decision problem.
DEFF Research Database (Denmark)
Tornøe, Christoffer Wenzel; Agersø, Henrik; Nielsen, Henrik Aalborg
2004-01-01
In this paper, the two non-linear mixed-effects programs NONMEM and NLME were compared for their use in population pharmacokinetic/pharmacodynamic (PK/PD) modelling. We have described the first-order conditional estimation (FOCE) method as implemented in NONMEM and the alternating algorithm in NLME...... proposed by Lindstrom and Bates. The two programs were tested using clinical PK/PD data of a new gonadotropin-releasing hormone (GnRH) antagonist degarelix currently being developed for prostate cancer treatment. The pharmacokinetics of intravenous administered degarelix was analysed using a three...
DEFF Research Database (Denmark)
Bozkurt, Hande; Quaglia, Alberto; Gernaey, Krist;
technologies to build a superstructure, the design problem was formulated as a Mixed Integer Nonlinear Programming problem (MINLP). The tool generates many process alternatives and evaluates them with respect to their optimality. The objective function minimizes the operation cost. The design problem is thus...... with the help of the tool. The resulting solutions to the optimization problem are discussed in detail....
求解非线性规划的原始对偶内点法%A Primal-dual Interior Point Method for Nonlinear Programming
Institute of Scientific and Technical Information of China (English)
张珊; 姜志侠
2008-01-01
In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way.
Bielawa, R. L.
1976-01-01
The differential equations of motion for the lateral and torsional deformations of a nonlinearly twisted rotor blade in steady flight conditions together with those additional aeroelastic features germane to composite bearingless rotors are derived. The differential equations are formulated in terms of uncoupled (zero pitch and twist) vibratory modes with exact coupling effects due to finite, time variable blade pitch and, to second order, twist. Also presented are derivations of the fully coupled inertia and aerodynamic load distributions, automatic pitch change coupling effects, structural redundancy characteristics of the composite bearingless rotor flexbeam - torque tube system in bending and torsion, and a description of the linearized equations appropriate for eigensolution analyses. Three appendixes are included presenting material appropriate to the digital computer program implementation of the analysis, program G400.
Winebrake, James J; Corbett, James J; Wang, Chengfeng; Farrell, Alexander E; Woods, Pippa
2005-04-01
Emissions from passenger ferries operating in urban harbors may contribute significantly to emissions inventories and commuter exposure to air pollution. In particular, ferries are problematic because of high emissions of oxides of nitrogen (NOx) and particulate matter (PM) from primarily unregulated diesel engines. This paper explores technical solutions to reduce pollution from passenger ferries operating in the New York-New Jersey Harbor. The paper discusses and demonstrates a mixed-integer, non-linear programming model used to identify optimal control strategies for meeting NOx and PM reduction targets for 45 privately owned commuter ferries in the harbor. Results from the model can be used by policy-makers to craft programs aimed at achieving least-cost reduction targets.
Computer-aided Framework for Design of Pure, Mixed and Blended Products
DEFF Research Database (Denmark)
2015-01-01
This paper presents a framework for computer-aided design of pure, mixed and blended chemical based products. The framework is a systematic approach to convert a Computer-aided Molecular, Mixture and Blend Design (CAMbD) formulation, based on needs and target properties, into a mixed integer non-......-linear program (MINLP). TheMINLP is sequentially solved through a decomposed optimization approach to solve the possibly large MINLP in a smaller set of sub-problems. The framework application is highlighted through a solvent design case study.......This paper presents a framework for computer-aided design of pure, mixed and blended chemical based products. The framework is a systematic approach to convert a Computer-aided Molecular, Mixture and Blend Design (CAMbD) formulation, based on needs and target properties, into a mixed integer non...
Institute of Scientific and Technical Information of China (English)
Gao Ning; Sun Wei
2015-01-01
Based on the study of supply chain (SC) and SC optimization in engineering projects, a mixed integer nonlinear programming (MINLP) optimization model is developed to minimize the total SC cost for international petrochemical en-gineering projects. A steam cracking project is selected and analyzed, from which typical SC characteristics in international engineering projects in the area of petrochemical industry are summarized. The MINLP model is therefore developed and applied to projects with detailed data. The optimization results are analyzed and compared by the MINLP model, indicat-ing that they are appropriate to SC management practice in engineering projects, and are consistent with the optimal price-effective strategy in procurement. As a result, the model could provide useful guidance to SC optimization of international engineering projects in petrochemical industry, and improve SC management by selecting more reliable and qualiifed part-ner enterprises in SC for the project.
Svalbonas, V.; Levine, H.; Ogilvie, P.
1975-01-01
Engineering programming information is presented for the STARS-2P (shell theory automated for rotational structures-2P (plasticity)) digital computer program, and FORTRAN 4 was used in writing the various subroutines. The execution of this program requires the use of thirteen temporary storage units. The program was initially written and debugged on the IBM 370-165 computer and converted to the UNIVAC 1108 computer, where it utilizes approximately 60,000 words of core. Only basic FORTRAN library routines are required by the program: sine, cosine, absolute value, and square root.
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Energy Technology Data Exchange (ETDEWEB)
Geniet, F; Leon, J [Physique Mathematique et Theorique, CNRS-UMR 5825, 34095 Montpellier (France)
2003-05-07
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
Institute of Scientific and Technical Information of China (English)
聂普焱; 彭小飞
2004-01-01
We transform the system of nonlinear equations into a nonlinear programming problem, which is attacked by feasible sequential quadratic programming(FSQP) method.We do not employ standard least square approach.We divide the equations into two groups. One group, which contains the equations with zero residual,is treated as equality constraints. The square of other equations is regarded as objective function. Two groups are updated in every step.Therefore, the subproblem is updated at every step, which avoids the difficulty that it is required to lie in feasible region for FSQP.
Jackson, M E; Gnadt, J W
1999-03-01
The object-oriented graphical programming language LabView was used to implement the numerical solution to a computational model of saccade generation in primates. The computational model simulates the activity and connectivity of anatomical strictures known to be involved in saccadic eye movements. The LabView program provides a graphical user interface to the model that makes it easy to observe and modify the behavior of each element of the model. Essential elements of the source code of the LabView program are presented and explained. A copy of the model is available for download from the internet.
El-Qulity, Said Ali; Mohamed, Ali Wagdy
2016-01-01
This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness.
Energy Technology Data Exchange (ETDEWEB)
Watson, C. R.; Cochran, M. I.; Thomas, J. M.; Eberhardt, L. L
1977-11-01
To find a mathematical model which describes (fits) data from a process which is fundamentally nonlinear, one usually uses nonlinear least-squares techniques on maxicomputers. These usually run in batch mode with the user supplying a model and initial ''guesstimates'' of its parameters. However, fitting the model to the data can be considered an art because computer algorithms either converge to true solutions, or converge to erroneous solutions, or fail to converge, depending on the quality of the guesstimates. It is slow and expensive to try enough runs to obtain a logical solution (unless one makes lucky initial guesses). An interactive BASIC procedure was developed which runs on either the PDP-11/34 under RT-11 or the PDP-11/70 under IAS. These programs help the investigator quickly fit the model to the data and statistically evaluate the differences between the two. The parameter estimates thus determined may then be used as guesstimates for the more precise maxicomputer codes. The key to the system is the re-enterant nature of the curve fitting routine (allowed only with a language such as INTERPRETED BASIC). The user supplies estimates of the parameters for the selected model (18 are currently available, and users can easily write their own). The computer tries a few iterative refinements (by using Taylor series expansion of partial derivatives to obtain linearization) of the estimates in an attempt to minimize the deviations between the values predicted by the model and the observed data. The user can observe as the program executes whether the result is a logical solution. If not, he may stop the process, enter new guesstimates, and examine those results, try again, or select a new model.
Ko, Andi Setiady; Chang, Ni-Bin
2008-07-01
Energy supply and use is of fundamental importance to society. Although the interactions between energy and environment were originally local in character, they have now widened to cover regional and global issues, such as acid rain and the greenhouse effect. It is for this reason that there is a need for covering the direct and indirect economic and environmental impacts of energy acquisition, transport, production and use. In this paper, particular attention is directed to ways of resolving conflict between economic and environmental goals by encouraging a power plant to consider co-firing biomass and refuse-derived fuel (RDF) with coal simultaneously. It aims at reducing the emission level of sulfur dioxide (SO(2)) in an uncertain environment, using the power plant in Michigan City, Indiana as an example. To assess the uncertainty by a comparative way both deterministic and grey nonlinear mixed integer programming (MIP) models were developed to minimize the net operating cost with respect to possible fuel combinations. It aims at generating the optimal portfolio of alternative fuels while maintaining the same electricity generation simultaneously. To ease the solution procedure stepwise relaxation algorithm was developed for solving the grey nonlinear MIP model. Breakeven alternative fuel value can be identified in the post-optimization stage for decision-making. Research findings show that the inclusion of RDF does not exhibit comparative advantage in terms of the net cost, albeit relatively lower air pollution impact. Yet it can be sustained by a charge system, subsidy program, or emission credit as the price of coal increases over time.
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nanda, Sudarsan
2013-01-01
"Nonlinear analysis" presents recent developments in calculus in Banach space, convex sets, convex functions, best approximation, fixed point theorems, nonlinear operators, variational inequality, complementary problem and semi-inner-product spaces. Nonlinear Analysis has become important and useful in the present days because many real world problems are nonlinear, nonconvex and nonsmooth in nature. Although basic concepts have been presented here but many results presented have not appeared in any book till now. The book could be used as a text for graduate students and also it will be useful for researchers working in this field.
Energy Technology Data Exchange (ETDEWEB)
Biffle, J.H.
1993-02-01
JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.
Energy Technology Data Exchange (ETDEWEB)
Biffle, J.H.; Blanford, M.L.
1994-05-01
JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.
Intramolecular and nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Davis, M.J. [Argonne National Laboratory, IL (United States)
1993-12-01
Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.
Arneson, Heather M.; Dousse, Nicholas; Langbort, Cedric
2014-01-01
We consider control design for positive compartmental systems in which each compartment's outflow rate is described by a concave function of the amount of material in the compartment.We address the problem of determining the routing of material between compartments to satisfy time-varying state constraints while ensuring that material reaches its intended destination over a finite time horizon. We give sufficient conditions for the existence of a time-varying state-dependent routing strategy which ensures that the closed-loop system satisfies basic network properties of positivity, conservation and interconnection while ensuring that capacity constraints are satisfied, when possible, or adjusted if a solution cannot be found. These conditions are formulated as a linear programming problem. Instances of this linear programming problem can be solved iteratively to generate a solution to the finite horizon routing problem. Results are given for the application of this control design method to an example problem. Key words: linear programming; control of networks; positive systems; controller constraints and structure.
Characterization of Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes
2016-04-20
Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 62601F...AFRL-RV-PS- AFRL-RV-PS- TR-2015-0182 TR-2015-0182 CHARACTERIZATION OF NON-LINEARIZED SPACECRAFT RELATIVE MOTION USING NONLINEAR NORMAL MODES Eric...STATEMENT. THOMAS LOVELL PAUL HAUSGEN, Ph.D. Program Manager Technical Advisor, Spacecraft Component Technology JOHN BEAUCHEMIN Chief Engineer
Institute of Scientific and Technical Information of China (English)
金中; 濮定国; 张宇; 蔡力
2008-01-01
A mechanism for proving global convergence in filter-SQP(sequence of quadratic programming)method with the nonlinear complementarity problem(NCP)function is described for constrained nonlinear optimization problem.We introduce an NCP function into the filter and construct a new SQP-filter algorithm.Such methods are characterized by their use of the dominance concept of multi-objective optimization,instead of a penalty parameter whose adjustment can be problematic.We prove that the algorithm has global convergence and superlinear convergence rates under some mild conditions.
Zhu, Hong-Ming; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2016-01-01
We present a direct approach to non-parametrically reconstruct the linear density field from an observed non-linear map. We solve for the unique displacement potential consistent with the non-linear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to $k\\sim 1\\ h/\\mathrm{Mpc}$ with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully non-linear fields, potentially substantially expanding the BAO and RSD information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates t
Nonlinear dynamics of structures
Oller, Sergio
2014-01-01
This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics. This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects. Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution are studied, and the theoretical concepts and its programming algorithms are presented.
Nonlinear optomechanics with graphene
Shaffer, Airlia; Patil, Yogesh Sharad; Cheung, Hil F. H.; Wang, Ke; Vengalattore, Mukund
2016-05-01
To date, studies of cavity optomechanics have been limited to exploiting the linear interactions between the light and mechanics. However, investigations of quantum signal transduction, quantum enhanced metrology and manybody physics with optomechanics each require strong, nonlinear interactions. Graphene nanomembranes are an exciting prospect for realizing such studies due to their inherently nonlinear nature and low mass. We fabricate large graphene nanomembranes and study their mechanical and optical properties. By using dark ground imaging techniques, we correlate their eigenmode shapes with the measured dissipation. We study their hysteretic response present even at low driving amplitudes, and their nonlinear dissipation. Finally, we discuss ongoing efforts to use these resonators for studies of quantum optomechanics and force sensing. This work is supported by the DARPA QuASAR program through a Grant from the ARO.
Nonlinear Analysis of Buckling
Directory of Open Access Journals (Sweden)
Psotný Martin
2014-06-01
Full Text Available The stability analysis of slender web loaded in compression was presented. To solve this problem, a specialized computer program based on FEM was created. The nonlinear finite element method equations were derived from the variational principle of minimum of potential energy. To obtain the nonlinear equilibrium paths, the Newton-Raphson iteration algorithm was used. Corresponding levels of the total potential energy were defined. The peculiarities of the effects of the initial imperfections were investigated. Special attention was focused on the influence of imperfections on the post-critical buckling mode. The stable and unstable paths of the nonlinear solution were separated. Obtained results were compared with those gained using ANSYS system.
Energy Technology Data Exchange (ETDEWEB)
Turner, D. D. [National Oceanic and Atmospheric Administration (NOAA), Boulder, CO (United States). Earth System Research Lab.; Knuteson, R. O. [Univ. of Wisconsin, Madison, WI (United States); Revercomb, H. E. [Univ. of Wisconsin, Madison, WI (United States); Dedecker, R. G. [Univ. of Wisconsin, Madison, WI (United States); Feltz, W. F. [Univ. of Wisconsin, Madison, WI (United States)
2004-09-01
Mercury Cadmium Telluride (MCT) detectors provide excellent sensitivity to infrared radiation and are used in passive infrared remote sensors such as the Atmospheric Emitted Radiance Interferometer (AERI). However, MCT detectors have a nonlinear response and thus this nonlinearity must be characterized and corrected to provide accurate infrared radiance observations. This paper discusses the significance of the nonlinearity correction applied to AERI data and its impacts on the parameters retrieved from the AERI spectra. It also evaluates the accuracy of the scheme used to determine the nonlinearity of the MCT detectors used in the Atmospheric Radiation Measurement (ARM) Program’s AERIs.
Optimal scheduling strategy for Elevator control based on nonlinear programming%基于非线性规划的电梯调度研究
Institute of Scientific and Technical Information of China (English)
陈希; 麦雪湖; 魏景焕
2011-01-01
针对上下班高峰期电梯分区调度的特点,本文首先利用Newton迭代的方法求出了不同分区下电梯平均运行时间t的具体数值,并用Matlab重新拟合出t的二次函数式,进而建立关于所有分区平均运行时间总和最小的非线性整数规划模型,通过计算机搜索算法求解出最优的电梯分区调度方案.结果发明这种方法容易操作,同时又具有很高的可用性和推广性.%We analyzed the fact of elevator running during the peak time, using the method of Newton iterationcal calculated all the average waiting time of elevators in different partition. Then taking passenger' waiting time as objective function, established a nonlinear programming model to work out the solutions. The answer shows that the model attains the purpose of energy saving and Customer Satisfaction improvement
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D.; Leung, Daniel; Liu, Norman; Meadows, Brian K.; Gordon, Frank; Bulsara, Adi R.; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
Nonlinear Modelling of Low Frequency Loudspeakers
DEFF Research Database (Denmark)
Olsen, Erling Sandermann
1997-01-01
In the Danish LoDist project on distortion from dynamic low-frequency loudspeakers, a detailed nonlinear model of loudspeakers has been developed. The model has been implemented in a PC program so that it can be used to create signals for listening tests and analysis. Also, different methods...... for describing the nonlinearities have been developed. Different aspects of modelling loudspeaker nonlinearities are discussed, and the program is briefly described....
Nonlinear Modelling of Low Frequency Loudspeakers
DEFF Research Database (Denmark)
Olsen, Erling Sandermann
1997-01-01
In the Danish LoDist project on distortion from dynamic low frequency loudspeakers a detailed nonlinear model of loudspeakers has been developed. The model has been implemented in a PC program so that it can be used to create signals for listening tests and analysis. Also, different methods...... for describing the nonlinearities have been developed. Different aspects of modelling loudspeaker nonlinearities are discussed and the program is briefly demonstrated....
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. (Bologna Univ. (Italy). Dipt. di Fisica)
1989-01-01
Research in nonlinear dynamics is rapidly expanding and its range of applications is extending beyond the traditional areas of science where it was first developed. Indeed while linear analysis and modelling, which has been very successful in mathematical physics and engineering, has become a mature science, many elementary phenomena of intrinsic nonlinear nature were recently experimentally detected and investigated, suggesting new theoretical work. Complex systems, as turbulent fluids, were known to be governed by intrinsically nonlinear laws since a long time ago, but received purely phenomenological descriptions. The pioneering works of Boltzmann and Poincare, probably because of their intrinsic difficulty, did not have a revolutionary impact at their time; it is only very recently that their message is reaching a significant number of mathematicians and physicists. Certainly the development of computers and computer graphics played an important role in developing geometric intuition of complex phenomena through simple numerical experiments, while a new mathematical framework to understand them was being developed.
Stochastic Nonlinear Aeroelasticity
2009-01-01
STOCHASTIC NONLINEAR AEROELASTICITY 5a. CONTRACT NUMBER In- house 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 0601102 6. AUTHOR(S) Philip S...ABSTRACT This report documents the culmination of in- house work in the area of uncertainty quantification and probabilistic techniques for... coff U∞ cs ea lw cw Figure 6: Wing and store geometry (left), wing box structural model (middle), flutter distribution (right
Nonlinear airship aeroelasticity
Bessert, N.; Frederich, O.
2005-12-01
The aeroelastic derivatives for today's aircraft are calculated in the concept phase using a standard procedure. This scheme has to be extended for large airships, due to various nonlinearities in structural and aerodynamic behaviour. In general, the structural model of an airship is physically as well as geometrically nonlinear. The main sources of nonlinearity are large deformations and the nonlinear material behaviour of membranes. The aerodynamic solution is also included in the nonlinear problem, because the deformed airship influences the surrounding flow. Due to these nonlinearities, the aeroelastic problem for airships can only be solved by an iterative procedure. As one possibility, the coupled aerodynamic and structural dynamic problem was handled using linked standard solvers. On the structural side, the Finite-Element program package ABAQUS was extended with an interface to the aerodynamic solver VSAERO. VSAERO is based on the aerodynamic panel method using potential flow theory. The equilibrium of the internal structural and the external aerodynamic forces leads to the structural response and a trimmed flight state for the specified flight conditions (e.g. speed, altitude). The application of small perturbations around a trimmed state produces reaction forces and moments. These constraint forces are then transferred into translational and rotational acceleration fields by performing an inertia relief analysis of the disturbed structural model. The change between the trimmed flight state and the disturbed one yields the respective aeroelastic derivatives. By including the calculated derivatives in the linearised equation of motion system, it is possible to judge the stability and controllability of the investigated airship.
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
Zaghian, Maryam; Cao, Wenhua; Liu, Wei; Kardar, Laleh; Randeniya, Sharmalee; Mohan, Radhe; Lim, Gino
2017-03-01
Robust optimization of intensity-modulated proton therapy (IMPT) takes uncertainties into account during spot weight optimization and leads to dose distributions that are resilient to uncertainties. Previous studies demonstrated benefits of linear programming (LP) for IMPT in terms of delivery efficiency by considerably reducing the number of spots required for the same quality of plans. However, a reduction in the number of spots may lead to loss of robustness. The purpose of this study was to evaluate and compare the performance in terms of plan quality and robustness of two robust optimization approaches using LP and nonlinear programming (NLP) models. The so-called "worst case dose" and "minmax" robust optimization approaches and conventional planning target volume (PTV)-based optimization approach were applied to designing IMPT plans for five patients: two with prostate cancer, one with skull-based cancer, and two with head and neck cancer. For each approach, both LP and NLP models were used. Thus, for each case, six sets of IMPT plans were generated and assessed: LP-PTV-based, NLP-PTV-based, LP-worst case dose, NLP-worst case dose, LP-minmax, and NLP-minmax. The four robust optimization methods behaved differently from patient to patient, and no method emerged as superior to the others in terms of nominal plan quality and robustness against uncertainties. The plans generated using LP-based robust optimization were more robust regarding patient setup and range uncertainties than were those generated using NLP-based robust optimization for the prostate cancer patients. However, the robustness of plans generated using NLP-based methods was superior for the skull-based and head and neck cancer patients. Overall, LP-based methods were suitable for the less challenging cancer cases in which all uncertainty scenarios were able to satisfy tight dose constraints, while NLP performed better in more difficult cases in which most uncertainty scenarios were hard to meet
2015-01-01
From the Back Cover: The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications re...
