Directory of Open Access Journals (Sweden)
V. S. Zarubin
2016-01-01
in its plane, and in the circular cylinder unlimited in length.An approximate numerical solution of the differential equation that is included in a nonlinear mathematical model of the thermal explosion enables us to obtain quantitative estimates of combination of determining parameters at which the limit state occurs in areas of not only canonical form. A capability to study of the thermal explosion state can be extended in the context of development of mathematical modeling methods, including methods of model analysis to describe the thermal state of solids.To analyse a mathematical model of the thermal explosion in a homogeneous solid the paper uses a variational approach based on the dual variational formulation of the appropriate nonlinear stationary problem of heat conduction in such a body. This formulation contains two alternative functional reaching the matching values in their stationary points corresponding to the true temperature distribution. This functional feature allows you to not only get an approximate quantitative estimate of the combination of parameters that determine the thermal explosion state, but also to find the greatest possible error in such estimation.
Directory of Open Access Journals (Sweden)
Felix Fritzen
2018-02-01
Full Text Available A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems is presented. First, the Galerkin reduced basis (RB formulation is presented, which fails at providing significant gains with respect to the computational efficiency for nonlinear problems. Renowned methods for the reduction of the computing time of nonlinear reduced order models are the Hyper-Reduction and the (Discrete Empirical Interpolation Method (EIM, DEIM. An algorithmic description and a methodological comparison of both methods are provided. The accuracy of the predictions of the hyper-reduced model and the (DEIM in comparison to the Galerkin RB is investigated. All three approaches are applied to a simple uncertainty quantification of a planar nonlinear thermal conduction problem. The results are compared to computationally intense finite element simulations.
Energy Technology Data Exchange (ETDEWEB)
Philip, Bobby, E-mail: philipb@ornl.gov [Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, TN 37831 (United States); Berrill, Mark A.; Allu, Srikanth; Hamilton, Steven P.; Sampath, Rahul S.; Clarno, Kevin T. [Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, TN 37831 (United States); Dilts, Gary A. [Los Alamos National Laboratory, PO Box 1663, Los Alamos, NM 87545 (United States)
2015-04-01
This paper describes an efficient and nonlinearly consistent parallel solution methodology for solving coupled nonlinear thermal transport problems that occur in nuclear reactor applications over hundreds of individual 3D physical subdomains. Efficiency is obtained by leveraging knowledge of the physical domains, the physics on individual domains, and the couplings between them for preconditioning within a Jacobian Free Newton Krylov method. Details of the computational infrastructure that enabled this work, namely the open source Advanced Multi-Physics (AMP) package developed by the authors is described. Details of verification and validation experiments, and parallel performance analysis in weak and strong scaling studies demonstrating the achieved efficiency of the algorithm are presented. Furthermore, numerical experiments demonstrate that the preconditioner developed is independent of the number of fuel subdomains in a fuel rod, which is particularly important when simulating different types of fuel rods. Finally, we demonstrate the power of the coupling methodology by considering problems with couplings between surface and volume physics and coupling of nonlinear thermal transport in fuel rods to an external radiation transport code.
A nonlinear oscillatory problem
International Nuclear Information System (INIS)
Zhou Qingqing.
1991-10-01
We have studied the nonlinear oscillatory problem of orthotropic cylindrical shell, we have analyzed the character of the oscillatory system. The stable condition of the oscillatory system has been given. (author). 6 refs
Formalev, V. F.; Kolesnik, S. A.
2017-11-01
The authors are the first to present a closed procedure for numerical solution of inverse coefficient problems of heat conduction in anisotropic materials used as heat-shielding ones in rocket and space equipment. The reconstructed components of the thermal-conductivity tensor depend on temperature (are nonlinear). The procedure includes the formation of experimental data, the implicit gradient-descent method, the economical absolutely stable method of numerical solution of parabolic problems containing mixed derivatives, the parametric identification, construction, and numerical solution of the problem for elements of sensitivity matrices, the development of a quadratic residual functional and regularizing functionals, and also the development of algorithms and software systems. The implicit gradient-descent method permits expanding the quadratic functional in a Taylor series with retention of the linear terms for the increments of the sought functions. This substantially improves the exactness and stability of solution of the inverse problems. Software systems are developed with account taken of the errors in experimental data and disregarding them. On the basis of a priori assumptions of the qualitative behavior of the functional dependences of the components of the thermal-conductivity tensor on temperature, regularizing functionals are constructed by means of which one can reconstruct the components of the thermal-conductivity tensor with an error no higher than the error of the experimental data. Results of the numerical solution of the inverse coefficient problems on reconstruction of nonlinear components of the thermal-conductivity tensor have been obtained and are discussed.
Problems in nonlinear resistive MHD
International Nuclear Information System (INIS)
Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L.
1998-01-01
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
Nonlinear problems in theoretical physics
International Nuclear Information System (INIS)
Ranada, A.F.
1979-01-01
This volume contains the lecture notes and review talks delivered at the 9th GIFT international seminar on theoretical physics on the general subject 'Nonlinear Problems in Theoretical Physics'. Mist contributions deal with recent developments in the theory of the spectral transformation and solitons, but there are also articles from the field of transport theory and plasma physics and an unconventional view of classical and quantum electrodynamics. All contributions to this volume will appear under their corresponding subject categories. (HJ)
A solution to nonlinearity problems
International Nuclear Information System (INIS)
Neuffer, D.V.
1989-01-01
New methods of correcting dynamic nonlinearities resulting from the multipole content of a synchrotron or transport line are presented. In a simplest form, correction elements are places at the center (C) of the accelerator half-cells as well as near the focusing (F) and defocusing (D) quadrupoles. In a first approximation, the corrector strengths follow Simpson's Rule, forming an accurate quasi-local canceling approximation to the nonlinearity. The F, C, and D correctors may also be used to obtain precise control of the horizontal, coupled, and vertical motion. Correction by three or more orders of magnitude can be obtained, and simple solutions to a fundamental problem in beam transport have been obtained. 13 refs., 1 fig., 1 tab
Optimization for nonlinear inverse problem
International Nuclear Information System (INIS)
Boyadzhiev, G.; Brandmayr, E.; Pinat, T.; Panza, G.F.
2007-06-01
The nonlinear inversion of geophysical data in general does not yield a unique solution, but a single model, representing the investigated field, is preferred for an easy geological interpretation of the observations. The analyzed region is constituted by a number of sub-regions where the multi-valued nonlinear inversion is applied, which leads to a multi-valued solution. Therefore, combining the values of the solution in each sub-region, many acceptable models are obtained for the entire region and this complicates the geological interpretation of geophysical investigations. In this paper are presented new methodologies, capable to select one model, among all acceptable ones, that satisfies different criteria of smoothness in the explored space of solutions. In this work we focus on the non-linear inversion of surface waves dispersion curves, which gives structural models of shear-wave velocity versus depth, but the basic concepts have a general validity. (author)
Nonlinear acceleration of transport criticality problems
International Nuclear Information System (INIS)
Park, H.; Knoll, D.A.; Newman, C.K.
2011-01-01
We present a nonlinear acceleration algorithm for the transport criticality problem. The algorithm combines the well-known nonlinear diffusion acceleration (NDA) with a recently developed, Newton-based, nonlinear criticality acceleration (NCA) algorithm. The algorithm first employs the NDA to reduce the system to scalar flux, then the NCA is applied to the resulting drift-diffusion system. We apply a nonlinear elimination technique to eliminate the eigenvalue from the Jacobian matrix. Numerical results show that the algorithm reduces the CPU time a factor of 400 in a very diffusive system, and a factor of 5 in a non-diffusive system. (author)
Thermal rectification in nonlinear quantum circuits
DEFF Research Database (Denmark)
Ruokola, T.; Ojanen, T.; Jauho, Antti-Pekka
2009-01-01
We present a theoretical study of radiative heat transport in nonlinear solid-state quantum circuits. We give a detailed account of heat rectification effects, i.e., the asymmetry of heat current with respect to a reversal of the thermal gradient, in a system consisting of two reservoirs at finit...
Combined algorithms in nonlinear problems of magnetostatics
International Nuclear Information System (INIS)
Gregus, M.; Khoromskij, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.
1988-01-01
To solve boundary problems of magnetostatics in unbounded two- and three-dimensional regions, we construct combined algorithms based on a combination of the method of boundary integral equations with the grid methods. We study the question of substantiation of the combined method of nonlinear magnetostatic problem without the preliminary discretization of equations and give some results on the convergence of iterative processes that arise in non-linear cases. We also discuss economical iterative processes and algorithms that solve boundary integral equations on certain surfaces. Finally, examples of numerical solutions of magnetostatic problems that arose when modelling the fields of electrophysical installations are given too. 14 refs.; 2 figs.; 1 tab
Advanced Research Workshop on Nonlinear Hyperbolic Problems
Serre, Denis; Raviart, Pierre-Arnaud
1987-01-01
The field of nonlinear hyperbolic problems has been expanding very fast over the past few years, and has applications - actual and potential - in aerodynamics, multifluid flows, combustion, detonics amongst other. The difficulties that arise in application are of theoretical as well as numerical nature. In fact, the papers in this volume of proceedings deal to a greater extent with theoretical problems emerging in the resolution of nonlinear hyperbolic systems than with numerical methods. The volume provides an excellent up-to-date review of the current research trends in this area.
Nonlinear Thermal Instability in Compressible Viscous Flows Without Heat Conductivity
Jiang, Fei
2018-04-01
We investigate the thermal instability of a smooth equilibrium state, in which the density function satisfies Schwarzschild's (instability) condition, to a compressible heat-conducting viscous flow without heat conductivity in the presence of a uniform gravitational field in a three-dimensional bounded domain. We show that the equilibrium state is linearly unstable by a modified variational method. Then, based on the constructed linearly unstable solutions and a local well-posedness result of classical solutions to the original nonlinear problem, we further construct the initial data of linearly unstable solutions to be the one of the original nonlinear problem, and establish an appropriate energy estimate of Gronwall-type. With the help of the established energy estimate, we finally show that the equilibrium state is nonlinearly unstable in the sense of Hadamard by a careful bootstrap instability argument.
Application of nonlinear Krylov acceleration to radiative transfer problems
International Nuclear Information System (INIS)
Till, A. T.; Adams, M. L.; Morel, J. E.
2013-01-01
The iterative solution technique used for radiative transfer is normally nested, with outer thermal iterations and inner transport iterations. We implement a nonlinear Krylov acceleration (NKA) method in the PDT code for radiative transfer problems that breaks nesting, resulting in more thermal iterations but significantly fewer total inner transport iterations. Using the metric of total inner transport iterations, we investigate a crooked-pipe-like problem and a pseudo-shock-tube problem. Using only sweep preconditioning, we compare NKA against a typical inner / outer method employing GMRES / Newton and find NKA to be comparable or superior. Finally, we demonstrate the efficacy of applying diffusion-based preconditioning to grey problems in conjunction with NKA. (authors)
International Nuclear Information System (INIS)
Chambarel, A.; Pumborios, M.
1992-01-01
This paper reports that many engineering problems concern the determination of a steady state solution in the case with strong thermal gradients, and results obtained using the finite-element technique are sometimes inaccurate, particularly for nonlinear problems with unadapted meshes. Building on previous results in linear problems, we propose an autoadaptive technique for nonlinear cases that uses quasi-Newtonian iterations to reevaluate an interpolation error estimation. The authors perfected an automatic refinement technique to solve the nonlinear thermal problem of temperature calculus in a cast-iron cylinder head of a diesel engine
Selected Problems in Nonlinear Dynamics and Sociophysics
Westley, Alexandra Renee
This Ph.D. dissertation focuses on a collection of problems on the dynamical behavior of nonlinear many-body systems, drawn from two substantially different areas. First, the dynamical behavior seen in strongly nonlinear lattices such as in the Fermi-Pasta-Ulam-Tsingou (FPUT) system (part I) and second, time evolution behavior of interacting living objects which can be broadly considered as sociophysics systems (part II). The studies on FPUT-like systems will comprise of five chapters, dedicated to the properties of solitary and anti-solitary waves in the system, how localized nonlinear excitations decay and spread throughout these lattices, how two colliding solitary waves can precipitate highly localized and stable excitations, a possible alternative way to view these localized excitations through Duffing oscillators, and finally an exploration of parametric resonance in an FPUT-like lattice. Part II consists of two problems in the context of sociophysics. I use molecular dynamics inspired simulations to study the size and the stability of social groups of chimpanzees (such as those seen in central Africa) and compare the results with existing observations on the stability of chimpanzee societies. Secondly, I use an agent-based model to simulate land battles between an intelligent army and an insurgency when both have access to equally powerful weaponry. The study considers genetic algorithm based adaptive strategies to infer the strategies needed for the intelligent army to win the battles.
Special problems: LBB, thermal effects
International Nuclear Information System (INIS)
Lin Chiwen
2001-01-01
This section presents the discussion of special problems in the reactor coolant system design, including LBB and thermal effects. First, the categories of fracture mechanics technology applicable to LBB is discussed. Two categories of fracture mechanics, namely: linear-elastic fracture mechanics (LEFM) and elastic-plastic fracture mechanics (EPFM) are discussed specifically. Next, basic concepts of LEFM are discussed. This will be followed by a discussion of EPFM, with more specific discussion of the methodology currently acceptable to NRC, with the emphasis on the J-integral approach. This is followed by a discussion of the NRC position and recommendations and basic requirements laid out by NRC. A specific example of LBB application to WPWR piping is used to identify the key steps to be followed, in order to satisfy the recommendations and requirements of NRC. An application of LBB to the WPWR reactor coolant loop piping is provided as further illustration of the methodology. This section focuses on the thermal effects which have not been addressed earlier, and the thermal effects which have caused particular concerns on potential reactor degradations, such as pressurized thermal shocks. The organization of this section is divided into the following subsections: linear-elastic fracture mechanics (LEFM); elastic-plastic fracture mechanics (EPFM); J concepts; NRC recommendations and requirements on the application of LBB; two specific applications of LBB to WPWR piping; PWR internals degradation; thermal fatigue considerations; a case study of pressurized thermal shock
Bayesian nonlinear regression for large small problems
Chakraborty, Sounak; Ghosh, Malay; Mallick, Bani K.
2012-01-01
Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. This is known as large p small n problem. Furthermore, the problem is more complicated when we have multiple correlated responses. We develop multivariate nonlinear regression models in this setup for accurate prediction. In this paper, we introduce a full Bayesian support vector regression model with Vapnik's ε-insensitive loss function, based on reproducing kernel Hilbert spaces (RKHS) under the multivariate correlated response setup. This provides a full probabilistic description of support vector machine (SVM) rather than an algorithm for fitting purposes. We have also introduced a multivariate version of the relevance vector machine (RVM). Instead of the original treatment of the RVM relying on the use of type II maximum likelihood estimates of the hyper-parameters, we put a prior on the hyper-parameters and use Markov chain Monte Carlo technique for computation. We have also proposed an empirical Bayes method for our RVM and SVM. Our methods are illustrated with a prediction problem in the near-infrared (NIR) spectroscopy. A simulation study is also undertaken to check the prediction accuracy of our models. © 2012 Elsevier Inc.
Bayesian nonlinear regression for large small problems
Chakraborty, Sounak
2012-07-01
Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. This is known as large p small n problem. Furthermore, the problem is more complicated when we have multiple correlated responses. We develop multivariate nonlinear regression models in this setup for accurate prediction. In this paper, we introduce a full Bayesian support vector regression model with Vapnik\\'s ε-insensitive loss function, based on reproducing kernel Hilbert spaces (RKHS) under the multivariate correlated response setup. This provides a full probabilistic description of support vector machine (SVM) rather than an algorithm for fitting purposes. We have also introduced a multivariate version of the relevance vector machine (RVM). Instead of the original treatment of the RVM relying on the use of type II maximum likelihood estimates of the hyper-parameters, we put a prior on the hyper-parameters and use Markov chain Monte Carlo technique for computation. We have also proposed an empirical Bayes method for our RVM and SVM. Our methods are illustrated with a prediction problem in the near-infrared (NIR) spectroscopy. A simulation study is also undertaken to check the prediction accuracy of our models. © 2012 Elsevier Inc.
Studies in nonlinear problems of energy
Energy Technology Data Exchange (ETDEWEB)
Matkowsky, B.J.
1992-07-01
Emphasis has been on combustion and flame propagation. The research program was on modeling, analysis and computation of combustion phenomena, with emphasis on transition from laminar to turbulent combustion. Nonlinear dynamics and pattern formation were investigated in the transition. Stability of combustion waves, and transitions to complex waves are described. Combustion waves possess large activation energies, so that chemical reactions are significant only in thin layers, or reaction zones. In limit of infinite activation energy, the zones shrink to moving surfaces, (fronts) which must be found during the analysis, so that (moving free boundary problems). The studies are carried out for limiting case with fronts, while the numerical studies are carried out for finite, though large, activation energy. Accurate resolution of the solution in the reaction zones is essential, otherwise false predictions of dynamics are possible. Since the the reaction zones move, adaptive pseudo-spectral methods were developed. The approach is based on a synergism of analytical and computational methods. The numerical computations build on and extend the analytical information. Furthermore, analytical solutions serve as benchmarks for testing the accuracy of the computation. Finally, ideas from analysis (singular perturbation theory) have induced new approaches to computations. The computational results suggest new analysis to be considered. Among the recent interesting results, was spatio-temporal chaos in combustion. One goal is extension of the adaptive pseudo-spectral methods to adaptive domain decomposition methods. Efforts have begun to develop such methods for problems with multiple reaction zones, corresponding to problems with more complex, and more realistic chemistry. Other topics included stochastics, oscillators, Rysteretic Josephson junctions, DC SQUID, Markov jumps, laser with saturable absorber, chemical physics, Brownian movement, combustion synthesis, etc.
An algorithm for nonlinear thermal analysis of fuel bearing pads
International Nuclear Information System (INIS)
Attia, M.H.; D'Silva, N.
1983-01-01
An algorithm has been developed for accurate prediction of the temperature field in a CANDU fuel bearing pad and the extent of the nucleate boiling in the crevice region. The methodology recognizes the nonlinear nature of the problem due to the fact that local boiling is both controlling and being controlled by the conditions of heat transfer at the boundaries. The finite difference model accounts for the volumetric effect of the thermal contact resistance at the bearing pad/pressure tube interface. It also allows the evaluation of the thermal barrier effect caused by applying an oxide film on the radiused surface of the bearing pad. Information pertaining to the distribution of the coefficient of heat transfer over water-cooled surfaces has been generated. Analysis of the results indicated the significance of considering the nonlinear behaviour of the system in determining its state of equilibrium. It also indicated that, depending on the thickness of the oxide layer and the position of the bearing pad along the core of the reactor, the nucleate boiling process can be prevented
Nonlinear thermal reduced model for Microwave Circuit Analysis
Chang, Christophe; Sommet, Raphael; Quéré, Raymond; Dueme, Ph.
2004-01-01
With the constant increase of transistor power density, electro thermal modeling is becoming a necessity for accurate prediction of device electrical performances. For this reason, this paper deals with a methodology to obtain a precise nonlinear thermal model based on Model Order Reduction of a three dimensional thermal Finite Element (FE) description. This reduced thermal model is based on the Ritz vector approach which ensure the steady state solution in every case. An equi...
Thermal shock problems in a plate
International Nuclear Information System (INIS)
Takeuti, Y.; Furukawa, T.
1981-01-01
The problems considered are coupled dynamic thermoelastic analysis in a plate. First we try to examine a problem of the coupled dynamic thermal stress problem with small time approximation for the finite region. Next, we treatise both effects individually by pursuing rigorous anaylsis without small time approximation. Finally we consider thermal shock problems in a plate against different values of heat transfer coefficient (Biot's number) for the time. In conclusion, for usual materials, the inertia effect may be disregarded in the pure thermal problems in contrast to the coupling effect which brings small lags in the temperature and thermal stress distributions. For the consideration of the maximum thermal stress problems, Manson's uncoupled quasi-static results give enough approximation to the thermal shock problems without significant error from our numerical results. The analysis is developed by the use of Laplace transforms and several useful graphical illustrations are given. (orig./HP)
Multisplitting for linear, least squares and nonlinear problems
Energy Technology Data Exchange (ETDEWEB)
Renaut, R.
1996-12-31
In earlier work, presented at the 1994 Iterative Methods meeting, a multisplitting (MS) method of block relaxation type was utilized for the solution of the least squares problem, and nonlinear unconstrained problems. This talk will focus on recent developments of the general approach and represents joint work both with Andreas Frommer, University of Wupertal for the linear problems and with Hans Mittelmann, Arizona State University for the nonlinear problems.
Energy Technology Data Exchange (ETDEWEB)
Cai, X C; Marcinkowski, L; Vassilevski, P S
2005-02-10
This paper extends previous results on nonlinear Schwarz preconditioning ([4]) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The non-local finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in [8]. Then, the algebraic construction from [9] of the corresponding non-linear finite element subproblems is applied to generate the subspace based nonlinear preconditioner. The overall nonlinearly preconditioned problem is solved by an inexact Newton method. Numerical illustration is also provided.
Nonlinear singular perturbation problems of arbitrary real orders
International Nuclear Information System (INIS)
Bijura, Angelina M.
2003-10-01
Higher order asymptotic solutions of singularly perturbed nonlinear fractional integral and derivatives of order 1/2 are investigated. It is particularly shown that whilst certain asymptotic expansions are applied successfully to linear equations and particular nonlinear problems, the standard formal asymptotic expansion is appropriate for the general class of nonlinear equations. This theory is then generalised to the general equation (of order β, 0 < β < 1). (author)
Analytical Solutions to Non-linear Mechanical Oscillation Problems
DEFF Research Database (Denmark)
Kaliji, H. D.; Ghadimi, M.; Barari, Amin
2011-01-01
In this paper, the Max-Min Method is utilized for solving the nonlinear oscillation problems. The proposed approach is applied to three systems with complex nonlinear terms in their motion equations. By means of this method, the dynamic behavior of oscillation systems can be easily approximated u...
Frictional Heating During Sliding of two Semi-Spaces with Arbitrary Thermal Nonlinearity
Directory of Open Access Journals (Sweden)
Och Ewa
2014-12-01
Full Text Available Analytical and numerical solution for transient thermal problems of friction were presented for semi limited bodies made from thermosensitive materials in which coefficient of thermal conductivity and specific heat arbitrarily depend on the temperature (materials with arbitrary non-linearity. With the constant power of friction assumption and imperfect thermal contact linearization of nonlinear problems formulated initial-boundary thermal conductivity, using Kirchhoff transformation is partial. In order to complete linearization, method of successive approximations was used. On the basis of obtained solutions a numerical analysis of two friction systems in which one element is constant (cermet FMC-845 and another is variable (grey iron ChNMKh or aluminum-based composite alloy AL MMC was conducted
A Linearized Relaxing Algorithm for the Specific Nonlinear Optimization Problem
Directory of Open Access Journals (Sweden)
Mio Horai
2016-01-01
Full Text Available We propose a new method for the specific nonlinear and nonconvex global optimization problem by using a linear relaxation technique. To simplify the specific nonlinear and nonconvex optimization problem, we transform the problem to the lower linear relaxation form, and we solve the linear relaxation optimization problem by the Branch and Bound Algorithm. Under some reasonable assumptions, the global convergence of the algorithm is certified for the problem. Numerical results show that this method is more efficient than the previous methods.
Ming, Yi; Li, Hui-Min; Ding, Ze-Jun
2016-03-01
Thermal rectification and negative differential thermal conductance were realized in harmonic chains in this work. We used the generalized Caldeira-Leggett model to study the heat flow. In contrast to most previous studies considering only the linear system-bath coupling, we considered the nonlinear system-bath coupling based on recent experiment [Eichler et al., Nat. Nanotech. 6, 339 (2011), 10.1038/nnano.2011.71]. When the linear coupling constant is weak, the multiphonon processes induced by the nonlinear coupling allow more phonons transport across the system-bath interface and hence the heat current is enhanced. Consequently, thermal rectification and negative differential thermal conductance are achieved when the nonlinear couplings are asymmetric. However, when the linear coupling constant is strong, the umklapp processes dominate the multiphonon processes. Nonlinear coupling suppresses the heat current. Thermal rectification is also achieved. But the direction of rectification is reversed compared to the results of weak linear coupling constant.
On a non-linear pseudodifferential boundary value problem
International Nuclear Information System (INIS)
Nguyen Minh Chuong.
1989-12-01
A pseudodifferential boundary value problem for operators with symbols taking values in Sobolev spaces and with non-linear right-hand side was studied. Existence and uniqueness theorems were proved. (author). 11 refs
Nonlinear diffusion problem arising in plasma physics
International Nuclear Information System (INIS)
Berryman, J.G.; Holland, C.J.
1978-01-01
In earlier studies of plasma diffusion with Okuda-Dawson scaling (D approx. n/sup -1/2/), perturbation theory indicated that arbitrary initial data should evolve rapidly toward the separation solution of the relevant nonlinear diffusion equation. Now a Lyapunov functional has been found which is strictly decreasing in time and bounded below. The rigorous proof that arbitrary initial data evolve toeard the separable solution is summarized. Rigorous bounds on the decay time are also presented
Non-linear electromagnetic interactions in thermal QED
International Nuclear Information System (INIS)
Brandt, F.T.; Frenkel, J.
1994-08-01
The behavior of the non-linear interactions between electromagnetic fields at high temperature is examined. It is shown that, in general, the log(T) dependence on the temperature of the Green functions is simply related to their UV behavior at zero-temperature. It is argued that the effective action describing the nonlinear thermal electromagnetic interactions has a finite limit as T -> ∞. This thermal action approaches, in the long wavelength limit, the negative of the corresponding zero-temperature action. (author). 12 refs, 1 fig
A Nonlinear Adaptive Filter for Gyro Thermal Bias Error Cancellation
Galante, Joseph M.; Sanner, Robert M.
2012-01-01
Deterministic errors in angular rate gyros, such as thermal biases, can have a significant impact on spacecraft attitude knowledge. In particular, thermal biases are often the dominant error source in MEMS gyros after calibration. Filters, such as J\\,fEKFs, are commonly used to mitigate the impact of gyro errors and gyro noise on spacecraft closed loop pointing accuracy, but often have difficulty in rapidly changing thermal environments and can be computationally expensive. In this report an existing nonlinear adaptive filter is used as the basis for a new nonlinear adaptive filter designed to estimate and cancel thermal bias effects. A description of the filter is presented along with an implementation suitable for discrete-time applications. A simulation analysis demonstrates the performance of the filter in the presence of noisy measurements and provides a comparison with existing techniques.
Dynamic nonlinear thermal optical effects in coupled ring resonators
Directory of Open Access Journals (Sweden)
Chenguang Huang
2012-09-01
Full Text Available We investigate the dynamic nonlinear thermal optical effects in a photonic system of two coupled ring resonators. A bus waveguide is used to couple light in and out of one of the coupled resonators. Based on the coupling from the bus to the resonator, the coupling between the resonators and the intrinsic loss of each individual resonator, the system transmission spectrum can be classified by three different categories: coupled-resonator-induced absorption, coupled-resonator-induced transparency and over coupled resonance splitting. Dynamic thermal optical effects due to linear absorption have been analyzed for each category as a function of the input power. The heat power in each resonator determines the thermal dynamics in this coupled resonator system. Multiple “shark fins” and power competition between resonators can be foreseen. Also, the nonlinear absorption induced thermal effects have been discussed.
Higher-order techniques for some problems of nonlinear control
Directory of Open Access Journals (Sweden)
Sarychev Andrey V.
2002-01-01
Full Text Available A natural first step when dealing with a nonlinear problem is an application of some version of linearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study nonlinear control systems in such cases. The presentation includes: nonlinear systems with impulsive and distribution-like inputs; second-order optimality conditions for bang–bang extremals of optimal control problems; methods of high-order averaging for studying stability and stabilization of time-variant control systems.
International Nuclear Information System (INIS)
Kobayashi, Akira; Ohnishi, Yuzo
1986-01-01
The nonlinearity of material properties used in the coupled mechanical-hydraulic-thermal analysis is investigated from the past literatures. Some nonlinearity that is respectively effective for the system is introduced into our computer code for analysis such a coupling problem by using finite element method. And the effects of nonlinearity of each material property on the coupled behavior in rock mass are examined for simple model and Stripa project model with the computer code. (author)
Extra phase noise from thermal fluctuations in nonlinear optical crystals
DEFF Research Database (Denmark)
César, J. E. S.; Coelho, A.S.; Cassemiro, K.N.
2009-01-01
We show theoretically and experimentally that scattered light by thermal phonons inside a second-order nonlinear crystal is the source of additional phase noise observed in optical parametric oscillators. This additional phase noise reduces the quantum correlations and has hitherto hindered the d...
Two problems in thermal field theory
Indian Academy of Sciences (India)
In this talk, I review recent progress made in two areas of thermal field theory. In par- ticular, I discuss various approaches for the calculation of the quark gluon plasma thermodynamical properties, and the problem of its photon production rate. Keywords. Thermal field theory; quark-gluon plasma. PACS Nos 11.10.Wx; 12.38.
New Exact Penalty Functions for Nonlinear Constrained Optimization Problems
Directory of Open Access Journals (Sweden)
Bingzhuang Liu
2014-01-01
Full Text Available For two kinds of nonlinear constrained optimization problems, we propose two simple penalty functions, respectively, by augmenting the dimension of the primal problem with a variable that controls the weight of the penalty terms. Both of the penalty functions enjoy improved smoothness. Under mild conditions, it can be proved that our penalty functions are both exact in the sense that local minimizers of the associated penalty problem are precisely the local minimizers of the original constrained problem.
Renormalization-group approach to nonlinear radiation-transport problems
International Nuclear Information System (INIS)
Chapline, G.F.
1980-01-01
A Monte Carlo method is derived for solving nonlinear radiation-transport problems that allows one to average over the effects of many photon absorptions and emissions at frequencies where the opacity is large. This method should allow one to treat radiation-transport problems with large optical depths, e.g., line-transport problems, with little increase in computational effort over that which is required for optically thin problems
IMPSOR, 3-D Boundary Problems Solution for Thermal Conductivity Calculation
International Nuclear Information System (INIS)
Wilson, D.G.; Williams, M.A.
1994-01-01
1 - Description of program or function: IMPSOR implements finite difference methods for multidimensional moving boundary problems with Dirichlet or Neumann boundary conditions. The geometry of the spatial domain is a rectangular parallelepiped with dimensions specified by the user. Dirichlet or Neumann boundary conditions may be specified on each face of the box independently. The user defines the initial and boundary conditions as well as the thermal and physical properties of the problem and several parameters for the numerical method, e.g. degree of implicitness, time-step size. 2 - Method of solution: The spatial domain is partitioned and the governing equation discretized, which yields a nonlinear system of equations at each time-step. This nonlinear system is solved using a successive over-relaxation (SOR) algorithm. For a given node, the previous iteration's temperature and thermal conductivity values are used for advanced points with current values at previous points. This constitutes a Gauss-Seidel iteration. Most of the computing time used by the numerical method is spent in the iterative solution of the nonlinear system. The SOR scheme employed is designed to accommodate vectorization on a Cray X-MP. 3 - Restrictions on the complexity of the problem: Maximum of 70,000 nodes
Thermal Rectification in Graded Nonlinear Transmission Lines
International Nuclear Information System (INIS)
Xu Wen; Chen Wei-Zhong; Tao Feng
2011-01-01
We consider heat conduction in a nonlinear inductance-capacitance (LC) transmission line with an inductance gradient by adding white-noise signals. It is found that the heat flux in the direction of inductance decrease is larger than that in the direction of inductance increase. When the low-inductance end is at higher temperature, the phonon density decreases due to conversion to high-frequency phonons, which can not move to the high-inductance end due to its lower cutoff frequency. However, when the high-inductance end is at higher temperature, the loss of phonon density can be compensated for because some high-frequency phonons can move to the low-inductance end dur to its higher cutoff frequency. This leads to the asymmetry of energy transfer. Discussion shows that this asymmetry exists in a particular range of temperatures, and increases with the increase of the difference between heat baths and the inductance gradient. (fundamental areas of phenomenology(including applications))
On a Highly Nonlinear Self-Obstacle Optimal Control Problem
Energy Technology Data Exchange (ETDEWEB)
Di Donato, Daniela, E-mail: daniela.didonato@unitn.it [University of Trento, Department of Mathematics (Italy); Mugnai, Dimitri, E-mail: dimitri.mugnai@unipg.it [Università di Perugia, Dipartimento di Matematica e Informatica (Italy)
2015-10-15
We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems.
On the solvability of initial boundary value problems for nonlinear ...
African Journals Online (AJOL)
In this paper, we study the initial boundary value problems for a non-linear time dependent Schrödinger equation with Dirichlet and Neumann boundary conditions, respectively. We prove the existence and uniqueness of solutions of the initial boundary value problems by using Galerkin's method. Keywords: Initial boundary ...
Non-linear elastic thermal stress analysis with phase changes
International Nuclear Information System (INIS)
Amada, S.; Yang, W.H.
1978-01-01
The non-linear elastic, thermal stress analysis with temperature induced phase changes in the materials is presented. An infinite plate (or body) with a circular hole (or tunnel) is subjected to a thermal loading on its inner surface. The peak temperature around the hole reaches beyond the melting point of the material. The non-linear diffusion equation is solved numerically using the finite difference method. The material properties change rapidly at temperatures where the change of crystal structures and solid-liquid transition occur. The elastic stresses induced by the transient non-homogeneous temperature distribution are calculated. The stresses change remarkably when the phase changes occur and there are residual stresses remaining in the plate after one cycle of thermal loading. (Auth.)
Jackson, C. E., Jr.
1977-01-01
A sample problem library containing 20 problems covering most facets of Nastran Thermal Analyzer modeling is presented. Areas discussed include radiative interchange, arbitrary nonlinear loads, transient temperature and steady-state structural plots, temperature-dependent conductivities, simulated multi-layer insulation, and constraint techniques. The use of the major control options and important DMAP alters is demonstrated.
Multigrid Reduction in Time for Nonlinear Parabolic Problems
Energy Technology Data Exchange (ETDEWEB)
Falgout, R. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Manteuffel, T. A. [Univ. of Colorado, Boulder, CO (United States); O' Neill, B. [Univ. of Colorado, Boulder, CO (United States); Schroder, J. B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-01-04
The need for parallel-in-time is being driven by changes in computer architectures, where future speed-ups will be available through greater concurrency, but not faster clock speeds, which are stagnant.This leads to a bottleneck for sequential time marching schemes, because they lack parallelism in the time dimension. Multigrid Reduction in Time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficient is defined as achieving similar performance when compared to a corresponding linear problem. As our benchmark, we use the p-Laplacian, where p = 4 corresponds to a well-known nonlinear diffusion equation and p = 2 corresponds to our benchmark linear diffusion problem. When considering linear problems and implicit methods, the use of optimal spatial solvers such as spatial multigrid imply that the cost of one time step evaluation is fixed across temporal levels, which have a large variation in time step sizes. This is not the case for nonlinear problems, where the work required increases dramatically on coarser time grids, where relatively large time steps lead to worse conditioned nonlinear solves and increased nonlinear iteration counts per time step evaluation. This is the key difficulty explored by this paper. We show that by using a variety of strategies, most importantly, spatial coarsening and an alternate initial guess to the nonlinear time-step solver, we can reduce the work per time step evaluation over all temporal levels to a range similar with the corresponding linear problem. This allows for parallel scaling behavior comparable to the corresponding linear problem.
Renormgroup symmetries in problems of nonlinear geometrical optics
International Nuclear Information System (INIS)
Kovalev, V.F.
1996-01-01
Utilization and further development of the previously announced approach [1,2] enables one to construct renormgroup symmetries for a boundary value problem for the system of equations which describes propagation of a powerful radiation in a nonlinear medium in geometrical optics approximation. With the help of renormgroup symmetries new rigorous and approximate analytical solutions of nonlinear geometrical optics equations are obtained. Explicit analytical expressions are presented that characterize spatial evolution of laser beam which has an arbitrary intensity dependence at the boundary of the nonlinear medium. (author)
First international conference on nonlinear problems in aviation and aerospace
International Nuclear Information System (INIS)
Sivasundaram, S.
1994-01-01
The International Conference on Nonlinear Problems in Aviation and Aerospace was held at Embry-Riddle Aeronautical University, Daytona Beach, Florida on May 9-11, 1996. This conference was sponsored by the International Federation of Nonlinear Analysts, International Federation of Information Processing, and Embry-Riddle Aeronautical University. Over one hundred engineers, scientists, and mathematicians from seventeen countries attended. These proceedings include keynote addresses, invited lectures, and contributed papers presented during the conference
θ-convex nonlinear programming problems
International Nuclear Information System (INIS)
Emam, T.
2008-01-01
A class of sets and a class of functions called θ-convex sets and θ-convex functions are introduced by relaxing the definitions of convex sets and operator θ on the sets and domain of definition of the functions. The optimally results for θ-convex programming problems are established.
Designs for thermal harvesting with nonlinear coordinate transformation
Ji, Qingxiang; Fang, Guodong; Liang, Jun
2018-04-01
In this paper a thermal concentrating design method was proposed based on the concept of generating function without knowing the needed coordinate transformation beforehand. The thermal harvesting performance was quantitatively characterized by heat concentrating efficiency and external temperature perturbation. Nonlinear transformations of different forms were employed to design high order thermal concentrators, and corresponding harvesting performances were investigated by numerical simulations. The numerical results shows that the form of coordinate transformation directly influences the distributions of heat flows inside the concentrator, consequently, influences the thermal harvesting behaviors significantly. The concentrating performance can be actively controlled and optimized by changing the form of coordinate transformations. The analysis in this paper offers a beneficial method to flexibly tune the harvesting performance of the thermal concentrator according to the requirements of practical applications.
A remark on some nonlinear elliptic problems
Directory of Open Access Journals (Sweden)
Lucio Boccardo
2002-10-01
Full Text Available We shall prove an existence result of $W_0^{1,p}(Omega$ solutions for the boundary value problem $$displylines{ -mathop{m div} a(x, u,abla u=F quadmbox{in }Omegacr u=0quadmbox{on }partialOmega }$$ with right hand side in $W^{-1,p'}(Omega$. The features of the equation are that no restrictions on the growth of the function $a(x,s,xi$ with respect to $s$ are assumed and that $a(x,s,xi$ with respect to $xi$ is monotone, but not strictly monotone. We overcome the difficulty of the uncontrolled growth of $a$ thanks to a suitable definition of solution (similar to the one introduced in cite{B6} for the study of the Dirichlet problem in $L^1$ and the difficulty of the not strict monotonicity thanks to a technique (the $L^1$-version of Minty's Lemma similar to the one used in cite{BO}.
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 ...
Zhang, Xiao-Liang; Liu, Zhi-Bo; Li, Xiao-Chun; Ma, Qiang; Chen, Xu-Dong; Tian, Jian-Guo; Xu, Yan-Fei; Chen, Yong-Sheng
2013-03-25
The nonlinear refraction (NLR) properties of graphene oxide (GO) in N, N-Dimethylformamide (DMF) was studied in nanosecond, picosecond and femtosecond time regimes by Z-scan technique. Results show that the dispersion of GO in DMF exhibits negative NLR properties in nanosecond time regime, which is mainly attributed to transient thermal effect in the dispersion. The dispersion also exhibits negative NLR in picosecond and femtosecond time regimes, which are arising from sp(2)- hybridized carbon domains and sp(3)- hybridized matrix in GO sheets. To illustrate the relations between NLR and nonlinear absorption (NLA), NLA properties of the dispersion were also studied in nanosecond, picosecond and femtosecond time regimes.
Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions
Directory of Open Access Journals (Sweden)
Ciprian G. Gal
2017-01-01
Full Text Available Given a bounded domain Ω⊂RN with a Lipschitz boundary ∂Ω and p,q∈(1,+∞, we consider the quasilinear elliptic equation -Δpu+α1u=f in Ω complemented with the generalized Wentzell-Robin type boundary conditions of the form bx∇up-2∂nu-ρbxΔq,Γu+α2u=g on ∂Ω. In the first part of the article, we give necessary and sufficient conditions in terms of the given functions f, g and the nonlinearities α1, α2, for the solvability of the above nonlinear elliptic boundary value problems with the nonlinear boundary conditions. In other words, we establish a sort of “nonlinear Fredholm alternative” for our problem which extends the corresponding Landesman and Lazer result for elliptic problems with linear homogeneous boundary conditions. In the second part, we give some additional results on existence and uniqueness and we study the regularity of the weak solutions for these classes of nonlinear problems. More precisely, we show some global a priori estimates for these weak solutions in an L∞-setting.
Galerkin approximations of nonlinear optimal control problems in Hilbert spaces
Directory of Open Access Journals (Sweden)
Mickael D. Chekroun
2017-07-01
Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.
Solution of Contact Problems for Nonlinear Gao Beam and Obstacle
Directory of Open Access Journals (Sweden)
J. Machalová
2015-01-01
Full Text Available Contact problem for a large deformed beam with an elastic obstacle is formulated, analyzed, and numerically solved. The beam model is governed by a nonlinear fourth-order differential equation developed by Gao, while the obstacle is considered as the elastic foundation of Winkler’s type in some distance under the beam. The problem is static without a friction and modeled either using Signorini conditions or by means of normal compliance contact conditions. The problems are then reformulated as optimal control problems which is useful both for theoretical aspects and for solution methods. Discretization is based on using the mixed finite element method with independent discretization and interpolations for foundation and beam elements. Numerical examples demonstrate usefulness of the presented solution method. Results for the nonlinear Gao beam are compared with results for the classical Euler-Bernoulli beam model.
New preconditioned conjugate gradient algorithms for nonlinear unconstrained optimization problems
International Nuclear Information System (INIS)
Al-Bayati, A.; Al-Asadi, N.
1997-01-01
This paper presents two new predilection conjugate gradient algorithms for nonlinear unconstrained optimization problems and examines their computational performance. Computational experience shows that the new proposed algorithms generally imp lone the efficiency of Nazareth's [13] preconditioned conjugate gradient algorithm. (authors). 16 refs., 1 tab
Experimental analysis of nonlinear problems in solid mechanics
International Nuclear Information System (INIS)
1982-01-01
The booklet presents abstracts of papers from the Euromech Colloqium No. 152 held from Sept. 20th to 24th, 1982 in Wuppertal, Federal Republic of Germany. All the papers are dealing with Experimental Analysis of Nonlinear Problems in Solid Mechanics. (RW)
Multiple solutions for inhomogeneous nonlinear elliptic problems arising in astrophyiscs
Directory of Open Access Journals (Sweden)
Marco Calahorrano
2004-04-01
Full Text Available Using variational methods we prove the existence and multiplicity of solutions for some nonlinear inhomogeneous elliptic problems on a bounded domain in $mathbb{R}^n$, with $ngeq 2$ and a smooth boundary, and when the domain is $mathbb{R}_+^n$
Some problems on nonlinear hyperbolic equations and applications
Peng, YueJun
2010-01-01
This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.
Adomian decomposition method for nonlinear Sturm-Liouville problems
Directory of Open Access Journals (Sweden)
Sennur Somali
2007-09-01
Full Text Available In this paper the Adomian decomposition method is applied to the nonlinear Sturm-Liouville problem-y" + y(tp=λy(t, y(t > 0, t ∈ I = (0, 1, y(0 = y(1 = 0, where p > 1 is a constant and λ > 0 is an eigenvalue parameter. Also, the eigenvalues and the behavior of eigenfuctions of the problem are demonstrated.
Computer Simulation in Problems of Thermal Strength
Directory of Open Access Journals (Sweden)
Olga I. Chelyapina
2012-05-01
Full Text Available This article discusses informative technology of using graphical programming environment LabVIEW 2009 when calculating and predicting the thermal strength of materials with an inhomogeneous structure. Algorithm for processing the experimental data was developed as part of the problem.
Some nonlinear problems in the manipulation of beams
International Nuclear Information System (INIS)
Sessler, A.M.
1990-01-01
An overview is given of nonlinear problems that arise in the manipulation of beams. Beams can be made of material particles or photons, can be intense or dilute, can be energetic or not, and they can be propagating in vacuum or in a medium. The nonlinear aspects of the motion are different in each case, and this diversity of behavior is categorized. Many examples are given, which serves to illustrate the categorization and, furthermore, display the richness of behavior encountered in the physics of beams. 25 refs., 5 figs
Thermal conductivity in one-dimensional nonlinear systems
Politi, Antonio; Giardinà, Cristian; Livi, Roberto; Vassalli, Massimo
2000-03-01
Thermal conducitivity of one-dimensional nonlinear systems typically diverges in the thermodynamic limit, whenever the momentum is conserved (i.e. in the absence of interactions with an external substrate). Evidence comes from detailed studies of Fermi-Pasta-Ulam and diatomic Toda chains. Here, we discuss the first example of a one-dimensional system obeying Fourier law : a chain of coupled rotators. Numerical estimates of the thermal conductivity obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those ones based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis of two variants of the rotator model.
Energy Technology Data Exchange (ETDEWEB)
Hayat, T. [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia); Muhammad, Taseer, E-mail: taseer_qau@yahoo.com [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Alsaedi, A.; Alhuthali, M.S. [Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia)
2015-07-01
Magnetohydrodynamic (MHD) three-dimensional flow of couple stress nanofluid in the presence of thermophoresis and Brownian motion effects is analyzed. Energy equation subject to nonlinear thermal radiation is taken into account. The flow is generated by a bidirectional stretching surface. Fluid is electrically conducting in the presence of a constant applied magnetic field. The induced magnetic field is neglected for a small magnetic Reynolds number. Mathematical formulation is performed using boundary layer analysis. Newly proposed boundary condition requiring zero nanoparticle mass flux is employed. The governing nonlinear mathematical problems are first converted into dimensionless expressions and then solved for the series solutions of velocities, temperature and nanoparticles concentration. Convergence of the constructed solutions is verified. Effects of emerging parameters on the temperature and nanoparticles concentration are plotted and discussed. Skin friction coefficients and Nusselt number are also computed and analyzed. It is found that the thermal boundary layer thickness is an increasing function of radiative effect. - Highlights: • Three-dimensional boundary layer flow of viscoelastic nanofluid is examined. • Nonlinear thermal radiation is analyzed. • Brownian motion and thermophoresis effects are present. • Recently developed condition requiring zero nanoparticle mass flux is implemented. • Construction of convergent solutions of nonlinear flow is possible.
Nonlinear Transient Thermal Analysis by the Force-Derivative Method
Balakrishnan, Narayani V.; Hou, Gene
1997-01-01
High-speed vehicles such as the Space Shuttle Orbiter must withstand severe aerodynamic heating during reentry through the atmosphere. The Shuttle skin and substructure are constructed primarily of aluminum, which must be protected during reentry with a thermal protection system (TPS) from being overheated beyond the allowable temperature limit, so that the structural integrity is maintained for subsequent flights. High-temperature reusable surface insulation (HRSI), a popular choice of passive insulation system, typically absorbs the incoming radiative or convective heat at its surface and then re-radiates most of it to the atmosphere while conducting the smallest amount possible to the structure by virtue of its low diffusivity. In order to ensure a successful thermal performance of the Shuttle under a prescribed reentry flight profile, a preflight reentry heating thermal analysis of the Shuttle must be done. The surface temperature profile, the transient response of the HRSI interior, and the structural temperatures are all required to evaluate the functioning of the HRSI. Transient temperature distributions which identify the regions of high temperature gradients, are also required to compute the thermal loads for a structural thermal stress analysis. Furthermore, a nonlinear analysis is necessary to account for the temperature-dependent thermal properties of the HRSI as well as to model radiation losses.
Thermal fluctuation problems encountered in LMFRs
International Nuclear Information System (INIS)
Gelineau, O.; Sperandio, M.; Martin, P.; Ricard, J.B.; Martin, L.; Bougault, A.
