Showing papers in "European Journal of Physics in 2005"
TL;DR: It is shown that short continuous recordings of the human locomotory apparatus possess properties typical of deterministic chaotic systems, and user-friendly programs are provided for each implemented method.
Abstract: We analyse the dynamics of human gait with simple nonlinear time series analysis methods that are appropriate for undergraduate courses. We show that short continuous recordings of the human locomotory apparatus possess properties typical of deterministic chaotic systems. To facilitate interest and enable the reproduction of presented results, as well as to promote applications of nonlinear time series analysis to other experimental systems, we provide user-friendly programs for each implemented method. Thus, we provide new insights into the dynamics of human locomotion, and make an effort to ease the inclusion of nonlinear time series analysis methods into the curriculum at an early stage of the educational process.
385 citations
TL;DR: In this paper, the chaotic behavior of a driven resonant circuit is studied directly from the experimental data using basic nonlinear time series analysis methods that are appropriate for undergraduate courses, and mutual information and false nearest neighbours are explained in detail, and used to obtain the best possible attractor reconstruction.
Abstract: The chaotic behaviour of a driven resonant circuit is studied directly from the experimental data. We use basic nonlinear time series analysis methods that are appropriate for undergraduate courses. Mutual information and false nearest neighbours are explained in detail, and used to obtain the best possible attractor reconstruction. For the reconstructed attractor, a determinism test is performed and the largest Lyapunov exponent is calculated. We show that the largest Lyapunov exponent is positive, which is a strong indicator for the chaotic behaviour of the system. To help the reader reproduce our results and to facilitate further applications on other experimental systems, we provide user-friendly programs with graphical interface for each implemented method on our Web page.
216 citations
TL;DR: After positively establishing the presence of determinism and stationarity in the studied electrocardiogram, the maximal Lyapunov exponent is calculated, thus providing interesting insights into the dynamics of the human heart.
Abstract: We analyse the human electrocardiogram with simple nonlinear time series analysis methods that are appropriate for graduate as well as undergraduate courses. In particular, attention is devoted to the notions of determinism and stationarity in physiological data. We emphasize that methods of nonlinear time series analysis can be successfully applied only if the studied data set originates from a deterministic stationary system. After positively establishing the presence of determinism and stationarity in the studied electrocardiogram, we calculate the maximal Lyapunov exponent, thus providing interesting insights into the dynamics of the human heart. Moreover, to facilitate interest and enable the integration of nonlinear time series analysis methods into the curriculum at an early stage of the educational process, we also provide user-friendly programs for each implemented method.
107 citations
TL;DR: In this paper, the role of the rigged Hilbert space in quantum mechanics is discussed, by way of a simple, exactly solvable example, and a thorough discussion on the physical significance of rigged Hilbert spaces.
Abstract: There is compelling evidence that, when a continuous spectrum is present, the natural mathematical setting for quantum mechanics is the rigged Hilbert space rather than just the Hilbert space. In particular, Dirac's bra-ket formalism is fully implemented by the rigged Hilbert space rather than just by the Hilbert space. In this paper, we provide a pedestrian introduction to the role the rigged Hilbert space plays in quantum mechanics, by way of a simple, exactly solvable example. The procedure will be constructive and based on a recent publication. We also provide a thorough discussion on the physical significance of the rigged Hilbert space.
99 citations
TL;DR: Two alternative expressions exist for the diffusive flux in inhomogeneous systems: Fick's law and the Fokker-Planck law as mentioned in this paper, and it is shown that in general, the latter is the preferred expression.
Abstract: Two alternative expressions exist for the diffusive flux in inhomogeneous systems: Fick's law and the Fokker-Planck law Here we re-examine the origin of these expressions and perform numerical and physical experiments to shed light on this duality We conclude that in general the Fokker-Planck expression should be conceded preference, in spite of the fact that Fick's law seems to be more popular
96 citations
TL;DR: The pioneering Fermi-Pasta-Ulam (FPU) numerical experiment played a major role in the history of computer simulation because it introduced this concept for the first time.
Abstract: The pioneering Fermi–Pasta–Ulam (FPU) numerical experiment played a major role in the history of computer simulation because it introduced this concept for the first time. Moreover, it raised a puzzling question which was answered more than 10 years later. After an introduction to this problem, we briefly review its history and then suggest some simple numerical experiments, with the Matlab© code provided, to study various aspects of the 'FPU' problem.