Introduction to nonlinear finite element analysis
Kim, Nam-Ho
2015-01-01
This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: · Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems · Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory · ...
Institute of Scientific and Technical Information of China (English)
孔亮亮; 江建慧; 肖杰; 蒋园园
2012-01-01
为了快速而准确地估计ARM处理器上的程序执行时间,研究了基于模拟的非线性程序执行时间估计器的结构.它由程序功能剖面生成模块和程序执行时间预测模块串联而成.程序功能剖面生成模块直接用精确指令模拟器Sim-profile实现；而基于程序执行中的动态指令数与执行时间在处理器上的非线性关系,对于程序执行时间预测模块的实现,首先设计了一种人工神经网络方案,再根据对人工神经网络局限性的判断,如局部最优问题、不适于解决小样本的回归、网络拓扑结构依赖先验知识等缺点,又提出了基于最小二乘支持向量机的方法.实验证明,这些非线性方法,特别是基于最小二乘支持向量机的方法,可以用较低的模拟代价获得较高的程序执行时间估计精度.%In order to accurately estimate execution cycles of programs running on ARM architectures as soon as possible, a simulation-based non-linear estimator is proposed. The estimator consists of two cascade modules: profiling program function module and program execution time prediction module. The module of profiling program function can be directly implemented by Sim-profile, an instruction-accurate simulator. According to the non-linear behavior of the program execution time in advanced processors and the dynamic instruction counts during program executions, the program execution time prediction module is implemented by an artificial neural network (ANN). However, besides the problem of local minimization, ANN is not suited to solve small-sample set regression. It depends on the priori knowledge of designers, which could determine the topology of the model and finally impact its performance. In order to conquer the limitations of ANN, a non-linear method based on the least squares support vector machine (LS-SVM) is further proposed to map the number of executed instructions into execution cycle counts. Experimental results show
Non-linear canonical correlation
van der Burg, Eeke; de Leeuw, Jan
1983-01-01
Non-linear canonical correlation analysis is a method for canonical correlation analysis with optimal scaling features. The method fits many kinds of discrete data. The different parameters are solved for in an alternating least squares way and the corresponding program is called CANALS. An
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
Institute of Scientific and Technical Information of China (English)
1996-01-01
3.1 A Unified Nonlinear Feedback Functional Method for Study Both Control and Synchronization of Spatiotemporal Chaos Fang Jinqing Ali M. K. (Department of Physics, The University of Lethbridge,Lethbridge, Alberta T1K 3M4,Canada) Two fundamental questions dominate future chaos control theories.The first is the problem of controlling hyperchaos in higher dimensional systems.The second question has yet to be addressed:the problem of controlling spatiotemporal chaos in a spatiotemporal system.In recent years, control and synchronization of spatiotemporal chaos and hyperchaos have became a much more important and challenging subject. The reason for this is the control and synchronism of such behaviours have extensive and great potential of interdisciplinary applications, such as security communication, information processing, medicine and so on. However, this subject is not much known and remains an outstanding open.
Parallel Nonlinear Optimization for Astrodynamic Navigation Project
National Aeronautics and Space Administration — CU Aerospace proposes the development of a new parallel nonlinear program (NLP) solver software package. NLPs allow the solution of complex optimization problems,...
非线性编辑系统分析及使用技巧%Application of Nonlinear Editing System in TV Program Producation
Institute of Scientific and Technical Information of China (English)
杨晓艳
2000-01-01
分析了非线性编辑系统的主要特点和Media 100的压缩技术，并对Media 100的使用提出了自己的见解。%The main features of nonlinear editing system, the compression technology inMedia 100 and the application techniques of Media 100 were analysed.
Institute of Scientific and Technical Information of China (English)
周丽美; 张立卫
2005-01-01
A system of differential equations is constructed to find Kuhn-Tucker points of a nonlinear programming problem with both equality and inequality constraints. It is proved that the Kuhn-Tucker point of the nonlinear programming problem is an asymptotically stable equilibrium point of the differential system and a numerical algorithm is given based on the numerical integration of the proposed system of ordinary differential equations.The convergence theorem of the numerical algorithm is demonstrated. Several illustrative examples show the effectiveness of the algorithm.%为了寻找带有等式约束和不等式约束的非线性规划问题的Kuhn-Tucker点,给出了一种微分方程系统.在一定的条件下,证明了非线性规划问题的Kuhn-Tucker点是微分方程系统的渐进稳定平衡点,并且基于一般微分方程系统的数值积分建立了一个数值算法,然后给出了该数值算法的收敛性定理.数值算例表明了该算法的有效性.
The nonlinear fixed gravimetric boundary value problem
Institute of Scientific and Technical Information of China (English)
于锦海; 朱灼文
1995-01-01
The properly-posedness of the nonlinear fixed gravimetric boundary value problem is shown with the help of nonlinear functional analysis and a new iterative method to solve the problem is also given, where each step of the iterative program is reduced to solving one and the same kind of oblique derivative boundary value problem with the same type. Furthermore, the convergence of the iterative program is proved with Schauder estimate of elliptic differential equation.
Nonlinear Materials Characterization Facility
Federal Laboratory Consortium — The Nonlinear Materials Characterization Facility conducts photophysical research and development of nonlinear materials operating in the visible spectrum to protect...
Nonlinear singular vectors and nonlinear singular values
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. The optimization problem related to the determination of nonlinear singular vectors and singular values is formulated. The general idea of this approach is demonstrated by a simple two-dimensional quasigeostrophic model in the atmospheric and oceanic sciences. The advantage and its applications of the new method to the predictability, ensemble forecast and finite-time nonlinear instability are discussed. This paper makes a necessary preparation for further theoretical and numerical investigations.
NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS
Institute of Scientific and Technical Information of China (English)
PENG SHIGE
2005-01-01
This paper deals with nonlinear expectations. The author obtains a nonlinear generalization of the well-known Kolmogorov's consistent theorem and then use it to construct filtration-consistent nonlinear expectations via nonlinear Markov chains. Compared to the author's previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probability measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations.The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.
Large nonlinear w$_{\\infty}$ algebras from nonlinear integrable deformations of self dual gravity
Castro, C
1994-01-01
A proposal for constructing a universal nonlinear {\\hat W}_{\\infty} algebra is made as the symmetry algebra of a rotational Killing-symmetry reduction of the nonlinear perturbations of Moyal-Integrable deformations of D=4 Self Dual Gravity (IDSDG). This is attained upon the construction of a nonlinear bracket based on nonlinear gauge theories associated with infinite dimensional Lie algebras. A Quantization and supersymmetrization program can also be carried out. The relevance to the Kadomtsev-Petviashvili hierarchy, 2D dilaton gravity, quantum gravity and black hole physics is discussed in the concluding remarks.
Institute of Scientific and Technical Information of China (English)
袁晓; 利洁婷; 王世其
2011-01-01
本文针对某公司电力容量扩展问题，采用一元线性回归模型拟合未来10年的需求量，再建立0—1非线性整数规划模型，并将该模型的0—1变量连续化处理，采用遗传算法中的GENOCOP算法求解。%In this paper,the next 10- year demand of a company for power capacity is fitted by monadic linear regression model. A model for 0 - 1 nonlinear integer programming is built, and the 0 - 1 variables of the model are disposed continuously. It is solved by the GENOCOP algorithm of genetic algorithm.
几何非线性新梁柱单元及结构程序设计%A geometric nonlinear new beam-column element and structure program design
Institute of Scientific and Technical Information of China (English)
张俊峰; 王利娟; 郝际平; 李天
2011-01-01
基于更新拉格朗日构形的增量虚位移原理,在其势能项中引入了全部6个应力分量,采用可计人单元剪切变形影响的三次多项式插值函数,详细推导了考虑剪切变形及翘曲的空间梁一柱单元几何非线性切线刚度矩阵.根据面向对象的程序设计思想,将整个有限元域划分为8个基本类,在单元基类的基础上派生了新的单元类,采用C++语言编制了面向对象的空间钢结构分析程序.几何非线性算例分析结果表明,本文提出的理论分析方法和计算程序是正确的和高效的.%According to the increment virtual displacement principle based on the updated Lagrange configuration,the potential energy associated with all six stress components was taken into account. The cubic interpolation function which can be used to consider the shear deformation effects has been applied to derive the geometrical nonlinear stiffness matrix of the space beam-column element considering the shear deformation and warping effects. Based on the object-oriented design conception, the finite element analysis domain is divided into eight classes. A new class is derived from the base element class. Using C+ + language,the spatial steel frame advanced analysis program is complied. Numerical examples including both geometric and material nonlinearities are used to demonstrate the accuracy and efficiency of the proposed analytical method and computer program.
Dynamics and vibrations progress in nonlinear analysis
Kachapi, Seyed Habibollah Hashemi
2014-01-01
Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems. There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between th...
A mathematical model for optimization of an integrated network logistic design
Directory of Open Access Journals (Sweden)
Lida Tafaghodi
2011-10-01
Full Text Available In this study, the integrated forward/reverse logistics network is investigated, and a capacitated multi-stage, multi-product logistics network design is proposed by formulating a generalized logistics network problem into a mixed-integer nonlinear programming model (MINLP for minimizing the total cost of the closed-loop supply chain network. Moreover, the proposed model is solved by using optimization solver, which provides the decisions related to the facility location problem, optimum quantity of shipped product, and facility capacity. Numerical results show the power of the proposed MINLP model to avoid th sub-optimality caused by separate design of forward and reverse logistics networks and to handle various transportation modes and periodic demand.
DEFF Research Database (Denmark)
Karunanithi, A.T.; Achenie, L.E.K.; Gani, Rafiqul
2005-01-01
and then the second part is solved to determine the optimal mixture. The decomposition of the CAMD MINLP model into relatively easy to solve subproblems is essentially a partitioning of the constraints from the original set. This approach is illustrated through two case studies. The first case study involves...... the design of an optimal extractant for the separation of acetic acid from water by liquid-liquid extraction. The results suggest that the new extractant would be able to perform better than the extractant being widely used for this separation. The second case study is an industrial problem involving......This paper presents a novel computer-aided molecular/mixture design (CAMD) methodology for the design of optimal solvents and solvent mixtures. The molecular/mixture design problem is formulated as a mixed integer nonlinear programming (MINLP) model in which a performance objective...
Directory of Open Access Journals (Sweden)
Javid Jouzdani
2016-01-01
Full Text Available With the constantly increasing pressure of the competitive environment, supply chain (SC decision makers are forced to consider several aspects of business climate. More specifically, they should take into account the endogenous features (e.g., available means of transportation, and the variety of products and exogenous criteria (e.g., the environmental uncertainty, and transportation system conditions. In this paper, a mixed integer nonlinear programming (MINLP model for dynamic design of a supply chain network is proposed. In this model, multiple products and multiple transportation modes, the time value of money, traffic congestion, and both supply-side and demand-side uncertainties are considered. Due to the complexity of such models, conventional solution methods are not applicable; therefore, two hybrid Electromagnetism-Like Algorithms (EMA are designed and discussed for tackling the problem. The numerical results show the applicability of the proposed model and the capabilities of the solution approaches to the MINLP problem.
Comparing coefficients of nested nonlinear probability models
DEFF Research Database (Denmark)
Kohler, Ulrich; Karlson, Kristian Bernt; Holm, Anders
2011-01-01
In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general decomposi......In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general...... decomposition method that is unaffected by the rescaling or attenuation bias that arise in cross-model comparisons in nonlinear models. It recovers the degree to which a control variable, Z, mediates or explains the relationship between X and a latent outcome variable, Y*, underlying the nonlinear probability...
Development of Organic Nonlinear Optical Materials
1992-10-22
10 SOVRCE Of FUNO#NG NUM#E*S DM J .j PROGRAM PR0jECT TA5. ~ *0. I1I TITLE &Vila* So.Ivety ClaUMC400NJ Development of Organic NonLinear Optical Materials (U...0102-LF-014-6603 UNCLASSIFIED (U) AFOSR Contract: F4962040-C 0097 FINAL REPORT Development of Organic Nonlinear Optical Materials by J. Sounnk IL
Sensor Network Design for Nonlinear Processes
Institute of Scientific and Technical Information of China (English)
李博; 陈丙珍
2003-01-01
This paper presents a method to design a cost-optimal nonredundant sensor network to observe all variables in a general nonlinear process. A mixed integer linear programming model was used to minimize the cost with data classification to check the observability of all unmeasured variables. This work is a starting point for designing sensor networks for general nonlinear processes based on various criteria, such as reliability and accuracy.
Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong
2015-01-01
This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.
Distributed nonlinear optical response
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov
2005-01-01
The purpose of the research presented here is to investigate basic physical properties in nonlinear optical materials with delayed or nonlocal nonlinearity. Soliton propagation, spectral broadening and the influence of the nonlocality or delay of the nonlinearity are the main focusses in the work...
Noncommutative Nonlinear Supersymmetry
Nishino, H; Nishino, Hitoshi; Rajpoot, Subhash
2002-01-01
We present noncommutative nonlinear supersymmetric theories. The first example is a non-polynomial Akulov-Volkov-type lagrangian with noncommutative nonlinear global supersymmetry in arbitrary space-time dimensions. The second example is the generalization of this lagrangian to Dirac-Born-Infeld lagrangian with nonlinear supersymmetry realized in dimensions D=2,3,4 and 6 (mod 8).
Fiber Nonlinearities: A Tutorial
Institute of Scientific and Technical Information of China (English)
Govind P. Agrawal
2003-01-01
Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications,the Raman amplification being only one of the recent examples. In this tutorial I review the vario us nonlinear effects occurring in optical fibers from both standpoints..
Fiber Nonlinearities: A Tutorial
Institute of Scientific and Technical Information of China (English)
Govind; P.; Agrawal
2003-01-01
Fiber nonlinearities have long been regarded as being mostly harmful for fiber-optic communication systems. Over the last few years, however, the nonlinear effects are increasingly being used for practical telecommunications applications, the Raman amplification being only one of the recent examples. In this tutorial I review the various nonlinear effects occurring in optical fibers from both standpoints..
PBH tests for nonlinear systems
Kawano, Yu; Ohtsuka, Toshiyuki
2017-01-01
Recently, concepts of nonlinear eigenvalues and eigenvectors are introduced. In this paper, we establish connections between the nonlinear eigenvalues and nonlinear accessibility/observability. In particular, we provide a generalization of Popov- Belevitch-Hautus (PBH) test to nonlinear accessibilit
Rucker, Dale F.; Ferré, Ty P. A.
2004-08-01
A MATLAB program was developed to invert first arrival travel time picks from zero offset profiling borehole ground penetrating radar traces to obtain the electromagnetic wave propagation velocities in soil. Zero-offset profiling refers to a mode of operation wherein the centers of the bistatic antennae being lowered to the same depth below ground for each measurement. The inversion uses a simulated annealing optimization routine, whereby the model attempts to reduce the root mean square error between the measured and modeled travel time by perturbing the velocity in a ray tracing routine. Measurement uncertainty is incorporated through the presentation of the ensemble mean and standard deviation from the results of a Monte Carlo simulation. The program features a pre-processor to modify or delete travel time information from the profile before inversion and post-processing through presentation of the ensemble statistics of the water contents inferred from the velocity profile. The program includes a novel application of a graphical user interface to animate the velocity fitting routine.
Nonlinear dynamics and complexity
Luo, Albert; Fu, Xilin
2014-01-01
This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.
Christensen, Steen; Cooley, Richard L.
2006-01-01
This report introduces and documents the Uncertainty (UNC) Process, a new Process in MODFLOW-2000 that calculates uncertainty measures for model parameters and for predictions produced by the model. Uncertainty measures can be computed by various methods, but when regression is applied to calibrate a model (for example when using the Parameter-Estimation Process of MODFLOW-2000) it is advantageous to also use regression-based methods to quantify uncertainty. For this reason the UNC Process computes (1) confidence intervals for parameters of the Parameter-Estimation Process and (2) confidence and prediction intervals for most types of functions that can be computed by a MODFLOW-2000 model calibrated by the Parameter-Estimation Process. The types of functions for which the Process works include hydraulic heads, hydraulic head differences, head-dependent flows computed by the head-dependent flow packages for drains (DRN6), rivers (RIV6), general-head boundaries (GHB6), streams (STR6), drain-return cells (DRT1), and constant-head boundaries (CHD), and for differences between flows computed by any of the mentioned flow packages. The UNC Process does not allow computation of intervals for the difference between flows computed by two different flow packages. The report also documents three programs, RESAN2-2k, BEALE2-2k, and CORFAC-2k, which are valuable for the evaluation of results from the Parameter-Estimation Process and for the preparation of input values for the UNC Process. RESAN2-2k and BEALE2-2k are significant updates of the residual analysis and modified Beale's measure programs first published by Cooley and Naff (1990) and later modified for use with MODFLOWP (Hill, 1994) and MODFLOW-2000 (Hill and others, 2000). CORFAC-2k is a new program that computes correction factors to be used by UNC.
DEFF Research Database (Denmark)
Fournier, David A.; Skaug, Hans J.; Ancheta, Johnoel
2011-01-01
Many criteria for statistical parameter estimation, such as maximum likelihood, are formulated as a nonlinear optimization problem.Automatic Differentiation Model Builder (ADMB) is a programming framework based on automatic differentiation, aimed at highly nonlinear models with a large number...
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
Antonella Fiacca; Nikolaos Matzakos; Nikolaos S Papageorgiou; Raffaella Servadei
2001-11-01
In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all $\\mathbb{R}$. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of $\\mathbb{R}$. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).
DEFF Research Database (Denmark)
Du, Yigang
without iteration steps. The ASA is implemented in combination with Field II and extended to simulate the pulsed ultrasound fields. The simulated results from a linear array transducer are made by the ASA based on Field II, and by a released non-linear simulation program- Abersim, respectively....... The calculation speed of the ASA is increased approximately by a factor of 140. For the second harmonic point spread function the error of the full width is 1.5% at -6 dB and 6.4% at -12 dB compared to Abersim. To further investigate the linear and non-linear ultrasound fields, hydrophone measurements.......3% relative to the measurement from a 1 inch diameter transducer. A preliminary study for harmonic imaging using synthetic aperture sequential beamforming (SASB) has been demonstrated. A wire phantom underwater measurement is made by an experimental synthetic aperture real-time ultrasound scanner (SARUS...
Some nonlinear space decomposition algorithms
Energy Technology Data Exchange (ETDEWEB)
Tai, Xue-Cheng; Espedal, M. [Univ. of Bergen (Norway)
1996-12-31
Convergence of a space decomposition method is proved for a general convex programming problem. The space decomposition refers to methods that decompose a space into sums of subspaces, which could be a domain decomposition or a multigrid method for partial differential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems. Two {open_quotes}hybrid{close_quotes} algorithms are also presented. They converge faster than the additive one and have better parallelism than the multiplicative method. Numerical tests with a two level domain decomposition for linear, nonlinear and interface elliptic problems are presented for the proposed algorithms.
Procurement planning in oil refining industries considering blending operations
DEFF Research Database (Denmark)
Oddsdottir, Thordis Anna; Grunow, Martin; Akkerman, Renzo
2013-01-01
This paper addresses procurement planning in oil refining, which has until now only had limited attention in the literature. We introduce a mixed integer nonlinear programming (MINLP) model and develop a novel two-stage solution approach, which aims at computational efficiency while addressing...... the problems due to discrepancies between a non-linear and a linearized formulation. The proposed model covers realistic settings by allowing the blending of crude oil in storage tanks, by modeling storage tanks and relevant processing units individually, and by handling more crude oil types and quality...
Energy Technology Data Exchange (ETDEWEB)
Bustamante-Cedeno, Enrique; Arora, Sant [Industrial and Systems Engineering Division, Mechanical Engineering Department, University of Minnesota, 111 Church Street, S.E., Minneapolis, MN 55455 (United States)
2009-04-15
In this paper, a Constructive Heuristic Algorithm (CHA) is presented to solve the Transmission Network Expansion Planning Problem (TNEP), a complex non-convex Mixed Integer Non-Linear Programming (MINLP) problem with multiple local minima. In the proposed algorithm, the non-linearities are resolved through the following feature: when discrete decision variables are given, the model becomes linear in the continuous variables. A CHA is developed which improves the current solution by implementing multiple step simultaneous changes over a number of saturated transmission lines, in contrast to the approach traditionally followed, which implements one change at a time. Solutions to test problems are computed. (author)
Development of a Nonlinear Internal Wave Tactical Decision Aid
2016-06-07
of a Nonlinear Internal Wave Tactical Decision Aid 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER...Development of a Nonlinear Internal Wave Tactical Decision Aid Christopher R. Jackson Global Ocean Associates 6220 Jean Louise Way Alexandria...www.internalwaveatlas.com LONG-TERM GOALS The long term goal of the project is to develop a prediction methodology for the occurrence of nonlinear
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Ionescu, Tudor C.; Scherpen, Jacquelien M. A.
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Hankel operator are studied and yield promising results.
Directory of Open Access Journals (Sweden)
W. L. Fouché
1983-03-01
Full Text Available In this article we discuss some aspects of nonlinear functional analysis. It included reviews of Banach’s contraction theorem, Schauder’s fixed point theorem, globalising techniques and applications of homotopy theory to nonlinear functional analysis. The author emphasises that fundamentally new ideas are required in order to achieve a better understanding of phenomena which contain both nonlinear and definite infinite dimensional features.
