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)
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
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)
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
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
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)
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.
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
Kono, Mitsuo
2010-01-01
A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.
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
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
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.)
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 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
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.
Singh, Devraj
2015-01-01
Numerical Problems in Physics, Volume 1 is intended to serve the need of the students pursuing graduate and post graduate courses in universities with Physics and Materials Science as subject including those appearing in engineering, medical, and civil services entrance examinations. KEY FEATURES: * 29 chapters on Optics, Wave & Oscillations, Electromagnetic Field Theory, Solid State Physics & Modern Physics * 540 solved numerical problems of various universities and ompetitive examinations * 523 multiple choice questions for quick and clear understanding of subject matter * 567 unsolved numerical problems for grasping concepts of the various topic in Physics * 49 Figures for understanding problems and concept
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)
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.
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)
Nonlinear physical systems spectral analysis, stability and bifurcations
Kirillov, Oleg N
2013-01-01
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam
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.
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.
Inverse operator theory method and its applications in nonlinear physics
International Nuclear Information System (INIS)
Fang Jinqing
1993-01-01
Inverse operator theory method, which has been developed by G. Adomian in recent years, and its applications in nonlinear physics are described systematically. The method can be an unified effective procedure for solution of nonlinear and/or stochastic continuous dynamical systems without usual restrictive assumption. It is realized by Mathematical Mechanization by us. It will have a profound on the modelling of problems of physics, mathematics, engineering, economics, biology, and so on. Some typical examples of the application are given and reviewed
Three religious rules of nonlinear physics
International Nuclear Information System (INIS)
Yankov, V.V.
1993-01-01
The theory of strong turbulence is a part of nonlinear physics. The three open-quotes religious rulesclose quotes of nonlinear physics present a heuristic viewpoint that can be used to qualitatively predict the evolution of nonlinear systems. These rules are as follows. (1) The basic results can be obtained from the conservation laws. If some kind of process is not forbidden by these laws, it generally occurs. If it doesn't this means that another conserved quantity imposing the constraint is being missed. (2) The universal law of open-quotes 20/80close quotes takes place: 20% of people drink 80% of beer. In other words, interesting processes usually take place in localized structures occupying a small share of volume. The localized structures interact weakly and therefore maintain their identity. For this reason they are universal and can be investigated. (3) The open-quotes general situationclose quotes is nonintegrable. The special case of exact solutions in integrable models represent a degenerate (nontypical) behavior. Particular exact solutions cannot be taken as representative solutions unless they are attractors. The presence of attractors simplifies the analysis and clarifies the situation. In plasma physics one deals with infinite-dimensional (PDE) systems distributed in space. The application of the religious rules 1 and 2 then leads to the following. If the conservation laws do not prohibit the development of singularities they do occur. If the singularities are prohibited, then stable localized structures take place. Solitons (or solitary waves) and vortices are examples of such stable structures. Wave collapse, wave-breaking, shock waves, magnetic reconnection and singularities in ideal Euler liquid are the examples of singularities. According to rule 3, exact solutions are very essential if they are attractors in some sense. Analysis of this problem is presented for solitons in nonintegrable wave systems and 2D vortices
Nonlinear aspects of quantum plasma physics
International Nuclear Information System (INIS)
Shukla, Padma K; Eliasson, B
2010-01-01
Dense quantum plasmas are ubiquitous in planetary interiors and in compact astrophysical objects (e.g., the interior of white dwarf stars, in magnetars, etc.), in semiconductors and micromechanical systems, as well as in the next-generation intense laser-solid density plasma interaction experiments and in quantum X-ray free-electron lasers. In contrast to classical plasmas, quantum plasmas have extremely high plasma number densities and low temperatures. Quantum plasmas are composed of electrons, positrons and holes, which are degenerate. Positrons (holes) have the same (slightly different) mass as electrons, but opposite charge. The degenerate charged particles (electrons, positrons, and holes) obey the Fermi-Dirac statistics. In quantum plasmas, there are new forces associated with (i) quantum statistical electron and positron pressures, (ii) electron and positron tunneling through the Bohm potential, and (iii) electron and positron angular momentum spin. Inclusion of these quantum forces allows the existence of very high-frequency dispersive electrostatic and electromagnetic waves (e.g., in the hard X-ray and gamma-ray regimes) with extremely short wavelengths. In this review paper, we present theoretical backgrounds for some important nonlinear aspects of wave-wave and wave-electron interactions in dense quantum plasmas. Specifically, we focus on nonlinear electrostatic electron and ion plasma waves, novel aspects of three-dimensional quantum electron fluid turbulence, as well as nonlinearly coupled intense electromagnetic waves and localized plasma wave structures. Also discussed are the phase-space kinetic structures and mechanisms that can generate quasistationary magnetic fields in dense quantum plasmas. The influence of the external magnetic field and the electron angular momentum spin on the electromagnetic wave dynamics is discussed. Finally, future perspectives of the nonlinear quantum plasma physics are highlighted. (reviews of topical problems)
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
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.
SYMMETRY, HAMILTONIAN PROBLEMS AND WAVELETS IN ACCELERATOR PHYSICS
International Nuclear Information System (INIS)
FEDOROVA, A.; ZEITLIN, M.; PARSA, Z.
2000-01-01
In this paper the authors consider applications of methods from wavelet analysis to nonlinear dynamical problems related to accelerator physics. In this approach they take into account underlying algebraical, geometrical and topological structures of corresponding problems
Mathematica for Theoretical Physics Classical Mechanics and Nonlinear Dynamics
Baumann, Gerd
2005-01-01
Mathematica for Theoretical Physics: Classical Mechanics and Nonlinear Dynamics This second edition of Baumann's Mathematica® in Theoretical Physics shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Each example and calculation can be evaluated by the reader, and the reader can change the example calculations and adopt the given code to related or similar problems. The second edition has been completely revised and expanded into two volumes: The first volume covers classical mechanics and nonlinear dynamics. Both topics are the basis of a regular mechanics course. The second volume covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus. New examples have been added and the representation has been reworked to provide a more interactive problem-solving presentation. This book can be used as a textbook or as a reference work, by students and researchers alike. A...
Mechanics problems in undergraduate physics
Strelkov, S P
2013-01-01
Problems in Undergraduate Physics, Volume I: Mechanics focuses on solutions to problems in physics. The book first discusses the fundamental problems in physics. Topics include laws of conservation of momentum and energy; dynamics of a point particle in circular motion; dynamics of a rotating rigid body; hydrostatics and aerostatics; and acoustics. The text also offers information on solutions to problems in physics. Answers to problems in kinematics, statics, gravity, elastic deformations, vibrations, and hydrostatics and aerostatics are discussed. Solutions to problems related to the laws of
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.
Problems of high energy physics
International Nuclear Information System (INIS)
Kadyshevskij, V.G.
1989-01-01
Some problems of high energy physics are discussed. The main attention is paid to describibg the standard model. The model comprises quantum chromodynamics and electroweak interaction theory. The problem of CP breaking is considered as well. 8 refs.; 1 tab
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
Reactor physics problems on HCPWR
International Nuclear Information System (INIS)
Ishiguro, Yukio; Akie, Hiroshi; Kaneko, Kunio; Sasaki, Makoto.
1986-01-01
Reactor physics problems on high conversion pressurized water reactors (HCPWRs) are discussed. Described in this report are outline of the HCPWR, expected accuracy for the various reactor physical qualities, and method for K-effective calculation in the resonance energy area. And requested further research problems are shown. The target value of the conversion ratio are also discussed. (author)
Obstacle problems in mathematical physics
Rodrigues, J-F
1987-01-01
The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics.The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of the free boundary and including some results on the obstacle Plateau problem. The last part examines the application to free boundary problems, namely the lubrication-cavitation problem, the elastoplastic problem, the Signorini (or the boundary obstacle) problem, the dam problem, the continuous casting problem, the electrochemical machining problem and the problem of the flow with wake in a channel past a profile.
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.
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.
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.
Nonlinear physics: Catastrophe, chaos and complexity
International Nuclear Information System (INIS)
Arecchi, F.T.
1992-01-01
Currently in the world of physics, there is open debate on the role of the three C's - catastrophe, chaos and complexity. Seen as new ideas or paradigms, incapable of being harmonized within the realm of traditional physics, these terms seem to be creating turmoil in the classical physics establishment whose foundations date back to the early seventeenth century. This paper first defines catastrophe, chaos and complexity and shows how these terms are all connected to nonlinear dynamics and how they have long since been present within scientific treatises. It also evidences the relationship of the three C's with the concept of organization, inappropriately called self-organization, and with recognition and decisional strategies of cognitive systems. Relevant to natural science, the development of these considerations is necessitating the re-examination of the role and capabilities of human knowledge and a return to inter-disciplinary scientific-philosophical debate
Progressive problems higher grade physics
Kennedy, William
2001-01-01
This book fully covers all three Units studied in Scotland's Higher Grade Physics course, providing a systematic array of problems (from the simplest to the most difficult) to lead variously abled pupils to examination success.
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...
Open problems in condensed matter physics, 1987
International Nuclear Information System (INIS)
Falicov, L.M.
1988-08-01
The 1970's and 1980's can be considered the third stage in the explosive development of condensed matter physics. After the very intensive research of the 1930's and 1940's, which followed the formulation of quantum mechanics, and the path-breaking activity of the 1950's and 1960's, the problems being faced now are much more complex and not always susceptible to simple modelling. The (subjectively) open problems discussed here are: high temperature superconductivity, its properties and the possible new mechanisms which lead to it; the integral and fractional quantum Hall effects; new forms of order in condensed-matter systems; the physics of disorder, especially the problem of spin glasses; the physics of complex anisotropic systems; the theoretical prediction of stable and metastable states of matter; the physics of highly correlated states (heavy fermions); the physics of artificially made structures, in particular heterostructures and highly metastable states of matter; the determination of the microscopic structure of surfaces; and chaos and highly nonlinear phnomena. 82 refs
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.
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 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
Higher-order techniques for some problems of nonlinear control
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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.
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].
Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics
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Khaled A. Gepreel
2013-01-01
Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.
New Exact Penalty Functions for Nonlinear Constrained Optimization Problems
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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
From Hamiltonian chaos to complex systems a nonlinear physics approach
Leonetti, Marc
2013-01-01
From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is a demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of research in various fields of physics and beyond, most notably with the perspective of application in complex systems. This book also: Illustrates the broad research influence of tools coming from dynamical systems, nonlinear physics, and statistical dynamics Adopts a pedagogic approach to facilitate understanding by non-specialists and students Presents applications in complex systems Includes 150 illustrations From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach is an ideal book for graduate students and researchers working in applied...
Philosophical problems of modern physics
International Nuclear Information System (INIS)
Mittelstaedt, P.
1976-01-01
This book treats the philosophical problems that have arisen in connection with the theories of relativity and quantum theory. The book begins with a discussion of the problems that were raised by the special theory of relativity; questions relating to the structure of space and time, especially the problem of the temporal sequence of events. Subsequently problems are considered that were raised by the general theory of relativity, and which question the validity and applicability of Euclidean geometry to empirical space. The physical results, and in particular the theory of the measuring process in quantum mechanics, are considered. Criticism of the concept of substance and of the law of causality in quantum theory are discussed. Finally, the validity and applicability of classical logic for the domain of quantum-theoretical propositions are dealt with. (B.R.H.)
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 ...
Causality problem in atomic physics
Energy Technology Data Exchange (ETDEWEB)
Bor, N
1985-10-01
The casuality problem in atomic physics is analysed by Bohr in a wide methodological context. The first part of the paper is a short historical essay picturing the entry of statistical concepts into physics. Bohr underlines a close relationship between an unavoidably probabilitic nature of the quantum theory and quantum postulates introducing the alien-to-classical-physics concepts of integrity, individuality of atomic processes. In the second central part of the paper Bohr discusses the casuality problems in atomic physics in detail and shows that their solution requires a careful analysis of the observation process. Proceeding from the program methodological requirement to describe the measuring instrumentation operation and observation results in the language of classical physics, he explains that the statistical character of the uncertainty relationships expresses a substantial specifically quantum constraint to the applicifically of classical conceptions analyses of microphenomena. Then Bohr refines in principle the notion ''phenomenon'', as one of the central notions among those he employed for the formulation of his complementarity principle. According to bohr a phenomenon should be under-stood as an unambiguously present situation of a completed experiment. Therefore, it is erroneous to speak of the phenomenon perturbation by the observation. The final part of the article deals with the discussion of methodological parallels of the quantum theory and relativity theory.
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.
Open problems in mathematical physics
International Nuclear Information System (INIS)
Coley, Alan A
2017-01-01
We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recent article proposing 42 fundamental questions (in physics) which must be answered on the road to full enlightenment (Allen and Lidstrom 2017 Phys. Scr . 92 012501). But paraphrasing a famous quote by the British football manager Bill Shankly, in response to the question of whether mathematics can answer the Ultimate Question of Life, the Universe, and Everything, mathematics is, of course, much more important than that. (invited comment)
Open problems in mathematical physics
Coley, Alan A.
2017-09-01
We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recent article proposing 42 fundamental questions (in physics) which must be answered on the road to full enlightenment (Allen and Lidstrom 2017 Phys. Scr. 92 012501). But paraphrasing a famous quote by the British football manager Bill Shankly, in response to the question of whether mathematics can answer the Ultimate Question of Life, the Universe, and Everything, mathematics is, of course, much more important than that.
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}.
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.
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 ...
Discontinuity and complexity in nonlinear physical systems
Baleanu, Dumitru; Luo, Albert
2014-01-01
This unique book explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed....
Finegold, M.; Mass, R.
1985-01-01
Good problem solvers and poor problem solvers in advanced physics (N=8) were significantly different in their ability in translating, planning, and physical reasoning, as well as in problem solving time; no differences in reliance on algebraic solutions and checking problems were noted. Implications for physics teaching are discussed. (DH)
On the physical solutions to the heat equation subjected to nonlinear boundary conditions
International Nuclear Information System (INIS)
Gama, R.M.S. da.
1990-01-01
This work consists of a discussion on the physical solutions to the steady-state heat transfer equation, when it is subjected to nonlinear boundary conditions. It will be presented a functional, whose minimum occurs for the (unique) physical solution to the condidered heat transfer problem, suitable for a large class of typical (nonlinear) boundary conditions (representing the radiative/convective loss from the body to the environment). It will be demonstrated that these problems admit-always one, and only one, physical solution (which represents the absolute temperature). (author)
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
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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.
Hidden physics models: Machine learning of nonlinear partial differential equations
Raissi, Maziar; Karniadakis, George Em
2018-03-01
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.
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.
Nonlinear physics of shear Alfvén waves
International Nuclear Information System (INIS)
Zonca, Fulvio; Chen, Liu
2014-01-01
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These 'nonlinear equilibria' or 'phase-space zonal structures' dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results
Nonlinear physics of shear Alfvén waves
Zonca, Fulvio; Chen, Liu
2014-02-01
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These "nonlinear equilibria" or "phase-space zonal structures" dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results.
Integrating Multimedia and Physics Problems
Titus, Aaron P.
1997-11-01
Although expert problem solvers typically use pictorial representations when solving problems, novices tend to proceed from the given problem statement to a mathematical solution without first developing a visual representation of the problem. For this reason, multimedia may be an effective tool to enhance students' success at solving problems. However, merely presenting a video of motion described in a problem is not necessarily the most effective method as was found in a recent study of students' responses on Web-based homework questions. Rather, multimedia-focused problems, where data relevant to solving the problem is embedded in a video or animation, may be the best use of multimedia in problem solving. Examples of multimedia-enhanced problems and multimedia-focused problems will be demonstrated, and their differences from "traditional" problems will be highlighted. Recommendations on the use of multimedia with problem solving and preliminary data on students' success at solving these problems will be discussed.
A Multivariate Model of Physics Problem Solving
Taasoobshirazi, Gita; Farley, John
2013-01-01
A model of expertise in physics problem solving was tested on undergraduate science, physics, and engineering majors enrolled in an introductory-level physics course. Structural equation modeling was used to test hypothesized relationships among variables linked to expertise in physics problem solving including motivation, metacognitive planning,…
All problems of theoretical physics
International Nuclear Information System (INIS)
Park, Bong Yeol
1991-09-01
This book introduces particle physics, nuclear physics, and condensed matter physics. It deals with trend of particle physics, gauge theory and renormalisation, Quark-Hadron phase transition, unified field theory and theory of internal string, supersymmetry and supergravity, Berry's connection and Quantum separation of slow versus fast dynamics, giant resonance, intermediate energy nuclear physics, unclear fission reactor physics, atomic structure of metastable defect in semiconductor, dynamics theory of condensation material world, and two-dimensional Ising model revisited.
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...
Physics constrained nonlinear regression models for time series
International Nuclear Information System (INIS)
Majda, Andrew J; Harlim, John
2013-01-01
A central issue in contemporary science is the development of data driven statistical nonlinear dynamical models for time series of partial observations of nature or a complex physical model. It has been established recently that ad hoc quadratic multi-level regression (MLR) models can have finite-time blow up of statistical solutions and/or pathological behaviour of their invariant measure. Here a new class of physics constrained multi-level quadratic regression models are introduced, analysed and applied to build reduced stochastic models from data of nonlinear systems. These models have the advantages of incorporating memory effects in time as well as the nonlinear noise from energy conserving nonlinear interactions. The mathematical guidelines for the performance and behaviour of these physics constrained MLR models as well as filtering algorithms for their implementation are developed here. Data driven applications of these new multi-level nonlinear regression models are developed for test models involving a nonlinear oscillator with memory effects and the difficult test case of the truncated Burgers–Hopf model. These new physics constrained quadratic MLR models are proposed here as process models for Bayesian estimation through Markov chain Monte Carlo algorithms of low frequency behaviour in complex physical data. (paper)
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.
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
Nonlinear evolution equations having a physical meaning
International Nuclear Information System (INIS)
Nakach, R.
1976-06-01
The non stationary self-similar solutions of the nonlinear evolution equations which can be solved by the inverse scattering method are studied. It turns out, as shown by means of several examples, that when the L linear operator associated with these equations, is of second order and only then, the self-similar solutions can be expressed in terms of the various Painleve's transcendents [fr
Nonlinear physics of twisted magnetic field lines
International Nuclear Information System (INIS)
Yoshida, Zensho
1998-01-01
Twisted magnetic field lines appear commonly in many different plasma systems, such as magnetic ropes created through interactions between the magnetosphere and the solar wind, magnetic clouds in the solar wind, solar corona, galactic jets, accretion discs, as well as fusion plasma devices. In this paper, we study the topological characterization of twisted magnetic fields, nonlinear effect induced by the Lorentz back reaction, length-scale bounds, and statistical distributions. (author)
Problems and solutions in quantum physics
Ficek, Zbigniew
2016-01-01
This book contains tutorial problems with solutions for the textbook Quantum Physics for Beginners. The reader studying the abstract field of quantum physics needs to solve plenty of practical, especially quantitative, problems. This book places emphasis on basic problems of quantum physics together with some instructive, simulating, and useful applications. A considerable range of complexity is presented by these problems, and not too many of them can be solved using formulas alone.
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)
Nonlinear physics with Maple for scientists and engineers
Enns, Richard H
1997-01-01
Philosophy of the Text This text has been designed to be an introductory survey of the basic concepts and applied mathematical methods of nonlinear science. Students in engineer ing, physics, chemistry, mathematics, computing science, and biology should be able to successfully use this text. In an effort to provide the students with a cutting edge approach to one of the most dynamic, often subtle, complex, and still rapidly evolving, areas of modern research-nonlinear physics-we have made extensive use of the symbolic, numeric, and plotting capabilities of Maple V Release 4 applied to examples from these disciplines. No prior knowledge of Maple or computer programming is assumed, the reader being gently introduced to Maple as an auxiliary tool as the concepts of nonlinear science are developed. The diskette which accompanies the text gives a wide variety of illustrative nonlinear examples solved with Maple. An accompanying laboratory manual of experimental activities keyed to the text allows the student the...
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)
Rooting the biggest problems in physics
DEFF Research Database (Denmark)
Javadi, Hossein; Forouzbakhsh, Farshid
2016-01-01
to combine these three theories of classical mechanics, quantum mechanics and relativity in order to reach to a unique physics. Eventually, by answering the unanswered questions, the physics problems will be solved. In this paper, the stems of physics problems are expressed and the solution of them...
Some non-linear physics in crystallographic structures
International Nuclear Information System (INIS)
Aubry, S.
1977-10-01
A summary of studies on simple but strongly nonlinear crystallographic models that make use of some methods in stochasticity is presented. Two one-dimensional models are described; one has been studied to understand some aspects of the nonlinear dynamics in crystals when close to the transition temperature, the other is for commensurability and incommensurability problems. Periodic orbits and the dynamics of a one-dimensional coupled double-well chain are considered, along with lattice locking and stochasticity
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.