1994-01-01
One of the most significant problems of LMFBRs deals with thermal fluctuations. The main reason is that LMFBRs operate with sodium coolant at very different temperatures which leads to the existence of several areas of transition between hot and cold sodium. These transitions areas which are the critical points, maybe found in the reactor block as well as in the secondary and auxiliary loops. The characteristics of these thermal fluctuations are not easy to quantify because of their complex (random) behaviour, and often demand the use of thermalhydraulic mock-up tests. A good knowledge of these phenomena is essential because of the potential high level of damage they can induce on structures. Two typical thermal fluctuation problems encountered on operation reactors are described. They were not originally anticipated at the design stage of the former Phenix and the latter Superphenix reactors. Description and the analyses performed to describe the damaging process are explained. A well known thermal fluctuation problem is presented. It is pointed out how the feedback from the damages observed on operating reactors is used to prevent the components from any high cycle fatigue
Nanoparticles and nonlinear thermal radiation properties in the rheology of polymeric material
Directory of Open Access Journals (Sweden)
M. Awais
2018-03-01
Full Text Available The present analysis is related to the dynamics of polymeric liquids (Oldroyd-B model with the presence of nanoparticles. The rheological system is considered under the application of nonlinear thermal radiations. Energy and concentration equations are presented when thermophoresis and Brownian motion effects are present. Bidirectional form of stretching is considered to interpret the three-dimensional flow dynamics of polymeric liquid. Making use of the similarity transformations, problem is reduced into ordinary differential system which is approximated by using HAM. Influence of physical parameters including Deborah number, thermophoresis and Brownian motion on velocity, temperature and mass fraction expressions are plotted and analyzed. Numerical values for local Sherwood and Nusselt numbers are presented and discussed. Keywords: Nanoparticles, Polymeric liquid, Oldroyd-B model, Nonlinear thermal radiation
Lectures on nonlinear evolution equations initial value problems
Racke, Reinhard
2015-01-01
This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value p...
Nonlinear problems in fluid dynamics and inverse scattering: Nonlinear waves and inverse scattering
Ablowitz, Mark J.
1994-12-01
Research investigations involving the fundamental understanding and applications of nonlinear wave motion and related studies of inverse scattering and numerical computation have been carried out and a number of significant results have been obtained. A class of nonlinear wave equations which can be solved by the inverse scattering transform (IST) have been studied, including the Kadaomtsev-Petviashvili (KP) equation, the Davey-Stewartson equation, and the 2+1 Toda system. The solutions obtained by IST correspond to the Cauchy initial value problem with decaying initial data. We have also solved two important systems via the IST method: a 'Volterra' system in 2+1 dimensions and a new one dimensional nonlinear equation which we refer to as the Toda differential-delay equation. Research in computational chaos in moderate to long time numerical simulations continues.
Molecular nonlinear dynamics and protein thermal uncertainty quantification
Xia, Kelin; Wei, Guo-Wei
2014-01-01
This work introduces molecular nonlinear dynamics (MND) as a new approach for describing protein folding and aggregation. By using a mode system, we show that the MND of disordered proteins is chaotic while that of folded proteins exhibits intrinsically low dimensional manifolds (ILDMs). The stability of ILDMs is found to strongly correlate with protein energies. We propose a novel method for protein thermal uncertainty quantification based on persistently invariant ILDMs. Extensive comparison with experimental data and the state-of-the-art methods in the field validate the proposed new method for protein B-factor prediction. PMID:24697365
On a mixed problem for a coupled nonlinear system
Directory of Open Access Journals (Sweden)
Marcondes R. Clark
1997-03-01
Full Text Available In this article we prove the existence and uniqueness of solutions to the mixed problem associated with the nonlinear system $$ u_{tt}-M(int_Omega |abla u|^2dxDelta u+|u|^ ho u+heta =f $$ $$ heta _t -Delta heta +u_{t}=g $$ where $M$ is a positive real function, and $f$ and $g$ are known real functions.
On discrete maximum principles for nonlinear elliptic problems
Czech Academy of Sciences Publication Activity Database
Karátson, J.; Korotov, S.; Křížek, Michal
2007-01-01
Roč. 76, č. 1 (2007), s. 99-108 ISSN 0378-4754 R&D Projects: GA MŠk 1P05ME749; GA AV ČR IAA1019201 Institutional research plan: CEZ:AV0Z10190503 Keywords : nonlinear elliptic problem * mixed boundary conditions * finite element method Subject RIV: BA - General Mathematics Impact factor: 0.738, year: 2007
Describing function theory as applied to thermal and neutronic problems
International Nuclear Information System (INIS)
Nassersharif, B.
1983-01-01
Describing functions have traditionally been used to obtain the solutions of systems of ordinary differential equations. In this work the describing function concept has been extended to include nonlinear, distributed parameter partial differential equations. A three-stage solution algorithm is presented which can be applied to any nonlinear partial differential equation. Two generalized integral transforms were developed as the T-transform for the time domain and the B-transform for the spatial domain. The thermal diffusion describing function (TDDF) is developed for conduction of heat in solids and a general iterative solution along with convergence criteria is presented. The proposed solution method is used to solve the problem of heat transfer in nuclear fuel rods with annular fuel pellets. As a special instance the solid cylindrical fuel pellet is examined. A computer program is written which uses the describing function concept for computing fuel pin temperatures in the radial direction during reactor transients. The second problem investigated was the neutron diffusion equation which is intrinsically different from the first case. Although, for most situations, it can be treated as a linear differential equation, the describing function method is still applicable. A describing function solution is derived for two possible cases: constant diffusion coefficient and variable diffusion coefficient. Two classes of describing functions are defined for each case which portray the leakage and absorption phenomena. For the specific case of a slab reactor criticality problem the comparison between analytical and describing function solutions revealed an excellent agreement
Hydromagnetic nonlinear thermally radiative nanoliquid flow with Newtonian heat and mass conditions
Directory of Open Access Journals (Sweden)
Muhammad Ijaz Khan
Full Text Available This paper communicates the analysis of MHD three-dimensional flow of Jeffrey nanoliquid over a stretchable surface. Flow due to a bidirectional surface is considered. Heat and mass transfer subject to volume fraction of nanoparticles, heat generation and nonlinear solar radiation are examined. Newtonian heat and mass transportation conditions are employed at surface. Concept of boundary layer is utilized to developed the mathematical problem. The boundary value problem is dictated by ten physical parameters: Deborah number, Hartman number, ratio of stretching rates, thermophoretic parameter, Brownian motion parameter, Prandtl number, temperature ratio parameter, conjugate heat and mass parameters and Lewis number. Convergent solutions are obtained using homotopic procedure. Convergence zone for obtained results is explicitly identified. The obtained solutions are interpreted physically. Keywords: Hydromagnetic flow, Viscoelastic nanofluid, Thermophoretic and Brownian moment, Nonlinear thermal radiation, Heat generation
A new integrability theory for certain nonlinear physical problems
International Nuclear Information System (INIS)
Berger, M.S.
1993-01-01
A new mathematically sound integrability theory for certain nonlinear problems defined by ordinary or partial differential equations is defined. The new theory works in an arbitrary finite number of space dimensions. Moreover, if a system is integrable in the new sense described here, it has a remarkable stability property that distinguishes if from any previously known integrability ideas. The new theory proceeds by establishing a ''global normal form'' for the problem at hand. This normal form holds subject to canonical coordinate transformations, extending such classical ideas by using new nonlinear methods of infinite dimensional functional analysis. The global normal form in question is related to the mathematical theory of singularities of mappings of H. Whitney and R. Thom extended globally and form finite to infinite dimensions. Thus bifurcation phenomena are naturally included in the new integrability theory. Typical examples include the classically nonintegrable Riccati equation, certain non-Euclidean mean field theories, certain parabolic reaction diffusion equations and the hyperbolic nonlinear telegrapher's equation. (Author)
Implicit solvers for large-scale nonlinear problems
International Nuclear Information System (INIS)
Keyes, David E; Reynolds, Daniel R; Woodward, Carol S
2006-01-01
Computational scientists are grappling with increasingly complex, multi-rate applications that couple such physical phenomena as fluid dynamics, electromagnetics, radiation transport, chemical and nuclear reactions, and wave and material propagation in inhomogeneous media. Parallel computers with large storage capacities are paving the way for high-resolution simulations of coupled problems; however, hardware improvements alone will not prove enough to enable simulations based on brute-force algorithmic approaches. To accurately capture nonlinear couplings between dynamically relevant phenomena, often while stepping over rapid adjustments to quasi-equilibria, simulation scientists are increasingly turning to implicit formulations that require a discrete nonlinear system to be solved for each time step or steady state solution. Recent advances in iterative methods have made fully implicit formulations a viable option for solution of these large-scale problems. In this paper, we overview one of the most effective iterative methods, Newton-Krylov, for nonlinear systems and point to software packages with its implementation. We illustrate the method with an example from magnetically confined plasma fusion and briefly survey other areas in which implicit methods have bestowed important advantages, such as allowing high-order temporal integration and providing a pathway to sensitivity analyses and optimization. Lastly, we overview algorithm extensions under development motivated by current SciDAC applications
Global Optimization of Nonlinear Blend-Scheduling Problems
Directory of Open Access Journals (Sweden)
Pedro A. Castillo Castillo
2017-04-01
Full Text Available The scheduling of gasoline-blending operations is an important problem in the oil refining industry. This problem not only exhibits the combinatorial nature that is intrinsic to scheduling problems, but also non-convex nonlinear behavior, due to the blending of various materials with different quality properties. In this work, a global optimization algorithm is proposed to solve a previously published continuous-time mixed-integer nonlinear scheduling model for gasoline blending. The model includes blend recipe optimization, the distribution problem, and several important operational features and constraints. The algorithm employs piecewise McCormick relaxation (PMCR and normalized multiparametric disaggregation technique (NMDT to compute estimates of the global optimum. These techniques partition the domain of one of the variables in a bilinear term and generate convex relaxations for each partition. By increasing the number of partitions and reducing the domain of the variables, the algorithm is able to refine the estimates of the global solution. The algorithm is compared to two commercial global solvers and two heuristic methods by solving four examples from the literature. Results show that the proposed global optimization algorithm performs on par with commercial solvers but is not as fast as heuristic approaches.
Lavrentiev regularization method for nonlinear ill-posed problems
International Nuclear Information System (INIS)
Kinh, Nguyen Van
2002-10-01
In this paper we shall be concerned with Lavientiev regularization method to reconstruct solutions x 0 of non ill-posed problems F(x)=y o , where instead of y 0 noisy data y δ is an element of X with absolut(y δ -y 0 ) ≤ δ are given and F:X→X is an accretive nonlinear operator from a real reflexive Banach space X into itself. In this regularization method solutions x α δ are obtained by solving the singularly perturbed nonlinear operator equation F(x)+α(x-x*)=y δ with some initial guess x*. Assuming certain conditions concerning the operator F and the smoothness of the element x*-x 0 we derive stability estimates which show that the accuracy of the regularized solutions is order optimal provided that the regularization parameter α has been chosen properly. (author)
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.
A Simple FEM Formulation Applied to Nonlinear Problems of Impact with Thermomechanical Coupling
Directory of Open Access Journals (Sweden)
João Paulo de Barros Cavalcante
Full Text Available Abstract The thermal effects of problems involving deformable structures are essential to describe the behavior of materials in feasible terms. Verifying the transformation of mechanical energy into heat it is possible to predict the modifications of mechanical properties of materials due to its temperature changes. The current paper presents the numerical development of a finite element method suitable for nonlinear structures coupled with thermomechanical behavior; including impact problems. A simple and effective alternative formulation is presented, called FEM positional, to deal with the dynamic nonlinear systems. The developed numerical is based on the minimum potential energy written in terms of nodal positions instead of displacements. The effects of geometrical, material and thermal nonlinearities are considered. The thermodynamically consistent formulation is based on the laws of thermodynamics and the Helmholtz free-energy, used to describe the thermoelastic and the thermoplastic behaviors. The coupled thermomechanical model can result in secondary effects that cause redistributions of internal efforts, depending on the history of deformation and material properties. The numerical results of the proposed formulation are compared with examples found in the literature.
Nonlinear Eigenvalue Problems in Elliptic Variational Inequalities: a local study
International Nuclear Information System (INIS)
Conrad, F.; Brauner, C.; Issard-Roch, F.; Nicolaenko, B.
1985-01-01
The authors consider a class of Nonlinear Eigenvalue Problems (N.L.E.P.) associated with Elliptic Variational Inequalities (E.V.I.). First the authors introduce the main tools for a local study of branches of solutions; the authors extend the linearization process required in the case of equations. Next the authors prove the existence of arcs of solutions close to regular vs singular points, and determine their local behavior up to the first order. Finally, the authors discuss the connection between their regularity condition and some stability concept. 37 references, 6 figures
Nonlinear triple-point problems on time scales
Directory of Open Access Journals (Sweden)
Douglas R. Anderson
2004-04-01
Full Text Available We establish the existence of multiple positive solutions to the nonlinear second-order triple-point boundary-value problem on time scales, $$displaylines{ u^{Delta abla}(t+h(tf(t,u(t=0, cr u(a=alpha u(b+delta u^Delta(a,quad eta u(c+gamma u^Delta(c=0 }$$ for $tin[a,c]subsetmathbb{T}$, where $mathbb{T}$ is a time scale, $eta, gamma, deltage 0$ with $Beta+gamma>0$, $0
Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media
Directory of Open Access Journals (Sweden)
Vicenţiu RăDulescu
2005-06-01
Full Text Available We study nonlinear eigenvalue problems of the type Ã¢ÂˆÂ’div(a(xÃ¢ÂˆÂ‡u=g(ÃŽÂ»,x,u in Ã¢Â„ÂN, where a(x is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on qualitative properties as multiplicity and location of solutions. Our approach is based on the critical point theory in Sobolev weighted spaces combined with a Caffarelli-Kohn-Nirenberg-type inequality. A specific minimax method is developed without making use of Palais-Smale condition.
Numerical solution of non-linear diffusion problems
International Nuclear Information System (INIS)
Carmen, A. del; Ferreri, J.C.
1998-01-01
This paper presents a method for the numerical solution of non-linear diffusion problems using finite-differences in moving grids. Due to the presence of steep fronts in the solution domain and to the presence of advective terms originating in the grid movement, an implicit TVD scheme, first order in time and second order in space has been developed. Some algebraic details of the derivation are given. Results are shown for the pure advection of a scalar as a test case and an example dealing with the slow spreading of viscous fluids over plane surfaces. The agreement between numerical and analytical solutions is excellent. (author). 8 refs., 3 figs
DEFF Research Database (Denmark)
Pu, Minhao; Chen, Yaohui; Yvind, Kresten
2014-01-01
Influence of thermal effects induced by nonlinear absorption on four-wave mixing in silicon waveguides is investigated. A conversion bandwidth reduction up to 63% is observed in simulation due to the thermal effects.......Influence of thermal effects induced by nonlinear absorption on four-wave mixing in silicon waveguides is investigated. A conversion bandwidth reduction up to 63% is observed in simulation due to the thermal effects....
Nonlinear problems of the theory of heterogeneous slightly curved shells
Kantor, B. Y.
1973-01-01
An account if given of the variational method of the solution of physically and geometrically nonlinear problems of the theory of heterogeneous slightly curved shells. Examined are the bending and supercritical behavior of plates and conical and spherical cupolas of variable thickness in a temperature field, taking into account the dependence of the elastic parameters on temperature. The bending, stability in general and load-bearing capacity of flexible isotropic elastic-plastic shells with different criteria of plasticity, taking into account compressibility and hardening. The effect of the plastic heterogeneity caused by heat treatment, surface work hardening and irradiation by fast neutron flux is investigated. Some problems of the dynamic behavior of flexible shells are solved. Calculations are performed in high approximations. Considerable attention is given to the construction of a machine algorithm and to the checking of the convergence of iterative processes.
Stokes phenomena and monodromy deformation problem for nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Chowdury, A.R.; Naskar, M.
1986-01-01
Following Flaschka and Newell, the inverse problem for Painleve IV is formulated with the help of similarity variables. The Painleve IV arises as the eliminant of the two second-order ordinary differential equations originating from the nonlinear Schrodinger equation. Asymptotic expansions are obtained near the singularities at zero and infinity of the complex eigenvalue plane. The corresponding analysis then displays the Stokes phenomena. The monodromy matrices connecting the solution Y /sub j/ in the sector S /sub j/ to that in S /sub j+1/ are fixed in structure by the imposition of certain conditions. It is then shown that a deformation keeping the monodromy data fixed leads to the nonlinear Schrodinger equation. While Flaschka and Newell did not make any absolute determination of the Stokes parameters, the present approach yields the values of the Stokes parameters in an explicit way, which in turn can determine the matrix connecting the solutions near zero and infinity. Finally, it is shown that the integral equation originating from the analyticity and asymptotic nature of the problem leads to the similarity solution previously determined by Boiti and Pampinelli
Nonlinear Preconditioning and its Application in Multicomponent Problems
Liu, Lulu
2015-12-07
The Multiplicative Schwarz Preconditioned Inexact Newton (MSPIN) algorithm is presented as a complement to Additive Schwarz Preconditioned Inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. The ASPIN framework, as an option for the outermost solver, successfully handles strong nonlinearities in computational fluid dynamics, but is barely explored for the highly nonlinear models of complex multiphase flow with capillarity, heterogeneity, and complex geometry. In this dissertation, the fully implicit ASPIN method is demonstrated for a finite volume discretization based on incompressible two-phase reservoir simulators in the presence of capillary forces and gravity. Numerical experiments show that the number of global nonlinear iterations is not only scalable with respect to the number of processors, but also significantly reduced compared with the standard inexact Newton method with a backtracking technique. Moreover, the ASPIN method, in contrast with the IMPES method, saves overall execution time because of the savings in timestep size. We consider the additive and multiplicative types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Moreover, we provide the convergence analysis of the MSPIN algorithm. Under suitable assumptions, it is shown that MSPIN is locally convergent, and desired superlinear or even quadratic convergence can be
Fault detection for nonlinear systems - A standard problem approach
DEFF Research Database (Denmark)
Stoustrup, Jakob; Niemann, Hans Henrik
1998-01-01
The paper describes a general method for designing (nonlinear) 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...
Initial boundary value problems of nonlinear wave equations in an exterior domain
International Nuclear Information System (INIS)
Chen Yunmei.
1987-06-01
In this paper, we investigate the existence and uniqueness of the global solutions to the initial boundary value problems of nonlinear wave equations in an exterior domain. When the space dimension n >= 3, the unique global solution of the above problem is obtained for small initial data, even if the nonlinear term is fully nonlinear and contains the unknown function itself. (author). 10 refs
Solving nonlinear nonstationary problem of heat-conductivity by finite element method
Directory of Open Access Journals (Sweden)
Антон Янович Карвацький
2016-11-01
Full Text Available Methodology and effective solving algorithm of non-linear dynamic problems of thermal and electric conductivity with significant temperature dependence of thermal and physical properties are given on the basis of finite element method (FEM and Newton linearization method. Discrete equations system FEM was obtained with the use of Galerkin method, where the main function is the finite element form function. The methodology based on successive solving problems of thermal and electrical conductivity has been examined in the work in order to minimize the requirements for calculating resources (RAM. in particular. Having used Mathcad software original programming code was developed to solve the given problem. After investigation of the received results, comparative analyses of accurate solution data and results of numerical solutions, obtained with the use of Matlab programming products, was held. The geometry of one fourth part of the finite sized cylinder was used to test the given numerical model. The discretization of the calculation part was fulfilled using the open programming software for automated Gmsh nets with tetrahedral units, while ParaView, which is an open programming code as well, was used to visualize the calculation results. It was found out that the maximum value violation of potential and temperature determination doesn`t exceed 0,2-0,83% in the given work according to the problem conditions
Linear differential equations to solve nonlinear mechanical problems: A novel approach
Nair, C. Radhakrishnan
2004-01-01
Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential equation is known. Using the known solution of the non-linear differential equation, linear differential equations are set up. The solutions of these linear differential equations are found using standard techniques. Then the solutions of the linear differe...
Optimization of Thermal Object Nonlinear Control Systems by Energy Efficiency Criterion.
Velichkin, Vladimir A.; Zavyalov, Vladimir A.
2018-03-01
This article presents the results of thermal object functioning control analysis (heat exchanger, dryer, heat treatment chamber, etc.). The results were used to determine a mathematical model of the generalized thermal control object. The appropriate optimality criterion was chosen to make the control more energy-efficient. The mathematical programming task was formulated based on the chosen optimality criterion, control object mathematical model and technological constraints. The “maximum energy efficiency” criterion helped avoid solving a system of nonlinear differential equations and solve the formulated problem of mathematical programming in an analytical way. It should be noted that in the case under review the search for optimal control and optimal trajectory reduces to solving an algebraic system of equations. In addition, it is shown that the optimal trajectory does not depend on the dynamic characteristics of the control object.
Nonlinear Preconditioning and its Application in Multicomponent Problems
Liu, Lulu
2015-01-01
the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest
Thermal effects, creep and nonlinear responde of concrete reactor vessels
International Nuclear Information System (INIS)
Bazant, Z.P.
1978-01-01
A new mathematical model for prediction of pore pressure and moisture transfer in concrete heated well beyond 100 0 C is outlined. The salient features of the model are:(1) the hypothesis taht the pore space available to capillary water grows with increasing temperature as well as increasing pressure in excess of saturation pressure, and (2) the hypothesis that moisture permeability increases by two orders of magnitude when passing 100 0 C. Permaability below 100 0 C is controlled by migration of adsorbed water through gel-pore sized necks on passages through the material; these necks are lost above 100 0 C and viscosity then governs. The driving force of moisture transfer may be considered as the gradient of pore pressure, which is defined as pressure of vapor rather than liquid water if concrete is not saturated. Thermodynamic properties of water may be used to determine sorption isotherms in saturated concrete. The theory is the necessary first step in rationally predicting thermal stresses and deformations, and assessing the danger of explosive spalling. However, analysis of creep and nonlinear triaxial behavior is also needed for this purpose. A brief review of recent achievements in these subjects is also given. (Author)
Pepi, John W.
2017-08-01
Thermally induced stress is readily calculated for linear elastic material properties using Hooke's law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes.
Variational problems arising in classical mechanics and nonlinear elasticity
International Nuclear Information System (INIS)
Spencer, P.
1999-01-01
In this thesis we consider two different classes of variational problems. First, one-dimensional problems arising from classical mechanics where the problem is to determine whether there is a unique function η 0 (x) which minimises the energy functional of the form I(η) = ∫ a b L(x,η(x), η'(x)) dx. We will investigate uniqueness by making a change of dependent and independent variables and showing that for a class of integrands L with a particular kind of scaling invariance the resulting integrand is completely convex. The change of variables arises by applying results from Lie group theory as applied in the study of differential equations and this work is motivated by [60] and [68]. Second, the problem of minimising energy functionals of the form E(u) = ∫ A W(∇u(x)) dx in the case of a nonlinear elastic body occupying an annular region A contains R 2 with u : A-bar → A-bar. This work is motivated by [57] (in particular the example of paragraph 4). We will consider rotationally symmetric deformations satisfying prescribed boundary conditions. We will show the existence of minimisers for stored energy functions of the form W(F) = g-tilde(vertical bar-F-vertical bar, det(F)) in a class of general rotationally symmetric deformations of a compressible annulus and for stored energy functions of the form W(F) = g-bar(vertical bar-F-vertical bar) in a class of rotationally symmetric deformations of an incompressible annulus. We will also show that in each case the minimisers are solutions of the full equilibrium equations. A model problem will be considered where the energy functional is the Dirichlet integral and it will be shown that the rotationally symmetric solution obtained is a minimiser among admissible non-rotationally symmetric deformations. In the case of an incompressible annulus, we will consider the Dirichlet integral as the energy functional and show that the rotationally symmetric equilibrium solutions in this case are weak local minimisers in
Application of HPEM to investigate the response and stability of nonlinear problems in vibration
DEFF Research Database (Denmark)
Mohammadi, M.H.; Mohammadi, A.; Kimiaeifar, A.
2010-01-01
In this work, a powerful analytical method, called He's Parameter Expanding Methods (HPEM) is used to obtain the exact solution of nonlinear problems in nonlinear vibration. In this work, the governing equation is obtained by using Lagrange method, then the nonlinear governing equation is solved...
Waleed Ahmed Khan, M.; Ijaz Khan, M.; Hayat, T.; Alsaedi, A.
2018-04-01
Entropy generation minimization (EGM) and heat transport in nonlinear radiative flow of nanomaterials over a thin moving needle has been discussed. Nonlinear thermal radiation and viscous dissipation terms are merged in the energy expression. Water is treated as ordinary fluid while nanomaterials comprise titanium dioxide, copper and aluminum oxide. The nonlinear governing expressions of flow problems are transferred to ordinary ones and then tackled for numerical results by Built-in-shooting technique. In first section of this investigation, the entropy expression is derived as a function of temperature and velocity gradients. Geometrical and physical flow field variables are utilized to make it nondimensionalized. An entropy generation analysis is utilized through second law of thermodynamics. The results of temperature, velocity, concentration, surface drag force and heat transfer rate are explored. Our outcomes reveal that surface drag force and Nusselt number (heat transfer) enhanced linearly for higher nanoparticle volume fraction. Furthermore drag force decays for aluminum oxide and it enhances for copper nanoparticles. In addition, the lowest heat transfer rate is achieved for higher radiative parameter. Temperature field is enhanced with increase in temperature ratio parameter.
Yaparova, N.
2017-10-01
We consider the problem of heating a cylindrical body with an internal thermal source when the main characteristics of the material such as specific heat, thermal conductivity and material density depend on the temperature at each point of the body. We can control the surface temperature and the heat flow from the surface inside the cylinder, but it is impossible to measure the temperature on axis and the initial temperature in the entire body. This problem is associated with the temperature measurement challenge and appears in non-destructive testing, in thermal monitoring of heat treatment and technical diagnostics of operating equipment. The mathematical model of heating is represented as nonlinear parabolic PDE with the unknown initial condition. In this problem, both the Dirichlet and Neumann boundary conditions are given and it is required to calculate the temperature values at the internal points of the body. To solve this problem, we propose the numerical method based on using of finite-difference equations and a regularization technique. The computational scheme involves solving the problem at each spatial step. As a result, we obtain the temperature function at each internal point of the cylinder beginning from the surface down to the axis. The application of the regularization technique ensures the stability of the scheme and allows us to significantly simplify the computational procedure. We investigate the stability of the computational scheme and prove the dependence of the stability on the discretization steps and error level of the measurement results. To obtain the experimental temperature error estimates, computational experiments were carried out. The computational results are consistent with the theoretical error estimates and confirm the efficiency and reliability of the proposed computational scheme.
Nonlinear problems in data-assimilation : Can synchronization help?
Tribbia, J. J.; Duane, G. S.
2009-12-01
Over the past several years, operational weather centers have initiated ensemble prediction and assimilation techniques to estimate the error covariance of forecasts in the short and the medium range. The ensemble techniques used are based on linear methods. The theory This technique s been shown to be a useful indicator of skill in the linear range where forecast errors are small relative to climatological variance. While this advance has been impressive, there are still ad hoc aspects of its use in practice, like the need for covariance inflation which are troubling. Furthermore, to be of utility in the nonlinear range an ensemble assimilation and prediction method must be capable of giving probabilistic information for the situation where a probability density forecast becomes multi-modal. A prototypical, simplest example of such a situation is the planetary-wave regime transition where the pdf is bimodal. Our recent research show how the inconsistencies and extensions of linear methodology can be consistently treated using the paradigm of synchronization which views the problems of assimilation and forecasting as that of optimizing the forecast model state with respect to the future evolution of the atmosphere.
ANCON, Space-Independent Reactor Kinetics with Linear or Nonlinear Thermal Feedback
International Nuclear Information System (INIS)
Vigil, John C.; Dugan, E.T.
1988-01-01
1 - Description of problem or function: ANCON solves the point-reactor kinetic equations including thermal feedback. Lump-type heat balance equations are used to represent the thermodynamics, and the heat capacity of each lump can vary with temperature. Thermal feedback can be either a linear or a non-linear function of lump temperature, and the impressed reactivity can be either a polynomial or sinusoidal function. 2 - Method of solution: In ANCON the system of coupled first-order differential equations is solved by a method based on continuous analytic continuation (references 2 and 3). The basic procedure consists of expanding all the dependent variables except reactivity in Taylor series, with a truncation error criterion, over successive intervals on the time axis. Variations of the basic procedure are used to increase the efficiency of the method in special situations. Automatic switching from the basic procedure to one of its variations (and vice-versa) may occur during the course of a transient. The method yields an analytic criterion for the magnitude of the time-step at any point in the transient. 3 - Restrictions on the complexity of the problem: The program is currently restricted to a maximum of six delayed neutron groups and a maximum of 56 lumps. Larger problems can be accommodated on a 65 K computer by increasing the dimensions of a few subscripted variables. Also, the code is currently restricted to a constant external transport delays, only the open-loop response of a reactor can be computed with ANCON
Thermal Aging Evaluation of Mod. 9Cr-1Mo Steel using Nonlinear Rayleigh Waves
Energy Technology Data Exchange (ETDEWEB)
Joo, Young-Sang; Kim, Hoe-Woong; Kim, Jong-Bum [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Marino, Daniel; Kim, Jin-Yeon; Jacobs, L.J [Georgia Institute of Technology, Atlanta (United States); Ruiz, Alberto [UMSNH, Morelia (Mexico)
2014-10-15
Thermal aging can pose a high risk to decreases in the mechanical properties such as strength or creep resistance. This can lead to an unexpected failure during long term operation. Nonlinear NDE techniques are preferred over conventional NDE techniques (linear ultrasonic measurements) because nonlinear ultrasonic techniques have shown their capability to detect a microstructural damage in the structures undergoing fatigue and creep. These nonlinear ultrasonic techniques make use of the fact that the dislocation density increases, which will create a nonlinear distortion of an ultrasonic wave; this damage causes the generation of measurable higher harmonic components in an initially mono-chromatic ultrasonic signal. This study investigates the recently developed non-contact nonlinear ultrasonic technique to detect the microstructural damage of mod. 9Cr-1Mo steel based on nonlinear Rayleigh wave with varying propagation distances. Nonlinear Rayleigh surface wave measurements using a non-contact, air-coupled ultrasonic transducer have been applied for the thermal aging evaluation of modified 9Cr-1Mo ferritic-martensitic steel. Thermal aging for various heat treatment times of mod.. 9Cr-1Mo steel specimens is performed to obtain the nucleation and growth of precipitated particles in specimens. The amplitudes of the first and second harmonics are measured along the propagation distance and the relative nonlinearity parameter is obtained from these amplitudes. The relative nonlinearity parameter shows a similar trend with the Rockwell C hardness.
Numerical methods for solution of some nonlinear problems of mathematical physics
International Nuclear Information System (INIS)
Zhidkov, E.P.
1981-01-01
The continuous analog of the Newton method and its application to some nonlinear problems of mathematical physics using a computer is considered. It is shown that the application of this method in JINR to the wide range of nonlinear problems has shown its universality and high efficiency [ru
A fast nonlinear conjugate gradient based method for 3D frictional contact problems
Zhao, J.; Vollebregt, E.A.H.; Oosterlee, C.W.
2014-01-01
This paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from a 3D frictional contact problem. It incorporates an active set strategy with a nonlinear conjugate gradient method. One novelty is to consider the tractions of each slip element in a polar
A fast nonlinear conjugate gradient based method for 3D concentrated frictional contact problems
J. Zhao (Jing); E.A.H. Vollebregt (Edwin); C.W. Oosterlee (Cornelis)
2015-01-01
htmlabstractThis paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from 3D concentrated frictional shift and rolling contact problems with dry Coulomb friction. The solver combines an active set strategy with a nonlinear conjugate gradient method. One
Thermally stimulated nonlinear refraction in gelatin stabilized Cu-PVP nanocomposite thin films
Energy Technology Data Exchange (ETDEWEB)
Tamgadge, Y. S., E-mail: ystamgadge@gmail.com; Atkare, D. V. [Department of Physics, Mahatma Fule Arts, Commerce & SitaramjiChoudhari Science College, Warud, Dist. Amravati (MS), India-444906 (India); Pahurkar, V. G.; Muley, G. G., E-mail: gajananggm@yahoo.co.in [Department of Physics, SantGadge Baba Amravati University, Amravati (MS), India-444602 (India); Talwatkar, S. S. [Department of Physics, D K Marathe and N G Acharya College, Chembur, Mumbai (MS), India-440071 (India); Sunatkari, A. L. [Department of Physics, Siddharth College of Arts, Science and Commerce, Fort, Mumbai (MS), India-440001 (India)
2016-05-06
This article illustrates investigations on thermally stimulated third order nonlinear refraction of Cu-PVP nanocomposite thin films. Cu nanoparticles have been synthesized using chemical reduction method and thin films in PVP matrix have been obtained using spin coating technique. Thin films have been characterized by X-ray diffraction (XRD) and Ultraviolet-visible (UV-vis) spectroscopyfor structural and linear optical studies. Third order nonlinear refraction studies have been performed using closed aperture z-scan technique under continuous wave (CW) He-Ne laser. Cu-PVP nanocomposites are found to exhibit strong nonlinear refractive index stimulated by thermal lensing effect.
Nanoparticles and nonlinear thermal radiation properties in the rheology of polymeric material
Awais, M.; Hayat, T.; Muqaddass, N.; Ali, A.; Aqsa; Awan, Saeed Ehsan
2018-03-01
The present analysis is related to the dynamics of polymeric liquids (Oldroyd-B model) with the presence of nanoparticles. The rheological system is considered under the application of nonlinear thermal radiations. Energy and concentration equations are presented when thermophoresis and Brownian motion effects are present. Bidirectional form of stretching is considered to interpret the three-dimensional flow dynamics of polymeric liquid. Making use of the similarity transformations, problem is reduced into ordinary differential system which is approximated by using HAM. Influence of physical parameters including Deborah number, thermophoresis and Brownian motion on velocity, temperature and mass fraction expressions are plotted and analyzed. Numerical values for local Sherwood and Nusselt numbers are presented and discussed.
Directory of Open Access Journals (Sweden)
T. Sajid
2018-03-01
Full Text Available The present article is about the study of Darcy-Forchheimer flow of Maxwell nanofluid over a linear stretching surface. Effects like variable thermal conductivity, activation energy, nonlinear thermal radiation is also incorporated for the analysis of heat and mass transfer. The governing nonlinear partial differential equations (PDEs with convective boundary conditions are first converted into the nonlinear ordinary differential equations (ODEs with the help of similarity transformation, and then the resulting nonlinear ODEs are solved with the help of shooting method and MATLAB built-in bvp4c solver. The impact of different physical parameters like Brownian motion, thermophoresis parameter, Reynolds number, magnetic parameter, nonlinear radiative heat flux, Prandtl number, Lewis number, reaction rate constant, activation energy and Biot number on Nusselt number, velocity, temperature and concentration profile has been discussed. It is viewed that both thermophoresis parameter and activation energy parameter has ascending effect on the concentration profile.
New results on the mathematical problems in nonlinear physics
International Nuclear Information System (INIS)
1980-01-01
The main topics treated in this report are: I) Existence of generalized Lagrangians. II) Conserved densities for odd-order polynomial evolution equations and linear evolution systems. III ) Conservation laws for Klein-Gordon, Di rae and Maxwell equations. IV) Stability conditions for finite-energy solutions of a non-linear Klein-Gordon equation. V) Hamiltonian approach to non-linear evolution equations and Backlund transformations. VI) Anharmonic vibrations: Status of results and new possible approaches. (Author) 83 refs
Costiner, Sorin; Taasan, Shlomo
1994-01-01
This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.
International Nuclear Information System (INIS)
Li, Weibin; Cho, Younho; Li, Xianqiang
2013-01-01
Ultrasonic guided wave techniques have been widely used for long range nondestructive detection in tube like structures. The present paper investigates the ultrasonic linear and nonlinear parameters for evaluating the thermal damage in aluminum pipe. Specimens were subjected to thermal loading. Flexible polyvinylidene fluoride (PVDF) comb transducers were used to generate and receive the ultrasonic waves. The second harmonic wave generation technique was used to check the material nonlinearity change after different heat loadings. The conventional linear ultrasonic approach based on attenuation was also used to evaluate the thermal damages in specimens. The results show that the proposed experimental setup is viable to assess the thermal damage in an aluminum pipe. The ultrasonic nonlinear parameter is a promising candidate for the prediction of micro damages in a tube like structure
The solution of a coupled system of nonlinear physical problems using the homotopy analysis method
International Nuclear Information System (INIS)
El-Wakil, S A; Abdou, M A
2010-01-01
In this article, the homotopy analysis method (HAM) has been applied to solve coupled nonlinear evolution equations in physics. The validity of this method has been successfully demonstrated by applying it to two nonlinear evolution equations, namely coupled nonlinear diffusion reaction equations and the (2+1)-dimensional Nizhnik-Novikov Veselov system. The results obtained by this method show good agreement with the ones obtained by other methods. The proposed method is a powerful and easy to use analytic tool for nonlinear problems and does not need small parameters in the equations. The HAM solutions contain an auxiliary parameter that provides a convenient way of controlling the convergence region of series solutions. The results obtained here reveal that the proposed method is very effective and simple for solving nonlinear evolution equations. The basic ideas of this approach can be widely employed to solve other strongly nonlinear problems.
From a Nonlinear, Nonconvex Variational Problem to a Linear, Convex Formulation
International Nuclear Information System (INIS)
Egozcue, J.; Meziat, R.; Pedregal, P.
2002-01-01
We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical and numerical nature
Mathematical problems in non-linear Physics: some results
International Nuclear Information System (INIS)
1979-01-01
The basic results presented in this report are the following: 1) Characterization of the range and Kernel of the variational derivative. 2) Determination of general conservation laws in linear evolution equations, as well as bounds for the number of polynomial conserved densities in non-linear evolution equations in two independent variables of even order. 3) Construction of the most general evolution equation which has a given family of conserved densities. 4) Regularity conditions for the validity of the Lie invariance method. 5) A simple class of perturbations in non-linear wave equations. 6) Soliton solutions in generalized KdV equations. (author)
Leibov Roman
2017-01-01
This paper presents a bilinear approach to nonlinear differential equations system approximation problem. Sometimes the nonlinear differential equations right-hand sides linearization is extremely difficult or even impossible. Then piecewise-linear approximation of nonlinear differential equations can be used. The bilinear differential equations allow to improve piecewise-linear differential equations behavior and reduce errors on the border of different linear differential equations systems ...
Non-linear thermal fluctuations in a diode
Kampen, N.G. van
As an example of non-linear noise the fluctuations in a circuit consisting of a diode and a condenser C are studied. From the master equation for this system the following results are derived. 1. (i) The equilibrium distribution of the voltage is rigorously Gaussian, the average voltage being
Energy Technology Data Exchange (ETDEWEB)
Zou, Li [Dalian Univ. of Technology, Dalian City (China). State Key Lab. of Structural Analysis for Industrial Equipment; Liang, Songxin; Li, Yawei [Dalian Univ. of Technology, Dalian City (China). School of Mathematical Sciences; Jeffrey, David J. [Univ. of Western Ontario, London (Canada). Dept. of Applied Mathematics
2017-06-01
Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.
Polyanin, A. D.; Sorokin, V. G.
2017-12-01
The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.
An inverse heat transfer problem for optimization of the thermal ...
Indian Academy of Sciences (India)
This paper takes a different approach towards identiﬁcation of the thermal process in machining, using inverse heat transfer problem. Inverse heat transfer method allows the closest possible experimental and analytical approximation of thermal state for a machining process. Based on a temperature measured at any point ...
Solving Large Scale Nonlinear Eigenvalue Problem in Next-Generation Accelerator Design
Energy Technology Data Exchange (ETDEWEB)
Liao, Ben-Shan; Bai, Zhaojun; /UC, Davis; Lee, Lie-Quan; Ko, Kwok; /SLAC
2006-09-28
A number of numerical methods, including inverse iteration, method of successive linear problem and nonlinear Arnoldi algorithm, are studied in this paper to solve a large scale nonlinear eigenvalue problem arising from finite element analysis of resonant frequencies and external Q{sub e} values of a waveguide loaded cavity in the next-generation accelerator design. They present a nonlinear Rayleigh-Ritz iterative projection algorithm, NRRIT in short and demonstrate that it is the most promising approach for a model scale cavity design. The NRRIT algorithm is an extension of the nonlinear Arnoldi algorithm due to Voss. Computational challenges of solving such a nonlinear eigenvalue problem for a full scale cavity design are outlined.
Domí nguez, Luis F.; Pistikopoulos, Efstratios N.
2012-01-01
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
Problem of the lithium peroxide thermal stability
International Nuclear Information System (INIS)
Nefedov, R A; Ferapontov, Yu A; Kozlova, N P
2016-01-01
The behavior of lithium peroxide and lithium peroxide monohydrate samples under heating in atmospheric air was studied by the method of thermogravimetric analysis (TGA) and differential thermal analysis (DTA). It was found that in the temperature range of 32°C to 82°C the interaction of lithium peroxides and steam with the formation of lithium peroxide monohydrate occurs, which was confirmed chemically and by X-ray Single-qualitative analysis. It was experimentally found that lithium peroxide starts to decompose into the lithium oxide and oxygen in the temperature range of 340 ÷ 348°C. It was established that the resulting thermal decomposition of lithium oxide, lithium peroxide at the temperature of 422°C melts with lithium carbonate eutecticly. The manifestation of polymorphism was not marked(seen or noticed) under the heating of studied samples of lithium peroxide and lithium peroxide monohydrate in the temperature range of 25°C ÷ 34°C. (paper)
Thermal problems on high flux beam lines
International Nuclear Information System (INIS)
Avery, R.T.
1983-09-01
Wiggler and undulator magnets can provide very intense photon flux densities to beam line components. This paper addresses some thermal/materials consequences due to such impingement. The LBL/Exxon/SSRL hybrid-wiggler Beam Line VI now nearing operation will be able to provide up to approx. 7 kW of total photon power at planned SPEAR operating conditions. The first masks are located at 6.5 meters from the source and may receive a peak power density (transverse to the beam) exceeding 20 kW/cm 2 . Significantly, this heat transfer rate exceeds that radiated from the sun's surface (7 kW/cm 2 ) and is comparable to that of welding torches. Clearing, cooling and configuration are of critical importance. Configurations for the first fixed mask, the movable mask, and the pivot mask on this beam line are presented together with considerations of thermal stress fatigue and of heat transfer by conduction to water-cooling circuits. Some preliminary information on heating of crystals and mirrors is also presented
Morozov-type discrepancy principle for nonlinear ill-posed problems ...
Indian Academy of Sciences (India)
For proving the existence of a regularization parameter under a Morozov-type discrepancy principle for Tikhonov regularization of nonlinear ill-posed problems, it is required to impose additional nonlinearity assumptions on the forward operator. Lipschitz continuity of the Freéchet derivative and requirement of the Lipschitz ...
Analytical Solution of Nonlinear Problems in Classical Dynamics by Means of Lagrange-Ham
DEFF Research Database (Denmark)
Kimiaeifar, Amin; Mahdavi, S. H; Rabbani, A.
2011-01-01
In this work, a powerful analytical method, called Homotopy Analysis Methods (HAM) is coupled with Lagrange method to obtain the exact solution for nonlinear problems in classic dynamics. In this work, the governing equations are obtained by using Lagrange method, and then the nonlinear governing...
Morozov-type discrepancy principle for nonlinear ill-posed problems ...
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... For proving the existence of a regularization parameter under a Morozov-type discrepancy principle for Tikhonov regularization of nonlinear ill-posed problems, it is required to impose additional nonlinearity assumptions on the forward operator. Lipschitz continuity of the Freéchet derivative and requirement ...
Nonlinear Modeling and Simulation of Thermal Effects in Microcantilever Resonators Dynamic
International Nuclear Information System (INIS)
Tadayon, M A; Sayyaadi, H; Jazar, G Nakhaie
2006-01-01
Thermal dependency of material characteristics in micro electromechanical systems strongly affects their performance, design, and control. Hence, it is essential to understand and model that in MEMS devices to optimize their designs. A thermal phenomenon introduces two main effects: damping due to internal friction, and softening due to Young modulus temperature relation. Based on some reported theoretical and experimental results, we model the thermal phenomena and use two Lorentzian functions to describe the restoring and damping forces caused by thermal phenomena. In order to emphasize the thermal effects, a nonlinear model of the MEMS, by considering capacitor nonlinearity, have been used. The response of the system is developed by employing multiple time scales perturbation method on nondimensionalized form of equations. Frequency response, resonant frequency and peak amplitude are examined for variation of dynamic parameters involved
The preparation problem in nonlinear extensions of quantum theory
Cavalcanti, Eric G.; Menicucci, Nicolas C.; Pienaar, Jacques L.
2012-01-01
Nonlinear modifications to the laws of quantum mechanics have been proposed as a possible way to consistently describe information processing in the presence of closed timelike curves. These have recently generated controversy due to possible exotic information-theoretic effects, including breaking quantum cryptography and radically speeding up both classical and quantum computers. The physical interpretation of such theories, however, is still unclear. We consider a large class of operationa...
International Nuclear Information System (INIS)
Kaw, P.K.; Singh, R.; Weiland, J.G.
2001-01-01
Analytical investigations of several linear and nonlinear features of ETG turbulence are reported. The linear theory includes effects such as finite beta induced electromagnetic shielding, coupling to electron magnetohydrodynamic modes like whistlers etc. It is argued that nonlinearly, turbulence and transport are dominated by radially extended modes called 'streamers'. A nonlinear mechanism generating streamers based on a modulational instability theory of the ETG turbulence is also presented. The saturation levels of the streamers using a Kelvin Helmholtz secondary instability mechanism are calculated and levels of the electron thermal transport due to streamers are estimated. (author)
An, Honglin; Fleming, Simon
2005-05-02
The spatial distribution of second-order nonlinearity in thermally poled optical fibers was characterized by second-harmonic microscopy. The second-order nonlinearity was found to be confined to a thin layer close to the anode surface and progressed further into the silica as the poling time increased. Position uncertainty of the anode metal wire was observed to have an effect, as the nonlinear layers were found not always symmetrically located around the nearest points between the anode and cathode. Optical microscopy results were obtained on etched poled fiber cross-sections and compared with those from second-harmonic microscopy.
A nonsmooth nonlinear conjugate gradient method for interactive contact force problems
DEFF Research Database (Denmark)
Silcowitz, Morten; Abel, Sarah Maria Niebe; Erleben, Kenny
2010-01-01
of a nonlinear complementarity problem (NCP), which can be solved using an iterative splitting method, such as the projected Gauss–Seidel (PGS) method. We present a novel method for solving the NCP problem by applying a Fletcher–Reeves type nonlinear nonsmooth conjugate gradient (NNCG) type method. We analyze...... and present experimental convergence behavior and properties of the new method. Our results show that the NNCG method has at least the same convergence rate as PGS, and in many cases better....
Non-linear analytic and coanalytic problems (Lp-theory, Clifford analysis, examples)
International Nuclear Information System (INIS)
Dubinskii, Yu A; Osipenko, A S
2000-01-01
Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the 'orthogonal' sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented
Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)
Dubinskii, Yu A.; Osipenko, A. S.
2000-02-01
Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.
Directory of Open Access Journals (Sweden)
Salih Yalcinbas
2016-01-01
Full Text Available In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of second order boundary value problem. This technique is essentially based on the truncated Fermat series and its matrix representations with collocation points. Using the matrix method, we reduce the problem system of nonlinear algebraic equations. Numerical examples are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and produces accurate results.
Morozov-type discrepancy principle for nonlinear ill-posed problems ...