Nonlinear Electrodynamics and QED
2003-01-01
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a guide for understanding the nature of the nonlinearity of electrodynamics at the subatomic level. Some established theories of nonlinear electrodynamics, namely, those of Mie, Born, and Infeld are presented in the language of the modern geometrical and topologi...
Institute of Scientific and Technical Information of China (English)
肖刚
2015-01-01
In order to decrease the fuel consumption under a finite thrust, a method of nonlinear program-ming is presented to solve the optimal control problem on the soft landing of a lunar probe.The lunar soft land-ing problem is transformed into a two point boundary value problem in mathematics.In consideration of the bound condition, applying on Lagrang principle, the two-point boundary value problem is converted into a pa-rameter optimization problem.The simulated result demonstrates that the proposed method leads to a success-ful implementation of the lunar soft landing, which shows that the proposed design scheme is effective.%为了减少有限推力作用下月球探测器软着陆所需的燃料消耗，提出了应用非线性规划方法来求解该最优控制问题。首先，将有限推力作用下月球软着陆问题转化为数学上的两点边值问题；在考虑边界条件的前提下，利用拉格朗日原理将该两点边值问题转化为针对控制变量的优化问题；然后应用非线性规划方法求解所形成的参数优化问题。实验仿真结果显示，该方法能够成功实现月面软着陆，表明提出的设计方法简单有效。
Kono, Mitsuo
2010-01-01
A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.
Nonlinear magnetic metamaterials.
Shadrivov, Ilya V; Kozyrev, Alexander B; van der Weide, Daniel W; Kivshar, Yuri S
2008-12-08
We study experimentally nonlinear tunable magnetic metamaterials operating at microwave frequencies. We fabricate the nonlinear metamaterial composed of double split-ring resonators where a varactor diode is introduced into each resonator so that the magnetic resonance can be tuned dynamically by varying the input power. We demonstrate that at higher powers the transmission of the metamaterial becomes power-dependent and, as a result, such metamaterial can demonstrate various nonlinear properties. In particular, we study experimentally the power-dependent shift of the transmission band and demonstrate nonlinearity-induced enhancement (or suppression) of wave transmission. (c) 2008 Optical Society of America
Organic nonlinear optical materials
Umegaki, S.
1987-01-01
Recently, it became clear that organic compounds with delocalized pi electrons show a great nonlinear optical response. Especially, secondary nonlinear optical constants of more than 2 digits were often seen in the molecular level compared to the existing inorganic crystals such as LiNbO3. The crystallization was continuously tried. Organic nonlinear optical crystals have a new future as materials for use in the applied physics such as photomodulation, optical frequency transformation, opto-bistabilization, and phase conjugation optics. Organic nonlinear optical materials, e.g., urea, O2NC6H4NH2, I, II, are reviewed with 50 references.
Nonlinearity-reduced interferometer
Wu, Chien-ming
2007-12-01
Periodic nonlinearity is a systematic error limiting the accuracy of displacement measurements at the nanometer level. It results from many causes such as the frequency mixing, polarization mixing, polarization-frequency mixing, and the ghost reflections. An interferometer having accuracy in displacement measurement of less than one-nanometer is necessary in nanometrology. To meet the requirement, the periodic nonlinearity should be less than deep sub-nanometer. In this paper, a nonlinearity-reduced interferometry has been proposed. Both the linear- and straightness-interferometer were tested. The developed interferometer demonstrated of a residual nonlinearity less than 25 pm.
Nonlinear Optimization with Financial Applications
Bartholomew-Biggs, Michael
2005-01-01
The book introduces the key ideas behind practical nonlinear optimization. Computational finance - an increasingly popular area of mathematics degree programs - is combined here with the study of an important class of numerical techniques. The financial content of the book is designed to be relevant and interesting to specialists. However, this material - which occupies about one-third of the text - is also sufficiently accessible to allow the book to be used on optimization courses of a more general nature. The essentials of most currently popular algorithms are described, and their performan
Lasers for nonlinear microscopy.
Wise, Frank
2013-03-01
Various versions of nonlinear microscopy are revolutionizing the life sciences, almost all of which are made possible because of the development of ultrafast lasers. In this article, the main properties and technical features of short-pulse lasers used in nonlinear microscopy are summarized. Recent research results on fiber lasers that will impact future instruments are also discussed.
Eaton, D F
1991-07-19
The current state of materials development in nonlinear optics is summarized, and the promise of these materials is critically evaluated. Properties and important materials constants of current commercial materials and of new, promising, inorganic and organic molecular and polymeric materials with potential in second- and third-order nonlinear optical applications are presented.
Billings, S. A.
1988-03-01
Time and frequency domain identification methods for nonlinear systems are reviewed. Parametric methods, prediction error methods, structure detection, model validation, and experiment design are discussed. Identification of a liquid level system, a heat exchanger, and a turbocharge automotive diesel engine are illustrated. Rational models are introduced. Spectral analysis for nonlinear systems is treated. Recursive estimation is mentioned.
Ionescu, T. C.; Scherpen, J. M. A.; Korytowski, A; Malanowski, K; Mitkowski, W; Szymkat, M
2009-01-01
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Christiansen, Peter Leth; Torner, L.
1999-01-01
We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear...
Controllability in nonlinear systems
Hirschorn, R. M.
1975-01-01
An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.
Menon, P. K. A.; Badgett, M. E.; Walker, R. A.
1992-01-01
Trajectory-control laws based on singular-perturbation theory and nonlinear dynamical modeling. Nonlinear maneuver autopilot commands flight-test trajectories of F-15 airplane. Underlying theory of controller enables separation of variables processed in fast and slow control loops, reducing amount of computation required.
Flexible scheduling model of crude oil operations under crude supply disturbance
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Today’s changeable market and resultant disturbance of crude oil supply require agile and flexible scheduling of crude oil operation. The objective of flexible scheduling is to keep stable crude oil op-eration and satisfy production demands under the circumstances of supply disturbance. In this paper, a new mixed integer non-linear programming (MINLP) formulation is set up for crude oil scheduling firstly, and then some heuristic rules worked out by some experts are proposed to linearize bilinear terms and prefix some binary variables in the MINLP model. These rules not only reduce the complexity of the MINLP model, but also can be used to solve the scheduling problems in various conditions. In case study, the new model with heuristic rules and the best models reported in the literature are com-pared and evaluated in three benchmark examples in the normal situation, and then three abnormal situations of supply delay are considered based on the new approach. The results of case study show that the new flexible approach can handle crude oil scheduling problems efficiently in both normal and abnormal conditions.
Flexible scheduling model of crude oil operations under crude supply disturbance
Institute of Scientific and Technical Information of China (English)
PAN Ming; QIAN Yu; LI Xiu-Xi
2009-01-01
Today's ohangeable market and resultant disturbance of orude oil supply require agile and flexible scheduling of crude oil operation. The objective of flexible scheduling is to keep stable crude oil op-eration and satisfy production demands under the circumstances of supply disturbance. In this paper, a new mixed integer non-linear programming (MINLP) formulation is set up for crude oil scheduling firstly, and then some heuristic rules worked out by some experts are proposed to linearize bilinear terms and prefix some binary variables in the MINLP model. These rules not only reduce the complexity of the MINLP model, but also can be used to solve the scheduling problems in various conditions. In oase study, the new model with heuristic rules and the best models reported in the literature are com-pared and evaluated in three benchmark examples in the normal situation, and then three abnormal situations of supply delay are considered based on the new approach. The results of case study show that the new flexible approach can handle crude oil scheduling problems efficiently in both normal and abnormal conditions.
Nonlinear optics and photonics
He, Guang S
2015-01-01
This book provides a comprehensive presentation on most of the major topics in nonlinear optics and photonics, with equal emphasis on principles, experiments, techniques, and applications. It covers many major new topics including optical solitons, multi-photon effects, nonlinear photoelectric effects, fast and slow light , and Terahertz photonics. Chapters 1-10 present the fundamentals of modern nonlinear optics, and could be used as a textbook with problems provided at the end of each chapter. Chapters 11-17 cover the more advanced topics of techniques and applications of nonlinear optics and photonics, serving as a highly informative reference for researchers and experts working in related areas. There are also 16 pages of color photographs to illustrate the visual appearances of some typical nonlinear optical effects and phenomena. The book could be adopted as a textbook for both undergraduates and graduate students, and serve as a useful reference work for researchers and experts in the fields of physics...
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
A Composite Algorithm for Mixed Integer Constrained Nonlinear Optimization.
1980-01-01
algorithm (FLEX) developed by Paviani and Himmelblau [53] is a direct search algorithm for constrained, nonlinear problems. It uses a variation on the...given in an appendix to Himmelblau [32]. Two changes were made to the program as listed in the rcference. Between card number 1340 and 1350 the...1972, pp. 293-308 (32] Himmelblau , D. M., Applied Nonlinear Programming, McGraw-Hill, 1972 (33] Himmelblau , D. M., "A Uniform Evaluation of Unconstrained
Zweig, George
2016-05-01
An earlier paper characterizing the linear mechanical response of the organ of Corti [J. Acoust. Soc. Am. 138, 1102-1121 (2015)] is extended to the nonlinear domain. Assuming the existence of nonlinear oscillators nonlocally coupled through the pressure they help create, the oscillator equations are derived and examined when the stimuli are modulated tones and clicks. The nonlinearities are constrained by the requirements of oscillator stability and the invariance of zero crossings in the click response to changes in click amplitude. The nonlinear oscillator equations for tones are solved in terms of the fluid pressure that drives them, and its time derivative, presumably a proxy for forces created by outer hair cells. The pressure equation is reduced to quadrature, the integrand depending on the oscillators' responses. The resulting nonlocally coupled nonlinear equations for the pressure, and oscillator amplitudes and phases, are solved numerically in terms of the fluid pressure at the stapes. Methods for determining the nonlinear damping directly from measurements are described. Once the oscillators have been characterized from their tone and click responses, the mechanical response of the cochlea to natural sounds may be computed numerically. Signal processing inspired by cochlear mechanics opens up a new area of nonlocal nonlinear time-frequency analysis.
Fast Programming Algorithm to Find Non-Linear Feedback Shift Register%快速寻找非线性反馈移位寄存器的编程算法
Institute of Scientific and Technical Information of China (English)
叶炜晨; 陈克非
2014-01-01
Non-linear feedback shift register (NLFSR) is a common device to generate pseudo-random sequences in stream cipher. However, there is still no effective mathematical algorithm to find NLFSRs for a given period or output sequence. This paper provides a quick method to find NLFSRs. This method is a programming algorithm based on compute unified device architecture (CUDA) and parallel computing, and can quickly find NLFSRs for the given period or output sequence. This method has very good performance on both simple and complex NLFSRs. With this new method, people can easily get a large amount of experimental data about NLFSRs. It will be a great help for the future research on the mathematical algorithm to find NLFSRs.%在流密码中，非线性反馈移位寄存器（non-linear feedback shift register，NLFSR）是一种常用的安全性较高的伪随机序列生成器。目前仍然没有一种普遍有效的数学算法，能够根据给定的序列或者序列周期，直接推导出NLFSR。提出了一种快速寻找NLFSR的编程算法。该算法基于统一计算架构（compute unified device architecture，CUDA）和并行计算来实现，计算速度快，尤其适用于处理高次数的复杂NLFSR。并且该算法可以快速大规模地计算出NLFSR，为未来研究寻找NLFSR的数学算法提供了大量的实验数据。
Explicit Nonlinear Model Predictive Control Theory and Applications
Grancharova, Alexandra
2012-01-01
Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...
A trust region algorithm for optimization with nonlinear equality and linear inequality constraints
Institute of Scientific and Technical Information of China (English)
陈中文; 韩继业
1996-01-01
A new algorithm of trust region type is presented to minimize a differentiable function ofmany variables with nonlinear equality and linear inequality constraints. Under the milder conditions, theglobal convergence of the main algorithm is proved. Moreover, since any nonlinear inequality constraint can beconverted into an equation by introducing a slack variable, the trust region method can be used in solving general nonlinear programming problems.
Agrawal, Govind P
2001-01-01
The Optical Society of America (OSA) and SPIE - The International Society for Optical Engineering have awarded Govind Agrawal with an honorable mention for the Joseph W. Goodman Book Writing Award for his work on Nonlinear Fiber Optics, 3rd edition.Nonlinear Fiber Optics, 3rd Edition, provides a comprehensive and up-to-date account of the nonlinear phenomena occurring inside optical fibers. It retains most of the material that appeared in the first edition, with the exception of Chapter 6, which is now devoted to the polarization effects relevant for light propagation in optical
Will Nonlinear Backcalculation Help?
DEFF Research Database (Denmark)
Ullidtz, Per
2000-01-01
demonstrates, that treating the subgrade as a nonlinear elastic material, can result in more realistic moduli and a much better agreement between measured and calculated stresses and strains.The response of nonlinear elastic materials can be calculated using the Finite Element Method (FEM). A much simpler...... approach is to use the Method of Equivalent Thicknesses (MET), modified for a nonlinear subgrade. The paper includes an example where moduli backcalculated using FEM, linear elastic theory and MET are compared. Stresses and strains predicted by the three methods are also compared to measured values...
Nonlinear graphene metamaterial
Nikolaenko, Andrey E; Atmatzakis, Evangelos; Luo, Zhiqiang; Shen, Ze Xiang; De Angelis, Francesco; Boden, Stuart A; Di Fabrizio, Enzo; Zheludev, Nikolay I
2012-01-01
We demonstrate that the broadband nonlinear optical response of graphene can be resonantly enhanced by more than an order of magnitude through hybridization with a plasmonic metamaterial,while retaining an ultrafast nonlinear response time of ~1 ps. Transmission modulation close to ~1% is seen at a pump uence of ~0.03 mJ/cm^2 at the wavelength of ~1600 nm. This approach allows to engineer and enhance graphene's nonlinearity within a broad wavelength range enabling applications in optical switching, mode-locking and pulse shaping.
Method for conducting nonlinear electrochemical impedance spectroscopy
Adler, Stuart B.; Wilson, Jamie R.; Huff, Shawn L.; Schwartz, Daniel T.
2015-06-02
A method for conducting nonlinear electrochemical impedance spectroscopy. The method includes quantifying the nonlinear response of an electrochemical system by measuring higher-order current or voltage harmonics generated by moderate-amplitude sinusoidal current or voltage perturbations. The method involves acquisition of the response signal followed by time apodization and fast Fourier transformation of the data into the frequency domain, where the magnitude and phase of each harmonic signal can be readily quantified. The method can be implemented on a computer as a software program.
Method for conducting nonlinear electrochemical impedance spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Adler, Stuart B.; Wilson, Jamie R.; Huff, Shawn L.; Schwartz, Daniel T.
2015-06-02
A method for conducting nonlinear electrochemical impedance spectroscopy. The method includes quantifying the nonlinear response of an electrochemical system by measuring higher-order current or voltage harmonics generated by moderate-amplitude sinusoidal current or voltage perturbations. The method involves acquisition of the response signal followed by time apodization and fast Fourier transformation of the data into the frequency domain, where the magnitude and phase of each harmonic signal can be readily quantified. The method can be implemented on a computer as a software program.
PRANC: Program for Analyzing Nonlinear Circuits.
1980-05-01
pin EL -,1 -lC~q RUN 210 I1 T’.. -(2 RUNll 32 0 1;1 T 7.-il _IONH),TYPE(N), CoFF CI1,1) COFF . 2). COFFRN 280 - , I_ I ,N 2S90 i 1’ -. 80F ( -f 3RUN 2800...INZR~ PA:T 07 THE NON1L-iNEO:RITY WITH THE LINER NTWK CR0 6-50 C CR0 660 T( COFF (:(,2).Efl0.00) GO TO 102 CR0 670 COl.L C2-TF:OT (Nn00,£2,T"yP7’ RUE
Dynamic structural correlation via nonlinear programming techniques
Ting, T.; Ojalvo, I. U.
1988-01-01
A solution to the correlation between structural dynamic test results and finite element analyses of the same components is presented in this paper. Basically, the method can be categorized as a Levenberg-Marquardt type Gauss-Newton method which requires only the differences between FE modal analyses and test results and their first derivatives with respect to preassigned design variables. With proper variable normalization and equation scaling, the method has been made numerically better-conditioned and the inclusion of the Levenberg-Marquardt technique overcomes any remaining difficulty encountered in inverting singular or near-singular matrices. An important feature is that each iteration requires only one function evaluation along with the associated design sensitivity analysis and so the procedure is computationally efficient.
Multipolar nonlinear nanophotonics
Smirnova, Daria
2016-01-01
Nonlinear nanophotonics is a rapidly developing field with many useful applications for a design of nonlinear nanoantennas, light sources, nanolasers, sensors, and ultrafast miniature metadevices. A tight confinement of the local electromagnetic fields in resonant photonic nanostructures can boost nonlinear optical effects, thus offering versatile opportunities for subwavelength control of light. To achieve the desired functionalities, it is essential to gain flexible control over the near- and far-field properties of nanostructures. Thus, both modal and multipolar analyses are widely exploited for engineering nonlinear scattering from resonant nanoscale elements, in particular for enhancing the near-field interaction, tailoring the far-field multipolar interference, and optimization of the radiation directionality. Here, we review the recent advances in this recently emerged research field ranging from metallic structures exhibiting localized plasmonic resonances to hybrid metal-dielectric and all-dielectric...
Solitons in nonlinear lattices
Kartashov, Yaroslav V; Torner, Lluis
2010-01-01
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are surveyed too, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions c...
Directory of Open Access Journals (Sweden)
Shakeeb Bin Hasan
2014-12-01
Full Text Available Contrary to traditional optical elements, plasmonic antennas made from nanostructured metals permit the localization of electromagnetic fields on length scales much smaller than the wavelength of light. This results in huge amplitudes for the electromagnetic field close to the antenna being conducive for the observation of nonlinear effects already at moderate pump powers. Thus, these antennas exhibit a promising potential to achieve optical frequency conversion and all-optical control of light at the nano-scale. This opens unprecedented opportunities for ultrafast nonlinear spectroscopy, sensing devices, on-chip optical frequency conversion, nonlinear optical metamaterials, and novel photon sources. Here, we review some of the recent advances in exploiting the potential of plasmonic antennas to realize robust nonlinear applications.
Leburn, Christopher; Reid, Derryck
2013-01-01
The field of ultrafast nonlinear optics is broad and multidisciplinary, and encompasses areas concerned with both the generation and measurement of ultrashort pulses of light, as well as those concerned with the applications of such pulses. Ultrashort pulses are extreme events – both in terms of their durations, and also the high peak powers which their short durations can facilitate. These extreme properties make them powerful experiment tools. On one hand, their ultrashort durations facilitate the probing and manipulation of matter on incredibly short timescales. On the other, their ultrashort durations can facilitate high peak powers which can drive highly nonlinear light-matter interaction processes. Ultrafast Nonlinear Optics covers a complete range of topics, both applied and fundamental in nature, within the area of ultrafast nonlinear optics. Chapters 1 to 4 are concerned with the generation and measurement of ultrashort pulses. Chapters 5 to 7 are concerned with fundamental applications of ultrasho...
DEFF Research Database (Denmark)
Nguyen-Duy, Khiem
and remains the prime source of energy in non-terrestrial applications such as those in sky-explorers. However, a renewable energy source is expensive, bulky, and its performance is weather dependent, which make testing of downstream converters very difficult. As a result, a nonlinear source emulator (NSE......) is a good solution to solve the problems associated with the use of real nonlinear sources in testing phases. However, a recent technical survey conducted during this work shows that most existing NSEs have only been concerned with simulating nonlinear systems in terrestrial applications. Furthermore......, their dynamic performance were not fast enough in order to imitate how a real nonlinear energy source would react under extreme conditions and operation modes. Particularly, a system in the sky can experience a step change of sunlight irradiation. Moreover, operation modes may include load step between nominal...
Introduction to nonlinear science
Nicolis, G
1995-01-01
One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...
Nonlinear magnetoinductive transmission lines
Lazarides, Nikos; Tsironis, G P
2011-01-01
Power transmission in one-dimensional nonlinear magnetic metamaterials driven at one end is investigated numerically and analytically in a wide frequency range. The nonlinear magnetic metamaterials are composed of varactor-loaded split-ring resonators which are coupled magnetically through their mutual inductances, forming thus a magnetoiductive transmission line. In the linear limit, significant power transmission along the array only appears for frequencies inside the linear magnetoinductive wave band. We present analytical, closed form solutions for the magnetoinductive waves transmitting the power in this regime, and their discrete frequency dispersion. When nonlinearity is important, more frequency bands with significant power transmission along the array may appear. In the equivalent circuit picture, the nonlinear magnetoiductive transmission line driven at one end by a relatively weak electromotive force, can be modeled by coupled resistive-inductive-capacitive (RLC) circuits with voltage-dependent cap...
Optimization under Nonlinear Constraints
1982-01-01
In this paper a timesaving method is proposed for maximizing likelihood functions when the parameter space is subject to nonlinear constraints, expressible as second order polynomials. The suggested approach is especially attractive when dealing with systems with many parameters.
Nonlinearity in nanomechanical cantilevers
DEFF Research Database (Denmark)
Villanueva Torrijo, Luis Guillermo; Karabalin, R. B.; Matheny, M. H.
2013-01-01
Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro-and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development....... These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation. DOI: 10.1103/PhysRevB.87.024304....... In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its...