Non-Linear Multi-Physics Analysis and Multi-Objective Optimization in Electroheating Applications
Czech Academy of Sciences Publication Activity Database
di Barba, P.; Doležel, Ivo; Mognaschi, M. E.; Savini, A.; Karban, P.
2014-01-01
Roč. 50, č. 2 (2014), s. 7016604-7016604 ISSN 0018-9464 Institutional support: RVO:61388998 Keywords : coupled multi-physics problems * finite element method * non-linear equations Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 1.386, year: 2014
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
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
Energy Technology Data Exchange (ETDEWEB)
Sagdeev, R Z
1984-01-01
The results of theoretical and experimental investigations of nonlinear and turbulent phenomena from a wide range of fields in physics are presented in reviews and reports. Topics examined include localized vortex formations in an ideal fluid, phase transitions in crystals, spatially nonuniform structures in condensed matter, solitons in molecular systems, the migration of quasi-particles in easily deformed crystals, bifurcations and dissipative structures in distributed kinetic systems, and structures in a nonlinear burning medium. Consideration is given to macroscopic motion generation in nonequilibrium media, the interaction of bulk and surface wave trains, near-threshold instabilities in hydrodynamics, solitons in nonlinear elastic rods with variable characteristics, the generation of solitons and vortices from chaos, and nonlinear electromagnetic-wave dissipation in an electron system.
Hierarchy problem and BSM physics
Indian Academy of Sciences (India)
Gautam Bhattacharyya
2017-10-05
Oct 5, 2017 ... One-loop quantum corrections to the Higgs boson mass from fermion ... physics? 3. Supersymmetry. Supersymmetry relates matter particles with force par- ticles, i.e. it .... Higgs remembers its Goldstone origin and its coupling.
New Approach to Analyzing Physics Problems: A Taxonomy of Introductory Physics Problems
Teodorescu, Raluca E.; Bennhold, Cornelius; Feldman, Gerald; Medsker, Larry
2013-01-01
This paper describes research on a classification of physics problems in the context of introductory physics courses. This classification, called the Taxonomy of Introductory Physics Problems (TIPP), relates physics problems to the cognitive processes required to solve them. TIPP was created in order to design educational objectives, to develop…
Parallel computing in plasma physics: Nonlinear instabilities
International Nuclear Information System (INIS)
Pohn, E.; Kamelander, G.; Shoucri, M.
2000-01-01
A Vlasov-Poisson-system is used for studying the time evolution of the charge-separation at a spatial one- as well as a two-dimensional plasma-edge. Ions are advanced in time using the Vlasov-equation. The whole three-dimensional velocity-space is considered leading to very time-consuming four-resp. five-dimensional fully kinetic simulations. In the 1D simulations electrons are assumed to behave adiabatic, i.e. they are Boltzmann-distributed, leading to a nonlinear Poisson-equation. In the 2D simulations a gyro-kinetic approximation is used for the electrons. The plasma is assumed to be initially neutral. The simulations are performed at an equidistant grid. A constant time-step is used for advancing the density-distribution function in time. The time-evolution of the distribution function is performed using a splitting scheme. Each dimension (x, y, υ x , υ y , υ z ) of the phase-space is advanced in time separately. The value of the distribution function for the next time is calculated from the value of an - in general - interstitial point at the present time (fractional shift). One-dimensional cubic-spline interpolation is used for calculating the interstitial function values. After the fractional shifts are performed for each dimension of the phase-space, a whole time-step for advancing the distribution function is finished. Afterwards the charge density is calculated, the Poisson-equation is solved and the electric field is calculated before the next time-step is performed. The fractional shift method sketched above was parallelized for p processors as follows. Considering first the shifts in y-direction, a proper parallelization strategy is to split the grid into p disjoint υ z -slices, which are sub-grids, each containing a different 1/p-th part of the υ z range but the whole range of all other dimensions. Each processor is responsible for performing the y-shifts on a different slice, which can be done in parallel without any communication between
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
Estimation of Physical Parameters in Linear and Nonlinear Dynamic Systems
DEFF Research Database (Denmark)
Knudsen, Morten
variance and confidence ellipsoid is demonstrated. The relation is based on a new theorem on maxima of an ellipsoid. The procedure for input signal design and physical parameter estimation is tested on a number of examples, linear as well as nonlinear and simulated as well as real processes, and it appears...
New analytical solutions for nonlinear physical models of the ...
Indian Academy of Sciences (India)
In mathematical physics, we studied two complex systems, the Maccari system and the coupled Higgs field equation. We construct sufficient exact solutions for nonlinear evolution equations. To study travelling wave solutions, we used a fractional complex transform to convert the particular partial differential equation of ...
Travelling wave solutions to nonlinear physical models by means
Indian Academy of Sciences (India)
This paper presents the ﬁrst integral method to carry out the integration of nonlinear partial differential equations in terms of travelling wave solutions. For illustration, three important equations of mathematical physics are analytically investigated. Through the established ﬁrst integrals, exact solutions are successfully ...
Travelling wave solutions to nonlinear physical models by means of ...
Indian Academy of Sciences (India)
Abstract. This paper presents the first integral method to carry out the integration of nonlinear ... NPDEs is an important and attractive research area. Not all ... cial types of analytic solutions to understand biological, physical and chemical phenomena ... Thus, based on the qualitative theory of ordinary differential equations.
International Nuclear Information System (INIS)
Benisti, D.
2011-01-01
This manuscript provides a theoretical description, sometimes illustrated by experimental results, of several examples of field-matter interaction in various domains of physics, showing how the same basic concepts and theoretical methods may be used in very different physics situations. The issues addressed here are nonlinear field-matter interaction in plasma physics within the framework of classical mechanics (with a particular emphasis on wave-particle interaction), the linear analysis of beam-plasma instabilities in the relativistic regime, and the quantum description of laser-atom interaction, including quantum electrodynamics. Novel methods are systematically introduced in order to solve some very old problems, like the nonlinear counterpart of the Landau damping rate in plasma physics, for example. Moreover, our results directly apply to inertial confinement fusion, laser propagation in an atomic vapor, ion acceleration in a magnetized plasma and the physics of the Reversed Field Pinch for magnetic fusion. (author)
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
lns physics, knowledge and problems
International Nuclear Information System (INIS)
Jacob, M.
1976-01-01
Reference is made to recent experimentation at the CERN intersecting storage ring (ISR) and experimentation at Fermilab. This is stated to have opened up a wide new domain as regards energy considerations. The ISR spans the 250 to 2000 GeV domain, whereas the Fermilab facilities reach 500 GeV. The many processes already studied are stated to show strikingly different energy behaviour. These commands do not attempt any systematic review of lns physics, but emphasise only a few important facts and questions. Three topics considered are (i) rising cross sections and related phenomena, (ii) scaling and short range order; and (iii) inelastic diffractive phenomena. Regarding (i) it is stated that all phenomena directly related to rising cross sections are amenable to simple logarithmic parametrisations that fit well with what is expected for very high energy behaviour. The very slow pace at which this occurs, however, remains a puzzle. With regard to (ii) the impressive stability of the phase space configuration of multiparticle events is stressed, which is translated in practice by scaling and short range order. Regarding (iii) diffractive excitation is an important topic in high energy hadron physics, and double diffractive excitation is an interesting study. It is stated that the stability of all large cross section hadronic processes with increasing energy is remarkable, and it is not understood why so many things change so slowly with increasing energy. What can be referred to as lns physics still carries many challenging questions. (U.K.)
The Magnetohydrodynamic Generator A Physics Olympiad Problem
Indian Academy of Sciences (India)
The Magnetohydrodynamic Generator A Physics Olympiad Problem (2001). Vijay A Singh ... Magnetohydrodynamics; generator; power; efficiency; Faraday's law; Physics Olympiad . Author Affiliations. Vijay A Singh1 Manish Kapoor2. Physics Department Indian Institute of Technology Kanpur 208016, India. MPE College ...
Using Isomorphic Problems to Learn Introductory Physics
Lin, Shih-Yin; Singh, Chandralekha
2011-01-01
In this study, we examine introductory physics students' ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred sixty-two students from a calculus-based and an algebra-based introductory physics course were given a quiz in the…
Inverse problem in nuclear physics
International Nuclear Information System (INIS)
Zakhariev, B.N.
1976-01-01
The method of reconstruction of interaction from the scattering data is formulated in the frame of the R-matrix theory in which the potential is determined by position of resonance Esub(lambda) and their reduced widths γ 2 lambda. In finite difference approximation for the Schroedinger equation this new approach allows to make the logics of the inverse problem IP more clear. A possibility of applications of IP formalism to various nuclear systems is discussed. (author)
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
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...
The chemistry and physics of nonlinear optical materials
International Nuclear Information System (INIS)
Velsko, S.P.; Eimerl, D.
1989-01-01
Recent efforts to engineer new nonlinear optical materials with specific desired characteristics has engendered a need for a theoretical description of optical properties which is readily accessible to chemists, yet correctly treats the essential physics of dielectric response. This paper describes a simple empirical molecular orbital model which gives useful insights into the relationship between chemical composition, crystalline structure, and optical susceptibilities. The authors compare the probabilities of finding new harmonic generators in various chemical classes. Rigorous bounds on the magnitudes of linear and nonlinear optical coefficients and their anisotropies are also discussed
Nonlinear Inference in Partially Observed Physical Systems and Deep Neural Networks
Rozdeba, Paul J.
The problem of model state and parameter estimation is a significant challenge in nonlinear systems. Due to practical considerations of experimental design, it is often the case that physical systems are partially observed, meaning that data is only available for a subset of the degrees of freedom required to fully model the observed system's behaviors and, ultimately, predict future observations. Estimation in this context is highly complicated by the presence of chaos, stochasticity, and measurement noise in dynamical systems. One of the aims of this dissertation is to simultaneously analyze state and parameter estimation in as a regularized inverse problem, where the introduction of a model makes it possible to reverse the forward problem of partial, noisy observation; and as a statistical inference problem using data assimilation to transfer information from measurements to the model states and parameters. Ultimately these two formulations achieve the same goal. Similar aspects that appear in both are highlighted as a means for better understanding the structure of the nonlinear inference problem. An alternative approach to data assimilation that uses model reduction is then examined as a way to eliminate unresolved nonlinear gating variables from neuron models. In this formulation, only measured variables enter into the model, and the resulting errors are themselves modeled by nonlinear stochastic processes with memory. Finally, variational annealing, a data assimilation method previously applied to dynamical systems, is introduced as a potentially useful tool for understanding deep neural network training in machine learning by exploiting similarities between the two problems.
What is physics problem solving competency?
DEFF Research Database (Denmark)
Niss, Martin
2018-01-01
on the nature of physics problem- solving competency. The first, Sommerfeld’s, is a “theory first, phenomenon second” approach. Here the relevant problems originate in one of the theories of physics and the job goal of the problem- solver is to make a mathematical analysis of the suitable equation......A central goal of physics education is to teach problem-solving competency, but the nature of this competency is not well-described in the literature. The present paperarticle uses recent historical scholarship on Arnold Sommerfeld and Enrico Fermi to identify and characterize two positions......(s) and then give a qualitative analysis of the phenomenon that arise from these mathematical results. Fermi’s position is a “phenomenon first, theory second” approach, where the starting point is a physical phenomenon that is analyzed and then brought into the realm of a physics theory. The two positions...
Experimental analysis of nonlinear oscillations in the undergraduate physics laboratory
International Nuclear Information System (INIS)
Moreno, R; Page, A; Riera, J; Hueso, J L
2014-01-01
In this paper, we present a simple experiment to introduce the nonlinear behaviour of oscillating systems in the undergraduate physics laboratory. The transverse oscillations of a spring allow reproduction of three totally different scenarios: linear oscillations, nonlinear oscillations reducible to linear for small displacements, and intrinsically nonlinear oscillations. The chosen approach consists of measuring the displacements using video photogrammetry and computing the velocities and the accelerations by means of a numerical differentiation algorithm. In this way, one can directly check the differential equation of the motion without having to integrate it, or perform an experimental study of the potential energy in each of the analysed scenarios. This experiment allows first year students to reflect on the consequences and the limits of the linearity assumption for small displacements that is so often made in technical studies. (paper)
XII seminar on problems of reactor physics
International Nuclear Information System (INIS)
Kryuchkov, Eh.F.; Naumov, V.I.
2003-01-01
Results of the XII seminar Physical problems of effective and safety use of nuclear materials taking place on the basis of MEPI (September, 2002) are discussed. Reports on the directions: physical problems of advanced nuclear-energetic technologies; account, control and nuclear material management; effective and safety use of nuclear materials at NPP; programming and software for the analysis of physical processes are performed. Of particular interest is reports on actual problems of nuclear energetics and fuel cycle, on ill-intentioned use of fissile materials, efficiency of long-lived isotopes transmutation and spent fuel management [ru
Collection of problems in physical chemistry
Bareš, Jirí; Fried, Vojtech
1961-01-01
Collection of Problems in Physical Chemistry provides illustrations and problems covering the field of physical chemistry. The material has been arranged into illustrations that are solved and supplemented by problems, thus enabling readers to determine the extent to which they have mastered each subject. Most of the illustrations and problems were taken from original papers, to which reference is made. The English edition of this book has been translated from the manuscript of the 2nd Czech edition. It has been changed slightly in some places and enlarged on in others on the basis of further
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.
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
Physics: Quantum problems solved through games
Maniscalco, Sabrina
2016-04-01
Humans are better than computers at performing certain tasks because of their intuition and superior visual processing. Video games are now being used to channel these abilities to solve problems in quantum physics. See Letter p.210
Conceptual Problem Solving in High School Physics
Docktor, Jennifer L.; Strand, Natalie E.; Mestre, José P.; Ross, Brian H.
2015-01-01
Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an…
A Boundary Value Problem for Introductory Physics?
Grundberg, Johan
2008-01-01
The Laplace equation has applications in several fields of physics, and problems involving this equation serve as paradigms for boundary value problems. In the case of the Laplace equation in a disc there is a well-known explicit formula for the solution: Poisson's integral. We show how one can derive this formula, and in addition two equivalent…
Conceptual problem solving in high school physics
Jennifer L. Docktor; Natalie E. Strand; José P. Mestre; Brian H. Ross
2015-01-01
Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an instructional approach called Conceptual Problem Solving (CPS) which guides students to identify principles, justify their use, and plan their solution in w...
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...
Foundations of Complex Systems Nonlinear Dynamics, Statistical Physics, and Prediction
Nicolis, Gregoire
2007-01-01
Complexity is emerging as a post-Newtonian paradigm for approaching a large body of phenomena of concern at the crossroads of physical, engineering, environmental, life and human sciences from a unifying point of view. This book outlines the foundations of modern complexity research as it arose from the cross-fertilization of ideas and tools from nonlinear science, statistical physics and numerical simulation. It is shown how these developments lead to an understanding, both qualitative and quantitative, of the complex systems encountered in nature and in everyday experience and, conversely, h
Using isomorphic problems to learn introductory physics
Directory of Open Access Journals (Sweden)
Shih-Yin Lin
2011-08-01
Full Text Available In this study, we examine introductory physics students’ ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred sixty-two students from a calculus-based and an algebra-based introductory physics course were given a quiz in the recitation in which they had to first learn from a solved problem provided and take advantage of what they learned from it to solve another problem (which we call the quiz problem which was isomorphic. Previous research suggests that the multiple-concept quiz problem is challenging for introductory students. Students in different recitation classes received different interventions in order to help them discern and exploit the underlying similarities of the isomorphic solved and quiz problems. We also conducted think-aloud interviews with four introductory students in order to understand in depth the difficulties they had and explore strategies to provide better scaffolding. We found that most students were able to learn from the solved problem to some extent with the scaffolding provided and invoke the relevant principles in the quiz problem. However, they were not necessarily able to apply the principles correctly. Research suggests that more scaffolding is needed to help students in applying these principles appropriately. We outline a few possible strategies for future investigation.
Using isomorphic problems to learn introductory physics
Lin, Shih-Yin; Singh, Chandralekha
2011-12-01
In this study, we examine introductory physics students’ ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred sixty-two students from a calculus-based and an algebra-based introductory physics course were given a quiz in the recitation in which they had to first learn from a solved problem provided and take advantage of what they learned from it to solve another problem (which we call the quiz problem) which was isomorphic. Previous research suggests that the multiple-concept quiz problem is challenging for introductory students. Students in different recitation classes received different interventions in order to help them discern and exploit the underlying similarities of the isomorphic solved and quiz problems. We also conducted think-aloud interviews with four introductory students in order to understand in depth the difficulties they had and explore strategies to provide better scaffolding. We found that most students were able to learn from the solved problem to some extent with the scaffolding provided and invoke the relevant principles in the quiz problem. However, they were not necessarily able to apply the principles correctly. Research suggests that more scaffolding is needed to help students in applying these principles appropriately. We outline a few possible strategies for future investigation.
An ansatz for solving nonlinear partial differential equations in mathematical physics.
Akbar, M Ali; Ali, Norhashidah Hj Mohd
2016-01-01
In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.
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
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.
Separable boundary-value problems in physics
Willatzen, Morten
2011-01-01
Innovative developments in science and technology require a thorough knowledge of applied mathematics, particularly in the field of differential equations and special functions. These are relevant in modeling and computing applications of electromagnetic theory and quantum theory, e.g. in photonics and nanotechnology. The problem of solving partial differential equations remains an important topic that is taught at both the undergraduate and graduate level. Separable Boundary-Value Problems in Physics is an accessible and comprehensive treatment of partial differential equations i
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
1000 Solved Problems in Modern Physics
Kamal, Ahmad A
2010-01-01
This book basically caters to the needs of undergraduates and graduates physics students in the area of modern physics, specially particle and nuclear physics. Lecturers/tutors may use it as a resource book. The contents of the book are based on the syllabi currently used in the undergraduate courses in USA, U.K., and other countries. The book is divided into 10 chapters, each chapter beginning with a brief but adequate summary and necessary formulas, tables and line diagrams followed by a variety of typical problems useful for assignments and exams. Detailed solutions are provided at the end of each chapter.
Conceptual problem solving in high school physics
Docktor, Jennifer L.; Strand, Natalie E.; Mestre, José P.; Ross, Brian H.
2015-12-01
Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an instructional approach called Conceptual Problem Solving (CPS) which guides students to identify principles, justify their use, and plan their solution in writing before solving a problem. The CPS approach was implemented by high school physics teachers at three schools for major theorems and conservation laws in mechanics and CPS-taught classes were compared to control classes taught using traditional problem solving methods. Information about the teachers' implementation of the approach was gathered from classroom observations and interviews, and the effectiveness of the approach was evaluated from a series of written assessments. Results indicated that teachers found CPS easy to integrate into their curricula, students engaged in classroom discussions and produced problem solutions of a higher quality than before, and students scored higher on conceptual and problem solving measures.
Conceptual problem solving in high school physics
Directory of Open Access Journals (Sweden)
Jennifer L. Docktor
2015-09-01
Full Text Available Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an instructional approach called Conceptual Problem Solving (CPS which guides students to identify principles, justify their use, and plan their solution in writing before solving a problem. The CPS approach was implemented by high school physics teachers at three schools for major theorems and conservation laws in mechanics and CPS-taught classes were compared to control classes taught using traditional problem solving methods. Information about the teachers’ implementation of the approach was gathered from classroom observations and interviews, and the effectiveness of the approach was evaluated from a series of written assessments. Results indicated that teachers found CPS easy to integrate into their curricula, students engaged in classroom discussions and produced problem solutions of a higher quality than before, and students scored higher on conceptual and problem solving measures.
Innovative applications of genetic algorithms to problems in accelerator physics
Directory of Open Access Journals (Sweden)
Alicia Hofler
2013-01-01
Full Text Available The genetic algorithm (GA is a powerful technique that implements the principles nature uses in biological evolution to optimize a multidimensional nonlinear problem. The GA works especially well for problems with a large number of local extrema, where traditional methods (such as conjugate gradient, steepest descent, and others fail or, at best, underperform. The field of accelerator physics, among others, abounds with problems which lend themselves to optimization via GAs. In this paper, we report on the successful application of GAs in several problems related to the existing Continuous Electron Beam Accelerator Facility nuclear physics machine, the proposed Medium-energy Electron-Ion Collider at Jefferson Lab, and a radio frequency gun-based injector. These encouraging results are a step forward in optimizing accelerator design and provide an impetus for application of GAs to other problems in the field. To that end, we discuss the details of the GAs used, include a newly devised enhancement which leads to improved convergence to the optimum, and make recommendations for future GA developments and accelerator applications.
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.
Statistical physics of hard optimization problems
International Nuclear Information System (INIS)
Zdeborova, L.
2009-01-01
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the non-deterministic polynomial (NP)-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this article is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfy ability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named ”locked” constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfy ability.
Statistical physics of hard optimization problems
International Nuclear Information System (INIS)
Zdeborova, L.