71 citations
TL;DR: In this paper, the electromagnetic form factors of spin-1/2 particles are known, but due to historical reasons only half of them are found in many textbooks, and the authors made an effort to derive and present the general result based only on the knowledge of the Dirac equation.
Abstract: The electromagnetic form factors of spin-1/2 particles are known, but due to historical reasons only half of them are found in many textbooks. Given the importance of the general result, its model independence, its connection to discrete symmetries and their violations we made an effort to derive and present the general result based only on the knowledge of the Dirac equation. We discuss the phenomenology connected directly with the form factors, and spin precession in external fields including time-reversal violating terms. We apply the formalism to spin–flip synchrotron radiation and suggest pedagogical projects.
67 citations
TL;DR: In this paper, the authors discuss phase-field models for modeling complex physical situations such as dendritic growth and multiphase flows, and discuss the main difficulty with these models is in their formulation, which incorporates the physical ingredients in a subtle way.
Abstract: Phase-field models are very attractive in view of their numerical simplicity With only a few lines of code, one can model complex physical situations such as dendritic growth From this point of view, they constitute very interesting tools for teaching purposes at graduate level The main difficulty with these models is in their formulation, which incorporates the physical ingredients in a subtle way We discuss these approaches on the basis of two examples: dendritic growth and multiphase flows
58 citations
TL;DR: In this paper, the most dominant conceptual hurdle that emerged in the students' explanations was centred around the notion of probability, and the analysis reported is done in terms of the various facets of probability encountered in the simulation and characterizes dynamics of this conceptual hurdle to appropriate understanding of the scattering and tunnelling process.
Abstract: This paper draws on part of a larger project looking at university students' learning difficulties associated with quantum mechanics. Here an unexpected and interesting aspect was brought to the fore while students were discussing a computer simulation of one-dimensional quantum scattering and tunnelling. In these explanations the most dominant conceptual hurdle that emerged in the students' explanations was centred around the notion of probability. To explore this further, categories of description of the variation in the understanding of probability were constituted. The analysis reported is done in terms of the various facets of probability encountered in the simulation and characterizes dynamics of this conceptual hurdle to appropriate understanding of the scattering and tunnelling process. Pedagogical implications are discussed.
56 citations
TL;DR: The angular momentum of a classical electromagnetic plane wave of arbitrary extent is predicted to be, on theoretical grounds, exactly zero as mentioned in this paper, however, finite sections of circularly polarized plane waves are found experimentally to carry angular momentum, and it is known that the contribution to the angular momentum arises from the edges of the beam.
Abstract: The angular momentum of a classical electromagnetic plane wave of arbitrary extent is predicted to be, on theoretical grounds, exactly zero. However, finite sections of circularly polarized plane waves are found experimentally to carry angular momentum, and it is known that the contribution to the angular momentum arises from the edges of the beam. A mathematical model is described that gives a quantitative account of this effect and resolves the paradox.
56 citations
TL;DR: In this article, the density-dependent distribution function of the orientation of the long axis of rod-like colloidal particles in the liquid crystalline nematic phase is numerically calculated as the solution of a nonlinear integral equation.
Abstract: The density-dependent distribution function of the orientation of the long axis of rod-like colloidal particles in the liquid crystalline nematic phase is numerically calculated as the solution of a nonlinear integral equation. From this solution, which is obtained by an iterative method that is explained in detail, the free energy, the pressure and the chemical potential can be computed, as well as the nematic order parameter. Moreover, the first-order phase transition from the disordered isotropic fluid phase to the nematic phase is analysed numerically. This study, presented at the level of advanced undergraduates or starting graduate students, not only illustrates the existence of liquid crystalline ordering for nonspherical particles, but also shows explicitly how thermodynamics, structure and symmetry are related.
TL;DR: This article investigated students' reasoning about energy in the context of quantum tunnelling using ungraded surveys, graded examination questions, individual clinical interviews and multiple-choice exams to build a picture of the types of responses that students typically give.