Nonlinear Stokes Mueller Polarimetry
Samim, Masood; Barzda, Virginijus
2015-01-01
The Stokes Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations. The overall algebraic form of the polarimetry is preserved, where the incoming and outgoing radiations are represented by column vectors and the intervening medium is represented by a matrix. Expressions for the generalized nonlinear Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, expanded by higher-dimensional analogues of Pauli matrices. In all cases, the outgoing radiation is represented by the conventional $4\\times 1$ Stokes vector, while dimensions of the incoming radiation Stokes vector and Mueller matrix depend on the order of the process being examined. In addition, relation between nonlinear susceptibilities and the measured Mueller matrices are explicitly provided. Finally, the approach of combining linear and nonlinear optical elements is discussed within the context of polarim...
Adaptive and Nonlinear Control
1992-02-29
in [22], we also applied the concept of zero dynamics to the problem of exact linearization of a nonlinear control system by dynamic feedback. Exact ...nonlinear systems, although it was well-known that the conditions for exact linearization are very stringent and consequently do not apply to a broad...29th IEEE Conference n Decision and Control, Invited Paper delivered by Dr. Gilliam. Exact Linearization of Zero Dynamics, 29th IEEE Conference on
Nonlinear Optics and Turbulence
1992-10-01
currently at Queen Mary College, London Patrick Dunne, (Ph.D., 1987, M.I.T., Hydrodynamic Stability, Nonlinear Waves), 1987-1988. Alecsander Dyachenko...U I I I U I I 3 9 3 V. BIOGRAPHIES A. FACULTY BRUCE BAYLY, 31, Ph.D. 1986, Princeton University. Postdoctoral visiting member 1986-88 at Courant...Caputo, A. C. Newell, and M. Shelley , "Nonlinear Wave Propagation Through a Random Medium and Soliton Tunneling", Integrable Systems and
Yang, Qianli; Pitkow, Xaq
2015-03-01
Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.
Nonlinear Multiantenna Detection Methods
Directory of Open Access Journals (Sweden)
Chen Sheng
2004-01-01
Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.
Nonlinear systems in medicine.
Higgins, John P
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.
Handbook of nonlinear optical crystals
Dmitriev, Valentin G; Nikogosyan, David N
1991-01-01
This Handbook of Nonlinear Optical Crystals provides a complete description of the properties and applications of nonlinear crystals In addition, it presents the most important equations for calculating the main parameters of nonlinear frequency converters This comprehensive reference work will be of great value to all scientists and engineers working in nonlinear optics, quantum electronics and laser physics
Nonlinear waves in strongly interacting relativistic fluids
Fogaça, D A; Filho, L G Ferreira
2013-01-01
During the past decades the study of strongly interacting fluids experienced a tremendous progress. In the relativistic heavy ion accelerators, specially the RHIC and LHC colliders, it became possible to study not only fluids made of hadronic matter but also fluids of quarks and gluons. Part of the physics program of these machines is the observation of waves in this strongly interacting medium. From the theoretical point of view, these waves are often treated with li-nearized hydrodynamics. In this text we review the attempts to go beyond linearization. We show how to use the Reductive Perturbation Method to expand the equations of (ideal and viscous) relativistic hydrodynamics to obtain nonlinear wave equations. These nonlinear wave equations govern the evolution of energy density perturbations (in hot quark gluon plasma) or baryon density perturbations (in cold quark gluon plasma and nuclear matter). Different nonlinear wave equations, such as the breaking wave, Korteweg-de Vries and Burgers equations, are...
Nonlinear Approaches in Engineering Applications
Jazar, Reza
2012-01-01
Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...
Identifying nonlinear biomechanical models by multicriteria analysis
Srdjevic, Zorica; Cveticanin, Livija
2012-02-01
In this study, the methodology developed by Srdjevic and Cveticanin (International Journal of Industrial Ergonomics 34 (2004) 307-318) for the nonbiased (objective) parameter identification of the linear biomechanical model exposed to vertical vibrations is extended to the identification of n-degree of freedom (DOF) nonlinear biomechanical models. The dynamic performance of the n-DOF nonlinear model is described in terms of response functions in the frequency domain, such as the driving-point mechanical impedance and seat-to-head transmissibility function. For randomly generated parameters of the model, nonlinear equations of motion are solved using the Runge-Kutta method. The appropriate data transformation from the time-to-frequency domain is performed by a discrete Fourier transformation. Squared deviations of the response functions from the target values are used as the model performance evaluation criteria, thus shifting the problem into the multicriteria framework. The objective weights of criteria are obtained by applying the Shannon entropy concept. The suggested methodology is programmed in Pascal and tested on a 4-DOF nonlinear lumped parameter biomechanical model. The identification process over the 2000 generated sets of parameters lasts less than 20 s. The model response obtained with the imbedded identified parameters correlates well with the target values, therefore, justifying the use of the underlying concept and the mathematical instruments and numerical tools applied. It should be noted that the identified nonlinear model has an improved accuracy of the biomechanical response compared to the accuracy of a linear model.
Institute of Scientific and Technical Information of China (English)
梅成才; 潘修强; 陈军杰
2013-01-01
Robotic manipulators have long been applied to industrial welding in the past decades. This study pays an emphasis on coaching the manipulator not to slew its five joints into the weldment of two orthogonally intersecting cylinders. Direct Collocation with Nonlinear Programming (DCNLP) is the key numerical method adopted in this study which discretizes the time history of the mo-tion into N segments and approximates the solutions in each segment by cubic polynomials. The constraint functions are comprised of the inequality constraints and defect equations. As soon as the constraint functions converge, the optimal solution is found.% 为了实现相贯线接缝的自动焊接，提出了一种基于直接配置非线性规划方法（DCNLP）的焊道轨迹运动控制方法。以两圆柱相贯自动焊接接管为例，通过将相贯线接缝曲线焊接时间离散化为N个时间区间，在每个区间内用三次多项式代表状态变量随时间变化的关系，使用Hermite-Simpson插值定义多项式，计算逼近的多项式和实际运动方程之间的差值。为使机器手臂各关节不掠入相贯圆柱体，研究亦设下额外的不等式限制方程，以确保关节不触及圆柱体，其中不等式限制方程加上缺陷方程构成所有的限制方程，当所有限制方程均满足时，迭代的结果就收敛，同时找到最优解。仿真结果表明DCNLP在处理焊接轨迹控制问题时具有较强的鲁棒性。
Energy Technology Data Exchange (ETDEWEB)
Davis, C.G.
1990-01-01
The advent of nonlinear pulsation theory really coincides with the development of the large computers after the second world war. Christy and Stobbie were the first to make use of finite difference techniques on computers to model the bumps'' observed in the classical Cepheid light and velocity curves, the so-called Hertzsprung'' sequence. Following this work a more sophisticated analysis of the light and velocity curves from the models was made by Simon and Davis using Fourier techniques. Recently a simpler amplitude equation formalism has been developed that helps explain this resonance mechanism. The determination of Population I Cepheid masses by nonlinear methods will be discussed. For the lower mass objects, such as RR Lyrae and BL Her. stars, we find general agreement using evolutionary masses and nonlinear pulsation theory. An apparent difficulty of nonlinear pulsation theory occurs in the understanding of double'' mode pulsation, which will also be discussed. Recent studies in nonlinear pulsation theory have dealt with the question of mode selection, period doubling and the trends towards chaotic behavior such as is observed in the transition from W Virginis to RV Tauri-like stars. 10 refs., 1 fig., 2 tabs.
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Nonlinear Dynamic Force Spectroscopy
Björnham, Oscar
2016-01-01
Dynamic force spectroscopy (DFS) is an experimental technique that is commonly used to assess information of the strength, energy landscape, and lifetime of noncovalent bio-molecular interactions. DFS traditionally requires an applied force that increases linearly with time so that the bio-complex under investigation is exposed to a constant loading rate. However, tethers or polymers can modulate the applied force in a nonlinear regime. For example, bacterial adhesion pili and polymers with worm-like chain properties are examples of structures that show nonlinear force responses. In these situations, the theory for traditional DFS cannot be readily applied. In this work we expand the theory for DFS to also include nonlinear external forces while still maintaining compatibility with the linear DFS theory. To validate the theory we modeled a bio-complex expressed on a stiff, an elastic and a worm-like chain polymer, using Monte Carlo methods, and assessed the corresponding rupture force spectra. It was found th...
Nonlinear optomechanical paddle nanocavities
Kaviani, Hamidreza; Wu, Marcelo; Ghobadi, Roohollah; Barclay, Paul E
2014-01-01
A photonic crystal optomechanical system combining strong nonlinear optomechanical coupling, low effective mass and large optical mode spacing is introduced. This nanoscale "paddle nanocavity" device supports mechanical resonances with effective mass of 300--600 fg which couple nonlinearly to co-localized optical modes with a quadratic optomechanical coupling coefficient $g^{(2)} > 2\\pi\\times400$ MHz/nm$^2$, and a two phonon to single photon optomechanical coupling rate $\\Delta \\omega_0 > 2\\pi\\times 16$ Hz. This coupling relies on strong phonon-photon interactions in a structure whose optical mode spectrum is highly non--degenerate. Simulations indicate that nonlinear optomechanical readout of thermally driven motion in these devices should be observable for T $> 50 $ mK, and that measurement of phonon shot noise is achievable.
Nonlinear Photonic Crystal Fibers
DEFF Research Database (Denmark)
Hansen, Kim Per
2004-01-01
, leading to reduced mode confinement and dispersion flexibility. In this thesis, we treat the nonlinear photonic crystal fiber – a special sub-class of photonic crystal fibers, the core of which has a diameter comparable to the wavelength of the light guided in the fiber. The small core results in a large...... nonlinear coefficient and in various applications, it is therefore possible to reduce the required fiber lengths quite dramatically, leading to increased stability and efficiency. Furthermore, it is possible to design these fibers with zero-dispersion at previously unreachable wavelengths, paving the way...... for completely new applications, especially in and near the visible wavelength region. One such application is supercontinuum generation. Supercontinuum generation is extreme broadening of pulses in a nonlinear medium (in this case a small-core fiber), and depending on the dispersion of the fiber, it is possible...
Schmidt, Bruno E; Ernotte, Guilmot; Clerici, Matteo; Morandotti, Roberto; Ibrahim, Heide; Legare, Francois
2016-01-01
In the framework of linear optics, light fields do not interact with each other in a medium. Yet, when their field amplitude becomes comparable to the electron binding energies of matter, the nonlinear motion of these electrons emits new dipole radiation whose amplitude, frequency and phase differ from the incoming fields. Such high fields are typically achieved with ultra-short, femtosecond (1fs = 10-15 sec.) laser pulses containing very broad frequency spectra. Here, the matter not only couples incoming and outgoing fields but also causes different spectral components to interact and mix through a convolution process. In this contribution, we describe how frequency domain nonlinear optics overcomes the shortcomings arising from this convolution in conventional time domain nonlinear optics1. We generate light fields with previously inaccessible properties because the uncontrolled coupling of amplitudes and phases is turned off. For example, arbitrary phase functions are transferred linearly to the second har...
Nonlinear Metamaterials for Holography
Almeida, Euclides; Prior, Yehiam
2015-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multi-layer metamaterial holograms where by the nonlinear process of Third Harmonic Generation, a background free image is formed at a new frequency which is the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analyzed and prospects for future device applications are discussed.
Multidimensional nonlinear descriptive analysis
Nishisato, Shizuhiko
2006-01-01
Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sampled randomly from a normal population and often involve nonlinear relations. This reference not only provides an overview of multidimensional nonlinear descriptive analysis (MUNDA) of discrete data, it also offers new results in a variety of fields. The first part of the book covers conceptual and technical preliminaries needed to understand the data analysis in subsequent chapters. The next two parts contain applications of MUNDA to diverse data types, with each chapter devoted to one type of categorical data, a brief historical comment, and basic skills peculiar to the data types. The final part examines several problems and then concludes with suggestions for futu...
Design Energy Efficient Water Utilization Systems Allowing Operation Split%考虑操作分解的热集成用水网络设计
Institute of Scientific and Technical Information of China (English)
廖祖维; 武锦涛; 蒋斌波; 王靖岱; 阳永荣
2008-01-01
This article deals with the design of energy efficient water utilization systems allowing operation split. Practical features such as operating flexibility and capital cost have made the number of sub operations an impor-tant parameter of the problem. By treating the direct and indirect heat transfers separately, target freshwater and en-ergy consumption as well as the operation split conditions are first obtained. Subsequently, a mixed integer non-linear programming (MINLP) model is established for the design of water network and the heat exchanger network (HEN). The proposed systematic approach is limited to a single contaminant. Example from literature is used to illustrate the applicability of the approach.
Optimal Component Lumping: problem formulation and solution techniques
DEFF Research Database (Denmark)
Lin, Bao; Leibovici, Claude F.; Jørgensen, Sten Bay
2008-01-01
to determine the lumping scheme. Given an objective function defined with a linear weighting rule, an optimal lumping problem is formulated as a mixed integer nonlinear programming (MINLP) problem both in discrete and in continuous settings. A reformulation of the original problem is also presented, which...... significantly reduces the number of independent variables. The application to a system with 144 components demonstrates that the optimal lumping problem can be efficiently solved with a stochastic optimization method, Tabu Search (TS) algorithm. The case study also reveals that the discrete formulation...
DEFF Research Database (Denmark)
Anvari-Moghaddam, Amjad; Quintero, Juan Carlos Vasquez; Guerrero, Josep M.
2015-01-01
. Moreover, the superior performance of the proposed energy management system is shown in comparison with the conventional models. The numerical results also indicate that through wise management of demand and generation sides, there is a possibility to reduce domestic energy use and improve the user......In this paper, an intelligent energy management system based on energy saving and user’s comfort is introduced and applied to a residential smart home as a case study. The proposed multi-objective mixed-integer nonlinear programming (MINLP)-based architecture takes the advantages of several key...
DEFF Research Database (Denmark)
Sueviriyapan, Natthapong; Siemanond, Kitipat; Quaglia, Alberto;
2014-01-01
-based mathematical problem was formulated as mixed integer linear (MILP) and mixed integer non-linear programming (MINLP) and strived to identify the best wastewater treatment processes among a set of predefined alternatives that produce a minimum total annualized cost, while meeting all wastewater specification...... of wastewater treatment technologies, as well as water allocation, limited reuse, and recycling strategies. Therefore, a water and wastewater treatment network design requires the integration of both economic and environmental perspectives. The aim of this work was to modify and develop a generic model...
Design of tailor-made chemical blend using a decomposition-based computer-aided approach
DEFF Research Database (Denmark)
Yunus, Nor Alafiza; Gernaey, Krist; Manan, Z.A.
2011-01-01
methodology for blended liquid products that identifies a set of feasible chemical blends. The blend design problem is formulated as a Mixed Integer Nonlinear Programming (MINLP) model where the objective is to find the optimal blended gasoline or diesel product subject to types of chemicals....... The application of this systematic and computer-aided approach is illustrated through a case study involving the design of blends of gasoline with oxygenated compounds resulting from degradation and fermentation of biomass for use in internal combustion engines. Emphasis is given here on the concepts used...
Agrawal, Govind
2012-01-01
Since the 4e appeared, a fast evolution of the field has occurred. The 5e of this classic work provides an up-to-date account of the nonlinear phenomena occurring inside optical fibers, the basis of all our telecommunications infastructure as well as being used in the medical field. Reflecting the big developments in research, this new edition includes major new content: slow light effects, which offers a reduction in noise and power consumption and more ordered network traffic-stimulated Brillouin scattering; vectorial treatment of highly nonlinear fibers; and a brand new chapter o
DEFF Research Database (Denmark)
Mosegaard, Klaus
2012-01-01
For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...
Fundamentals of nonlinear optics
Powers, Peter E
2011-01-01
Peter Powers's rigorous but simple description of a difficult field keeps the reader's attention throughout. … All chapters contain a list of references and large numbers of practice examples to be worked through. … By carefully working through the proposed problems, students will develop a sound understanding of the fundamental principles and applications. … the book serves perfectly for an introductory-level course for second- and third-order nonlinear optical phenomena. The author's writing style is refreshing and original. I expect that Fundamentals of Nonlinear Optics will fast become pop
Tunable nonlinear graphene metasurfaces
Smirnova, Daria A; Kivshar, Yuri S; Khanikaev, Alexander B
2015-01-01
We introduce the concept of nonlinear graphene metasurfaces employing the controllable interaction between a graphene layer and a planar metamaterial. Such hybrid metasurfaces support two types of subradiant resonant modes, asymmetric modes of structured metamaterial elements ("metamolecules") and graphene plasmons exhibiting strong mutual coupling and avoided dispersion crossing. High tunability of graphene plasmons facilitates strong interaction between the subradiant modes, modifying the spectral position and lifetime of the associated Fano resonances. We demonstrate that strong resonant interaction, combined with the subwavelength localization of plasmons, leads to the enhanced nonlinear response and high efficiency of the second-harmonic generation.
Utilizing nonlinearity of transistors for reconfigurable chaos computation
Ditto, William; Kia, Behnam
2014-03-01
A VLSI circuit design for chaos computing is presented that exploits the intrinsic nonlinearity of transistors to implement a novel approach for conventional and chaotic computing circuit design. In conventional digital circuit design and implementation, transistors are simply switched on or off. We argue that by using the full range of nonlinear dynamics of transistors, we can design and build more efficient computational elements and logic blocks. Furthermore, the nonlinearity of these transistor circuits can be used to program the logic block to implement different types of computational elements that can be reconfigured. Because the intrinsic nonlinear dynamics of the transistors are utilized the resulting circuits typically require fewer transistors compared to conventional digital circuits as we exploit the intrinsic nonlinearity of the transistors to realize computations. This work was done with support from ONR grant N00014-12-1-0026 and from an ONR STTR and First Pass Engineering.
Nonlinear effects in optical fibers
Ferreira, Mario F
2011-01-01
Cutting-edge coverage of nonlinear phenomena occurring inside optical fibers Nonlinear fiber optics is a specialized part of fiber optics dealing with optical nonlinearities and their applications. As fiber-optic communication systems have become more advanced and complex, the nonlinear effects in optical fibers have increased in importance, as they adversely affect system performance. Paradoxically, the same nonlinear phenomena also offer the promise of addressing the bandwidth bottleneck for signal processing for future ultra-high speed optical networks. Nonlinear Effects in Optical Fiber
Geometric and material nonlinear analysis of tensegrity structures
Institute of Scientific and Technical Information of China (English)
Hoang Chi Tran; Jaehong Lee
2011-01-01
A numerical method is presented for the large deflection in elastic analysis of tensegrity structures including both geometric and material nonlinearities.The geometric nonlinearity is considered based on both total Lagrangian and updated Lagrangian formulations,while the material nonlinearity is treated through elastoplastic stressstrain relationship.The nonlinear equilibrium equations are solved using an incremental-iterative scheme in conjunction with the modified Newton-Raphson method.A computer program is developed to predict the mechanical responses of tensegrity systems under tensile,compressive and flexural loadings.Numerical results obtained are compared with those reported in the literature to demonstrate the accuracy and efficiency of the proposed program.The flexural behavior of the double layer quadruplex tensegrity grid is sufficiently good for lightweight large-span structural applications.On the other hand,its bending strength capacity is not sensitive to the self-stress level.
Nonlinear elliptic systems with exponential nonlinearities
Directory of Open Access Journals (Sweden)
Said El Manouni
2002-12-01
Full Text Available In this paper we investigate the existence of solutions for {gather*} -mathop{m div}( a(| abla u | ^N| abla u |^{N-2}u = f(x,u,v quad mbox{in } Omega -mathop{m div}(a(| abla v| ^N| abla v |^{N-2}v = g(x,u,v quad mbox{in } Omega u(x = v(x = 0 quad mbox{on }partial Omega. end{gather*} Where $Omega$ is a bounded domain in ${mathbb{R}}^N$, $Ngeq 2$, $f$ and $g$ are nonlinearities having an exponential growth on $Omega$ and $a$ is a continuous function satisfying some conditions which ensure the existence of solutions.
Nonlinearity and disorder: Classification and stability of nonlinear impurity modes
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole
2001-01-01
We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-10-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Ritz, Christian; Parmigiani, Giovanni
2009-01-01
R is a rapidly evolving lingua franca of graphical display and statistical analysis of experiments from the applied sciences. This book provides a coherent treatment of nonlinear regression with R by means of examples from a diversity of applied sciences such as biology, chemistry, engineering, medicine and toxicology.
Gorban, A. N.; Karlin, I.V.
2003-01-01
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation, Phenomenology and Quasi-chemical representation of the Boltzmann equation, Kinetic models, Discrete velocity models, Direct simulation, Lattice Gas and Lattice Boltzmann models, Minimal Boltzmann models for flows at low Knudsen number, Other kinetic equati...
DEFF Research Database (Denmark)
Jørgensen, Michael Finn
1995-01-01
It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...
Nonlinear phased array imaging
Croxford, Anthony J.; Cheng, Jingwei; Potter, Jack N.