2009-01-01
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the non-deterministic polynomial-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an non-deterministic polynomial-complete problem the practically arising instances might, in fact, be easy to solve. The principal the question we address in the article is: How to recognize if an non-deterministic polynomial-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfiability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named 'locked' constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfiability (Authors)
Statistical physics of hard optimization problems
Zdeborová, Lenka
2009-06-01
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the non-deterministic polynomial (NP)-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this article is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfiability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named "locked" constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfiability.
Frontiers of plasma physics. III. The implications of nonlinearity
International Nuclear Information System (INIS)
Bardwell, S.
1977-01-01
In the first two articles of this series, Bardwell reviewed the experimental evidence that points to an inherent nonlinear quality in plasmas. Evidence from strongly turbulent plasmas, where the energy in the plasma's collective motions is comparable to the energy in random motion, leads to the speculation that high energy-density plasmas can provide insight into previously inaccessible regimes of physical behavior. Both laboratory and astrophysical plasmas show a marked tendency to generate self-ordered, large-scale structures; islands of self-generated magnetic field, circulation cells, vortices, and filaments are among the most remarkable of these. These self-ordered phenomena, Bardwell reports, challenge in a fundamental way the conceptual tools of physics as they are presently understood. In part two of this series, Bardwell draws on the connection between linearity and entropy, a topic also examined in Levitt's companion piece in the September 1976 FEF Newsletter, to conclude that these difficulties in plasma physics stem from the invalid extension of contemporary physics, which is basically linear, to high-energy density regimes of a plasma; contemporary physics in these cases is inapplicable. Readers without a background in mathematics should not be deterred by the mathematical formalism in the last section of the article; the text can be understood without a detailed mastery of the mathematical formulae
A collection of problems for physics teaching
International Nuclear Information System (INIS)
Groeber, S; Jodl, H-J
2010-01-01
Problems are an important instrument for teachers to mediate physics content and for learners to adopt this content. This collection of problems is not only suited to traditional teaching and learning in lectures or student labs, but also to all kinds of new ways of teaching and learning, such as self-study, long-distance teaching, project-oriented learning and the use of remote labs/web experiments. We focus on Rutherford's scattering experiment, electron diffraction, Millikan's experiment and the use of pendulums to measure the dependence of gravitational acceleration on latitude. The collection contains about 50 problems with 160 subtasks and solutions, altogether 100 pages. Structure, content, range and the added value of the problems are described. The whole collection can be downloaded for free from http://rcl.physik.uni-kl.de.
The causality problem in atomic physics
International Nuclear Information System (INIS)
Bor, N.
1985-01-01
The casuality problem in atomic physics is analysed by Bohr in a wide methodological context. The first part of the paper is a short historical essay picturing the entry of statistical concepts into physics. Bohr underlines a close relationship between an unavoidably probabilitic nature of the quantum theory and quantum postulates introducing the alien-to-classical-physics concepts of integrity, individuality of atomic processes. In the second central part of the paper Bohr discusses the casuality problems in atomic physics in detail and shows that their solution requires a careful analysis of the observation process. Proceeding from the program methodological requirement to describe the measuring instrumentation operation and observation results in the language of classical physics, he explains that the statistical character of the uncertainty relationships expresses a substantial specifically quantum constraint to the applicifically of classical conceptions analyses of microphenomena. Then Bohr refines in principle the notion ''phenomenon'', as one of the central notions among those he employed for the formulation of his complementarity principle. According to bohr a phenomenon should be under-stood as an unambiguously present situation of a completed experiment. Therefore, it is erroneous to speak of the phenomenon perturbation by the observation. The final part of the article deals with the discussion of methodological parallels of the quantum theory and relativity theory
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
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
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 ...
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.
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.
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
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 ...
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
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.
Selected problems in experimental intermediate energy physics
International Nuclear Information System (INIS)
Mayes, B.W.; Hungerford, E.V.; Pinsky, L.S.
1990-09-01
The objectives of this research program are to: investigate forefront problems in experimental intermediate energy physics; educate students in this field of research; and, develop the instrumentation necessary to undertake this experimental program. Generally, the research is designed to search for physical processes which cannot be explained by conventional models of elementary interactions. This includes the use of nuclear targets where the nucleus provides a many body environment of strongly perturbation of a known interaction by this environment. Unfortunately, such effects may be masked by the complexity of the many body problem and may be difficult to observe. Therefore, experiments must be carefully chosen and analyzed for deviations from the more conventional models. There were three major thrusts of the program; strange particle physics, where a strange quark is embedded in the nuclear medium; muon electro-weak decay, which involves a search for a violation of the standard model of the electro-weak interaction; and measurement of the spin dependent structure function of the neutron
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
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 ...
New exact travelling wave solutions of nonlinear physical models
International Nuclear Information System (INIS)
Bekir, Ahmet; Cevikel, Adem C.
2009-01-01
In this work, we established abundant travelling wave solutions for some nonlinear evolution equations. This method was used to construct travelling wave solutions of nonlinear evolution equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The ((G ' )/G )-expansion method presents a wider applicability for handling nonlinear wave equations.
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.
Main physical problems of superhigh energy accelerators
International Nuclear Information System (INIS)
Lapidus, L.I.
1979-01-01
A survey is given of the state and prospects for the scientific researches to be carried out at the largest charged particle accelerators now under construction. The fundamental problems of the elementary particle physics are considered which can be solved on the base of experiments at high-energy accelerators. The problems to be solved involve development of the theory of various quark number, accurate determination of the charged and neutral intermediate vector boson masses in the Weinberg-Salam theory, the problem of production of t-quark, W -+ - and Z deg bosons, Higgs mesons and investigation of their interactions, examination of quark and lepton spectra, studies on the effects of strong interactions. As a result of the investigations on hadrons at maximum momentum transfers, the data on space-time structure at short distances can be obtained. It is emphasized that there are no engineering barriers to the construction of such accelerators. The main problem lies in financial investment. A conclusion is drawn that the next generation of accelerators will be developed on the base of cooperation between many countries [ru
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.
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...
Physics Teachers' Education (PTE): Problems and Challenges
Sassi, Elena; Michelini, Marisa
A vast majority of the research results acknowledge the crucial role of teacher's education, as a vital tool in enhancing the quality of physics education. The projects like PISA, ROSE and TIMMS showcase the impact of teacher's education as a qualitative improvement in the physics learning environment. In Physics Education Research (PER), the impact of teacher's education had been addressed for the its role in the enhancement of positive interest among the students. The current world-wide state of the art characterizes a large variety of boundary conditions, traditions and practices that are being followed. In our present context, we foucus and discuss on the multidimensional challanges such as competencies needed, degrees required, problems encountered, support to be provided and the basic pre-requirements of Teacher's education for the secondary schools. We present some of the teaching methods and practices followed in coherent with, both, the Student centered and open learning environments along with some of the useful didactical indicators. Also, we potray a couple of research-based examples successfully experimented in Italy. Finally we propose some useful recommendations along with the criteria to be followed in the teachers education for the overall improvement.
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
Inverse problems in classical and quantum physics
International Nuclear Information System (INIS)
Almasy, A.A.
2007-01-01
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A
Inverse problems in classical and quantum physics
Energy Technology Data Exchange (ETDEWEB)
Almasy, A.A.
2007-06-29
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A
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.
Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2012-01-01
Full Text Available We put a direct new method to construct the rational Jacobi elliptic solutions for nonlinear differential difference equations which may be called the rational Jacobi elliptic functions method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential difference equations in mathematical physics via the lattice equation and the discrete nonlinear Schrodinger equation with a saturable nonlinearity. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.
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.
Semi-physical Simulation Platform of a Parafoil Nonlinear Dynamic System
International Nuclear Information System (INIS)
Gao Hai-Tao; Yang Sheng-Bo; Zhu Er-Lin; Sun Qing-Lin; Chen Zeng-Qiang; Kang Xiao-Feng
2013-01-01
Focusing on the problems in the process of simulation and experiment on a parafoil nonlinear dynamic system, such as limited methods, high cost and low efficiency we present a semi-physical simulation platform. It is designed by connecting parts of physical objects to a computer, and remedies the defect that a computer simulation is divorced from a real environment absolutely. The main components of the platform and its functions, as well as simulation flows, are introduced. The feasibility and validity are verified through a simulation experiment. The experimental results show that the platform has significance for improving the quality of the parafoil fixed-point airdrop system, shortening the development cycle and saving cost
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.
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.
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.
Identification and optimization problems in plasma physics
International Nuclear Information System (INIS)
Gilbert, J.C.
1986-06-01
Parameter identification of the current in a tokamak plasma is studied. Plasma equilibrium in a vacuum container with a diaphragm is analyzed. A variable metric method with reduced optimization with nonlinear equality constraints; and a quasi-Newton reduced optimization method with constraints giving priority to restoration are presented [fr
Some mathematical problems in non-linear Physics
International Nuclear Information System (INIS)
1983-01-01
The main results contained in this report are the following: I) A general analysis of non-autonomous conserved densities for simple linear evolution systems. II) Partial differential systems within a wide class are converted into Lagrange an form. III) Rigorous criteria for existence of integrating factor matrices. IV) Isolation of all third-order evolution equations with high order symmetries and conservation laws. (Author) 3 refs
On the physical basis of pattern formation in nonlinear systems
International Nuclear Information System (INIS)
Sanduloviciu, M.; Lozneanu, E.; Popescu, S.
2003-01-01
Spatial, respectively spatiotemporal patterns appear in a gaseous conductor (plasma) when an external constraint produces a local gradient of electron kinetic energy. Under such conditions, collective quantum effects related to the spatial separation of the excitation and ionization cross-sections determine the appearance of adjacent opposite space charges. The state of the resulting space charge configuration depends on the self-enhancement process of positive ions production, which destabilizes the system. Thus, a spatial pattern in the form of a stable double layer appears after self-organization when the above gradient is smaller than that for which the double layer transits into a moving phase (spatiotemporal pattern). The proposed explanation, based on investigations performed on self-organization phenomena observed in gaseous conductors, suggests a new possibility to clarify the challenging problems concerning the actual physical basis of pattern formation in semiconductors
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
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.
Addressing Mathematization Obstacles with Unformalized Problems in Physics Education
DEFF Research Database (Denmark)
Niss, Martin
2018-01-01
Abstract: Solving a physics problem requires that the problem solver either implicitly or explicitly structure the problem situation in such a way that she can set up the mathematical equations based on the relevant physics. This part of the mathematization process has been shown to cause obstacles...... for students (Niss, 2016). In the paper, we show how the students’ ability to perform this mathematization process can be trained by using so-called unformalized physics problems. Some examples of how this training can be done are provided from a course on problem solving in physics taught at Roskilde...
Some problems of physics of ultrahigh energy cosmic rays
International Nuclear Information System (INIS)
Isaev, P.S.
1999-01-01
Nearest 15-20 years will be years of flourishing of experimental researches into the energy of cosmic rays at > or ∼ 10 15 eV and of new discoveries in the physics of elementary particles of ultrahigh energies. Unsolved problems of modern physics of ultrahigh energy cosmic rays, which are relevant to the problems of elementary particles physics, are reviewed
Some problems of high-energy elementary particle physics
International Nuclear Information System (INIS)
Isaev, P.S.
1995-01-01
The problems of high-energy elementary particle physics are discussed. It is pointed out that the modern theory of elementary-particle physics has no solutions of some large physical problems: origin of the mass, electric charge, identity of particle masses, change of the mass of elementary particles in time and others. 7 refs
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
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
Vladimir P. Agapov
2017-01-01
Full Text Available Abstract. Objectives Modern building codes prescribe the calculation of building structures taking into account the nonlinearity of deformation. To achieve this goal, the task is to develop a methodology for calculating prestressed reinforced concrete beams, taking into account physical and geometric nonlinearity. Methods The methodology is based on nonlinear calculation algorithms implemented and tested in the computation complex PRINS (a program for calculating engineering constructions for other types of construction. As a tool for solving this problem, the finite element method is used. Non-linear calculation of constructions is carried out by the PRINS computational complex using the stepwise iterative method. In this case, an equation is constructed and solved at the loading step, using modified Lagrangian coordinates. Results The basic formulas necessary for both the formation and the solution of a system of nonlinear algebraic equations by the stepwise iteration method are given, taking into account the loading, unloading and possible additional loading. A method for simulating prestressing is described by setting the temperature action on the reinforcement and stressing steel rod. Different approaches to accounting for physical and geometric nonlinearity of reinforced concrete beam rods are considered. A calculation example of a flat beam is given, in which the behaviour of the beam is analysed at various stages of its loading up to destruction. Conclusion A program is developed for the calculation of flat and spatially reinforced concrete beams taking into account the nonlinearity of deformation. The program is adapted to the computational complex PRINS and as part of this complex is available to a wide range of engineering, scientific and technical specialists.
Nonlinear VLF Wave Physics in the Radiation Belts
Crabtree, C. E.; Tejero, E. M.; Ganguli, G.; Mithaiwala, M.; Rudakov, L.; Hospodarsky, G. B.; Kletzing, C.
2014-12-01
Electromagnetic VLF waves, such as whistler mode waves, both control the lifetime of trapped electrons in the radiation belts by pitch-angle scattering and are responsible for the energization of electrons during storms. Traditional approaches to understanding the influence of waves on trapped electrons have assumed that the wave characteristics (frequency spectrum, wave-normal angle distribution, etc.) were both stationary in time and amplitude independent from event to event. In situ data from modern satellite missions, such as the Van Allen probes, are showing that this assumption may not be justified. In addition, recent theoretical results [Crabtree et al. 2012] show that the threshold for nonlinear wave scattering can often be met by naturally occurring VLF waves in the magnetosphere, with wave magnetic fields of the order of 50-100 pT inside the plasmapause. Nonlinear wave scattering (Nonlinear Landau Damping) is an amplitude dependent mechanism that can strongly alter VLF wave propagation [Ganguli et al. 2010], primarily by altering the direction of propagation. Laboratory results have confirmed the dramatic change in propagation direction when the pump wave has sufficient amplitude to exceed the nonlinear threshold [Tejero et al. 2014]. Nonlinear scattering can alter the macroscopic dynamics of waves in the radiation belts leading to the formation of a long-lasting wave-cavity [Crabtree et al. 2012] and, when amplification is present, a multi-pass amplifier [Ganguli et al., 2012]. Such nonlinear wave effects can dramatically reduce electron lifetimes. Nonlinear wave dynamics such as these occur when there are more than one wave present, such a condition necessarily violates the assumption of traditional wave-normal analysis [Santolik et al., 2003] which rely on the plane wave assumption. To investigate nonlinear wave dynamics using modern in situ data we apply the maximum entropy method [Skilling and Bryan, 1984] to solve for the wave distribution function
On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation
Directory of Open Access Journals (Sweden)
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
2010-09-30
Hyperfast Modeling of Nonlinear Ocean Waves A. R. Osborne Dipartimento di Fisica Generale, Università di Torino Via Pietro Giuria 1, 10125...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Universit?i Torino,Dipartimento di Fisica Generale,Via Pietro Giuria 1,10125 Torino, Italy, 8. PERFORMING
Nonlinear approaches in engineering applications 2
Jazar, Reza N
2013-01-01
Provides updated principles and applications of the nonlinear approaches in solving engineering and physics problems Demonstrates how nonlinear approaches may open avenues to better, safer, cheaper systems with less energy consumption Has a strong emphasis on the application, physical meaning, and methodologies of nonlinear approaches in different engineering and science problems
Nonlinear Whistler Wave Physics in the Radiation Belts
Crabtree, Chris
2016-10-01
Wave particle interactions between electrons and whistler waves are a dominant mechanism for controlling the dynamics of energetic electrons in the radiation belts. They are responsible for loss, via pitch-angle scattering of electrons into the loss cone, and energization to millions of electron volts. It has previously been theorized that large amplitude waves on the whistler branch may scatter their wave-vector nonlinearly via nonlinear Landau damping leading to important consequences for the global distribution of whistler wave energy density and hence the energetic electrons. It can dramatically reduce the lifetime of energetic electrons in the radiation belts by increasing the pitch angle scattering rate. The fundamental building block of this theory has now been confirmed through laboratory experiments. Here we report on in situ observations of wave electro-magnetic fields from the EMFISIS instrument on board NASA's Van Allen Probes that show the signatures of nonlinear scattering of whistler waves in the inner radiation belts. In the outer radiation belts, whistler mode chorus is believed to be responsible for the energization of electrons from 10s of Kev to MeV energies. Chorus is characterized by bursty large amplitude whistler mode waves with frequencies that change as a function of time on timescales corresponding to their growth. Theories explaining the chirping have been developed for decades based on electron trapping dynamics in a coherent wave. New high time resolution wave data from the Van Allen probes and advanced spectral techniques are revealing that the wave dynamics is highly structured, with sub-elements consisting of multiple chirping waves with discrete frequency hops between sub-elements. Laboratory experiments with energetic electron beams are currently reproducing the complex frequency vs time dynamics of whistler waves and in addition revealing signatures of wave-wave and beat-wave nonlinear wave-particle interactions. These new data
An Experimental Concept for Probing Nonlinear Physics in Radiation Belts
Crabtree, C. E.; Ganguli, G.; Tejero, E. M.; Amatucci, B.; Siefring, C. L.
2017-12-01
A sounding rocket experiment, Space Measurement of Rocket-Released Turbulence (SMART), can be used to probe the nonlinear response to a known stimulus injected into the radiation belt. Release of high-speed neutral barium atoms (8- 10 km/s) generated by a shaped charge explosion in the ionosphere can be used as the source of free energy to seed weak turbulence in the ionosphere. The Ba atoms are photo-ionized forming a ring velocity distribution of heavy Ba+ that is known to generate lower hybrid waves. Induced nonlinear scattering will convert the lower hybrid waves into EM whistler/magnetosonic waves. The escape of the whistlers from the ionospheric region into the radiation belts has been studied and their observable signatures quantified. The novelty of the SMART experiment is to make coordinated measurement of the cause and effect of the turbulence in space plasmas and from that to deduce the role of nonlinear scattering in the radiation belts. Sounding rocket will carry a Ba release module and an instrumented daughter section that includes vector wave magnetic and electric field sensors, Langmuir probes and energetic particle detectors. The goal of these measurements is to determine the whistler and lower hybrid wave amplitudes and spectrum in the ionospheric source region and look for precipitated particles. The Ba release may occur at 600-700 km near apogee. Ground based cameras and radio diagnostics can be used to characterize the Ba and Ba+ release. The Van Allen Probes can be used to detect the propagation of the scattering-generated whistler waves and their effects in the radiation belts. By detecting whistlers and measuring their energy density in the radiation belts the SMART mission will confirm the nonlinear generation of whistlers through scattering of lower hybrid along with other nonlinear responses of the radiation belts and their connection to weak turbulence.
The construction of the representation in solving a physics problem
Directory of Open Access Journals (Sweden)
Enrique A. Coleoni
2001-09-01
Full Text Available Written solutions of a physics problem provided by high school students in a physics olympiad are analysed. The study was done on the basis of theoretical developments which take into account peculiarities of the understanding of scientific problems. Some errors are typefied according to failures at different levels of the representation process. A categorization is proposed suggesting the possibility of reinterpreting some mistakes made by physics students in problem solving.
Helping Students with Problems: What Physical Educators Can Do.
Jones, C. J.; Nelson, Barbara
1985-01-01
Children often have trouble finding effective ways to deal with daily stress. Physical educators work in an environment where they can observe and study their students. Suggestions are offered for physical education teachers dealing with students with problems. (DF)
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 School and Workshop on Nonlinear Mathematical Physics and Natural Hazards
Kouteva-Guentcheva, Mihaela
2015-01-01
This book is devoted to current advances in the field of nonlinear mathematical physics and modeling of critical phenomena that can lead to catastrophic events. Pursuing a multidisciplinary approach, it gathers the work of scientists who are developing mathematical and computational methods for the study and analysis of nonlinear phenomena and who are working actively to apply these tools and create conditions to mitigate and reduce the negative consequences of natural and socio-economic disaster risk. This book summarizes the contributions of the International School and Workshop on Nonlinear Mathematical Physics and Natural Hazards, organized within the framework of the South East Europe Network in Mathematical and Theoretical Physics (SEENET MTP) and supported by UNESCO. It was held at the Bulgarian Academy of Sciences from November 28 to December 2, 2013. The contributions are divided into two major parts in keeping with the scientific program of the meeting. Among the topics covered in Part I (Nonlinear...
Health physics problems encountered in the Saclay linear accelerator
International Nuclear Information System (INIS)
Delsaut, R.
1979-01-01
The safety and health physics problems specific to the Saclay linear accelerator are presented: activation (of gases, dust, water, structural materials, targets); individual dosimetry; the safety engineering [fr
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
Skill Levels of Prospective Physics Teachers on Problem Posing
Cildir, Sema; Sezen, Nazan
2011-01-01
Problem posing is one of the topics which the educators thoroughly accentuate. Problem posing skill is defined as an introvert activity of a student's learning. In this study, skill levels of prospective physics teachers on problem posing were determined and their views on problem posing were evaluated. To this end, prospective teachers were given…
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
Using Analogy to Solve a Three-Step Physics Problem
Lin, Shih-Yin; Singh, Chandralekha
2010-10-01
In a companion paper, we discuss students' ability to take advantage of what they learn from a solved problem and transfer their learning to solve a quiz problem that has different surface features but the same underlying physics principles. Here, we discuss students' ability to perform analogical reasoning between another pair of problems. Both the problems can be solved using the same physics principles. However, the solved problem provided was a two-step problem (which can be solved by decomposing it into two sub-problems) while the quiz problem was a three-step problem. We find that it is challenging for students to extend what they learned from a two-step problem to solve a three-step problem.