Abstract: We report on a multi-year, multi-institution study to investigate students' reasoning about energy in the context of quantum tunnelling. We use ungraded surveys, graded examination questions, individual clinical interviews and multiple-choice exams to build a picture of the types of responses that students typically give. We find that two descriptions of tunnelling through a square barrier are particularly common. Students often state that tunnelling particles lose energy while tunnelling. When sketching wavefunctions, students also show a shift in the axis of oscillation, as if the height of the axis of oscillation indicated the energy of the particle. We find inconsistencies between students' conceptual, mathematical and graphical models of quantum tunnelling. As part of a curriculum in quantum physics, we have developed instructional materials designed to help students develop a more robust and less inconsistent picture of tunnelling, and present data suggesting that we have succeeded in doing so.
TL;DR: In this paper, a desktop experiment to demonstrate the linear and quadratic velocity dependence of drag on an object falling in a resistive medium was developed for an undergraduate laboratory, where the motion of ball bearings dropped into a cylinder filled with fluid was captured and measured using computer-based imaging.
Abstract: A desktop experiment to demonstrate the linear and quadratic velocity dependence of drag on an object falling in a resistive medium was developed for an undergraduate laboratory. The motion of ball bearings dropped into a cylinder filled with fluid is captured and measured using computer-based imaging. The terminal velocity of falling spheres is measured as a function of size at low and high Reynolds number, and the results are compared to predicted scaling laws for models containing a drag force that is linear or quadratic with velocity.
TL;DR: In this article, a simple new method that provides instructive insights into the dynamics of chaotic time-continuous systems that yield strange attractors as solutions in the phase space is described.
Abstract: We describe a simple new method that provides instructive insights into the dynamics of chaotic time-continuous systems that yield strange attractors as solutions in the phase space. In particular, we show that the norm of the vector field component that is orthogonal to the trajectory is an excellent quantity for visualizing the attraction of strange attractors, thus promoting the understanding of their formation and overall structure. Furthermore, based on the existence of zero orthogonal field strengths in planes that form low-dimensional strange attractors, we also provide an innovative explanation for the origin of chaotic behaviour. For instructive purposes, we first apply the method to a simple limit cycle attractor, and then analyse two paradigmatic mathematical models for classical time-continuous chaos. To facilitate the use of our method in graduate as well as undergraduate courses, we also provide user-friendly programs in which the presented theory is implemented.
TL;DR: In this article, an apparatus was devised using the Traube Stalagmometer for the determination of the surface tension of the alcohols methanol, ethanol, propan-1-ol and butan 1-ol.
Abstract: An apparatus was devised using the Traube Stalagmometer for the determination of the surface tension of the alcohols methanol, ethanol, propan-1-ol and butan-1-ol. Measurements were made under atmospheric pressure at temperatures between 288.15 K and 313.15 K. The surface tension values were correlated with temperature and surface thermodynamic parameters, namely surface entropy and surface enthalpy, were also calculated. The results obtained are in agreement with the literature and they are promising for the use of this low cost arrangement for accurate measurement of surface tension. Surface tension values were obtained with a maximum error of 0.5 mN m−1 and a maximum standard deviation of 0.8 mN m−1. We recommend this arrangement for students in advanced university courses and it can also be used for research work.
TL;DR: In this article, a chaotic oscillator for training laboratories accompanying courses on nonlinear dynamics and chaos for undergraduate, postgraduate and PhD students is described, which consists of an operational amplifier, an LCR resonance loop, an extra capacitor, a diode as a nonlinear element and three auxiliary resistors.
Abstract: A novel, very simple chaotic oscillator is described. It is intended for training laboratories accompanying courses on nonlinear dynamics and chaos for undergraduate, postgraduate and PhD students. The oscillator consists of an operational amplifier, an LCR resonance loop, an extra capacitor, a diode as a nonlinear element and three auxiliary resistors. Chaotic oscillations are demonstrated both experimentally and numerically.
[...]
TL;DR: The unitary Newtonian concept of mass has now fragmented into various "masses", including inertial mass, active gravitational mass, and passive gravitational mass as discussed by the authors, and it has not been entirely successful.
Abstract: Efforts after Newton to reform the concept of mass have not been entirely successful. The unitary Newtonian concept has now fragmented into various 'masses', including inertial mass, active gravitational mass and passive gravitational mass. This paper attempts to clarify the concept of mass.
TL;DR: In this article, the exact and approximate calculation of integrals that appear in formulae for the period of anharmonic oscillators and other problems of interest in classical mechanics is presented.
Abstract: In this paper, we present a straightforward systematic method for the exact and approximate calculation of integrals that appear in formulae for the period of anharmonic oscillators and other problems of interest in classical mechanics.