2016-04-01
A technique is presented for imaging acoustic nonlinearity within a specimen using ultrasonic phased arrays. Acoustic nonlinearity is measured by evaluating the difference in energy of the transmission bandwidth within the diffuse field produced through different focusing modes. The two different modes being classical beam forming, where delays are applied to different element of a phased array to physically focus the energy at a single location (parallel firing) and focusing in post processing, whereby one element at a time is fired and a focused image produced in post processing (sequential firing). Although these two approaches are linearly equivalent the difference in physical displacement within the specimen leads to differences in nonlinear effects. These differences are localized to the areas where the amplitude is different, essentially confining the differences to the focal point. Direct measurement at the focal point are however difficult to make. In order to measure this the diffuse field is used. It is a statistical property of the diffuse field that it represents the total energy in the system. If the energy in the diffuse field for both the sequential and parallel firing case is measured then the difference between these, within the input signal bandwidth, is largely due to differences at the focal spot. This difference therefore gives a localized measurement of where energy is moving out of the transmission bandwidth due to nonlinear effects. This technique is used to image fatigue cracks and other damage types undetectable with conventional linear ultrasonic measurements.
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-11-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Trirefringence in nonlinear metamaterials
De Lorenci, Vitorio A
2012-01-01
We study the propagation of electromagnetic waves in the limit of geometrical optics for a class of nearly transparent nonlinear uniaxial metamaterials for which their permittivity tensors present a negative principal component. Their permeability are assumed positive and dependent on the electric field. We show that light waves experience triple refraction -- trirefringence. Additionally to the ordinary wave, two extraordinary waves propagate in such media.
Borghi, M.; Castellan, C.; Signorini, S.; Trenti, A.; Pavesi, L.
2017-09-01
Silicon photonics is a technology based on fabricating integrated optical circuits by using the same paradigms as the dominant electronics industry. After twenty years of fervid development, silicon photonics is entering the market with low cost, high performance and mass-manufacturable optical devices. Until now, most silicon photonic devices have been based on linear optical effects, despite the many phenomenologies associated with nonlinear optics in both bulk materials and integrated waveguides. Silicon and silicon-based materials have strong optical nonlinearities which are enhanced in integrated devices by the small cross-section of the high-index contrast silicon waveguides or photonic crystals. Here the photons are made to strongly interact with the medium where they propagate. This is the central argument of nonlinear silicon photonics. It is the aim of this review to describe the state-of-the-art in the field. Starting from the basic nonlinearities in a silicon waveguide or in optical resonator geometries, many phenomena and applications are described—including frequency generation, frequency conversion, frequency-comb generation, supercontinuum generation, soliton formation, temporal imaging and time lensing, Raman lasing, and comb spectroscopy. Emerging quantum photonics applications, such as entangled photon sources, heralded single-photon sources and integrated quantum photonic circuits are also addressed at the end of this review.
Nonlinear fibre optics overview
DEFF Research Database (Denmark)
Travers, J. C.; Frosz, Michael Henoch; Dudley, J. M.
2010-01-01
, provides a background to the associated nonlinear optical processes, treats the generation mechanisms from continuous wave to femtosecond pulse pump regimes and highlights the diverse applications. A full discussion of numerical methods and comprehensive computer code are also provided, enabling readers...
Tsia, Kevin K.; Jalali, Bahram
2010-05-01
An intriguing optical property of silicon is that it exhibits a large third-order optical nonlinearity, with orders-ofmagnitude larger than that of silica glass in the telecommunication band. This allows efficient nonlinear optical interaction at relatively low power levels in a small footprint. Indeed, we have witnessed a stunning progress in harnessing the Raman and Kerr effects in silicon as the mechanisms for enabling chip-scale optical amplification, lasing, and wavelength conversion - functions that until recently were perceived to be beyond the reach of silicon. With all the continuous efforts developing novel techniques, nonlinear silicon photonics is expected to be able to reach even beyond the prior achievements. Instead of providing a comprehensive overview of this field, this manuscript highlights a number of new branches of nonlinear silicon photonics, which have not been fully recognized in the past. In particular, they are two-photon photovoltaic effect, mid-wave infrared (MWIR) silicon photonics, broadband Raman effects, inverse Raman scattering, and periodically-poled silicon (PePSi). These novel effects and techniques could create a new paradigm for silicon photonics and extend its utility beyond the traditionally anticipated applications.
Leitao, J C; Gerlach, M; Altmann, E G
2016-01-01
One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g., patents) scale nonlinearly with the population~x of the cities in which they appear, i.e., $y\\sim x^\\beta, \\beta \
Nonlinear Gravitational Lagrangians revisited
Magnano, Guido
2016-01-01
The Legendre transformation method, applied in 1987 to deal with purely metric gravitational Lagrangians with nonlinear dependence on the Ricci tensor, is extended to metric-affine models and is shown to provide a concise and insightful comparison of the dynamical content of the two variational frameworks.
Nonlinearities in Microwave Superconductivity
Ledenyov, Dimitri O.; Ledenyov, Viktor O.
2012-01-01
The research is focused on the modeling of nonlinear properties of High Temperature Superconducting (HTS) thin films, using Bardeen, Cooper, Schrieffer and Lumped Element Circuit theories, with purpose to enhance microwave power handling capabilities of microwave filters and optimize design of microwave circuits in micro- and nano- electronics.
Nonlinear tsunami generation mechanism
Directory of Open Access Journals (Sweden)
M. A. Nosov
2001-01-01
Full Text Available The nonlinear mechanism of long gravitational surface water wave generation by high-frequency bottom oscillations in a water layer of constant depth is investigated analytically. The connection between the surface wave amplitude and the parameters of bottom oscillations and source length is investigated.
DEFF Research Database (Denmark)
Mosekilde, Erik
Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...
Terahertz semiconductor nonlinear optics
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias
2013-01-01
nonlinearity in doped semiconductors originates from the near-instantaneous heating of free electrons in the ponderomotive potential created by electric field of the THz pulse, leading to ultrafast increase of electron effective mass by intervalley scattering. Modification of effective mass in turn leads...
Nonlinear Optical Terahertz Technology Project
National Aeronautics and Space Administration — Our approach is based on high-Q optical WGM resonators made with a nonlinear crystal. Such resonators have been demonstrated to dramatically enhance nonlinear...
Phase retrieval using nonlinear diversity.
Lu, Chien-Hung; Barsi, Christopher; Williams, Matthew O; Kutz, J Nathan; Fleischer, Jason W
2013-04-01
We extend the Gerchberg-Saxton algorithm to phase retrieval in a nonlinear system. Using a tunable photorefractive crystal, we experimentally demonstrate the noninterferometric technique by reconstructing an unknown phase object from optical intensity measurements taken at different nonlinear strengths.
Strong nonlinear oscillators analytical solutions
Cveticanin, Livija
2017-01-01
This book outlines an analytical solution procedure of the pure nonlinear oscillator system, offering a solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter. Includes exercises.
Recent Advances in Explicit Multiparametric Nonlinear Model Predictive Control
Domínguez, Luis F.
2011-01-19
In this paper we present recent advances in multiparametric nonlinear programming (mp-NLP) algorithms for explicit nonlinear model predictive control (mp-NMPC). Three mp-NLP algorithms for NMPC are discussed, based on which novel mp-NMPC controllers are derived. The performance of the explicit controllers are then tested and compared in a simulation example involving the operation of a continuous stirred-tank reactor (CSTR). © 2010 American Chemical Society.
A Null Space Approach for Solving Nonlinear Complementarity Problems
Institute of Scientific and Technical Information of China (English)
Pu-yan Nie
2006-01-01
In this work, null space techniques are employed to tackle nonlinear complementarity problems(NCPs). NCP conditions are transform into a nonlinear programming problem, which is handled by null space algorithms. The NCP conditions are divided into two groups. Some equalities and inequalities in an NCP are treated as constraints. While other equalities and inequalities in an NCP are to be regarded as objective function.Two groups are all updated in every step. Null space approaches are extended to nonlinear complementarity problems. Two different solvers are employed for an NCP in an algorithm.
Reproducing Kernel Particle Method for Non-Linear Fracture Analysis
Institute of Scientific and Technical Information of China (English)
Cao Zhongqing; Zhou Benkuan; Chen Dapeng
2006-01-01
To study the non-linear fracture, a non-linear constitutive model for piezoelectric ceramics was proposed, in which the polarization switching and saturation were taken into account. Based on the model, the non-linear fracture analysis was implemented using reproducing kernel particle method (RKPM). Using local J-integral as a fracture criterion, a relation curve of fracture loads against electric fields was obtained. Qualitatively, the curve is in agreement with the experimental observations reported in literature. The reproducing equation, the shape function of RKPM, and the transformation method to impose essential boundary conditions for meshless methods were also introduced. The computation was implemented using object-oriented programming method.
Cubication of Conservative Nonlinear Oscillators
Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada
2009-01-01
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…
Terahertz Nonlinear Optics in Semiconductors
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias C.
2013-01-01
We demonstrate the nonlinear optical effects – selfphase modulation and saturable absorption of a single-cycle THz pulse in a semiconductor. Resulting from THz-induced modulation of Drude plasma, these nonlinear optical effects, in particular, lead to self-shortening and nonlinear spectral...
Fault Detection for Nonlinear Systems
DEFF Research Database (Denmark)
Stoustrup, Jakob; Niemann, H.H.
1998-01-01
The paper describes a general method for designing fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension of methods based...
Guide to ASIAC Computer Programs
1994-07-01
structural model . Such programs are also often used to plot both deformed and undeformed structure or graphically display stresses, temperatures, and...element models of aerospace structures and in research in structural analysis and optimization. Last updated in 1978. ANALYZE-PC This is a micro-computer...nonlinearities may be due to material nonlinearity, in which case elastic, hyperelastic, and hypoelastic material behavior may be considered, or the nonlinear
Nonlinear electrostatic drift Kelvin-Helmholtz instability
Sharma, Avadhesh C.; Srivastava, Krishna M.
1993-01-01
Nonlinear analysis of electrostatic drift Kelvin-Helmholtz instability is performed. It is shown that the analysis leads to the propagation of the weakly nonlinear dispersive waves, and the nonlinear behavior is governed by the nonlinear Burger's equation.
St. Germain, Brad David
The development and optimization of liquid rocket engines is an integral part of space vehicle design, since most Earth-to-orbit launch vehicles to date have used liquid rockets as their main propulsion system. Rocket engine design tools range in fidelity from very simple conceptual level tools to full computational fluid dynamics (CFD) simulations. The level of fidelity of interest in this research is a design tool that determines engine thrust and specific impulse as well as models the powerhead of the engine. This is the highest level of fidelity applicable to a conceptual level design environment where faster running analyses are desired. The optimization of liquid rocket engines using a powerhead analysis tool is a difficult problem, because it involves both continuous and discrete inputs as well as a nonlinear design space. Example continuous inputs are the main combustion chamber pressure, nozzle area ratio, engine mixture ratio, and desired thrust. Example discrete variable inputs are the engine cycle (staged-combustion, gas generator, etc.), fuel/oxidizer combination, and engine material choices. Nonlinear optimization problems involving both continuous and discrete inputs are referred to as Mixed-Integer Nonlinear Programming (MINLP) problems. Many methods exist in literature for solving MINLP problems; however none are applicable for this research. All of the existing MINLP methods require the relaxation of the discrete variables as part of their analysis procedure. This means that the discrete choices must be evaluated at non-discrete values. This is not possible with an engine powerhead design code. Therefore, a new optimization method was developed that uses modified response surface equations to provide lower bounds of the continuous design space for each unique discrete variable combination. These lower bounds are then used to efficiently solve the optimization problem. The new optimization procedure was used to find optimal rocket engine designs
Optothermal nonlinearity of silica aerogel
Braidotti, Maria Chiara; Fleming, Adam; Samuels, Michiel C; Di Falco, Andrea; Conti, Claudio
2016-01-01
We report on the characterization of silica aerogel thermal optical nonlinearity, obtained by z-scan technique. The results show that typical silica aerogels have nonlinear optical coefficient similar to that of glass $(\\simeq 10^{-12} $m$^2/$W), with negligible optical nonlinear absorption. The non\\-li\\-near coefficient can be increased to values in the range of $10^{-10} $m$^2/$W by embedding an absorbing dye in the aerogel. This value is one order of magnitude higher than that observed in the pure dye and in typical highly nonlinear materials like liquid crystals.
Essentials of nonlinear optics
Murti, Y V G S
2014-01-01
Current literature on Nonlinear Optics varies widely in terms of content, style, and coverage of specific topics, relative emphasis of areas and the depth of treatment. While most of these books are excellent resources for the researchers, there is a strong need for books appropriate for presenting the subject at the undergraduate or postgraduate levels in Universities. The need for such a book to serve as a textbook at the level of the bachelors and masters courses was felt by the authors while teaching courses on nonlinear optics to students of both science and engineering during the past two decades. This book has emerged from an attempt to address the requirement of presenting the subject at college level. A one-semester course covering the essentials can effectively be designed based on this.
Nonlinear metamaterials for holography
Almeida, Euclides; Bitton, Ora; Prior, Yehiam
2016-08-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency--the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed.
Nonlinear metamaterials for holography
Almeida, Euclides; Bitton, Ora
2016-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency—the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed. PMID:27545581
Van Leeuwen, Peter Jan; Reich, Sebastian
2015-01-01
This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.
Nonlinearity without Superluminality
Kent, A
2002-01-01
Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signalling. As Gisin and Polchinski first pointed out, this is not true for general nonlinear modifications of the Schroedinger equation. Excluding superluminal signalling has thus been taken to rule out most nonlinear versions of quantum theory. The no superluminal signalling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by non-relativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which di...
Monte Carlo and nonlinearities
Dauchet, Jérémi; Blanco, Stéphane; Caliot, Cyril; Charon, Julien; Coustet, Christophe; Hafi, Mouna El; Eymet, Vincent; Farges, Olivier; Forest, Vincent; Fournier, Richard; Galtier, Mathieu; Gautrais, Jacques; Khuong, Anaïs; Pelissier, Lionel; Piaud, Benjamin; Roger, Maxime; Terrée, Guillaume; Weitz, Sebastian
2016-01-01
The Monte Carlo method is widely used to numerically predict systems behaviour. However, its powerful incremental design assumes a strong premise which has severely limited application so far: the estimation process must combine linearly over dimensions. Here we show that this premise can be alleviated by projecting nonlinearities on a polynomial basis and increasing the configuration-space dimension. Considering phytoplankton growth in light-limited environments, radiative transfer in planetary atmospheres, electromagnetic scattering by particles and concentrated-solar-power-plant productions, we prove the real world usability of this advance on four test-cases that were so far regarded as impracticable by Monte Carlo approaches. We also illustrate an outstanding feature of our method when applied to sharp problems with interacting particles: handling rare events is now straightforward. Overall, our extension preserves the features that made the method popular: addressing nonlinearities does not compromise o...
Nonlinear Photonics 2014: introduction.
Akhmediev, N; Kartashov, Yaroslav
2015-01-12
International Conference "Nonlinear Photonics-2014" took place in Barcelona, Spain on July 27-31, 2014. It was a part of the "Advanced Photonics Congress" which is becoming a traditional notable event in the world of photonics. The current focus issue of Optics Express contains contributions from the participants of the Conference and the Congress. The articles in this focus issue by no means represent the total number of the congress contributions (around 400). However, it demonstrates wide range of topics covered at the event. The next conference of this series is to be held in 2016 in Australia, which is the home of many researchers working in the field of photonics in general and nonlinear photonics in particular.
Nonlinear fractional relaxation
Indian Academy of Sciences (India)
A Tofighi
2012-04-01
We deﬁne a nonlinear model for fractional relaxation phenomena. We use -expansion method to analyse this model. By studying the fundamental solutions of this model we ﬁnd that when → 0 the model exhibits a fast decay rate and when → ∞ the model exhibits a power-law decay. By analysing the frequency response we ﬁnd a logarithmic enhancement for the relative ratio of susceptibility.
Indian Academy of Sciences (India)
Ramaswamy Jaganathan; Sudeshna Sinha
2005-03-01
Motivated by studies on -deformed physical systems related to quantum group structures, and by the elements of Tsallis statistical mechanics, the concept of -deformed nonlinear maps is introduced. As a specific example, a -deformation procedure is applied to the logistic map. Compared to the canonical logistic map, the resulting family of -logistic maps is shown to have a wider spectrum of interesting behaviours, including the co-existence of attractors – a phenomenon rare in one-dimensional maps.
Controllability of nonlinear systems.
Sussmann, H. J.; Jurdjevic, V.
1972-01-01
Discussion of the controllability of nonlinear systems described by the equation dx/dt - F(x,u). Concepts formulated by Chow (1939) and Lobry (1970) are applied to establish criteria for F and its derivatives to obtain qualitative information on sets which can be obtained from x which denotes a variable of state in an arbitrary, real, analytical manifold. It is shown that controllability implies strong accessibility for a large class of manifolds including Euclidean spaces.-
2007-03-01
IEEE Transactions on Automatic Control , AC- 48, pp. 1712-1723, (2003). [14] C.I. Byrnes, A. Isidori...Nonlinear internal models for output regulation,” IEEE Transactions on Automatic Control , AC-49, pp. 2244-2247, (2004). [15] C.I. Byrnes, F. Celani, A...approach,” IEEE Transactions on Automatic Control , 48 (Dec. 2003), 2172–2190. 2. C. I. Byrnes, “Differential Forms and Dynamical Systems,” to appear
Filamentation with nonlinear Bessel vortices.
Jukna, V; Milián, C; Xie, C; Itina, T; Dudley, J; Courvoisier, F; Couairon, A
2014-10-20
We present a new type of ring-shaped filaments featured by stationary nonlinear high-order Bessel solutions to the laser beam propagation equation. Two different regimes are identified by direct numerical simulations of the nonlinear propagation of axicon focused Gaussian beams carrying helicity in a Kerr medium with multiphoton absorption: the stable nonlinear propagation regime corresponds to a slow beam reshaping into one of the stationary nonlinear high-order Bessel solutions, called nonlinear Bessel vortices. The region of existence of nonlinear Bessel vortices is found semi-analytically. The influence of the Kerr nonlinearity and nonlinear losses on the beam shape is presented. Direct numerical simulations highlight the role of attractors played by nonlinear Bessel vortices in the stable propagation regime. Large input powers or small cone angles lead to the unstable propagation regime where nonlinear Bessel vortices break up into an helical multiple filament pattern or a more irregular structure. Nonlinear Bessel vortices are shown to be sufficiently intense to generate a ring-shaped filamentary ionized channel in the medium which is foreseen as opening the way to novel applications in laser material processing of transparent dielectrics.
Strongly nonlinear oscillators analytical solutions
Cveticanin, Livija
2014-01-01
This book provides the presentation of the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. The book presents the original author’s method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter is considered. Special attention is given to the one and two mass oscillatory systems with two-degrees-of-freedom. The criteria for the deterministic chaos in ideal and non-ideal pure nonlinear oscillators are derived analytically. The method for suppressing chaos is developed. Important problems are discussed in didactic exercises. The book is self-consistent and suitable as a textbook for students and also for profess...
Quantum well nonlinear microcavities
Oudar, J. L.; Kuszelewicz, R.; Sfez, B.; Pellat, D.; Azoulay, R.
We report on recent progress in reducing the power threshold of all-optical bistable quantum well vertical microcavities. Significant improvements are achieved through an increase of the cavity finesse, together with a reduction of the device active layer thickness. A critical intensity of 5 μW/μm 2 has been observed on a microcavity of finesse 250, with a nonlinear medium of only 18 GaAs quantum wells of 10 nm thickness. Further improvements of the Bragg mirror quality resulted in a finesse of 700 and a power-lifetime product of 15 fJ/μm 2. Microresonator pixellation allows to obtain 2-dimensional arrays. A thermally-induced alloy-mixing technique is described, which produced a 110 meV carrier confinement energy, together with a refractive index change of -.012, averaged over the 2.6 μm nonlinear medium thickness. The resulting electrical and optical confinement is shown to improve the nonlinear characteristics, by limiting lateral carrier diffusion and light diffraction.
DEFF Research Database (Denmark)
Hostrup, Martin; Gani, Rafiqul; Kravanja, Zdravko
1999-01-01
This paper presents an integrated approach to the solution of process synthesis, design and analysis problems. Integration is achieved by combining two different techniques, synthesis based on thermodynamic insights and structural optimization together with a simulation engine and a properties...
DEFF Research Database (Denmark)
Gani, Rafiqul; Hostrup, Martin; Kravanja, Z.
2001-01-01
This paper presents an integrated approach to the solution of process synthesis, design and analysis problems. Integration is achieved by combining two different process synthesis techniques, one based on thermodynamic insights and the other based on structural optimisation, together...... with a simulation engine and a properties prediction package. Process flowsheets with or without reaction blocks are considered in this paper. Results from three illustrative case studies, highlighting different features of the integrated approach, are presented. (C) 2001 Elsevier Science Ltd. All rights reserved....
DEFF Research Database (Denmark)
Hostrup, Martin; Gani, Rafiqul; Kravanja, Zdravko;
1999-01-01
This paper presents an integrated approach to the solution of process synthesis, design and analysis problems. Integration is achieved by combining two different techniques, synthesis based on thermodynamic insights and structural optimization together with a simulation engine and a properties...... prediction package. Results from three case studies, highlighting different features of the integrated approach, are presented....
DEFF Research Database (Denmark)
Quaglia, Alberto; Sarup, Bent; Sin, Gürkan
Although being a mature and well established industry segment, over the last few decades the vegetable oil industry has been facing many important new challenges due to emerging new products (such as biodiesel and nutraceuticals compounds), as well as new trends and regulations with regards...