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)
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.
Inquiry-based problem solving in introductory physics
Koleci, Carolann
What makes problem solving in physics difficult? How do students solve physics problems, and how does this compare to an expert physicist's strategy? Over the past twenty years, physics education research has revealed several differences between novice and expert problem solving. The work of Chi, Feltovich, and Glaser demonstrates that novices tend to categorize problems based on surface features, while experts categorize according to theory, principles, or concepts1. If there are differences between how problems are categorized, then are there differences between how physics problems are solved? Learning more about the problem solving process, including how students like to learn and what is most effective, requires both qualitative and quantitative analysis. In an effort to learn how novices and experts solve introductory electricity problems, a series of in-depth interviews were conducted, transcribed, and analyzed, using both qualitative and quantitative methods. One-way ANOVA tests were performed in order to learn if there are any significant problem solving differences between: (a) novices and experts, (b) genders, (c) students who like to answer questions in class and those who don't, (d) students who like to ask questions in class and those who don't, (e) students employing an interrogative approach to problem solving and those who don't, and (f) those who like physics and those who dislike it. The results of both the qualitative and quantitative methods reveal that inquiry-based problem solving is prevalent among novices and experts, and frequently leads to the correct physics. These findings serve as impetus for the third dimension of this work: the development of Choose Your Own Adventure Physics(c) (CYOAP), an innovative teaching tool in physics which encourages inquiry-based problem solving. 1Chi, M., P. Feltovich, R. Glaser, "Categorization and Representation of Physics Problems by Experts and Novices", Cognitive Science, 5, 121--152 (1981).
Problems in physical modeling of magnetic materials
International Nuclear Information System (INIS)
Della Torre, E.
2004-01-01
Physical modeling of magnetic materials should give insights into the basic processes involved and should be able to extrapolate results to new situations that the models were not necessarily intended to solve. Thus, for example, if a model is designed to describe a static magnetization curve, it should also be able to describe aspects of magnetization dynamics. Both micromagnetic modeling and Preisach modeling, the two most popular magnetic models, fulfill this requirement, but in the process of fulfilling this requirement, they both had to be modified in some ways. Hence, we should view physical modeling as an iterative process whereby we start with some simple assumptions and refine them as reality requires. In the process of refining these assumptions, we should try to appeal to physical arguments for the modifications, if we are to come up with good models. If we consider phenomenological models, on the other hand, that is as axiomatic models requiring no physical justification, we can follow them logically to see the end and examine the consequences of their assumptions. In this way, we can learn the properties, limitations and achievements of the particular model. Physical and phenomenological models complement each other in furthering our understanding of the behavior of magnetic materials
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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.
Computational physics problem solving with Python
Landau, Rubin H; Bordeianu, Cristian C
2015-01-01
The use of computation and simulation has become an essential part of the scientific process. Being able to transform a theory into an algorithm requires significant theoretical insight, detailed physical and mathematical understanding, and a working level of competency in programming. This upper-division text provides an unusually broad survey of the topics of modern computational physics from a multidisciplinary, computational science point of view. Its philosophy is rooted in learning by doing (assisted by many model programs), with new scientific materials as well as with the Python progr
On some common problems in particle physics and nuclei physics
International Nuclear Information System (INIS)
Vinh Mau, R.
1976-01-01
Results of recent studies on the use of a nuclear potential derived from the present knowledge in particle physics, in nuclei and systems composed by nucleon-antinucleon pairs, are presented and discussed
Instruction Emphasizing Effort Improves Physics Problem Solving
Li, Daoquan
2012-01-01
Effectively using strategies to solve complex problems is an important educational goal and is implicated in successful academic performance. However, people often do not spontaneously use the effective strategies unless they are motivated to do so. The present study was designed to test whether educating students about the importance of effort in…
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.
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons
Kröger, H.
2003-01-01
We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.
International Nuclear Information System (INIS)
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
200 more puzzling physics problems with hints and solutions
Gnädig, Péter; Vigh, Máté
2016-01-01
Like its predecessor, 200 Puzzling Physics Problems, this book is aimed at strengthening students' grasp of the laws of physics by applying them to situations that are practical, and to problems that yield more easily to intuitive insight than to brute-force methods and complex mathematics. The problems are chosen almost exclusively from classical, non-quantum physics, but are no easier for that. They are intriguingly posed in accessible non-technical language, and require readers to select an appropriate analysis framework and decide which branches of physics are involved. The general level of sophistication needed is that of the exceptional school student, the good undergraduate, or the competent graduate student; some physics professors may find some of the more difficult questions challenging. By contrast, the mathematical demands are relatively minimal, and seldom go beyond elementary calculus. This further book of physics problems is not only instructive and challenging, but also enjoyable.
Exercises and problems in mathematical methods of physics
Cicogna, Giampaolo
2018-01-01
This book presents exercises and problems in the mathematical methods of physics with the aim of offering undergraduate students an alternative way to explore and fully understand the mathematical notions on which modern physics is based. The exercises and problems are proposed not in a random order but rather in a sequence that maximizes their educational value. Each section and subsection starts with exercises based on first definitions, followed by groups of problems devoted to intermediate and, subsequently, more elaborate situations. Some of the problems are unavoidably "routine", but others bring to the forenontrivial properties that are often omitted or barely mentioned in textbooks. There are also problems where the reader is guided to obtain important results that are usually stated in textbooks without complete proofs. In all, some 350 solved problems covering all mathematical notions useful to physics are included. While the book is intended primarily for undergraduate students of physics, students...
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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
International Nuclear Information System (INIS)
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.
''Physics as meaning circuit'': three problems
International Nuclear Information System (INIS)
Wheeler, J.A.
1986-01-01
This paper presents the ''meaning circuit.'' Physics gives light and sound and pressure, tools of communication. It gives biology and chemistry and, through them, communicators. Communication between communicators gives meaning. Meaning calls for the asking of questions, but the asking of one question stands in a complementary relation in the asking of another. The reception of an answer demands distinguishability. Mathematical analysis of distinguishability demands probability amplitudes. Complementarity demands that these probability amplitudes be complex. A complex probability amplitude has a phase. The change of phase around a closed loop can be regarded as the definition and measure and even the sole form of existence of the ''flux of field'' through that loop. Fields so defined -- electrodynamic, geometrodynamic and chromodynamic -- give rise to particles and physics, thus closing the circuit
Nonconservative stability problems of modern physics
Kirillov, Oleg N
2013-01-01
This work gives a complete overview on the subject of nonconservative stability from the modern point of view. Relevant mathematical concepts are presented, as well as rigorous stability results and numerous classical and contemporary examples from mechanics and physics.The book shall serve to present and prospective specialists providing the current state of knowledge in this actively developing field. The understanding of this theory is vital for many areas of technology, as dissipative effects in rotor dynamics orcelestial mechanics.
Inverse periodic problem for the discrete approximation of the Schroedinger nonlinear equation
International Nuclear Information System (INIS)
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...
Internet Computer Coaches for Introductory Physics Problem Solving
Xu Ryan, Qing
2013-01-01
The ability to solve problems in a variety of contexts is becoming increasingly important in our rapidly changing technological society. Problem-solving is a complex process that is important for everyday life and crucial for learning physics. Although there is a great deal of effort to improve student problem solving skills throughout the…
Contemporary health physics problems and solutions
Bevelacqua, Joseph John
2009-01-01
This is the first text specifically designed to train potential health physicists to think and respond like professionals. Written by a former chairman of the American Board of Health Physics Comprehensive Panel of Examiners with more than 20 years of professional and academic experience in the field, it offers a balanced presentation of all the theoretical and practical issues essential for a full working knowledge of radiation exposure assessments. As the only book to cover the entire radiation protection field, it includes detailed coverage of the medical, university, reactor, fuel cycle, e
Iterative Runge–Kutta-type methods for nonlinear ill-posed problems
International Nuclear Information System (INIS)
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.
Physical dynamics of quasi-particles in nonlinear wave equations
Energy Technology Data Exchange (ETDEWEB)
Christov, Ivan [Department of Mathematics, Texas A and M University, College Station, TX 77843-3368 (United States)], E-mail: christov@alum.mit.edu; Christov, C.I. [Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010 (United States)], E-mail: christov@louisiana.edu
2008-02-04
By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field.
Physical dynamics of quasi-particles in nonlinear wave equations
International Nuclear Information System (INIS)
Christov, Ivan; Christov, C.I.
2008-01-01
By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field
Quantum theory from a nonlinear perspective Riccati equations in fundamental physics
Schuch, Dieter
2018-01-01
This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in ...
Actual problems of giant resonance physics
International Nuclear Information System (INIS)
Zhalov, M.B.; Sliv, L.A.
1982-01-01
The raper deals with the discussion of theoretical problems associated with investigation into nuclear giant multipole resoonances (GMR). Analysis of test data on inelastic scattering of particles on nuclei is carried out to obtain the main GMR characteristics from the present experimental data. Giant isoscalar resonances and their structures in the random phase approximatmion (RPA) with Skyrm forces described by the microscopic theory are discussed. Cross section of 40 Ca excitation in reaction of α-particle inelastic scattering calculated in RPA with exact accountancy of one-nucleon continuum is graphically displayed as an example. Modified RPA used for calculation of GMR width is suggested. Conducted is comparison of energies of 40 Ca, 58 Ni, 90 Zr, 208 Pb nuclei isoscalar resonances calculated in RPA and their contributions to energy weighted sum rule the results of which are tabulated. Integral strength of resonance excitation in RPA by inelastic-scattered α particles and protons on 40 Ca and 208 Pb nuclei is considered. Channels of GMR disintegration are discussed. The most significant theoretical and experimental problems the solution of which is necessary for complete investigation of GMR are pointed out
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
Mathematical models of physics problems (physics research and technology)
Anchordoqui, Luis Alfredo
2013-01-01
This textbook is intended to provide a foundation for a one-semester introductory course on the advanced mathematical methods that form the cornerstones of the hard sciences and engineering. The work is suitable for first year graduate or advanced undergraduate students in the fields of Physics, Astronomy and Engineering. This text therefore employs a condensed narrative sufficient to prepare graduate and advanced undergraduate students for the level of mathematics expected in more advanced graduate physics courses, without too much exposition on related but non-essential material. In contrast to the two semesters traditionally devoted to mathematical methods for physicists, the material in this book has been quite distilled, making it a suitable guide for a one-semester course. The assumption is that the student, once versed in the fundamentals, can master more esoteric aspects of these topics on his or her own if and when the need arises during the course of conducting research. The book focuses on two cor...
Neutrino physics and the flavor problem
International Nuclear Information System (INIS)
King, S. F.; Peddie, I. N. R.
2004-01-01
We consider the problem of trying to understand the recently measured neutrino data simultaneously with understanding the hierarchical form of quark and charged-lepton Yukawa matrices. We summarize the data that a successful model of neutrino mass must predict, and then move on to attempting to do so in the context of spontaneously broken 'family' symmetries. We consider first an abelian U(1) family symmetry, which appears in the context of a type-I string model. Then we consider a model based on a non-abelian SU(3) F , which is the maximal family group consistent with an SO(10) GUT. In this case, the symmetry is more constraining, and is examined in the context of SUSY field theory.
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.
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.
Directory of Open Access Journals (Sweden)
Enrique Castillo
2016-01-01
Full Text Available We first show that monomial ratio equations are not only very common in Physics and Engineering, but the natural type of equations in many practical problems. More precisely, in the case of models involving scale variables if the used formulas are not of this type they are not physically valid. The consequence is that when estimating the model parameters we are faced with systems of monomial ratio equations that are nonlinear and difficult to solve. In this paper, we provide an original algorithm to obtain the unique solutions of systems of equations made of linear combinations of monomial ratios whose coefficient matrix has a proper null space with low dimension that permits solving the problem in a simple way. Finally, we illustrate the proposed methods by their application to two practical problems from the hydraulic and structural fields.
NATO Advanced Research Workshop on Recent advances in Nonlinear Dynamics and Complex System Physics
Casati, Giulio; Complex Phenomena in Nanoscale Systems
2009-01-01
Nanoscale physics has become one of the rapidly developing areas of contemporary physics because of its direct relevance to newly emerging area, nanotechnologies. Nanoscale devices and quantum functional materials are usually constructed based on the results of fundamental studies on nanoscale physics. Therefore studying physical phenomena in nanosized systems is of importance for progressive development of nanotechnologies. In this context study of complex phenomena in such systems and using them for controlling purposes is of great practical importance. Namely, such studies are brought together in this book, which contains 27 papers on various aspects of nanoscale physics and nonlinear dynamics.
Nonlinear optical and atomic systems at the interface of physics and mathematics
Garreau, Jean-Claude
2015-01-01
Focusing on the interface between mathematics and physics, this book offers an introduction to the physics, the mathematics, and the numerical simulation of nonlinear systems in optics and atomic physics. The text covers a wide spectrum of current research on the subject, which is an extremely active field in physics and mathematical physics, with a very broad range of implications, both for fundamental science and technological applications: light propagation in microstructured optical fibers, Bose-Einstein condensates, disordered systems, and the newly emerging field of nonlinear quantum mechanics. Accessible to PhD students, this book will also be of interest to post-doctoral researchers and seasoned academics.
Two centre problems in relativistic atomic physics
Energy Technology Data Exchange (ETDEWEB)
McConnell, Sean R.
2013-01-09
The work contained within this thesis is concerned with the explanation and usage of a set of theoretical procedures for the study of static and dynamic two-centre problems in the relativistic framework of Dirac's equation. Two distinctly different theories for handling time-dependent atomic interactions are reviewed, namely semi-classical perturbation theory and a non-perturbative numerical technique based on the coupled channel equation to directly solve the time-dependent, two-centre Dirac equation. The non-perturbative numerical technique has been developed independently and the calculations performed with it are entirely new. Calculations for ionisation cross sections and state occupancies are conducted for both these methods. The non-perturbative technique for relativistic two-centre problems is extensively explained and, given its novelty, a probity test is conducted between this technique and that of the well established perturbation theory in calculating K-and L-shell ionisation cross sections for the alpha decay of initially Hydrogen-like Polonium. To that end, an in depth outline of the perturbative technique is also made for both collision and decay processes. As well as the comparison test mentioned, this technique is also applied to the analysis of cross sections of the promotion of a single electron into the positive continuum from either a K- or L-shell due to the alpha decay of heavy, neutral nuclei (Gadolinium, Polonium and Thorium). Dirac-Coulomb eigenfunctions centred on the parent nucleus of the decay pair are taken as the basis for use in the cross section calculations utilising first order, semi-classical pertubation theory. The excellent congruence between both techniques justifies the usage of the non-perturbative algorithms in the subsequent analysis of collisions between very heavy, highly charged ions. As such, a set of calculations are performed examining the bound and continuum state occupancy of the electronic levels during a
Reactor physics special problem in 11. ENFIR
International Nuclear Information System (INIS)
Leszczynski, Francisco
1997-01-01
In this report, the computation method and the results of the work performed of the special topic on reactor physics proposed for the 11. ENFIR is presented. MCNP 4.2 has been adopted as the only code to perform the calculations. The full core of the IPEN-MB-1 critical unit has been modelled without important approximations. The specifications given by the Organizer Commission of the Special Topic were followed. The nuclear libraries adopted were those included on the MCNPDAT package, mainly from ENDF/B-V, except indium data, not included in this package. For indium, data obtained from LANL, based on ENDF/B-VI were used. The results are: critical position of the control banks assuming simultaneous movement: percent of extraction: (49±1)% ; excess of reactivity of the core: ρ =( 3590 ±50)pcm ; total reactivity of the one control rod bank: ρ= (4000±50) pcm. The reactivity curve of the control rods is included also. (author)
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.
Directory of Open Access Journals (Sweden)
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.
New analytical solutions for nonlinear physical models of the ...
Indian Academy of Sciences (India)
2016-10-18
Oct 18, 2016 ... Graphical representations along with the numerical data reinforce the efficacy of the proce- dure used. The specified idea is very effective, pragmatic for partial differential equations of fractional order and could be protracted to other physical phenomena. Keywords. Rational exp(−ϕ(η))-expansion method; ...
The Missing Curriculum in Physics Problem-Solving Education
Williams, Mobolaji
2018-05-01
Physics is often seen as an excellent introduction to science because it allows students to learn not only the laws governing the world around them, but also, through the problems students solve, a way of thinking which is conducive to solving problems outside of physics and even outside of science. In this article, we contest this latter idea and argue that in physics classes, students do not learn widely applicable problem-solving skills because physics education almost exclusively requires students to solve well-defined problems rather than the less-defined problems which better model problem solving outside of a formal class. Using personal, constructed, and the historical accounts of Schrödinger's development of the wave equation and Feynman's development of path integrals, we argue that what is missing in problem-solving education is practice in identifying gaps in knowledge and in framing these knowledge gaps as questions of the kind answerable using techniques students have learned. We discuss why these elements are typically not taught as part of the problem-solving curriculum and end with suggestions on how to incorporate these missing elements into physics classes.
Physical health problems in adults with Prader-Willi syndrome.
Sinnema, Margje; Maaskant, Marian A; van Schrojenstein Lantman-de Valk, Henny M J; van Nieuwpoort, I Caroline; Drent, Madeleine L; Curfs, Leopold M G; Schrander-Stumpel, Constance T R M
2011-09-01
Prader-Willi syndrome (PWS) is a genetic disorder which is characterized by severe hypotonia and feeding problems in early infancy. In later childhood and adolescence, this is followed by hyperphagia and extreme obesity if the diet is not strictly controlled. Data on physical health problems in adults with PWS are scarce. We report on the prevalence of physical health problems in a Dutch cohort of adults with PWS in relation to age, BMI, and genetic subtype. Participants (n = 102) were retrieved via the Dutch Prader-Willi Parent Association and through physicians specializing in persons with intellectual disabilities (ID). Details regarding physical health problem spanning the participants' lifespan were collected from caretakers through semi-structured interviews. Cardiovascular problems included diabetes mellitus, hypertension, and cerebrovascular accidents. Respiratory infections were frequent in adulthood. In males, cryptorchidism was almost universal, for which 28/48 males had a history of surgery, mostly orchidopexy. None of the women had a regular menstrual cycle. Sixteen individuals had a diagnosis of osteoporosis. Spinal deformation, hip dysplasia, and foot abnormalities were common. Skinpicking, leg edema, and erysipelas were frequent dermatological problems. The findings in our group support the notion that the prevalence of physical health problems is underestimated. This underscores the importance of developing monitoring programs which would help to recognize physical health problems at an early stage. Copyright © 2011 Wiley-Liss, Inc.
Uraltseva, N N
1995-01-01
This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p
Hidayati, H.; Ramli, R.
2018-04-01
This paper aims to provide a description of the implementation of Physic Problem Solving strategy combined with concept maps in General Physics learning at Department of Physics, Universitas Negeri Padang. Action research has been conducted in two cycles where each end of the cycle is reflected and improved for the next cycle. Implementation of Physics Problem Solving strategy combined with concept map can increase student activity in solving general physics problem with an average increase of 15% and can improve student learning outcomes from 42,7 in the cycle I become 62,7 in cycle II in general physics at the Universitas Negeri Padang. In the future, the implementation of Physic Problem Solving strategy combined with concept maps will need to be considered in Physics courses.
Directory of Open Access Journals (Sweden)
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.)
The philosophical aspect of learning inverse problems of mathematical physics
Directory of Open Access Journals (Sweden)
Виктор Семенович Корнилов
2018-12-01
Full Text Available The article describes specific questions student learning inverse problems of mathematical physics. When teaching inverse problems of mathematical physics to the understanding of the students brought the information that the inverse problems of mathematical physics with a philosophical point of view are the problems of determining the unknown causes of known consequences, and the search for their solutions have great scientific and educational potential. The reasons are specified in the form of unknown coefficients, right side, initial conditions of the mathematical model of inverse problems, and as a consequence are functionals of the solution of this mathematical model. In the process of learning the inverse problems of mathematical physics focuses on the philosophical aspects of the phenomenon of information and identify cause-effect relations. It is emphasized that in the process of logical analysis applied and humanitarian character, students realize that information is always related to the fundamental philosophical questions that the analysis applied and the humanitarian aspects of the obtained results the inverse problem of mathematical physics allows students to make appropriate inferences about the studied process and to, ultimately, new information, to study its properties and understand its value. Philosophical understanding of the notion of information opens up to students a new methodological opportunities to comprehend the world and helps us to reinterpret existing science and philosophy of the theory related to the disclosure of the interrelationship of all phenomena of reality.