TL;DR: In this article, two alternative methods, based on the Lindstedt-Poincare technique, for the removal of secular terms from the equations of perturbation theory were discussed and compared.
Abstract: We discuss two alternative methods, based on the Lindstedt–Poincare technique, for the removal of secular terms from the equations of perturbation theory. We calculate the period of an anharmonic oscillator by means of both approaches and show that one of them is more accurate for all values of the coupling constant. We believe that present discussion and comparison may be a suitable exercise for teaching perturbation theory in advanced undergraduate courses on classical mechanics.
TL;DR: In this article, it was shown that the existing laws of reflection and refraction of light seem to be ambiguous in respect of generality and their validity in a broad sense is questionable.
Abstract: This paper discloses two important discoveries These are: (i) discovery of ambiguity in the well-established laws of reflection and refraction of light which have been in regular use for many years, and (ii) discovery of generalized vectorial laws of reflection and refraction of light The existing definitions of angle of incidence, angle of reflection and angle of refraction are considered first Each of these definitions is found to be ambiguous, not in compliance with the fundamental definition of angle in geometry Two typical questions (one in the case of reflection and the other for refraction) have been addressed, which cannot be dealt with by using the existing laws of reflection and refraction of light Thus, the existing laws of reflection and refraction of light seem to be ambiguous in respect of generality and their validity in a broad sense is questionable With a view to removing the ambiguities, proper definitions of the above three angles are given first and then the statement of the generalized vectorial law of reflection (as well as that of refraction) has been offered
TL;DR: In this paper, the phenomenon of parametric resonance in a linear torsion spring oscillator caused by a square-wave modulation of its moment of inertia is explained and investigated both analytically and with the help of a computer simulation.
Abstract: The phenomenon of parametric resonance in a linear torsion spring oscillator caused by a square-wave modulation of its moment of inertia is explained and investigated both analytically and with the help of a computer simulation. Characteristics of parametric resonance and regeneration are found and discussed in detail. Ranges of frequencies within which parametric excitation is possible are determined. Stationary oscillations at the boundaries of these ranges and at the threshold conditions are investigated.
TL;DR: This work study the movement of a damped coupled oscillation system as a linear combination of two normal modes, i.e. the symmetric and antisymmetric modes, and shows a very good agreement with the theory.
Abstract: The applications of the digital video image to the investigation of physical phenomena have increased enormously in recent years. The advances in computer technology and image recognition techniques allow the analysis of more complex problems. In this work, we study the movement of a damped coupled oscillation system. The motion is considered as a linear combination of two normal modes, i.e. the symmetric and antisymmetric modes. The image of the experiment is recorded with a video camera and analysed by means of software developed in our laboratory. The results show a very good agreement with the theory.
TL;DR: In this paper, a new derivation of the expressions for momentum and energy of a relativistic particle is presented, which requires only knowledge of the composition law for velocities along one spatial dimension.
Abstract: We present a new derivation of the expressions for momentum and energy of a relativistic particle. In contrast to the procedures commonly adopted in textbooks, the one suggested here requires only knowledge of the composition law for velocities along one spatial dimension, and does not make use of the concept of relativistic mass, or of the formalism of 4-vectors. The basic ideas are very general and can be applied also to kinematics different from the Newtonian and Einstein ones, in order to construct the corresponding dynamics.
TL;DR: In this paper, an experimental apparatus has been designed and built in our laboratory that allows the students to carry out experiments based on the application of the Wilson plot method, which is an outstanding tool in practical applications and in laboratory research activities that involve analysis of heat exchangers.
Abstract: The Wilson plot is a technique to estimate the film coefficients in several types of heat transfer processes and to obtain general heat transfer correlations. This method is an outstanding tool in practical applications and in laboratory research activities that involve analysis of heat exchangers. Moreover, the application of this method is simple enough to be taught in laboratory practices for students at university and doctoral level of physics and engineering. Therefore, an experimental apparatus has been designed and built in our laboratory that allows the students to carry out experiments based on the application of the Wilson plot method. In this note, the principles of the method are explained, the experimental apparatus is described and representative results of the experimental data taken from the apparatus and the application of the Wilson plot method are shown.
TL;DR: In this article, a three-month research project for undergraduate students about the mass-radius relation of compact stars is described. And the authors derive some conditions for the existence of a third family of stars in the form of the equation of state and its different global properties.