Nonlinear Pricing in Energy and Environmental Markets
Ito, Koichiro
This dissertation consists of three empirical studies on nonlinear pricing in energy and environmental markets. The first investigates how consumers respond to multi-tier nonlinear price schedules for residential electricity. Chapter 2 asks a similar research question for residential water pricing. Finally, I examine the effect of nonlinear financial rewards for energy conservation by applying a regression discontinuity design to a large-scale electricity rebate program that was implemented in California. Economic theory generally assumes that consumers respond to marginal prices when making economic decisions, but this assumption may not hold for complex price schedules. The chapter "Do Consumers Respond to Marginal or Average Price? Evidence from Nonlinear Electricity Pricing" provides empirical evidence that consumers respond to average price rather than marginal price when faced with nonlinear electricity price schedules. Nonlinear price schedules, such as progressive income tax rates and multi-tier electricity prices, complicate economic decisions by creating multiple marginal prices for the same good. Evidence from laboratory experiments suggests that consumers facing such price schedules may respond to average price as a heuristic. I empirically test this prediction using field data by exploiting price variation across a spatial discontinuity in electric utility service areas. The territory border of two electric utilities lies within several city boundaries in southern California. As a result, nearly identical households experience substantially different nonlinear electricity price schedules. Using monthly household-level panel data from 1999 to 2008, I find strong evidence that consumers respond to average price rather than marginal or expected marginal price. I show that even though this sub-optimizing behavior has a minimal impact on individual welfare, it can critically alter the policy implications of nonlinear pricing. The second chapter " How Do
Solving Nonlinear Euler Equations with Arbitrary Accuracy
Dyson, Rodger W.
2005-01-01
A computer program that efficiently solves the time-dependent, nonlinear Euler equations in two dimensions to an arbitrarily high order of accuracy has been developed. The program implements a modified form of a prior arbitrary- accuracy simulation algorithm that is a member of the class of algorithms known in the art as modified expansion solution approximation (MESA) schemes. Whereas millions of lines of code were needed to implement the prior MESA algorithm, it is possible to implement the present MESA algorithm by use of one or a few pages of Fortran code, the exact amount depending on the specific application. The ability to solve the Euler equations to arbitrarily high accuracy is especially beneficial in simulations of aeroacoustic effects in settings in which fully nonlinear behavior is expected - for example, at stagnation points of fan blades, where linearizing assumptions break down. At these locations, it is necessary to solve the full nonlinear Euler equations, and inasmuch as the acoustical energy is of the order of 4 to 5 orders of magnitude below that of the mean flow, it is necessary to achieve an overall fractional error of less than 10-6 in order to faithfully simulate entropy, vortical, and acoustical waves.
A Trust-region-based Sequential Quadratic Programming Algorithm
DEFF Research Database (Denmark)
Henriksen, Lars Christian; Poulsen, Niels Kjølstad
This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....
Comparison of Simulated and Measured Non-linear Ultrasound Fields
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt
2011-01-01
In this paper results from a non-linear AS (angular spectrum) based ultrasound simulation program are compared to water-tank measurements. A circular concave transducer with a diameter of 1 inch (25.4 mm) is used as the emitting source. The measured pulses are rst compared with the linear...... simulation program Field II, which will be used to generate the source for the AS simulation. The generated non-linear ultrasound eld is measured by a hydrophone in the focal plane. The second harmonic component from the measurement is compared with the AS simulation, which is used to calculate both...
Optimal nonlinear feedback control of quasi-Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
朱位秋; 应祖光
1999-01-01
An innovative strategy for optimal nonlinear feedback control of linear or nonlinear stochastic dynamic systems is proposed based on the stochastic averaging method for quasi-Hamiltonian systems and stochastic dynamic programming principle. Feedback control forces of a system are divided into conservative parts and dissipative parts. The conservative parts are so selected that the energy distribution in the controlled system is as requested as possible. Then the response of the system with known conservative control forces is reduced to a controlled diffusion process by using the stochastic averaging method. The dissipative parts of control forces are obtained from solving the stochastic dynamic programming equation.
Nonlinear robust hierarchical control for nonlinear uncertain systems
Directory of Open Access Journals (Sweden)
Leonessa Alexander
1999-01-01
Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.
Nonlinear scattering in plasmonic nanostructures
Chu, Shi-Wei
2016-09-01
Nonlinear phenomena provide novel light manipulation capabilities and innovative applications. Recently, we discovered nonlinear saturation on single-particle scattering of gold nanospheres by continuous-wave laser excitation and innovatively applied to improve microscopic resolution down to λ/8. However, the nonlinearity was limited to the green-orange plasmonic band of gold nanosphere, and the underlying mechanism has not yet been fully understood. In this work, we demonstrated that nonlinear scattering exists for various material/geometry combinations, thus expanding the applicable wavelength range. For near-infrared, gold nanorod is used, while for blue-violet, silver nanospheres are adopted. In terms of mechanism, the nonlinearity may originate from interband/intraband absorption, hot electron, or hot lattice, which are spectrally mixed in the case of gold nanosphere. For gold nanorod and silver nanosphere, nonlinear scattering occurs at plasmonic resonances, which are spectrally far from interband/intraband absorptions, so they are excluded. We found that the nonlinear index is much larger than possible contributions from hot electrons in literature. Therefore, we conclude that hot lattice is the major mechanism. In addition, we propose that similar to z-scan, which is the standard method to characterize nonlinearity of a thin sample, laser scanning microscopy should be adopted as the standard method to characterize nonlinearity from a nanostructure. Our work not only provides the physical mechanism of the nonlinear scattering, but also paves the way toward multi-color superresolution imaging based on non-bleaching plasmonic scattering.
Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, Kim Ø; Salerno, M.
2006-01-01
A class of discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowi......-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated....
Dichromatic nonlinear eigenmodes in slab waveguide with chi(2) nonlinearity.
Darmanyan, S A; Nevière, M
2001-03-01
The existence of purely nonlinear eigenmodes in a waveguiding structure composed of a slab with quadratic nonlinearity surrounded by (non)linear claddings is reported. Modes having bright and dark solitonlike shapes and consisting of two mutually locked harmonics are identified. Asymmetrical modes are shown to exist in symmetrical environments. Constraints for the existence of the modes are derived in terms of parameters of guiding structure materials.
A Collection of Nonlinear Aircraft Simulations in MATLAB
Garza, Frederico R.; Morelli, Eugene A.
2003-01-01
Nonlinear six degree-of-freedom simulations for a variety of aircraft were created using MATLAB. Data for aircraft geometry, aerodynamic characteristics, mass / inertia properties, and engine characteristics were obtained from open literature publications documenting wind tunnel experiments and flight tests. Each nonlinear simulation was implemented within a common framework in MATLAB, and includes an interface with another commercially-available program to read pilot inputs and produce a three-dimensional (3-D) display of the simulated airplane motion. Aircraft simulations include the General Dynamics F-16 Fighting Falcon, Convair F-106B Delta Dart, Grumman F-14 Tomcat, McDonnell Douglas F-4 Phantom, NASA Langley Free-Flying Aircraft for Sub-scale Experimental Research (FASER), NASA HL-20 Lifting Body, NASA / DARPA X-31 Enhanced Fighter Maneuverability Demonstrator, and the Vought A-7 Corsair II. All nonlinear simulations and 3-D displays run in real time in response to pilot inputs, using contemporary desktop personal computer hardware. The simulations can also be run in batch mode. Each nonlinear simulation includes the full nonlinear dynamics of the bare airframe, with a scaled direct connection from pilot inputs to control surface deflections to provide adequate pilot control. Since all the nonlinear simulations are implemented entirely in MATLAB, user-defined control laws can be added in a straightforward fashion, and the simulations are portable across various computing platforms. Routines for trim, linearization, and numerical integration are included. The general nonlinear simulation framework and the specifics for each particular aircraft are documented.
Optimization model for the design of distributed wastewater treatment networks
Directory of Open Access Journals (Sweden)
Ibrić Nidret
2012-01-01
Full Text Available In this paper we address the synthesis problem of distributed wastewater networks using mathematical programming approach based on the superstructure optimization. We present a generalized superstructure and optimization model for the design of the distributed wastewater treatment networks. The superstructure includes splitters, treatment units, mixers, with all feasible interconnections including water recirculation. Based on the superstructure the optimization model is presented. The optimization model is given as a nonlinear programming (NLP problem where the objective function can be defined to minimize the total amount of wastewater treated in treatment operations or to minimize the total treatment costs. The NLP model is extended to a mixed integer nonlinear programming (MINLP problem where binary variables are used for the selection of the wastewater treatment technologies. The bounds for all flowrates and concentrations in the wastewater network are specified as general equations. The proposed models are solved using the global optimization solvers (BARON and LINDOGlobal. The application of the proposed models is illustrated on the two wastewater network problems of different complexity. First one is formulated as the NLP and the second one as the MINLP. For the second one the parametric and structural optimization is performed at the same time where optimal flowrates, concentrations as well as optimal technologies for the wastewater treatment are selected. Using the proposed model both problems are solved to global optimality.
Nonlinear Schrodinger equation with chaotic, random, and nonperiodic nonlinearity
Cardoso, W B; Avelar, A T; Bazeia, D; Hussein, M S
2009-01-01
In this paper we deal with a nonlinear Schr\\"{o}dinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time coordinates and to check its robustness under these conditions. Comparing with a real system, the perturbation can be related to, e.g., impurities in crystalline structures, or coupling to a thermal reservoir which, on the average, enhances the nonlinearity. We also discuss the relevance of such random perturbations to the dynamics of Bose-Einstein Condensates and their collective excitations and transport.
Implementation of Nonlinear Control Laws for an Optical Delay Line
Hench, John J.; Lurie, Boris; Grogan, Robert; Johnson, Richard
2000-01-01
This paper discusses the implementation of a globally stable nonlinear controller algorithm for the Real-Time Interferometer Control System Testbed (RICST) brassboard optical delay line (ODL) developed for the Interferometry Technology Program at the Jet Propulsion Laboratory. The control methodology essentially employs loop shaping to implement linear control laws. while utilizing nonlinear elements as means of ameliorating the effects of actuator saturation in its coarse, main, and vernier stages. The linear controllers were implemented as high-order digital filters and were designed using Bode integral techniques to determine the loop shape. The nonlinear techniques encompass the areas of exact linearization, anti-windup control, nonlinear rate limiting and modal control. Details of the design procedure are given as well as data from the actual mechanism.
Nonlinear physics with Maple for scientists and engineers
Enns, Richard H
1997-01-01
Philosophy of the Text This text has been designed to be an introductory survey of the basic concepts and applied mathematical methods of nonlinear science. Students in engineer ing, physics, chemistry, mathematics, computing science, and biology should be able to successfully use this text. In an effort to provide the students with a cutting edge approach to one of the most dynamic, often subtle, complex, and still rapidly evolving, areas of modern research-nonlinear physics-we have made extensive use of the symbolic, numeric, and plotting capabilities of Maple V Release 4 applied to examples from these disciplines. No prior knowledge of Maple or computer programming is assumed, the reader being gently introduced to Maple as an auxiliary tool as the concepts of nonlinear science are developed. The diskette which accompanies the text gives a wide variety of illustrative nonlinear examples solved with Maple. An accompanying laboratory manual of experimental activities keyed to the text allows the student the...
Stolz, A; Markey, L; Francs, G Colas des; Bouhelier, A
2013-01-01
We introduce strongly-coupled optical gap antennas to interface optical radiation with current-carrying electrons at the nanoscale. The transducer relies on the nonlinear optical and electrical properties of an optical antenna operating in the tunneling regime. We discuss the underlying physical mechanisms controlling the conversion and demonstrate that a two-wire optical antenna can provide advanced optoelectronic functionalities beyond tailoring the electromagnetic response of a single emitter. Interfacing an electronic command layer with a nanoscale optical device may thus be facilitated by the optical rectennas discussed here.
Nonlinear surface electromagnetic phenomena
Ponath, H-E
1991-01-01
In recent years the physics of electromagnetic surface phenomena has developed rapidly, evolving into technologies for communications and industry, such as fiber and integrated optics. The variety of phenomena based on electromagnetism at surfaces is rich and this book was written with the aim of summarizing the available knowledge in selected areas of the field. The book contains reviews written by solid state and optical physicists on the nonlinear interaction of electromagnetic waves at and with surfaces and films. Both the physical phenomena and some potential applications are
Nonlinear electrodynamics with birefringence
Kruglov, S I
2015-01-01
A new model of nonlinear electrodynamics with three parameters is suggested. The phenomena of vacuum birefringence takes place when there is the external constant magnetic field. We calculate the indices of refraction for two polarizations of electromagnetic waves, parallel and perpendicular to the magnetic induction field. From the Bir\\'{e}fringence Magn\\'{e}tique du Vide (BMV) experiment one of the coefficients, $\\gamma\\approx 10^{-20}$ T$^{-2}$, was estimated. The canonical, symmetrical Belinfante energy-momentum tensors and dilatation current were obtained. The dilatation symmetry and the dual symmetry are broken in the model considered.
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Nonlinear dynamics in psychology
Directory of Open Access Journals (Sweden)
Stephen J. Guastello
2001-01-01
Full Text Available This article provides a survey of the applications of nonlinear dynamical systems theory to substantive problems encountered in the full scope of psychological science. Applications are organized into three topical areas – cognitive science, social and organizational psychology, and personality and clinical psychology. Both theoretical and empirical studies are considered with an emphasis on works that capture the broadest scope of issues that are of substantive interest to psychological theory. A budding literature on the implications of NDS principles in professional practice is reported also.
2009-11-18
analytic semigroup T(t) ~ eAl is exponentially stable (Notice that it is also a contraction semigroup ). 3. Be 3(U, Z) and P e £(W, 2) are bounded. 4. Ce...quite often in practice, .4 is self-adjoint. We also note that, since we assume (—A) is sectorial, we work with the semigroup exp(.4f) rather than...Uniform Output Regulation of Nonlinear Sys- tems: A convergent Dynamics Approach, Birkhauser, Boston, 2006. 23 135] A. Pazy, Semigroups of Linear
Directory of Open Access Journals (Sweden)
DJAIRO G. DEFIGUEIREDO
2000-12-01
Full Text Available In this paper we treat the question of the existence of solutions of boundary value problems for systems of nonlinear elliptic equations of the form - deltau = f (x, u, v,Ñu,Ñv, - deltav = g(x, u, v, Ñu, Ñv, in omega, We discuss several classes of such systems using both variational and topological methods. The notion of criticality takes into consideration the coupling, which plays important roles in both a priori estimates for the solutions and Palais-Smale conditions for the associated functional in the variational case.
Optimization Formulations for the Maximum Nonlinear Buckling Load of Composite Structures
DEFF Research Database (Denmark)
Lindgaard, Esben; Lund, Erik
2011-01-01
, benchmarked on a number of numerical examples of laminated composite structures for the maximization of the buckling load considering fiber angle design variables. The optimization formulations are based on either linear or geometrically nonlinear analysis and formulated as mathematical programming problems...... solved using gradient based techniques. The developed local criterion is formulated such it captures nonlinear effects upon loading and proves useful for both analysis purposes and as a criterion for use in nonlinear buckling optimization. © 2010 Springer-Verlag....
Global Analysis of Nonlinear Dynamics
Luo, Albert
2012-01-01
Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of internationally recognized researchers is intended to stimulate interests in global analysis of complex and high-dimensional nonlinear dynamical systems, whose global properties are largely unexplored at this time. This book also: Presents recent developments in global analysis of non-linear dynamical systems Provides in-depth considerations and extensions of cell mapping methods Adopts an inclusive style accessible to non-specialists and graduate students Global Analysis of Nonlinear Dynamics is an ideal reference for the community of nonlinear dynamics in different disciplines including engineering, applied mathematics, meteorology, life science, computational science, and medicine.
Nonlinear evolution of drift instabilities
Energy Technology Data Exchange (ETDEWEB)
Lee, W.W.; Krommes, J.A.; Oberman, C.R.; Smith, R.A.
1984-01-01
The nonlinear evolution of collisionless drift instabilities in a shear-free magnetic field has been studied by means of gyrokinetic particle simulation as well as numerical integration of model mode-coupling equations. The purpose of the investigation is to identify relevant nonlinear mechanisms responsible for the steady-state drift wave fluctuations. It is found that the saturation of the instability is mainly caused by the nonlinear E x B convection of the resonant electrons and their associated velocity space nonlinearity. The latter also induces energy exchange between the competing modes, which, in turn, gives rise to enhanced diffusion. The nonlinear E x B convection of the ions, which contributes to the nonlinear frequency shift, is also an important ingredient for the saturation.
Rashidian Vaziri, Mohammad Reza
2013-07-10
In this paper, the Z-scan theory for nonlocal nonlinear media has been further developed when nonlinear absorption and nonlinear refraction appear simultaneously. To this end, the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample has been generalized. It is shown that this kind of phase shift will reduce correctly to its known counterpart for the case of pure refractive nonlinearity. Using this generalized form of phase shift, the basic formulas for closed- and open-aperture beam transmittances in the far field have been provided, and a simple procedure for interpreting the Z-scan results has been proposed. In this procedure, by separately performing open- and closed-aperture Z-scan experiments and using the represented relations for the far-field transmittances, one can measure the nonlinear absorption coefficient and nonlinear index of refraction as well as the order of nonlocality. Theoretically, it is shown that when the absorptive nonlinearity is present in addition to the refractive nonlinearity, the sample nonlocal response can noticeably suppress the peak and enhance the valley of the Z-scan closed-aperture transmittance curves, which is due to the nonlocal action's ability to change the beam transverse dimensions.
Solving non-linear Horn clauses using a linear Horn clause solver
DEFF Research Database (Denmark)
Kafle, Bishoksan; Gallagher, John Patrick; Ganty, Pierre
2016-01-01
In this paper we show that checking satisfiability of a set of non-linear Horn clauses (also called a non-linear Horn clause program) can be achieved using a solver for linear Horn clauses. We achieve this by interleaving a program transformation with a satisfiability checker for linear Horn...... clauses (also called a solver for linear Horn clauses). The program transformation is based on the notion of tree dimension, which we apply to a set of non-linear clauses, yielding a set whose derivation trees have bounded dimension. Such a set of clauses can be linearised. The main algorithm...
de Jong, Roelof
2005-07-01
This program incorporates a number of tests to analyse the count rate dependent non-linearity seen in NICMOS spectro-photometric observations. In visit 1 we will observe a few fields with stars of a range in luminosity in NGC1850 with NICMOS in NIC1 in F090M, F110W and F160W and NIC2 F110W, F160W, and F180W. We will repeat the observations with flatfield lamp on, creating artificially high count-rates, allowing tests of NICMOS linearity as function of count rate. To access the effect of charge trapping and persistence, we first take darks {so there is not too much charge already trapped}, than take exposures with the lamp off, exposures with the lamp on, and repeat at the end with lamp off. Finally, we continue with taking darks during occultation. In visit 2 we will observe spectro-photometric standard P041C using the G096 and G141 grisms in NIC3, and repeat the lamp off/on/off test to artificially create a high background. In visits 3&4 we repeat photometry measurements of faint standard stars SNAP-2 and WD1657+343, on which the NICMOS non-linearity was originally discovered using grism observations. These measurements are repeated, because previous photometry was obtained with too short exposure times, hence substantially affected by charge trapping non-linearity. Measurements will be made with NIC1: Visit 5 forms the persistence test of the program. The bright star GL-390 {used in a previous persistence test} will iluminate the 3 NICMOS detectors in turn for a fixed time, saturating the center many times, after which a series of darks will be taken to measure the persistence {i.e. trapped electrons and the decay time of the traps}. To determine the wavelength dependence of the trap chance, exposures of the bright star in different filters will be taken, as well as one in the G096 grism with NIC3. Most exposures will be 128s long, but two exposures in the 3rd orbit will be 3x longer, to seperate the effects of count rate versus total counts of the trap
Topics on nonlinear generalized functions
Colombeau, J F
2011-01-01
The aim of this paper is to give the text of a recent introduction to nonlinear generalized functions exposed in my talk in the congress gf2011, which was asked by several participants. Three representative topics were presented: two recalls "Nonlinear generalized functions and their connections with distribution theory", "Examples of applications", and a recent development: "Locally convex topologies and compactness: a functional analysis of nonlinear generalized functions".
Nonlinear Ultrasonic Phased Array Imaging
Potter, J. N.; Croxford, A. J.; Wilcox, P. D.
2014-10-01
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
Nonlinear ultrasonic phased array imaging
Potter, J N; Croxford, A.J.; Wilcox, P. D.
2014-01-01
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging t...
Research on Nonlinear Dynamical Systems.
1983-01-10
investigated fundamental aspects of functional differential equations, including qualitative questions (stability, nonlinear oscillations ), in 142,45,47,52...Bifurcation in the Duffing equation with several parameters, II. Proc. of the Royal Society of Edinburgh, Series A, 79A (1977), pp.317-326. 1I.J (with ;Ibtoas...Lecture Notes in Mathematics, Vol. 730 (1979). [54] Nonlinear oscillations in equations with delays. Proc. at A.M.S. 10th Summer Seminar on Nonlinear
Nonlinear ultrasonic phased array imaging.