MAUVE: A New Strategy for Solving and Grading Physics Problems
Hill, Nicole Breanne
2016-05-01
MAUVE (magnitude, answer, units, variables, and equations) is a framework and rubric to help students and teachers through the process of clearly solving and assessing solutions to introductory physics problems. Success in introductory physics often derives from an understanding of units, a command over dimensional analysis, and good bookkeeping. I developed MAUVE for an introductory-level environmental physics course as an easy-to-remember checklist to help students construct organized and thoughtful solutions to physics problems. Environmental physics is a core physics course for environmental and sustainability science (ESS) majors that teaches principles of radiation, thermodynamics, and mechanics within the context of the environment and sustainable energy systems. ESS student concentrations include environmental biology, applied ecology, biogeochemistry, and natural resources. The MAUVE rubric, inspired by nature, has encouraged my students to produce legible and tactical work, and has significantly clarified the grading process.
Including Critical Thinking and Problem Solving in Physical Education
Pill, Shane; SueSee, Brendan
2017-01-01
Many physical education curriculum frameworks include statements about the inclusion of critical inquiry processes and the development of creativity and problem-solving skills. The learning environment created by physical education can encourage or limit the application and development of the learners' cognitive resources for critical and creative…
How some infinities cause problems in classical physical theories
Atkinson, David; Peijnenburg, Jeanne; Allo, P.; van Kerhove, B.
2014-01-01
In this paper we review a 1992 excursion of Jean Paul Van Bendegem into physics, ‘How Infinities Cause Problems in Classical Physical Theories’, in the light of two later models concerning colliding balls, of Pérez Laraudogoitia and of Alper and Bridger, respectively. We show that Van Bendegem
Statistical and particle physics: Common problems and techniques
International Nuclear Information System (INIS)
Bowler, K.C.; Mc Kane, A.J.
1984-01-01
These proceedings contain statistical mechanical studies in condensed matter physics; interfacial problems in statistical physics; string theory; general monte carlo methods and their application to Lattice gauge theories; topological excitations in field theory; phase transformation kinetics; and studies of chaotic systems
MAUVE: A New Strategy for Solving and Grading Physics Problems
Hill, Nicole Breanne
2016-01-01
MAUVE (magnitude, answer, units, variables, and equations) is a framework and rubric to help students and teachers through the process of clearly solving and assessing solutions to introductory physics problems. Success in introductory physics often derives from an understanding of units, a command over dimensional analysis, and good bookkeeping.…
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...
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
Unfolding in particle physics: A window on solving inverse problems
International Nuclear Information System (INIS)
Spano, F.
2013-01-01
Unfolding is the ensemble of techniques aimed at resolving inverse, ill-posed problems. A pedagogical introduction to the origin and main problems related to unfolding is presented and used as the the stepping stone towards the illustration of some of the most common techniques that are currently used in particle physics experiments. (authors)
The Importance of Monitoring Skills in Physics Problem Solving
Ali, Marlina; Talib, Corrienna-Abd; Hasniza Ibrahim, Nor; Surif, Johari; Halim Abdullah, Abdul
2016-01-01
The purpose of this paper is to show how important "monitoring" is as metacognitive skills in solving physics problems in the field mechanics. Based on test scores, twenty one students were divided into two groups: more successful (MS) and less successful (LS) problem solvers. Students were allowed to think-aloud while they worked on…
Determining Students' Attitude towards Physics through Problem-Solving Strategy
Erdemir, Naki
2009-01-01
In this study, the effects of teacher-directed and self-directed problem-solving strategies on students' attitudes toward physics were explored. Problem-solving strategies were used with the experimental group, while the control group was instructed using traditional teaching methods. The study was conducted with 270 students at various high…
Physical health problems in adults with Prader-Willi syndrome
Sinnema, M.; Maaskant, M.A.; Schrojenstein Lantman-de Valk, H.M.J. van; Nieuwpoort, I.C. van; Drent, M.L.; Curfs, L.M.G.; Schrander-Stumpel, C.T.R.M.
2011-01-01
Prader-Willi syndrome (PWS) is a genetic disorder which is characterized by severe hypotonia and feeding problems in early infancy. In later childhood and adolescence, this is followed by hyperphagia and extreme obesity if the diet is not strictly controlled. Data on physical health problems in
Karkar , Sami; Vergez , Christophe; Cochelin , Bruno
2012-01-01
International audience; We propose a new approach based on numerical continuation and bifurcation analysis for the study of physical models of instruments that produce self- sustained oscillation. Numerical continuation consists in following how a given solution of a set of equations is modified when one (or several) parameter of these equations are allowed to vary. Several physical models (clarinet, saxophone, and violin) are formulated as nonlinear dynamical systems, whose periodic solution...
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
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.
Computer methods in physics 250 problems with guided solutions
Landau, Rubin H
2018-01-01
Our future scientists and professionals must be conversant in computational techniques. In order to facilitate integration of computer methods into existing physics courses, this textbook offers a large number of worked examples and problems with fully guided solutions in Python as well as other languages (Mathematica, Java, C, Fortran, and Maple). Its also intended as a self-study guide for learning how to use computer methods in physics. The authors include an introductory chapter on numerical tools and indication of computational and physics difficulty level for each problem.
Doing physics with scientific notebook a problem solving approach
Gallant, Joseph
2012-01-01
The goal of this book is to teach undergraduate students how to use Scientific Notebook (SNB) to solve physics problems. SNB software combines word processing and mathematics in standard notation with the power of symbolic computation. As its name implies, SNB can be used as a notebook in which students set up a math or science problem, write and solve equations, and analyze and discuss their results. Written by a physics teacher with over 20 years experience, this text includes topics that have educational value, fit within the typical physics curriculum, and show the benefits of using SNB.
Nonlinear physics of the ionosphere and LOIS/LOFAR
International Nuclear Information System (INIS)
Thide, Bo
2007-01-01
The ionosphere is the only large-scale plasma laboratory without walls that we have direct access to. Here we can study, both in situ and from the ground, basic small- and large-scale processes and fundamental physical principles that control planet Earth's interaction with its space environment. From results obtained in systematic, repeatable experiments, where we can vary the stimulus and observe its response in a controlled, laboratory-like manner, we can draw conclusions on similar physical processes occurring naturally in the Earth's plasma environment as well as in parts of the plasma universe that are not easily accessible to direct probing. Of particular interest is electromagnetic turbulence excited in the ionosphere by beams of particles (photons, electrons) and its manifestation in terms of secondary radiation (electrostatic and electromagnetic waves), structure formation (solitons, cavitons, alfveons, hybrons, striations) and the associated exchange of energy, linear momentum and angular momentum. The primarily astrophysics-oriented, distributed radio telescope Low Frequency Array (LOFAR) currently under construction in the Netherlands, Germany and France, will operate in a frequency range (10-240 MHz), close to fundamental ionospheric plasma resonance/cut-off frequencies, with a sensitivity that is orders of magnitude higher than any radio (or radar) facility used so far. The LOFAR Outrigger in Scandinavia (LOIS) radio and radar facility, with one station in Vaexjoe in southern Sweden and three more planned in the same area (Ronneby, Kalmar, Lund) plus one near Poznan in Poland, supplements LOFAR with optimized Earth and space observing extensions. For this purpose LOIS will operate in the same frequency range as LOFAR (but extended on the low-frequency side) and will augment the observation capability to enable direct radio imaging of plasma vorticity
Statistical physics of hard combinatorial optimization: Vertex cover problem
Zhao, Jin-Hua; Zhou, Hai-Jun
2014-07-01
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper, we use the vertex cover problem, a basic nondeterministic-polynomial (NP)-complete combinatorial optimization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.
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
Heuristic versus statistical physics approach to optimization problems
International Nuclear Information System (INIS)
Jedrzejek, C.; Cieplinski, L.
1995-01-01
Optimization is a crucial ingredient of many calculation schemes in science and engineering. In this paper we assess several classes of methods: heuristic algorithms, methods directly relying on statistical physics such as the mean-field method and simulated annealing; and Hopfield-type neural networks and genetic algorithms partly related to statistical physics. We perform the analysis for three types of problems: (1) the Travelling Salesman Problem, (2) vector quantization, and (3) traffic control problem in multistage interconnection network. In general, heuristic algorithms perform better (except for genetic algorithms) and much faster but have to be specific for every problem. The key to improving the performance could be to include heuristic features into general purpose statistical physics methods. (author)
Problem Solving in Physics: Undergraduates' Framing, Procedures, and Decision Making
Modir, Bahar
In this dissertation I will start with the broad research question of what does problem solving in upper division physics look like? My focus in this study is on students' problem solving in physics theory courses. Some mathematical formalisms are common across all physics core courses such as using the process of separation of variables, doing Taylor series, or using the orthogonality properties of mathematical functions to set terms equal to zero. However, there are slight differences in their use of these mathematical formalisms across different courses, possibly because of how students map different physical systems to these processes. Thus, my first main research question aims to answer how students perform these recurring processes across upper division physics courses. I break this broad question into three particular research questions: What knowledge pieces do students use to make connections between physics and procedural math? How do students use their knowledge pieces coherently to provide reasoning strategies in estimation problems? How do students look ahead into the problem to read the information out of the physical scenario to align their use of math in physics? Building on the previous body of the literature, I will use the theory family of Knowledge in Pieces and provide evidence to expand this theoretical foundation. I will compare my study with previous studies and provide suggestions on how to generalize these theory expansions for future use. My experimental data mostly come from video-based classroom data. Students in groups of 2-4 students solve in-class problems in quantum mechanics and electromagnetic fields 1 courses collaboratively. In addition, I will analyze clinical interviews to demonstrate how a single case study student plays an epistemic game to estimate the total energy in a hurricane. My second research question is more focused on a particular instructional context. How do students frame problem solving in quantum mechanics? I
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.
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.
Mental, physical and social health problems of call centre workers
Directory of Open Access Journals (Sweden)
P Bhuyar
2008-01-01
Full Text Available Background: Call centre workers in BPO face unique occupational hazards - mental, physical and psychosocial. Material & Method: A sample 100 call centre workers of both sexes and from two cities Pune and Mumbai were surveyed by both qualitative and quantitative methods for the above health problems. Results: A high proportion of workers faced sleep disturbances and associated mental stress and anxiety. Sleep disturbance and anxiety was significantly more in international call centres compared to domestic. There was also disturbance in circadian rhythms due to night shift. Physical problems such as musculoskeletal disorders, obesity, eye, and hearing problems were also present. Psychosocial problems included disruption in family life, use of tobacco and alcohol, and faulty eating habits. Conclusion: Better personal management, health education and more research is indicated to study the health problems in this emerging occupation.
Partially specified physics problems: university students' attitudes and performance
International Nuclear Information System (INIS)
Marusic, M; Erceg, N; Slisko, J
2011-01-01
In this research we asked the fourth year students (N = 50) of a technical faculty of the University of Split (Republic of Croatia) to solve a partially specified physics problem related to gravitational force. The task for the students was to decide whether the situation described in the problem is feasible or not. Nevertheless, the formulation of the problem is such that it does not give students any explicit advice regarding what to calculate or how to judge the feasibility of the given situation in the real world. The research was carried out using a structured written exam method. The worksheet was structured in order to assess explicitly a few elements of the students' problem-solving performance. Based on their results, the examinees were classified into four categories, depending on what they could or could not accomplish during problem solving. A majority of students were not able to solve the given physical problem completely. A selection of students' and professors' observations is also included. Our results show that traditionally formulated numerical exercises, which are mostly used in physics teaching, do not develop students' abilities in higher-order thinking (i.e. planning, decision making or result evaluation) to a desirable extent. We suggest that partially specified problems should be given to students, both in problem-solving sessions and exams, in order to prepare them for dealing with ill-structured tasks in real life.
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.
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.
An efficient algorithm for some highly nonlinear fractional PDEs in mathematical physics.
Directory of Open Access Journals (Sweden)
Jamshad Ahmad
Full Text Available In this paper, a fractional complex transform (FCT is used to convert the given fractional partial differential equations (FPDEs into corresponding partial differential equations (PDEs and subsequently Reduced Differential Transform Method (RDTM is applied on the transformed system of linear and nonlinear time-fractional PDEs. The results so obtained are re-stated by making use of inverse transformation which yields it in terms of original variables. It is observed that the proposed algorithm is highly efficient and appropriate for fractional PDEs and hence can be extended to other complex problems of diversified nonlinear nature.
Library of problem-oriented programs for solving problems of atomic and nuclear physics
International Nuclear Information System (INIS)
Kharitonov, Yu.I.
1976-01-01
The Data Centre of the Leningrad Institute of Nuclear Physics (LIYaF) is working on the establishment of a library of problem-oriented computer programs for solving problems of atomic and nuclear physics. This paper lists and describes briefly the programs presently available to the Data Centre. The descriptions include the program code numbers, the program language, the translator for which the program is designed, and the program scope
de Mul, F.F.M.; Martin Batlle, C.; Martin i Batlle, Cristina; de Bruijn, Imme; Rinzema, K.; Rinzema, Kees
2003-01-01
Teaching physics to first-year university students (in the USA: junior/senior level) is often hampered by their lack of skills in the underlying mathematics, and that in turn may block their understanding of the physics and their ability to solve problems. Examples are vector algebra, differential
Designing and using multiple-possibility physics problems in physics courses
Shekoyan, Vazgen
2012-02-01
One important aspect of physics instruction is helping students develop better problem solving expertise. Besides enhancing the content knowledge, problems help students develop different cognitive abilities and skills. This presentation focuses on multiple-possibility problems (alternatively called ill-structured problems). These problems are different from traditional ``end of chapter'' single-possibility problems. They do not have one right answer and thus the student has to examine different possibilities, assumptions and evaluate the outcomes. To solve such problems one has to engage in a cognitive monitoring called epistemic cognition. It is an important part of thinking in real life. Physicists routinely use epistemic cognition when they solve problems. I have explored the instructional value of using such problems in introductory physics courses.
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Complex network problems in physics, computer science and biology
Cojocaru, Radu Ionut
There is a close relation between physics and mathematics and the exchange of ideas between these two sciences are well established. However until few years ago there was no such a close relation between physics and computer science. Even more, only recently biologists started to use methods and tools from statistical physics in order to study the behavior of complex system. In this thesis we concentrate on applying and analyzing several methods borrowed from computer science to biology and also we use methods from statistical physics in solving hard problems from computer science. In recent years physicists have been interested in studying the behavior of complex networks. Physics is an experimental science in which theoretical predictions are compared to experiments. In this definition, the term prediction plays a very important role: although the system is complex, it is still possible to get predictions for its behavior, but these predictions are of a probabilistic nature. Spin glasses, lattice gases or the Potts model are a few examples of complex systems in physics. Spin glasses and many frustrated antiferromagnets map exactly to computer science problems in the NP-hard class defined in Chapter 1. In Chapter 1 we discuss a common result from artificial intelligence (AI) which shows that there are some problems which are NP-complete, with the implication that these problems are difficult to solve. We introduce a few well known hard problems from computer science (Satisfiability, Coloring, Vertex Cover together with Maximum Independent Set and Number Partitioning) and then discuss their mapping to problems from physics. In Chapter 2 we provide a short review of combinatorial optimization algorithms and their applications to ground state problems in disordered systems. We discuss the cavity method initially developed for studying the Sherrington-Kirkpatrick model of spin glasses. We extend this model to the study of a specific case of spin glass on the Bethe
Relations between nonlinear Riccati equations and other equations in fundamental physics
International Nuclear Information System (INIS)
Schuch, Dieter
2014-01-01
Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract ''quantizations'' such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown
Yu, Kyung-Hun; Suk, Min-Hwa; Kang, Shin-Woo; Shin, Yun-A
2014-10-01
The purpose of this study was to investigate the effect of combined linear and nonlinear periodic training on physical fitness and competition times in finswimmers. The linear resistance training model (6 days/week) and nonlinear underwater training (4 days/week) were applied to 12 finswimmers (age, 16.08± 1.44 yr; career, 3.78± 1.90 yr) for 12 weeks. Body composition measures included weight, body mass index (BMI), percent fat, and fat-free mass. Physical fitness measures included trunk flexion forward, trunk extension backward, sargent jump, 1-repetition-maximum (1 RM) squat, 1 RM dead lift, knee extension, knee flexion, trunk extension, trunk flexion, and competition times. Body composition and physical fitness were improved after the 12-week periodic training program. Weight, BMI, and percent fat were significantly decreased, and trunk flexion forward, trunk extension backward, sargent jump, 1 RM squat, 1 RM dead lift, and knee extension (right) were significantly increased. The 50- and 100-m times significantly decreased in all 12 athletes. After 12 weeks of training, all finswimmers who participated in this study improved their times in a public competition. These data indicate that combined linear and nonlinear periodic training enhanced the physical fitness and competition times in finswimmers.
2014-10-01
Theoretical physics is the first step for the development of science and technology. For more than 100 years it has delivered new and sophisticated discoveries which have changed human views of their surroundings and universe. Theoretical physics has also revealed that the governing law in our universe is not deterministic, and it is undoubtedly the foundation of our modern civilization. Contrary to its importance, research in theoretical physics is not well advanced in some developing countries such as Indonesia. This workshop provides the formal meeting in Indonesia devoted to the field of theoretical physics and is organized to cover all subjects of theoretical physics as well as nonlinear phenomena in order to create a gathering place for the theorists in Indonesia and surrounding countries, to motivate young physicists to keep doing active researches in the field and to encourage constructive communication among the community members. Following the success of the tenth previous meetings in this conference series, the eleventh conference was held in Sebelas Maret University (UNS), Surakarta, Indonesia on 15 February 2014. In addition, the conference was proceeded by School of Advance Physics at Gadjah Mada University (UGM), Yogyakarta, on 16-17 February 2014. The conference is expected to provide distinguished experts and students from various research fields of theoretical physics and nonlinear phenomena in Indonesia as well as from other continents the opportunities to present their works and to enhance contacts among them. The introduction to the conference is continued in the pdf.
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
Internet computer coaches for introductory physics problem solving
Xu Ryan, Qing
The ability to solve problems in a variety of contexts is becoming increasingly important in our rapidly changing technological society. Problem-solving is a complex process that is important for everyday life and crucial for learning physics. Although there is a great deal of effort to improve student problem solving skills throughout the educational system, national studies have shown that the majority of students emerge from such courses having made little progress toward developing good problem-solving skills. The Physics Education Research Group at the University of Minnesota has been developing Internet computer coaches to help students become more expert-like problem solvers. During the Fall 2011 and Spring 2013 semesters, the coaches were introduced into large sections (200+ students) of the calculus based introductory mechanics course at the University of Minnesota. This dissertation, will address the research background of the project, including the pedagogical design of the coaches and the assessment of problem solving. The methodological framework of conducting experiments will be explained. The data collected from the large-scale experimental studies will be discussed from the following aspects: the usage and usability of these coaches; the usefulness perceived by students; and the usefulness measured by final exam and problem solving rubric. It will also address the implications drawn from this study, including using this data to direct future coach design and difficulties in conducting authentic assessment of problem-solving.
Application of the group-theoretical method to physical problems
Abd-el-malek, Mina B.
1998-01-01
The concept of the theory of continuous groups of transformations has attracted the attention of applied mathematicians and engineers to solve many physical problems in the engineering sciences. Three applications are presented in this paper. The first one is the problem of time-dependent vertical temperature distribution in a stagnant lake. Two cases have been considered for the forms of the water parameters, namely water density and thermal conductivity. The second application is the unstea...
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
Energy Technology Data Exchange (ETDEWEB)
Yildiz, Nihat, E-mail: nyildiz@cumhuriyet.edu.t [Cumhuriyet University, Faculty of Science and Literature, Department of Physics, 58140 Sivas (Turkey); San, Sait Eren; Okutan, Mustafa [Department of Physics, Gebze Institute of Technology, P.O. Box 141, Gebze 41400, Kocaeli (Turkey); Kaya, Hueseyin [Cumhuriyet University, Faculty of Science and Literature, Department of Physics, 58140 Sivas (Turkey)
2010-04-15
Among other significant obstacles, inherent nonlinearity in experimental physical response data poses severe difficulty in empirical physical formula (EPF) construction. In this paper, we applied a novel method (namely layered feedforward neural network (LFNN) approach) to produce explicit nonlinear EPFs for experimental nonlinear electro-optical responses of doped nematic liquid crystals (NLCs). Our motivation was that, as we showed in a previous theoretical work, an appropriate LFNN, due to its exceptional nonlinear function approximation capabilities, is highly relevant to EPF construction. Therefore, in this paper, we obtained excellently produced LFNN approximation functions as our desired EPFs for above-mentioned highly nonlinear response data of NLCs. In other words, by using suitable LFNNs, we successfully fitted the experimentally measured response and predicted the new (yet-to-be measured) response data. The experimental data (response versus input) were diffraction and dielectric properties versus bias voltage; and they were all taken from our previous experimental work. We conclude that in general, LFNN can be applied to construct various types of EPFs for the corresponding various nonlinear physical perturbation (thermal, electronic, molecular, electric, optical, etc.) data of doped NLCs.