Indian Academy of Sciences (India)
[3] Engl H W, Kunisch K and Neubauer A, Convergence rates for Tikhonov regularization of nonliner problems, Inverse Problems 5 (1989) 523–540. [4] Hanke M, Neubauer A and Scherzer O, A convergence analysis of Landweber iteration for nonlinear ill-posed problems, Numer. Math. 72 (1995) 21–37. [5] Hofmann B and ...
Costiner, Sorin; Ta'asan, Shlomo
1995-07-01
Algorithms for nonlinear eigenvalue problems (EP's) often require solving self-consistently a large number of EP's. Convergence difficulties may occur if the solution is not sought in an appropriate region, if global constraints have to be satisfied, or if close or equal eigenvalues are present. Multigrid (MG) algorithms for nonlinear problems and for EP's obtained from discretizations of partial differential EP have often been shown to be more efficient than single level algorithms. This paper presents MG techniques and a MG algorithm for nonlinear Schrödinger Poisson EP's. The algorithm overcomes the above mentioned difficulties combining the following techniques: a MG simultaneous treatment of the eigenvectors and nonlinearity, and with the global constrains; MG stable subspace continuation techniques for the treatment of nonlinearity; and a MG projection coupled with backrotations for separation of solutions. These techniques keep the solutions in an appropriate region, where the algorithm converges fast, and reduce the large number of self-consistent iterations to only a few or one MG simultaneous iteration. The MG projection makes it possible to efficiently overcome difficulties related to clusters of close and equal eigenvalues. Computational examples for the nonlinear Schrödinger-Poisson EP in two and three dimensions, presenting special computational difficulties that are due to the nonlinearity and to the equal and closely clustered eigenvalues are demonstrated. For these cases, the algorithm requires O(qN) operations for the calculation of q eigenvectors of size N and for the corresponding eigenvalues. One MG simultaneous cycle per fine level was performed. The total computational cost is equivalent to only a few Gauss-Seidel relaxations per eigenvector. An asymptotic convergence rate of 0.15 per MG cycle is attained.
DOUBLE TRIALS METHOD FOR NONLINEAR PROBLEMS ARISING IN HEAT TRANSFER
Directory of Open Access Journals (Sweden)
Chun-Hui He
2011-01-01
Full Text Available According to an ancient Chinese algorithm, the Ying Buzu Shu, in about second century BC, known as the rule of double false position in West after 1202 AD, two trial roots are assumed to solve algebraic equations. The solution procedure can be extended to solve nonlinear differential equations by constructing an approximate solution with an unknown parameter, and the unknown parameter can be easily determined using the Ying Buzu Shu. An example in heat transfer is given to elucidate the solution procedure.
Analytical vs. Simulation Solution Techniques for Pulse Problems in Non-linear Stochastic Dynamics
DEFF Research Database (Denmark)
Iwankiewicz, R.; Nielsen, Søren R. K.
Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically-numerical tec......Advantages and disadvantages of available analytical and simulation techniques for pulse problems in non-linear stochastic dynamics are discussed. First, random pulse problems, both those which do and do not lead to Markov theory, are presented. Next, the analytical and analytically...
DEFF Research Database (Denmark)
Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari
2010-01-01
and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However......, as with other analytical techniques, certain limitations restrict the wide application of perturbation methods, most important of which is the dependence of these methods on the existence of a small parameter in the equation. Disappointingly, the majority of nonlinear problems have no small parameter at all......Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...
A nonlinear effective thermal conductivity model for carbon nanotube and nanofiber suspensions
Energy Technology Data Exchange (ETDEWEB)
Koo, J; Kang, Y [Department of Mechanical Engineering Kyung Hee University, 1, Seocheon-dong, Giheung-gu, Yongin-si, Gyeonggi-do 446-701 (Korea, Republic of); Kleinstreuer, C [Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, 3211 Broughton Hall, Raleigh, NC 27695-7910 (United States)], E-mail: jmkoo@khu.ac.kr
2008-09-17
It has been experimentally demonstrated that suspensions of carbon nanotubes (CNTs) and nanofibers (CNFs) significantly increase the thermal conductivity of nanofluids; however, a physically sound theory of the underlying phenomenon is still missing. In this study, the nonlinear nature of the effective thermal conductivity enhancement with the particle concentration of CNT and CNF nanofluids is explained physically using the excluded volume concept. Specifically, the number of contacting CNTs and CNFs could be calculated by using the excluded volume concept, where the distance for heat to travel in a cylinder between the contacting cylinders in the thermal network of percolating CNTs and CNFs increased with the excluded volume. In contrast to the effective thermal conductivity model of Sastry et al (2008 Nanotechnology 19 055704) the present revised model could reproduce the nonlinear increase of the thermal conductivity with particle concentration, as well as the dependence on the diameter and aspect ratio of the CNTs and CNFs. It was found that the alignment of CNTs and CNFs due to the long range repulsion force decreases the excluded volume, leading to both the convex and concave nonlinear as well as linear increase of the thermal conductivity with particle concentration. The difference between various carrier fluids of the suspensions could be explained as the result of the change in the excluded volume in different base fluids.
Barreto, Roberto; Florencia Carusela, M.; Monastra, Alejandro G.
2017-10-01
We investigate the role that nonlinearity in the interatomic potential has on the thermal conductance of a suspended nanoribbon when it is subjected to a longitudinal strain. To focus on the first cubic and quartic nonlinear terms of a general potential, we propose an atomic system based on an α-β Fermi-Pasta-Ulam nearest neighbor interaction. We perform classical molecular dynamics simulations to investigate the contribution of longitudinal, transversal and flexural modes to the thermal conductance as a function of the α-β parameters and the applied strain. We compare the cases where atoms are allowed to vibrate only in plane (2D) with the case of vibrations in and out of plane (3D). We find that the dependence of conductance on α and β relies on a crossover phenomenon between linear/nonlinear delocalized/localized flexural and transversal modes, driven by an on/off switch of the strain.
International Nuclear Information System (INIS)
Kabir, A.F.; Bolourchi, S.
1991-01-01
A feasibility study was conducted for addition of consolidated fuel racks to an existing reinforced concrete spent fuel storage pool of a Mark I BWR plant. Nonlinear analysis of a detailed three-dimensional model of the fuel pool, considering cracking in concrete under gravity and thermal load conditions, showed that the pool has reserve capacities to carry the additional loads. (author)
Some contributions to non-linear physic: Mathematical problems
International Nuclear Information System (INIS)
1981-01-01
The main results contained in this report are the following: i ) Lagrangian universality holds in a precisely defined weak sense. II ) Isolation of 5th order polynomial evolution equations having high order conservation laws. III ) Hamiltonian formulation of a wide class of non-linear evolution equations. IV) Some properties of the symmetries of Gardner-like systems. v) Characterization of the range and Kernel of ζ/ζ u α , |α | - 1. vi) A generalized variational approach and application to the anharmonic oscillator. v II ) Relativistic correction and quasi-classical approximation to the anechoic oscillator. VII ) Properties of a special class of 6th-order anharmonic oscillators. ix) A new method for constructing conserved densities In PDE. (Author) 97 refs
Nonlinear radiation transport problems involving widely varying mean free paths
International Nuclear Information System (INIS)
Chapline, G. Jr.; Wood, L.
1976-01-01
In this report a method is given for modifying the Monte-Carlo approach so that one can accurately treat problems that involve both large and small mean free paths. This method purports to offer the advantages of the general Monte Carlo technique as far as relatively great accuracy of simulation of microscopic physical phenomena is concerned, and the advantage of a diffusion theory approach as far as decent time steps in thick problems are concerned; it does suffer from something of the statistical fluctuation problems of the Monte Carlo, although in analytically attenuated and modified form
Paradox in a non-linear capacitated transportation problem
Directory of Open Access Journals (Sweden)
Dahiya Kalpana
2006-01-01
Full Text Available This paper discusses a paradox in fixed charge capacitated transportation problem where the objective function is the sum of two linear fractional functions consisting of variables costs and fixed charges respectively. A paradox arises when the transportation problem admits of an objective function value which is lower than the optimal objective function value, by transporting larger quantities of goods over the same route. A sufficient condition for the existence of a paradox is established. Paradoxical range of flow is obtained for any given flow in which the corresponding objective function value is less than the optimum value of the given transportation problem. Numerical illustration is included in support of theory.
Dissipative Control Systems and Disturbance Attenuation for Nonlinear H∞ Problems
International Nuclear Information System (INIS)
Frankowska, H.; Quincampoix, M.
1999-01-01
We characterize functions satisfying a dissipative inequality associated with a control problem. Such a characterization is provided in terms of an epicontingent solution, or a viscosity supersolution to a partial differential equation called Isaacs' equation. Links between supersolutions and epicontingent solutions to Isaacs' equation are studied. Finally, we derive (possibly discontinuous) disturbance attenuation feedback of the H ∞ problem from contingent formulation of Isaacs' equation
Nonlinear Multidimensional Assignment Problems Efficient Conic Optimization Methods and Applications
2015-06-24
WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Arizona State University School of Mathematical & Statistical Sciences 901 S...SUPPLEMENTARY NOTES 14. ABSTRACT The major goals of this project were completed: the exact solution of previously unsolved challenging combinatorial optimization... combinatorial optimization problem, the Directional Sensor Problem, was solved in two ways. First, heuristically in an engineering fashion and second, exactly
Problems associated with accelerated thermal aging of electrical equipment
International Nuclear Information System (INIS)
Isgro, J.R.
1984-01-01
This paper discusses the potential problems that may be experienced when accounting for aging mechanisms in organic polymers when utilizing accelerated thermal aging techniques for electrical equipment qualification. Included are discussions of actual experiences and problems encountered in the qualification of electrical and electronic equipment for a complete nuclear power plant. The wide variety of approaches to thermal accelerated aging by various manufacturers of diverse equipment types provides depth to the discussion. A description of how to account for aging mechanisms is also presented
SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis
Energy Technology Data Exchange (ETDEWEB)
Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.
1998-08-01
This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. The notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.
Cross-constrained problems for nonlinear Schrodinger equation with harmonic potential
Directory of Open Access Journals (Sweden)
Runzhang Xu
2012-11-01
Full Text Available This article studies a nonlinear Schodinger equation with harmonic potential by constructing different cross-constrained problems. By comparing the different cross-constrained problems, we derive different sharp criterion and different invariant manifolds that separate the global solutions and blowup solutions. Moreover, we conclude that some manifolds are empty due to the essence of the cross-constrained problems. Besides, we compare the three cross-constrained problems and the three depths of the potential wells. In this way, we explain the gaps in [J. Shu and J. Zhang, Nonlinear Shrodinger equation with harmonic potential, Journal of Mathematical Physics, 47, 063503 (2006], which was pointed out in [R. Xu and Y. Liu, Remarks on nonlinear Schrodinger equation with harmonic potential, Journal of Mathematical Physics, 49, 043512 (2008].
Directory of Open Access Journals (Sweden)
Alain Mignot
2005-09-01
Full Text Available This paper shows the existence of a solution of the quasi-static unilateral contact problem with nonlocal friction law for nonlinear elastic materials. We set up a variational incremental problem which admits a solution, when the friction coefficient is small enough, and then by passing to the limit with respect to time we obtain a solution.
Existence of bounded solutions of Neumann problem for a nonlinear degenerate elliptic equation
Directory of Open Access Journals (Sweden)
Salvatore Bonafede
2017-10-01
Full Text Available We prove the existence of bounded solutions of Neumann problem for nonlinear degenerate elliptic equations of second order in divergence form. We also study some properties as the Phragmen-Lindelof property and the asymptotic behavior of the solutions of Dirichlet problem associated to our equation in an unbounded domain.
COYOTE: a finite element computer program for nonlinear heat conduction problems
International Nuclear Information System (INIS)
Gartling, D.K.
1978-06-01
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 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.
Thermally Stable Heterocyclic Imines as New Potential Nonlinear Optical Materials
Nesterov, Volodymyr V.; Antipin, Mikhail Y.; Nesterov, Vladimir N.; Moore, Craig E.; Cardelino, Beatriz H.; Timofeeva, Tatiana V.
2004-01-01
In the course of a search for new thermostable acentric nonlinear optical crystalline materials, several heterocyclic imine derivatives were designed, with the general structure D-pi-A(D'). Introduction of a donor amino group (D') into the acceptor moiety was expected to bring H-bonds into their crystal structures, and so to elevate their melting points and assist in an acentric molecular packing. Six heterocycle-containing compounds of this type were prepared, single crystals were grown for five of them, and these crystals were characterized by X-ray analysis. A significant melting temperature elevation was found for all of the synthesized compounds. Three of the compounds were also found to crystallize in acentric space groups. One of the acentric compounds is built as a three-dimensional H-bonded molecular network. In the other two compounds, with very similar molecular structure, the molecules form one-dimensional H-bonded head-to-head associates (chains). These chains are parallel in two different crystallographic directions and form very unusual interpenetrating chain patterns in an acentric crystal. Two of the compounds crystallized with centrosymmetric molecular packing.
Muravyov, Alexander A.
1999-01-01
In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.
A Weak Solution of a Stochastic Nonlinear Problem
Directory of Open Access Journals (Sweden)
M. L. Hadji
2015-01-01
Full Text Available We consider a problem modeling a porous medium with a random perturbation. This model occurs in many applications such as biology, medical sciences, oil exploitation, and chemical engineering. Many authors focused their study mostly on the deterministic case. The more classical one was due to Biot in the 50s, where he suggested to ignore everything that happens at the microscopic level, to apply the principles of the continuum mechanics at the macroscopic level. Here we consider a stochastic problem, that is, a problem with a random perturbation. First we prove a result on the existence and uniqueness of the solution, by making use of the weak formulation. Furthermore, we use a numerical scheme based on finite differences to present numerical results.
Some New Results in Astrophysical Problems of Nonlinear Theory of Radiative Transfer
Pikichyan, H. V.
2017-07-01
In the interpretation of the observed astrophysical spectra, a decisive role is related to nonlinear problems of radiative transfer, because the processes of multiple interactions of matter of cosmic medium with the exciting intense radiation ubiquitously occur in astrophysical objects, and in their vicinities. Whereas, the intensity of the exciting radiation changes the physical properties of the original medium, and itself was modified, simultaneously, in a self-consistent manner under its influence. In the present report, we show that the consistent application of the principle of invariance in the nonlinear problem of bilateral external illumination of a scattering/absorbing one-dimensional anisotropic medium of finite geometrical thickness allows for simplifications that were previously considered as a prerogative only of linear problems. The nonlinear problem is analyzed through the three methods of the principle of invariance: (i) an adding of layers, (ii) its limiting form, described by differential equations of invariant imbedding, and (iii) a transition to the, so-called, functional equations of the "Ambartsumyan's complete invariance". Thereby, as an alternative to the Boltzmann equation, a new type of equations, so-called "kinetic equations of equivalence", are obtained. By the introduction of new functions - the so-called "linear images" of solution of nonlinear problem of radiative transfer, the linear structure of the solution of the nonlinear problem under study is further revealed. Linear images allow to convert naturally the statistical characteristics of random walk of a "single quantum" or their "beam of unit intensity", as well as widely known "probabilistic interpretation of phenomena of transfer", to the field of nonlinear problems. The structure of the equations obtained for determination of linear images is typical of linear problems.
Transient thermal stress problem for a circumferentially cracked hollow cylinder
Nied, H. F.; Erdogan, F.
1982-01-01
The transient thermal stress problem for a hollow elasticity cylinder containing an internal circumferential edge crack is considered. It is assumed that the problem is axisymmetric with regard to the crack geometry and the loading, and that the inertia effects are negligible. The problem is solved for a cylinder which is suddenly cooled from inside. First the transient temperature and stress distributions in an uncracked cylinder are calculated. By using the equal and opposite of this thermal stress as the crack surface traction in the isothermal cylinder the crack problem is then solved and the stress intensity factor is calculated. The numerical results are obtained as a function of the Fourier number tD/b(2) representing the time for various inner-to-outer radius ratios and relative crack depths, where D and b are respectively the coefficient of diffusivity and the outer radius of the cylinder.
Consensus problem in directed networks of multi-agents via nonlinear protocols
International Nuclear Information System (INIS)
Liu Xiwei; Chen Tianping; Lu Wenlian
2009-01-01
In this Letter, the consensus problem via distributed nonlinear protocols for directed networks is investigated. Its dynamical behaviors are described by ordinary differential equations (ODEs). Based on graph theory, matrix theory and the Lyapunov direct method, some sufficient conditions of nonlinear protocols guaranteeing asymptotical or exponential consensus are presented and rigorously proved. The main contribution of this work is that for nonlinearly coupled networks, we generalize the results for undirected networks to directed networks. Consensus under pinning control technique is also developed here. Simulations are also given to show the validity of the theories.
Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations
Nakamura, Gen; Vashisth, Manmohan
2017-01-01
In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\\geq 3$. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear isotropic wave equation with the speed $\\sqrt{\\gamma(x)}$ at each point $x$ in a given spacial domain. For any small solution $u=u(t,x)$ of this non-linear equation, we have the linear isotr...
Strongly nonlinear nonhomogeneous elliptic unilateral problems with L^1 data and no sign conditions
Directory of Open Access Journals (Sweden)
Elhoussine Azroul
2012-05-01
Full Text Available In this article, we prove the existence of solutions to unilateral problems involving nonlinear operators of the form: $$ Au+H(x,u,abla u=f $$ where $A$ is a Leray Lions operator from $W_0^{1,p(x}(Omega$ into its dual $W^{-1,p'(x}(Omega$ and $H(x,s,xi$ is the nonlinear term satisfying some growth condition but no sign condition. The right hand side $f$ belong to $L^1(Omega$.
Topological approximation methods for evolutionary problem of nonlinear hydrodynamics
Zvyagin, Victor
2008-01-01
The authors present functional analytical methods for solving a class of partial differential equations. The results have important applications to the numerical treatment of rheology (specific examples are the behaviour of blood or print colours) and to other applications in fluid mechanics. A class of methods for solving problems in hydrodynamics is presented.
Optimal Control Problems for Nonlinear Variational Evolution Inequalities
Directory of Open Access Journals (Sweden)
Eun-Young Ju
2013-01-01
Full Text Available We deal with optimal control problems governed by semilinear parabolic type equations and in particular described by variational inequalities. We will also characterize the optimal controls by giving necessary conditions for optimality by proving the Gâteaux differentiability of solution mapping on control variables.
Badia, Santiago; Martín, Alberto F.; Planas, Ramon
2014-10-01
The thermally coupled incompressible inductionless magnetohydrodynamics (MHD) problem models the flow of an electrically charged fluid under the influence of an external electromagnetic field with thermal coupling. This system of partial differential equations is strongly coupled and highly nonlinear for real cases of interest. Therefore, fully implicit time integration schemes are very desirable in order to capture the different physical scales of the problem at hand. However, solving the multiphysics linear systems of equations resulting from such algorithms is a very challenging task which requires efficient and scalable preconditioners. In this work, a new family of recursive block LU preconditioners is designed and tested for solving the thermally coupled inductionless MHD equations. These preconditioners are obtained after splitting the fully coupled matrix into one-physics problems for every variable (velocity, pressure, current density, electric potential and temperature) that can be optimally solved, e.g., using preconditioned domain decomposition algorithms. The main idea is to arrange the original matrix into an (arbitrary) 2 × 2 block matrix, and consider an LU preconditioner obtained by approximating the corresponding Schur complement. For every one of the diagonal blocks in the LU preconditioner, if it involves more than one type of unknowns, we proceed the same way in a recursive fashion. This approach is stated in an abstract way, and can be straightforwardly applied to other multiphysics problems. Further, we precisely explain a flexible and general software design for the code implementation of this type of preconditioners.
Cho, Yumi
2018-05-01
We study nonlinear elliptic problems with nonstandard growth and ellipticity related to an N-function. We establish global Calderón-Zygmund estimates of the weak solutions in the framework of Orlicz spaces over bounded non-smooth domains. Moreover, we prove a global regularity result for asymptotically regular problems which are getting close to the regular problems considered, when the gradient variable goes to infinity.
Quasi-stability of a vector trajectorial problem with non-linear partial criteria
Directory of Open Access Journals (Sweden)
Vladimir A. Emelichev
2003-10-01
Full Text Available Multi-objective (vector combinatorial problem of finding the Pareto set with four kinds of non-linear partial criteria is considered. Necessary and sufficient conditions of that kind of stability of the problem (quasi-stability are obtained. The problem is a discrete analogue of the lower semicontinuity by Hausdorff of the optimal mapping. Mathematics Subject Classification 2000: 90C10, 90C05, 90C29, 90C31.
Energy Technology Data Exchange (ETDEWEB)
Bouaricha, A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.; Schnabel, R.B. [Colorado Univ., Boulder, CO (United States). Dept. of Computer Science
1996-12-31
This paper describes a modular software package for solving systems of nonlinear equations and nonlinear least squares problems, using a new class of methods called tensor methods. It is intended for small to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or approximate it by finite differences at each iteration. The software allows the user to select between a tensor method and a standard method based upon a linear model. The tensor method models F({ital x}) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies, a line search and a two- dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small and medium-sized problems in iterations and function evaluations.
Contributions to thermal and fluid dynamic problems in nuclear technology
International Nuclear Information System (INIS)
Mueller, U.; Krebs, L.; Rust, K.
1984-02-01
The majority of contributions compiled in this report deals with thermal and fluid dynamic problems in nuclear engineering. Especially problems of heat transfer and cooling are represented which may arise during and afer a loss-of-coolant accident both in light water reactors and in liquid metal cooled fast breeder reactors. Papers on the mass transfer in pressurized water, tribological problems in sodium cooled reactors, the fluid dynamics of pulsed column, and fundamental investigations of convective flows supplement these contributions on problems connected with accidents. Furthermore, a keynote paper presents the individual activities relating to the reliability of reactor components, a field recently included in our research program. Technical solutions to special problems are closely connected to the investigations based on experiments. Therefore, several contributions deal with new developments in technology and measuring techniques. (orig.) [de
Energy Technology Data Exchange (ETDEWEB)
Kaikina, Elena I., E-mail: ekaikina@matmor.unam.mx [Centro de Ciencias Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán (Mexico)
2013-11-15
We consider the inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation, formulated on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time.
International Nuclear Information System (INIS)
Kaikina, Elena I.
2013-01-01
We consider the inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation, formulated on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time
Avdyushev, Victor A.
2017-12-01
Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the
A boundary control problem with a nonlinear reaction term
Directory of Open Access Journals (Sweden)
John R. Cannon
2009-04-01
Full Text Available The authors study the problem $u_t=u_{xx}-au$, $0
Directory of Open Access Journals (Sweden)
Blank Arkadiy
2017-01-01
Full Text Available The results of the systematic experimental analysis of the thermal nonlinear electro-optic properties of photoelectric converters with silicon vertical cells in comparison with solar elements and elements on the basis of In/Ga/As are presented. The parameters of the linear and quadratic approximations for the investigated dependences are determined, that allows constructing a scalable analytic model of the converter with a given type of the working elements switching.
Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces
Directory of Open Access Journals (Sweden)
Cho Yeol
2011-01-01
Full Text Available Abstract In this paper, the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To overcome the difficulties, due to the presence of a proper convex lower semi-continuous function, φ and a mapping g, which appeared in the considered problem, we have used some applications of the resolvent operator technique. We would like to point out that although many authors have proved results for finding solutions of the systems of nonlinear set-valued (mixed variational inequalities problems, it is clear that it cannot be directly applied to the problems that we have considered in this paper because of φ and g. 2000 AMS Subject Classification: 47H05; 47H09; 47J25; 65J15.
Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems
International Nuclear Information System (INIS)
Haber, E; Horesh, L; Tenorio, L
2010-01-01
Design of experiments for discrete ill-posed problems is a relatively new area of research. While there has been some limited work concerning the linear case, little has been done to study design criteria and numerical methods for ill-posed nonlinear problems. We present an algorithmic framework for nonlinear experimental design with an efficient numerical implementation. The data are modeled as indirect, noisy observations of the model collected via a set of plausible experiments. An inversion estimate based on these data is obtained by a weighted Tikhonov regularization whose weights control the contribution of the different experiments to the data misfit term. These weights are selected by minimization of an empirical estimate of the Bayes risk that is penalized to promote sparsity. This formulation entails a bilevel optimization problem that is solved using a simple descent method. We demonstrate the viability of our design with a problem in electromagnetic imaging based on direct current resistivity and magnetotelluric data
On the solvability of initial-value problems for nonlinear implicit difference equations
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Ha Thi Ngoc Yen
2004-07-01
Full Text Available Our aim is twofold. First, we propose a natural definition of index for linear nonautonomous implicit difference equations, which is similar to that of linear differential-algebraic equations. Then we extend this index notion to a class of nonlinear implicit difference equations and prove some existence theorems for their initial-value problems.
Admissible solutions for a class of nonlinear parabolic problem with non-negative data
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Petzeltová, Hana; Simondon, F.
2001-01-01
Roč. 131, č. 5 (2001), s. 857-883 ISSN 0308-2105 R&D Projects: GA AV ČR IAA1019703 Keywords : admissible solutions%nonlinear parabolic problem * admissible solutions * comparison principle * non-negative data Subject RIV: BA - General Mathematics Impact factor: 0.441, year: 2001
Directory of Open Access Journals (Sweden)
Xiaofeng Zhang
2017-12-01
Full Text Available In this paper, we consider the existence of positive solutions to a singular semipositone boundary value problem of nonlinear fractional differential equations. By applying the fixed point index theorem, some new results for the existence of positive solutions are obtained. In addition, an example is presented to demonstrate the application of our main results.
Czech Academy of Sciences Publication Activity Database
Lukšan, Ladislav; Vlček, Jan
1998-01-01
Roč. 5, č. 3 (1998), s. 219-247 ISSN 1070-5325 R&D Projects: GA ČR GA201/96/0918 Keywords : nonlinear programming * sparse problems * equality constraints * truncated Newton method * augmented Lagrangian function * indefinite systems * indefinite preconditioners * conjugate gradient method * residual smoothing Subject RIV: BA - General Mathematics Impact factor: 0.741, year: 1998
Czech Academy of Sciences Publication Activity Database
Mukhigulashvili, Sulkhan; Půža, B.
2015-01-01
Roč. 2015, January (2015), s. 17 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2015 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1
Alternative solution algorithm for coupled thermal-hydraulic problems
International Nuclear Information System (INIS)
Farnsworth, D.A.; Rice, J.G.
1986-01-01
A thermal-hydraulic system involves flow of a fluid for which a combined solution of the continuity, momentum, and energy equations is required. When the solutions of the energy and momentum fields are dependent on each other, the system is said to be thermally coupled. A common problem encountered in the numerical solution of strongly coupled thermal-hydraulic problems is a very slow rate of convergence or a complete lack of convergence. Many times this degradation in convergence is due to the lack of true coupling between the energy and momentum fields during the iteration process. In the most widely used solution algorithms - such as the SIMPLE algorithm and its many variants - a sequential solution technique is required. That is, the solution process alternates between the flow and energy fields until a converged solution is obtained. This approach allows only implicit energy-momentum coupling. To improve the convergence rate for strongly coupled problems, a practical solution algorithm that can accommodate true energy-momentum coupling terms was developed. A complete simultaneous (versus sequential) solution of the governing conservation equations utilizing a line-by-line solution was developed and direct coupling terms between the momentum and energy fields were added utilizing a modified Newton-Raphson technique
On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation
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Mesloub Said
2008-01-01
Full Text Available This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.
TRUMP3-JR: a finite difference computer program for nonlinear heat conduction problems
International Nuclear Information System (INIS)
Ikushima, Takeshi
1984-02-01
Computer program TRUMP3-JR is a revised version of TRUMP3 which is a finite difference computer program used for the solution of multi-dimensional nonlinear heat conduction problems. Pre- and post-processings for input data generation and graphical representations of calculation results of TRUMP3 are avaiable in TRUMP3-JR. The calculation equations, program descriptions and user's instruction are presented. A sample problem is described to demonstrate the use of the program. (author)
Directory of Open Access Journals (Sweden)
M. G. Crandall
1999-07-01
Full Text Available We study existence of continuous weak (viscosity solutions of Dirichlet and Cauchy-Dirichlet problems for fully nonlinear uniformly elliptic and parabolic equations. Two types of results are obtained in contexts where uniqueness of solutions fails or is unknown. For equations with merely measurable coefficients we prove solvability of the problem, while in the continuous case we construct maximal and minimal solutions. Necessary barriers on external cones are also constructed.
International Nuclear Information System (INIS)
Ruas, V.
1982-09-01
A class of simplicial finite elements for solving incompressible elasticity problems in n-dimensional space, n=2 or 3, is presented. An asymmetric structure of the shape functions with respect to the centroid of the simplex, renders them particularly stable in the large strain case, in which the incompressibility condition is nonlinear. It is proved that under certain assembling conditions of the elements, there exists a solution to the corresponding discrete problems. Numerical examples illustrate the efficiency of the method. (Author) [pt
A Kind of Nonlinear Programming Problem Based on Mixed Fuzzy Relation Equations Constraints
Li, Jinquan; Feng, Shuang; Mi, Honghai
In this work, a kind of nonlinear programming problem with non-differential objective function and under the constraints expressed by a system of mixed fuzzy relation equations is investigated. First, some properties of this kind of optimization problem are obtained. Then, a polynomial-time algorithm for this kind of optimization problem is proposed based on these properties. Furthermore, we show that this algorithm is optimal for the considered optimization problem in this paper. Finally, numerical examples are provided to illustrate our algorithms.
Response of Non-Linear Shock Absorbers-Boundary Value Problem Analysis
Rahman, M. A.; Ahmed, U.; Uddin, M. S.
2013-08-01
A nonlinear boundary value problem of two degrees-of-freedom (DOF) untuned vibration damper systems using nonlinear springs and dampers has been numerically studied. As far as untuned damper is concerned, sixteen different combinations of linear and nonlinear springs and dampers have been comprehensively analyzed taking into account transient terms. For different cases, a comparative study is made for response versus time for different spring and damper types at three important frequency ratios: one at r = 1, one at r > 1 and one at r <1. The response of the system is changed because of the spring and damper nonlinearities; the change is different for different cases. Accordingly, an initially stable absorber may become unstable with time and vice versa. The analysis also shows that higher nonlinearity terms make the system more unstable. Numerical simulation includes transient vibrations. Although problems are much more complicated compared to those for a tuned absorber, a comparison of the results generated by the present numerical scheme with the exact one shows quite a reasonable agreement
Grants, Ilmars; Gerbeth, Gunter
2010-07-01
The stability of a thermally stratified liquid metal flow is considered numerically. The flow is driven by a rotating magnetic field in a cylinder heated from above and cooled from below. The stable thermal stratification turns out to destabilize the flow. This is explained by the fact that a stable stratification suppresses the secondary meridional flow, thus indirectly enhancing the primary rotation. The instability in the form of Taylor-Görtler rolls is consequently promoted. These rolls can only be excited by finite disturbances in the isothermal flow. A sufficiently strong thermal stratification transforms this nonlinear bypass instability into a linear one reducing, thus, the critical value of the magnetic driving force. A weaker temperature gradient delays the linear instability but makes the bypass transition more likely. We quantify the non-normal and nonlinear components of this transition by direct numerical simulation of the flow response to noise. It is observed that the flow sensitivity to finite disturbances increases considerably under the action of a stable thermal stratification. The capabilities of the random forcing approach to identify disconnected coherent states in a general case are discussed.
Spectral methods for a nonlinear initial value problem involving pseudo differential operators
International Nuclear Information System (INIS)
Pasciak, J.E.
1982-01-01
Spectral methods (Fourier methods) for approximating the solution of a nonlinear initial value problem involving pseudo differential operators are defined and analyzed. A semidiscrete approximation to the nonlinear equation based on an L 2 projection is described. The semidiscrete L 2 approximation is shown to be a priori stable and convergent under sufficient decay and smoothness assumptions on the initial data. It is shown that the semidiscrete method converges with infinite order, that is, higher order decay and smoothness assumptions imply higher order error bounds. Spectral schemes based on spacial collocation are also discussed
Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's
Cai, Wei; Wang, Jian-Zhong
1993-01-01
We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.
On the Cauchy problem for nonlinear Schrödinger equations with rotation
Antonelli, Paolo; Marahrens, Daniel; Sparber, Christof
2011-01-01
We consider the Cauchy problem for (energy-subcritical) nonlinear Schrödinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for superuid quantum gases in rotating traps. We prove global existence (in the energy space) for defocusing nonlinearities without any restriction on the rotation frequency, generalizing earlier results given in [11, 12]. Moreover, we find that the rotation term has a considerable in fiuence in proving finite time blow-up in the focusing case.
Domain decomposition based iterative methods for nonlinear elliptic finite element problems
Energy Technology Data Exchange (ETDEWEB)
Cai, X.C. [Univ. of Colorado, Boulder, CO (United States)
1994-12-31
The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.
On the Cauchy problem for nonlinear Schrödinger equations with rotation
Antonelli, Paolo
2011-10-01
We consider the Cauchy problem for (energy-subcritical) nonlinear Schrödinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for superuid quantum gases in rotating traps. We prove global existence (in the energy space) for defocusing nonlinearities without any restriction on the rotation frequency, generalizing earlier results given in [11, 12]. Moreover, we find that the rotation term has a considerable in fiuence in proving finite time blow-up in the focusing case.
International Nuclear Information System (INIS)
Reigada, Ramon; Sarmiento, Antonio; Romero, Aldo H.; Sancho, J. M.; Lindenberg, Katja
2000-01-01
We present a model in which the immediate environment of a bistable system is a molecular chain which in turn is connected to a thermal environment of the Langevin form. The molecular chain consists of masses connected by harmonic or by anharmonic springs. The distribution, intensity, and mobility of thermal fluctuations in these chains is strongly dependent on the nature of the springs and leads to different transition dynamics for the activated process. Thus, all else (temperature, damping, coupling parameters between the chain and the bistable system) being the same, the hard chain may provide an environment described as diffusion-limited and more effective in the activation process, while the soft chain may provide an environment described as energy-limited and less effective. The importance of a detailed understanding of the thermal environment toward the understanding of the activation process itself is thus highlighted. (c) 2000 American Institute of Physics
Iterative solution of a nonlinear system arising in phase change problems
International Nuclear Information System (INIS)
Williams, M.A.
1987-01-01
We consider several iterative methods for solving the nonlinear system arising from an enthalpy formulation of a phase change problem. We present the formulation of the problem. Implicit discretization of the governing equations results in a mildly nonlinear system at each time step. We discuss solving this system using Jacobi, Gauss-Seidel, and SOR iterations and a new modified preconditioned conjugate gradient (MPCG) algorithm. The new MPCG algorithm and its properties are discussed in detail. Numerical results are presented comparing the performance of the SOR algorithm and the MPCG algorithm with 1-step SSOR preconditioning. The MPCG algorithm exhibits a superlinear rate of convergence. The SOR algorithm exhibits a linear rate of convergence. Thus, the MPCG algorithm requires fewer iterations to converge than the SOR algorithm. However in most cases, the SOR algorithm requires less total computation time than the MPCG algorithm. Hence, the SOR algorithm appears to be more appropriate for the class of problems considered. 27 refs., 11 figs
International Nuclear Information System (INIS)
Semenova, V.N.
2016-01-01
A boundary value problem for a nonlinear second order differential equation has been considered. A numerical method has been proposed to solve this problem using power series. Results of numerical experiments have been presented in the paper [ru
State and parameter estimation in nonlinear systems as an optimal tracking problem
International Nuclear Information System (INIS)
Creveling, Daniel R.; Gill, Philip E.; Abarbanel, Henry D.I.
2008-01-01
In verifying and validating models of nonlinear processes it is important to incorporate information from observations in an efficient manner. Using the idea of synchronization of nonlinear dynamical systems, we present a framework for connecting a data signal with a model in a way that minimizes the required coupling yet allows the estimation of unknown parameters in the model. The need to evaluate unknown parameters in models of nonlinear physical, biophysical, and engineering systems occurs throughout the development of phenomenological or reduced models of dynamics. Our approach builds on existing work that uses synchronization as a tool for parameter estimation. We address some of the critical issues in that work and provide a practical framework for finding an accurate solution. In particular, we show the equivalence of this problem to that of tracking within an optimal control framework. This equivalence allows the application of powerful numerical methods that provide robust practical tools for model development and validation
Directory of Open Access Journals (Sweden)
Yahaya Shagaiya Daniel
2018-04-01
Full Text Available The combined effects of thermal stratification, applied electric and magnetic fields, thermal radiation, viscous dissipation and Joules heating are numerically studied on a boundary layer flow of electrical conducting nanofluid over a nonlinearly stretching sheet with variable thickness. The governing equations which are partial differential equations are converted to a couple of ordinary differential equations with suitable similarity transformation techniques and are solved using implicit finite difference scheme. The electrical conducting nanofluid particle fraction on the boundary is passively rather than actively controlled. The effects of the emerging parameters on the electrical conducting nanofluid velocity, temperature, and nanoparticles concentration volume fraction with skin friction, heat transfer characteristics are examined with the aids of graphs and tabular form. It is observed that the variable thickness enhances the fluid velocity, temperature, and nanoparticle concentration volume fraction. The heat and mass transfer rate at the surface increases with thermal stratification resulting to a reduction in the fluid temperature. Electric field enhances the nanofluid velocity which resolved the sticking effects caused by a magnetic field which suppressed the profiles. Radiative heat transfer and viscous dissipation are sensitive to an increase in the fluid temperature and thicker thermal boundary layer thickness. Comparison with published results is examined and presented. Keywords: MHD nanofluid, Variable thickness, Thermal radiation, Similarity solution, Thermal stratification
Special function solutions of a spectral problem for a nonlinear quantum oscillator
International Nuclear Information System (INIS)
Schulze-Halberg, A; Morris, J R
2012-01-01
We construct exact solutions of a spectral problem involving the Schrödinger equation for a nonlinear, one-parameter oscillator potential. In contrast to a previous analysis of the problem (Carinena et al 2007 Ann. Phys. 322 434–59), where solutions were given through a Rodrigues-type formula, our approach leads to closed-form representations of the solutions in terms of special functions, not containing any derivative operators. We show normalizability and orthogonality of our solutions, as well as correct reduction of the problem to the harmonic oscillator model, if the parameter in the potential gets close to zero. (paper)
Multi-level nonlinear diffusion acceleration method for multigroup transport k-Eigenvalue problems
International Nuclear Information System (INIS)
Anistratov, Dmitriy Y.
2011-01-01
The nonlinear diffusion acceleration (NDA) method is an efficient and flexible transport iterative scheme for solving reactor-physics problems. This paper presents a fast iterative algorithm for solving multigroup neutron transport eigenvalue problems in 1D slab geometry. The proposed method is defined by a multi-level system of equations that includes multigroup and effective one-group low-order NDA equations. The Eigenvalue is evaluated in the exact projected solution space of smallest dimensionality, namely, by solving the effective one- group eigenvalue transport problem. Numerical results that illustrate performance of the new algorithm are demonstrated. (author)
The Cauchy problem for non-linear Klein-Gordon equations
International Nuclear Information System (INIS)
Simon, J.C.H.; Taflin, E.
1993-01-01
We consider in R n+1 , n≥2, the non-linear Klein-Gordon equation. We prove for such an equation that there is neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. The inverse of the wave operator linearizes the non-linear equation. If, moreover, the equation is manifestly Poincare covariant then the non-linear representation of the Poincare-Lie algebra, associated with the non-linear Klein-Gordon equation is integrated to a non-linear representation of the Poincare group on an invariant neighbourhood of zero in the Hilbert space. This representation is linearized by the inverse of the wave operator. The Hilbert space is, in both cases, the closure of the space of the differentiable vectors for the linear representation of the Poincare group, associated with the Klein-Gordon equation, with respect to a norm defined by the representation of the enveloping algebra. (orig.)
Directory of Open Access Journals (Sweden)
Sie Long Kek
2015-01-01
Full Text Available A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.
A method of solution of the elastic-plastic thermal stress problem
International Nuclear Information System (INIS)
Rafalski, P.
1975-01-01
The purpose of the work is an improvement of the numerical technique for calculating the thermal stress distribution in an elastic-plastic structural element. The work consists of two parts. In the first a new method of solution of the thermal stress problem for the elastic-plastic body is presented. In the second a particular numerical technique, based on the above method, for calculating the stress and strain fields is proposed. A new mathematical approach consists in treating the stress and strain fields as mathematical objects defined in the space-time domain. The methods commonly applied use the stress and strain fields defined in the space domain and establish the relations between them at a given instant t. They reduce the problem to the system of ordinary differential equations with respect to time, which are usually solved with a step-by-step technique. The new method reduces the problem to the system of nonlinear algebraic equations. In the work the Hilbert space of admissible tensor fields is constructed. This space is the orthogonal sum of two subspaces: of statically admissible and kinematically admissible fields. Two alternative orthogonality conditions, which correspond to the equilibrium and compatibility equations with the appropriate boundary conditions, are derived. The results of the work are to be used for construction of the computer program for calculation the stress and strain fields in the elastic-plastic body with a prescribed temperature field in the interior and appropriate displacement and force conditions on the boundary
Directory of Open Access Journals (Sweden)
Koh Kim Jie
2017-01-01
Full Text Available Quadratic damping nonlinearity is challenging for displacement based structural dynamics problem as the problem is nonlinear in time derivative of the primitive variable. For such nonlinearity, the formulation of tangent stiffness matrix is not lucid in the literature. Consequently, ambiguity related to kinematics update arises when implementing the time integration-iterative algorithm. In present work, an Euler-Bernoulli beam vibration problem with quadratic damping nonlinearity is addressed as the main source of quadratic damping nonlinearity arises from drag force estimation, which is generally valid only for slender structures. Employing Newton-Raphson formulation, tangent stiffness components associated with quadratic damping nonlinearity requires velocity input for evaluation purpose. For this reason, two mathematically equivalent algorithm structures with different kinematics arrangement are tested. Both algorithm structures result in the same accuracy and convergence characteristic of solution.
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-05-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.
International Nuclear Information System (INIS)
Kaltenbacher, Barbara; Kirchner, Alana; Vexler, Boris
2011-01-01
Parameter identification problems for partial differential equations usually lead to nonlinear inverse problems. A typical property of such problems is their instability, which requires regularization techniques, like, e.g., Tikhonov regularization. The main focus of this paper will be on efficient methods for determining a suitable regularization parameter by using adaptive finite element discretizations based on goal-oriented error estimators. A well-established method for the determination of a regularization parameter is the discrepancy principle where the residual norm, considered as a function i of the regularization parameter, should equal an appropriate multiple of the noise level. We suggest to solve the resulting scalar nonlinear equation by an inexact Newton method, where in each iteration step, a regularized problem is solved at a different discretization level. The proposed algorithm is an extension of the method suggested in Griesbaum A et al (2008 Inverse Problems 24 025025) for linear inverse problems, where goal-oriented error estimators for i and its derivative are used for adaptive refinement strategies in order to keep the discretization level as coarse as possible to save computational effort but fine enough to guarantee global convergence of the inexact Newton method. This concept leads to a highly efficient method for determining the Tikhonov regularization parameter for nonlinear ill-posed problems. Moreover, we prove that with the so-obtained regularization parameter and an also adaptively discretized Tikhonov minimizer, usual convergence and regularization results from the continuous setting can be recovered. As a matter of fact, it is shown that it suffices to use stationary points of the Tikhonov functional. The efficiency of the proposed method is demonstrated by means of numerical experiments. (paper)
A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems
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S. S. Motsa
2013-01-01
Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.
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MOHAMED KEZZAR
2015-08-01
Full Text Available In this research, an efficient technique of computation considered as a modified decomposition method was proposed and then successfully applied for solving the nonlinear problem of the two dimensional flow of an incompressible viscous fluid between nonparallel plane walls. In fact this method gives the nonlinear term Nu and the solution of the studied problem as a power series. The proposed iterative procedure gives on the one hand a computationally efficient formulation with an acceleration of convergence rate and on the other hand finds the solution without any discretization, linearization or restrictive assumptions. The comparison of our results with those of numerical treatment and other earlier works shows clearly the higher accuracy and efficiency of the used Modified Decomposition Method.
Numerical treatment of the unsteady hydromagnetic thermal boundary layer problem
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Drymonitou, M.A.; Geroyannis, V.S.; Goudas, C.L.
1980-01-01
This paper presents a suitable numerical method for the treatment of the unsteady hydromagnetic thermal boundary layer problem for flows past an infinite porous flat plate, the motion of which is governed by a general time-dependent law, under the influence of a transverse externally set magnetic field. The normal velocity of suction/injection at the plate is also assumed to be time-dependent. The results obtained on the basis of numerical approximations seem to compare favourably with earlier results (Pande et al., 1976; Tokis, 1978). Analytical approximations are given for the cases of a plate (i) generally accelerated and (ii) harmonically oscillating. The direct numerical treatment is obviously advantageous since it allows handling of cases where the known methods for analytical approximations are not applicable. This problem is closely related to the motions and heat transfer occurring locally on the surfaces of stars. (orig.)
Splines employment for inverse problem of nonstationary thermal conduction
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Nikonov, S.P.; Spolitak, S.I.
1985-01-01
An analytical solution has been obtained for an inverse problem of nonstationary thermal conduction which is faced in nonstationary heat transfer data processing when the rewetting in channels with uniform annular fuel element imitators is investigated. In solving the problem both boundary conditions and power density within the imitator are regularized via cubic splines constructed with the use of Reinsch algorithm. The solution can be applied for calculation of temperature distribution in the imitator and the heat flux in two-dimensional approximation (r-z geometry) under the condition that the rewetting front velocity is known, and in one-dimensional r-approximation in cases with negligible axial transport or when there is a lack of data about the temperature disturbance source velocity along the channel
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Sen, S.; Roy Chowdhury, A.
1989-06-01
The nonlinear Alfven waves are governed by the Vector Derivative nonlinear Schroedinger (VDNLS) equation, which for parallel or quasi parallel propagation reduces to the Derivative Nonlinear Schroedinger (DNLS) equation for the circularly polarized waves. We have formulated the Quantum Inverse problem for a new type of Nonlinear Schroedinger Equation which has many properties similar to the usual NLS problem but the structure of classical and quantum R matrix are distinctly different. The commutation rules of the scattering data are obtained and the Algebraic Bethe Ansatz is formulated to derive the eigenvalue equation for the energy of the excited states. 10 refs
Marudhu, G.; Krishnan, S.; Palanichamy, M.
2016-03-01
A novel nonlinear optical crystal of 4-Aminopyridinium monophthalate (4-APMP) was grown by slow evaporation technique using methanol as solvent. Single crystal X-ray diffraction analysis confirms that the grown crystal belongs to orthorhombic system. The presence of functional groups was qualitatively determined by FTIR analysis. The optical absorption studies reveal very low absorption in the entire visible region. The fluorescence emission spectrum shows the emission is in blue region. The thermal stability of the grown crystal is found to be around 197.2 °C. The SHG efficiency of the grown crystal is found to be 1.1 times than that of KDP crystals.
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Qingkai Kong
2012-02-01
Full Text Available In this paper, we study the existence and multiplicity of positive solutions of a class of nonlinear fractional boundary value problems with Dirichlet boundary conditions. By applying the fixed point theory on cones we establish a series of criteria for the existence of one, two, any arbitrary finite number, and an infinite number of positive solutions. A criterion for the nonexistence of positive solutions is also derived. Several examples are given for demonstration.
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Alexander N. Kvitko
2017-01-01
Full Text Available An algorithm for constructing a control function that transfers a wide class of stationary nonlinear systems of ordinary differential equations from an initial state to a final state under certain control restrictions is proposed. The algorithm is designed to be convenient for numerical implementation. A constructive criterion of the desired transfer possibility is presented. The problem of an interorbital flight is considered as a test example and it is simulated numerically with the presented method.
Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management
Koleva, M. N.
2011-11-01
In this work we consider a nonlinear parabolic equation, obtained from Riccati like transformation of the Hamilton-Jacobi-Bellman equation, arising in pension saving management. We discuss two numerical iterative methods for solving the model problem—fully implicit Picard method and mixed Picard-Newton method, which preserves the parabolic characteristics of the differential problem. Numerical experiments for comparison the accuracy and effectiveness of the algorithms are discussed. Finally, observations are given.
Positive solutions for a nonlinear periodic boundary-value problem with a parameter
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Jingliang Qiu
2012-08-01
Full Text Available Using topological degree theory with a partially ordered structure of space, sufficient conditions for the existence and multiplicity of positive solutions for a second-order nonlinear periodic boundary-value problem are established. Inspired by ideas in Guo and Lakshmikantham [6], we study the dependence of positive periodic solutions as a parameter approaches infinity, $$ lim_{lambdao +infty}|x_{lambda}|=+infty,quadhbox{or}quad lim_{lambdao+infty}|x_{lambda}|=0. $$
On the Cauchy problem for a Sobolev-type equation with quadratic non-linearity
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Aristov, Anatoly I
2011-01-01
We investigate the asymptotic behaviour as t→∞ of the solution of the Cauchy problem for a Sobolev-type equation with quadratic non-linearity and develop ideas used by I. A. Shishmarev and other authors in the study of classical and Sobolev-type equations. Conditions are found under which it is possible to consider the case of an arbitrary dimension of the spatial variable.
Existence of solutions to nonlinear parabolic unilateral problems with an obstacle depending on time
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Nabila Bellal
2014-10-01
Full Text Available Using the penalty method, we prove the existence of solutions to nonlinear parabolic unilateral problems with an obstacle depending on time. To find a solution, the original inequality is transformed into an equality by adding a positive function on the right-hand side and a complementary condition. This result can be seen as a generalization of the results by Mokrane in [11] where the obstacle is zero.
Inverse periodic problem for the discrete approximation of the Schroedinger nonlinear equation
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Bogolyubov, N.N.; Prikarpatskij, A.K.; AN Ukrainskoj SSR, Lvov. Inst. Prikladnykh Problem Mekhaniki i Matematiki)
1982-01-01
The problem of numerical solution of the Schroedinger nonlinear equation (1) iPSIsub(t) = PSIsub(xx)+-2(PSI)sup(2)PSI. The numerical solution of nonlinear differential equation supposes its discrete approximation is required for the realization of the computer calculation process. Tor the equation (1) there exists the following discrete approximation by variable x(2) iPSIsub(n, t) = (PSIsub(n+1)-2PSIsub(n)+PSIsub(n-1))/(Δx)sup(2)+-(PSIsub(n))sup(2)(PSIsub(n+1)+PSIsub(n-1)), n=0, +-1, +-2... where PSIsub(n)(+) is the corresponding value of PSI(x, t) function in the node and divisions with the equilibrium step Δx. The main problem is obtaining analytically exact solutions of the equations (2). The analysis of the equation system (2) is performed on the base of the discrete analogue of the periodic variant of the inverse scattering problem method developed with the aid of nonlinear equations of the Korteweg-de Vries type. Obtained in explicit form are analytical solutions of the equations system (2). The solutions are expressed through the Riemann THETA-function [ru
Energy Technology Data Exchange (ETDEWEB)
Carey, G.F.; Young, D.M.
1993-12-31
The program outlined here is directed to research on methods, algorithms, and software for distributed parallel supercomputers. Of particular interest are finite element methods and finite difference methods together with sparse iterative solution schemes for scientific and engineering computations of very large-scale systems. Both linear and nonlinear problems will be investigated. In the nonlinear case, applications with bifurcation to multiple solutions will be considered using continuation strategies. The parallelizable numerical methods of particular interest are a family of partitioning schemes embracing domain decomposition, element-by-element strategies, and multi-level techniques. The methods will be further developed incorporating parallel iterative solution algorithms with associated preconditioners in parallel computer software. The schemes will be implemented on distributed memory parallel architectures such as the CRAY MPP, Intel Paragon, the NCUBE3, and the Connection Machine. We will also consider other new architectures such as the Kendall-Square (KSQ) and proposed machines such as the TERA. The applications will focus on large-scale three-dimensional nonlinear flow and reservoir problems with strong convective transport contributions. These are legitimate grand challenge class computational fluid dynamics (CFD) problems of significant practical interest to DOE. The methods developed and algorithms will, however, be of wider interest.
Gazzola, Filippo; Sweers, Guido
2010-01-01
This monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or - since, in contrast to second order equations, a general form of a comparison principle does not exist - on “near positivity.” The required kernel estimates are also presented in detail. As for nonlinear problems, several techniques well-known from second order equations cannot be utilized and have to be replaced by new and different methods. Subcritical, critical and supercritical nonlinearities are discussed and various existence and nonexistence results are proved. The interplay with the positivity topic from the ﬁrst part is emphasized and, moreover, a far-reaching Gidas-Ni-Nirenbe...
Non-linear thermal and structural analysis of a typical spent fuel silo
International Nuclear Information System (INIS)
Alvarez, L.M.; Mancini, G.R.; Spina, O.A.F.; Sala, G.; Paglia, F.
1993-01-01
A numerical method for the non-linear structural analysis of a typical reinforced concrete spent fuel silo under thermal loads is proposed. The numerical time integration was performed by means of a time explicit axisymmetric finite-difference numerical operator. An analysis was made of influences by heat, viscoelasticity and cracking upon the concrete behaviour between concrete pouring stage and the first period of the silo's normal operation. The following parameters were considered for the heat generation and transmission process: Heat generated during the concrete's hardening stage, Solar radiation effects, Natural convection, Spent-fuel heat generation. For the modelling of the reinforced concrete behaviour, use was made of a simplified formulation of: Visco-elastic effects, Thermal cracking, Steel reinforcement. A comparison between some experimental temperature characteristic values obtained from the numerical integration process and empirical data obtained from a 1:1 scaled prototype was also carried out. (author)
Iterative Runge–Kutta-type methods for nonlinear ill-posed problems
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Böckmann, C; Pornsawad, P
2008-01-01
We present a regularization method for solving nonlinear ill-posed problems by applying the family of Runge–Kutta methods to an initial value problem, in particular, to the asymptotical regularization method. We prove that the developed iterative regularization method converges to a solution under certain conditions and with a general stopping rule. Some particular iterative regularization methods are numerically implemented. Numerical results of the examples show that the developed Runge–Kutta-type regularization methods yield stable solutions and that particular implicit methods are very efficient in saving iteration steps
Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin
2016-01-01
This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.
POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
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FAOUZI HADDOUCHI
2015-11-01
Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.
International Nuclear Information System (INIS)
Leaf, G.K.; Minkoff, M.
1982-01-01
1 - Description of problem or function: DISPL1 is a software package for solving second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types. The package is designed primarily for chemical kinetics- diffusion problems, although not limited to these problems. Fairly general nonlinear boundary conditions are allowed as well as inter- face conditions for problems in an inhomogeneous medium. The spatial domain is one- or two-dimensional with rectangular Cartesian, cylindrical, or spherical (in one dimension only) geometry. 2 - Method of solution: The numerical method is based on the use of Galerkin's procedure combined with the use of B-Splines (C.W.R. de-Boor's B-spline package) to generate a system of ordinary differential equations. These equations are solved by a sophisticated ODE software package which is a modified version of Hindmarsh's GEAR package, NESC Abstract 592. 3 - Restrictions on the complexity of the problem: The spatial domain must be rectangular with sides parallel to the coordinate geometry. Cross derivative terms are not permitted in the PDE. The order of the B-Splines is at most 12. Other parameters such as the number of mesh points in each coordinate direction, the number of PDE's etc. are set in a macro table used by the MORTRAn2 preprocessor in generating the object code
A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise
Clason, Christian
2012-01-01
This work is concerned with nonlinear parameter identification in partial differential equations subject to impulsive noise. To cope with the non-Gaussian nature of the noise, we consider a model with L 1 fitting. However, the nonsmoothness of the problem makes its efficient numerical solution challenging. By approximating this problem using a family of smoothed functionals, a semismooth Newton method becomes applicable. In particular, its superlinear convergence is proved under a second-order condition. The convergence of the solution to the approximating problem as the smoothing parameter goes to zero is shown. A strategy for adaptively selecting the regularization parameter based on a balancing principle is suggested. The efficiency of the method is illustrated on several benchmark inverse problems of recovering coefficients in elliptic differential equations, for which one- and two-dimensional numerical examples are presented. © by SIAM.
Luo, Xiaodong
2014-10-01
The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies, the authors proposed an observation-space-based strategy, called residual nudging, to improve the stability of the EnKF when dealing with linear observation operators. The main idea behind residual nudging is to monitor and, if necessary, adjust the distances (misfits) between the real observations and the simulated ones of the state estimates, in the hope that by doing so one may be able to obtain better estimation accuracy. In the present study, residual nudging is extended and modified in order to handle nonlinear observation operators. Such extension and modification result in an iterative filtering framework that, under suitable conditions, is able to achieve the objective of residual nudging for data assimilation problems with nonlinear observation operators. The 40-dimensional Lorenz-96 model is used to illustrate the performance of the iterative filter. Numerical results show that, while a normal EnKF may diverge with nonlinear observation operators, the proposed iterative filter remains stable and leads to reasonable estimation accuracy under various experimental settings.
International Nuclear Information System (INIS)
Barhen, J.; Bjerke, M.A.; Cacuci, D.G.; Mullins, C.B.; Wagschal, G.G.
1982-01-01
An advanced methodology for performing systematic uncertainty analysis of time-dependent nonlinear systems is presented. This methodology includes a capability for reducing uncertainties in system parameters and responses by using Bayesian inference techniques to consistently combine prior knowledge with additional experimental information. The determination of best estimates for the system parameters, for the responses, and for their respective covariances is treated as a time-dependent constrained minimization problem. Three alternative formalisms for solving this problem are developed. The two ''off-line'' formalisms, with and without ''foresight'' characteristics, require the generation of a complete sensitivity data base prior to performing the uncertainty analysis. The ''online'' formalism, in which uncertainty analysis is performed interactively with the system analysis code, is best suited for treatment of large-scale highly nonlinear time-dependent problems. This methodology is applied to the uncertainty analysis of a transient upflow of a high pressure water heat transfer experiment. For comparison, an uncertainty analysis using sensitivities computed by standard response surface techniques is also performed. The results of the analysis indicate the following. Major reduction of the discrepancies in the calculation/experiment ratios is achieved by using the new methodology. Incorporation of in-bundle measurements in the uncertainty analysis significantly reduces system uncertainties. Accuracy of sensitivities generated by response-surface techniques should be carefully assessed prior to using them as a basis for uncertainty analyses of transient reactor safety problems
Hayat, T.; Khan, M. Ijaz; Qayyum, Sumaira; Alsaedi, A.; Khan, M. Imran
2018-03-01
This research addressed entropy generation for MHD stagnation point flow of viscous nanofluid over a stretching surface. Characteristics of heat transport are analyzed through nonlinear radiation and heat generation/absorption. Nanoliquid features for Brownian moment and thermophoresis have been considered. Fluid in the presence of constant applied inclined magnetic field is considered. Flow problem is mathematically modeled and governing expressions are changed into nonlinear ordinary ones by utilizing appropriate transformations. The effects of pertinent variables on velocity, nanoparticle concentration and temperature are discussed graphically. Furthermore Brownian motion and thermophoresis effects on entropy generation and Bejan number have been examined. Total entropy generation is inspected through various flow variables. Consideration is mainly given to the convergence process. Velocity, temperature and mass gradients at the surface of sheet are calculated numerically.
Geometrical Method for Thermal Instability of Nonlinearly Charged BTZ Black Holes
International Nuclear Information System (INIS)
Panahiyan, Shahram; Hendi, Seyed Hossein; Eslam Panah, Behzad
2015-01-01
We consider three-dimensional BTZ black holes with three models of nonlinear electrodynamics as source. Calculating heat capacity, we study the stability and phase transitions of these black holes. We show that Maxwell, logarithmic, and exponential theories yield only type one phase transition which is related to the root(s) of heat capacity, whereas, for correction form of nonlinear electrodynamics, heat capacity contains two roots and one divergence point. Next, we use geometrical approach for studying classical thermodynamical behavior of the system. We show that Weinhold and Ruppeiner metrics fail to provide fruitful results and the consequences of the Quevedo approach are not completely matched to the heat capacity results. Then, we employ a new metric for solving this problem. We show that this approach is successful and all divergencies of its Ricci scalar and phase transition points coincide. We also show that there is no phase transition for uncharged BTZ black holes.
On some nonlinear problems arising in the physics of ionized gases
International Nuclear Information System (INIS)
Hilhorst-Goldman, D.
1981-01-01
The author reports results obtained by rigorous analysis of a nonlinear differential equation for the electron density nsub(e) in a specific type of electrical discharge. The problem is essentially two-dimensional. She discusses in particular the escape of electrons to infinity above a critical temperature and the boundary layer exhibited by nsub(e) near zero temperature. A singular boundary value problem arising in a pre-breakdown gas discharge is discussed. A Coulomb gas is considered in a special experimental situation: the pre-breakdown gas discharge between two electrodes. The equation for the negative charge density can be formulated as a nonlinear parabolic equation degenerate at the origin. The existence and uniqueness of the solution are proved as well as the asymptotic stability of its unique steady state. Some results are also given about the rate of convergence. The variational characterisation of the limit solution of a singular perturbation problem and variational analysis of a perturbed free boundary problem are considered. (Auth./C.F.)
Arbitrary Lagrangian-Eulerian method for non-linear problems of geomechanics
International Nuclear Information System (INIS)
Nazem, M; Carter, J P; Airey, D W
2010-01-01
In many geotechnical problems it is vital to consider the geometrical non-linearity caused by large deformation in order to capture a more realistic model of the true behaviour. The solutions so obtained should then be more accurate and reliable, which should ultimately lead to cheaper and safer design. The Arbitrary Lagrangian-Eulerian (ALE) method originated from fluid mechanics, but has now been well established for solving large deformation problems in geomechanics. This paper provides an overview of the ALE method and its challenges in tackling problems involving non-linearities due to material behaviour, large deformation, changing boundary conditions and time-dependency, including material rate effects and inertia effects in dynamic loading applications. Important aspects of ALE implementation into a finite element framework will also be discussed. This method is then employed to solve some interesting and challenging geotechnical problems such as the dynamic bearing capacity of footings on soft soils, consolidation of a soil layer under a footing, and the modelling of dynamic penetration of objects into soil layers.
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Omar Abu Arqub
2014-01-01
Full Text Available The purpose of this paper is to present a new kind of analytical method, the so-called residual power series, to predict and represent the multiplicity of solutions to nonlinear boundary value problems of fractional order. The present method is capable of calculating all branches of solutions simultaneously, even if these multiple solutions are very close and thus rather difficult to distinguish even by numerical techniques. To verify the computational efficiency of the designed proposed technique, two nonlinear models are performed, one of them arises in mixed convection flows and the other one arises in heat transfer, which both admit multiple solutions. The results reveal that the method is very effective, straightforward, and powerful for formulating these multiple solutions.
Eigenvalue solutions in finite element thermal transient problems
International Nuclear Information System (INIS)
Stoker, J.R.
1975-01-01
The eigenvalue economiser concept can be useful in solving large finite element transient heat flow problems in which the boundary heat transfer coefficients are constant. The usual economiser theory is equivalent to applying a unit thermal 'force' to each of a small sub-set of nodes on the finite element mesh, and then calculating sets of resulting steady state temperatures. Subsequently it is assumed that the required transient temperature distributions can be approximated by a linear combination of this comparatively small set of master temperatures. The accuracy of a reduced eigenvalue calculation depends upon a good choice of master nodes, which presupposes at least a little knowledge about what sort of shape is expected in the unknown temperature distributions. There are some instances, however, where a reasonably good idea exists of the required shapes, permitting a modification to the economiser process which leads to greater economy in the number of master temperatures. The suggested new approach is to use manually prescribed temperature distributions as the master distributions, rather than using temperatures resulting from unit thermal forces. Thus, with a little pre-knowledge one may write down a set of master distributions which, as a linear combination, can represent the required solution over the range of interest to a reasonable engineering accuracy, and using the minimum number of variables. The proposed modified eigenvalue economiser technique then uses the master distributions in an automatic way to arrive at the required solution. The technique is illustrated by some simple finite element examples
Cooling problems of thermal power plants. Physical model studies
International Nuclear Information System (INIS)
Neale, L.C.
1975-01-01
The Alden Research Laboratories of Worcester Polytechnic Institute has for many years conducted physical model studies, which are normally classified as river or structural hydraulic studies. Since 1952 one aspect of these studies has involved the heated discharge from steam power plants. The early studies on such problems concentrated on improving the thermal efficiency of the system. This was accomplished by minimizing recirculation and by assuring full use of available cold water supplies. With the growing awareness of the impact of thermal power generation on the environment attention has been redirected to reducing the effect of heated discharges on the biology of the receiving body of water. More specifically the efforts of designers and operators of power plants are aimed at meeting or complying with standards established by various governmental agencies. Thus the studies involve developing means of minimizing surface temperatures at an outfall or establishing a local area of higher temperature with limits specified in terms of areas or distances. The physical models used for these studies have varied widely in scope, size, and operating features. These models have covered large areas with both distorted geometric scales and uniform dimensions. Instrumentations has also varied from simple mercury thermometers to computer control and processing of hundreds of thermocouple indicators
Initial-value problem for the Gardner equation applied to nonlinear internal waves
Rouvinskaya, Ekaterina; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim
2017-04-01
The Gardner equation is a fundamental mathematical model for the description of weakly nonlinear weakly dispersive internal waves, when cubic nonlinearity cannot be neglected. Within this model coefficients of quadratic and cubic nonlinearity can both be positive as well as negative, depending on background conditions of the medium, where waves propagate (sea water density stratification, shear flow profile) [Rouvinskaya et al., 2014, Kurkina et al., 2011, 2015]. For the investigation of weakly dispersive behavior in the framework of nondimensional Gardner equation with fixed (positive) sign of quadratic nonlinearity and positive or negative cubic nonlinearity {eq1} partial η/partial t+6η( {1± η} )partial η/partial x+partial ^3η/partial x^3=0, } the series of numerical experiments of initial-value problem was carried out for evolution of a bell-shaped impulse of negative polarity (opposite to the sign of quadratic nonlinear coefficient): {eq2} η(x,t=0)=-asech2 ( {x/x0 } ), for which amplitude a and width x0 was varied. Similar initial-value problem was considered in the paper [Trillo et al., 2016] for the Korteweg - de Vries equation. For the Gardner equation with different signs of cubic nonlinearity the initial-value problem for piece-wise constant initial condition was considered in detail in [Grimshaw et al., 2002, 2010]. It is widely known, for example, [Pelinovsky et al., 2007], that the Gardner equation (1) with negative cubic nonlinearity has a family of classic solitary wave solutions with only positive polarity,and with limiting amplitude equal to 1. Therefore evolution of impulses (2) of negative polarity (whose amplitudes a were varied from 0.1 to 3, and widths at the level of a/2 were equal to triple width of solitons with the same amplitude for a 1) was going on a universal scenario with the generation of nonlinear Airy wave. For the Gardner equation (1) with the positive cubic nonlinearity coefficient there exist two one-parametric families of
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Ureña Antonio J
2002-01-01
Full Text Available A generalization of the well-known Hartman–Nagumo inequality to the case of the vector ordinary -Laplacian and classical degree theory provide existence results for some associated nonlinear boundary value problems.
Fymat, A. L.
1976-01-01
The paper studies the inversion of the radiative transfer equation describing the interaction of electromagnetic radiation with atmospheric aerosols. The interaction can be considered as the propagation in the aerosol medium of two light beams: the direct beam in the line-of-sight attenuated by absorption and scattering, and the diffuse beam arising from scattering into the viewing direction, which propagates more or less in random fashion. The latter beam has single scattering and multiple scattering contributions. In the former case and for single scattering, the problem is reducible to first-kind Fredholm equations, while for multiple scattering it is necessary to invert partial integrodifferential equations. A nonlinear minimization search method, applicable to the solution of both types of problems has been developed, and is applied here to the problem of monitoring aerosol pollution, namely the complex refractive index and size distribution of aerosol particles.
Application of the Green's function method to some nonlinear problems of an electron storage ring
International Nuclear Information System (INIS)
Kheifets, S.
1984-01-01
One of the most important characteristics of an electron storage ring is the size of the beam. However analytical calculations of beam size are beset with problems and the computational methods and programs which are used to overcome these are inadequate for all problems in which stochastic noise is an essential part. Two examples are, for an electron storage ring, beam-size evaluation including beam-beam interactions, and finding the beam size for a nonlinear machine. The method described should overcome some of the problems. It uses the Green's function method applied to the Fokker-Planck equation governing the distribution function in the phase space of particle motion. The new step is to consider the particle motion in two degrees of freedom rather than in one dimension. The technique is described fully and is then applied to a strong-focusing machine. (U.K.)
Masood, W.; Mirza, Arshad M.
2010-11-01
Linear and nonlinear properties of coupled Shukla-Varma (SV) and convective cell modes in the presence of electron thermal effects are studied in a nonuniform magnetoplasma composed of electrons, ions, and extremely massive and negatively charged immobile dust grains. In the linear case, the modified dispersion relation is given and, in the nonlinear case, stationary solutions of the nonlinear equations that govern the dynamics of coupled SV and convective cell modes are obtained. It is found that electrostatic dipolar and vortex street type solutions can appear in such a plasma. The relevance of the present investigation with regard to the Earth's mesosphere as well as in ionospheric plasmas is also pointed out.
International Nuclear Information System (INIS)
Masood, W.; Mirza, Arshad M.
2010-01-01
Linear and nonlinear properties of coupled Shukla-Varma (SV) and convective cell modes in the presence of electron thermal effects are studied in a nonuniform magnetoplasma composed of electrons, ions, and extremely massive and negatively charged immobile dust grains. In the linear case, the modified dispersion relation is given and, in the nonlinear case, stationary solutions of the nonlinear equations that govern the dynamics of coupled SV and convective cell modes are obtained. It is found that electrostatic dipolar and vortex street type solutions can appear in such a plasma. The relevance of the present investigation with regard to the Earth's mesosphere as well as in ionospheric plasmas is also pointed out.
International Nuclear Information System (INIS)
Lu Yanlin; Zhou Xiao; Qu Jiadi; Dou Yikang; He Yinbiao
2005-01-01
An efficient scheme, 3-D thermal weight function (TWF) method, and a novel numerical technique, multiple virtual crack extension (MVCE) technique, were developed for determination of histories of transient stress intensity factor (SIF) distributions along 3-D crack fronts of a body subjected to thermal shock. The TWF is a universal function, which is dependent only on the crack configuration and body geometry. TWF is independent of time during thermal shock, so the whole history of transient SIF distributions along crack fronts can be directly calculated through integration of the products of TWF and transient temperatures and temperature gradients. The repeated determinations of the distributions of stresses (or displacements) fields for individual time instants are thus avoided in the TWF method. An expression of the basic equation for the 3-D universal weight function method for Mode I in an isotropic elastic body is derived. This equation can also be derived from Bueckner-Rice's 3-D WF formulations in the framework of transformation strain. It can be understood from this equation that the so-called thermal WF is in fact coincident with the mechanical WF except for some constants of elasticity. The details and formulations of the MVCE technique are given for elliptical cracks. The MVCE technique possesses several advantages. The specially selected linearly independent VCE modes can directly be used as shape functions for the interpolation of unknown SIFs. As a result, the coefficient matrix of the final system of equations in the MVCE method is a triple-diagonal matrix and the values of the coefficients on the main diagonal are large. The system of equations has good numerical properties. The number of linearly independent VCE modes that can be introduced in a problem is unlimited. Complex situations in which the SIFs vary dramatically along crack fronts can be numerically well simulated by the MVCE technique. An integrated system of programs for solving the
Belmiloudi, A.; Mahé, F.
2014-01-01
International audience; The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydration of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions J. Numerical si...
Elwakil, S. A.; El-hanbaly, A. M.; Elgarayh, A.; El-Shewy, E. K.; Kassem, A. I.
2014-11-01
The properties of nonlinear electron-acoustic rogue waves have been investigated in an unmagnetized collisionless four-component plasma system consisting of a cold electron fluid, non-thermal hot electrons obeying a non-thermal distribution, an electron beam and stationary ions. It is found that the basic set of fluid equations is reduced to a nonlinear Schrodinger equation. The dependence of rogue wave profiles on the electron beam and energetic population parameter are discussed. The results of the present investigation may be applicable in auroral zone plasma.
Barashkov, M. S.; Bel'Diugin, I. M.; Zolotarev, M. V.; Kruzhilin, Iu. I.; Krymskii, M. I.
1989-04-01
A four-wave mirror with thermal nonlinearity has been experimentally realized with the interaction of corunning waves under parametric feedback with a nonreciprocal element. The effective reflection of a sequence of pulses with duration of about 300 ns from a neodymium-glass laser with maximal reflection coefficients greater than 30 has been demonstrated. The quality of the radiation reflected from the mirror is studied. A significant reduction in the steady-state lasing threshold has been shown with thermal nonlinearity at small angles of the interacting beam convergence, compared to the case of counterrunning convergence.
Group-invariant solutions of nonlinear elastodynamic problems of plates and shells
International Nuclear Information System (INIS)
Dzhupanov, V.A.; Vassilev, V.M.; Dzhondzhorov, P.A.
1993-01-01
Plates and shells are basic structural components in nuclear reactors and their equipment. The prediction of the dynamic response of these components to fast transient loadings (e.g., loadings caused by earthquakes, missile impacts, etc.) is a quite important problem in the general context of the design, reliability and safety of nuclear power stations. Due to the extreme loading conditions a more adequate treatment of the foregoing problem should rest on a suitable nonlinear shell model, which would allow large deflections of the structures regarded to be taken into account. Such a model is provided in the nonlinear Donnell-Mushtari-Vlasov (DMV) theory. The governing system of equations of the DMV theory consists of two coupled nonlinear fourth order partial differential equations in three independent and two dependent variables. It is clear, as the case stands, that the obtaining solutions to this system directly, by using any of the general analytical or numerical techniques, would involve considerable difficulties. In the present paper, the invariance of the governing equations of DMV theory for plates and cylindrical shells relative to local Lie groups of local point transformations will be employed to get some advantages in connection with the aforementioned problem. First, the symmetry of a functional, corresponding to the governing equations of DMV theory for plates and cylindrical shells is studied. Next, the densities in the corresponding conservation laws are determined on the basis of Noether theorem. Finally, we study a class of invariant solutions of the governing equations. As is well known, group-invariant solutions are often intermediate asymptotics for a wider class of solutions of the corresponding equations. When such solutions are considered, the number of the independent variables can be reduced. For the class of invariant solutions studied here, the system of governing equations converts into a system of ordinary differential equations
Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem
DEFF Research Database (Denmark)
Delbary, Fabrice; Knudsen, Kim
2014-01-01
to the generalized Laplace equation. The 3D problem was solved in theory in late 1980s using complex geometrical optics solutions and a scattering transform. Several approximations to the reconstruction method have been suggested and implemented numerically in the literature, but here, for the first time, a complete...... computer implementation of the full nonlinear algorithm is given. First a boundary integral equation is solved by a Nystrom method for the traces of the complex geometrical optics solutions, second the scattering transform is computed and inverted using fast Fourier transform, and finally a boundary value...
One-dimensional singular problems involving the p-Laplacian and nonlinearities indefinite in sign
Kaufmann, Uriel; Medri, Iván
2015-01-01
Let $\\Omega$ be a bounded open interval, let $p>1$ and $\\gamma>0$, and let $m:\\Omega\\rightarrow\\mathbb{R}$ be a function that may change sign in $\\Omega $. In this article we study the existence and nonexistence of positive solutions for one-dimensional singular problems of the form $-(\\left\\vert u^{\\prime}\\right\\vert ^{p-2}u^{\\prime})^{\\prime}=m\\left( x\\right) u^{-\\gamma}$ in $\\Omega$, $u=0$ on $\\partial\\Omega$. As a consequence we also derive existence results for other related nonlinearities.
Numerical solution of large nonlinear boundary value problems by quadratic minimization techniques
International Nuclear Information System (INIS)
Glowinski, R.; Le Tallec, P.
1984-01-01
The objective of this paper is to describe the numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques. In all the different situations where these techniques were applied, the methodology remains the same and is organized as follows: 1) derive a variational formulation of the original boundary value problem, and approximate it by Galerkin methods; 2) transform this variational formulation into a quadratic minimization problem (least squares methods) or into a sequence of quadratic minimization problems (augmented lagrangian decomposition); 3) solve each quadratic minimization problem by a conjugate gradient method with preconditioning, the preconditioning matrix being sparse, positive definite, and fixed once for all in the iterative process. This paper will illustrate the methodology above on two different examples: the description of least squares solution methods and their application to the solution of the unsteady Navier-Stokes equations for incompressible viscous fluids; the description of augmented lagrangian decomposition techniques and their application to the solution of equilibrium problems in finite elasticity
Nonlinear thermal convection in a layer of nanofluid under G-jitter and internal heating effects
Directory of Open Access Journals (Sweden)
Bhadauria B. S.
2014-01-01
Full Text Available This paper deals with a mathematical model of controlling heat transfer in nanofluids. The time-periodic vertical vibrations of the system are considered to effect an external control of heat transport along with internal heating effects. A weakly non-linear stability analysis is based on the five-mode Lorenz model using which the Nusselt number is obtained as a function of the thermal Rayleigh number, nano-particle concentration based Rayleigh number, Prandtl number, Lewis number, modified diffusivity ratio, amplitude and frequency of modulation. It is shown that modulation can be effectively used to control convection and thereby heat transport. Further, it is found that the effect of internal Rayleigh number is to enhance the heat and nano-particles transport.
Directory of Open Access Journals (Sweden)
M.M. Bhatti
2017-06-01
Full Text Available Biologically-inspired propulsion systems are currently receiving significant interest in the aerospace sector. Since many spacecraft propulsion systems operate at high temperatures, thermal radiation is important as a mode of heat transfer. Motivated by these developments, in the present article, the influence of nonlinear thermal radiation (via the Rosseland diffusion flux model has been studied on the laminar, incompressible, dissipative EMHD (Electro-magneto-hydrodynamic peristaltic propulsive flow of a non-Newtonian (Jefferys viscoelastic dusty fluid containing solid particles through a porous planar channel. The fluid is electrically-conducting and a constant static magnetic field is applied transverse to the flow direction (channel walls. Slip effects are also included. Magnetic induction effects are neglected. The mathematical formulation is based on continuity, momentum and energy equations with appropriate boundary conditions, which are simplified by neglecting the inertial forces and taking the long wavelength and lubrication approximations. The boundary value problem is then rendered non-dimensional with appropriate variables and the resulting system of reduced ordinary differential equations is solved analytically. The impact of various emerging parameters dictating the non-Newtonian propulsive flow i.e. Prandtl number, radiation parameter, Hartmann number, permeability parameter, Eckert number, particle volume fraction, electric field and slip parameter are depicted graphically. Increasing particle volume fraction is observed to suppress temperature magnitudes. Furthermore the computations demonstrate that an increase in particle volume fraction reduces the pumping rate in retrograde pumping region whereas it causes the opposite effect in the co-pumping region. The trapping mechanism is also visualized with the aid of streamline contour plots. Increasing thermal radiation elevates temperatures. Increasing Hartmann (magnetic body
Nonlinear analysis of thermally and electrically actuated functionally graded material microbeam.
Li, Yingli; Meguid, S A; Fu, Yiming; Xu, Daolin
2014-02-08
In this paper, we provide a unified and self-consistent treatment of a functionally graded material (FGM) microbeam with varying thermal conductivity subjected to non-uniform or uniform temperature field. Specifically, it is our objective to determine the effect of the microscopic size of the beam, the electrostatic gap, the temperature field and material property on the pull-in voltage of the microbeam under different boundary conditions. The non-uniform temperature field is obtained by integrating the steady-state heat conduction equation. The governing equations account for the microbeam size by introducing an internal material length-scale parameter that is based on the modified couple stress theory. Furthermore, it takes into account Casimir and van der Waals forces, and the associated electrostatic force with the first-order fringing field effects. The resulting nonlinear differential equations were converted to a coupled system of algebraic equations using the differential quadrature method. The outcome of our work shows the dramatic effect and dependence of the pull-in voltage of the FGM microbeam upon the temperature field, its gradient for a given boundary condition. Specifically, both uniform and non-uniform thermal loading can actuate the FGM microbeam even without an applied voltage. Our work also reveals that the non-uniform temperature field is more effective than the uniform temperature field in actuating a FGM cantilever-type microbeam. For the clamped-clamped case, care must be taken to account for the effective use of thermal loading in the design of microbeams. It is also observed that uniform thermal loading will lead to a reduction in the pull-in voltage of a FGM microbeam for all the three boundary conditions considered.
International Nuclear Information System (INIS)
Yun, Sung Hwan
2004-02-01
Radiative transfer is a complex phenomenon in which radiation field interacts with material. This thermal radiative transfer phenomenon is composed of two equations which are the balance equation of photons and the material energy balance equation. The two equations involve non-linearity due to the temperature and that makes the radiative transfer equation more difficult to solve. During the last several years, there have been many efforts to solve the non-linear radiative transfer problems by Monte Carlo method. Among them, it is known that Semi-Analog Monte Carlo (SMC) method developed by Ahrens and Larsen is accurate regard-less of the time step size in low temperature region. But their works are limited to one-dimensional, low temperature problems. In this thesis, we suggest some method to remove their limitations in the SMC method and apply to the more realistic problems. An initially cold problem was solved over entire temperature region by using piecewise linear interpolation of the heat capacity, while heat capacity is still fitted as a cubic curve within the lowest temperature region. If we assume the heat capacity to be linear in each temperature region, the non-linearity still remains in the radiative transfer equations. We then introduce the first-order Taylor expansion to linearize the non-linear radiative transfer equations. During the linearization procedure, absorption-reemission phenomena may be described by a conventional reemission time sampling scheme which is similar to the repetitive sampling scheme in particle transport Monte Carlo method. But this scheme causes significant stochastic errors, which necessitates many histories. Thus, we present a new reemission time sampling scheme which reduces stochastic errors by storing the information of absorption times. The results of the comparison of the two schemes show that the new scheme has less stochastic errors. Therefore, the improved SMC method is able to solve more realistic problems with
Chang, Hung-Chieh; Lin, Pei-Chun
2014-02-01
Economic dispatch is the short-term determination of the optimal output from a number of electricity generation facilities to meet the system load while providing power. As such, it represents one of the main optimization problems in the operation of electrical power systems. This article presents techniques to substantially improve the efficiency of the canonical coordinates method (CCM) algorithm when applied to nonlinear combined heat and power economic dispatch (CHPED) problems. The improvement is to eliminate the need to solve a system of nonlinear differential equations, which appears in the line search process in the CCM algorithm. The modified algorithm was tested and the analytical solution was verified using nonlinear CHPED optimization problems, thereby demonstrating the effectiveness of the algorithm. The CCM methods proved numerically stable and, in the case of nonlinear programs, produced solutions with unprecedented accuracy within a reasonable time.
Yang, Haijian
2016-07-26
Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.
Yang, Haijian; Yang, Chao; Sun, Shuyu
2016-01-01
Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.
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.
CASKETSS-HEAT: a finite difference computer program for nonlinear heat conduction problems
International Nuclear Information System (INIS)
Ikushima, Takeshi
1988-12-01
A heat conduction program CASKETSS-HEAT has been developed. CASKETSS-HEAT is a finite difference computer program used for the solution of multi-dimensional nonlinear heat conduction problems. Main features of CASKETSS-HEAT are as follows. (1) One, two and three-dimensional geometries for heat conduction calculation are available. (2) Convection and radiation heat transfer of boundry can be specified. (3) Phase change and chemical change can be treated. (4) Finned surface heat transfer can be treated easily. (5) Data memory allocation in the program is variable according to problem size. (6) The program is a compatible heat transfer analysis program to the stress analysis program SAP4 and SAP5. (7) Pre- and post-processing for input data generation and graphic representation of calculation results are available. In the paper, brief illustration of calculation method, input data and sample calculation are presented. (author)
Discrete and continuum links to a nonlinear coupled transport problem of interacting populations
Duong, M. H.; Muntean, A.; Richardson, O. M.
2017-07-01
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind are inspired by the dynamics of pedestrian flows in open spaces and are intimately connected to cross-diffusion and thermo-diffusion problems holding a variational structure. The tools we use include a suitable structure of the relative entropy controlling TV-norms, the construction of Lyapunov functionals and particular closed-form solutions to nonlinear transport equations, a hydrodynamics limiting procedure due to Philipowski, as well as the construction of numerical approximates to both the continuum limit problem in 2D and to the original interacting particle systems.
Directory of Open Access Journals (Sweden)
Chen Yuming
2011-01-01
Full Text Available Though boundary value problems for fractional differential equations have been extensively studied, most of the studies focus on scalar equations and the fractional order between 1 and 2. On the other hand, delay is natural in practical systems. However, not much has been done for fractional differential equations with delays. Therefore, in this paper, we consider a boundary value problem of a general delayed nonlinear fractional system. With the help of some fixed point theorems and the properties of the Green function, we establish several sets of sufficient conditions on the existence of positive solutions. The obtained results extend and include some existing ones and are illustrated with some examples for their feasibility.
Mathematical and numerical study of nonlinear boundary problems related to plasma physics
International Nuclear Information System (INIS)
Sermange, M.
1982-06-01
After the study of some equations based on the Hodgkin-Huxley model, the work presented here is concerned with nonlinear boundary problems in MHD. They are gathered in two subjects: equilibrium equations and stability equations. The axisymmetric MHD equilibrium equations with free boundary have been studied by different authors, particularly the existence, regularity, unicity and non-unicity. Here, bifurcation, convergence of calculation methods existence of solutions in a discontinuous frame are studied. MHD stability can be determined by the principle of Bernstein et al; the mathematical work concerned here bears on the equivalence, in the case of two-dimensional or axisymmetric stability, between this model and a scalar eigenvalue problem which is introduced. At last, modules for computing MHD equilibrium for the simulation of plasma confinement in a tokamak are described [fr
A limited memory BFGS method for a nonlinear inverse problem in digital breast tomosynthesis
Landi, G.; Loli Piccolomini, E.; Nagy, J. G.
2017-09-01
Digital breast tomosynthesis (DBT) is an imaging technique that allows the reconstruction of a pseudo three-dimensional image of the breast from a finite number of low-dose two-dimensional projections obtained by different x-ray tube angles. An issue that is often ignored in DBT is the fact that an x-ray beam is polyenergetic, i.e. it is composed of photons with different levels of energy. The polyenergetic model requires solving a large-scale, nonlinear inverse problem, which is more expensive than the typically used simplified, linear monoenergetic model. However, the polyenergetic model is much less susceptible to beam hardening artifacts, which show up as dark streaks and cupping (i.e. background nonuniformities) in the reconstructed image. In addition, it has been shown that the polyenergetic model can be exploited to obtain additional quantitative information about the material of the object being imaged. In this paper we consider the multimaterial polyenergetic DBT model, and solve the nonlinear inverse problem with a limited memory BFGS quasi-Newton method. Regularization is enforced at each iteration using a diagonally modified approximation of the Hessian matrix, and by truncating the iterations.
Solution of the nonlinear inverse scattering problem by T-matrix completion. I. Theory.
Levinson, Howard W; Markel, Vadim A
2016-10-01
We propose a conceptually different method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology, and other applications. The method is inspired by the theory of nonlocality of physical interactions and utilizes the relevant formalism. We formulate the ISP as a problem whose goal is to determine an unknown interaction potential V from external scattering data. Although we seek a local (diagonally dominated) V as the solution to the posed problem, we allow V to be nonlocal at the intermediate stages of iterations. This allows us to utilize the one-to-one correspondence between V and the T matrix of the problem. Here it is important to realize that not every T corresponds to a diagonal V and we, therefore, relax the usual condition of strict diagonality (locality) of V. An iterative algorithm is proposed in which we seek T that is (i) compatible with the measured scattering data and (ii) corresponds to an interaction potential V that is as diagonally dominated as possible. We refer to this algorithm as to the data-compatible T-matrix completion. This paper is Part I in a two-part series and contains theory only. Numerical examples of image reconstruction in a strongly nonlinear regime are given in Part II [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043318 (2016)10.1103/PhysRevE.94.043318]. The method described in this paper is particularly well suited for very large data sets that become increasingly available with the use of modern measurement techniques and instrumentation.
International Nuclear Information System (INIS)
Vora, Heli; Nielsen, Bent; Du, Xu
2014-01-01
Graphene is a promising candidate for building fast and ultra-sensitive bolometric detectors due to its weak electron-phonon coupling and low heat capacity. In order to realize a practical graphene-based bolometer, several important issues, including the nature of radiation response, coupling efficiency to the radiation and the thermal conductance need to be carefully studied. Addressing these issues, we present graphene-superconductor junctions as a viable option to achieve efficient and sensitive bolometers, with the superconductor contacts serving as hot electron barriers. For a graphene-superconductor device with highly transparent interfaces, the resistance readout in the presence of radio frequency radiation is dominated by non-linear response. On the other hand, a graphene-superconductor tunnel device shows dominantly bolometric response to radiation. For graphene devices fabricated on SiO 2 substrates, we confirm recent theoretical predictions of T 2 temperature dependence of phonon thermal conductance in the presence of disorder in the graphene channel at low temperatures
Thermal-Induced Non-linearity of Ag Nano-fluid Prepared using γ-Radiation Method
International Nuclear Information System (INIS)
Esmaeil Shahriari; Wan Mahmood Mat Yunus; Zainal Abidin Talib; Elias Saion
2011-01-01
The non-linear refractive index of Ag nano-fluids prepared by γ-radiation method was investigated using a single beam z-scan technique. Under CW 532 nm laser excitation with power output of 40 mW, the Ag nano-fluids showed a large thermal-induced non-linear refractive index. In the present work it was determined that the non-linear refractive index for Ag nano-fluids is -4.80x10 -8 cm 2 / W. The value of Δn 0 was calculated to be -2.05x10 -4 . Our measurements also confirmed that the non-linear phenomenon was caused by the self-defocusing process making them good candidates for non linear optical devices. (author)
International Nuclear Information System (INIS)
Keanini, R.G.
2011-01-01
Research highlights: → Systematic approach for physically probing nonlinear and random evolution problems. → Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. → Organization of near-molecular scale vorticity mediated by hydrodynamic modes. → Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the
Implementation of a multi-layer perception for a non-linear control problem
International Nuclear Information System (INIS)
Lister, J.B.; Schnurrenberger, H.; Marmillod, P.
1990-12-01
We present the practical application of a 1-hidden-layer multilayer perception (MLP) to provide a non-linear continuous multi-variable mapping with 42 inputs and 13 outputs. The problem resolved is one of extracting information from experimental signals with a bandwidth of many kilohertz. We have an exact model of the inverse mapping of this problem, but we have no explicit form of the required forward mapping. This is the typical situation in data interpretation. The MLP was trained to provide this mapping by learning on 500 input-output examples. The success of the off-line solution to this problem using an MLP led us to examine the robustness of the MLP to different noise sources. We found that the MLP is more robust than an approximate linear mapping of the same problem. 12 bits of resolution in the weights are necessary to avoid a significant loss of precision. The practical implementation of large analog weight matrices using DAS-multipliers and a simple segmented sigmoid is also presented. A General Adaptive Recipe (GAR) for improving the performance of conventional back-propagation was developed. The GAR uses an adaptive step length and both the bias terms and the initial weight seeding are determined by the network size. The GAR was found to be robust and much faster than conventional back-propagation. (author) 20 figs., 1 tab., 15 refs
International Nuclear Information System (INIS)
Tran Duc Van
1994-01-01
The notion of global quasi-classical solutions of the Cauchy problems for first-order nonlinear partial differential equations is presented, some uniqueness theorems and a stability result are established by the method based on the theory of differential inclusions. In particular, the answer to an open problem of S.N. Kruzhkov is given. (author). 10 refs, 1 fig
Directory of Open Access Journals (Sweden)
U. Filobello-Nino
2015-01-01
Full Text Available We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM. Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results.
Non-intrusive reduced order modeling of nonlinear problems using neural networks
Hesthaven, J. S.; Ubbiali, S.
2018-06-01
We develop a non-intrusive reduced basis (RB) method for parametrized steady-state partial differential equations (PDEs). The method extracts a reduced basis from a collection of high-fidelity solutions via a proper orthogonal decomposition (POD) and employs artificial neural networks (ANNs), particularly multi-layer perceptrons (MLPs), to accurately approximate the coefficients of the reduced model. The search for the optimal number of neurons and the minimum amount of training samples to avoid overfitting is carried out in the offline phase through an automatic routine, relying upon a joint use of the Latin hypercube sampling (LHS) and the Levenberg-Marquardt (LM) training algorithm. This guarantees a complete offline-online decoupling, leading to an efficient RB method - referred to as POD-NN - suitable also for general nonlinear problems with a non-affine parametric dependence. Numerical studies are presented for the nonlinear Poisson equation and for driven cavity viscous flows, modeled through the steady incompressible Navier-Stokes equations. Both physical and geometrical parametrizations are considered. Several results confirm the accuracy of the POD-NN method and show the substantial speed-up enabled at the online stage as compared to a traditional RB strategy.
Agarwal, Shilpi; Rana, Puneet
2016-04-01
In this paper, we examine a layer of Oldroyd-B nanofluid for linear and nonlinear regimes under local thermal non-equilibrium conditions for the classical Rayleigh-Bénard problem. The free-free boundary condition has been implemented with the flux for nanoparticle concentration being zero at edges. The Oberbeck-Boussinesq approximation holds good and for the rotational effect Coriolis term is included in the momentum equation. A two-temperature model explains the effect of local thermal non-equilibrium among the particle and fluid phases. The criteria for onset of stationary convection has been derived as a function of the non-dimensionalized parameters involved including the Taylor number. The assumed boundary conditions negate the possibility of overstability due to the absence of opposing forces responsible for it. The thermal Nusselt number has been obtained utilizing a weak nonlinear theory in terms of various pertinent parameters in the steady and transient mode, and has been depicted graphically. The main findings signify that the rotation has a stabilizing effect on the system. The stress relaxation parameter λ_1 inhibits whereas the strain retardation parameter λ_2 exhibits heat transfer utilizing Al2O3 nanofluids.