Potter, J N; Croxford, A J; Wilcox, P D
2014-10-03
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
Remote Atmospheric Nonlinear Optical Magnetometry
2014-04-28
Boyd , Nonlinear Optics (Elsevier, Burlington, MA, 2008). [13] M. Scully and S. Zubairy, Quantum Optics (Cambridge U. Press, Cambridge, UK, 1997...Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6703--14-9548 Remote Atmospheric Nonlinear Optical Magnetometry PhilliP SPrangle...b. ABSTRACT c. THIS PAGE 18. NUMBER OF PAGES 17. LIMITATION OF ABSTRACT Remote Atmospheric Nonlinear Optical Magnetometry Phillip Sprangle, Luke
Applications of nonlinear fiber optics
Agrawal, Govind
2008-01-01
* The only book describing applications of nonlinear fiber optics * Two new chapters on the latest developments: highly nonlinear fibers and quantum applications* Coverage of biomedical applications* Problems provided at the end of each chapterThe development of new highly nonlinear fibers - referred to as microstructured fibers, holey fibers and photonic crystal fibers - is the next generation technology for all-optical signal processing and biomedical applications. This new edition has been thoroughly updated to incorporate these key technology developments.The bo
Linearization of conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Alvarez, M L [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E; Pascual, I [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-03-11
A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for the complete range of oscillation amplitudes. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of the technique.
Problems in nonlinear resistive MHD
Energy Technology Data Exchange (ETDEWEB)
Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L. [General Atomics, San Diego, CA (United States)
1998-12-31
Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1.
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Focus issue introduction: nonlinear optics.
Boulanger, Benoît; Cundiff, Steven T; Gauthier, Daniel J; Karlsson, Magnus; Lu, Yan-Qing; Norwood, Robert A; Skryabin, Dmitry; Taira, Takunori
2011-11-07
It is now fifty years since the original observation of second harmonic generation ushered in the field of nonlinear optics, close on the heels of the invention of the laser. This feature issue celebrates this anniversary with papers that span the range from new nonlinear optical materials, through the increasingly novel methods that have been developed for phase matching, to emerging areas such as nonlinear metamaterials and plasmonic enhancement of optical properties. It is clear that the next fifty years of nonlinear optics will witness a proliferation of new applications with increasing technological impact.
Nonlocal homogenization for nonlinear metamaterials
Gorlach, Maxim A; Lapine, Mikhail; Kivshar, Yuri S; Belov, Pavel A
2016-01-01
We present a consistent theoretical approach for calculating effective nonlinear susceptibilities of metamaterials taking into account both frequency and spatial dispersion. Employing the discrete dipole model, we demonstrate that effects of spatial dispersion become especially pronounced in the vicinity of effective permittivity resonance where nonlinear susceptibilities reach their maxima. In that case spatial dispersion may enable simultaneous generation of two harmonic signals with the same frequency and polarization but different wave vectors. We also prove that the derived expressions for nonlinear susceptibilities transform into the known form when spatial dispersion effects are negligible. In addition to revealing new physical phenomena, our results provide useful theoretical tools for analysing resonant nonlinear metamaterials.
Nonlinear Peltier effect in semiconductors
Zebarjadi, Mona; Esfarjani, Keivan; Shakouri, Ali
2007-09-01
Nonlinear Peltier coefficient of a doped InGaAs semiconductor is calculated numerically using the Monte Carlo technique. The Peltier coefficient is also obtained analytically for single parabolic band semiconductors assuming a shifted Fermi-Dirac electronic distribution under an applied bias. Analytical results are in agreement with numerical simulations. Key material parameters affecting the nonlinear behavior are doping concentration, effective mass, and electron-phonon coupling. Current density thresholds at which nonlinear behavior is observable are extracted from numerical data. It is shown that the nonlinear Peltier effect can be used to enhance cooling of thin film microrefrigerator devices especially at low temperatures.
Nonlinearities in Behavioral Macroeconomics.
Gomes, Orlando
2017-07-01
This article undertakes a journey across the literature on behavioral macroeconomics, with attention concentrated on the nonlinearities that the behavioral approach typically suggests or implies. The emphasis is placed on thinking the macro economy as a living organism, composed of many interacting parts, each one having a will of its own, which is in sharp contrast with the mechanism of the orthodox view (well represented by the neoclassical or new Keynesian dynamic stochastic general equilibrium - DSGE - model). The paper advocates that a thorough understanding of individual behavior in collective contexts is the only possible avenue to further explore macroeconomic phenomena and the often observed 'anomalies' that the benchmark DSGE macro framework is unable to explain or justify. After a reflection on the role of behavioral traits as a fundamental component of a new way of thinking the economy, the article proceeds with a debate on some of the most relevant frameworks in the literature that somehow link macro behavior and nonlinearities; covered subjects include macro models with disequilibrium rules, agent-based models that highlight interaction and complexity, evolutionary switching frameworks, and inattention based decision problems. These subjects have, as a fundamental point in common, the use of behavioral elements to transform existing interpretations of the economic reality, making it more evident how irregular fluctuations emerge and unfold on the aggregate.
Improved nonlinear prediction method
Adenan, Nur Hamiza; Md Noorani, Mohd Salmi
2014-06-01
The analysis and prediction of time series data have been addressed by researchers. Many techniques have been developed to be applied in various areas, such as weather forecasting, financial markets and hydrological phenomena involving data that are contaminated by noise. Therefore, various techniques to improve the method have been introduced to analyze and predict time series data. In respect of the importance of analysis and the accuracy of the prediction result, a study was undertaken to test the effectiveness of the improved nonlinear prediction method for data that contain noise. The improved nonlinear prediction method involves the formation of composite serial data based on the successive differences of the time series. Then, the phase space reconstruction was performed on the composite data (one-dimensional) to reconstruct a number of space dimensions. Finally the local linear approximation method was employed to make a prediction based on the phase space. This improved method was tested with data series Logistics that contain 0%, 5%, 10%, 20% and 30% of noise. The results show that by using the improved method, the predictions were found to be in close agreement with the observed ones. The correlation coefficient was close to one when the improved method was applied on data with up to 10% noise. Thus, an improvement to analyze data with noise without involving any noise reduction method was introduced to predict the time series data.
Simulations of nonlinear continuous wave pressure fields in FOCUS
Zhao, Xiaofeng; Hamilton, Mark F.; McGough, Robert J.
2017-03-01
The Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation is a parabolic approximation to the Westervelt equation that models the effects of diffraction, attenuation, and nonlinearity. Although the KZK equation is only valid in the far field of the paraxial region for mildly focused or unfocused transducers, the KZK equation is widely applied in medical ultrasound simulations. For a continuous wave input, the KZK equation is effectively modeled by the Bergen Code [J. Berntsen, Numerical Calculations of Finite Amplitude Sound Beams, in M. F. Hamilton and D. T. Blackstock, editors, Frontiers of Nonlinear Acoustics: Proceedings of 12th ISNA, Elsevier, 1990], which is a finite difference model that utilizes operator splitting. Similar C++ routines have been developed for FOCUS, the `Fast Object-Oriented C++ Ultrasound Simulator' (http://www.egr.msu.edu/˜fultras-web) to calculate nonlinear pressure fields generated by axisymmetric flat circular and spherically focused ultrasound transducers. This new routine complements an existing FOCUS program that models nonlinear ultrasound propagation with the angular spectrum approach [P. T. Christopher and K. J. Parker, J. Acoust. Soc. Am. 90, 488-499 (1991)]. Results obtained from these two nonlinear ultrasound simulation approaches are evaluated and compared for continuous wave linear simulations. The simulation results match closely in the farfield of the paraxial region, but the results differ in the nearfield. The nonlinear pressure field generated by a spherically focused transducer with a peak surface pressure of 0.2MPa radiating in a lossy medium with β = 3.5 is simulated, and the computation times are also evaluated. The nonlinear simulation results demonstrate acceptable agreement in the focal zone. These two related nonlinear simulation approaches are now included with FOCUS to enable convenient simulations of nonlinear pressure fields on desktop and laptop computers.
Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion
Directory of Open Access Journals (Sweden)
Jun Wang
2013-01-01
Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.
复杂流程工业系统的优化综合与柔性分析%Optimal Synthesis and Flexibility Analysis of Complex Process Industrial System
Institute of Scientific and Technical Information of China (English)
张健; 陈丙珍; 胡山鹰; 徐强
2001-01-01
MINLP模型在优化综合与柔性分析中起着重要作用，具有两种表示方法：代数法和逻辑法，后者在模型表达与求解方面有很多优点。MINLP模型中还可以集成启发性知识，也就是工程经验，以加快求解速度，并使结果更加合理。对于凸的MINLP问题，目前比较成熟的算法有分支界定法、外近似法和广义Bender函数法。对于非凸MINLP问题，其求解算法目前尚在研究中，已提出的有罚函数法、αBB算法和符号重建算法。此外，一些基于随机搜索的方法也得到了应用，并且在实践中取得了较好的结果。%The mixed-integer nonlinear programming (MINLP) models are widely used in optim al synthesis and flexibility analysis. There are two types of MINLP model: the alge braic MINLP model and the logic MINLP model, and the latter has many advantages in expressin g and solving.Logic and heuristic knowledge can also be integrated into MINLP model for proces s synthesis.Hard logic knowledge cannot be violated, and heuristic rule can be violated when needed. Every heuristic rule has a penalty factor, when it is broken, a penalty will be added into the object function. There are three solution algorithms for convex MINLP models: the branc h-and-bound algorithm, the outer approximation algorithm and the generalized Benders decompo sition algorithm. All these three methods generate a descending upper-bond sequence an d a increasing lower-bond sequence, and the convergence of the two sequences is the optimal so lution. The branch-and-bound algorithm make a computational-tree, in which every node is a relaxed subproblem. The outer approximation algorithm solves a series of NLP subproblems and MILP main problems, and the main problems are the linearization of the original probl em. The generalized Benders decomposition algorithm divides the variables into complex v ariables and simple variables, and projects the original problem into the complex
Nonlinear dynamic macromodeling techniques for audio systems
Ogrodzki, Jan; Bieńkowski, Piotr
2015-09-01
This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.
NONLINEAR MODEL PREDICTIVE CONTROL OF CHEMICAL PROCESSES
Directory of Open Access Journals (Sweden)
R. G. SILVA
1999-03-01
Full Text Available A new algorithm for model predictive control is presented. The algorithm utilizes a simultaneous solution and optimization strategy to solve the model's differential equations. The equations are discretized by equidistant collocation, and along with the algebraic model equations are included as constraints in a nonlinear programming (NLP problem. This algorithm is compared with the algorithm that uses orthogonal collocation on finite elements. The equidistant collocation algorithm results in simpler equations, providing a decrease in computation time for the control moves. Simulation results are presented and show a satisfactory performance of this algorithm.
Cluster Formation and Joint Power-Bandwidth Allocation for Imperfect NOMA in DL-HetNets
Celik, Abdulkadir
2017-04-15
Non-orthogonal multiple access (NOMA) has recently drawn attentions on its ability to fairly serve multiple users on the same radio resource with a desirable performance. However, achievable NOMA gain is primarily limited by channel gain disparity and successive interference cancellation (SIC) receiver characteristics. Accordingly, we introduce an imperfect SIC receiver model considering the power disparity and sensitivity constraints, delay tolerance, and residual interference due to detection and estimation errors. Then, a generic cluster formation (CF) and Power-Bandwidth Allocation (PBA) is formulated as a mixed-integer non-linear programming (MINLP) problem for downlink (DL) heterogeneous networks (HetNets). After dividing the MINLP problem into mixed-integer and non-linear subprobems, we first transform CF into a multi-partite matching, which is solved sequentially using bi-partite matching techniques. For sumrate maximization, max-min fairness, and energy & spectrum efficiency objectives, we secondly put highly non-convex joint PBA into a convex form using geometric programming (GP). Extensive simulations unleash the potential of NOMA to handle large number of users, traffic offloading, and user fairness.
Nonlinear Evolution of Ferroelectric Domains
Institute of Scientific and Technical Information of China (English)
WeiLU; Dai－NingFANG; 等
1997-01-01
The nonlinear evolution of ferroelectric domains is investigated in the paper and amodel is proposed which can be applied to numerical computation.Numerical results show that the model can accurately predict some nonlinear behavior and consist with those experimental results.
Nonlinear Electrodynamics and black holes
Breton, N; Breton, Nora; Garcia-Salcedo, Ricardo
2007-01-01
It is addressed the issue of black holes with nonlinear electromagnetic field, focussing mainly in the Born-Infeld case. The main features of these systems are described, for instance, geodesics, energy conditions, thermodynamics and isolated horizon aspects. Also are revised some black hole solutions of alternative nonlinear electrodynamics and its inconveniences.
Space curves, anholonomy and nonlinearity
Indian Academy of Sciences (India)
Radha Balakrishnan
2005-04-01
Using classical differential geometry, we discuss the phenomenon of anholonomy that gets associated with a static and a moving curve. We obtain the expressions for the respective geometric phases in the two cases and interpret them. We show that there is a close connection between anholonomy and nonlinearity in a wide class of nonlinear systems.
Balancing for unstable nonlinear systems
Scherpen, J.M.A.
1993-01-01
A previously obtained method of balancing for stable nonlinear systems is extended to unstable nonlinear systems. The similarity invariants obtained by the concept of LQG balancing for an unstable linear system can also be obtained by considering a past and future energy function of the system. By c
Nonlinear diffusion and superconducting hysteresis
Energy Technology Data Exchange (ETDEWEB)
Mayergoyz, I.D. [Univ. of Maryland, College Park, MD (United States)
1996-12-31
Nonlinear diffusion of electromagnetic fields in superconductors with ideal and gradual resistive transitions is studied. Analytical results obtained for linear and nonlinear polarizations of electromagnetic fields are reported. These results lead to various extensions of the critical state model for superconducting hysteresis.
Looking back at the gifi system of nonlinear multivariate analysis
van der Heijden, Peter G M; van Buuren, Stef
2016-01-01
Gifi was the nom de plume for a group of researchers led by Jan de Leeuw at the University of Leiden. Between 1970 and 1990 the group produced a stream of theoretical papers and computer programs in the area of nonlinear multivariate analysis that were very innovative. In an informal way this paper
Energy Technology Data Exchange (ETDEWEB)
Lallart, Mickael; Guyomar, Daniel, E-mail: mickael.lallart@insa-lyon.fr [LGEF, INSA-Lyon, Universite de Lyon, 8 rue de la Physique, F-69621 (France)
2011-10-29
The proliferation of wearable and left-behind devices has raised the issue of powering such systems. While primary batteries have been widely used in order to address this issue, recent trends have focused on energy harvesting products that feature high reliability and low maintenance issues. Among all the ambient sources available for energy harvesting, vibrations and heat have been of significant interest among the research community for small-scale devices. However, the conversion abilities of materials are still limited when dealing with systems featuring small dimensions. The purpose of this paper is to presents an up-to-date view of nonlinear approaches for increasing the efficiency of electromechanical and electrocaloric conversion mechanisms. From the modeling of the operation principles of the different architectures, a comparative analysis will be exposed, emphasizing the advantages and drawbacks of the presented concepts, in terms of maximal output power (under constant vibration magnitude or taking into account the damping effect), load independence, and implementation easiness.
Fainberg, B D
2015-01-01
Purely organic materials with negative and near-zero dielectric permittivity can be easily fabricated. Here we develop a theory of nonlinear non-steady-state organic plasmonics with strong laser pulses. The bistability response of the electron-vibrational model of organic materials in the condensed phase has been demonstrated. Non-steady-state organic plasmonics enable us to obtain near-zero dielectric permittivity during a short time. We have proposed to use non-steady-state organic plasmonics for the enhancement of intersite dipolar energy-transfer interaction in the quantum dot wire that influences on electron transport through nanojunctions. Such interactions can compensate Coulomb repulsions for particular conditions. We propose the exciton control of Coulomb blocking in the quantum dot wire based on the non-steady-state near-zero dielectric permittivity of the organic host medium.
2016-01-01
This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. Due to the interdisciplinary nature of the subject, the book should be of interest to mathematicians (pure and applied), physicists and engineers. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the...
Nonlinear estimation and classification
Hansen, Mark; Holmes, Christopher; Mallick, Bani; Yu, Bin
2003-01-01
Researchers in many disciplines face the formidable task of analyzing massive amounts of high-dimensional and highly-structured data This is due in part to recent advances in data collection and computing technologies As a result, fundamental statistical research is being undertaken in a variety of different fields Driven by the complexity of these new problems, and fueled by the explosion of available computer power, highly adaptive, non-linear procedures are now essential components of modern "data analysis," a term that we liberally interpret to include speech and pattern recognition, classification, data compression and signal processing The development of new, flexible methods combines advances from many sources, including approximation theory, numerical analysis, machine learning, signal processing and statistics The proposed workshop intends to bring together eminent experts from these fields in order to exchange ideas and forge directions for the future
Nonlinear transmission sputtering
Bitensky, I. S.; Sigmund, P.
1996-05-01
General expressions have been derived for the nonlinear yield of transmission sputtering for an incident polyatomic ion under the assumption that the molecule breaks up on entering the target and that sputter yields are enhanced due to proximity of atomic trajectories. Special attention is given to the case of negligible Coulomb explosion where projectile atoms penetrate independently. For weakly overlapping trajectories, the yield enhancement factor of a polyatomic molecule can be expressed by that of a diatom, amended with a correction for triple correlations if necessary. This expression is in good agreement with recent experimental findings on phenylalanine targets. Pertinent results on multiple scattering of atomic ions are reviewed and applied to independently-moving fragment atoms. The merits of measurements at variable layer thickness in addition to variable projectile energy are mentioned.
Perspectives on Nonlinear Filtering
Law, Kody
2015-01-07
The solution to the problem of nonlinear filtering may be given either as an estimate of the signal (and ideally some measure of concentration), or as a full posterior distribution. Similarly, one may evaluate the fidelity of the filter either by its ability to track the signal or its proximity to the posterior filtering distribution. Hence, the field enjoys a lively symbiosis between probability and control theory, and there are plenty of applications which benefit from algorithmic advances, from signal processing, to econometrics, to large-scale ocean, atmosphere, and climate modeling. This talk will survey some recent theoretical results involving accurate signal tracking with noise-free (degenerate) dynamics in high-dimensions (infinite, in principle, but say d between 103 and 108 , depending on the size of your application and your computer), and high-fidelity approximations of the filtering distribution in low dimensions (say d between 1 and several 10s).
Nonlinear rotordynamics analysis
Day, W. B.; Zalik, R. A.
1986-01-01
Three analytic consequences of the nonlinear Jeffcott equations are examined. The primary application of these analyses is directed toward understanding the excessive vibrations recorded in the Liquid Oxygen (LOX) pump of the Space Shuttle Main Engine (SSME) during hot firing ground testing. The first task is to provide bounds on the coefficients of the equations which delimit the two cases of numerical solution as a circle or an annulus. The second task examines the mathematical generalization to multiple forcing functions, which includes the special problems of mass imbalance, side force, rubbing, and combination of these forces. Finally, stability and boundedness of the steady-state solutions is discussed and related to the corresponding linear problem.
Institute of Scientific and Technical Information of China (English)
杜学武; 梁玉梅; 张连生
2006-01-01
In this paper, a class of augmented Lagrangians of Di Pillo and Grippo (DGALs) was considered, for solving equality-con strained problems via unconstrained minimization techniques. The relationship was further discussed between the unconstrained minimizero of DGALs on the product space of problem variables and multipliers, and the solutions of the constrained problem and the corre sponding values of the Lagrange multipliers. The resulting properties indicate more precisely that this class of DGALs is exact multiplier penalty functions. Therefore, a solution of the equality-constrained problem and the corresponding values of the Lagrange multipliers can be found by performing a single unconstrained minimization of a DGAL on the product space of problem variables and multipliers.Key words nonlinear programming, constrained optimization, augmented Lagrangians, augmented Lagrangisns of Di Pillo and Grippo.
Nonlinearities in vegetation functioning
Ceballos-Núñez, Verónika; Müller, Markus; Metzler, Holger; Sierra, Carlos
2016-04-01
Given the current drastic changes in climate and atmospheric CO2 concentrations, and the role of vegetation in the global carbon cycle, there is increasing attention to the carbon allocation component in biosphere terrestrial models. Improving the representation of C allocation in models could be the key to having better predictions of the fate of C once it enters the vegetation and is partitioned to C pools of different residence times. C allocation has often been modeled using systems of ordinary differential equations, and it has been hypothesized that most models can be generalized with a specific form of a linear dynamical system. However, several studies have highlighted discrepancies between empirical observations and model predictions, attributing these differences to problems with model structure. Although efforts have been made to compare different models, the outcome of these qualitative assessments has been a conceptual categorization of them. In this contribution, we introduce a new effort to identify the main properties of groups of models by studying their mathematical structure. For this purpose, we performed a literature research of the relevant models of carbon allocation in vegetation and developed a database with their representation in symbolic mathematics. We used the Python package SymPy for symbolic mathematics as a common language and manipulated the models to calculate their Jacobian matrix at fixed points and their eigenvalues, among other mathematical analyses. Our preliminary results show a tendency of inverse proportionality between model complexity and size of time/space scale; complex interactions between the variables controlling carbon allocation in vegetation tend to operate at shorter time/space scales, and vice-versa. Most importantly, we found that although the linear structure is common, other structures with non-linearities have been also proposed. We, therefore, propose a new General Model that can accommodate these
Nonlinear field space cosmology
Mielczarek, Jakub; Trześniewski, Tomasz
2017-08-01
We consider the FRW cosmological model in which the matter content of the Universe (playing the role of an inflaton or quintessence) is given by a novel generalization of the massive scalar field. The latter is a scalar version of the recently introduced nonlinear field space theory, where the physical phase space of a given field is assumed to be compactified at large energies. For our analysis, we choose the simple case of a field with the spherical phase space and endow it with the generalized Hamiltonian analogous to the XXZ Heisenberg model, normally describing a system of spins in condensed matter physics. Subsequently, we study both the homogenous cosmological sector and linear perturbations of such a test field. In the homogenous sector, we find that nonlinearity of the field phase space is becoming relevant for large volumes of the Universe and can lead to a recollapse, and possibly also at very high energies, leading to the phase of a bounce. Quantization of the field is performed in the limit where the nontrivial nature of its phase space can be neglected, while there is a nonvanishing contribution from the Lorentz symmetry breaking term of the Hamiltonian. As a result, in the leading order of the XXZ anisotropy parameter, we find that the inflationary spectral index remains unmodified with respect to the standard case but the total amplitude of perturbations is subject to a correction. The Bunch-Davies vacuum state also becomes appropriately corrected. The proposed new approach is bringing cosmology and condensed matter physics closer together, which may turn out to be beneficial for both disciplines.