International Nuclear Information System (INIS)
Yildiz, Nihat; San, Sait Eren; Okutan, Mustafa; Kaya, Hueseyin
2010-01-01
Among other significant obstacles, inherent nonlinearity in experimental physical response data poses severe difficulty in empirical physical formula (EPF) construction. In this paper, we applied a novel method (namely layered feedforward neural network (LFNN) approach) to produce explicit nonlinear EPFs for experimental nonlinear electro-optical responses of doped nematic liquid crystals (NLCs). Our motivation was that, as we showed in a previous theoretical work, an appropriate LFNN, due to its exceptional nonlinear function approximation capabilities, is highly relevant to EPF construction. Therefore, in this paper, we obtained excellently produced LFNN approximation functions as our desired EPFs for above-mentioned highly nonlinear response data of NLCs. In other words, by using suitable LFNNs, we successfully fitted the experimentally measured response and predicted the new (yet-to-be measured) response data. The experimental data (response versus input) were diffraction and dielectric properties versus bias voltage; and they were all taken from our previous experimental work. We conclude that in general, LFNN can be applied to construct various types of EPFs for the corresponding various nonlinear physical perturbation (thermal, electronic, molecular, electric, optical, etc.) data of doped NLCs.
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.
Impact of Y2K problem on physical protection system
International Nuclear Information System (INIS)
Kumar, R.; Swadia, N.S.; Zanwar, P.S.; Mishra, G.P.; Salunke, A.S.; Nigam, R.K.
1999-01-01
Year 2000 related system failures/problems in Physical Protection System pose no threat to general safety and functioning of any nuclear facility. But there can be potential security threats having radiation safety and non-proliferation concern and hence should be given due importance. Reviewing and testing Physical Protection System for Y2K compliance are easier than other systems as it does not directly affect operation of the plant. The existing emergency response capability at the nuclear facilities should be utilizes effectively to mitigate any Y2K induced events on Physical Protection System with dedicated manpower and channeled efforts
Mathematical mechanic using physical reasoning to solve problems
Levi, Mark
2009-01-01
Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist. Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can
Exact multiplicity results for quasilinear boundary-value problems with cubic-like nonlinearities
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
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)
Some open problems in the physics of disordered systems
Indian Academy of Sciences (India)
Some problems in the physics of disordered systems are pointed out; most of these arise from experiments. Keywords. Disordered systems; electron localization; metal insulator transitions. PACS Nos 71.55. .... overlapping the free electron Fermi sphere, the Fermi surface is cut up into a large number of small electron and ...
Studies of Visual Attention in Physics Problem Solving
Madsen, Adrian M.
2013-01-01
The work described here represents an effort to understand and influence visual attention while solving physics problems containing a diagram. Our visual system is guided by two types of processes--top-down and bottom-up. The top-down processes are internal and determined by ones prior knowledge and goals. The bottom-up processes are external and…
Chemical physics of decomposition of energetic materials. Problems and prospects
International Nuclear Information System (INIS)
Smirnov, Lev P
2004-01-01
The review is concerned with analysis of the results obtained in the kinetic and mechanistic studies on decomposition of energetic materials (explosives, powders and solid propellants). It is shown that the state-of-the art in this field is inadequate to the potential of modern chemical kinetics and chemical physics. Unsolved problems are outlined and ways of their solution are proposed.
Video-based problems in introductory mechanics physics courses
International Nuclear Information System (INIS)
Gröber, Sebastian; Klein, Pascal; Kuhn, Jochen
2014-01-01
Introductory mechanics physics courses at the transition from school to university are a challenge for students. They are faced with an abrupt and necessary increase of theoretical content and requirements on their conceptual understanding of phyiscs. In order to support this transition we replaced part of the mandatory weekly theory-based paper-and-pencil problems with video analysis problems of equal content and level of difficulty. Video-based problems (VBP) are a new problem format for teaching physics from a linked sequence of theoretical and video-based experimental tasks. Experimental tasks are related to the well-known concept of video motion analysis. This introduction of an experimental part in recitations allows the establishment of theory–experiment interplay as well as connections between physical content and context fields such as nature, technique, everyday life and applied physics by conducting model-and context-related experiments. Furthermore, laws and formulas as predominantly representative forms are extended by the use of diagrams and vectors. In this paper we give general reasons for this approach, describe the structure and added values of VBP, and show that they cover a relevant part of mechanics courses at university. Emphasis is put on theory–experiment interplay as a structural added value of VBP to promote students' construction of knowledge and conceptual understanding. (paper)
Uniqueness of inverse scattering problem in local quantum physics
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: schroer@cbpf.br
2001-06-01
It is shown that the a Bisognano-Wichmann-Unruh inspired formulation of local quantum physics which starts from wedge-localized algebras, leads to a uniqueness proof for the scattering problem. The important mathematical tool is the thermal KMS aspect of localization and its strengthening by the requirement of crossing symmetry for generalized formfactors. (author)
Parallel Solution of Robust Nonlinear Model Predictive Control Problems in Batch Crystallization
Directory of Open Access Journals (Sweden)
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.
The emerging problem of physical child abuse in South Korea.
Hahm, H C; Guterman, N B
2001-05-01
South Korea has had remarkably high incidence and prevalence rates of physical violence against children, yet the problem has received only limited public and professional attention until very recently. This article represents the first attempt in English to systematically analyze South Korea's recent epidemiological studies on child maltreatment. Discussed are sociocultural factors that have contributed both to delays in child protection laws and a low public awareness of the problem of child abuse. The article highlights methodological issues concerning the definition of physical abuse in South Korea and the complex attitudes toward violence. It also examines the role of the Korean women's movement in the reform of family laws and the recent establishment of new child protection legislation. Suggestions for future directions for the problem of child maltreatment within South Korea are presented.
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.
Docktor, Jennifer L.; Dornfeld, Jay; Frodermann, Evan; Heller, Kenneth; Hsu, Leonardo; Jackson, Koblar Alan; Mason, Andrew; Ryan, Qing X.; Yang, Jie
2016-06-01
Problem solving is a complex process valuable in everyday life and crucial for learning in the STEM fields. To support the development of problem-solving skills it is important for researchers and curriculum developers to have practical tools that can measure the difference between novice and expert problem-solving performance in authentic classroom work. It is also useful if such tools can be employed by instructors to guide their pedagogy. We describe the design, development, and testing of a simple rubric to assess written solutions to problems given in undergraduate introductory physics courses. In particular, we present evidence for the validity, reliability, and utility of the instrument. The rubric identifies five general problem-solving processes and defines the criteria to attain a score in each: organizing problem information into a Useful Description, selecting appropriate principles (Physics Approach), applying those principles to the specific conditions in the problem (Specific Application of Physics), using Mathematical Procedures appropriately, and displaying evidence of an organized reasoning pattern (Logical Progression).
Directory of Open Access Journals (Sweden)
Jennifer L. Docktor
2016-05-01
Full Text Available Problem solving is a complex process valuable in everyday life and crucial for learning in the STEM fields. To support the development of problem-solving skills it is important for researchers and curriculum developers to have practical tools that can measure the difference between novice and expert problem-solving performance in authentic classroom work. It is also useful if such tools can be employed by instructors to guide their pedagogy. We describe the design, development, and testing of a simple rubric to assess written solutions to problems given in undergraduate introductory physics courses. In particular, we present evidence for the validity, reliability, and utility of the instrument. The rubric identifies five general problem-solving processes and defines the criteria to attain a score in each: organizing problem information into a Useful Description, selecting appropriate principles (Physics Approach, applying those principles to the specific conditions in the problem (Specific Application of Physics, using Mathematical Procedures appropriately, and displaying evidence of an organized reasoning pattern (Logical Progression.
Understanding student use of differentials in physics integration problems
Directory of Open Access Journals (Sweden)
Dehui Hu
2013-07-01
Full Text Available This study focuses on students’ use of the mathematical concept of differentials in physics problem solving. For instance, in electrostatics, students need to set up an integral to find the electric field due to a charged bar, an activity that involves the application of mathematical differentials (e.g., dr, dq. In this paper we aim to explore students’ reasoning about the differential concept in physics problems. We conducted group teaching or learning interviews with 13 engineering students enrolled in a second-semester calculus-based physics course. We amalgamated two frameworks—the resources framework and the conceptual metaphor framework—to analyze students’ reasoning about differential concept. Categorizing the mathematical resources involved in students’ mathematical thinking in physics provides us deeper insights into how students use mathematics in physics. Identifying the conceptual metaphors in students’ discourse illustrates the role of concrete experiential notions in students’ construction of mathematical reasoning. These two frameworks serve different purposes, and we illustrate how they can be pieced together to provide a better understanding of students’ mathematical thinking in physics.
SECONDARY PHYSICAL EDUCATION AVOIDANCE AND GENDER: PROBLEMS AND ANTIDOTES
Directory of Open Access Journals (Sweden)
Thomas Ryan
2012-07-01
Full Text Available Our goal was to locate and evaluate the barriers that impact and cause females to avoid secondary elective physical education courses. We sought to find answers to stop the further decline of female enrolment in secondary physical education by looking into curricula, program and instructional variables. Anecdotal evidence informed this study which was very much exploratory, building upon several key facts. First, Ontario (Canada secondary students are only required to take one credit (course in physical education in order to graduate and second, most students take the required physical education course in grade nine which is their first year of high school. Following this there is an average of 10% fewer females in every physical education class in the province of Ontario and only an average of 12% are enrolled in physical education each year. Several issues were identified and explored including self-confidence; motivation; perceived value of physical activity; opportunities for physical activity; marking scheme; competition; co-ed classes; teaching approach; and peers as possible problems and solutions.
Lee, Miriam Chang Yi; Chow, Jia Yi; Button, Chris; Tan, Clara Wee Keat
2017-01-01
Nonlinear Pedagogy is an exploratory approach to teaching and learning Physical Education that can be potentially effective to help children acquire relevant twenty-first century competencies. Underpinned by Ecological Dynamics, the focus of Nonlinear Pedagogy is on the learner and includes the provision of less prescriptive instructions and…
Girls and Women with Physical Disabilities: Needs and Problems
Directory of Open Access Journals (Sweden)
Maryam Sharifian-Sani
2006-07-01
Full Text Available Objective: By taking into account that understanding the primary needs of disabled girls and women is essential in finding a suitable solution to their problems, the main objective of the current research was based on the investigation of the needs and the problems of girls and women with physical disabilities in Tehran (capital of Iran. Materials & Methods: This research has been carried out in a descriptive manner. The participants of this research were 216 girls and women with physical disability who were selected among 1395 clients of the welfare organization in Tehran through a systematic randomized method. Data collection was carried out using an 82-question questionnaire designed by the researchers. The questionnaire compiled by reviewing current resources on the subject and based on discussions carried out within focus groups. It was finalized after determining its validity and reliability. Results: Examining the needs and problems of girls and women with physical disability, in general, made clear their priorities in each area. Priorities for educational needs: promoting the awareness of society through education, providing vocational training employment needs: accessible transportation, allocation of special employment opportunities for them (quota system need for starting a family: the possibility of meeting their future husbands before marriage provided by their families, consultation before marriage their main needs regarding transportation: improving pedestrian pavements and public pathways, provision of a special transport service taking account of their particular disability need for rehabilitation services: rehabilitation aids and educational services leisure time: financial help for using sports-recreational facilities, provision of sports facilities for girls and women with physical disability their needs for establishing communication:, receiving a normal reaction from non-disabled people while dealing with their needs and
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
Directory of Open Access Journals (Sweden)
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
What is Time in Some Modern Physics Theories: Interpretation Problems
Directory of Open Access Journals (Sweden)
Karpenko Ivan A.
2016-03-01
Full Text Available The article deals with the problem of time in the context of several theories of modem physics. This fundamental concept inevitably arises in physical theories, but so far there is no adequate description of it in the philosophy of science. In the theory of relativity, quantum field theory. Standard Model of particle physics, theory of loop quantum gravity, superstring theory and other most recent theories the idea of time is shown explicitly or not. Sometimes, such as in the special theory of relativity, it plays a significant role and sometimes it does not. But anyway it exists and is implied by the content of the theory, which in some cases directly includes its mathematical tools. Fundamental difference of space-time processes in microcosm and macrocosm is of particular importance for solving the problem. In this regard, a need to understand the time in the way it appears in modem physics, to describe it in the language of philosophy arises (satisfactory for time description mathematical tools also do not exist. This will give an opportunity to get closer to the answer on question of time characteristics. And even if we do not obtain the exact answer, we will still be able to formulate the right question about its nature. For this purpose, the present research carries out analysis of the key theories of modern physics with regard to historical and scientific, historical and philosophical perspectives, hi some cases, this gives an opportunity to detect the succession of the associated with time perception ideas, their development, as well as the origination of fundamentally new ones. During the analysis, the conect characteristics of time are formulated from the point of view of physical theory and the attempt to state the nature of time is made. On the ground of conducted research, the conclusions about current state of the problem and its future solution perspectives are drawn.
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
Photo-physics of third-order nonlinear optical processes in organic dyes
International Nuclear Information System (INIS)
Delysse, Stephane
1997-01-01
We study some aspects of the nonlinear picosecond photo-physics in organic dyes using Kerr ellipsometry. The aim is to establish link between the photo-physics and nonlinear optics in these compounds. First, we study coherent processes directly linked to the third-order susceptibility. Thus, we measure two-photon absorption spectra of large internal charge transfer dyes. We take into account all coupling between three electronic states which can interfere to explain the particular response of some stilbene dyes. On the second hand, we expose a more photophysical approach to determine the S 1 → S n transition energies and moments using the measurement of excited state absorption cross sections. These results allow the prediction of the susceptibilities relevant to alternative nonlinear optical methods. Nevertheless, the stationary approach hides the complex relaxation processes which can take place in organic dyes. As an illustration, we study the formation and disappearance of a TICT (Twisted intramolecular charge transfer) in a pyrylium salt in solvents of increasing viscosity. (author) [fr
1000 Solved Problems in Classical Physics An Exercise Book
Kamal, Ahmad A
2011-01-01
This book basically caters to the needs of undergraduate and graduate physics students in classical physics, especially Classical Mechanics and Electricity and Electromagnetism. Lecturers/Tutors may use it as a resource book. The contents of the book are based on the syllabi currently used in the undergraduate courses in the USA, U.K., and other countries. The book consists of 15 chapters, each one beginning with a brief but adequate summary and necessary formulas and Line diagrams followed by a variety of typical problems useful for assignments and exams. Detailed solutions are provided at the end of each chapter.
Argaw, Aweke Shishigu; Haile, Beyene Bashu; Ayalew, Beyene Tesfaw; Kuma, Shiferaw Gadisa
2017-01-01
Through the learning of physics, students will acquire problem solving skills which are relevant to their daily life. Determining the best way in which students learn physics takes a priority in physics education. The goal of the present study was to determine the effect of problem based learning strategy on students' problem solving skills and…
International Nuclear Information System (INIS)
Harlim, John; Mahdi, Adam; Majda, Andrew J.
2014-01-01
A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partial noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model
Assessing first-order emulator inference for physical parameters in nonlinear mechanistic models
Hooten, Mevin B.; Leeds, William B.; Fiechter, Jerome; Wikle, Christopher K.
2011-01-01
We present an approach for estimating physical parameters in nonlinear models that relies on an approximation to the mechanistic model itself for computational efficiency. The proposed methodology is validated and applied in two different modeling scenarios: (a) Simulation and (b) lower trophic level ocean ecosystem model. The approach we develop relies on the ability to predict right singular vectors (resulting from a decomposition of computer model experimental output) based on the computer model input and an experimental set of parameters. Critically, we model the right singular vectors in terms of the model parameters via a nonlinear statistical model. Specifically, we focus our attention on first-order models of these right singular vectors rather than the second-order (covariance) structure.
F-DDIA: A Framework for Detecting Data Injection Attacks in Nonlinear Cyber-Physical Systems
Directory of Open Access Journals (Sweden)
Jingxuan Wang
2017-01-01
Full Text Available Data injection attacks in a cyber-physical system aim at manipulating a number of measurements to alter the estimated real-time system states. Many researchers recently focus on how to detect such attacks. However, most of the detection methods do not work well for the nonlinear systems. In this paper, we present a compressive sampling methodology to identify the attack, which allows determining how many and which measurement signals are launched. The sparsity feature is used. Generally, our methodology can be applied to both linear and nonlinear systems. The experimental testing, which includes realistic load patterns from NYISO with various attack scenarios in the IEEE 14-bus system, confirms that our detector performs remarkably well.
International Nuclear Information System (INIS)
Stroppe, Heribert; Streitenberger, Peter; Specht, Eckard; Zeitler, Juergen; Langer, Heinz
2017-01-01
The present book is the unification of the proved problem collections for the basic physical training of studyings of especially engineering courses at technical colleges and universities. The book contains - didactically prepared and structured in the style of a textbook as well as with increasing difficulty - a total of 960 exemplary and additional tasks from the fields mechanics, heat, electricity and magnetism, oscillations and waves, as well as atomic and nuclear physics. For the exemplary problems the whole solution path and the complete calculation process with explanation of the relevant physical laws are extensively presented, for the additional problems for the self-control only the solutions and, if necessary, intermediate calculations are given. The examples and problems with mostly practice-oriented content are selected in such a way that they largely cover the matter treated in courses and exercises and make by their didactical preparation an effective repetition and optimal examination-preparation possible.
Toward the automated analysis of plasma physics problems
International Nuclear Information System (INIS)
Mynick, H.E.
1989-04-01
A program (CALC) is described, which carries out nontrivial plasma physics calculations, in a manner intended to emulate the approach of a human theorist. This includes the initial process of gathering the relevant equations from a plasma knowledge base, and then determining how to solve them. Solution of the sets of equations governing physics problems, which in general have a nonuniform,irregular structure, not amenable to solution by standardized algorithmic procedures, is facilitated by an analysis of the structure of the equations and the relations among them. This often permits decompositions of the full problem into subproblems, and other simplifications in form, which renders the resultant subsystems soluble by more standardized tools. CALC's operation is illustrated by a detailed description of its treatment of a sample plasma calculation. 5 refs., 3 figs
The hierarchy problem and Physics Beyond the Standard Model
Indian Academy of Sciences (India)
boson. Without the Higgs, theory is not unitary. Gautam Bhattacharyya ... highest scale of the theory. Thus physics at several orders of ... Hu. ≃ −|μ2| + O(1) m2. ˜t mh ≃ 125 GeV ⇒ m˜t ∼ few TeV ⇒ large cancellation ⇒ little hierarchy problem. Large mt drives M. 2. Hu negative. EWSB dynamically triggered by RG. 2. 4. 6. 8.
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
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)
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
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)
Mathematical modeling and applications in nonlinear dynamics
Merdan, Hüseyin
2016-01-01
The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...
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.)
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.
Physical activity problem-solving inventory for adolescents: Development and initial validation
Youth encounter physical activity barriers, often called problems. The purpose of problem-solving is to generate solutions to overcome the barriers. Enhancing problem-solving ability may enable youth to be more physically active. Therefore, a method for reliably assessing physical activity problem-s...
Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques
International Nuclear Information System (INIS)
Carretero-González, R; Frantzeskakis, D J; Kevrekidis, P G
2008-01-01
The aim of this review is to introduce the reader to some of the physical notions and the mathematical methods that are relevant to the study of nonlinear waves in Bose–Einstein condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyse some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g. the linear or the nonlinear limit or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools. (invited article)
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
Recent topics in nonlinear PDE
International Nuclear Information System (INIS)
Mimura, Masayasu; Nishida, Takaaki
1984-01-01
The meeting on the subject of nonlinear partial differential equations was held at Hiroshima University in February, 1983. Leading and active mathematicians were invited to talk on their current research interests in nonlinear pdes occuring in the areas of fluid dynamics, free boundary problems, population dynamics and mathematical physics. This volume contains the theory of nonlinear pdes and the related topics which have been recently developed in Japan. (Auth.)
Expert and novice categorization of introductory physics problems
Wolf, Steven Frederick
Since it was first published 30 years ago, Chi et al.'s seminal paper on expert and novice categorization of introductory problems led to a plethora of follow-up studies within and outside of the area of physics [Chi et al. Cognitive Science 5, 121 -- 152 (1981)]. These studies frequently encompass "card-sorting" exercises whereby the participants group problems. The study firmly established the paradigm that novices categorize physics problems by "surface features" (e.g. "incline," "pendulum," "projectile motion,"... ), while experts use "deep structure" (e.g. "energy conservation," "Newton 2,"... ). While this technique certainly allows insights into problem solving approaches, simple descriptive statistics more often than not fail to find significant differences between experts and novices. In most experiments, the clean-cut outcome of the original study cannot be reproduced. Given the widespread implications of the original study, the frequent failure to reproduce its findings warrants a closer look. We developed a less subjective statistical analysis method for the card sorting outcome and studied how the "successful" outcome of the experiment depends on the choice of the original card set. Thus, in a first step, we are moving beyond descriptive statistics, and develop a novel microscopic approach that takes into account the individual identity of the cards and uses graph theory and models to visualize, analyze, and interpret problem categorization experiments. These graphs are compared macroscopically, using standard graph theoretic statistics, and microscopically, using a distance metric that we have developed. This macroscopic sorting behavior is described using our Cognitive Categorization Model. The microscopic comparison allows us to visualize our sorters using Principal Components Analysis and compare the expert sorters to the novice sorters as a group. In the second step, we ask the question: Which properties of problems are most important in problem
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).