Mixing in thermally stratified nonlinear spin-up with uniform boundary fluxes
International Nuclear Information System (INIS)
Baghdasarian, Meline; Pacheco-Vega, Arturo; Pacheco, J. Rafael; Verzicco, Roberto
2014-01-01
Studies of stratified spin-up experiments in enclosed cylinders have reported the presence of small pockets of well-mixed fluids but quantitative measurements of the mixedness of the fluid has been lacking. Previous numerical simulations have not addressed these measurements. Here we present numerical simulations that explain how the combined effect of spin-up and thermal boundary conditions enhances or hinders mixing of a fluid in a cylinder. The energy of the system is characterized by splitting the potential energy into diabatic and adiabatic components, and measurements of efficiency of mixing are based on both, the ratio of dissipation of available potential energy to forcing and variance of temperature. The numerical simulations of the Navier–Stokes equations for the problem with different sets of thermal boundary conditions at the horizontal walls helped shed some light on the physical mechanisms of mixing, for which a clear explanation was absent
Mixing in thermally stratified nonlinear spin-up with uniform boundary fluxes
Energy Technology Data Exchange (ETDEWEB)
Baghdasarian, Meline; Pacheco-Vega, Arturo [Department of Mechanical Engineering, California State University, Los Angeles, Los Angeles, California 90032 (United States); Pacheco, J. Rafael, E-mail: rpacheco@asu.edu [SAP Americas Inc., Scottsdale, Arizona 85251 (United States); School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287 (United States); Environmental Fluid Dynamics Laboratories, Department of Civil Engineering and Geological Sciences, The University of Notre Dame, South Bend, Indiana 46556 (United States); Verzicco, Roberto [Dipartimento di Ingegneria Meccanica, Universita di Roma “Tor Vergata”, Via del Politecnico 1, 00133, Roma (Italy); PoF, University of Twente, 7500 AE Enschede (Netherlands)
2014-09-15
Studies of stratified spin-up experiments in enclosed cylinders have reported the presence of small pockets of well-mixed fluids but quantitative measurements of the mixedness of the fluid has been lacking. Previous numerical simulations have not addressed these measurements. Here we present numerical simulations that explain how the combined effect of spin-up and thermal boundary conditions enhances or hinders mixing of a fluid in a cylinder. The energy of the system is characterized by splitting the potential energy into diabatic and adiabatic components, and measurements of efficiency of mixing are based on both, the ratio of dissipation of available potential energy to forcing and variance of temperature. The numerical simulations of the Navier–Stokes equations for the problem with different sets of thermal boundary conditions at the horizontal walls helped shed some light on the physical mechanisms of mixing, for which a clear explanation was absent.
Exact multiplicity results for quasilinear boundary-value problems with cubic-like nonlinearities
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Idris Addou
2000-01-01
Full Text Available We consider the boundary-value problem $$displaylines{ -(varphi_p (u'' =lambda f(u mbox{ in }(0,1 cr u(0 = u(1 =0,, }$$ where $p>1$, $lambda >0$ and $varphi_p (x =| x|^{p-2}x$. The nonlinearity $f$ is cubic-like with three distinct roots 0=a less than b less than c. By means of a quadrature method, we provide the exact number of solutions for all $lambda >0$. This way we extend a recent result, for $p=2$, by Korman et al. cite{KormanLiOuyang} to the general case $p>1$. We shall prove that when 1less than $pleq 2$ the structure of the solution set is exactly the same as that studied in the case $p=2$ by Korman et al. cite{KormanLiOuyang}, and strictly different in the case $p>2$.
Inexact Newton–Landweber iteration for solving nonlinear inverse problems in Banach spaces
International Nuclear Information System (INIS)
Jin, Qinian
2012-01-01
By making use of duality mappings, we formulate an inexact Newton–Landweber iteration method for solving nonlinear inverse problems in Banach spaces. The method consists of two components: an outer Newton iteration and an inner scheme providing the increments by applying the Landweber iteration in Banach spaces to the local linearized equations. It has the advantage of reducing computational work by computing more cheap steps in each inner scheme. We first prove a convergence result for the exact data case. When the data are given approximately, we terminate the method by a discrepancy principle and obtain a weak convergence result. Finally, we test the method by reporting some numerical simulations concerning the sparsity recovery and the noisy data containing outliers. (paper)
A chaos-based evolutionary algorithm for general nonlinear programming problems
International Nuclear Information System (INIS)
El-Shorbagy, M.A.; Mousa, A.A.; Nasr, S.M.
2016-01-01
In this paper we present a chaos-based evolutionary algorithm (EA) for solving nonlinear programming problems named chaotic genetic algorithm (CGA). CGA integrates genetic algorithm (GA) and chaotic local search (CLS) strategy to accelerate the optimum seeking operation and to speed the convergence to the global solution. The integration of global search represented in genetic algorithm and CLS procedures should offer the advantages of both optimization methods while offsetting their disadvantages. By this way, it is intended to enhance the global convergence and to prevent to stick on a local solution. The inherent characteristics of chaos can enhance optimization algorithms by enabling it to escape from local solutions and increase the convergence to reach to the global solution. Twelve chaotic maps have been analyzed in the proposed approach. The simulation results using the set of CEC’2005 show that the application of chaotic mapping may be an effective strategy to improve the performances of EAs.
Minimax terminal approach problem in two-level hierarchical nonlinear discrete-time dynamical system
Energy Technology Data Exchange (ETDEWEB)
Shorikov, A. F., E-mail: afshorikov@mail.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002, Russia Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation)
2015-11-30
We consider a discrete–time dynamical system consisting of three controllable objects. The motions of all objects are given by the corresponding vector nonlinear or linear discrete–time recurrent vector relations, and control system for its has two levels: basic (first or I level) that is dominating and subordinate level (second or II level) and both have different criterions of functioning and united a priori by determined informational and control connections defined in advance. For the dynamical system in question, we propose a mathematical formalization in the form of solving a multistep problem of two-level hierarchical minimax program control over the terminal approach process with incomplete information and give a general scheme for its solving.
Grolet, Aurelien; Thouverez, Fabrice
2015-02-01
This paper is devoted to the study of vibration of mechanical systems with geometric nonlinearities. The harmonic balance method is used to derive systems of polynomial equations whose solutions give the frequency component of the possible steady states. Groebner basis methods are used for computing all solutions of polynomial systems. This approach allows to reduce the complete system to an unique polynomial equation in one variable driving all solutions of the problem. In addition, in order to decrease the number of variables, we propose to first work on the undamped system, and recover solution of the damped system using a continuation on the damping parameter. The search for multiple solutions is illustrated on a simple system, where the influence of the retained number of harmonic is studied. Finally, the procedure is applied on a simple cyclic system and we give a representation of the multiple states versus frequency.
Robust Optimization Using Supremum of the Objective Function for Nonlinear Programming Problems
International Nuclear Information System (INIS)
Lee, Se Jung; Park, Gyung Jin
2014-01-01
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
Regularity of the solutions to a nonlinear boundary problem with indefinite weight
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Aomar Anane
2011-01-01
Full Text Available In this paper we study the regularity of the solutions to the problemDelta_p u = |u|^{p−2}u in the bounded smooth domainOmega ⊂ R^N,with|∇u|^{p−2} partial_{nu} u = lambda V (x|u|^{p−2}u + h as a nonlinear boundary condition, where partial Omega is C^{2,beta}, with beta ∈]0, 1[, and V is a weight in L^s(partial Omega and h ∈ L^s(partial Omega for some s ≥ 1. We prove that all solutions are in L^{infty}(Omega cap L^{infty}(Omega, and using the D.Debenedetto’s theorem of regularity in [1] we conclude that those solutions are in C^{1,alpha} overline{Omega} for some alpha ∈ ]0, 1[.
Eigenvalue problem and nonlinear evolution of kink modes in a toroidal plasma
International Nuclear Information System (INIS)
Ogino, T.; Takeda, S.; Sanuki, H.; Kamimura, T.
1979-04-01
The internal kink modes of a cylindrical plasma are investigated by a linear eigen value problem and their nonlinear evolution is studied by 3-dimensional MHD simulation based on the rectangular column model under the fixed boundary condition. The growth rates in two cases, namely uniform and diffused current profiles are analyzed in detail, which agree with the analytical estimation by Shafranov. The time evolution of the m = 1 mode showed that q > 1 is satisfied at the relaxation time (q safety factor), a stable configuration like a horse shoe (a new equilibrium) was formed. Also, the time evolution of the pressure p for the m = 2 mode showed that a stable configuration like a pair of anchors was formed. (author)
Parallel Solution of Robust Nonlinear Model Predictive Control Problems in Batch Crystallization
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Yankai Cao
2016-06-01
Full Text Available Representing the uncertainties with a set of scenarios, the optimization problem resulting from a robust nonlinear model predictive control (NMPC strategy at each sampling instance can be viewed as a large-scale stochastic program. This paper solves these optimization problems using the parallel Schur complement method developed to solve stochastic programs on distributed and shared memory machines. The control strategy is illustrated with a case study of a multidimensional unseeded batch crystallization process. For this application, a robust NMPC based on min–max optimization guarantees satisfaction of all state and input constraints for a set of uncertainty realizations, and also provides better robust performance compared with open-loop optimal control, nominal NMPC, and robust NMPC minimizing the expected performance at each sampling instance. The performance of robust NMPC can be improved by generating optimization scenarios using Bayesian inference. With the efficient parallel solver, the solution time of one optimization problem is reduced from 6.7 min to 0.5 min, allowing for real-time application.
Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem
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R. J. Moitsheki
2012-01-01
Full Text Available We consider the one-dimensional steady fin problem with the Dirichlet boundary condition at one end and the Neumann boundary condition at the other. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. We perform preliminary group classification to determine forms of the arbitrary functions appearing in the considered equation for which the principal Lie algebra is extended. Some invariant solutions are constructed. The effects of thermogeometric fin parameter and the exponent on temperature are studied. Also, the fin efficiency is analyzed.
Solving the problems of thermal effects and outputs
International Nuclear Information System (INIS)
Jaske, R.T.
1974-01-01
All energy used ultimately appears in the environment as a thermal release, this paper points out, and many of the measures taken to reduce other types of pollutants ultimately increase thermal pollution because energy is required to operate the pollution control equipment. A number of measures that may be taken to reduce the ratio of net energy use to gross national product are pointed out
DEFF Research Database (Denmark)
Hubmer, Simon; Sherina, Ekaterina; Neubauer, Andreas
2018-01-01
. The main result of this paper is the verification of a nonlinearity condition in an infinite dimensional Hilbert space context. This condition guarantees convergence of iterative regularization methods. Furthermore, numerical examples for recovery of the Lam´e parameters from displacement data simulating......We consider a problem of quantitative static elastography, the estimation of the Lam´e parameters from internal displacement field data. This problem is formulated as a nonlinear operator equation. To solve this equation, we investigate the Landweber iteration both analytically and numerically...... a static elastography experiment are presented....
International Nuclear Information System (INIS)
Saitoh, Ayumu; Matsui, Nobuyuki; Itoh, Taku; Kamitani, Atsushi; Nakamura, Hiroaki
2011-01-01
A new method has been proposed for implementing essential boundary conditions to the Element-Free Galerkin Method (EFGM) without using the Lagrange multiplier. Furthermore, the performance of the proposed method has been investigated for a nonlinear Poisson problem. The results of computations show that, as interpolation functions become closer to delta functions, the accuracy of the solution is improved on the boundary. In addition, the accuracy of the proposed method is higher than that of the conventional EFGM. Therefore, it might be concluded that the proposed method is useful for solving the nonlinear Poisson problem. (author)
Memetic Algorithms to Solve a Global Nonlinear Optimization Problem. A Review
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M. K. Sakharov
2015-01-01
Full Text Available In recent decades, evolutionary algorithms have proven themselves as the powerful optimization techniques of search engine. Their popularity is due to the fact that they are easy to implement and can be used in all areas, since they are based on the idea of universal evolution. For example, in the problems of a large number of local optima, the traditional optimization methods, usually, fail in finding the global optimum. To solve such problems using a variety of stochastic methods, in particular, the so-called population-based algorithms, which are a kind of evolutionary methods. The main disadvantage of this class of methods is their slow convergence to the exact solution in the neighborhood of the global optimum, as these methods incapable to use the local information about the landscape of the function. This often limits their use in largescale real-world problems where the computation time is a critical factor.One of the promising directions in the field of modern evolutionary computation are memetic algorithms, which can be regarded as a combination of population search of the global optimum and local procedures for verifying solutions, which gives a synergistic effect. In the context of memetic algorithms, the meme is an implementation of the local optimization method to refine solution in the search.The concept of memetic algorithms provides ample opportunities for the development of various modifications of these algorithms, which can vary the frequency of the local search, the conditions of its end, and so on. The practically significant memetic algorithm modifications involve the simultaneous use of different memes. Such algorithms are called multi-memetic.The paper gives statement of the global problem of nonlinear unconstrained optimization, describes the most promising areas of AI modifications, including hybridization and metaoptimization. The main content of the work is the classification and review of existing varieties of
Initial-Boundary Value Problem Solution of the Nonlinear Shallow-water Wave Equations
Kanoglu, U.; Aydin, B.
2014-12-01
The hodograph transformation solutions of the one-dimensional nonlinear shallow-water wave (NSW) equations are usually obtained through integral transform techniques such as Fourier-Bessel transforms. However, the original formulation of Carrier and Greenspan (1958 J Fluid Mech) and its variant Carrier et al. (2003 J Fluid Mech) involve evaluation integrals. Since elliptic integrals are highly singular as discussed in Carrier et al. (2003), this solution methodology requires either approximation of the associated integrands by smooth functions or selection of regular initial/boundary data. It should be noted that Kanoglu (2004 J Fluid Mech) partly resolves this issue by simplifying the resulting integrals in closed form. Here, the hodograph transform approach is coupled with the classical eigenfunction expansion method rather than integral transform techniques and a new analytical model for nonlinear long wave propagation over a plane beach is derived. This approach is based on the solution methodology used in Aydın & Kanoglu (2007 CMES-Comp Model Eng) for wind set-down relaxation problem. In contrast to classical initial- or boundary-value problem solutions, here, the NSW equations are formulated to yield an initial-boundary value problem (IBVP) solution. In general, initial wave profile with nonzero initial velocity distribution is assumed and the flow variables are given in the form of Fourier-Bessel series. The results reveal that the developed method allows accurate estimation of the spatial and temporal variation of the flow quantities, i.e., free-surface height and depth-averaged velocity, with much less computational effort compared to the integral transform techniques such as Carrier et al. (2003), Kanoglu (2004), Tinti & Tonini (2005 J Fluid Mech), and Kanoglu & Synolakis (2006 Phys Rev Lett). Acknowledgments: This work is funded by project ASTARTE- Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3 ENV
Energy Technology Data Exchange (ETDEWEB)
Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H. [Univ. of Texas, Austin, TX (United States)
1996-12-31
The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.
TECHNOLOGICAL AND ENVIRONMENTAL PROBLEMS CONNECTED WITH THERMAL CONVERSION OF SEWAGE SLUDGE
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Alina Żogała
2016-02-01
Full Text Available Overview of the most common technological and environmental problems connected with thermal conversion of sewage sludge was presented in the article. Such issues as the influence of content of moisture and mineral matter on fuel properties of sludge, problem of emission of pollutants, problem of management of solid residue, risk of corrosion, were described. Besides, consolidated characteristic of the most important methods of thermal conversion of sewage sludge, with their advantages and disadvantages, was presented in the paper.
International Nuclear Information System (INIS)
Arjunan, S.; Mohan Kumar, R.; Mohan, R.; Jayavel, R.
2008-01-01
L-arginine trifluoroacetate, an organic nonlinear optical material, has been synthesized from aqueous solution. Bulk single crystal of dimension 57 mm x 5 mm x 3 mm has been grown by temperature lowering technique. Powder X-ray diffraction studies confirmed the monoclinic structure of the grown L-arginine trifluoroacetate crystal. Linear optical property of the grown crystal has been studied by UV-vis spectrum. Dielectric response of the L-arginine trifluoroacetate crystal was analysed for different frequencies and temperatures in detail. Microhardness study on the sample reveals that the crystal possesses relatively higher hardness compared to many organic crystals. Thermal analyses confirmed that the L-arginine trifluoroacetate material is thermally stable upto 212 deg. C. The etching studies have been performed to assess the perfection of the L-arginine trifluoroacetate crystal. Kurtz powder second harmonic generation test confirms the nonlinear optical properties of the as-grown L-arginine trifluoroacetate crystal
Energy Technology Data Exchange (ETDEWEB)
NONE
1999-12-31
This conference day was jointly organized by the `university group of thermal engineering (GUT)` and the French association of thermal engineers. This book of proceedings contains 7 papers entitled: `energy spectra of a passive scalar undergoing advection by a chaotic flow`; `analysis of chaotic behaviours: from topological characterization to modeling`; `temperature homogeneity by Lagrangian chaos in a direct current flow heat exchanger: numerical approach`; ` thermal instabilities in a mixed convection phenomenon: nonlinear dynamics`; `experimental characterization study of the 3-D Lagrangian chaos by thermal analogy`; `influence of coherent structures on the mixing of a passive scalar`; `evaluation of the performance index of a chaotic advection effect heat exchanger for a wide range of Reynolds numbers`. (J.S.)
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-12-31
This conference day was jointly organized by the `university group of thermal engineering (GUT)` and the French association of thermal engineers. This book of proceedings contains 7 papers entitled: `energy spectra of a passive scalar undergoing advection by a chaotic flow`; `analysis of chaotic behaviours: from topological characterization to modeling`; `temperature homogeneity by Lagrangian chaos in a direct current flow heat exchanger: numerical approach`; ` thermal instabilities in a mixed convection phenomenon: nonlinear dynamics`; `experimental characterization study of the 3-D Lagrangian chaos by thermal analogy`; `influence of coherent structures on the mixing of a passive scalar`; `evaluation of the performance index of a chaotic advection effect heat exchanger for a wide range of Reynolds numbers`. (J.S.)
Rasouli, Saifollah; Sakha, Fereshteh; Mojarrad, Aida G.; Zakavi, Saeed
2018-05-01
In this work, measurement of thermally induced nonlinear refractive index of meso-tetraphenylporphyrin (H2TPP) at different concentrations in 1,2-dicoloroethane using a double-grating interferometer set-up in a pump-probe configuration is reported. The formation of aggregates of H2TPP at concentrations greater than ca. 5 × 10-5 M was evident by deviation from Beer's law. An almost focused pump beam passes through the solution. A part of the pump beam energy is absorbed by the sample and therefore a thermal lens is generated in the sample. An expanded probe beam propagates through the sample and indicates the sample refractive index changes. Just after the sample a band-pass filter cuts off the pump beam from the path but the distorted probe beam passes through a double-grating interferometer consisting of two similar diffraction gratings with a few centimetres distance. A CCD camera is installed after the interferometer in which on its sensitive area two diffraction orders of the gratings are overlying and producing interference pattern. The refractive index changes of the sample are obtained from the phase distribution of the successive interference patterns recorded at different times after turning on of the pump beam using Fourier transform method. In this study, for different concentrations of H2TPP in 1,2-dichloroethane solution the thermal nonlinear refractive index is determined. Also, we present the measurement of the temperature changes induced by the pump beam in the solution. We found that value of nonlinear refractive index increased by increasing the concentration up to a concentration of 5 × 10-4 M and then decreased at higher concentrations. In addition, we have investigated the stability of the observed thermal nonlinearity after a period of two weeks from the sample preparation.
Studies in nonlinear problems of energy. Progress report, January 1, 1992--December 31, 1992
Energy Technology Data Exchange (ETDEWEB)
Matkowsky, B.J.
1992-07-01
Emphasis has been on combustion and flame propagation. The research program was on modeling, analysis and computation of combustion phenomena, with emphasis on transition from laminar to turbulent combustion. Nonlinear dynamics and pattern formation were investigated in the transition. Stability of combustion waves, and transitions to complex waves are described. Combustion waves possess large activation energies, so that chemical reactions are significant only in thin layers, or reaction zones. In limit of infinite activation energy, the zones shrink to moving surfaces, (fronts) which must be found during the analysis, so that (moving free boundary problems). The studies are carried out for limiting case with fronts, while the numerical studies are carried out for finite, though large, activation energy. Accurate resolution of the solution in the reaction zones is essential, otherwise false predictions of dynamics are possible. Since the the reaction zones move, adaptive pseudo-spectral methods were developed. The approach is based on a synergism of analytical and computational methods. The numerical computations build on and extend the analytical information. Furthermore, analytical solutions serve as benchmarks for testing the accuracy of the computation. Finally, ideas from analysis (singular perturbation theory) have induced new approaches to computations. The computational results suggest new analysis to be considered. Among the recent interesting results, was spatio-temporal chaos in combustion. One goal is extension of the adaptive pseudo-spectral methods to adaptive domain decomposition methods. Efforts have begun to develop such methods for problems with multiple reaction zones, corresponding to problems with more complex, and more realistic chemistry. Other topics included stochastics, oscillators, Rysteretic Josephson junctions, DC SQUID, Markov jumps, laser with saturable absorber, chemical physics, Brownian movement, combustion synthesis, etc.
Prospects for solving environmental problems pertinent to thermal power stations
Energy Technology Data Exchange (ETDEWEB)
A.G. Tumanovskii; V.R. Kotler [OAO All-Russia Thermal Engineering Institute, Moscow (Russian Federation)
2007-06-15
Possible ways to protect the atmosphere and water basin against harmful emissions and effluent waters discharged from thermal power stations are considered. Data on the effectiveness of different methods for removing NOx, SO{sub 2}, and ash particles, as well as heavy metals and CO{sub 2}, from these emissions and discharges are presented.
Directory of Open Access Journals (Sweden)
Pratibha Joshi
2014-12-01
Full Text Available In this paper, we have achieved high order solution of a three dimensional nonlinear diffusive-convective problem using modified variational iteration method. The efficiency of this approach has been shown by solving two examples. All computational work has been performed in MATHEMATICA.
International Nuclear Information System (INIS)
Nguyen Buong.
1992-11-01
The purpose of this paper is to investigate convergence rates for an operator version of Tikhonov regularization constructed by dual mapping for nonlinear ill-posed problems involving monotone operators in real reflective Banach spaces. The obtained results are considered in combination with finite-dimensional approximations for the space. An example is considered for illustration. (author). 15 refs
International Nuclear Information System (INIS)
Sokolow, Adam; Sen, Surajit
2007-01-01
An energy pulse refers to a spatially compact energy bundle. In nonlinear pulse propagation, the nonlinearity of the relevant dynamical equations could lead to pulse propagation that is nondispersive or weakly dispersive in space and time. Nonlinear pulse propagation through layered media with widely varying pulse transmission properties is not wave-like and a problem of broad interest in many areas such as optics, geophysics, atmospheric physics and ocean sciences. We study nonlinear pulse propagation through a semi-infinite sequence of layers where the layers can have arbitrary energy transmission properties. By assuming that the layers are rigid, we are able to develop exact expressions for the backscattered energy received at the surface layer. The present study is likely to be relevant in the context of energy transport through soil and similar complex media. Our study reveals a surprising connection between the problem of pulse propagation and the number patterns in the well known Pascal's and Catalan's triangles and hence provides an analytic benchmark in a challenging problem of broad interest. We close with comments on the relationship between this study and the vast body of literature on the problem of wave localization in disordered systems
Directory of Open Access Journals (Sweden)
Mitsuhiro Nakao
2014-01-01
Full Text Available We prove the existence and uniqueness of a global decaying solution to the initial boundary value problem for the quasilinear wave equation with Kelvin-Voigt dissipation and a derivative nonlinearity. To derive the required estimates of the solutions we employ a 'loan' method and use a difference inequality on the energy.
Fulcher, Lewis P.
1979-01-01
Presents an exact solution to the nonlinear Faraday's law problem of a rod sliding on frictionless rails with resistance. Compares the results with perturbation calculations based on the methods of Poisson and Pincare and of Kryloff and Bogoliuboff. (Author/GA)
Non-linear time series extreme events and integer value problems
Turkman, Kamil Feridun; Zea Bermudez, Patrícia
2014-01-01
This book offers a useful combination of probabilistic and statistical tools for analyzing nonlinear time series. Key features of the book include a study of the extremal behavior of nonlinear time series and a comprehensive list of nonlinear models that address different aspects of nonlinearity. Several inferential methods, including quasi likelihood methods, sequential Markov Chain Monte Carlo Methods and particle filters, are also included so as to provide an overall view of the available tools for parameter estimation for nonlinear models. A chapter on integer time series models based on several thinning operations, which brings together all recent advances made in this area, is also included. Readers should have attended a prior course on linear time series, and a good grasp of simulation-based inferential methods is recommended. This book offers a valuable resource for second-year graduate students and researchers in statistics and other scientific areas who need a basic understanding of nonlinear time ...
Directory of Open Access Journals (Sweden)
Tatiana Kavitova
2012-08-01
Full Text Available We prove a comparison principle for solutions of the Cauchy problem of the nonlinear pseudoparabolic equation $u_t=Delta u_t+ Deltavarphi(u +h(t,u$ with nonnegative bounded initial data. We show stabilization of a maximal solution to a maximal solution of the Cauchy problem for the corresponding ordinary differential equation $vartheta'(t=h(t,vartheta$ as $|x|oinfty$ under certain conditions on an initial datum.
Nonlinear dynamic modeling of a V-shaped metal based thermally driven MEMS actuator for RF switches
Bakri-Kassem, Maher; Dhaouadi, Rached; Arabi, Mohamed; Estahbanati, Shahabeddin V.; Abdel-Rahman, Eihab
2018-05-01
In this paper, we propose a new dynamic model to describe the nonlinear characteristics of a V-shaped (chevron) metallic-based thermally driven MEMS actuator. We developed two models for the thermal actuator with two configurations. The first MEMS configuration has a small tip connected to the shuttle, while the second configuration has a folded spring and a wide beam attached to the shuttle. A detailed finite element model (FEM) and a lumped element model (LEM) are proposed for each configuration to completely characterize the electro-thermal and thermo-mechanical behaviors. The nonlinear resistivity of the polysilicon layer is extracted from the measured current-voltage (I-V) characteristics of the actuator and the simulated corresponding temperatures in the FEM model, knowing the resistivity of the polysilicon at room temperature from the manufacture’s handbook. Both developed models include the nonlinear temperature-dependent material properties. Numerical simulations in comparison with experimental data using a dedicated MEMS test apparatus verify the accuracy of the proposed LEM model to represent the complex dynamics of the thermal MEMS actuator. The LEM and FEM simulation results show an accuracy ranging from a maximum of 13% error down to a minimum of 1.4% error. The actuator with the lower thermal load to air that includes a folded spring (FS), also known as high surface area actuator is compared to the actuator without FS, also known as low surface area actuator, in terms of the I-V characteristics, power consumption, and experimental static and dynamic responses of the tip displacement.
Thermal shock problems of bonded structure for plasma facing components
International Nuclear Information System (INIS)
Shibui, M.; Kuroda, T.; Kubota, Y.
1991-01-01
Thermal shock tests have been performed on W(Re)/Cu and Mo/Cu duplex structures with a particular emphasis on two failure modes: failure on the heated surface and failure near the bonding interface. The results indicate that failure of the duplex structure largely depends on the constraint of thermal strain on the heated surface and on the ductility changes of armour materials. Rapid debonding of the bonding interface may be attributed to the yielding of armour materials. This leads to a residual bending deformation when the armour cools down. Arguments are also presented in this paper on two parameter characterization of the failure of armour materials and on stress distribution near the free edge of the bonding interface. (orig.)
Transmutor demo unit and thermal into electrical energy transformation problems
International Nuclear Information System (INIS)
Matal, O.; Fiedler, J.
1999-01-01
In the three circuits layout of the transmutor the heat is transferred from the primary through the secondary circuits by a favourable heat carrier into the tertiary circuit where the thermal into electrical energy transformation in turbo-generator comes into force. Properties as well as parameters of the heat carrier in the secondary circuit affect basically both the conceptual layout of the tertiary circuit and consequently investments costs for its realization and the effectiveness of the transformation of thermal into electrical energy. For several heat carriers considered for the transmutor secondary circuit particular tertiary circuit concepts for the demonstration transmutor unit of approx. 15 W thermal power rate are analyzed, layout features and possibilities of turbogenerator selection are commented and investment costs as well as effectiveness of thermal into electrical energy transformation are estimated. Some of the results are as follows: (i) Heat carrier properties influence thermodynamics of the TDU water/steam cycle substantially. One of the dominant parameters is the melting (freezing) temperature of the heat carrier. (ii) Heat carrier properties influence investment costs of components of the TDU tertiary circuit substantially. Dominantly influenced are costs of the steam generator, steam turbine and high pressure regeneration system. (iii) If the heat carrier has to be a molten salt than a salt with a low melting temperature is recommended to be selected, for example KHF2. (iv) Eutectic alloy Pb-Bi as the heat carrier serves changes to design the TDU with efficient thermodynamics, with acceptable low investment costs of the tertiary as well as secondary circuit components and with an acceptable level of the nuclear safety
Energy Technology Data Exchange (ETDEWEB)
Vy, Nguyen Duy, E-mail: nguyenduyvy@tdt.edu.vn [Theoretical Physics Research Group, Ton Duc Thang University, Ho Chi Minh City 756636 (Viet Nam); Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City 756636 (Viet Nam); Tri Dat, Le [Faculty of Physics and Engineering Physics, University of Science, Ho Chi Minh City 748355 (Viet Nam); Iida, Takuya [Department of Physical Science, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531 (Japan)
2016-08-01
Bimaterial cantilevers have recently been used in, for example, the calorimetric analysis with picowatt resolution in microscopic space based on state-of-the-art atomic force microscopes. However, thermally induced effects usually change physical properties of the cantilevers, such as the resonance frequency, which reduce the accuracy of the measurements. Here, we propose an approach to circumvent this problem that uses an optical microcavity formed between a metallic layer coated on the back of the cantilever and one coated at the end of an optical fiber irradiating the cantilever. In addition to increasing the sensitivity, the optical rigidity of this system diminishes the thermally induced frequency shift. For a coating thickness of several tens of nanometers, the input power is 5–10 μW. These values can be evaluated from parameters derived by directly irradiating the cantilever in the absence of the microcavity. The system has the potential of using the cantilever both as a thermometer without frequency shifting and as a sensor with nanometer-controlled accuracy.
Inverse Tasks In The Tsunami Problem: Nonlinear Regression With Inaccurate Input Data
Lavrentiev, M.; Shchemel, A.; Simonov, K.
A variant of modified training functional that allows considering inaccurate input data is suggested. A limiting case when a part of input data is completely undefined, and, therefore, a problem of reconstruction of hidden parameters should be solved, is also considered. Some numerical experiments are presented. It is assumed that a dependence of known output variables on known input ones should be found is the classic problem definition, which is widely used in the majority of neural nets algorithms. The quality of approximation is evaluated as a performance function. Often the error of the task is evaluated as squared distance between known input data and predicted data multiplied by weighed coefficients. These coefficients may be named "precision coefficients". When inputs are not known exactly, natural generalization of performance function is adding member that responsible for distance between known inputs and shifted inputs, which lessen model's error. It is desirable that the set of variable parameters is compact for training to be con- verging. In the above problem it is possible to choose variants of demands of a priori compactness, which allow meaningful interpretation in the smoothness of the model dependence. Two kinds of regularization was used, first limited squares of coefficients responsible for nonlinearity and second limited multiplication of the above coeffi- cients and linear coefficients. Asymptotic universality of neural net ability to approxi- mate various smooth functions with any accuracy by increase of the number of tunable parameters is often the base for selecting a type of neural net approximation. It is pos- sible to show that used neural net will approach to Fourier integral transform, which approximate abilities are known, with increasing of the number of tunable parameters. In the limiting case, when input data is set with zero precision, the problem of recon- struction of hidden parameters with observed output data appears. The
Directory of Open Access Journals (Sweden)
M. H. Liao
2013-08-01
Full Text Available The thermo-elastic strain is induced by through silicon vias (TSV due to the difference of thermal expansion coefficients between the copper (∼18 ppm/ °C and silicon (∼2.8 ppm/ °C when the structure is exposed to a thermal ramp budget in the three dimensional integrated circuit (3DIC process. These thermal expansion stresses are high enough to introduce the delamination on the interfaces between the copper, silicon, and isolated dielectric. A compact analytic model for the strain field induced by different layouts of thermal copper filled TSVs with the linear superposition principle is found to have large errors due to the strong stress interaction between TSVs. In this work, a nonlinear stress analytic model with different TSV layouts is demonstrated by the finite element method and the analysis of the Mohr's circle. The characteristics of stress are also measured by the atomic force microscope-raman technique with nanometer level space resolution. The change of the electron mobility with the consideration of this nonlinear stress model for the strong interactions between TSVs is ∼2–6% smaller in comparison with those from the consideration of the linear stress superposition principle only.
Huang, Yi; Zhang, Xingyi; Zhou, You-He
2016-07-01
The vibration of a permanent magnet (PM) levitated upon a high temperature superconductor (HTS) shows anomalous motion under external disturbance. In this paper we construct a cantilevered beam experimental setup composed of a bulk PM and a thermally insulated cylindrical YBa2Cu3O x superconductor. When the levitation system is disturbed by vertical excitation, the thermal character of the superconductor surface could be measured directly. Our experiments on a clean and large single-domain superconductor show that a giant temperature spike appears once the levitated PM experiences period doubling oscillation. We develop a numerical simulation for the analysis of the nonlinear vibration of the levitated PM coupled with the nonlinear electromagnetic force between the PM and HTS, taking into account heat diffusion. Using this procedure, we explore the electromagnetic and thermal properties at the thermally insulated HTS surface when the levitated PM shows a period doubling vibration. We find a remarkable difference between the experimental results and simulation. In order to interpret this temperature difference, we suggest a type of flux motion triggered by the electromagnetic force when it is far larger than the pinning force of the superconductor. The quantitative approach is based on the analysis process of the partial flux jump as a result of the flux creep. Finally, the calculated result is shown to be very close to the experimental result.
Directory of Open Access Journals (Sweden)
Mahmoud Bayat
Full Text Available This review features a survey of some recent developments in asymptotic techniques and new developments, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the achieved approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to over-come the shortcomings.In this review we have applied different powerful analytical methods to solve high nonlinear problems in engineering vibrations. Some patterns are given to illustrate the effectiveness and convenience of the methodologies.
International Nuclear Information System (INIS)
Biffle, J.H.
1991-01-01
1 - Description of program or function: JAC is a two-dimensional finite element program for solving large deformation, temperature dependent, quasi-static mechanics problems with the nonlinear conjugate gradient (CG) technique. Either plane strain or axisymmetric geometry may be used with material descriptions which include temperature dependent elastic-plastic, temperature dependent secondary creep, and isothermal soil models. The nonlinear effects examined include material and geometric nonlinearities due to large rotations, large strains, and surface which slide relative to one another. JAC is vectorized to perform efficiently on the Cray1 computer. A restart capability is included. 2 - Method of solution: The nonlinear conjugate gradient method is employed in a two-dimensional plane strain or axisymmetric setting with various techniques for accelerating convergence. Sliding interface conditions are also implemented. A four-node Lagrangian uniform strain element is used with orthogonal hourglass viscosity to control the zero energy modes. Three sets of continuum equations are needed - kinematic statements, constitutive equations, and equations of equilibrium - to describe the deformed configuration of the body. 3 - Restrictions on the complexity of the problem - Maxima of: 10 load and solution control functions, 4 materials. The strain rate is assumed constant over a time interval. Current large rotation theory is applicable to a maximum shear strain of 1.0. JAC should be used with caution for large shear strains. Problem size is limited only by available memory
Analysis result for OECD benchmark on thermal fatigue problem
International Nuclear Information System (INIS)
Kamaya, Masayuki; Nakamura, Akira; Fujii, Yuzou
2005-01-01
The main objective of this analysis is to understand the crack growth behavior under three-dimensional (3D) thermal fatigue by conducting 3D crack initiation and propagation analyses. The possibility of crack propagation through the wall thickness of pipe, and the accuracy of the prediction of crack initiation and propagation are of major interest. In this report, in order to estimate the heat transfer coefficients and evaluate the thermal stress, conventional finite element analysis (FEA) is conducted. Then, the crack driving force is evaluated by using the finite element alternating method (FEAM), which can derive the stress intensity factor (SIF) under 3D mechanical loading based on finite element analysis without generating the mesh for a cracked body. Through these two realistic 3D numerical analyses, it has been tried to predict the crack initiation and propagation behavior. The thermal fatigue crack initiation and propagation behavior were numerically analyzed. The conventional FEA was conducted in order to estimate the heat transfer coefficient and evaluate the thermal stress. Then, the FEAM was conducted to evaluate the SIFs of surface single cracks and interacting multiple cracks, and crack growth was evaluated. The results are summarized as follows: 1. The heat transfer coefficients were estimated as H air = 40 W/m 2 K and H water = 5000 W/m 2 K. This allows simulation of the change in temperature with time at the crack initiation points obtained by the experiment. 2. The maximum stress occurred along the line of symmetry and the maximum Mises equivalent stress was 572 MPa. 3. By taking the effect of mean stress into account according to the modified Goodman diagram, the equivalent stress range and the number of cycles to crack initiation were estimated as 1093 MPa and 3.8x10 4 , respectively, although the tensile strength was assumed to be 600 MPa. 4. It was shown from the evaluated SIFs that longitudinal cracks can penetrate the wall of the pipe
Czech Academy of Sciences Publication Activity Database
Dilna, N.; Rontó, András
2010-01-01
Roč. 60, č. 3 (2010), s. 327-338 ISSN 0139-9918 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : non-linear boundary value-problem * functional differential equation * non-local condition * unique solvability * differential inequality Subject RIV: BA - General Mathematics Impact factor: 0.316, year: 2010 http://link.springer.com/article/10.2478%2Fs12175-010-0015-9
DEFF Research Database (Denmark)
Ghoreishi, Newsha; Sørensen, Jan Corfixen; Jørgensen, Bo Nørregaard
2015-01-01
Non-trivial real world decision-making processes usually involve multiple parties having potentially conflicting interests over a set of issues. State-of-the-art multi-objective evolutionary algorithms (MOEA) are well known to solve this class of complex real-world problems. In this paper, we...... compare the performance of state-of-the-art multi-objective evolutionary algorithms to solve a non-linear multi-objective multi-issue optimisation problem found in Greenhouse climate control. The chosen algorithms in the study includes NSGAII, eNSGAII, eMOEA, PAES, PESAII and SPEAII. The performance...... of all aforementioned algorithms is assessed and compared using performance indicators to evaluate proximity, diversity and consistency. Our insights to this comparative study enhanced our understanding of MOEAs performance in order to solve a non-linear complex climate control problem. The empirical...
International Nuclear Information System (INIS)
Wilson, G.L.; Rydin, R.A.; Orivuori, S.
1988-01-01
Two highly efficient nonlinear time-dependent heat conduction methodologies, the nonlinear time-dependent nodal integral technique (NTDNT) and IVOHEAT are compared using one- and two-dimensional time-dependent benchmark problems. The NTDNT is completely based on newly developed time-dependent nodal integral methods, whereas IVOHEAT is based on finite elements in space and Crank-Nicholson finite differences in time. IVOHEAT contains the geometric flexibility of the finite element approach, whereas the nodal integral method is constrained at present to Cartesian geometry. For test problems where both methods are equally applicable, the nodal integral method is approximately six times more efficient per dimension than IVOHEAT when a comparable overall accuracy is chosen. This translates to a factor of 200 for a three-dimensional problem having relatively homogeneous regions, and to a smaller advantage as the degree of heterogeneity increases
International Nuclear Information System (INIS)
Ritenour, R.L.
1989-01-01
The single collision thermalization (SCT) approximation models the thermalization process by assuming that neutrons attain a thermalized distribution with only a single collision within the moderating material, independent of the neutron's incident energy. The physical intuition on which this approximation is based is that the salient properties of neutron thermalization are accounted for in the first collision, and the effects of subsequent collisions tend to average out statistically. The independence of the neutron incident and outscattering energy leads to variable separability in the scattering kernel and, thus, significant simplification of the neutron thermalization problem. The approximation also addresses detailed balance and neutron conservation concerns. All of the tests performed on the SCT approximation yielded excellent results. The significance of the SCT approximation is that it greatly simplifies thermalization calculations for CNS design. Preliminary investigations with cases involving strong absorbers also indicates that this approximation may have broader applicability, as in the upgrading of the thermalization codes
HEATING6 analysis of international thermal benchmark problem sets 1 and 2
International Nuclear Information System (INIS)
Childs, K.W.; Bryan, C.B.
1986-10-01
In order to assess the heat transfer computer codes used in the analysis of nuclear fuel shipping casks, the Nuclear Energy Agency Committee on Reactor Physics has defined seven problems for benchmarking thermal codes. All seven of these problems have been solved using the HEATING6 heat transfer code. This report presents the results of five of the problems. The remaining two problems were used in a previous benchmarking of thermal codes used in the United States, and their solutions have been previously published
An inverse heat transfer problem for optimization of the thermal ...
Indian Academy of Sciences (India)
Department of Production Engineering, Faculty of Technical Science, ... ductivity of manufacturing and high levels of machining quality and accuracy, are the most ... inverse problems are today successfully applied in identification, design, control and optimiza- ...... of Machine Tools and Manufacture, 35(5): 751–760.
Directory of Open Access Journals (Sweden)
Azza Hassan Amer
2017-12-01
Full Text Available Geometric programming problem is a powerful tool for solving some special type nonlinear programming problems. In the last few years we have seen a very rapid development on solving multiobjective geometric programming problem. A few mathematical programming methods namely fuzzy programming, goal programming and weighting methods have been applied in the recent past to find the compromise solution. In this paper, -constraint method has been applied in bi-level multiobjective geometric programming problem to find the Pareto optimal solution at each level. The equivalent mathematical programming problems are formulated to find their corresponding value of the objective function based on the duality theorem at eash level. Here, we have developed a new algorithm for fuzzy programming technique to solve bi-level multiobjective geometric programming problems to find an optimal compromise solution. Finally the solution procedure of the fuzzy technique is illustrated by a numerical example
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).
Directory of Open Access Journals (Sweden)
J. Gwinner
2013-01-01
Full Text Available The purpose of this paper is twofold. Firstly we consider nonlinear nonsmooth elliptic boundary value problems, and also related parabolic initial boundary value problems that model in a simplified way steady-state unilateral contact with Tresca friction in solid mechanics, respectively, stem from nonlinear transient heat conduction with unilateral boundary conditions. Here a recent duality approach, that augments the classical Babuška-Brezzi saddle point formulation for mixed variational problems to twofold saddle point formulations, is extended to the nonsmooth problems under consideration. This approach leads to variational inequalities of mixed form for three coupled fields as unknowns and to related differential mixed variational inequalities in the time-dependent case. Secondly we are concerned with the stability of the solution set of a general class of differential mixed variational inequalities. Here we present a novel upper set convergence result with respect to perturbations in the data, including perturbations of the associated nonlinear maps, the nonsmooth convex functionals, and the convex constraint set. We employ epiconvergence for the convergence of the functionals and Mosco convergence for set convergence. We impose weak convergence assumptions on the perturbed maps using the monotonicity method of Browder and Minty.
International Nuclear Information System (INIS)
Andrianov, I.V.; Danishevsky, V.V.
1994-01-01
Asymptotic approaches for nonlinear dynamics of continual system are developed well for the infinite in spatial variables. For the systems with finite sizes we have an infinite number of resonance, and Poincare-Lighthill-Go method does riot work. Using of averaging procedure or method of multiple scales leads to the infinite systems of nonlinear algebraic or ordinary differential equations systems and then using truncation method. which does not gives possibility to obtain all important properties of the solutions
Some problems on non-linear semigroups and the blow-up of integral solutions
International Nuclear Information System (INIS)
Pavel, N.H.
1983-07-01
After some introductory remarks, this highly mathematical document considers a unifying approach in the theory of non-linear semigroups. Then a brief survey is given on blow-up of mild solutions from the semilinear case. Finally, the global behavior of solutions to non-linear evolution equations is addressed; it is found that classical results on the behavior of the maximal solution u as t up-arrow tsub(max) hold also for integral solutions
On the thermal raleigh problem in partially ionized argon
International Nuclear Information System (INIS)
Hutten Mansfeld, A.C.B.
1976-01-01
A partially ionized gas is created by the reflection of a shock wave with incident Mach numbers in the range 7 to 10 and an initial pressure of 5 Torr against the cold end wall of a shock tube. Heat exchange between the plasma and this cold wall induces several relaxation processes in the thermal boundary layer. Of these, relaxation of i) the electron and heavy particles temperature and ii) the degree of ionization towards a local thermodynamic equilibrium state are considered. In the model, transport and relaxation processes are treated simultaneously. A classification on the basis of relaxation phenomena is performed, i.e., simplified sets of equations are obtained in a systematic way from the frozen or equilibrium limits of the relaxation processes. A finite difference numerical solution for the different models is obtained. Because the boundary conditions are of mixed type and the relaxation processes show aspects of stiffness, the application of a backward implicit discretization scheme is necessary. As a diagnostic tool, a two wavelength version of the laser schlieren method is used. The measurements provide time histories of both the electron and atom number density gradients
Neilson, Peter D; Neilson, Megan D
2005-09-01
Adaptive model theory (AMT) is a computational theory that addresses the difficult control problem posed by the musculoskeletal system in interaction with the environment. It proposes that the nervous system creates motor maps and task-dependent synergies to solve the problems of redundancy and limited central resources. These lead to the adaptive formation of task-dependent feedback/feedforward controllers able to generate stable, noninteractive control and render nonlinear interactions unobservable in sensory-motor relationships. AMT offers a unified account of how the nervous system might achieve these solutions by forming internal models. This is presented as the design of a simulator consisting of neural adaptive filters based on cerebellar circuitry. It incorporates a new network module that adaptively models (in real time) nonlinear relationships between inputs with changing and uncertain spectral and amplitude probability density functions as is the case for sensory and motor signals.
Optimization of lift gas allocation in a gas lifted oil field as non-linear optimization problem
Directory of Open Access Journals (Sweden)
Roshan Sharma
2012-01-01
Full Text Available Proper allocation and distribution of lift gas is necessary for maximizing total oil production from a field with gas lifted oil wells. When the supply of the lift gas is limited, the total available gas should be optimally distributed among the oil wells of the field such that the total production of oil from the field is maximized. This paper describes a non-linear optimization problem with constraints associated with the optimal distribution of the lift gas. A non-linear objective function is developed using a simple dynamic model of the oil field where the decision variables represent the lift gas flow rate set points of each oil well of the field. The lift gas optimization problem is solved using the emph'fmincon' solver found in MATLAB. As an alternative and for verification, hill climbing method is utilized for solving the optimization problem. Using both of these methods, it has been shown that after optimization, the total oil production is increased by about 4. For multiple oil wells sharing lift gas from a common source, a cascade control strategy along with a nonlinear steady state optimizer behaves as a self-optimizing control structure when the total supply of lift gas is assumed to be the only input disturbance present in the process. Simulation results show that repeated optimization performed after the first time optimization under the presence of the input disturbance has no effect in the total oil production.
Knight, Norman F., Jr.; Warren, Jerry E.; Elliott, Kenny B.; Song, Kyongchan; Raju, Ivatury S.
2012-01-01
Elastic-plastic, large-deflection nonlinear thermo-mechanical stress analyses are performed for the Space Shuttle external tank s intertank stringers. Detailed threedimensional finite element models are developed and used to investigate the stringer s elastic-plastic response for different thermal and mechanical loading events from assembly through flight. Assembly strains caused by initial installation on an intertank panel are accounted for in the analyses. Thermal loading due to tanking was determined to be the bounding loading event. The cryogenic shrinkage caused by tanking resulted in a rotation of the intertank chord flange towards the center of the intertank, which in turn loaded the intertank stringer feet. The analyses suggest that the strain levels near the first three fasteners remain sufficiently high that a failure may occur. The analyses also confirmed that the installation of radius blocks on the stringer feet ends results in an increase in the stringer capability.