Abstract: We report on a three-month research project for undergraduate students about the mass–radius relation of compact stars. The equation of state used is constrained at low densities by well-established equations of state of the nuclear phase (the solid crust) and then extended to higher densities with a phenomenological, parametric approach. A first-order phase transition from hadronic matter to a phase of higher density, assumed to be quark matter, is studied in addition. The mass–radius relation is obtained by solving numerically the Tolman–Oppenheimer–Volkoff equation. We derive some conditions for the existence of a third family of compact stars in the form of the equation of state and its different global properties.
TL;DR: In this paper, a four-electrode equipment which can be made available in the physics laboratory was designed and fabricated for measuring current and potential values so as to obtain the resistivity values.
Abstract: A four-electrode equipment which can be made available in the physics laboratory was designed and fabricated for measuring current and potential values so as to obtain the resistivity values. Readings taken from our chosen location using both Wenner and Schlumberger arrays were analysed. In the resistivity method, the Wenner configuration discriminates between resistivities of different geoelectric lateral layers while the Schlumberger configuration is used for the 'depth sounding'. The theory behind the resistivity method was introduced with some degree of sophistication. Experimentally determined values of depth to surface were correlated with the values determined from the excavated site and this gave a good correlation. It was observed that the resistivity value in the chosen location increases with the depth and the Schlumberger method was seen to have a greater penetration than the Wenner.
TL;DR: In this paper, the authors investigated the nonlinear dynamics of automobile braking and showed that the friction coefficient between vehicle tyres and road surface depends upon vehicle speed and wheel angular speed, and showed how antilock brake systems approach optimum braking performance.
Abstract: The nonlinear dynamics of automobile braking are investigated. Nonlinearity arises because of the manner in which the friction coefficient between vehicle tyres and road surface depends upon vehicle speed and wheel angular speed. We show how antilock brake systems approach optimum braking performance.
TL;DR: In this paper, the decaying vertical oscillation of a sphere attached to the lower end of a spring in containers with different liquids is analyzed under a standard framework and some important mismatches between observation and theory are found, which are attributed to oversimplifications in the formulation of the drag force.
Abstract: A simple model of damped harmonic motion is usually presented in undergraduate physics textbooks and straightforwardly applied for a variety of well-known experiments in student laboratories. Results for the decaying vertical oscillation of a sphere attached to the lower end of a spring in containers with different liquids are analysed here under this standard framework. Some important mismatches between observation and theory are found, which are attributed to oversimplifications in the formulation of the drag force. A more elaborate expression for the latter within a semiempirical approach is then introduced and a more appropriate description of the measurements is shown to be attained. Two coefficients account for experimental corrections, which under certain conditions permit in addition the calculation of specific fluid quantities associated with the oscillating sphere. Rough relations between viscosity and damping factor under appropriate limits are derived. The laboratory experience may also be used to introduce the concept of a semiempirical model and exhibit its utility in physics.
TL;DR: In this paper, the time evolution of entanglement in the Stern-Gerlach experiment is analyzed in detail, in connection with the two-component wavefunction description of spin-1/2 particles.
Abstract: Basic aspects of quantum entanglement are illustrated in connection with the two-component wavefunction description of spin-1/2 particles. In particular, the time evolution of entanglement in the Stern–Gerlach experiment is analysed in detail.
TL;DR: In this paper, it was shown that the null result of the Michelson-Morley experiment in vacuum is deeply connected with the notion of time, which can be deduced from the assumption that all good clocks can be used to measure time with the same results, independently of the machinery involved in their manufacturing.
Abstract: In this work, we show that the null result of the Michelson–Morley experiment in vacuum is deeply connected with the notion of time. It can be deduced, without any mathematics, from the assumption only that all good clocks can be used to measure time with the same results, independently of the machinery involved in their manufacturing. A second important assumption, intrinsic to the very notion of time, is that clocks measure time in the same way in different frames, i.e., the notion of time is the same in all inertial frames. Under this assumption, we point out that the 'postulate' of constancy of the 'two-way' speed of light in vacuum in all frames independently of the state of motion of the emitting body is also strongly related to the concept of time, together with the existence of a limit speed in the 'rest frame'. This postulate simply results from the construction of clocks where 'tic–tacs' are made by objects travelling with the limit speed, taken to be the speed of light.