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.
Do New Caledonian crows solve physical problems through causal reasoning?
Taylor, A.H.; Hunt, G.R.; Medina, F.S.; Gray, R.D.
2008-01-01
The extent to which animals other than humans can reason about physical problems is contentious. The benchmark test for this ability has been the trap-tube task. We presented New Caledonian crows with a series of two-trap versions of this problem. Three out of six crows solved the initial trap-tube. These crows continued to avoid the trap when the arbitrary features that had previously been associated with successful performances were removed. However, they did not avoid the trap when a hole and a functional trap were in the tube. In contrast to a recent primate study, the three crows then solved a causally equivalent but visually distinct problem—the trap-table task. The performance of the three crows across the four transfers made explanations based on chance, associative learning, visual and tactile generalization, and previous dispositions unlikely. Our findings suggest that New Caledonian crows can solve complex physical problems by reasoning both causally and analogically about causal relations. Causal and analogical reasoning may form the basis of the New Caledonian crow's exceptional tool skills. PMID:18796393
Directory of Open Access Journals (Sweden)
Francisco Savall Alemany
2017-01-01
Full Text Available The effectiveness of the problem based teaching on the science learning has been highlighted by the didactic research. This teaching model is characterized by organizing the units around problems and by proposing a research plan to find a solution which requires concepts and models to be introduced in a functional way, as possible solutions to the problem. In this article we present a problem based unit for teaching quantum physics in introductory physics courses and we analyze in detail the teaching strategy that we follow to build a model to explain the emission and absorption of radiation.
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
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
Problems and progress in radiation physics of semiconductors
International Nuclear Information System (INIS)
Vinetskij, V.L.
1982-01-01
A survey of the current status of radiation physics of semiconductors comprises the analysis of some new problems and poses the statement of concern. The essential difference between the probability of interstitial-vacancy pair occurrence W(T) in elastic collisions and the generally accepted step distribution with a typical ''threshold'' energy Tsub(d) is indicated. The role of diffusion and reaction evolution of primary defects leading to specific properties of the cluster formation process is shown. Special features of defect formation in spatially inhomogeneous semiconductors, in particular for elastic stresses present, are described. Among most important advances in the radiation physics of semiconductors there are the discovery of non-activation motion of the ''extra'' atom in silicon, the observation of a low activation energy value for the vacancy diffusion, the understanding of subthreshold mechanism of defect formation and radiation-induced diffusion, the effects of laser annealing of defects and oriented crystallization
Physics and astrophysics a selection of key problems
Ginzburg, Vitalii Lazarevich
2013-01-01
Physics and Astrophysics discusses some major problems concerned with macrophysics. Such topics as the controlled thermonuclear fusion, high- temperature superconductivity, and metallic exciton liquid in semiconductors are covered. The definition and elements related to microphysics are discussed. This section focuses on mass spectrum, quarks and gluons, and the interaction of particles at high and super high energies. The book gives a brief overview of the general theory of relativity. The production and origin of gravitational waves are discussed in detail. Cosmology is the study of space an
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
Balta, Nuri; Mason, Andrew J.; Singh, Chandralekha
2016-01-01
Students' attitudes and approaches to physics problem solving can impact how well they learn physics and how successful they are in solving physics problems. Prior research in the U.S. using a validated Attitude and Approaches to Problem Solving (AAPS) survey suggests that there are major differences between students in introductory physics and…
Abstracts of the fourth international conference on modern problems of nuclear physics
International Nuclear Information System (INIS)
2001-09-01
The Fourth International Conference on modern problems of nuclear physics was held on 25-29 September, 2001 in Tashkent, Uzbekistan. The specialists discussed various aspects of modern problems of both fundamental and applied nuclear physics. More than 300 talks were presented in the meeting on the following subjects: particle physics, relativistic nuclear physics and physics of atomic nuclei; applied nuclear physics; radiation solid state physics, condensed matter physics; activation analysis, radiochemistry, isotopes. (M.K.)
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.
Intuitive physics knowledge, physics problem solving and the role of mathematical equations
Directory of Open Access Journals (Sweden)
Laura Buteler
2012-09-01
Full Text Available The present work explores the role that mathematical equations play in modifying students’ physical intuition (diSessa, 1993. The work is carried out assuming that students achieve a great deal of the refinement in their physical intuitions during problem solving (Sherin, 2006. The study is guided by the question of how the use of mathematical equations contributes to this refinement. The authors aim at expanding on Sherin´s (2006 hypothesis, suggesting a more bounding relation between physical intuitions and mathematics. In this scenario, intuitions play a more compelling role in “deciding” which equations are acceptable and which are not. Our hypothesis is constructed on the basis of three cases: the first published by Sherin (2006 and two more from registries of our own. The three cases are compared and analyzed in relation to the role of mathematical equations in refining – or not – the intuitive knowledge students bring to play during problem solving.
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
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.
Maries, Alexandru; Singh, Chandralekha
2018-01-01
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a problem into a representation that is easier to exploit for solving it. One major focus while helping introductory physics students learn effective problem solving is to help them understand that drawing diagrams can facilitate problem solution. We conducted an…
Behaviour of mathematics and physics students in solving problem of Vector-Physics context
Sardi; Rizal, M.; Mansyur, J.
2018-04-01
This research aimed to describe behaviors of mathematics and physics students in solving problem of the vector concept in physics context. The subjects of the research were students who enrolled in Mathematics Education Study Program and Physics Education Study Program of FKIP Universitas Tadulako. The selected participants were students who received the highest score in vector fundamental concept test in each study program. The data were collected through thinking-aloud activity followed by an interview. The steps of data analysis included data reduction, display, and conclusion drawing. The credibility of the data was tested using a triangulation method. Based on the data analysis, it can be concluded that the two groups of students did not show fundamental differences in problem-solving behavior, especially in the steps of understanding the problem (identifying, collecting and analyzing facts and information), planning (looking for alternative strategies) and conducting the alternative strategy. The two groups were differ only in the evaluation aspect. In contrast to Physics students who evaluated their answer, mathematics students did not conducted an evaluation activity on their work. However, the difference was not caused by the differences in background knowledge.
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.
van den Berg, G. P.
1998-03-01
Since some 20 years most Dutch universities have one or more science shops. Central shops handle research questions for all disciplines. Specialized shops are part of a department of chemistry or medicine, history, social science, etc. The shops have evolved rather differently, but their main mission still is to help social groups that lack money and have no easy access to scientific knowledge, e.g. neighbourhood, environmental, third world or patient groups. Most also help non-commercial organizations such as schools, trade unions or local authorities. Low-cost help can be provided because students do the work as part of their training, mainly in student projects (literature search, practical work, graduation, etc.). A total staff of 80, helped by 600 students, 250 voluntary and 50 paid researchers, handle 1500 questions resulting in 300 reports (estimated figures 1995). Science shops for physics (`Physics Shop', PS) have to deal with practical problems, generally involving classical physics. Major topics are noise, vibration, radiation, indoor climate and energy: most of the work lies in estimating/measuring relevant parameters, assessing impact, seeking solutions. The 3 Dutch PS's have developed in different directions. One is run entirely by students and deals with small, concrete problems. The second PS is managed by a co-ordinator who mediates between client groups and physics staff members who assist students in small and larger projects. The third has a lot of in-house expertise, and the shop staff is in direct contact with client groups as well as students who work in the PS itself. In questions submitted to the PS it is not always immediately clear what to do or how to do it because of the non-scientific phrasing of the problems and problems include non-physical (e.g. technical, health or legal) aspects. Also, difficulties in solving the problems are typically not in the underlying physics, but in the lack of accurate data and of control of the complex
Physics students' approaches to learning and cognitive processes in solving physics problems
Bouchard, Josee
This study examined traditional instruction and problem-based learning (PBL) approaches to teaching and the extent to which they foster the development of desirable cognitive processes, including metacognition, critical thinking, physical intuition, and problem solving among undergraduate physics students. The study also examined students' approaches to learning and their perceived role as physics students. The research took place in the context of advanced courses of electromagnetism at a Canadian research university. The cognitive science, expertise, physics and science education, instructional psychology, and discourse processes literature provided the framework and background to conceptualize and structure this study. A within-stage mixed-model design was used and a number of instruments, including a survey, observation grids, and problem sets were developed specifically for this study. A special one-week long problem-based learning (PBL) intervention was also designed. Interviews with the instructors participating in the study provided complementary data. Findings include evidence that students in general engage in metacognitive processes in the organization of their personal study time. However, this potential, including the development of other cognitive processes, might not be stimulated as much as it could in the traditional lecture instructional context. The PBL approach was deemed as more empowering for the students. An unexpected finding came from the realisation that a simple exposure to a structured exercise of problem-solving (pre-test) was sufficient to produce superior planning and solving strategies on a second exposure (post-test) even for the students who had not been exposed to any special treatment. Maturation was ruled out as a potential threat to the validity of this finding. Another promising finding appears to be that the problem-based learning (PBL) intervention tends to foster the development of cognitive competencies, particularly
Abstracts of the third international conference on modern problems of nuclear physics
Energy Technology Data Exchange (ETDEWEB)
NONE
1999-08-01
The Third Uzbekistan Conference on modern problems of nuclear physics was held on 23-27 August, 1999 in Bukhara, Uzbekistan. The specialists discussed various aspects of modern problems of both fundamental and applied nuclear physics. More than 300 talks were presented in the meeting on the following subjects: particle physics, relativistic nuclear physics and physics of atomic nuclei; activation analysis, radiochemistry, isotopes, applied nuclear physics; radiation solid state physics. (A.A.D.)
Abstracts of the fifth international conference on modern problems of nuclear physics
Energy Technology Data Exchange (ETDEWEB)
NONE
2003-08-01
The Fifth Uzbekistan Conference on modern problems of nuclear physics was held on 12-15 August, 2003 in Samarkand, Uzbekistan. The specialists discussed various aspects of modern problems of both fundamental and applied nuclear physics. More than 300 talks were presented in the meeting on the following subjects: particle physics, relativistic nuclear physics and physics of atomic nuclei; activation analysis, radiochemistry, isotopes, applied nuclear physics; radiation solid state physics.
Abstracts of the fifth international conference on modern problems of nuclear physics
International Nuclear Information System (INIS)
2003-08-01
The Fifth Uzbekistan Conference on modern problems of nuclear physics was held on 12-15 August, 2003 in Samarkand, Uzbekistan. The specialists discussed various aspects of modern problems of both fundamental and applied nuclear physics. More than 300 talks were presented in the meeting on the following subjects: particle physics, relativistic nuclear physics and physics of atomic nuclei; activation analysis, radiochemistry, isotopes, applied nuclear physics; radiation solid state physics
International Nuclear Information System (INIS)
2014-01-01
The third International youth scientific school-conference took place 10-13 April 2014 year in Moscow on the basis National Research Nuclear University MEPhI and RAS Lebedev P.N. Physical Institute. The actual scientific problems of current fundamental and applied physics as well as nuclear and physical technologies were discussed. This book of abstracts contains many interesting items devoted problems of theoretical physics and astrophysics, nuclear physics, nanotecnology, laser physics and plasma physics [ru
International Nuclear Information System (INIS)
Boyd, R.W.
1992-01-01
Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
1992-12-01
Inverse operator theory method (IOTM) has developed rapidly in the last few years. It is an effective and useful procedure for quantitative solution of nonlinear or stochastic continuous dynamical systems. Solutions are obtained in series form for deterministic equations, and in the case of stochastic equation it gives statistic measures of the solution process. A very important advantage of the IOTM is to eliminate a number of restrictive and assumption on the nature of stochastic processes. Therefore, it provides more realistic solutions. The IOTM and its mathematics-mechanization (MM) are briefly introduced. They are used successfully to study the chaotic behaviors of the nonlinear dynamical systems for the first time in the world. As typical examples, the Lorentz equation, generalized Duffing equation, two coupled generalized Duffing equations are investigated by the use of the IOTM and the MM. The results are in good agreement with ones by the Runge-Kutta method (RKM). It has higher accuracy and faster convergence. So the IOTM realized by the MM is of potential application valuable in nonlinear science
On the physical problems of investigations on colliding beams
International Nuclear Information System (INIS)
Gerasimov, S.B.; Zhuravlev, V.I.
1983-01-01
Physical problems planned for investigations with accelerating facilities at the 0.5-2 TeV energy of colliding hadrons (pp- or p anti p) and with e + e - storage rings with the total particle energy of 100-200 GeV in the center-of-mass system are briefly reviewed. The following prospective aspects of experimental investigations are discussed: electroweak interactions and properties of W- and Z-bosons (sector of vector calibration fields), Higgs mesons and their production (sector of scalar fields), production and disintegration of t-quarks and check-up of QCD statements in the e + e - reactions. Perspective trends in the theory development are considered. They are: the great unification theory, technicolor, supersymmetry, models of composite quarks and leptons. To perform all these fundamental investigations, accelerators of a new class are necessary. The authors consider their construction to be justified by the results expected
Disciplinary Knots and Learning Problems in Waves Physics
Di Renzone, Simone; Frati, Serena; Montalbano, Vera
An investigation on student understanding of waves is performed during an optional laboratory realized in informal extracurricular way with few, interested and talented pupils. The background and smart intuitions of students rendered the learning path very dynamic and ambitious. The activities started by investigating the basic properties of waves by means of a Shive wave machine. In order to make quantitative observed phenomena, the students used a camcorder and series of measures were obtained from the captured images. By checking the resulting data, it arose some learning difficulties especially in activities related to the laboratory. This experience was the starting point for a further analysis on disciplinary knots and learning problems in the physics of waves in order to elaborate a teaching-learning proposal on this topic.
Nuclear Physics Solutions to the Primordial Lithium Problem
Directory of Open Access Journals (Sweden)
Williams E.
2012-10-01
Full Text Available The primordial lithium problem is one of the major outstanding issues in the standard model of the Big Bang. Measurements of the baryon to photon ratio in the cosmic microwave background constrain model predictions, giving abundances of 7Li two to four times larger than observed via spectroscopic measurements of metal-poor stars. In an attempt to reconcile this discrepancy, significant effort has been directed at measuring reaction cross sections of light nuclei at astrophysically relevant energies. However, there remain reaction cross sections with large uncertainties, and some that have not yet been measured. Particularly relevant are those involving the destruction of 7Be, a progenitor of 7Li. Key issues that can be improved by nuclear physics input will be highlighted, and the applicability of detectors and event reconstruction techniques recently developed at the ANU will be discussed.
Directory of Open Access Journals (Sweden)
Etienne Thoret
2016-06-01
Full Text Available In this paper, a flexible control strategy for a synthesis model dedicated to nonlinear friction phenomena is proposed. This model enables to synthesize different types of sound sources, such as creaky doors, singing glasses, squeaking wet plates or bowed strings. Based on the perceptual stance that a sound is perceived as the result of an action on an object we propose a genuine source/filter synthesis approach that enables to elude physical constraints induced by the coupling between the interacting objects. This approach makes it possible to independently control and freely combine the action and the object. Different implementations and applications related to computer animation, gesture learning for rehabilitation and expert gestures are presented at the end of this paper.
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
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.
Some problems of quantum cosmology and dark matter physics
Wang, Jin
The quantum cosmology is studied of the string universe obtained by embedding the Robertson-Walker metric in the nonlinear sigma model. It was found that initially the universe exists in a series of metastable bound states with the scale factor taking discrete values. Then it tunnels through a barrier and comes out in an inflationary state. This tunneling (or evolution in imaginary time) also has the effect of heating up the matter field so that we have a condition of chaotic inflation. The asymptotic solutions agree with those obtained from the classical Einstein equations. Quantum cosmology was considered of a 4-D universe using the effective action of superstrings. Both Hartle-Hawking and Vilenkin boundary conditions were applied to the solution of Wheeler-DeWitt equation. Under certain conditions (fermions added) the universe was found to tunnel through to the Lorentzian regime from the Euclidean regime and time is dynamically generated. Chudnovsky and Vilenkin's idea was applied to possible existence of cosmic strings in the Sun. Stellar evolution with cosmic strings at solar age gives a radius and luminosity of the star which are in contradiction with observation. The astrophysical bound was studied on the change of gravitational constant with time. It was found that (G/G) less than 10-12yr-1 is the condition that has to be satisfied in order not to cause the conflict with observation. The effect was studied of axions on the steller evolution of a 10 solar mass star model. If the axion mass is larger than .1 ev the star's age is significantly different at late stages, compared to the star without axions. It is argued that if cosmions (or WIMPS) solve the solar neutrino problem, then they must also play an important role in the evolution of low mass star main sequence stars. If they do so, then a simple (long mean free path) model for the interaction of cosmions with baryons leads to changes in the structure of the nuclear-burning core which may in principle
International Nuclear Information System (INIS)
Lutpullaev, S.L.; Atabaev, I.G.; Abdurakhmanov, A.A.
2013-11-01
The International conference dedicated to the seventieth anniversary of Physical-technical institute, SPA 'Physics-Sun' 'Fundamental and applied problems of physics' was held on 14-15 November, 2013 in Tashkent, Uzbekistan. Specialists discussed various aspects of modern problems of relativistic nuclear physics and physics of atomic nuclei, solid state physics, various applications of new materials. More than 225 talks were presented in the meeting. (k.m.)
Wang, W. L.; Zhou, Z. R.; Yu, D. S.; Qin, Q. H.; Iwnicki, S.
2017-10-01
A full nonlinear physical 'in-service' model was built for a rail vehicle secondary suspension hydraulic damper with shim-pack-type valves. In the modelling process, a shim pack deflection theory with an equivalent-pressure correction factor was proposed, and a Finite Element Analysis (FEA) approach was applied. Bench test results validated the damper model over its full velocity range and thus also proved that the proposed shim pack deflection theory and the FEA-based parameter identification approach are effective. The validated full damper model was subsequently incorporated into a detailed vehicle dynamics simulation to study how its key in-service parameter variations influence the secondary-suspension-related vehicle system dynamics. The obtained nonlinear physical in-service damper model and the vehicle dynamic response characteristics in this study could be used in the product design optimization and nonlinear optimal specifications of high-speed rail hydraulic dampers.
Differences in Visual Attention between Those Who Correctly and Incorrectly Answer Physics Problems
Madsen, Adrian M.; Larson, Adam M.; Loschky, Lester C.; Rebello, N. Sanjay
2012-01-01
This study investigated how visual attention differed between those who correctly versus incorrectly answered introductory physics problems. We recorded eye movements of 24 individuals on six different conceptual physics problems where the necessary information to solve the problem was contained in a diagram. The problems also contained areas…
Abstracts of the sixth international conference on modern problems of nuclear physics
International Nuclear Information System (INIS)
Yuldashev, B.; Fazylov, M.; Ibragimova, E.; Salikhbaev, U.
2006-09-01
The Sixth International Conference on modern problems of nuclear physics was held on 19-22 September, 2006 in Tashkent, Uzbekistan. The specialists discussed various aspects of modern problems of both fundamental and applied nuclear physics. About 275 talks were presented in the meetingof on the following subjects: particle physics, relativistic nuclear physics and physics of atomic nuclei; radiation physics of condenced matter; nuclear applications in industry, medicine, biology and agriculture; nuclear and radiation safety, non prolifaration issues. (K.M.)
Abstracts of the sixth international conference on modern problems of nuclear physics
Energy Technology Data Exchange (ETDEWEB)
Yuldashev, B; Fazylov, M; Ibragimova, E; Salikhbaev, U [eds.
2006-09-15
The Sixth International Conference on modern problems of nuclear physics was held on 19-22 September, 2006 in Tashkent, Uzbekistan. The specialists discussed various aspects of modern problems of both fundamental and applied nuclear physics. About 275 talks were presented in the meetingof on the following subjects: particle physics, relativistic nuclear physics and physics of atomic nuclei; radiation physics of condenced matter; nuclear applications in industry, medicine, biology and agriculture; nuclear and radiation safety, non prolifaration issues. (K.M.)
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.