A nonlinear eigenvalue problem for self-similar spherical force-free magnetic fields
Energy Technology Data Exchange (ETDEWEB)
Lerche, I. [Institut für Geowissenschaften, Naturwissenschaftliche Fakultät III, Martin-Luther Universität, D-06099 Halle (Germany); Low, B. C. [High Altitude Observatory, National Center for Atmospheric Research, Boulder, Colorado 80307 (United States)
2014-10-15
An axisymmetric force-free magnetic field B(r, θ) in spherical coordinates is defined by a function r sin θB{sub φ}=Q(A) relating its azimuthal component to its poloidal flux-function A. The power law r sin θB{sub φ}=aA|A|{sup 1/n}, n a positive constant, admits separable fields with A=(A{sub n}(θ))/(r{sup n}) , posing a nonlinear boundary-value problem for the constant parameter a as an eigenvalue and A{sub n}(θ) as its eigenfunction [B. C. Low and Y. Q Lou, Astrophys. J. 352, 343 (1990)]. A complete analysis is presented of the eigenvalue spectrum for a given n, providing a unified understanding of the eigenfunctions and the physical relationship between the field's degree of multi-polarity and rate of radial decay via the parameter n. These force-free fields, self-similar on spheres of constant r, have basic astrophysical applications. As explicit solutions they have, over the years, served as standard benchmarks for testing 3D numerical codes developed to compute general force-free fields in the solar corona. The study presented includes a set of illustrative multipolar field solutions to address the magnetohydrodynamics (MHD) issues underlying the observation that the solar corona has a statistical preference for negative and positive magnetic helicities in its northern and southern hemispheres, respectively; a hemispherical effect, unchanging as the Sun's global field reverses polarity in successive eleven-year cycles. Generalizing these force-free fields to the separable form B=(H(θ,φ))/(r{sup n+2}) promises field solutions of even richer topological varieties but allowing for φ-dependence greatly complicates the governing equations that have remained intractable. The axisymmetric results obtained are discussed in relation to this generalization and the Parker Magnetostatic Theorem. The axisymmetric solutions are mathematically related to a family of 3D time-dependent ideal MHD solutions for a polytropic fluid of index γ = 4
Effects of vortex-like and non-thermal ion distributions on non-linear dust-acoustic waves
International Nuclear Information System (INIS)
Mamun, A.A.; Cairns, R.A.; Shukla, P.K.
1996-01-01
The effects of vortex-like and non-thermal ion distributions are incorporated in the study of nonlinear dust-acoustic waves in an unmagnetized dusty plasma. It is found that owing to the departure from the Boltzmann ion distribution to a vortex-like phase space distribution, the dynamics of small but finite amplitude dust-acoustic waves is governed by a modified Kortweg endash de Vries equation. The latter admits a stationary dust-acoustic solitary wave solution, which has larger amplitude, smaller width, and higher propagation velocity than that involving adiabatic ions. On the other hand, consideration of a non-thermal ion distribution provides the possibility of coexistence of large amplitude rarefactive as well as compressive dust-acoustic solitary waves, whereas these structures appear independently when the wave amplitudes become infinitely small. The present investigation should help us to understand the salient features of the non-linear dust-acoustic waves that have been observed in a recent numerical simulation study. copyright 1996 American Institute of Physics
Directory of Open Access Journals (Sweden)
Yurii M. Streliaiev
2016-06-01
Full Text Available Three-dimensional quasistatic contact problem of two linearly elastic bodies' interaction with Coulomb friction taken into account is considered. The boundary conditions of the problem have been simplified by the modification of the Coulomb's law of friction. This modification is based on the introducing of a delay in normal contact tractions that bound tangent contact tractions in the Coulomb's law of friction expressions. At this statement the problem is reduced to a sequence of similar systems of nonlinear integral equations describing bodies' interaction at each step of loading. A method for an approximate solution of the integral equations system corresponded to each step of loading is applied. This method consists of system regularization, discretization of regularized system and iterative process application for solving the discretized system. A numerical solution of a contact problem of an elastic sphere with an elastic half-space interaction under increasing and subsequently decreasing normal compressive force has been obtained.
Estimation of the thermal properties in alloys as an inverse problem
International Nuclear Information System (INIS)
Zueco, J.; Alhama, F.
2005-01-01
This paper provides an efficient numerical method for estimating the thermal conductivity and heat capacity of alloys, as a function of the temperature, starting from temperature measurements (including errors) in heating and cooling processes. The proposed procedure is a modification of the known function estimation technique, typical of the inverse problem field, in conjunction with the network simulation method (already checked in many non-lineal problems) as the numerical tool. Estimations only require a point of measurement. The methodology is applied for determining these thermal properties in alloys within ranges of temperature where allotropic changes take place. These changes are characterized by sharp temperature dependencies. (Author) 13 refs
Directory of Open Access Journals (Sweden)
S.N. Nnamchi
2010-01-01
Full Text Available Determination of the thermal conductivity and the specific heat capacity of neem seeds (Azadirachta indica A. Juss usingthe inverse method is the main subject of this work. One-dimensional formulation of heat conduction problem in a spherewas used. Finite difference method was adopted for the solution of the heat conduction problem. The thermal conductivityand the specific heat capacity were determined by least square method in conjunction with Levenberg-Marquardt algorithm.The results obtained compare favourably with those obtained experimentally. These results are useful in the analysis ofneem seeds drying and leaching processes.
Directory of Open Access Journals (Sweden)
Suheel Abdullah Malik
2014-01-01
Full Text Available We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA, interior point algorithm (IPA, and active set algorithm (ASA. The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.
Rosenberg, D. E.; Alafifi, A.
2016-12-01
Water resources systems analysis often focuses on finding optimal solutions. Yet an optimal solution is optimal only for the modelled issues and managers often seek near-optimal alternatives that address un-modelled objectives, preferences, limits, uncertainties, and other issues. Early on, Modelling to Generate Alternatives (MGA) formalized near-optimal as the region comprising the original problem constraints plus a new constraint that allowed performance within a specified tolerance of the optimal objective function value. MGA identified a few maximally-different alternatives from the near-optimal region. Subsequent work applied Markov Chain Monte Carlo (MCMC) sampling to generate a larger number of alternatives that span the near-optimal region of linear problems or select portions for non-linear problems. We extend the MCMC Hit-And-Run method to generate alternatives that span the full extent of the near-optimal region for non-linear, non-convex problems. First, start at a feasible hit point within the near-optimal region, then run a random distance in a random direction to a new hit point. Next, repeat until generating the desired number of alternatives. The key step at each iterate is to run a random distance along the line in the specified direction to a new hit point. If linear equity constraints exist, we construct an orthogonal basis and use a null space transformation to confine hits and runs to a lower-dimensional space. Linear inequity constraints define the convex bounds on the line that runs through the current hit point in the specified direction. We then use slice sampling to identify a new hit point along the line within bounds defined by the non-linear inequity constraints. This technique is computationally efficient compared to prior near-optimal alternative generation techniques such MGA, MCMC Metropolis-Hastings, evolutionary, or firefly algorithms because search at each iteration is confined to the hit line, the algorithm can move in one
Directory of Open Access Journals (Sweden)
Qiying Wei
2009-01-01
Full Text Available By using the well-known Schauder fixed point theorem and upper and lower solution method, we present some existence criteria for positive solution of an -point singular -Laplacian dynamic equation on time scales with the sign changing nonlinearity. These results are new even for the corresponding differential (=ℝ and difference equations (=ℤ, as well as in general time scales setting. As an application, an example is given to illustrate the results.
1987-07-01
fields (see also Chapter 4 of Ref. 22). Like our investigation, theirs is based on the Khokhlov-Zabolotskaya-Kuznetsov ( KZK ) equa- tion [23,24...25,26], also based on the KZK e(iualiou, is limited to weakly nonlinear systems. However, the practical case of a focused circular source with gain of...iment. The demonstrated abihty of the KZK equation to accurately model focused sound fields from reahstic sources [i.e., having abrupt edges and
Yothers, Mitchell P.; Browder, Aaron E.; Bumm, Lloyd A.
2017-01-01
We have developed a real-space method to correct distortion due to thermal drift and piezoelectric actuator nonlinearities on scanning tunneling microscope images using Matlab. The method uses the known structures typically present in high-resolution atomic and molecularly resolved images as an internal standard. Each image feature (atom or molecule) is first identified in the image. The locations of each feature's nearest neighbors are used to measure the local distortion at that location. The local distortion map across the image is simultaneously fit to our distortion model, which includes thermal drift in addition to piezoelectric actuator hysteresis and creep. The image coordinates of the features and image pixels are corrected using an inverse transform from the distortion model. We call this technique the thermal-drift, hysteresis, and creep transform. Performing the correction in real space allows defects, domain boundaries, and step edges to be excluded with a spatial mask. Additional real-space image analyses are now possible with these corrected images. Using graphite(0001) as a model system, we show lattice fitting to the corrected image, averaged unit cell images, and symmetry-averaged unit cell images. Statistical analysis of the distribution of the image features around their best-fit lattice sites measures the aggregate noise in the image, which can be expressed as feature confidence ellipsoids.
Yothers, Mitchell P; Browder, Aaron E; Bumm, Lloyd A
2017-01-01
We have developed a real-space method to correct distortion due to thermal drift and piezoelectric actuator nonlinearities on scanning tunneling microscope images using Matlab. The method uses the known structures typically present in high-resolution atomic and molecularly resolved images as an internal standard. Each image feature (atom or molecule) is first identified in the image. The locations of each feature's nearest neighbors are used to measure the local distortion at that location. The local distortion map across the image is simultaneously fit to our distortion model, which includes thermal drift in addition to piezoelectric actuator hysteresis and creep. The image coordinates of the features and image pixels are corrected using an inverse transform from the distortion model. We call this technique the thermal-drift, hysteresis, and creep transform. Performing the correction in real space allows defects, domain boundaries, and step edges to be excluded with a spatial mask. Additional real-space image analyses are now possible with these corrected images. Using graphite(0001) as a model system, we show lattice fitting to the corrected image, averaged unit cell images, and symmetry-averaged unit cell images. Statistical analysis of the distribution of the image features around their best-fit lattice sites measures the aggregate noise in the image, which can be expressed as feature confidence ellipsoids.
International Nuclear Information System (INIS)
Jeeju, P.P.; Jayalekshmi, S.; Chandrasekharan, K.; Sudheesh, P.
2013-01-01
Highly transparent and thermally stable zinc oxide (ZnO)/poly(styrene)–poly(methyl methacrylate) (PS–PMMA) nanocomposite films have been deposited on glass substrates, from the ZnO incorporated (PS–PMMA) solutions in toluene, using spin coating technique. A chemical route at room temperature is used to synthesize the ZnO nanoparticles. Transmission electron microscope and high-resolution transmission electron microscope images show that the ZnO nanoparticles are of size around 10 nm. The composite films have been characterized by X-ray diffraction, Fourier transform infrared spectroscopy, atomic force microscopy, Ultraviolet–visible–Near Infrared (UV–vis–NIR) spectroscopy, Thermo-gravimetric analysis, photoluminescence (PL) spectroscopy and Z-scan technique. From the UV–vis–NIR spectra it is observed that the ZnO/PS–PMMA nanocomposite films with 10 wt.% ZnO content exhibit excellent shielding property in the UV region and, high transparency in the visible region. The PL spectrum of the composite films is different from that of ZnO and PS–PMMA blend and exhibits an excitonic emission peak at ∼ 375 nm. The optical absorptive nonlinearity in the nanocomposite films is investigated using open aperture Z-scan technique. The results indicate optical limiting type nonlinearity in the films due to two photon absorption. A transmittance minimum of around 0.25 has been observed in the ZnO/PS–PMMA nanocomposite films which is much lower compared to that in ZnO/PMMA and ZnO/PS nanocomposite films. The ZnO/PS–PMMA nanocomposite films also show a self-defocusing type negative nonlinear refraction in closed aperture Z-scan experiment. These nanocomposite films extend ample scope of applications as excellent optical limiters and efficient UV protectors. - Highlights: ► Transparent, ZnO/poly(styrene)–poly(methyl methacrylate) composite films are prepared. ► The nanocomposite films with 10 wt.% ZnO content exhibit good UV-shielding property.
Energy Technology Data Exchange (ETDEWEB)
Jeeju, P.P., E-mail: jeejupp@gmail.com [Division for Research in Advanced Materials, Department of Physics, Cochin University of Science and Technology, Kochi 682 022, Kerala (India); Jayalekshmi, S., E-mail: jayalekshmi@cusat.ac.in [Division for Research in Advanced Materials, Department of Physics, Cochin University of Science and Technology, Kochi 682 022, Kerala (India); Chandrasekharan, K.; Sudheesh, P. [Department of Physics, National Institute of Technology, Calicut, Kerala (India)
2013-03-01
Highly transparent and thermally stable zinc oxide (ZnO)/poly(styrene)–poly(methyl methacrylate) (PS–PMMA) nanocomposite films have been deposited on glass substrates, from the ZnO incorporated (PS–PMMA) solutions in toluene, using spin coating technique. A chemical route at room temperature is used to synthesize the ZnO nanoparticles. Transmission electron microscope and high-resolution transmission electron microscope images show that the ZnO nanoparticles are of size around 10 nm. The composite films have been characterized by X-ray diffraction, Fourier transform infrared spectroscopy, atomic force microscopy, Ultraviolet–visible–Near Infrared (UV–vis–NIR) spectroscopy, Thermo-gravimetric analysis, photoluminescence (PL) spectroscopy and Z-scan technique. From the UV–vis–NIR spectra it is observed that the ZnO/PS–PMMA nanocomposite films with 10 wt.% ZnO content exhibit excellent shielding property in the UV region and, high transparency in the visible region. The PL spectrum of the composite films is different from that of ZnO and PS–PMMA blend and exhibits an excitonic emission peak at ∼ 375 nm. The optical absorptive nonlinearity in the nanocomposite films is investigated using open aperture Z-scan technique. The results indicate optical limiting type nonlinearity in the films due to two photon absorption. A transmittance minimum of around 0.25 has been observed in the ZnO/PS–PMMA nanocomposite films which is much lower compared to that in ZnO/PMMA and ZnO/PS nanocomposite films. The ZnO/PS–PMMA nanocomposite films also show a self-defocusing type negative nonlinear refraction in closed aperture Z-scan experiment. These nanocomposite films extend ample scope of applications as excellent optical limiters and efficient UV protectors. - Highlights: ► Transparent, ZnO/poly(styrene)–poly(methyl methacrylate) composite films are prepared. ► The nanocomposite films with 10 wt.% ZnO content exhibit good UV-shielding property.
Energy Technology Data Exchange (ETDEWEB)
Falikov, A A; Vakhrushev, V V; Kuul, V S; Samoilov, O B; Tarasov, G I [OKBM, Nizhny Novgorod (Russian Federation)
1997-09-01
The paper briefly reviews the specific thermal-hydraulic problems for AST-type NHRs, the experimental investigations that have been carried out in the RF, and the design procedures and computer codes used for AST-500 thermohydraulic characteristics and safety validation. (author). 13 refs, 10 figs, 1 tab.
International Nuclear Information System (INIS)
Manakov, S V; Santini, P M
2008-01-01
We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev-Petviashvili (dKP) equation. We showed, in particular, that the associated inverse problems can be expressed in terms of nonlinear Riemann-Hilbert problems on the real axis. In this paper, we make use of the nonlinear Riemann-Hilbert problem of dKP (i) to construct the longtime behaviour of the solutions of its Cauchy problem; (ii) to characterize a class of implicit solutions; (iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions of dKP, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking
Energy Technology Data Exchange (ETDEWEB)
Manakov, S V [Landau Institute for Theoretical Physics, Moscow (Russian Federation); Santini, P M [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , and Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Piazz.le Aldo Moro 2, I-00185 Rome (Italy)
2008-02-08
We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev-Petviashvili (dKP) equation. We showed, in particular, that the associated inverse problems can be expressed in terms of nonlinear Riemann-Hilbert problems on the real axis. In this paper, we make use of the nonlinear Riemann-Hilbert problem of dKP (i) to construct the longtime behaviour of the solutions of its Cauchy problem; (ii) to characterize a class of implicit solutions; (iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions of dKP, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking.
DEFF Research Database (Denmark)
Stolpe, Mathias; Bendsøe, Martin P.
2007-01-01
This paper present some initial results pertaining to a search for globally optimal solutions to a challenging benchmark example proposed by Zhou and Rozvany. This means that we are dealing with global optimization of the classical single load minimum compliance topology design problem with a fixed...... finite element discretization and with discrete design variables. Global optimality is achieved by the implementation of some specially constructed convergent nonlinear branch and cut methods, based on the use of natural relaxations and by applying strengthening constraints (linear valid inequalities...
1986-03-31
Martins, J.A.C. and Campos , L.T. [1986], "Existence and Local Uniqueness of Solutions to Contact Problems in Elasticity with Nonlinear Friction...noisy and ttoubl esome vibt.t4ons. If the sound generated by the friction-induced oscillations of Rviolin strings may be the delight of all music lovers...formulation. See 0den and Martins - [1985] and Rabier, Martins, Oden and Campos [1986]. - It is now simple to show, in a 6o’uman manner, that, for
International Nuclear Information System (INIS)
Vasileva, D.P.
1993-01-01
Blow-up and global time self-similar solutions of a boundary problem for a nonlinear equation u t = Δ u σ+1 + u β are found in the case β = σ + 1. It is shown that they describe the asymptotic behavior of a wide class of initial perturbations. A numerical investigation of the solutions in the case β>σ + 1 is also made. A hypothesis is done that the behavior for large times of global time solutions is described by the self-similar solutions of the equation without source.(author). 20 refs.; 9 figs
DEFF Research Database (Denmark)
Stolpe, Mathias; Bendsøe, Martin P.
2007-01-01
This paper present some initial results pertaining to a search for globally optimal solutions to a challenging benchmark example proposed by Zhou and Rozvany. This means that we are dealing with global optimization of the classical single load minimum compliance topology design problem with a fixed...... finite element discretization and with discrete design variables. Global optimality is achieved by the implementation of some specially constructed convergent nonlinear branch and cut methods, based on the use of natural relaxations and by applying strengthening constraints (linear valid inequalities......) and cuts....
Simandoux, Olivier; Prost, Amaury; Gateau, Jérôme; Bossy, Emmanuel
2015-03-01
In this work, we experimentally investigate thermal-based nonlinear photoacoustic generation as a mean to discriminate between different types of absorbing particles. The photoacoustic generation from solutions of dye molecules and gold nanospheres (same optical densities) was detected using a high frequency ultrasound transducer (20 MHz). Photoacoustic emission was observed with gold nanospheres at low fluence for an equilibrium temperature around 4 °C, where the linear photoacoustic effect in water vanishes, highlighting the nonlinear emission from the solution of nanospheres. The photoacoustic amplitude was also studied as a function of the equilibrium temperature from 2 °C to 20 °C. While the photoacoustic amplitude from the dye molecules vanished around 4 °C, the photoacoustic amplitude from the gold nanospheres remained significant over the whole temperature range. Our preliminary results suggest that in the context of high frequency photoacoustic imaging, nanoparticles may be discriminated from molecular absorbers based on nanoscale temperature rises.
Energy Technology Data Exchange (ETDEWEB)
Heasler, Patrick G.; Posse, Christian; Hylden, Jeff L.; Anderson, Kevin K.
2007-06-13
This paper presents a nonlinear Bayesian regression algorithm for the purpose of detecting and estimating gas plume content from hyper-spectral data. Remote sensing data, by its very nature, is collected under less controlled conditions than laboratory data. As a result, the physics-based model that is used to describe the relationship between the observed remotesensing spectra, and the terrestrial (or atmospheric) parameters that we desire to estimate, is typically littered with many unknown "nuisance" parameters (parameters that we are not interested in estimating, but also appear in the model). Bayesian methods are well-suited for this context as they automatically incorporate the uncertainties associated with all nuisance parameters into the error estimates of the parameters of interest. The nonlinear Bayesian regression methodology is illustrated on realistic simulated data from a three-layer model for longwave infrared (LWIR) measurements from a passive instrument. This shows that this approach should permit more accurate estimation as well as a more reasonable description of estimate uncertainty.
Nonlinear thermally induced distortions of a laser beam in a cryogenic disk amplifier
International Nuclear Information System (INIS)
Vyatkin, A G; Khazanov, Efim A
2009-01-01
Taking into account the temperature dependences of the heat conductivity, the refractive index, and the thermal expansion coefficient, we calculated the temperature, elastic stresses, a thermally induced lens and depolarisation of a beam in a cryogenic disk amplifier (an Yb:YAG disk placed between a copper cylinder and a sapphire disk cooled by liquid nitrogen). When the active element (the thickness is 0.6 mm, the orientation is [001], the atomic concentration of Yb is 10%) is pumped by radiation from a diode laser (the beam diameter is 6 mm), the temperature does not exceed 140 K for the heat release power of 100 W. In this case, elastic stresses in the active element are six times lower than the maximum permissible value. The focal distance of the thermally induced lens is 5.5 m and the depolarisation rate is 0.038% per two passes through the active element. Although the heat conductivity of the active element rapidly decreases with temperature, the thermal load can be increased by 1.5-2 times when the dimensions of the active element remain constant. (active media)
Yu, Yi; Wu, Yonggang; Hu, Binqi; Liu, Xinglong
2018-01-01
The dispatching of hydro-thermal system is a nonlinear programming problem with multiple constraints and high dimensions and the solution techniques of the model have been a hotspot in research. Based on the advantage of that the artificial bee colony algorithm (ABC) can efficiently solve the high-dimensional problem, an improved artificial bee colony algorithm has been proposed to solve DHTS problem in this paper. The improvements of the proposed algorithm include two aspects. On one hand, local search can be guided in efficiency by the information of the global optimal solution and its gradient in each generation. The global optimal solution improves the search efficiency of the algorithm but loses diversity, while the gradient can weaken the loss of diversity caused by the global optimal solution. On the other hand, inspired by genetic algorithm, the nectar resource which has not been updated in limit generation is transformed to a new one by using selection, crossover and mutation, which can ensure individual diversity and make full use of prior information for improving the global search ability of the algorithm. The two improvements of ABC algorithm are proved to be effective via a classical numeral example at last. Among which the genetic operator for the promotion of the ABC algorithm's performance is significant. The results are also compared with those of other state-of-the-art algorithms, the enhanced ABC algorithm has general advantages in minimum cost, average cost and maximum cost which shows its usability and effectiveness. The achievements in this paper provide a new method for solving the DHTS problems, and also offer a novel reference for the improvement of mechanism and the application of algorithms.
Directory of Open Access Journals (Sweden)
Yi Yu
Full Text Available The dispatching of hydro-thermal system is a nonlinear programming problem with multiple constraints and high dimensions and the solution techniques of the model have been a hotspot in research. Based on the advantage of that the artificial bee colony algorithm (ABC can efficiently solve the high-dimensional problem, an improved artificial bee colony algorithm has been proposed to solve DHTS problem in this paper. The improvements of the proposed algorithm include two aspects. On one hand, local search can be guided in efficiency by the information of the global optimal solution and its gradient in each generation. The global optimal solution improves the search efficiency of the algorithm but loses diversity, while the gradient can weaken the loss of diversity caused by the global optimal solution. On the other hand, inspired by genetic algorithm, the nectar resource which has not been updated in limit generation is transformed to a new one by using selection, crossover and mutation, which can ensure individual diversity and make full use of prior information for improving the global search ability of the algorithm. The two improvements of ABC algorithm are proved to be effective via a classical numeral example at last. Among which the genetic operator for the promotion of the ABC algorithm's performance is significant. The results are also compared with those of other state-of-the-art algorithms, the enhanced ABC algorithm has general advantages in minimum cost, average cost and maximum cost which shows its usability and effectiveness. The achievements in this paper provide a new method for solving the DHTS problems, and also offer a novel reference for the improvement of mechanism and the application of algorithms.
On a non-linear problem posed by the temperature determination in an electrically heated plate
International Nuclear Information System (INIS)
Gerber, R.
1958-01-01
Let us consider a flat plate, electrically heated, with one face thermally insulated and the other face isothermal. It is shown that a two-dimensional perturbation of the insulated face has no influence on the temperature of this face. (author) [fr
Directory of Open Access Journals (Sweden)
Zulqurnain Sabir
2014-06-01
Full Text Available In this paper, computational intelligence technique are presented for solving multi-point nonlinear boundary value problems based on artificial neural networks, evolutionary computing approach, and active-set technique. The neural network is to provide convenient methods for obtaining useful model based on unsupervised error for the differential equations. The motivation for presenting this work comes actually from the aim of introducing a reliable framework that combines the powerful features of ANN optimized with soft computing frameworks to cope with such challenging system. The applicability and reliability of such methods have been monitored thoroughly for various boundary value problems arises in science, engineering and biotechnology as well. Comprehensive numerical experimentations have been performed to validate the accuracy, convergence, and robustness of the designed scheme. Comparative studies have also been made with available standard solution to analyze the correctness of the proposed scheme.
DEFF Research Database (Denmark)
Bendtsen, Claus; Nielsen, Ole Holm; Hansen, Lars Bruno
2001-01-01
The quantum mechanical ground state of electrons is described by Density Functional Theory, which leads to large minimization problems. An efficient minimization method uses a self-consistent field (SCF) solution of large eigenvalue problems. The iterative Davidson algorithm is often used, and we...
Continuous Dependence on Modeling in the Cauchy Problem for Nonlinear Elliptic Equations.
1987-04-01
problema di Cauchy per le equazione di tipo ellitico, Ann. Mat. Pura Appl., 46 (1958), pp. 131-153 [18] P. W. Schaefer, On the Cauchy problem for an...Continued) PP 438 PP 448 Fletcher, Jean W. Supply Problems in the Naval Reserve, Cymrot, Donald J., Military Retiremnt and Social Security: A 14 pp
Lesiak, Piotr; Budaszewski, Daniel; Bednarska, Karolina; Wójcik, Michał; Sobotka, Piotr; Chychłowski, Miłosz; Woliński, Tomasz R.
2017-05-01
In this work we studied a newly reported class of nonlinear effects observed in 5CB liquid crystals doped with gold nanoparticles (GNPs). The size of the GNP was determined by direct TEM imaging and by X-ray scattering of the diluted NP solution. GNPs was coated by thiols with the ratio of mesogenic to n-alkyl thiols varying from 1:2 to 1:1. The research involved comparing properties of both undoped and doped 5CB (nematic LC) by infiltrating LC cell and microholes of the photonic crystal fiber (PCF) separately. In our experiment the PCF fiber type LMA-10 made by NKT Photonics as host material has been used.
International Nuclear Information System (INIS)
Huang, C.-H.; Li, J.-X.
2006-01-01
A non-linear optimal control algorithm is examined in this study for the diffusion process of semiconductor materials. The purpose of this algorithm is to estimate an optimal control function such that the homogeneity of the concentration can be controlled during the diffusion process and the diffusion-induced stresses for the semiconductor materials can thus be reduced. The validation of this optimal control analysis utilizing the conjugate gradient method of minimization is analysed by using numerical experiments. Three different diffusion processing times are given and the corresponding optimal control functions are to be determined. Results show that the diffusion time can be shortened significantly by applying the optimal control function at the boundary and the homogeneity of the concentration is also guaranteed. This control function can be obtained within a very short CPU time on a Pentium III 600 MHz PC
Ganesh Kumar, K.; Rudraswamy, N. G.; Gireesha, B. J.; Krishnamurthy, M. R.
2017-09-01
Present exploration discusses the combined effect of viscous dissipation and Joule heating on three dimensional flow and heat transfer of a Jeffrey nanofluid in the presence of nonlinear thermal radiation. Here the flow is generated over bidirectional stretching sheet in the presence of applied magnetic field by accounting thermophoresis and Brownian motion of nanoparticles. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. These nonlinear ordinary differential equations are solved numerically by using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. Graphically results are presented and discussed for various parameters. Validation of the current method is proved by comparing our results with the existing results under limiting situations. It can be concluded that combined effect of Joule and viscous heating increases the temperature profile and thermal boundary layer thickness.
International Nuclear Information System (INIS)
Caroline, M. Lydia; Sankar, R.; Indirani, R.M.; Vasudevan, S.
2009-01-01
Good transparent bulk single crystals of L-alanine (nonlinear optical material) have been grown successfully by slow cooling technique from aqueous solution at pH value of 2.0. Optically transparent crystals with dimensions 2.4 cm x 1.2 cm x 1.6 cm, were grown by optimizing the growth parameters within a growth period of 2 weeks. The crystallinity of L-alanine crystal was confirmed by the powder X-ray diffraction study and diffraction peaks are indexed. The vibrational structure of the molecule is elucidated from FTIR spectra. The thermal behaviour of the grown crystal was investigated by thermogravimetric (TG) and differential thermal analyses (DTA) techniques in a nitrogen atmosphere. The result showed that the material starts decomposing at 297 deg. C. Its optical behaviour has been examined by UV-vis spectral analysis, which shows the absence of absorbance between the wavelengths ranging from 200 to 1200 nm. The NLO property was confirmed by the powder technique of Kurtz and Perry. The dielectric behaviour of the sample was also studied for the first time
A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise
Clason, Christian; Jin, Bangti
2012-01-01
-order condition. The convergence of the solution to the approximating problem as the smoothing parameter goes to zero is shown. A strategy for adaptively selecting the regularization parameter based on a balancing principle is suggested. The efficiency
International Nuclear Information System (INIS)
Dmitriy Y. Anistratov; Adrian Constantinescu; Loren Roberts; William Wieselquist
2007-01-01
This is a project in the field of fundamental research on numerical methods for solving the particle transport equation. Numerous practical problems require to use unstructured meshes, for example, detailed nuclear reactor assembly-level calculations, large-scale reactor core calculations, radiative hydrodynamics problems, where the mesh is determined by hydrodynamic processes, and well-logging problems in which the media structure has very complicated geometry. Currently this is an area of very active research in numerical transport theory. main issues in developing numerical methods for solving the transport equation are the accuracy of the numerical solution and effectiveness of iteration procedure. The problem in case of unstructured grids is that it is very difficult to derive an iteration algorithm that will be unconditionally stable
Solution for Nonlinear Three-Dimensional Intercept Problem with Minimum Energy
Directory of Open Access Journals (Sweden)
Henzeh Leeghim
2013-01-01
a minimum-energy application, which then generates both the desired initial interceptor velocity and the TOF for the minimum-energy transfer. The optimization problem is formulated by using the classical Lagrangian f and g coefficients, which map initial position and velocity vectors to future times, and a universal time variable x. A Newton-Raphson iteration algorithm is introduced for iteratively solving the problem. A generalized problem formulation is introduced for minimizing the TOF as part of the optimization problem. Several examples are presented, and the results are compared with the Hohmann transfer solution approaches. The resulting minimum-energy intercept solution algorithm is expected to be broadly useful as a starting iterative for applications spanning: targeting, rendezvous, interplanetary trajectory design, and so on.
IR-to-visible image upconverter under nonlinear crystal thermal gradient operation.
Maestre, H; Torregrosa, A J; Fernández-Pousa, C R; Capmany, J
2018-01-22
In this work we study the enhancement of the field-of-view of an infrared image up-converter by means of a thermal gradient in a PPLN crystal. Our work focuses on compact upconverters, in which both a short PPLN crystal length and high numerical aperture lenses are employed. We found a qualitative increase in both wavelength and angular tolerances, compared to a constant temperature upconverter, which makes it necessary a correct IR wavelength allocation in order to effectively increase the up-converted area.
Periaux, J.
1979-01-01
The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.
Solution of large nonlinear time-dependent problems using reduced coordinates
International Nuclear Information System (INIS)
Mish, K.D.
1987-01-01
This research is concerned with the idea of reducing a large time-dependent problem, such as one obtained from a finite-element discretization, down to a more manageable size while preserving the most-important physical behavior of the solution. This reduction process is motivated by the concept of a projection operator on a Hilbert Space, and leads to the Lanczos Algorithm for generation of approximate eigenvectors of a large symmetric matrix. The Lanczos Algorithm is then used to develop a reduced form of the spatial component of a time-dependent problem. The solution of the remaining temporal part of the problem is considered from the standpoint of numerical-integration schemes in the time domain. All of these theoretical results are combined to motivate the proposed reduced coordinate algorithm. This algorithm is then developed, discussed, and compared to related methods from the mechanics literature. The proposed reduced coordinate method is then applied to the solution of some representative problems in mechanics. The results of these problems are discussed, conclusions are drawn, and suggestions are made for related future research
Gardner, Robin P.; Xu, Libai
2009-10-01
The Center for Engineering Applications of Radioisotopes (CEAR) has been working for over a decade on the Monte Carlo library least-squares (MCLLS) approach for treating non-linear radiation analyzer problems including: (1) prompt gamma-ray neutron activation analysis (PGNAA) for bulk analysis, (2) energy-dispersive X-ray fluorescence (EDXRF) analyzers, and (3) carbon/oxygen tool analysis in oil well logging. This approach essentially consists of using Monte Carlo simulation to generate the libraries of all the elements to be analyzed plus any other required background libraries. These libraries are then used in the linear library least-squares (LLS) approach with unknown sample spectra to analyze for all elements in the sample. Iterations of this are used until the LLS values agree with the composition used to generate the libraries. The current status of the methods (and topics) necessary to implement the MCLLS approach is reported. This includes: (1) the Monte Carlo codes such as CEARXRF, CEARCPG, and CEARCO for forward generation of the necessary elemental library spectra for the LLS calculation for X-ray fluorescence, neutron capture prompt gamma-ray analyzers, and carbon/oxygen tools; (2) the correction of spectral pulse pile-up (PPU) distortion by Monte Carlo simulation with the code CEARIPPU; (3) generation of detector response functions (DRF) for detectors with linear and non-linear responses for Monte Carlo simulation of pulse-height spectra; and (4) the use of the differential operator (DO) technique to make the necessary iterations for non-linear responses practical. In addition to commonly analyzed single spectra, coincidence spectra or even two-dimensional (2-D) coincidence spectra can also be used in the MCLLS approach and may provide more accurate results.
Numerical solution of problems concerning the thermal convection of a variable-viscosity liquid
Zherebiatev, I. F.; Lukianov, A. T.; Podkopaev, Iu. L.
A stabilizing-correction scheme is constructed for integrating the fourth-order equation describing the dynamics of a viscous incompressible liquid. As an example, a solution is obtained to the problem of the solidification of a liquid in a rectangular region with allowance for convective energy transfer in the liquid phase as well as temperature-dependent changes of viscosity. It is noted that the proposed method can be used to study steady-state problems of thermal convection in ingots obtained through continuous casting.
ANISOTROPIC THERMAL CONDUCTION AND THE COOLING FLOW PROBLEM IN GALAXY CLUSTERS
International Nuclear Information System (INIS)
Parrish, Ian J.; Sharma, Prateek; Quataert, Eliot
2009-01-01
We examine the long-standing cooling flow problem in galaxy clusters with three-dimensional magnetohydrodynamics simulations of isolated clusters including radiative cooling and anisotropic thermal conduction along magnetic field lines. The central regions of the intracluster medium (ICM) can have cooling timescales of ∼200 Myr or shorter-in order to prevent a cooling catastrophe the ICM must be heated by some mechanism such as active galactic nucleus feedback or thermal conduction from the thermal reservoir at large radii. The cores of galaxy clusters are linearly unstable to the heat-flux-driven buoyancy instability (HBI), which significantly changes the thermodynamics of the cluster core. The HBI is a convective, buoyancy-driven instability that rearranges the magnetic field to be preferentially perpendicular to the temperature gradient. For a wide range of parameters, our simulations demonstrate that in the presence of the HBI, the effective radial thermal conductivity is reduced to ∼<10% of the full Spitzer conductivity. With this suppression of conductive heating, the cooling catastrophe occurs on a timescale comparable to the central cooling time of the cluster. Thermal conduction alone is thus unlikely to stabilize clusters with low central entropies and short central cooling timescales. High central entropy clusters have sufficiently long cooling times that conduction can help stave off the cooling catastrophe for cosmologically interesting timescales.
Atluri, S. N.; Nakagaki, M.; Kathiresan, K.
1980-01-01
In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.
Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities
Indian Academy of Sciences (India)
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 R R . Assuming the existence of an upper and of a lower ...
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.
Directory of Open Access Journals (Sweden)
Hongjian Wang
2014-01-01
Full Text Available We present a support vector regression-based adaptive divided difference filter (SVRADDF algorithm for improving the low state estimation accuracy of nonlinear systems, which are typically affected by large initial estimation errors and imprecise prior knowledge of process and measurement noises. The derivative-free SVRADDF algorithm is significantly simpler to compute than other methods and is implemented using only functional evaluations. The SVRADDF algorithm involves the use of the theoretical and actual covariance of the innovation sequence. Support vector regression (SVR is employed to generate the adaptive factor to tune the noise covariance at each sampling instant when the measurement update step executes, which improves the algorithm’s robustness. The performance of the proposed algorithm is evaluated by estimating states for (i an underwater nonmaneuvering target bearing-only tracking system and (ii maneuvering target bearing-only tracking in an air-traffic control system. The simulation results show that the proposed SVRADDF algorithm exhibits better performance when compared with a traditional DDF algorithm.
Hall, Philip
1989-01-01
Goertler vortices are thought to be the cause of transition in many fluid flows of practical importance. A review of the different stages of vortex growth is given. In the linear regime, nonparallel effects completely govern this growth, and parallel flow theories do not capture the essential features of the development of the vortices. A detailed comparison between the parallel and nonparallel theories is given and it is shown that at small vortex wavelengths, the parallel flow theories have some validity; otherwise nonparallel effects are dominant. New results for the receptivity problem for Goertler vortices are given; in particular vortices induced by free stream perturbations impinging on the leading edge of the walls are considered. It is found that the most dangerous mode of this type can be isolated and it's neutral curve is determined. This curve agrees very closely with the available experimental data. A discussion of the different regimes of growth of nonlinear vortices is also given. Again it is shown that, unless the vortex wavelength is small, nonparallel effects are dominant. Some new results for nonlinear vortices of 0(1) wavelengths are given and compared to experimental observations.
Czech Academy of Sciences Publication Activity Database
Mukhigulashvili, Sulkhan
-, č. 35 (2015), s. 23-50 ISSN 1126-8042 Institutional support: RVO:67985840 Keywords : higher order functional differential equations * Dirichlet boundary value problem * strong singularity Subject RIV: BA - General Mathematics http://ijpam.uniud.it/online_issue/201535/03-Mukhigulashvili.pdf
Primal and Dual Penalty Methods for Contact Problems with Geometrical Non-linearities
Czech Academy of Sciences Publication Activity Database
Vondrák, V.; Dostál, Z.; Dobiáš, Jiří; Pták, Svatopluk
-, č. 5 (2005), s. 449-450 ISSN 1617-7061. [GAMM Annual Meeting 2005. Luxembourg, 28.03.2005-01.04.2005] R&D Projects: GA ČR(CZ) GA101/05/0423 Institutional research plan: CEZ:AV0Z20760514 Keywords : primal penalty * dual penalty * contact problem Subject RIV: BA - General Mathematics
Combined effects of changing-sign potential and critical nonlinearities in Kirchhoff type problems
Directory of Open Access Journals (Sweden)
Gao-Sheng Liu
2016-08-01
Full Text Available In this article, we study the existence and multiplicity of positive solutions for a class of Kirchhoff type problems involving changing-sign potential and critical growth terms. Using the concentration compactness principle and Nehari manifold, we obtain the existence and multiplicity of nonzero non-negative solutions.
Linear, non-linear and thermal properties of single crystal of LHMHCl
Kulshrestha, Shobha; Shrivastava, A. K.
2018-05-01
The single crystal of amino acid of L-histidine monohydrochloride was grown by slow evaporation technique at room temperature. High optical quality and appropriate size of crystals were grown under optimized growth conditions. The grown crystals were transparent. Crystals are characterized with different characterizations such as Solubility test, UV-Visible, optical band gap (Eg). With the help of optical data to be calculate absorption coefficient (α), extinction coefficient (k), refractive index (n), dielectric constant (ɛ). These optical constants are shows favorable conditions for photonics devices. Second harmonic generation (NLO) test show the green light emission which is confirm that crystal have properties for laser application. Thermal stability of grown crystal is confirmed by TG/DTA.
Gasinski, Leszek
2005-01-01
Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.
Directory of Open Access Journals (Sweden)
Jiuping Xu
2012-01-01
Full Text Available The aim of this study is to deal with a minimum cost network flow problem (MCNFP in a large-scale construction project using a nonlinear multiobjective bilevel model with birandom variables. The main target of the upper level is to minimize both direct and transportation time costs. The target of the lower level is to minimize transportation costs. After an analysis of the birandom variables, an expectation multiobjective bilevel programming model with chance constraints is formulated to incorporate decision makers’ preferences. To solve the identified special conditions, an equivalent crisp model is proposed with an additional multiobjective bilevel particle swarm optimization (MOBLPSO developed to solve the model. The Shuibuya Hydropower Project is used as a real-world example to verify the proposed approach. Results and analysis are presented to highlight the performances of the MOBLPSO, which is very effective and efficient compared to a genetic algorithm and a simulated annealing algorithm.
Energy Technology Data Exchange (ETDEWEB)
Cobb, J.W.
1995-02-01
There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.
Non-linear singular problems in p-adic analysis: associative algebras of p-adic distributions
International Nuclear Information System (INIS)
Albeverio, S; Khrennikov, A Yu; Shelkovich, V M
2005-01-01
We propose an algebraic theory which can be used for solving both linear and non-linear singular problems of p-adic analysis related to p-adic distributions (generalized functions). We construct the p-adic Colombeau-Egorov algebra of generalized functions, in which Vladimirov's pseudo-differential operator plays the role of differentiation. This algebra is closed under Fourier transformation and associative convolution. Pointvalues of generalized functions are defined, and it turns out that any generalized function is uniquely determined by its pointvalues. We also construct an associative algebra of asymptotic distributions, which is generated by the linear span of the set of associated homogeneous p-adic distributions. This algebra is embedded in the Colombeau-Egorov algebra as a subalgebra. In addition, a new technique for constructing weak asymptotics is developed
International Nuclear Information System (INIS)
Gardner, R.P.; Guo, P.; Sood, A.; Mayo, C.W.; Dobbs, C.L.
1998-01-01
A review of our work on the application of the PGNAA method as applied to five industrial applications is given. Some introductory material is first given on the importance and use of Monte Carlo simulation in this area, some comments on the place of PGNAA in elemental analysis, and a brief description of the Monte Carlo - Library Least-Squares (MCLLS) approach to the nonlinear inverse PGNAA analysis problem. Then the applications of PGNAA are discussed for: (1) on-line bulk coal analysis, (2) nuclear oil well logging, (3) vitrified waste, (4) the analysis of sodium and aluminium in 'green liquor' in the presence of chlorine, and (5) the conveyor belt sorting of aluminum alloy samples. It is concluded that PGNAA is a rapidly emerging important new technology and measurement approach. (author)
Kamali, M.; Shamsi, M.; Saidi, A. R.
2018-03-01
As a first endeavor, the effect of nonlinear elastic foundation on the postbuckling behavior of smart magneto-electro-elastic (MEE) composite nanotubes is investigated. The composite nanotube is affected by a non-uniform thermal environment. A typical MEE composite nanotube consists of microtubules (MTs) and carbon nanotubes (CNTs) with a MEE cylindrical nanoshell for smart control. It is assumed that the nanoscale layers of the system are coupled by a polymer matrix or filament network depending on the application. In addition to thermal loads, magneto-electro-mechanical loads are applied to the composite nanostructure. Length scale effects are taken into account using the nonlocal elasticity theory. The principle of virtual work and von Karman's relations are used to derive the nonlinear governing differential equations of MEE CNT-MT nanotubes. Using Galerkin's method, nonlinear critical buckling loads are determined. Various types of non-uniform temperature distribution in the radial direction are considered. Finally, the effects of various parameters such as the nonlinear constant of elastic medium, thermal loading factor and small scale coefficient on the postbuckling of MEE CNT-MT nanotubes are studied.
Pasekov, V P
2013-03-01
The paper considers the problems in the adaptive evolution of life-history traits for individuals in the nonlinear Leslie model of age-structured population. The possibility to predict adaptation results as the values of organism's traits (properties) that provide for the maximum of a certain function of traits (optimization criterion) is studied. An ideal criterion of this type is Darwinian fitness as a characteristic of success of an individual's life history. Criticism of the optimization approach is associated with the fact that it does not take into account the changes in the environmental conditions (in a broad sense) caused by evolution, thereby leading to losses in the adequacy of the criterion. In addition, the justification for this criterion under stationary conditions is not usually rigorous. It has been suggested to overcome these objections in terms of the adaptive dynamics theory using the concept of invasive fitness. The reasons are given that favor the application of the average number of offspring for an individual, R(L), as an optimization criterion in the nonlinear Leslie model. According to the theory of quantitative genetics, the selection for fertility (that is, for a set of correlated quantitative traits determined by both multiple loci and the environment) leads to an increase in R(L). In terms of adaptive dynamics, the maximum R(L) corresponds to the evolutionary stability and, in certain cases, convergent stability of the values for traits. The search for evolutionarily stable values on the background of limited resources for reproduction is a problem of linear programming.
Umbarkar, A. J.; Balande, U. T.; Seth, P. D.
2017-06-01
The field of nature inspired computing and optimization techniques have evolved to solve difficult optimization problems in diverse fields of engineering, science and technology. The firefly attraction process is mimicked in the algorithm for solving optimization problems. In Firefly Algorithm (FA) sorting of fireflies is done by using sorting algorithm. The original FA is proposed with bubble sort for ranking the fireflies. In this paper, the quick sort replaces bubble sort to decrease the time complexity of FA. The dataset used is unconstrained benchmark functions from CEC 2005 [22]. The comparison of FA using bubble sort and FA using quick sort is performed with respect to best, worst, mean, standard deviation, number of comparisons and execution time. The experimental result shows that FA using quick sort requires less number of comparisons but requires more execution time. The increased number of fireflies helps to converge into optimal solution whereas by varying dimension for algorithm performed better at a lower dimension than higher dimension.
Efficient Non-Linear Finite Element Implementation of Elasto-Plasticity for Geotechnical Problems
DEFF Research Database (Denmark)
Clausen, Johan
-Coulomb yield criterion and the corresponding plastic potential possess corners and an apex, which causes numerical difficulties. A simple, elegant and efficient solution to these problems is presented in this thesis. The solution is based on a transformation into principal stress space and is valid for all...... linear isotropic plasticity models in which corners and apexes are encountered. The validity and merits of the proposed solution are examined in relation to the Mohr-Coulomb and the Modified Mohr-Coulomb material models. It is found that the proposed method compares well with existing methods......-Brown material. The efficiency and validity are demonstrated by comparing the finite-element results with well-known solutions for simple geometries. A common geotechnical problem is the assessment of slope stability. For slopes with simple geometries and consisting of a linear Mohr-Coulomb material, this can...
A nonlinear free boundary problem with a self-driven Bernoulli condition
Dipierro, Serena; Karakhanyan, Aram; Valdinoci, Enrico
2017-01-01
We study a Bernoulli type free boundary problem with two phases J[u]=∫Ω|∇u(x)|2dx+Φ(M−(u),M+(u)),u−u¯∈W1,20(Ω), where u¯∈W1,2(Ω) is a given boundary datum. Here, M1 and M2 are weighted volumes of {u≤0}∩Ω and {u>0}∩Ω, respectively, and Φ is a nonnegative function of two real variables. We show that, for this problem, the Bernoulli constant, which determines the gradient jump condition across the free boundary, is of global type and it is indeed determined by the weighted volumes of the phas...
On Algorithms for Nonlinear Minimax and Min-Max-Min Problems and Their Efficiency
2011-03-01
dissertation is complete, I can finally stay home after dinner to play Wii with you. LET’S GO Mario and Yellow Mushroom... xv THIS PAGE INTENTIONALLY... balance the accuracy of the approximation with problem ill-conditioning. The sim- plest smoothing algorithm creates an accurate smooth approximating...sizing in electronic circuit boards (Chen & Fan, 1998), obstacle avoidance for robots (Kirjner- Neto & Polak, 1998), optimal design centering
Contribution to the study of thermal-hydraulic problems in nuclear reactors
International Nuclear Information System (INIS)
Cognet, G.