NONLINEAR STABILITY FOR EADY'S MODEL
Institute of Scientific and Technical Information of China (English)
LIU Yong-ming; QIU Ling-cun
2005-01-01
Poincaré type integral inequality plays an important role in the study of nonlinear stability ( in the sense of Arnold's second theorem) for three-dimensional quasigeostophic flow. The nonlinear stability of Eady's model is one of the most important cases in the application of the method. But the best nonlinear stability criterion obtained so far and the linear stability criterion are not coincident. The two criteria coincide only when the period of the channel is infinite.additional conservation law of momentum and by rigorous estimate of integral inequality. So the new nonlinear stability criterion was obtained, which shows that for Eady 's model in the periodic channel, the linear stable implies the nonlinear stable.
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...
Terahertz Nonlinearity in Graphene Plasmons
Jadidi, Mohammad M; Winnerl, Stephan; Sushkov, Andrei B; Drew, H Dennis; Murphy, Thomas E; Mittendorff, Martin
2015-01-01
Sub-wavelength graphene structures support localized plasmonic resonances in the terahertz and mid-infrared spectral regimes. The strong field confinement at the resonant frequency is predicted to significantly enhance the light-graphene interaction, which could enable nonlinear optics at low intensity in atomically thin, sub-wavelength devices. To date, the nonlinear response of graphene plasmons and their energy loss dynamics have not been experimentally studied. We measure and theoretically model the terahertz nonlinear response and energy relaxation dynamics of plasmons in graphene nanoribbons. We employ a THz pump-THz probe technique at the plasmon frequency and observe a strong saturation of plasmon absorption followed by a 10 ps relaxation time. The observed nonlinearity is enhanced by two orders of magnitude compared to unpatterned graphene with no plasmon resonance. We further present a thermal model for the nonlinear plasmonic absorption that supports the experimental results.
Fast Numerical Nonlinear Fourier Transforms
Wahls, Sander
2014-01-01
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be sinusoidal. Physically relevant waveforms are often available for the analysis instead. The details of the transform depend on the waveforms underlying the analysis, which in turn are specified through the implicit assumption that the signal is governed by a certain evolution equation. For example, water waves generated by the Korteweg-de Vries equation can be expressed in terms of cnoidal waves. Light waves in optical fiber governed by the nonlinear Schr\\"dinger equation (NSE) are another example. Nonlinear analogs of classic problems such as spectral analysis and filtering arise in many applications, with information transmission in optical fiber, as proposed by Yousefi and Kschischang, being a very recent one. The nonlinear Fourier transform is eminently suited to address them ...
Properties of Nonlinear Dynamo Waves
Tobias, S. M.
1997-01-01
Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However, the nonlinearities included are (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by considering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave he achieved. Moreover, this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.
Cubication of conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, Augusto; Alvarez, Mariela L [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, Elena; Pascual, Inmaculada [Departamento de Optica, FarmacologIa y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-09-15
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A, while in a Taylor expansion of the restoring force these coefficients are independent of A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain an approximate frequency-amplitude relation as a function of the complete elliptic integral of the first kind. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of this scheme.
Nonlinear Oscillators in Space Physics
Lester,Daniel; Thronson, Harley
2011-01-01
We discuss dynamical systems that produce an oscillation without an external time dependent source. Numerical results are presented for nonlinear oscillators in the Em1h's atmosphere, foremost the quasi-biennial oscillation (QBOl. These fluid dynamical oscillators, like the solar dynamo, have in common that one of the variables in a governing equation is strongly nonlinear and that the nonlinearity, to first order, has particular form. of 3rd or odd power. It is shown that this form of nonlinearity can produce the fundamental li'equency of the internal oscillation. which has a period that is favored by the dynamical condition of the fluid. The fundamental frequency maintains the oscillation, with no energy input to the system at that particular frequency. Nonlinearities of 2nd or even power could not maintain the oscillation.
Asymptotic expansions in nonlinear rotordynamics
Day, William B.
1987-01-01
This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot-firing ground testing. Deadband, side force, and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency, is defined and used to develop the solutions of the nonlinear Jeffcott equations as singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.
Nonlinear hyperbolic waves in multidimensions
Prasad, Phoolan
2001-01-01
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts...
Analysis of Nonlinear Electromagnetic Metamaterials
Poutrina, Ekaterina; Smith, David R
2010-01-01
We analyze the properties of a nonlinear metamaterial formed by integrating nonlinear components or materials into the capacitive regions of metamaterial elements. A straightforward homogenization procedure leads to general expressions for the nonlinear susceptibilities of the composite metamaterial medium. The expressions are convenient, as they enable inhomogeneous system of scattering elements to be described as a continuous medium using the standard notation of nonlinear optics. We illustrate the validity and accuracy of our theoretical framework by performing measurements on a fabricated metamaterial sample composed of an array of split ring resonators (SRRs) with packaged varactors embedded in the capacitive gaps in a manner similar to that of Wang et al. [Opt. Express 16, 16058 (2008)]. Because the SRRs exhibit a predominant magnetic response to electromagnetic fields, the varactor-loaded SRR composite can be described as a magnetic material with nonlinear terms in its effective magnetic susceptibility...
Bubble nonlinear dynamics and stimulated scattering process
Jie, Shi; De-Sen, Yang; Sheng-Guo, Shi; Bo, Hu; Hao-Yang, Zhang; Shi-Yong, Hu
2016-02-01
A complete understanding of the bubble dynamics is deemed necessary in order to achieve their full potential applications in industry and medicine. For this purpose it is first needed to expand our knowledge of a single bubble behavior under different possible conditions including the frequency and pressure variations of the sound field. In addition, stimulated scattering of sound on a bubble is a special effect in sound field, and its characteristics are associated with bubble oscillation mode. A bubble in liquid can be considered as a representative example of nonlinear dynamical system theory with its resonance, and its dynamics characteristics can be described by the Keller-Miksis equation. The nonlinear dynamics of an acoustically excited gas bubble in water is investigated by using theoretical and numerical analysis methods. Our results show its strongly nonlinear behavior with respect to the pressure amplitude and excitation frequency as the control parameters, and give an intuitive insight into stimulated sound scattering on a bubble. It is seen that the stimulated sound scattering is different from common dynamical behaviors, such as bifurcation and chaos, which is the result of the nonlinear resonance of a bubble under the excitation of a high amplitude acoustic sound wave essentially. The numerical analysis results show that the threshold of stimulated sound scattering is smaller than those of bifurcation and chaos in the common condition. Project supported by the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT1228) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 11204050 and 11204049).
System Identification for Nonlinear FOPDT Model with Input-Dependent Dead-Time
DEFF Research Database (Denmark)
Sun, Zhen; Yang, Zhenyu
2011-01-01
. In order to identify these parameters in an online manner, the considered system is discretized at first. Then, the nonlinear FOPDT identification problem is formulated as a stochastic Mixed Integer Non-Linear Programming problem, and an identification algorithm is proposed by combining the Branch......An on-line iterative method of system identification for a kind of nonlinear FOPDT system is proposed in the paper. The considered nonlinear FOPDT model is an extension of the standard FOPDT model by means that its dead time depends on the input signal and the other parameters are time dependent...
Nonlinear FOPDT Model Identification for the Superheat Dynamic in a Refrigeration System
DEFF Research Database (Denmark)
Yang, Zhenyu; Sun, Zhen; Andersen, Casper
2011-01-01
the considered system is discretized, the nonlinear FOPDT identification problem is formulated as a Mixed Integer Non-Linear Programming problem, and then an identification algorithm is proposed by combining the Branch-and-Bound method and Least Square technique, in order to on-line identify these time......An on-line nonlinear FOPDT system identification method is proposed and applied to model the superheat dynamic in a supermarket refrigeration system. The considered nonlinear FOPDT model is an extension of the standard FOPDT model by means that its parameters are time dependent. After...
Optimization of hardening/softening behavior of plane frame structures using nonlinear normal modes
DEFF Research Database (Denmark)
Dou, Suguang; Jensen, Jakob Søndergaard
2016-01-01
/softening behavior of nonlinear mechanical systems. The iterative optimization procedure consists of calculation of nonlinear normal modes, solving an adjoint equation system for sensitivity analysis and an update of design variables using a mathematical programming tool. We demonstrate the method with examples......Devices that exploit essential nonlinear behavior such as hardening/softening and inter-modal coupling effects are increasingly used in engineering and fundamental studies. Based on nonlinear normal modes, we present a gradient-based structural optimization method for tailoring the hardening...
The Nonlinear Analytical Envelope Equation in quadratic nonlinear crystals
Bache, Morten
2016-01-01
We here derive the so-called Nonlinear Analytical Envelope Equation (NAEE) inspired by the work of Conforti et al. [M. Conforti, A. Marini, T. X. Tran, D. Faccio, and F. Biancalana, "Interaction between optical fields and their conjugates in nonlinear media," Opt. Express 21, 31239-31252 (2013)], whose notation we follow. We present a complete model that includes $\\chi^{(2)}$ terms [M. Conforti, F. Baronio, and C. De Angelis, "Nonlinear envelope equation for broadband optical pulses in quadratic media," Phys. Rev. A 81, 053841 (2010)], $\\chi^{(3)}$ terms, and then extend the model to delayed Raman effects in the $\\chi^{(3)}$ term. We therefore get a complete model for ultrafast pulse propagation in quadratic nonlinear crystals similar to the Nonlinear Wave Equation in Frequency domain [H. Guo, X. Zeng, B. Zhou, and M. Bache, "Nonlinear wave equation in frequency domain: accurate modeling of ultrafast interaction in anisotropic nonlinear media," J. Opt. Soc. Am. B 30, 494-504 (2013)], but where the envelope is...
Breatherlike impurity modes in discrete nonlinear lattices
DEFF Research Database (Denmark)
Hennig, D.; Rasmussen, Kim; Tsironis, G. P.
1995-01-01
We investigate the properties of a disordered generalized discrete nonlinear Schrodinger equation, containing both diagonal and nondiagonal nonlinear terms. The equation models a Linear host lattice doped with nonlinear impurities. We find different types of impurity states that form itinerant...
Self-Assembly of Nanocomposite Nonlinear Optical Materials for Photonic Devices Project
National Aeronautics and Space Administration — This program targets the development of new highly anisotropic nonlinear optical nanocomposite materials for NASA and non-NASA applications in advanced photonic and...
Handheld Nonlinear Detection of Delamination and Intrusion Faults in Composites Project
National Aeronautics and Space Administration — In Phase I of the SBIR program, LEEOAT Company will develop a hand-held high-resolution ultrasonic nonlinear imager for non-destructive inspection (NDI) of...
Hays, J. R.
1969-01-01
Lumped parametric system models are simplified and computationally advantageous in the frequency domain of linear systems. Nonlinear least squares computer program finds the least square best estimate for any number of parameters in an arbitrarily complicated model.
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
Energy Technology Data Exchange (ETDEWEB)
Tataronis, J. A.
2004-06-01
This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfvkn continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named “accumulation continuum” and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory.
Spatial solitons in nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2000-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero.......We study solitons in one-dimensional quadratic nonlinear photonic crystals with periodic linear and nonlinear susceptibilities. We show that such crystals support stable bright and dark solitons, even when the effective quadratic nonlinearity is zero....
Resource Letter NO-1: Nonlinear Optics
Garmire, Elsa
2011-03-01
This Resource Letter provides a guide to the literature on nonlinear optics. Books, journals, and websites are introduced that cover the general subject. Journal articles and websites are cited covering the following topics: second-order nonlinearities in transparent media including second-harmonic generation and optical parametric oscillation, third-order and higher nonlinearities, nonlinear refractive index, absorptive nonlinearities such as saturable absorption and multiphoton absorption, and scattering nonlinearities such as stimulated Raman scattering and stimulated Brillouin scattering. Steady-state and transient phenomena, fiber optics, solitons, nonlinear wave mixing, optical phase conjugation, nonlinear spectroscopy, and multiphoton microscopy are all outlined.
PREFACE Integrability and nonlinear phenomena Integrability and nonlinear phenomena
Gómez-Ullate, David; Lombardo, Sara; Mañas, Manuel; Mazzocco, Marta; Nijhoff, Frank; Sommacal, Matteo
2010-10-01
Back in 1967, Clifford Gardner, John Greene, Martin Kruskal and Robert Miura published a seminal paper in Physical Review Letters which was to become a cornerstone in the theory of integrable systems. In 2006, the authors of this paper received the AMS Steele Prize. In this award the AMS pointed out that `In applications of mathematics, solitons and their descendants (kinks, anti-kinks, instantons, and breathers) have entered and changed such diverse fields as nonlinear optics, plasma physics, and ocean, atmospheric, and planetary sciences. Nonlinearity has undergone a revolution: from a nuisance to be eliminated, to a new tool to be exploited.' From this discovery the modern theory of integrability bloomed, leading scientists to a deep understanding of many nonlinear phenomena which is by no means reachable by perturbation methods or other previous tools from linear theories. Nonlinear phenomena appear everywhere in nature, their description and understanding is therefore of great interest both from the theoretical and applicative point of view. If a nonlinear phenomenon can be represented by an integrable system then we have at our disposal a variety of tools to achieve a better mathematical description of the phenomenon. This special issue is largely dedicated to investigations of nonlinear phenomena which are related to the concept of integrability, either involving integrable systems themselves or because they use techniques from the theory of integrability. The idea of this special issue originated during the 18th edition of the Nonlinear Evolution Equations and Dynamical Systems (NEEDS) workshop, held at Isola Rossa, Sardinia, Italy, 16-23 May 2009 (http://needs-conferences.net/2009/). The issue benefits from the occasion offered by the meeting, in particular by its mini-workshops programme, and contains invited review papers and contributed papers. It is worth pointing out that there was an open call for papers and all contributions were peer reviewed
Neurodynamics: nonlinear dynamics and neurobiology.
Abarbanel, H D; Rabinovich, M I
2001-08-01
The use of methods from contemporary nonlinear dynamics in studying neurobiology has been rather limited.Yet, nonlinear dynamics has become a practical tool for analyzing data and verifying models. This has led to productive coupling of nonlinear dynamics with experiments in neurobiology in which the neural circuits are forced with constant stimuli, with slowly varying stimuli, with periodic stimuli, and with more complex information-bearing stimuli. Analysis of these more complex stimuli of neural circuits goes to the heart of how one is to understand the encoding and transmission of information by nervous systems.
Dissipative Nonlinear Dynamics in Holography
Basu, Pallab
2013-01-01
We look at the response of a nonlinearly coupled scalar field in an asymptotically AdS black brane geometry and find a behaviour very similar to that of known dissipative nonlinear systems like the chaotic pendulum. Transition to chaos proceeds through a series of period-doubling bifurcations. The presence of dissipation, crucial to this behaviour, arises naturally in a black hole background from the ingoing conditions imposed at the horizon. AdS/CFT translates our solution to a chaotic response of the operator dual to the scalar field. Our setup can also be used to study quench-like behaviour in strongly coupled nonlinear systems.
Acoustic-gravity nonlinear structures
Directory of Open Access Journals (Sweden)
D. Jovanović
2002-01-01
Full Text Available A catalogue of nonlinear vortex structures associated with acoustic-gravity perturbations in the Earth's atmosphere is presented. Besides the previously known Kelvin-Stewart cat's eyes, dipolar and tripolar structures, new solutions having the form of a row of counter-rotating vortices, and several weakly two-dimensional vortex chains are given. The existence conditions for these nonlinear structures are discussed with respect to the presence of inhomogeneities of the shear flows. The mode-coupling mechanism for the nonlinear generation of shear flows in the presence of linearly unstable acoustic-gravity waves, possibly also leading to intermittency and chaos, is presented.
Nonlinear effects in Thomson backscattering
Maroli, C.; Petrillo, V.; Tomassini, P.; Serafini, L.
2013-03-01
We analyze the nonlinear classical effects of the X/γ radiation produced by Thomson/Compton sources. We confirm the development of spectral fringes of the radiation on axis, which comports broadening, shift, and deformation of the spectrum. For the nominal parameters of the SPARC-LAB Thomson scattering and of the European Proposal for the gamma source ELI-NP, however, the radiation, when collected in the suitable acceptance angle, does not reveal many differences from that predicted by the linear model and the nonlinear redshift is subdominant with respect to the quantum recoil. An experiment aimed to the study of the nonlinearities is proposed on the SPARC-LAB source.
Nonlinear Dynamic Phenomena in Mechanics
Warminski, Jerzy; Cartmell, Matthew P
2012-01-01
Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear
Nonlinear Optics: Principles and Applications
DEFF Research Database (Denmark)
Rottwitt, Karsten; Tidemand-Lichtenberg, Peter
As nonlinear optics further develops as a field of research in electromagnetic wave propagation, its state-of-the-art technologies will continue to strongly impact real-world applications in a variety of fields useful to the practicing scientist and engineer. From basic principles to examples...... of applications, Nonlinear Optics: Principles and Applications effectively bridges physics and mathematics with relevant applied material for real-world use. The book progresses naturally from fundamental aspects to illustrative examples, and presents a strong theoretical foundation that equips the reader...... and matter, this text focuses on the physical understanding of nonlinear optics, and explores optical material response functions in the time and frequency domain....
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
Lin Xiao-Gang; Liu Wen-Jun; Lei Ming
2016-03-01
Oscillating solitons are obtained in nonlinear optics. Analytical study of the variable coefficient nonlinear Schrödinger equation, which is used to describe the soliton propagation in those systems, is carried out using the Hirota’s bilinear method. The bilinear forms and analytic soliton solutions are derived, and the relevant properties and features of oscillating solitons are illustrated. Oscillating solitons are controlled by the reciprocal of the group velocity and Kerr nonlinearity. Results of this paper will be valuable to the study of dispersion-managed optical communication system and mode-locked fibre lasers.
Nonlinear dynamics: Challenges and perspectives
Indian Academy of Sciences (India)
M Lakshmanan
2005-04-01
The study of nonlinear dynamics has been an active area of research since 1960s, after certain path-breaking discoveries, leading to the concepts of solitons, integrability, bifurcations, chaos and spatio-temporal patterns, to name a few. Several new techniques and methods have been developed to understand nonlinear systems at different levels. Along with these, a multitude of potential applications of nonlinear dynamics have also been enunciated. In spite of these developments, several challenges, some of them fundamental and others on the efficacy of these methods in developing cutting edge technologies, remain to be tackled. In this article, a brief personal perspective of these issues is presented.
Femtosecond nonlinear polarization evolution based on cascade quadratic nonlinearities.
Liu, X; Ilday, F O; Beckwitt, K; Wise, F W
2000-09-15
We experimentally demonstrate that one can exploit nonlinear phase shifts produced in type I phase-mismatched second-harmonic generation to produce intensity-dependent polarization evolution with 100-fs pulses. An amplitude modulator based on nonlinear polarization rotation provides passive amplitude-modulation depth of up to ~50%. Applications of the amplitude and phase modulations to mode locking of femtosecond bulk and fiber lasers are promising and are discussed.
Hybrid quantum systems for enhanced nonlinear optical susceptibilities
Sullivan, Dennis; Kuzyk, Mark G
2016-01-01
Significant effort has been expended in the search for materials with ultra-fast nonlinear-optical susceptibilities, but most fall far below the fundamental limits. This work applies a theoretical materials development program that has identified a promising new hybrid made of a nanorod and a molecule. This system uses the electrostatic dipole moment of the molecule to break the symmetry of the metallic nanostructure that shifts the energy spectrum to make it optimal for a nonlinear-optical response near the fundamental limit. The structural parameters are varied to determine the ideal configuration, providing guidelines for making the best structures.
UV Nano Lights - Nonlinear Quantum Dot-Plasmon Coupling
2016-06-20
AFRL-AFOSR-JP-TR-2016-0072 UV Nano-Lights - Nonlinear Quantum Dot-Plasmon Coupling Eric Waclawik QUEENSLAND UNIVERSITY OF TECHNOLOGY Final Report 06...Final 3. DATES COVERED (From - To) 03 Feb 2014 to 02 Feb 2016 4. TITLE AND SUBTITLE UV Nano-Lights - Nonlinear Quantum Dot-Plasmon Coupling 5a...CONTRACT NUMBER 5b. GRANT NUMBER FA2386-14-1-4056 5c. PROGRAM ELEMENT NUMBER 61102F 6. AUTHOR(S) Eric Waclawik 5d. PROJECT NUMBER 5e. TASK NUMBER 5f