Directory of Open Access Journals (Sweden)
Sophie D Walsh
Full Text Available Then aims of the current study were 1 to provide cross-national estimates of the prevalence of physical fighting and weapon carrying among adolescents aged 11-15 years; (2 To examine the possible effects of physical fighting and weapon carrying on the occurrence of physical (medically treated injuries and emotional health outcomes (multiple health complaints among adolescents within the theoretical framework of Problem Behaviour Theory. 20,125 adolescents aged 11-15 in five countries (Belgium, Israel, USA, Canada, FYR Macedonia were surveyed via the 2006 Health Behaviour in School Aged Children survey. Prevalence was calculated for physical fighting and weapon carrying along with physical and emotional measures that potentially result from violence. Regression analyses were used to quantify associations between violence/weapon carrying and the potential health consequences within each country. Large variations in fighting and weapon carrying were observed across countries. Boys reported more frequent episodes of fighting/weapon carrying and medically attended injuries in every country, while girls reported more emotional symptoms. Although there were some notable variations in findings between different participating countries, increased weapon carrying and physical fighting were both independently and consistently associated with more frequent reports of the potential health outcomes. Adolescents engaging in fighting and weapon carrying are also at risk for physical and emotional health outcomes. Involvement in fighting and weapon carrying can be seen as part of a constellation of risk behaviours with obvious health implications. Our findings also highlight the importance of the cultural context when examining the nature of violent behaviour for adolescents.
Problems and solutions in quantum chemistry and physics
Johnson, Charles S
1988-01-01
Unusually varied problems, with detailed solutions, cover quantum mechanics, wave mechanics, angular momentum, molecular spectroscopy, scattering theory, more. 280 problems, plus 139 supplementary exercises.
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)
Pooria Akbarzadeh
2017-07-01
Full Text Available In this paper, the problem of laminar nanofluid flow which results from the nonlinear stretching of a flat sheet is investigated numerically. In this paper, a modified variable physical properties model for analyzing nanofluids flow and heat transfer is introduced. In this model, the effective viscosity, density, and thermal conductivity of the solid-liquid mixture (nanofluids which are commonly utilized in the homogenous single-phase model, are locally combined with the prevalent single-phase model. A numerical similarity solution is considered which depends on the local Prandtl number, local Brownian motion number, local Lewis number, and local thermophoresis number. The results are compared to the prevalent single-phase model. This comparison depicts that the prevalent single-phase model has a considerable deviation for predicting the behavior of nanofluids flow especially in dimensionless temperature and nanoparticle volume fraction. In addition the effect of the governing parameters such as Prandtl number, the Brownian motion number, the thermophoresis parameter, the Lewis number, and etc. on the velocity, temperature, and volume fraction distribution and the dimensionless heat and mass transfer rates are examined.
International Nuclear Information System (INIS)
Khoroshun, L.P.
1995-01-01
The characteristic features of the deformation and failure of actual materials in the vicinity of a crack tip are due to their physical nonlinearity in the stress-concentration zone, which is a result of plasticity, microfailure, or a nonlinear dependence of the interatomic forces on the distance. Therefore, adequate models of the failure mechanics must be nonlinear, in principle, although linear failure mechanics is applicable if the zone of nonlinear deformation is small in comparison with the crack length. Models of crack mechanics are based on analytical solutions of the problem of the stress-strain state in the vicinity of the crack. On account of the complexity of the problem, nonlinear models are bason on approximate schematic solutions. In the Leonov-Panasyuk-Dugdale nonlinear model, one of the best known, the actual two-dimensional plastic zone (the nonlinearity zone) is replaced by a narrow one-dimensional zone, which is then modeled by extending the crack with a specified normal load equal to the yield point. The condition of finite stress is applied here, and hence the length of the plastic zone is determined. As a result of this approximation, the displacement in the plastic zone at the abscissa is nonzero
Problems of describing the cumulative effect in relativistic nuclear physics
International Nuclear Information System (INIS)
Baldin, A.M.
1979-01-01
The problem of describing the cumulative effect i.e., the particle production on nuclei in the range kinematically forbidden for one-nucleon collisions, is studied. Discrimination of events containing cumulative particles fixes configurations in the wave function of a nucleus, when several nucleons are closely spaced and their quark-parton components are collectivized. For the cumulative processes under consideration large distances between quarks are very important. The fundamental facts and theoretical interpretation of the quantum field theory and of the condensed media theory in the relativistic nuclear physics are presented in brief. The collisions of the relativistic nuclei with low momentum transfers is considered in a fast moving coordinate system. The basic parameter determining this type of collisions is the energy of nucleon binding in nuclei. It has been shown that the short-range correlation model provides a good presentation of many characteristics of the multiple particle production and it may be regarded as an approximate universal property of hadron interactions
Open problems and future prospects for hypernuclear physics
International Nuclear Information System (INIS)
Dover, C.B.
1992-01-01
We appraise the current status of our knowledge of hypernuclear structure physics, and emphasize the unsolved problems. The prospects for significant advances in high resolution hypernuclear spectroscopy with CW electron beams at CEBAF or intense pion beams at the proposed PILAC facility at LPF are discussed. These facilities could greatly extend our understanding of strangeness S = -1 hypernuclear systems. For S = -2 systems, new events have been seen in a (K - ,K + ) hybrid counter-emulsion experiment at KEK in Japan. We give a theoretical interpretation of one of these events, as well as some further possibilities for the exploration of ΛΛ hypernuclear spectroscopy via Ξ - -atoms. We mention some possible enhancements of (K - ,K + ) or (K - ,K 0 ) cross sections to discrete states, due to ΞN-ΛΛ configuration mixing in a shell model description of S = -2 hypernuclei. Finally, we explore the possibilities for producing multi-strange nuclei or droplets of strange quark matter (''strangelets'') in relativistic heavy ion collisions
Physics background of nuclear power: problems and prospects
International Nuclear Information System (INIS)
Slowinski, B.
2004-01-01
The problem of energy production on a large scale for rapidly increasing world population is at the present time a major one and of vital importance. As a consequence, within the approach of energy sustainable development various ways of energy gain are now subjected to thorough and comprehensive analysis from the viewpoint of more and more rigorous and stringent criteria, the main are safe operation, commercial competition, reserves of energy sources and not devastating the earth. With this in mind it becomes apparent that just in not so distant future the energy production on a global scale should be no oxygen consuming and, consequently, no creating carbon dioxide which accumulation in ocean waters could lead to catastrophic changes in the ecosystem of our planet which regenerative capabilities are constantly diminish as a result of mankind activity. The unique way that can completely satisfies the above-mentioned conditions can be only nuclear power (NP). But the future NP should be safe, much more efficient and no producing radioactive waste. In the present work we give a short overview of physics basis of such a NP. In particular, we describe in brief the most realistic suggestions for NP - Accelerator Driven Systems [1] and Hybrid Cascade Reactor Systems [2], and the results and ways of investigation in the field of transmutation of radioactive waste [3,4
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
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Bhattacharjee, Amitava
2012-01-01
To celebrate Professor Robert Dewar's 65th birthday, a Symposium was held on 31 October 2009 in Atlanta, Georgia, just before the 51st Annual Meeting of the Division of Plasma Physics of the American Physical Society. The Symposium was attended by many of Bob's colleagues, friends, postdoctoral colleagues and students (present and former). Boyd Blackwell, Anthony Cooper, Chris Hegna, Stuart Hudson, John Krommes, Alexander Pletzer, Ellen Zweibel, and I gave talks that covered various aspects of Bob's wide-ranging scholarship, and his leadership in the Australian and the US fusion program. At the Symposium, Bob gave an insightful talk, published in this issue as a paper with D Leykam. This paper makes available for the first time unpublished results from Bob's M Sc Thesis on a general method for calculating the potential around a `dressed' test particle in an isotropic and collisionless plasma. The paper is interesting not only because it provides a glimpse of the type of elegant applied mathematics that we have come to associate with Bob, but also because he discusses some leitmotifs in his intellectual evolution since the time he was a graduate student at the University of Melbourne and Princeton University. Through his early encounter with quantum field theory, Bob appreciated the power of Lagrangian and Hamiltonian formalisms, which he used with great effectiveness in nonlinear dynamics and plasma physics. A question that animates much of his work is one that underlies the `dressed' particle problem: if one is given a Hamiltonian with an unperturbed (or `bare') part and an interaction part, how is one to obtain a canonical transformation to `the oscillation centre' thatwould reduce the interaction part to an irreducible residual part while incorporating the rest in a renormalized zeroth-order Hamiltonian? One summer in Princeton, I worked with Bob on a possible variational formulation for this problem, and failed. I was daunted enough by my failure that I turned
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....
Examining End-of-Chapter Problems across Editions of an Introductory Calculus-Based Physics Textbook
Xiao, Bin
2016-01-01
End-Of-Chapter (EOC) problems have been part of many physics education studies. Typically, only problems "localized" as relevant to a single chapter were used. This work examines how well this type of problem represents all EOC problems and whether EOC problems found in leading textbooks have changed over the past several decades. To…
Rebello, Carina M.
This study explored the effects of alternative forms of argumentation on undergraduates' physics solutions in introductory calculus-based physics. A two-phase concurrent mixed methods design was employed to investigate relationships between undergraduates' written argumentation abilities, conceptual quality of problem solutions, as well as approaches and strategies for solving argumentative physics problems across multiple physics topics. Participants were assigned via stratified sampling to one of three conditions (control, guided construct, or guided evaluate) based on gender and pre-test scores on a conceptual instrument. The guided construct and guided evaluate groups received tasks and prompts drawn from literature to facilitate argument construction or evaluation. Using a multiple case study design, with each condition serving as a case, interviews were conducted consisting of a think-aloud problem solving session paired with a semi-structured interview. The analysis of problem solving strategies was guided by the theoretical framework on epistemic games adapted by Tuminaro and Redish (2007). This study provides empirical evidence that integration of written argumentation into physics problems can potentially improve the conceptual quality of solutions, expand their repertoire of problem solving strategies and show promise for addressing the gender gap in physics. The study suggests further avenues for research in this area and implications for designing and implementing argumentation tasks in introductory college physics.
International Nuclear Information System (INIS)
Yao Ruo-Xia; Wang Wei; Chen Ting-Hua
2014-01-01
Motivated by the widely used ansätz method and starting from the modified Riemann—Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper. (general)
Lin, Shih-Yin; Singh, Chandralekha
2013-01-01
In this study, we examine introductory physics students' ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. 382 students from a calculus-based and an algebra-based introductory physics course were administered a quiz in the recitation…
The Fall in Older Adults: Physical and Cognitive Problems.
Laurence, Bernard Demanze; Michel, Lacour
2017-01-01
The aging of posture and balance function alters the quality of life in older people and causes serious problems in terms of public health and socio-economic costs for our modern societies. This article reviews the various causes of imbalance and dizziness in the elderly, and considers how to prevent falls, and how to rehabilitate a faller subject in order to regain a good quality of life. Two effective ways of intervention are discussed, emphasizing the crucial role of physical activity and cognitive stimulation, classic or using the latest technical advances in virtual reality and video games. Fall in the elderly result from aging mechanisms acting on both the sensorimotor and cognitive spheres. The structural and functional integrity of the peripheral sensory receptors and the musculoskeletal system deteriorate with age. The brain ages and the executive functions, memory, learning, cortical processing of information, sharing of attentional resources and concentration, are modified in the elderly. Psychological affective factors such as depression, anxiety and stress contribute also to speed up the sensorimotor and cognitive decline. The rehabilitation of the postural balance in the elderly must take into account all of these components. The aging of the population and the increased of lifespan are a challenge for our modern societies regarding the major health and socio-economic questions they raise. The fall in the elderly being one of the dramatic consequences of the aging equilibration function, it is therefore imperative to develop rehabilitation procedures of balance. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.
Analytical derivation: An epistemic game for solving mathematically based physics problems
Bajracharya, Rabindra R.; Thompson, John R.
2016-06-01
Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the analytical derivation game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four "pseudophysics" problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the analytical derivation game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.
Research Projects in Physics: A Mechanism for Teaching Ill-Structured Problem Solving
Milbourne, Jeff; Bennett, Jonathan
2017-10-01
Physics education research has a tradition of studying problem solving, exploring themes such as physical intuition and differences between expert and novice problem solvers. However, most of this work has focused on traditional, or well-structured, problems, similar to what might appear in a textbook. Less work has been done with open-ended, or ill-structured, problems, similar to the types of problems students might face in their professional lives. Given the national discourse on educational system reform aligned with 21st century skills, including problem solving, it is critical to provide educational experiences that help students learn to solve all types of problems, including ill-structured problems.
Incorporating Problem-Based Learning in Physical Education Teacher Education
Hushman, Glenn; Napper-Owen, Gloria
2011-01-01
Problem-based learning (PBL) is an educational method that identifies a problem as a context for student learning. Critical-thinking skills, deductive reasoning, knowledge, and behaviors are developed as students learn how theory can be applied to practical settings. Problem-based learning encourages self-direction, lifelong learning, and sharing…
Research Projects in Physics: A Mechanism for Teaching Ill-Structured Problem Solving
Milbourne, Jeff; Bennett, Jonathan
2017-01-01
Physics education research has a tradition of studying problem solving, exploring themes such as physical intuition and differences between expert and novice problem solvers. However, most of this work has focused on traditional, or well-structured, problems, similar to what might appear in a textbook. Less work has been done with open-ended, or…
Cosmic Plasmas, Physics 418 Problem Set for Lecture 1: Elements
International Nuclear Information System (INIS)
Thyagaraja, A.
2002-01-01
The problems (in this set and those for Lectures 2,3) are designed to bring out key points made in the lectures and clarify them through explicit examples. Hints for their solutions are provided in some cases. Problems which are 'hard' are starred; they will be dealt with in the 'problems class', at least in outline. Solutions to the problems will be handed out separately. Some additional problems are also provided for entertainment for those who wish to go deeper into the subject. They are optional extras and will not be required as a part of this course. (author)
Shukla, P. K.; Bingham, R.; Stenflo, L.; Dawson, J. M.
1996-01-01
of turbulence and the formation of coherent structures, particle and heat transport, plasma based charged particle acceleration by intense electrostatic waves that are created by powerful short laser beams, etc. Specifically, the review talks presented the general picture of the subject matter at hand and the underlying physics, whereas the remaining topical talks and the posters described the present state-of-the-art in the field. Instead of presenting the technical details, the speakers kept a good balance in injecting both the physics and the mathematical techniques to their audience. It was noted that despite the diversity of the physical problems, the mathematical equations governing particular phenomena and their solutions remain somewhat similar. Most contributions from the Trieste meeting appear in the form of a collection of articles in this Topical Issue of Physica Scripta, which will be distributed to all the delegates. We are grateful to the ICTP director Professor M A Virasoro and the deputy director Professor L Bertocchi for their generous support and warm hospitality at the ICTP. Thanks are also due to Professor G Denardo of the ICTP and Professor M H A Hassan of the Third World Academy of Sciences (TWAS, ICTP) for their constant and wholehearted support in our endeavours. We would like to express our gratitude to the ICTP and the Commission of the European Union (through the HCM networks on Dusty Plasmas and Nonlinear Phenomena in the Microphysics of Collisionless Plasmas) for providing partial financial support to our activities at Trieste. Finally, our cordial thanks are extended to the speakers and the attendees for their contributions which resulted in the success of this workshop. Specifically, we appreciate the speakers for delivering excellent talks, supplying well prepared manuscripts for publication, and enhancing the plasma physics activity at the ICTP. The excellent work of MS Ave Lusenti is gratefully acknowledged.
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
Rebello, Carina M.
2012-01-01
This study explored the effects of alternative forms of argumentation on undergraduates' physics solutions in introductory calculus-based physics. A two-phase concurrent mixed methods design was employed to investigate relationships between undergraduates' written argumentation abilities, conceptual quality of problem solutions, as well…
Non-linear characterisation of the physical model of an ancient masonry bridge
International Nuclear Information System (INIS)
Fragonara, L Zanotti; Ceravolo, R; Matta, E; Quattrone, A; De Stefano, A; Pecorelli, M
2012-01-01
This paper presents the non-linear investigations carried out on a scaled model of a two-span masonry arch bridge. The model has been built in order to study the effect of the central pile settlement due to riverbank erosion. Progressive damage was induced in several steps by applying increasing settlements at the central pier. For each settlement step, harmonic shaker tests were conducted under different excitation levels, this allowing for the non-linear identification of the progressively damaged system. The shaker tests have been performed at resonance with the modal frequency of the structure, which were determined from a previous linear identification. Estimated non-linearity parameters, which result from the systematic application of restoring force based identification algorithms, can corroborate models to be used in the reassessment of existing structures. The method used for non-linear identification allows monitoring the evolution of non-linear parameters or indicators which can be used in damage and safety assessment.
Use of model analysis to analyse Thai students’ attitudes and approaches to physics problem solving
Rakkapao, S.; Prasitpong, S.
2018-03-01
This study applies the model analysis technique to explore the distribution of Thai students’ attitudes and approaches to physics problem solving and how those attitudes and approaches change as a result of different experiences in physics learning. We administered the Attitudes and Approaches to Problem Solving (AAPS) survey to over 700 Thai university students from five different levels, namely students entering science, first-year science students, and second-, third- and fourth-year physics students. We found that their inferred mental states were generally mixed. The largest gap between physics experts and all levels of the students was about the role of equations and formulas in physics problem solving, and in views towards difficult problems. Most participants of all levels believed that being able to handle the mathematics is the most important part of physics problem solving. Most students’ views did not change even though they gained experiences in physics learning.
Current problems in applied mathematics and mathematical physics
Samarskii, A. A.
Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.
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
Directory of Open Access Journals (Sweden)
Shih-Yin Lin
2013-10-01
Full Text Available In this study, we examine introductory physics students’ ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. 382 students from a calculus-based and an algebra-based introductory physics course were administered a quiz in the recitation in which they had to learn from a solved problem provided and take advantage of what they learned from it to solve another isomorphic problem (which we call the quiz problem. The solved problem provided has two subproblems while the quiz problem has three subproblems, which is known from previous research to be challenging for introductory students. In addition to the solved problem, students also received extra scaffolding supports that were intended to help them discern and exploit the underlying similarities of the isomorphic solved and quiz problems. The data analysis suggests that students had great difficulty in transferring what they learned from a two-step problem to a three-step problem. Although most students were able to learn from the solved problem to some extent with the scaffolding provided and invoke the relevant principles in the quiz problem, they were not necessarily able to apply the principles correctly. We also conducted think-aloud interviews with six introductory students in order to understand in depth the difficulties they had and explore strategies to provide better scaffolding. The interviews suggest that students often superficially mapped the principles employed in the solved problem to the quiz problem without necessarily understanding the governing conditions underlying each principle and examining the applicability of the principle in the new situation in an in-depth manner. Findings suggest that more scaffolding is needed to help students in transferring from a two-step problem to a three-step problem and applying the physics principles appropriately. We outline a few
Lin, Shih-Yin; Singh, Chandralekha
2013-12-01
In this study, we examine introductory physics students’ ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. 382 students from a calculus-based and an algebra-based introductory physics course were administered a quiz in the recitation in which they had to learn from a solved problem provided and take advantage of what they learned from it to solve another isomorphic problem (which we call the quiz problem). The solved problem provided has two subproblems while the quiz problem has three subproblems, which is known from previous research to be challenging for introductory students. In addition to the solved problem, students also received extra scaffolding supports that were intended to help them discern and exploit the underlying similarities of the isomorphic solved and quiz problems. The data analysis suggests that students had great difficulty in transferring what they learned from a two-step problem to a three-step problem. Although most students were able to learn from the solved problem to some extent with the scaffolding provided and invoke the relevant principles in the quiz problem, they were not necessarily able to apply the principles correctly. We also conducted think-aloud interviews with six introductory students in order to understand in depth the difficulties they had and explore strategies to provide better scaffolding. The interviews suggest that students often superficially mapped the principles employed in the solved problem to the quiz problem without necessarily understanding the governing conditions underlying each principle and examining the applicability of the principle in the new situation in an in-depth manner. Findings suggest that more scaffolding is needed to help students in transferring from a two-step problem to a three-step problem and applying the physics principles appropriately. We outline a few possible strategies
Secondary Physical Education Avoidance and Gender: Problems and Antidotes
Ryan, Thomas; Poirier, Yves
2012-01-01
Our goal was to locate and evaluate the barriers that impact and cause females to avoid secondary elective physical education courses. We sought to find answers to stop the further decline of female enrolment in secondary physical education by looking into curricula, program and instructional variables. Anecdotal evidence informed this study which…
International Nuclear Information System (INIS)
2012-01-01
On October, 30 - November, 2 in State Scientific Center of the Russian Federation - Institute for Physics and Power Engineering named after A.I. Leypunsky a seminar Neutron-physical problems of nuclear power engineering - Neutronika-2012 took place. On the seminar the following problems were discussed: justification of neutron-physical characteristics of reactor facilities and innovation projects; constant support of neutron-physical calculations of nuclear power installations; numerical simulation during solving reactor physics problems; simulation of neutron-physical processes in reactor facilities by Monte Carlo method; development and verification of programs for reactor facilities neutron-physical calculations; algorithms and programs for solving nonstationary problems of neutron-physical calculation of nuclear reactors; analysis of integral and reactor experiments, experimental database; justification of nuclear and radiation safety of fuel cycle [ru
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.