1998-01-01
In nuclear reactors, whatever the type considered, Pressurized Water Water Reactors (PWRs), Fast Breeder reactors (FBRs)..., thermal-hydraulics, the science of fluid mechanics and thermal behaviour, plays an essential role, both in nominal operating and accidental conditions. Fluid can either be the primary fluid (liquid or gas) or a very specific fluid called corium, which, in case of severe accident, could result from core and environning structure melting. The work reported here represents a 20-year contribution to thermal-hydraulic issues which could occur in FBRs and PWRs. Working on these two types of reactors, both in nominal and severe accident situations, has allowed me to compare the problems and to realize the importance of communication between research teams. The evolution in the complexity of studied problems, unavoidable in order to reduce costs and significantly improve safety, has led me from numerical modelling of single-phase flow turbulence to high temperature real melt experiments. The difficulties encountered in understanding the observed phenomena and in increasing experimental databases for computer code qualification have often entailed my participation in specific measurement device developments or adaptations, in particular non-intrusive devices generally based on optical techniques. Being concerned about the end-use of this research work, I actively participated in 'in-situ' thermalhydraulic experiments in the FBRs: Phenix and Super-Phenix, of which I appreciated their undeniable scientific contribution. In my opinion, the thermal-hydraulic questions related to severe accidents are the most complex as they are at the cross-roads of several scientific specialities. Consequently, they require a multi-disciplinary approach and a continuous see-saw motion between experimentalists and modelling teams. After a brief description of the various problems encountered, the main ones are reported. Finally, the importance for research teams to
International Nuclear Information System (INIS)
Blanc, Gilles
1996-01-01
This work is devoted to the solution of the inverse multidimensional heat conduction problem. The first part is the determination of a methodology for determining the minimum number of sensors and the best sensor locations. The method is applied to a 20 problem but the extension to 30 problems is quite obvious. This methodology is based on the study of the rate of representation. This new concept allows to determine the quantity and the quality of the information obtain from the various sensors. The rate of representation is a useful tool for experimental design. lt can be determined very quickly by the transposed matrix method. This approach was validated with an experimental set-up. The second part is the development of a method that uses thermal strain measurement instead of temperature measurements to estimate the unknown thermal boundary conditions. We showed that this new sensor has two advantages in comparison with the classical temperature measurements: higher frequency can be estimated and smaller number of sensors can be used for 20 problems. The main weakness is, presently, the fact that the method can only be applied to beams. The results obtained from the numerical simulations were validated by the analysis of experimental data obtained on an experimental set-up especially designed and built for this study. (author) [fr
An efficient chaos embedded hybrid approach for hydro-thermal unit commitment problem
International Nuclear Information System (INIS)
Yuan, Xiaohui; Ji, Bin; Yuan, Yanbin; Ikram, Rana M.; Zhang, Xiaopan; Huang, Yuehua
2015-01-01
Highlights: • Thermal unit commitment is considered in hydrothermal generation scheduling (SHTGS). • Two newly proposed promising optimization algorithms are combined to solving SHTGS. • The proposed method is enhanced by integrating a chaotic local search strategy. • Heuristic search strategies are applied to handle the constraints of the SHTGS. • The results verify the proposed method is feasible and efficient for handling SHTGS. - Abstract: This paper establishes a model to deal with the short-term hydrothermal generation scheduling (SHTGS) problem. The problem is composed of three interconnected parts: short-term hydrothermal coordination, thermal unit commitment and economic load dispatch. An efficient hybrid method composed of chaotic backtracking search optimization algorithm and binary charged system search algorithm (CBSA–BCSS) is proposed to solve this problem. In order to analyze the effect of the chaotic map on the performance of the method, three different chaotic maps are adopted to integrate into the proposed method and the corresponding consequences are achieved. Furthermore, efficient heuristic search strategies are adopted to handle with the complicated constraints of the SHTGS system. Finally, a hydrothermal unit commitment system is utilized to verify the feasibility and effectiveness of the proposed method. The results demonstrate the efficiency of the hybrid optimization method and the appropriation of the constraint handling strategies. The comparison of the solutions achieved by different methods shows that the proposed method has higher efficiency in terms of solving SHTGS problem
International Nuclear Information System (INIS)
Diaz, J. I.; Galiano, G.; Padial, J. F.
1999-01-01
We study the uniqueness of solutions of a semilinear elliptic problem obtained from an inverse formulation when the nonlinear terms of the equation are prescribed in a general class of real functions. The inverse problem arises in the modeling of the magnetic confinement of a plasma in a Stellarator device. The uniqueness proof relies on an L ∞ -estimate on the solution of an auxiliary nonlocal problem formulated in terms of the relative rearrangement of a datum with respect to the solution
CSIR Research Space (South Africa)
Mhlongo, MD
2014-05-01
Full Text Available and heat transfer coefficient.This work has been extended in [11] whereby the introduction of the Kirchhoff transformation linearized the one-dimensional fin problem when heat transfer is a differential consequence of thermal conductivity. Symmetry methods... 𝑥 ( 𝜉 ) , 𝜁 𝑥𝑥 = 𝐷 𝑥 (𝜁 𝑥 ) − 𝜃 𝐷 𝑥 ( 𝜉 ) , (46) 10 Advances in Mathematical Physics Table 10: Lie bracket of the admitted symmetry algebra for𝑚 ̸= 𝑛, 𝑛 ̸= − 1 and various 𝑓(𝑥). 𝑓(𝑥) = 𝑥 𝑎 𝑎 = 0 𝑛 arbitrary 𝑓(𝑥) = 𝑥𝑎...
The inverse problem of determining several coefficients in a nonlinear Lotka–Volterra system
International Nuclear Information System (INIS)
Roques, Lionel; Cristofol, Michel
2012-01-01
In this paper, we prove a uniqueness result in the inverse problem of determining several non-constant coefficients of a system of two parabolic equations, which corresponds to a Lotka–Volterra competition model. Our result gives a sufficient condition for the uniqueness of the determination of four coefficients of the system. This sufficient condition only involves pointwise measurements of the solution (u, v) of the system and of the spatial derivative ∂u/∂x or ∂v/∂x of one component at a single point x 0 , during a time interval (0, ε). Our results are illustrated by numerical computations. (paper)
Blow up of solutions to ordinary differential equations arising in nonlinear dispersive problems
Directory of Open Access Journals (Sweden)
Milena Dimova
2018-03-01
Full Text Available We study a new class of ordinary differential equations with blow up solutions. Necessary and sufficient conditions for finite blow up time are proved. Based on the new differential equation, a revised version of the concavity method of Levine is proposed. As an application we investigate the non-existence of global solutions to the Cauchy problem of Klein-Gordon, and to the double dispersive equations. We obtain necessary and sufficient condition for finite time blow up with arbitrary positive energy. A very general sufficient condition for blow up is also given.
Strictly positive solutions for one-dimensional nonlinear problems involving the p-Laplacian
Kaufmann, Uriel; Medri, Ivan
2013-01-01
Let $\\Omega$ be a bounded open interval, and let $p>1$ and $q\\in\\left(0,p-1\\right) $. Let $m\\in L^{p^{\\prime}}\\left(\\Omega\\right) $ and $0\\leq c\\in L^{\\infty}\\left(\\Omega\\right) $. We study existence of strictly positive solutions for elliptic problems of the form $-\\left(\\left\\| u^{\\prime}\\right\\|^{p-2}u^{\\prime}\\right) ^{\\prime}+c\\left(x\\right) u^{p-1}=m\\left(x\\right) u^{q}$ in $\\Omega$, $u=0$ on $\\partial\\Omega$. We mention that our results are new even in the case $c\\equiv0$.
Modeling nonlinear problems in the mechanics of strings and rods the role of the balance laws
O'Reilly, Oliver M
2017-01-01
This book presents theories of deformable elastic strings and rods and their application to broad classes of problems. Readers will gain insights into the formulation and analysis of models for mechanical and biological systems. Emphasis is placed on how the balance laws interplay with constitutive relations to form a set of governing equations. For certain classes of problems, it is shown how a balance of material momentum can play a key role in forming the equations of motion. The first half of the book is devoted to the purely mechanical theory of a string and its applications. The second half of the book is devoted to rod theories, including Euler’s theory of the elastica, Kirchhoff ’s theory of an elastic rod, and a range of Cosserat rod theories. A variety of classic and recent applications of these rod theories are examined. Two supplemental chapters, the first on continuum mechanics of three-dimensional continua and the second on methods from variational calculus, are included to provide relevant ...
Umarani, P.; Jagannathan, K.
2018-02-01
The Potassium hexachloro cadmate (IV) (PHC) single crystal was grown from the aqueous of the solution by a controlled evaporation method. Single crystal XRD solved the structure. FTIR is used to identify the functional groups of grown crystal. The UV-Vis-NIR spectrometer was used to find out the UV cut off region and to calculate the optical band gap of the Potassium hexachloro cadmate (IV) single crystal. The EDAX spectrum has been used to identify the compounds present in title compound. The TG-DTA profile shows the thermal stability of the grown crystal of Potassium hexachloro cadmate (IV). The Vicker's hardness measurement was used to calculate the material hardness of the title compound. The dielectric loss and constant varied with frequencies and activation energy is also calculated. The solid state parameters like plasma energy, Penn gap, Fermi energy, electronic polarizability using Penn analysis and Clausius-Mossotti equation were also calculated for the title compound. The Z-scan technique is used to calculate the third order nonlinear susceptibility of a real and imaginary part.
Sudhakar, K.; Nandhini, S.; Muniyappan, S.; Arumanayagam, T.; Vivek, P.; Murugakoothan, P.
2018-04-01
Ammonium sulfate hydrogen sulphamate (ASHS), an inorganic nonlinear optical crystal, was grown from the aqueous solution by slow evaporation solution growth technique. The single-crystal XRD confirms that the grown single crystal belongs to the orthorhombic system with the space group of Pna21. Powder XRD confirms the crystalline nature and the diffraction planes were indexed. Crystalline perfection of grown crystal was analysed by high-resolution X-ray diffraction rocking curve technique. UV-Vis-NIR studies revealed that ASHS crystal has optical transparency 65% and lower cut-off wavelength at 218 nm. The violet light emission of the crystal was identified by photoluminescence studies. The particle size-dependent second-harmonic generation efficiency for ASHS crystal was evaluated by Kurtz-Perry powder technique using Nd:YAG laser which established the existence of phase matching. Surface laser damage threshold value was evaluated using Nd:YAG laser. Optical homogeneity of the crystal was evaluated using modified channel spectrum method through birefringence study. Thermal analysis reveals that ASHS crystal is stable up to 213 °C. The mechanical behaviour of the ASHS crystal was analysed using Vickers microhardness study.
International Nuclear Information System (INIS)
Snider, D.M.
1981-02-01
INVERT 1.0 is a digital computer program written in FORTRAN IV which calculates the surface heat flux of a one-dimensional solid using an interior-measured temperature and a physical description of the solid. By using two interior-measured temperatures, INVERT 1.0 can provide a solution for the heat flux at two surfaces, the heat flux at a boundary and the time dependent power, or the heat flux at a boundary and the time varying thermal conductivity of a material composing the solid. The analytical solution to inversion problem is described for the one-dimensional cylinder, sphere, or rectangular slab. The program structure, input instructions, and sample problems demonstrating the accuracy of the solution technique are included
International Nuclear Information System (INIS)
Carlson, K.E.; Ransom, V.H.; Roth, P.A.
1987-03-01
The ATHENA (Advanced Thermal Hydraulic Energy Network Analyzer) code has been developed to perform transient simulation of the thermal hydraulic systems that may be found in fusion reactors, space reactors, and other advanced systems. As an assessment of current capability the code was applied to a number of physical problems, both conceptual and actual experiments. Results indicate that the numerical solution to the basic conservation equations is technically sound, and that generally good agreement can be obtained when modeling relevant hydrodynamic experiments. The assessment also demonstrates basic fusion system modeling capability and verifies compatibility of the code with both CDC and CRAY mainframes. Areas where improvements could be made include constitutive modeling, which describes the interfacial exchange term. 13 refs., 84 figs
DEFF Research Database (Denmark)
Sorokin, Vladislav; Thomsen, Jon Juel
2015-01-01
Parametrically excited systems appear in many fields of science and technology, intrinsically or imposed purposefully; e.g. spatially periodic structures represent an important class of such systems [4]. When the parametric excitation can be considered weak, classical asymptotic methods like...... the method of averaging [2] or multiple scales [6] can be applied. However, with many practically important applications this simplification is inadequate, e.g. with spatially periodic structures it restricts the possibility to affect their effective dynamic properties by a structural parameter modulation...... of considerable magnitude. Approximate methods based on Floquet theory [4] for analyzing problems involving parametric excitation, e.g. the classical Hill’s method of infinite determinants [3,4], can be employed also in cases of strong excitation; however, with Floquet theory being applicable only for linear...
Xu, Y; Li, N
2014-09-01
Biological species have produced many simple but efficient rules in their complex and critical survival activities such as hunting and mating. A common feature observed in several biological motion strategies is that the predator only moves along paths in a carefully selected or iteratively refined subspace (or manifold), which might be able to explain why these motion strategies are effective. In this paper, a unified linear algebraic formulation representing such a predator-prey relationship is developed to simplify the construction and refinement process of the subspace (or manifold). Specifically, the following three motion strategies are studied and modified: motion camouflage, constant absolute target direction and local pursuit. The framework constructed based on this varying subspace concept could significantly reduce the computational cost in solving a class of nonlinear constrained optimal trajectory planning problems, particularly for the case with severe constraints. Two non-trivial examples, a ground robot and a hypersonic aircraft trajectory optimization problem, are used to show the capabilities of the algorithms in this new computational framework.
International Nuclear Information System (INIS)
Xu, Y; Li, N
2014-01-01
Biological species have produced many simple but efficient rules in their complex and critical survival activities such as hunting and mating. A common feature observed in several biological motion strategies is that the predator only moves along paths in a carefully selected or iteratively refined subspace (or manifold), which might be able to explain why these motion strategies are effective. In this paper, a unified linear algebraic formulation representing such a predator–prey relationship is developed to simplify the construction and refinement process of the subspace (or manifold). Specifically, the following three motion strategies are studied and modified: motion camouflage, constant absolute target direction and local pursuit. The framework constructed based on this varying subspace concept could significantly reduce the computational cost in solving a class of nonlinear constrained optimal trajectory planning problems, particularly for the case with severe constraints. Two non-trivial examples, a ground robot and a hypersonic aircraft trajectory optimization problem, are used to show the capabilities of the algorithms in this new computational framework. (paper)
Hamilton, Mark F.
1989-08-01
Four projects are discussed in this annual summary report, all of which involve basic research in nonlinear acoustics: Scattering of Sound by Sound, a theoretical study of two nonconlinear Gaussian beams which interact to produce sum and difference frequency sound; Parametric Receiving Arrays, a theoretical study of parametric reception in a reverberant environment; Nonlinear Effects in Asymmetric Sound Beams, a numerical study of two dimensional finite amplitude sound fields; and Pulsed Finite Amplitude Sound Beams, a numerical time domain solution of the KZK equation.
Data-driven non-linear elasticity: constitutive manifold construction and problem discretization
Ibañez, Ruben; Borzacchiello, Domenico; Aguado, Jose Vicente; Abisset-Chavanne, Emmanuelle; Cueto, Elias; Ladeveze, Pierre; Chinesta, Francisco
2017-11-01
The use of constitutive equations calibrated from data has been implemented into standard numerical solvers for successfully addressing a variety problems encountered in simulation-based engineering sciences (SBES). However, the complexity remains constantly increasing due to the need of increasingly detailed models as well as the use of engineered materials. Data-Driven simulation constitutes a potential change of paradigm in SBES. Standard simulation in computational mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy,\\ldots ), whereas the second one consists of models that scientists have extracted from collected, either natural or synthetic, data. Data-driven (or data-intensive) simulation consists of directly linking experimental data to computers in order to perform numerical simulations. These simulations will employ laws, universally recognized as epistemic, while minimizing the need of explicit, often phenomenological, models. The main drawback of such an approach is the large amount of required data, some of them inaccessible from the nowadays testing facilities. Such difficulty can be circumvented in many cases, and in any case alleviated, by considering complex tests, collecting as many data as possible and then using a data-driven inverse approach in order to generate the whole constitutive manifold from few complex experimental tests, as discussed in the present work.
Mixed gradient-Tikhonov methods for solving nonlinear ill-posed problems in Banach spaces
International Nuclear Information System (INIS)
Margotti, Fábio
2016-01-01
Tikhonov regularization is a very useful and widely used method for finding stable solutions of ill-posed problems. A good choice of the penalization functional as well as a careful selection of the topologies of the involved spaces is fundamental to the quality of the reconstructions. These choices can be combined with some a priori information about the solution in order to preserve desired characteristics like sparsity constraints for example. To prove convergence and stability properties of this method, one usually has to assume that a minimizer of the Tikhonov functional is known. In practical situations however, the exact computation of a minimizer is very difficult and even finding an approximation can be a very challenging and expensive task if the involved spaces have poor convexity or smoothness properties. In this paper we propose a method to attenuate this gap between theory and practice, applying a gradient-like method to a Tikhonov functional in order to approximate a minimizer. Using only available information, we explicitly calculate a maximal step-size which ensures a monotonically decreasing error. The resulting algorithm performs only finitely many steps and terminates using the discrepancy principle. In particular the knowledge of a minimizer or even its existence does not need to be assumed. Under standard assumptions, we prove convergence and stability results in relatively general Banach spaces, and subsequently, test its performance numerically, reconstructing conductivities with sparsely located inclusions and different kinds of noise in the 2D electrical impedance tomography. (paper)
Zhai, Chengbo; Hao, Mengru
2014-01-01
By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by -D(0+)(ν1)y1(t) = λ1a1(t)f(y1(t), y2(t)), - D(0+)(ν2)y2(t) = λ2a2(t)g(y1(t), y2(t)), where D(0+)(ν) is the standard Riemann-Liouville fractional derivative, ν1, ν2 ∈ (n - 1, n] for n > 3 and n ∈ N, subject to the boundary conditions y1((i))(0) = 0 = y ((i))(0), for 0 ≤ i ≤ n - 2, and [D(0+)(α)y1(t)] t=1 = 0 = [D(0+ (α)y2(t)] t=1, for 1 ≤ α ≤ n - 2, or y1((i))(0) = 0 = y ((i))(0), for 0 ≤ i ≤ n - 2, and [D(0+)(α)y1(t)] t=1 = ϕ1(y1), [D(0+)(α)y2(t)] t=1 = ϕ2(y2), for 1 ≤ α ≤ n - 2, ϕ1, ϕ2 ∈ C([0,1], R). Our results are new and complement previously known results. As an application, we also give an example to demonstrate our result.
Barashkov, M. S.; Bel'dyugin, Igor'M.; Zolotarev, M. V.; Kruzhilin, Yu I.; Krymskiĭ, M. I.; Oshkin, S. P.; Starkov, G. S.; Umnov, A. F.; Kharchenko, M. A.
1989-04-01
A four-wave mirror exhibiting a thermal nonlinearity was used in a study of the interaction of concurrent waves under parametric feedback conditions in the presence of a nonreciprocal element. Strong reflection of a series of pulses of ~ 300 ns duration from a neodymium glass laser was demonstrated: the maximum reflection coefficient was in excess of 30. An analysis was made of the quality of the radiation reflected from this four-mirror parametric feedback system. A considerable reduction was observed in the steady-state threshold for the operation of this mirror with a thermal nonlinearity when the angles of convergence of the interacting beams were small compared with the case of head-on collision of the waves.
Chichirova, N. D.; Chichirov, A. A.; Saitov, S. R.
2017-11-01
The introduction of baromembrane water treatment technologies for water desalination at Russian thermal power plants was beganed more than 25 years ago. These technologies have demonstrated their definite advantage over the traditional technologies of additional water treatment for steam boilers. However, there are problems associated with the reliability and economy of their work. The first problem is a large volume of waste water (up to 60% of the initial water). The second problem a expensive and unique chemical reagents complex (biocides, antiscalants, washing compositions) is required for units stable and troublefree operation. Each manufacturer develops his own chemical composition for a certain membrane type. This leads to a significant increase in reagents cost, as well as creates dependence of the technology consumer on the certain supplier. The third problem is that the reliability of the baromembrane units depends directly on the water preliminary treatment. The popular pre-cleaning technology with coagulation of aluminum oxychloride proves to be unacceptable during seasonal changes in the quality of the source water at a number of stations. As a result, pollution, poisoning and lesion of the membrane structure or deterioration of their mechanical properties are observed. The report presents ways to solve these problems.
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Chaudhari Virendra Kumar
2017-01-01
Full Text Available This paper deals with the investigation of nonlinear free vibration behavior of elastically supported carbon nanotube reinforced composite (CNTRC beam subjected to thermal loading with random system properties. Material properties of each constituent’s material, volume fraction exponent and foundation parameters are considered as uncorrelated Gaussian random input variables. The beam is supported by a Pasternak foundation with Winkler cubic nonlinearity. The higher order shear deformation theory (HSDT with von-Karman non-linearity is used to formulate the governing equation using Hamilton principle. Convergence and validation study is carried out through the comparison with the available results in the literature for authenticity and accuracy of the present approach used in the analysis. First order perturbation technique (FOPT,Second order perturbation technique (SOPT and Monte Carlo simulation (MCS methods are employed to investigate the effect of geometric configuration, volume fraction exponent, foundation parameters, distribution of reinforcement and thermal loading on nonlinear vibration characteristics CNTRC beam.The present work signifies the accurate analysis of vibrational behaviour influences by different random variables. Results are presented in terms of mean, variance (COV and probability density function (PDF for various aforementioned parameters.
International Nuclear Information System (INIS)
Haines, M.G.; Bond, D.J.; Chuaqui, H.H.
1983-01-01
The paper reports experimental and theoretical contributions to the understanding of non-linear heat flow and the phenomenon of jet-like filamentary structures in inertial-confinement fusion. When lateral heat flow is minimized, through applying more carefully a radially symmetric irradiation at 1.05 and 0.53 μm on a spherical target, it is found that a heat flux in excess of 10% of the free-streaming limit is consistent with simulations and experimental measurements with particle and X-ray diagnostics. A similar result has been found in a scaled experiment in a plasma of electron density 4x10 16 cm - 3 when the condition Tsub(e) approx.=Tsub(i) is satisfied. These results are in marked contrast to earlier assertions, mainly from plane-target measurements, that the flux limiter is 3%, but in agreement with theoretical calculations of steady non-linear heat flow using a discrete-ordinate method. Thus, no anomalous inhibition of heat flow is found, consistent with theoretical predictions that ion-acoustic turbulence is of no importance in dense (n>=10 21 cm - 3 , T approx.= 1 keV) plasmas. However, in the low-density scaled experiment, under conditions where Tsub(e)>>Tsub(i) is found that ion-acoustic turbulence is present, and the flux limiter is 4%. By using shadowgraphic and schlieren techniques with an optical diagnostic probe, fine-scale jet-like structures have been observed on a scale-length of approx. 10 μm on spherical targets. They occur even outside the laser-irradiated region, and are not connected with irregularities in the laser beam; they are more pronounced with higher-Z materials and with shorter-wavelength lasers, and have megagauss magnetic fields associated with them. Electromagnetic instabilities driven by heat flow are the probable cause of the jets, and of the three known modes the thermal instability, enhanced by radiation loss, agrees more closely with the experiments than the Weibel and thermomagnetic modes, since the latter only occur
Directory of Open Access Journals (Sweden)
Luisa Toscano
2016-01-01
Full Text Available A new result of solvability for a wide class of systems of variational equations depending on parameters and governed by nonmonotone operators is found in a Banach real and reflexive space with applications to Dirichlet and Neumann problems related to nonlinear elliptic systems.
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Shihuang Hong
2009-01-01
Full Text Available We present sufficient conditions for the existence of at least twin or triple positive solutions of a nonlinear four-point singular boundary value problem with a p-Laplacian dynamic equation on a time scale. Our results are obtained via some new multiple fixed point theorems.
International Nuclear Information System (INIS)
Koteras, J.R.
1996-01-01
The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region
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Maximilian B Maier
Full Text Available The effect of high pressure thermal (HPT processing on the inactivation of spores of proteolytic type B Clostridium botulinum TMW 2.357 in four differently composed low-acid foods (green peas with ham, steamed sole, vegetable soup, braised veal was studied in an industrially feasible pressure range and temperatures between 100 and 120°C. Inactivation curves exhibited rapid inactivation during compression and decompression followed by strong tailing effects. The highest inactivation (approx. 6-log cycle reduction was obtained in braised veal at 600 MPa and 110°C after 300 s pressure-holding time. In general, inactivation curves exhibited similar negative exponential shapes, but maximum achievable inactivation levels were lower in foods with higher fat contents. At high treatment temperatures, spore inactivation was more effective at lower pressure levels (300 vs. 600 MPa, which indicates a non-linear pressure/temperature-dependence of the HPT spore inactivation efficiency. A comparison of spore inactivation levels achievable using HPT treatments versus a conventional heat sterilization treatment (121.1°C, 3 min illustrates the potential of combining high pressures and temperatures to replace conventional retorting with the possibility to reduce the process temperature or shorten the processing time. Finally, experiments using varying spore inoculation levels suggested the presence of a resistant fraction comprising approximately 0.01% of a spore population as reason for the pronounced tailing effects in survivor curves. The loss of the high resistance properties upon cultivation indicates that those differences develop during sporulation and are not linked to permanent modifications at the genetic level.
Problems of thermal IR-imaging in evaluation of burn wounds
International Nuclear Information System (INIS)
Nowakowski, A.
2009-01-01
Results of the research devoted to application of thermal IR-imaging in diagnostics of burn wounds are discussed. The main aim of the work was to develop an effective method for quantitative evaluation of the depth of a burn wound and for classification of regions for surgical treatment. The criterion of determination the area of the wound to be treated surgically is the time, which should not exceed three weeks for natural healing of a burn wound. Prediction that the healing process may last longer is concluded by immediate surgical intervention. We concentrate on using for this purpose QIRT - NDT TI methods (Quantitative Infra-Red Thermography - Non-Destructive Testing Thermal Imaging); especially - active dynamic thermography - ADT. In this work both, classical thermography using a high quality thermal camera as well as ADT are applied and the results of analysis are joined, allowing multimodality diagnostic approach and improved classification of burns requiring surgical treatment. Now our work in application of thermal imaging in determination of burns is continued for around 10 years, as the first publication showing our methodology was presented in 1999. In 2001, during the Thermosense conference, we have been awarded the Andronicos Kantsios Award for the work on Medical applications of model based dynamic thermography. Important reports of our experience in classical as well as ADT thermography are already published. Now we concentrate on practical aspects of the problem, trying to construct a measuring set to be operative even by not experienced staff and meeting all of necessary requirements for clinical applications. (author)
Marlowe, M. B.; Moore, R. A.; Whetstone, W. D.
1979-01-01
User instructions are given for performing linear and nonlinear steady state and transient thermal analyses with SPAR thermal analysis processors TGEO, SSTA, and TRTA. It is assumed that the user is familiar with basic SPAR operations and basic heat transfer theory.
International Nuclear Information System (INIS)
Coz Diaz, J.J. del; Garcia Nieto, P.J.; Suarez Sierra, J.L.; Penuelas Sanchez, I.
2008-01-01
The aim of this work was carried out the optimization and numerical study by the finite element method of internal hollow bricks walls in order to determine the best candidate brick from the thermal point of view. With respect to the energy saving for housing and industrial structures, there is also a great interest in light building materials with good physical and thermal behaviors, which fulfills all thermal requirements of the new CTE Spanish rule. The conduction, convection and radiation phenomena are taking into account in this study for six different types of bricks varying the material conductivity obtained from five experimental tests. Mathematically, the non-linearity is due to the radiation boundary condition inside the inner recesses of the bricks. Optimization of the walls is carried out from the finite element analysis of the new hollow brick geometries by means of the average mass overall thermal efficiency and the equivalent thermal conductivity. Based on the previous thermal analysis and the optimization procedure described in this paper, the best candidate was chosen and then a full 1.22 x 0.23 x 1.05 m wall made of these bricks was simulated for fifteen different compositions. The main variables influencing the thermal conductivity of these walls are illustrated for different concrete and mortar properties and the temperature distribution is shown for some typical configurations. Finally, in order to select the appropriate wall satisfying the CTE requirements, detailed instructions are given and conclusions of this work are exposed
Energy Technology Data Exchange (ETDEWEB)
Del Coz Diaz, J.J.; Suarez Sierra, J.L.; Penuelas Sanchez, I. [Edificio Departamental Viesques, No. 7-33204 Gijon, Asturias (Spain); Garcia Nieto, P.J. [Departamento de Matematicas, Facultad de Ciencias, C/Calvo Sotelo s/n, 33007 Oviedo, Asturias (Spain)
2008-06-15
The aim of this work was carried out the optimization and numerical study by the finite element method of internal hollow bricks walls in order to determine the best candidate brick from the thermal point of view. With respect to the energy saving for housing and industrial structures, there is also a great interest in light building materials with good physical and thermal behaviors, which fulfills all thermal requirements of the new CTE Spanish rule. The conduction, convection and radiation phenomena are taking into account in this study for six different types of bricks varying the material conductivity obtained from five experimental tests. Mathematically, the non-linearity is due to the radiation boundary condition inside the inner recesses of the bricks. Optimization of the walls is carried out from the finite element analysis of the new hollow brick geometries by means of the average mass overall thermal efficiency and the equivalent thermal conductivity. Based on the previous thermal analysis and the optimization procedure described in this paper, the best candidate was chosen and then a full 1.22 x 0.23 x 1.05 m wall made of these bricks was simulated for fifteen different compositions. The main variables influencing the thermal conductivity of these walls are illustrated for different concrete and mortar properties and the temperature distribution is shown for some typical configurations. Finally, in order to select the appropriate wall satisfying the CTE requirements, detailed instructions are given and conclusions of this work are exposed. (author)
Energy Technology Data Exchange (ETDEWEB)
Coz Diaz, J.J. del [Edificio Departamental Viesques, No. 7-33204 Gijon, Asturias (Spain)], E-mail: juanjo@constru.uniovi.es; Garcia Nieto, P.J. [Departamento de Matematicas, Facultad de Ciencias, C/Calvo Sotelo s/n, 33007 Oviedo, Asturias (Spain); Suarez Sierra, J.L.; Penuelas Sanchez, I. [Edificio Departamental Viesques, No. 7-33204 Gijon, Asturias (Spain)
2008-06-15
The aim of this work was carried out the optimization and numerical study by the finite element method of internal hollow bricks walls in order to determine the best candidate brick from the thermal point of view. With respect to the energy saving for housing and industrial structures, there is also a great interest in light building materials with good physical and thermal behaviors, which fulfills all thermal requirements of the new CTE Spanish rule. The conduction, convection and radiation phenomena are taking into account in this study for six different types of bricks varying the material conductivity obtained from five experimental tests. Mathematically, the non-linearity is due to the radiation boundary condition inside the inner recesses of the bricks. Optimization of the walls is carried out from the finite element analysis of the new hollow brick geometries by means of the average mass overall thermal efficiency and the equivalent thermal conductivity. Based on the previous thermal analysis and the optimization procedure described in this paper, the best candidate was chosen and then a full 1.22 x 0.23 x 1.05 m wall made of these bricks was simulated for fifteen different compositions. The main variables influencing the thermal conductivity of these walls are illustrated for different concrete and mortar properties and the temperature distribution is shown for some typical configurations. Finally, in order to select the appropriate wall satisfying the CTE requirements, detailed instructions are given and conclusions of this work are exposed.
Sengupta, Tapan K.; Sharma, Nidhi; Sengupta, Aditi
2018-05-01
An enstrophy-based non-linear instability analysis of the Navier-Stokes equation for two-dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as an example. This problem admits a time-dependent analytical solution as the base flow, whose instability is traced here. The numerical study of the evolution of the Taylor-Green vortices shows that the flow becomes turbulent, but an explanation for this transition has not been advanced so far. The deviation of the numerical solution from the analytical solution is studied here using a high accuracy compact scheme on a non-uniform grid (NUC6), with the fourth-order Runge-Kutta method. The stream function-vorticity (ψ, ω) formulation of the governing equations is solved here in a periodic square domain with four vortices at t = 0. Simulations performed at different Reynolds numbers reveal that numerical errors in computations induce a breakdown of symmetry and simultaneous fragmentation of vortices. It is shown that the actual physical instability is triggered by the growth of disturbances and is explained by the evolution of disturbance mechanical energy and enstrophy. The disturbance evolution equations have been traced by looking at (a) disturbance mechanical energy of the Navier-Stokes equation, as described in the work of Sengupta et al., "Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003), and (b) the creation of rotationality via the enstrophy transport equation in the work of Sengupta et al., "Diffusion in inhomogeneous flows: Unique equilibrium state in an internal flow," Comput. Fluids 88, 440-451 (2013).
Energy Technology Data Exchange (ETDEWEB)
Mulione, G. [Catania, Univ. (Italy). Dip. di Matematica; Rionero, S. [Napoli, Univ. (Italy). Dip. di Matematica e applicazioni
1998-07-01
The Lyapunov direct method is applied to study nonlinear stability of a basic motionless state to imposed linear temperature and concentration fields of a binary fluid mixture heated and salted from below, in the Oberbeck-Boussinesq scheme. Stress-free and rigid surfaces are considered and absence of Hopf bifurcation is assumed. We prove the coincidence of the linear and (unconditional) nonlinear critical stability limits, when the ratio between the Schmidt and the Prandtl numbers is less or equal to 1. Precisely, we obtain necessary and sufficient conditions of unconditional nonlinear exponential stability of the basic motionless state. [Italian] Si applica il metodo diretto di Lyapunov allo studio della stabilita' non lineare esponenziale della soluzione di conduzione-diffusione di una miscela fluida binaria riscaldata e salata da sotto, nello schema di Oberbeck-Boussinesq. Si considerano superfici rigide e 'stress-free'; si supponeche non ci sia biforcazione di Hpf. Supposto che il rapporto fra i numeri di Schmidt e di Prandtl e' minore o uguale a 1, si prova la coincidenza tra i paramentri critici della stabilita' lineare e non lineare. Si ottengono condizioni necessarie e sufficienti di stabilita' non lineare esponenziale del moto base.
Directory of Open Access Journals (Sweden)
Chi-Chang Wang
2013-09-01
Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.
Hamilton, Mark F.
1990-12-01
This report discusses five projects all of which involve basic theoretical research in nonlinear acoustics: (1) pulsed finite amplitude sound beams are studied with a recently developed time domain computer algorithm that solves the KZK nonlinear parabolic wave equation; (2) nonlinear acoustic wave propagation in a liquid layer is a study of harmonic generation and acoustic soliton information in a liquid between a rigid and a free surface; (3) nonlinear effects in asymmetric cylindrical sound beams is a study of source asymmetries and scattering of sound by sound at high intensity; (4) effects of absorption on the interaction of sound beams is a completed study of the role of absorption in second harmonic generation and scattering of sound by sound; and (5) parametric receiving arrays is a completed study of parametric reception in a reverberant environment.
Zou, Jiajun
2018-01-01
Concentrating solar thermal power (CSP) industry is a strategic emerging industry in China. Its further development is of great significance for promoting the energy revolution, achieving energy saving and emission reduction. In this paper, China’s CSP industry is systematically analysed. First of all, the status quo is elaborated from the perspectives of relevant policies and regulations, market and generation technology development. Secondly, the problems and the underlying reasons of China’s CSP industry are deeply studied. On this basis, the future trends of CSP are expounded on the three levels of policy, market and power generation technology. Finally, a series of feasible countermeasures are put forward, designed to promote the development of CSP industry and the transformation of energy structure.
International Nuclear Information System (INIS)
Kandil, T.; Ayad, N.M.; Abdel Haleam, A.; Mahmoud, M.
2013-01-01
Egypt thermal research reactor (ETRR-2) was subjected to several Power Quality Problems such as voltage sags/swells, harmonics distortion, and short interruption. ETRR-2 encompasses a wide range of loads which are very sensitive to voltage variations and this leads to several unplanned shutdowns of the reactor due to trigger of the Reactor Protection System (RPS). The Dynamic Voltage Restorer (DVR) has recently been introduced to protect sensitive loads from voltage sags and other voltage disturbances. It is considered as one of the most efficient and effective solution. Its appeal includes smaller size and fast dynamic response to the disturbance. This paper describes a proposal of a DVR to improve power quality in ETRR-2 electrical distribution systems . The control of the compensation voltage is based on d-q-o algorithm. Simulation is carried out by Matlab/Simulink to verify the performance of the proposed method
PREFACE: MicroTherm' 2013 - Microtechnology and Thermal Problems in Electronics
Lisik, Zbigniew; Raj, Ewa
2014-04-01
MicroTherm is an International Conference on Microtechnology and Thermal Problems in Electronics organised as a cyclic event since 1996. The success of the first seminar, which was devoted mainly to thermal management aspects, and the successive conferences have led us to the tenth edition. Since the first meeting, the scope of the conference has expanded, following the progress of electronics. Now, it covers subjects connected with extreme temperature, electronics, sensors and measurement techniques, modelling, simulation, wide band-gap materials, packaging and reliability, renewable energy sources and photonics with special emphasis on microelectronic technologies. MicroTherm' 2013 was held in Lodz, Poland, on 25-28 June 2013. The programme consistied of invited talks and nine regular sessions in the form of planar discussions and poster presentations, including a Students' Session. The Students' session gave an opportunity for students and young researchers to present their first achievements in the field of science. The next MicroTherm Conference is going to be held on 22-25 June 2015, in Lodz — a beautiful, post-industrial city located in the centre of Poland. Please, feel invited to MicroTherm' 2015 (www.microtherm.dsod.pl). Ewa Raj and Zbigniew Lisik Editors
Simulation of Thermal Flow Problems via a Hybrid Immersed Boundary-Lattice Boltzmann Method
Directory of Open Access Journals (Sweden)
J. Wu
2012-01-01
Full Text Available A hybrid immersed boundary-lattice Boltzmann method (IB-LBM is presented in this work to simulate the thermal flow problems. In current approach, the flow field is resolved by using our recently developed boundary condition-enforced IB-LBM (Wu and Shu, (2009. The nonslip boundary condition on the solid boundary is enforced in simulation. At the same time, to capture the temperature development, the conventional energy equation is resolved. To model the effect of immersed boundary on temperature field, the heat source term is introduced. Different from previous studies, the heat source term is set as unknown rather than predetermined. Inspired by the idea in (Wu and Shu, (2009, the unknown is calculated in such a way that the temperature at the boundary interpolated from the corrected temperature field accurately satisfies the thermal boundary condition. In addition, based on the resolved temperature correction, an efficient way to compute the local and average Nusselt numbers is also proposed in this work. As compared with traditional implementation, no approximation for temperature gradients is required. To validate the present method, the numerical simulations of forced convection are carried out. The obtained results show good agreement with data in the literature.
The NTF Inlet Guide Vanes Thermal Gradient Problem and Its Mitigation
Venkat, Venki S.; Paryz, Roman W.; Bissett, Owen W.; Kilgore, W.
2013-01-01
The National Transonic Facility (NTF) utilizes Inlet Guide Vanes (IGV) to provide precise, quick response Mach number control for the tunnel. During cryogenic operations, the massive IGV structure can experience large thermal gradients, measured as "Delta T or (Delta)T", between the IGV ring and its support structure called the transfer case. If these temperature gradients are too large, the IGV structure can be stressed beyond its safety limit and cease operation. In recent years, (Delta)T readings exceeding the prescribed safety limits were observed frequently during cryogenic operations, particularly during model access. The tactical operation methods of the tunnel to minimize (Delta)T did not always succeed. One obvious option to remedy this condition is to warm up the IGV structure by disabling the main drive operation, but this "natural" warm up method can takes days in some cases, resulting in productivity loss. This paper documents the thermal gradient problem associated with the IGV structure during cryogenic operation and how the facility has recently achieved an acceptable mitigation which has resulted in improved efficiency of operations.
The microwave thermal thruster and its application to the launch problem
Parkin, Kevin L. G.
Nuclear thermal thrusters long ago bypassed the 50-year-old specific impulse (Isp) limitation of conventional thrusters, using nuclear powered heat exchangers in place of conventional combustion to heat a hydrogen propellant. These heat exchanger thrusters experimentally achieved an Isp of 825 seconds, but with a thrust-to-weight ratio (T/W) of less than ten they have thus far been too heavy to propel rockets into orbit. This thesis proposes a new idea to achieve both high Isp and high T/W The Microwave Thermal Thruster. This thruster covers the underside of a rocket aeroshell with a lightweight microwave absorbent heat exchange layer that may double as a re-entry heat shield. By illuminating the layer with microwaves directed from a ground-based phased array, an Isp of 700--900 seconds and T/W of 50--150 is possible using a hydrogen propellant. The single propellant simplifies vehicle design, and the high Isp increases payload fraction and structural margins. These factors combined could have a profound effect on the economics of building and reusing rockets. A laboratory-scale microwave thermal heat exchanger is constructed using a single channel in a cylindrical microwave resonant cavity, and new type of coupled electromagnetic-conduction-convection model is developed to simulate it. The resonant cavity approach to small-scale testing reveals several drawbacks, including an unexpected oscillatory behavior. Stable operation of the laboratory-scale thruster is nevertheless successful, and the simulations are consistent with the experimental results. In addition to proposing a new type of propulsion and demonstrating it, this thesis provides three other principal contributions: The first is a new perspective on the launch problem, placing it in a wider economic context. The second is a new type of ascent trajectory that significantly reduces the diameter, and hence cost, of the ground-based phased array. The third is an eclectic collection of data, techniques, and
Energy Technology Data Exchange (ETDEWEB)
Del Coz Diaz, J.J.; Rodriguez, A. Martin; Martinez-Luengas, A. Lozano; Biempica, C. Betegon [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain); Nieto, P.J. Garcia [Departamento de Matematicas, Facultad de Ciencias, C/Calvo Sotelo s/n, 33007 Oviedo, Asturias (Spain)
2006-06-15
The finite element method (FEM) is applied to the non-linear complex heat transfer analysis of light concrete hollow brick walls. The non-linearity is due to the radiation boundary condition inside the inner holes of the bricks. The conduction and convection phenomena are taking into account in this study for three different values of the conductivity mortar and two values for the brick. Finally, the numerical and experimental results are compared and a good agreement is shown. [Author].
Energy Technology Data Exchange (ETDEWEB)
Diaz del Coz, J.J. [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain)]. E-mail: juanjo@constru.uniovi.es; Nieto, P.J. Garcia [Departamento de Matematicas, Facultad de Ciencias, C/Calvo Sotelo s/n, 33007 Oviedo, Asturias (Spain); Rodriguez, A. Martin [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain); Martinez-Luengas, A. Lozano [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain); Biempica, C. Betegon [Department of Construction, University of Oviedo, Edificio Departamental Viesques No 7, Dpcho. 7.1.02 Campus de Viesques, 33204 Gijon, Asturias (Spain)
2006-06-15
The finite element method (FEM) is applied to the non-linear complex heat transfer analysis of light concrete hollow brick walls. The non-linearity is due to the radiation boundary condition inside the inner holes of the bricks. The conduction and convection phenomena are taking into account in this study for three different values of the conductivity mortar and two values for the brick. Finally, the numerical and experimental results are compared and a good agreement is shown.
International Nuclear Information System (INIS)
Diaz del Coz, J.J.; Nieto, P.J. Garcia; Rodriguez, A. Martin; Martinez-Luengas, A. Lozano; Biempica, C. Betegon
2006-01-01
The finite element method (FEM) is applied to the non-linear complex heat transfer analysis of light concrete hollow brick walls. The non-linearity is due to the radiation boundary condition inside the inner holes of the bricks. The conduction and convection phenomena are taking into account in this study for three different values of the conductivity mortar and two values for the brick. Finally, the numerical and experimental results are compared and a good agreement is shown
Energy Technology Data Exchange (ETDEWEB)
NONE
1980-07-01
The main topics treated in this report are: I) Existence of generalized Lagrangians. II) Conserved densities for odd-order polynomial evolution equations and linear evolution systems. III ) Conservation laws for Klein-Gordon, Di rae and Maxwell equations. IV) Stability conditions for finite-energy solutions of a non-linear Klein-Gordon equation. V) Hamiltonian approach to non-linear evolution equations and Backlund transformations. VI) Anharmonic vibrations: Status of results and new possible approaches. (Author) 83 refs.
International Nuclear Information System (INIS)
Selbach, Sverre M.; Tolchard, Julian R.; Fossdal, Anita; Grande, Tor
2012-01-01
The crystal structure, anisotropic thermal expansion and structural phase transition of the perovskite LaFeO 3 has been studied by high-temperature X-ray diffraction from room temperature to 1533 K. The structural evolution of the orthorhombic phase with space group Pbnm and the rhombohedral phase with R3 ¯ c structure of LaFeO 3 is reported in terms of lattice parameters, thermal expansion coefficients, atomic positions, octahedral rotations and polyhedral volumes. Non-linear lattice expansion across the antiferromagnetic to paramagnetic transition of LaFeO 3 at T N =735 K was compared to the corresponding behavior of the ferroelectric antiferromagnet BiFeO 3 to gain insight to the magnetoelectric coupling in BiFeO 3 , which is also multiferroic. The first order phase transition of LaFeO 3 from Pbnm to R3 ¯ c was observed at 1228±9 K, and a subsequent transition to Pm3 ¯ m was extrapolated to occur at 2140±30 K. The stability of the Pbnm and R3 ¯ c polymorphs of LaFeO 3 is discussed in terms of the competing enthalpy and entropy of the two crystal polymorphs and the thermal evolution of the polyhedral volume ratio V A /V B . - Graphical abstract: Aniostropic thermal evolution of the lattice parameters and phase transition of LaFeO 3 . Highlights: ► The crystal structure of LaFeO 3 is studied by HTXRD from RT to 1533 K. ► A non-linear expansion across the Néel temperature is observed for LaFeO 3 . ► The ratio V A /V B is used to rationalize the thermal evolution of the structure.
Kuznets, E I; Bobrov, A F; Bekreneva, L N; Mikhailova, L I; Utekhin, B A; Pruzhinina, T I; Iakovleva, E V; Chadov, V I
1996-01-01
The problem of evaluating and predicting the thermal status of a cosmonaut in the long-term space mission is a pressing one and remains to be solved. The previous studies indicated that the best plan to be followed is to evaluate the thermal status of a cosmonaut during his egress into outer space with the use of the procedure of parotid thermometry of the mean body temperature.
SU-E-J-161: Inverse Problems for Optical Parameters in Laser Induced Thermal Therapy
International Nuclear Information System (INIS)
Fahrenholtz, SJ; Stafford, RJ; Fuentes, DT
2014-01-01
Purpose: Magnetic resonance-guided laser-induced thermal therapy (MRgLITT) is investigated as a neurosurgical intervention for oncological applications throughout the body by active post market studies. Real-time MR temperature imaging is used to monitor ablative thermal delivery in the clinic. Additionally, brain MRgLITT could improve through effective planning for laser fiber's placement. Mathematical bioheat models have been extensively investigated but require reliable patient specific physical parameter data, e.g. optical parameters. This abstract applies an inverse problem algorithm to characterize optical parameter data obtained from previous MRgLITT interventions. Methods: The implemented inverse problem has three primary components: a parameter-space search algorithm, a physics model, and training data. First, the parameter-space search algorithm uses a gradient-based quasi-Newton method to optimize the effective optical attenuation coefficient, μ-eff. A parameter reduction reduces the amount of optical parameter-space the algorithm must search. Second, the physics model is a simplified bioheat model for homogeneous tissue where closed-form Green's functions represent the exact solution. Third, the training data was temperature imaging data from 23 MRgLITT oncological brain ablations (980 nm wavelength) from seven different patients. Results: To three significant figures, the descriptive statistics for μ-eff were 1470 m −1 mean, 1360 m −1 median, 369 m −1 standard deviation, 933 m −1 minimum and 2260 m −1 maximum. The standard deviation normalized by the mean was 25.0%. The inverse problem took <30 minutes to optimize all 23 datasets. Conclusion: As expected, the inferred average is biased by underlying physics model. However, the standard deviation normalized by the mean is smaller than literature values and indicates an increased precision in the characterization of the optical parameters needed to plan MRgLITT procedures. This investigation
Directory of Open Access Journals (Sweden)
Wei Han
2008-01-01
Full Text Available Several existence theorems of twin positive solutions are established for a nonlinear m-point boundary value problem of third-order p-Laplacian dynamic equations on time scales by using a fixed point theorem. We present two theorems and four corollaries which generalize the results of related literature. As an application, an example to demonstrate our results is given. The obtained conditions are different from some known results.
Lee, H. P.
1977-01-01
The NASTRAN Thermal Analyzer Manual describes the fundamental and theoretical treatment of the finite element method, with emphasis on the derivations of the constituent matrices of different elements and solution algorithms. Necessary information and data relating to the practical applications of engineering modeling are included.
Hayat, T.; Shah, Faisal; Alsaedi, A.; Hussain, Zakir
The present analysis aims to report the consequences of nonlinear radiation, convective condition and heterogeneous-homogeneous reactions in Darcy-Forchheimer flow over a non-linear stretching sheet with variable thickness. Non-uniform magnetic field and nonuniform heat generation/absorption are accounted. The governing boundary layer partial differential equations are converted into a system of nonlinear ordinary differential equations. The computations are organized and the effects of physical variables such as thickness parameter, power index, Hartman number, inertia and porous parameters, radiation parameter, Biot number, Prandtl number, ratio parameter, heat generation parameter and homogeneous-heterogeneous reaction parameter are investigated. The variations of skin friction coefficient and Nusselt number for different interesting variables are plotted and discussed. It is noticed that Biot number and heat generation variable lead to enhance the temperature distribution. The solutal boundary layer thickness decreases for larger homogeneous variable while reverse trend is seen for heterogeneous reaction.
International Nuclear Information System (INIS)
Górecki, K; Zarȩbski, J
2014-01-01
The paper is devoted to modelling thermal properties of semiconductor devices at the steady state. The dc thermal model of a semiconductor device taking into account the multipath heat flow is proposed. Some results of calculations and measurements of thermal resistance of a power MOSFET operating at different cooling conditions are presented. The obtained results of calculations fit the results of measurements, which proves the correctness of the proposed model.
International Nuclear Information System (INIS)
Wabnitz, Stefan; Wetzel, Benjamin
2014-01-01
We investigate the spontaneous growth of noise that accompanies the nonlinear evolution of seeded modulation instability into Fermi–Pasta–Ulam recurrence. Results from the Floquet linear stability analysis of periodic solutions of the three-wave truncation are compared with full numerical solutions of the nonlinear Schrödinger equation. The predicted initial stage of noise growth is in a good agreement with simulations, and is expected to provide further insight into the subsequent dynamics of the field evolution after recurrence breakup
Energy Technology Data Exchange (ETDEWEB)
Wabnitz, Stefan, E-mail: stefan.wabnitz@unibs.it [Dipartimento di Ingegneria dell' Informazione, Università degli Studi di Brescia, via Branze 38, 25123 Brescia (Italy); Wetzel, Benjamin [INRS-EMT, 1650 Blvd. Lionel-Boulet, Varennes, Québec J3X 1S2 (Canada)
2014-07-25
We investigate the spontaneous growth of noise that accompanies the nonlinear evolution of seeded modulation instability into Fermi–Pasta–Ulam recurrence. Results from the Floquet linear stability analysis of periodic solutions of the three-wave truncation are compared with full numerical solutions of the nonlinear Schrödinger equation. The predicted initial stage of noise growth is in a good agreement with simulations, and is expected to provide further insight into the subsequent dynamics of the field evolution after recurrence breakup.
Directory of Open Access Journals (Sweden)
Adeshina S. Adegoke
2017-11-01
Full Text Available This paper studied the nonlinear vibrations of top-tensioned cantilevered pipes conveying pressurized steady two-phase flow under thermal loading. The coupled axial and transverse governing partial differential equations of motion of the system were derived based on Hamilton’s mechanics, with the centerline assumed to be extensible. Using the multiple-scale perturbation technique, natural frequencies, mode shapes, and first order approximate solutions of the steady-state response of the pipes were obtained. The multiple-scale assessment reveals that at some frequencies the system is uncoupled, while at some frequencies a 1:2 coupling exists between the axial and the transverse frequencies of the pipe. Nonlinear frequencies versus the amplitude displacement of the cantilever pipe, conveying two-phase flow at super-critical mixture velocity for the uncoupled scenario, exhibit a nonlinear hardening behavior; an increment in the void fractions of the two-phase flow results in a reduction in the pipe’s transverse vibration frequencies and the coupled amplitude of the system. However, increases in the temperature difference, pressure, and the presence of top tension were observed to increase the pipe’s transverse vibration frequencies without a significant change in the coupled amplitude of the system.
International Nuclear Information System (INIS)
Shadid, J.N.; Smith, T.M.; Cyr, E.C.; Wildey, T.M.; Pawlowski, R.P.
2016-01-01
A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.
Energy Technology Data Exchange (ETDEWEB)
Shadid, J.N., E-mail: jnshadi@sandia.gov [Sandia National Laboratories, Computational Mathematics Department (United States); Department of Mathematics and Statistics, University of New Mexico (United States); Smith, T.M. [Sandia National Laboratories, Multiphysics Applications Department (United States); Cyr, E.C. [Sandia National Laboratories, Computational Mathematics Department (United States); Wildey, T.M. [Sandia National Laboratories, Optimization and UQ Department (United States); Pawlowski, R.P. [Sandia National Laboratories, Multiphysics Applications Department (United States)
2016-09-15
A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.
Energy Technology Data Exchange (ETDEWEB)
Delbos, F.
2004-11-01
Reflexion tomography allows the determination of a subsurface velocity model from the travel times of seismic waves. The introduction of a priori information in this inverse problem can lead to the resolution of a constrained non-linear least-squares problem. The goal of the thesis is to improve the resolution techniques of this optimization problem, whose main difficulties are its ill-conditioning, its large scale and an expensive cost function in terms of CPU time. Thanks to a detailed study of the problem and to numerous numerical experiments, we justify the use of a sequential quadratic programming method, in which the tangential quadratic programs are solved by an original augmented Lagrangian method. We show the global linear convergence of the latter. The efficiency and robustness of the approach are demonstrated on several synthetic examples and on two real data cases. (author)
International Nuclear Information System (INIS)
Zhidkov, P.E.
1996-01-01
First, the eigenvalue problem on the segment [0,1] for the Sturm-Liouville operator with a potential depending on the spectral parameter with the zero Dirichlet boundary conditions is considered. For this problem, under some hypotheses on the potential, it is proved that the necessary and sufficient condition for an arbitrary system of eigenfunctions, possessing a unique function with n roots in the interval (0,1) for an arbitrary non-negative integer number n, being complete in the space L 2 (0,1) is the linear independence of the functions from this system in the space L 2 (0,1). Then, this result is applied to the investigation of an eigenvalue problem for a nonlinear operator on the Sturm-Liouville type. For this problem, the completeness of the system of its eigenfunctions in the space L 2 (0,1) is proved. (author). 12 refs
Energy Technology Data Exchange (ETDEWEB)
Delbos, F
2004-11-01
Reflexion tomography allows the determination of a subsurface velocity model from the travel times of seismic waves. The introduction of a priori information in this inverse problem can lead to the resolution of a constrained non-linear least-squares problem. The goal of the thesis is to improve the resolution techniques of this optimization problem, whose main difficulties are its ill-conditioning, its large scale and an expensive cost function in terms of CPU time. Thanks to a detailed study of the problem and to numerous numerical experiments, we justify the use of a sequential quadratic programming method, in which the tangential quadratic programs are solved by an original augmented Lagrangian method. We show the global linear convergence of the latter. The efficiency and robustness of the approach are demonstrated on several synthetic examples and on two real data cases. (author)
Nageshwari, M.; Kumari, C. Rathika Thaya; Vinitha, G.; Mohamed, M. Peer; Sudha, S.; Caroline, M. Lydia
2018-03-01
L-Methionine-Succinic acid (2/1) (LMSA), 2C5H11NO2S·C4H6O4, a novel nonlinear optical material which belongs to the class of organic category was grown-up for the first time by the technique of slow evaporation. Purity of LMSA was improved using repetitive recrystallization. LMSA was analyzed by single crystal and powder X-ray diffraction investigation to affirm the crystal structure and crystalline character. The single crystal XRD revealed that LMSA corresponds to the crystal system of triclinic with P1 as space group showing the asymmetric unit consists of a neutral succinic acid molecule and two methionine residues which are crystallographically independent existing in zwitterionic form. The functional groups existing in LMSA was accomplished using Fourier transform infrared spectroscopy. The optical transparency and the band gap energy were identified utilizing UV-Visible spectrum. The optical constants specifically reflectance and extinction coefficient clearly indicate the elevated transparency of LMSA. The thermal analyses affirmed its thermal stability. The luminescence behavior of LMSA has been analyzed by Photoluminescence (PL) spectral study. The mechanical, laser damage threshold and dielectric investigation of LMSA was done to suggest the material for practical applications. The second and third harmonic generation efficacy was confirmed by means of Kurtz-Perry and Z-scan procedure which attest its potentiality in the domain of nonlinear optics.
Yang, Linlin; Li, Nianbei; Li, Baowen
2014-12-01
The temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential (soft-KG) are investigated systematically. Similarly to the previously studied hard-KG lattices, the existence of renormalized phonons is also confirmed in soft-KG lattices. In particular, the temperature dependence of the renormalized phonon frequency predicted by a classical field theory is verified by detailed numerical simulations. However, the thermal conductivities of soft-KG lattices exhibit the opposite trend in temperature dependence in comparison with those of hard-KG lattices. The interesting thing is that the temperature-dependent thermal conductivities of both soft- and hard-KG lattices can be interpreted in the same framework of effective phonon theory. According to the effective phonon theory, the exponents of the power-law dependence of the thermal conductivities as a function of temperature are only determined by the exponents of the soft or hard on-site potentials. These theoretical predictions are consistently verified very well by extensive numerical simulations.
Yang, Linlin; Li, Nianbei; Li, Baowen
2014-12-01
The temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential (soft-KG) are investigated systematically. Similarly to the previously studied hard-KG lattices, the existence of renormalized phonons is also confirmed in soft-KG lattices. In particular, the temperature dependence of the renormalized phonon frequency predicted by a classical field theory is verified by detailed numerical simulations. However, the thermal conductivities of soft-KG lattices exhibit the opposite trend in temperature dependence in comparison with those of hard-KG lattices. The interesting thing is that the temperature-dependent thermal conductivities of both soft- and hard-KG lattices can be interpreted in the same framework of effective phonon theory. According to the effective phonon theory, the exponents of the power-law dependence of the thermal conductivities as a function of temperature are only determined by the exponents of the soft or hard on-site potentials. These theoretical predictions are consistently verified very well by extensive numerical simulations.
Directory of Open Access Journals (Sweden)
T. Hayat
Full Text Available The present analysis aims to report the consequences of nonlinear radiation, convective condition and heterogeneous-homogeneous reactions in Darcy-Forchheimer flow over a non-linear stretching sheet with variable thickness. Non-uniform magnetic field and nonuniform heat generation/absorption are accounted. The governing boundary layer partial differential equations are converted into a system of nonlinear ordinary differential equations. The computations are organized and the effects of physical variables such as thickness parameter, power index, Hartman number, inertia and porous parameters, radiation parameter, Biot number, Prandtl number, ratio parameter, heat generation parameter and homogeneous-heterogeneous reaction parameter are investigated. The variations of skin friction coefficient and Nusselt number for different interesting variables are plotted and discussed. It is noticed that Biot number and heat generation variable lead to enhance the temperature distribution. The solutal boundary layer thickness decreases for larger homogeneous variable while reverse trend is seen for heterogeneous reaction. Keywords: Variable sheet thickness, Darcy-Forchheimer flow, Homogeneous-heterogeneous reactions, Power-law surface velocity, Convective condition, Heat generation/absorption, Nonlinear radiation
International Nuclear Information System (INIS)
Stanco, L.; Vaccaro, V.G.; Funk, U.; Krueger, U.; Mika, K.; Wuestefeld, G.
1982-03-01
In the first part of this report a physical model is presented, which describes the deforming of a bunch in a storage ring influenced only by its own space charge field. A system of two differential equations for the density and the momentum of the particles is set up, which is independent of any special machine parameter. Due to the sign of the inductance of the chamber walls and the sign of the dispersion of the revolution frequency, we distinguish between a de-bunching and a self-bunching situation. The de-bunching corresponds to a nonlinear hyperbolic propagation problem well-known in gas dynamics, and the self-bunching to a nonlinear elliptic initial value problem. The second part deals with a mathematical and numerical treatment of an approximate equation for the hyperbolic case. For this nonlinear second order partial differential equation we first present three particular integrals: the solution by separating the variables, the similarity solution, and the solution for a parabolic initial distribution of the density. For a more realistic initial condition, we must resort to other methods: Results are obtained in three different ways, first from a highly accurate Taylor series expansion, second from a common finite difference method, and thirdly from the numerical method of characteristics. The appearance of a shock discontinuity is furthermore established in each of these cases. (orig.)
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 the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...
DEFF Research Database (Denmark)
Andersen, Thomas; Andersen, Michael A. E.; Thomsen, Ole Cornelius
2012-01-01
As the trend within power electronic still goes in the direction of higher power density and higher efficiency, it is necessary to develop new topologies and push the limit for the existing technology. Piezoelectric transformers are a fast developing technology to improve efficiency and increase ...... is developed to explain nonlinearities as voltage jumps and voltage saturation and thereby avoid the complex theory of electro elasticity. The model is based on the hypothesis of self-heating and tested with measurements with good correlation....
Energy Technology Data Exchange (ETDEWEB)
Cognet, G
1998-07-07
In nuclear reactors, whatever the type considered, Pressurized Water Water Reactors (PWRs), Fast Breeder reactors (FBRs)..., thermal-hydraulics, the science of fluid mechanics and thermal behaviour, plays an essential role, both in nominal operating and accidental conditions. Fluid can either be the primary fluid (liquid or gas) or a very specific fluid called corium, which, in case of severe accident, could result from core and environning structure melting. The work reported here represents a 20-year contribution to thermal-hydraulic issues which could occur in FBRs and PWRs. Working on these two types of reactors, both in nominal and severe accident situations, has allowed me to compare the problems and to realize the importance of communication between research teams. The evolution in the complexity of studied problems, unavoidable in order to reduce costs and significantly improve safety, has led me from numerical modelling of single-phase flow turbulence to high temperature real melt experiments. The difficulties encountered in understanding the observed phenomena and in increasing experimental databases for computer code qualification have often entailed my participation in specific measurement device developments or adaptations, in particular non-intrusive devices generally based on optical techniques. Being concerned about the end-use of this research work, I actively participated in `in-situ` thermalhydraulic experiments in the FBRs: Phenix and Super-Phenix, of which I appreciated their undeniable scientific contribution. In my opinion, the thermal-hydraulic questions related to severe accidents are the most complex as they are at the cross-roads of several scientific specialities. Consequently, they require a multi-disciplinary approach and a continuous see-saw motion between experimentalists and modelling teams. After a brief description of the various problems encountered, the main ones are reported. Finally, the importance for research teams to
Verification of thermal-hydraulic computer codes against standard problems for WWER reflooding
International Nuclear Information System (INIS)
Alexander D Efanov; Vladimir N Vinogradov; Victor V Sergeev; Oleg A Sudnitsyn
2005-01-01
Full text of publication follows: The computational assessment of reactor core components behavior under accident conditions is impossible without knowledge of the thermal-hydraulic processes occurring in this case. The adequacy of the results obtained using the computer codes to the real processes is verified by carrying out a number of standard problems. In 2000-2003, the fulfillment of three Russian standard problems on WWER core reflooding was arranged using the experiments on full-height electrically heated WWER 37-rod bundle model cooldown in regimes of bottom (SP-1), top (SP-2) and combined (SP-3) reflooding. The representatives from the eight MINATOM's organizations took part in this work, in the course of which the 'blind' and posttest calculations were performed using various versions of the RELAP5, ATHLET, CATHARE, COBRA-TF, TRAP, KORSAR computer codes. The paper presents a brief description of the test facility, test section, test scenarios and conditions as well as the basic results of computational analysis of the experiments. The analysis of the test data revealed a significantly non-one-dimensional nature of cooldown and rewetting of heater rods heated up to a high temperature in a model bundle. This was most pronounced at top and combined reflooding. The verification of the model reflooding computer codes showed that most of computer codes fairly predict the peak rod temperature and the time of bundle cooldown. The exception is provided by the results of calculations with the ATHLET and CATHARE codes. The nature and rate of rewetting front advance in the lower half of the bundle are fairly predicted practically by all computer codes. The disagreement between the calculations and experimental results for the upper half of the bundle is caused by the difficulties of computational simulation of multidimensional effects by 1-D computer codes. In this regard, a quasi-two-dimensional computer code COBRA-TF offers certain advantages. Overall, the closest
Kvitko, A. N.
2018-01-01
An algorithm convenient for numerical implementation is proposed for constructing differentiable control functions that transfer a wide class of nonlinear nonstationary systems of ordinary differential equations from an initial state to a given point of the phase space. Constructive sufficient conditions imposed on the right-hand side of the controlled system are obtained under which this transfer is possible. The control of a robotic manipulator is considered, and its numerical simulation is performed.
International Nuclear Information System (INIS)
Afuwape, A.U.; Omari, P.
1987-11-01
This paper deals with the solvability of the nonlinear operator equations in normed spaces Lx=EGx+f, where L is a linear map with possible nontrivial kernel. Applications are given to the existence of periodic solutions for the third order scalar differential equation x'''+ax''+bx'+cx+g(t,x)=p(t), under various conditions on the interaction of g(t,x)/x with spectral configurations of a, b and c. (author). 48 refs
A comparison of two Fem-based methods for the solution of the nonlinear output regulation problem
Czech Academy of Sciences Publication Activity Database
Rehák, Branislav; Čelikovský, Sergej; Ruiz-León, J.; Orozco-Mora, J.
2009-01-01
Roč. 45, č. 3 (2009), s. 427-444 ISSN 0023-5954 R&D Projects: GA ČR GP102/07/P413; GA ČR(CZ) GA102/08/0186 Institutional research plan: CEZ:AV0Z10750506 Keywords : nonlinear output regulation * singularly perturbed equation * byroscope Subject RIV: BC - Control Systems Theory Impact factor: 0.445, year: 2009
International Nuclear Information System (INIS)
Dokhane, A.; Henning, D.; Chawla, R.; Rizwan-Uddin
2003-01-01
BWR stability analysis at PSI, as at other research centres, is usually carried out employing complex system codes. However, these do not allow a detailed investigation of the complete manifold of all possible solutions of the associated nonlinear differential equation set. A novel analytical, reduced order model for BWR stability has been developed at PSI, in several successive steps. In the first step, the thermal-hydraulic model was used for studying the thermal-hydraulic instabilities. A study was then conducted of the one-channel nuclear-coupled thermal-hydraulic dynamics in a BWR by adding a simple point kinetic model for neutron kinetics and a model for the fuel heat conduction dynamics. In this paper, a two-channel nuclear-coupled thermal-hydraulic model is introduced to simulate the out-of phase oscillations in a BWR. This model comprises three parts: spatial mode neutron kinetics with the fundamental and fist azimuthal modes; fuel heat conduction dynamics; and thermal-hydraulics model. This present model is an extension of the Karve et al. model i.e., a drift flux model is used instead of the homogeneous equilibrium model for two-phase flow, and lambda modes are used instead of the omega modes for the neutron kinetics. This two-channel model is employed in stability and bifurcation analyses, carried out using the bifurcation code BIFDD. The stability boundary (SB) and the nature of the Poincare-Andronov-Hopf bifurcation (PAF-B) are determined and visualized in a suitable two-dimensional parameter/state space. A comparative study of the homogeneous equilibrium model (HEM) and the drift flux model (DFM) is carried out to investigate the effects of the DFM parameters the void distribution parameter C 0 and the drift velocity V gi -on the SB, the nature of PAH bifurcation, and on the type of oscillation mode (in-phase or out-of-phase). (author)
Photostable nonlinear optical polycarbonates
Faccini, M.; Balakrishnan, M.; Diemeer, Mart; Torosantucci, Riccardo; Driessen, A.; Reinhoudt, David; Verboom, Willem
2008-01-01
Highly thermal and photostable nonlinear optical polymers were obtained by covalently incorporating the tricyanovinylidenediphenylaminobenzene (TCVDPA) chromophore to a polycarbonate backbone. NLO polycarbonates with different chromophore attachment modes and flexibilities were synthesized. In spite
Devi, S. Reena; Kalaiyarasi, S.; Zahid, I. MD.; Kumar, R. Mohan
2016-11-01
An ionic organic optical crystal of 4-methylpyridinium p-nitrophenolate was grown from methanol by slow evaporation method at ambient temperature. Powder and single crystal X-ray diffraction studies revealed the crystal system and its crystalline perfection. The rocking curve recorded from HRXRD study confirmed the crystal quality. FTIR spectral analysis confirmed the functional groups present in the title compound. UV-visible spectral study revealed the optical window and band gap of grown crystal. The thermal, electrical and surface laser damage threshold properties of harvested crystal were examined by using TGA/DTA, LCR/Impedance Analyzer and Nd:YAG laser system respectively. The third order nonlinear optical property of grown crystal was elucidated by Z-scan technique.
Comments on an Analytical Thermal Agglomeration for Problems with Surface Growth
Energy Technology Data Exchange (ETDEWEB)
Hodge, N. E. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2017-03-22
Up until Dec 2016, the thermal agglomeration was very heuristic, and as such, difficult to define. The lack of predictability became problematic, and the current notes represent the first real attempt to systematize the specification of the agglomerated process parameters.
Liao, Fuyuan; Jan, Yih-Kuen
2017-01-01
Diabetic foot ulcers (DFU) are a major complication in diabetics. Impaired microvascular reactivity is a major contributor to the development of DFU and has been traditionally quantified by time-domain or frequency-domain measures of skin blood flow (SBF). These measures, however, are unable to characterize the changes of nonlinear dynamics of SBF associated with diabetes and peripheral neuropathy. The objective of this study was to investigate altered nonlinear dynamics of skin blood flow in the plantar foot of diabetics with peripheral neuropathy. 18 type 2 diabetics with peripheral neuropathy and 8 healthy controls were recruited. SBF at the first metatarsal head in response to a loading pressure of 300 mmHg and a local heating was measured using laser Doppler flowmetry. A sample entropy approach was used to quantify the degree of regularity of SBF. Our results showed that the regularity degree of SBF in the diabetic foot underwent only small changes during post-occlusive reactive hyperemia and thermally induced biphasic response compared to non-diabetics. SBF of the diabetic foot has higher degree of irregularity during reactive hyperemia because of attenuated myogenic activity, and demonstrated higher regularity during the biphasic response largely due to significantly enhanced cardiac activities. This study suggests that the regularity degree of SBF at the first metatarsal head could be used to assess impaired microvascular reactivity and thus may be used to assess the risk for DFU in diabetics with peripheralneuropathy.
Energy Technology Data Exchange (ETDEWEB)
Hendi, S.H. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Panah, B.E. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); ICRANet, Pescara (Italy); Panahiyan, S. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Helmholtz-Institut Jena, Jena (Germany); Shahid Beheshti University, Physics Department, Tehran (Iran, Islamic Republic of); Momennia, M. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of)
2017-09-15
This paper is devoted to an investigation of nonlinearly charged dilatonic black holes in the context of gravity's rainbow with two cases: (1) by considering the usual entropy, (2) in the presence of first order logarithmic correction of the entropy. First, exact black hole solutions of dilatonic Born-Infeld gravity with an energy dependent Liouville-type potential are obtained. Then, thermodynamic properties of the mentioned cases are studied, separately. It will be shown that although mass, entropy and the heat capacity are modified due to the presence of a first order correction, the temperature remains independent of it. Furthermore, it will be shown that divergences of the heat capacity, hence phase transition points are also independent of a first order correction, whereas the stability conditions are highly sensitive to variation of the correction parameter. Except for the effects of a first order correction, we will also present a limit on the values of the dilatonic parameter and show that it is possible to recognize AdS and dS thermodynamical behaviors for two specific branches of the dilatonic parameter. In addition, the effects of nonlinear electromagnetic field and energy functions on the thermodynamical behavior of the solutions will be highlighted and dependency of critical behavior, on these generalizations will be investigated. (orig.)
International Nuclear Information System (INIS)
Hendi, S.H.; Panah, B.E.; Panahiyan, S.; Momennia, M.
2017-01-01
This paper is devoted to an investigation of nonlinearly charged dilatonic black holes in the context of gravity's rainbow with two cases: (1) by considering the usual entropy, (2) in the presence of first order logarithmic correction of the entropy. First, exact black hole solutions of dilatonic Born-Infeld gravity with an energy dependent Liouville-type potential are obtained. Then, thermodynamic properties of the mentioned cases are studied, separately. It will be shown that although mass, entropy and the heat capacity are modified due to the presence of a first order correction, the temperature remains independent of it. Furthermore, it will be shown that divergences of the heat capacity, hence phase transition points are also independent of a first order correction, whereas the stability conditions are highly sensitive to variation of the correction parameter. Except for the effects of a first order correction, we will also present a limit on the values of the dilatonic parameter and show that it is possible to recognize AdS and dS thermodynamical behaviors for two specific branches of the dilatonic parameter. In addition, the effects of nonlinear electromagnetic field and energy functions on the thermodynamical behavior of the solutions will be highlighted and dependency of critical behavior, on these generalizations will be investigated. (orig.)
International Nuclear Information System (INIS)
Biswas, Kaushik; Sontakke, Atul D.; Annapurna, K.
2010-01-01
A series of calcium lanthanum metaborate glasses in the composition (wt%) of 23.88CaO-28.33La 2 O 3 -47.79B 2 O 3 modified with TiO 2 up to 20 wt% are prepared by a melt quenching technique to study the influence of TiO 2 on their thermal, structural, linear and nonlinear optical properties. The differential thermal analysis (DTA) studies have demonstrated significant effects due to the presence of TiO 2 on the glass forming ability and crystallization situations. The glass with 15 wt% TiO 2 has achieved a eutectic composition and also exhibited a better glass forming ability among the glasses studied. The FT-IR spectra of these glasses show mainly vibration modes corresponding to stretching of BO 3 trigonal, BO 4 tetrahedral units and of B-O-B bending bonds. At higher concentrations of TiO 2 , development of vibration band around 400 cm -1 has indicated the formation of TiO 6 structural units in the glass network. The red shift of optical absorption edge (UV cutoff) shows a monotonous decrease in direct and indirect optical band gap energies (E opt ) with an increase of TiO 2 content in the glasses based on their absorption spectra. The optical transparency of these glasses is found to be varied from 64 to 87% within the wavelength range 450-1100 nm depending on the TiO 2 content. Besides these studies, linear refractive indices, the nonlinear optical properties of these glasses have also been evaluated.
Energy Technology Data Exchange (ETDEWEB)
Yin, Hongyao [Department of Chemistry, Shanghai Normal University, Shanghai 200234 (China); Xiao, Haibo, E-mail: xiaohb@shnu.edu.cn [Department of Chemistry, Shanghai Normal University, Shanghai 200234 (China); Ding, Lei [Department of Chemistry, Shanghai Normal University, Shanghai 200234 (China); Zhang, Chun; Ren, Aiming [State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023 (China); Li, Bo [Key Laboratory of Polar Materials and Devices, Ministry of Education, East China Normal University, Shanghai 200241 (China)
2015-02-01
A spirobifluorene-bridged donor/donor chromophore, 2,7-bis-(4-(N,N-diphenylamino)phen-1-yl)-9,9′-spirobifluorene (SPF-TP), was found to combine excellent transparency in the near UV–visible region (λ{sub cut-off} ≤ 420 nm), large two-photon absorption cross-section (4.5 × 10{sup 3}GM) and high thermal stability (T{sub d} = 501 °C). In comparison to the reported two-photon absorption molecules, SPF-TP represents the best thermal stability so far described in the literature. The main electronic factors explaining the high two-photon absorption activities of SPF-TP were analyzed by theoretical calculations. Cyclic voltammograms were employed to explore the causes of the excellent transparency of SPF-TP. It was found that the spiroconjugation effect is responsible for the excellent nonlinearity/transparency/thermal stability trade-off in SPF-TP. In addition, SPF-TP is also a good two-photon induced blue fluorescent material with high fluorescence quantum yield (Φ = 0.90, in THF). - Highlights: • We report a molecule exhibiting excellent transparency. • The two-photon absorption cross-section is as large as 4.5 × 10{sup 3}GM. • The molecule exhibits excellent thermal stability. • The molecule is a good two-photon induced blue fluorescent material. • The spiroconjugation effect explains the excellent properties.
International Nuclear Information System (INIS)
Yin, Hongyao; Xiao, Haibo; Ding, Lei; Zhang, Chun; Ren, Aiming; Li, Bo
2015-01-01
A spirobifluorene-bridged donor/donor chromophore, 2,7-bis-(4-(N,N-diphenylamino)phen-1-yl)-9,9′-spirobifluorene (SPF-TP), was found to combine excellent transparency in the near UV–visible region (λ cut-off ≤ 420 nm), large two-photon absorption cross-section (4.5 × 10 3 GM) and high thermal stability (T d = 501 °C). In comparison to the reported two-photon absorption molecules, SPF-TP represents the best thermal stability so far described in the literature. The main electronic factors explaining the high two-photon absorption activities of SPF-TP were analyzed by theoretical calculations. Cyclic voltammograms were employed to explore the causes of the excellent transparency of SPF-TP. It was found that the spiroconjugation effect is responsible for the excellent nonlinearity/transparency/thermal stability trade-off in SPF-TP. In addition, SPF-TP is also a good two-photon induced blue fluorescent material with high fluorescence quantum yield (Φ = 0.90, in THF). - Highlights: • We report a molecule exhibiting excellent transparency. • The two-photon absorption cross-section is as large as 4.5 × 10 3 GM. • The molecule exhibits excellent thermal stability. • The molecule is a good two-photon induced blue fluorescent material. • The spiroconjugation effect explains the excellent properties
International Nuclear Information System (INIS)
Rahmattulla, A.A.; Taghite, M.B.
1996-01-01
In this paper was studied a thermal problem with the fourier boundary conditions on the edges of the holes in a periodically perforated plate of a heat exchanger. This problem contains several reduced parameters which can be very small (the period ε of the distribution of the holes, the reduced thickness e of the plate and the three Biot numbers relative to the different parts of the boundary). The homogenization technique was used to estimate the field of temperatures attainable in the upper plate, depending on the relative order of magnitude of the smell parameters. (authors). 9 refs
International Nuclear Information System (INIS)
Sakhnovich, Alexander
2008-01-01
A Borg–Marchenko-type uniqueness theorem (in terms of the Weyl function) is obtained here for the system auxiliary to the N-wave equation. A procedure to solve the inverse problem is used for this purpose. The asymptotic condition on the Weyl function, under which the inverse problem is uniquely solvable, is completed by a new and simple sufficient condition on the potential, which implies this asymptotic condition. The evolution of the Weyl function is discussed and the solution of an initial-boundary-value problem for the N-wave equation follows. Explicit solutions of an inverse problem are obtained. The system with a shifted argument is treated
Liu, Tianyang; Chan, Hiu Ning; Grimshaw, Roger; Chow, Kwok Wing
2017-11-01
The spatial structure of small disturbances in stratified flows without background shear, usually named the `Taylor-Goldstein equation', is studied by employing the Boussinesq approximation (variation in density ignored except in the buoyancy). Analytical solutions are derived for special wavenumbers when the Brunt-Väisälä frequency is quadratic in hyperbolic secant, by comparison with coupled systems of nonlinear Schrödinger equations intensively studied in the literature. Cases of coupled Schrödinger equations with four, five and six components are utilized as concrete examples. Dispersion curves for arbitrary wavenumbers are obtained numerically. The computations of the group velocity, second harmonic, induced mean flow, and the second derivative of the angular frequency can all be facilitated by these exact linear eigenfunctions of the Taylor-Goldstein equation in terms of hyperbolic function, leading to a cubic Schrödinger equation for the evolution of a wavepacket. The occurrence of internal rogue waves can be predicted if the dispersion and cubic nonlinearity terms of the Schrödinger equations are of the same sign. Partial financial support has been provided by the Research Grants Council contract HKU 17200815.
Directory of Open Access Journals (Sweden)
Tomasz S. Zabawa
2005-01-01
Full Text Available The Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations of elliptic type is considered. It is shown the existence of solutions to this problem. The result is based on Chaplygin's method of lower and upper functions.
Karuppasamy, P.; Senthil Pandian, Muthu; Ramasamy, P.; Verma, Sunil
2018-05-01
The optically good quality single crystals of triphenylphosphine oxide 4-nitrophenol (TP4N) with maximum dimension of 15 × 10 × 5 mm3 were grown by slow evaporation solution technique (SEST) at room temperature. The cell dimensions of the grown TP4N crystal were confirmed by single crystal X-ray diffraction (SXRD) and the crystalline purity was confirmed and planes were indexed by powder X-ray diffraction (PXRD) analysis. Functional groups of TP4N crystal were confirmed by Fourier transform infrared (FTIR) spectral analysis. The optical transmittance of the grown crystal was determined by the UV-Vis NIR spectral analysis and it has good optical transparency in the entire visible region. The band tail (Urbach) energy of the grown crystal was analyzed and it appears to be minimum, which indicates that the TP4N has good crystallinity. The position of valence band (Ev) and conduction band (Ec) of the TP4N have been determined from the electron affinity energy (EA) and the ionization energy (EI) of its elements and using the optical band gap. The thermal behaviour of the grown crystal was investigated by thermogravimetric and differential thermal analysis (TG-DTA). Vickers microhardness analysis was carried out to identify the mechanical stability of the grown crystal and their indentation size effect (ISE) was explained by the Meyer's law (ML), Hays-Kendall's (HK) approach, proportional specimen resistance (PSR) model, modified PSR model (MPSR), elastic/plastic deformation (EPD) model and indentation induced cracking (IIC) model. Chemical etching study was carried out to find the etch pit density (EPD) of the grown crystal. Laser damage threshold (LDT) value was measured by using Nd:YAG laser (1064 nm). The dielectric permittivity (ε՛) and dielectric loss (tan δ) as a function of frequency was measured. The electronic polarizability (α) of the TP4N crystal was calculated. It is well matched to the value which was calculated from Clausius-Mossotti relation
Ferreira, Ana C. M.; Teixeira, Senhorinha F. C. F.; Silva, Rui G.; Silva, Ângela M.
2018-04-01
Cogeneration allows the optimal use of the primary energy sources and significant reductions in carbon emissions. Its use has great potential for applications in the residential sector. This study aims to develop a methodology for thermal-economic optimisation of small-scale micro-gas turbine for cogeneration purposes, able to fulfil domestic energy needs with a thermal power out of 125 kW. A constrained non-linear optimisation model was built. The objective function is the maximisation of the annual worth from the combined heat and power, representing the balance between the annual incomes and the expenditures subject to physical and economic constraints. A genetic algorithm coded in the java programming language was developed. An optimal micro-gas turbine able to produce 103.5 kW of electrical power with a positive annual profit (i.e. 11,925 €/year) was disclosed. The investment can be recovered in 4 years and 9 months, which is less than half of system lifetime expectancy.
Energy Technology Data Exchange (ETDEWEB)
Tanaka, Masaaki, E-mail: tanaka.masaaki@jaea.go.jp
2014-11-15
Highlights: • Outline of numerical simulation code MUGTHES for fluid-structure thermal interaction was described. • The grid convergence index (GCI) method was applied according to the ASME V and V-20 guide. • Uncertainty of MUGTHES can be successfully quantified for thermal-hydraulic problems and unsteady heat conduction problems in the structure. • Validation for fluid-structure thermal interaction problem in a T-junction piping system was well conducted. - Abstract: Thermal fatigue caused by thermal mixing phenomena is one of the most important issues in design and safety assessment of fast breeder reactors. A numerical simulation code MUGTHES consisting of two calculation modules for unsteady thermal-hydraulics analysis and unsteady heat conduction analysis in structure has been developed to predict thermal mixing phenomena and to estimate thermal response of structure under the thermal interaction between fluid and structure fields. Although verification and validation (V and V) of MUGTHES has been required, actual procedure for uncertainty quantification is not fixed yet. In order to specify an actual procedure of V and V, uncertainty quantifications with the grid convergence index (GCI) estimation according to the existing guidelines were conducted in fundamental laminar flow problems for the thermal-hydraulics analysis module, and also uncertainty for the structure heat conduction analysis module and conjugate heat transfer model was quantified in comparison with the theoretical solutions of unsteady heat conduction problems. After the verification, MUGTHES was validated for a practical fluid-structure thermal interaction problem in T-junction piping system compared with measured results of velocity and temperatures of fluid and structure. Through the numerical simulations in the verification and validation, uncertainty of the code was successfully estimated and applicability of the code to the thermal fatigue issue was confirmed.
International Nuclear Information System (INIS)
Botto, D.; Zucca, S.; Gola, M.M.
2003-01-01
In the literature many works have been written dealing with the task of on-line calculation of temperature and thermal stress for machine components and structures, in order to evaluate fatigue damage accumulation and estimate residual life. One of the most widespread methodologies is the Green's function technique (GFT), by which machine parameters such as fluid temperatures, pressures and flow rates are converted into metal temperature transients and thermal stresses. However, since the GFT is based upon the linear superposition principle, it cannot be directly used in the case of varying heat transfer coefficients. In the present work, a different methodology is proposed, based upon CMS for temperature transient calculation and upon the GFT for the related thermal stress evaluation. This new approach allows variable heat transfer coefficients to be accounted for. The methodology is applied for two different case studies, taken from the literature: a thick pipe and a nozzle connected to a spherical head, both subjected to multiple convective boundary conditions
Energy Technology Data Exchange (ETDEWEB)
NONE
1981-07-01
The main results contained in this report are the following: i ) Lagrangian universality holds in a precisely defined weak sense. II ) Isolation of 5th order polynomial evolution equations having high order conservation laws. III ) Hamiltonian formulation of a wide class of non-linear evolution equations. IV) Some properties of the symmetries of Gardner-like systems. v) Characterization of the range and Kernel of {zeta}/{zeta} u{sub {alpha}}, |{alpha} | - 1. vi) A generalized variational approach and application to the anharmonic oscillator. v II ) Relativistic correction and quasi-classical approximation to the anechoic oscillator. VII ) Properties of a special class of 6th-order anharmonic oscillators. ix) A new method for constructing conserved densities In PDE. (Author) 97 refs.
On the curve of critical exponents for nonlinear elliptic problems in the case of a zero mass
Il'yasov, Ya. Sh.
2017-03-01
For semilinear elliptic equations -Δ u = λ| u| p-2 u-| u| q-2 u, boundary value problems in bounded and unbounded domains are considered. In the plane of exponents p × q, the so-called curves of critical exponents are defined that divide this plane into domains with qualitatively different properties of the boundary value problems and the corresponding parabolic equations. New solvability conditions for boundary value problems, conditions for the stability and instability of stationary solutions, and conditions for the existence of global solutions to parabolic equations are found.
Directory of Open Access Journals (Sweden)
Aliasghar Baziar
2015-03-01
Full Text Available Abstract In order to handle large scale problems this study has used shuffled frog leaping algorithm. This algorithm is an optimization method based on natural memetics that uses a new two-phase modification to it to have a better search in the problem space. The suggested algorithm is evaluated by comparing to some well known algorithms using several benchmark optimization problems. The simulation results have clearly shown the superiority of this algorithm over other well-known methods in the area.
Dhavamurthy, M.; Peramaiyan, G.; Babu, K. Syed Suresh; Mohan, R.
2015-04-01
Organosulfur nonlinear optical single crystals of orthorhombic bis(guanidinium) 5-sulfosalicylate (2CH6N3 +·C7H4O6S2-·H2O) with dimension 14 mm × 4 mm × 5 mm have been grown from methanol and water solvents in 1:1 ratio by the slow evaporation growth technique. The crystal structure and morphology of the crystals have been studied by single-crystal X-ray diffraction. FTIR spectroscopic studies were carried out to identify the functional groups and vibrational modes present in the grown crystals. The UV-Vis spectrum was studied to analyze the linear optical properties of the grown crystals. The thermal gravimetric analysis was conducted on the grown crystals, and the result revealed that the grown crystal is thermally stable up to 65 °C. The dielectric tensor components ɛ 11, ɛ 22 and ɛ 33 of BG5SS crystal were evaluated as a function of frequency at 40 °C. The surface laser damage threshold for the grown crystal was measured using Nd:YAG laser. Further, Vickers micro-hardness study was carried out to analyze the mechanical strength of the grown crystals for various loads.
Jayanalina, T.; Rajarajan, G.; Boopathi, K.; Sreevani, K.
2015-09-01
A new organic nonlinear optical crystal 2-amino-5-chloropyridinium-L-tartarate [2A5CPLTA] has been synthesized and the crystals were grown by slow evaporation solution technique at room temperature using methanol as solvent. The crystal structure of the title compound has been determined by the single crystal X-ray diffraction study and it belongs to the monoclinic system with noncentrosymmetric space group P21. The presence of functional groups was ascertained by Fourier transform infrared analysis. The transmittance and lower cut off of the grown crystal was ascertained by the UV-vis-NIR spectroscopy. Thermal studies reveled that 2A5CPLTA crystal is thermally stable up to 144 °C. The dielectric measurements of the grown crystal were carried out with different frequencies and temperatures. Vickers micro hardness measurement was carried out to study the mechanical behavior of the grown crystal. The second harmonic generation of the title crystal was confirmed by the Kurtz-Perry powder test employing the Nd: YAG laser as the source.
International Nuclear Information System (INIS)
Miranda, Carlos A. de J.; Libardi, Rosani M.P.; Boari, Zoroastro de M.
2009-01-01
An analytical methodology was developed to predict the thermal stress level that occurs in a metallic matrix composite reinforced with SiC particles, when the temperature decreases from 600 deg C to 20 deg C during the fabrication process. This analytical development is based on the Eshelby method, dislocation mechanisms, and the Maxwell-Boltzmann distribution model. The material was assumed to have a linear elastic behavior. The analytical results from this formulation were verified against numerical linear analyses that were performed over a set of random non-uniform distribution of particles that covers a wide range of volumetric ratios. To stick with the analytical hypothesis, particles with round geometry were used. Each stress distribution, represented by the isostress curves at ΔT=-580 deg C, was analyzed with an image analyzer. A statistical procedure was applied to obtain the most probable thermal stress level. Analytical and numerical results compared very well. Plastic deformation as well as particle geometry can alter significantly the stress field in the material. To account for these effects, in this work, several numerical analyses were performed considering the non-linear behavior for the aluminum matrix and distinct particle geometries. Two distinct sets of data with were used. To allow a direct comparison, the first set has the same models (particle form, size and distribution) as used previously. The second set analyze quadrilateral particles and present very tight range of volumetric ratio, closer to what is found in actual SiC composites. A simple and fast algorithm was developed to analyze the new results. The comparison of these results with the previous ones shows, as expected, the strong influence of the elastic-plastic behavior of the aluminum matrix on the composite thermal stress distribution due to its manufacturing process and shows, also, a small influence of the particles geometry and volumetric ratio. (author)
Thermal convection and nonlinear effects of a superfluid 3He-4He mixture in a porous medium
International Nuclear Information System (INIS)
Chien, L.C.L.
1986-01-01
The convective instability of one-component classical fluids in a porous medium confined between two unbounded slabs was studied. This system behaves like a high Prandtl number bulk fluid. It has boundary conditions similar to the stress-free boundary conditions of bulk one-component classical fluids. Both the amplitude expansion method and the Galerkin method were used to investigate the nonlinear steady convection. Two dimensional rolls are the only stable motion at the onset of convection. Beyond threshold, the steady convection rolls become unstable to formation of cross-roll and zigzag instabilities. Applying the phase-dynamics approach for the zigzag instability, the author obtained the diffusion coefficient D, which can signal the onset of instability. Also investigated was the convective instability of superfluid 3 He- 4 He mixtures in porous media. Assuming no interaction between the average superflow and the porous medium and treating the normal flow in the equation of motion like a classical fluid in a porous medium, it was found that the superfluid mixtures in a porous medium. To investigate the effects of a lateral boundary, the convective instability of classical one-component fluids in porous media inside a box was studied. The zigzag instability does not exist because of the boundary conditions at the side of the box
Energy Technology Data Exchange (ETDEWEB)
Roche, J.M.; Padet, C.; Padet, J.P. [Faculte des Sciences de Reims, 51 (France). Laboratoire de Thermomecanique
1996-12-31
This workshop day was jointly organized by the French society of thermal engineers (SFT) and the university group of thermal engineers (GUT). This compilation of proceedings comprises 8 papers dealing with: tendencies and ultimate tendencies of a non-linear phenomenon - scale of observation; quantification of the chaotic regime using the estimation of the information dimension; chaotic mixing and heat transfer between concentric confocal ellipses: experimental and numerical results; development of thermal instabilities in a mixed convection horizontal flow: the Lagrangian point of view; non-linear dynamics of surface instabilities: droplets and liquid columns; on the validity of global criterion when characterizing chaotic behaviour in two-dimensional flows; study of the hydrodynamical instabilities of natural convection flows in cavities partially filled with a porous medium; analytical study of induced instabilities at the nucleated ebullition - film ebullition transition. (J.S.)
International Nuclear Information System (INIS)
Nelipa, N.F.
1978-01-01
The existence of the solution of the nonlinear, singular equations of quantum field theory is discussed. By making use of the Banach's and Schauder's fixed point theorems, the condition of the existence of these equations is found. As some illustration, these methods were applied to the equations for the π-scattering on static nucleon. The investigations of the other equations of quantum field theory (Chew-Low, double dispersin relation, Green's function) lead to the similar result. The application of the Newton-Kantorovich method to the Chew-Low equations also gives the similar result. What are the causes of such situation[ The main suggestions which the author has used were that the Banach's, the Schauder's, and the Newton-Kantorovich methods were applied and the Hoelder space was choosen. It may be that the method are crude. It may be that the solutions do not belong to the Hoelder space. Now it is rather difficult to say which role each of these two suggestions plays. (Kobatake, H.)
Modeling Thermally Driven Flow Problems with a Grid-Free Vortex Filament Scheme: Part 1
2018-02-01
simulation FMM Fast Multipole Method GPUs graphic processing units LES Large Eddy Simulation M-O Monin-Obukhov MPI Message Passing Interface Re Reynolds...mail.mil>. Grid-free representation of turbulent flow via vortex filaments offers a means for large eddy simulations that faithfully and efficiently...particle, Lagrangian, turbulence, grid-free, large eddy simulation , natural convection, thermal bubble 56 Pat Collins 301-394-5617Unclassified
Mahadevan, M.; Arivanandhan, M.; Elangovan, K.; Anandan, P.; Ramachandran, K.
2017-07-01
Good quality single crystals of sodium acid phthalate (NaAP) were grown by slow evaporation technique. Single crystal X-ray diffraction study of the grown crystal reveals that the crystal belongs to orthorhombic system with space group B2ab. Fourier transform infrared spectrum confirms the presence of the functional groups of the grown material. Inductively coupled plasma emission spectroscopy analysis is used to confirm the presence of Na element in the sample. Thermal analysis of the NaAP crystal shows that the crystal is stable up to 140°C. Optical transmittance of the grown crystal was recorded in the wavelength range from 200 and 800 nm using UV-Vis-NIR spectrophotometer. The second harmonic generation of NaAP was analysed using Kurtz powder technique.