Showing papers in "American Journal of Physics in 2004"
TL;DR: In this paper, it was shown that the least-squares estimation method of fitting the best straight line to data points having normally distributed errors yields identical results for the slope and intercept of the line as does the method of maximum likelihood estimation.
Abstract: It has long been recognized that the least-squares estimation method of fitting the best straight line to data points having normally distributed errors yields identical results for the slope and intercept of the line as does the method of maximum likelihood estimation. We show that, contrary to previous understanding, these two methods also give identical results for the standard errors in slope and intercept, provided that the least-squares estimation expressions are evaluated at the least-squares-adjusted points rather than at the observed points as has been done traditionally. This unification of standard errors holds when both x and y observations are subject to correlated errors that vary from point to point. All known correct regression solutions in the literature, including various special cases, can be derived from the original York equations. We present a compact set of equations for the slope, intercept, and newly unified standard errors.
883 citations
TL;DR: The Origin of Oil and the Future of Fossil Fuels: A New Outlook and Discussion of Alternative Energy Sources is presented.
Abstract: Preface to the 2008 Edition ix Acknowledgments xv CHAPTER 1: Overview 1 CHAPTER 2: The Origin of Oil 14 CHAPTER 3: Oil Reservoirs and Oil Traps 40 CHAPTER 4: Finding It 70 CHAPTER 5: Drilling Methods 88 CHAPTER 6: Size and Discoverability of Oil Fields 113 CHAPTER 7: Hubbert Revisited 133 CHAPTER 8: Rate Plots 150 CHAPTER 9: The Future of Fossil Fuels 159 CHAPTER 10: Alternative Energy Sources 176 CHAPTER 11: A New Outlook 186 Notes 191 Index 205
466 citations
TL;DR: In this paper, two versions of a diagnostic instrument were developed, each consisting of 29 questions, for high school and university students' reasoning regarding direct current resistive electric circuits often differ from the accepted explanations.
Abstract: Both high school and university students’ reasoning regarding direct current resistive electric circuits often differ from the accepted explanations. At present, there are no standard diagnostic tests on electric circuits. Two versions of a diagnostic instrument were developed, each consisting of 29 questions. The information provided by this test can provide instructors with a way of evaluating the progress and conceptual difficulties of their students. The analysis indicates that students, especially females, tend to hold multiple misconceptions, even after instruction. During interviews, the idea that the battery is a constant source of current was used most often in answering the questions. Students tended to focus on the current in solving problems and to confuse terms, often assigning the properties of current to voltage and/or resistance.
437 citations
402 citations
TL;DR: The authors compared student learning from different modes of presenting classroom demonstrations to determine how much students learn from traditionally presented demonstrations, and whether learning can be enhanced by simply changing the mode of presentation to increase student engagement.
Abstract: We compared student learning from different modes of presenting classroom demonstrations to determine how much students learn from traditionally presented demonstrations, and whether learning can be enhanced by simply changing the mode of presentation to increase student engagement. We find that students who passively observe demonstrations understand the underlying concepts no better than students who do not see the demonstration at all, in agreement with previous studies. Learning is enhanced, however, by increasing student engagement; students who predict the demonstration outcome before seeing it, however, display significantly greater understanding.
265 citations
TL;DR: In this paper, a Monte Carlo algorithm for doing simulations in classical statistical physics in a different way is described, where instead of sampling the probability distribution at a fixed temperature, a random walk is performed in energy space to extract an estimate for the density of states.
Abstract: We describe a Monte Carlo algorithm for doing simulations in classical statistical physics in a different way. Instead of sampling the probability distribution at a fixed temperature, a random walk is performed in energy space to extract an estimate for the density of states. The probability can be computed at any temperature by weighting the density of states by the appropriate Boltzmann factor. Thermodynamic properties can be determined from suitable derivatives of the partition function and, unlike “standard” methods, the free energy and entropy can also be computed directly. To demonstrate the simplicity and power of the algorithm, we apply it to models exhibiting first-order or second-order phase transitions.
237 citations
TL;DR: In this paper, the authors studied pump-probe spectroscopy of Rb vapor and explained the importance of hyperfine pumping in the formation of the sub-Doppler spectrum.
Abstract: We study pump–probe spectroscopy of Rb vapor. Absorption spectra are presented for a weak probe beam in a room temperature vapor subject to a strong counter propagating pump beam of identical frequency. The importance of hyperfine pumping in the formation of the sub-Doppler spectrum is explained. For typical experimental parameters we clarify why the standard designation of “saturated absorption” spectroscopy is a misnomer. In contrast to saturated absorption, the details of the transient solution are crucial and hyperfine pumping leads to a modification of the absorption for detunings of many tens of natural linewidths from resonance.
159 citations
TL;DR: In this paper, the transport properties of single asymmetric nanopores in polyetheylene terephthalate (PET) were examined and it was shown that the nanopores are cation selective and rectify the current with the preferential direction of cation flow from the narrow entrance toward the wide opening of the pore.
Abstract: The transport properties of single asymmetric nanopores in polyetheylene terephthalate (PET) are examined. The pores were produced by a track etching technique based on the irradiation of the foils by swift heavy ions and subsequent chemical etching. Electrical conductivity measurements show that the nanopores in PET are cation selective and rectify the current with the preferential direction of cation flow from the narrow entrance toward the wide opening of the pore. Moreover, the pore transports potassium ions against the concentration gradient if stimulated by external field fluctuations. We show that the rectifying and pumping effects are based on the ratchet mechanism.
152 citations
TL;DR: The Resource Letter as mentioned in this paper provides a guide to the literature on research in problem-solving, especially in physics, with two audiences in mind: physicists who are (or might become) engaged in research on problem solving, and physics instructors who are interested in using research results to improve their students' learning of problem solving.
Abstract: This Resource Letter provides a guide to the literature on research in problem solving, especially in physics. The references were compiled with two audiences in mind: physicists who are (or might become) engaged in research on problem solving, and physics instructors who are interested in using research results to improve their students’ learning of problem solving. In addition to general references, journal articles and books are cited for the following topics: cognitive aspects of problem solving, expert-novice problem-solver characteristics, problem solving in mathematics, alternative problem types, curricular interventions, and the use of computers in problem solving.
146 citations
TL;DR: The butterfly metaphor was predated by more than 70 years by the grasshopper effect as mentioned in this paper and has become a popular metaphor for sensitive dependence on initial conditions, the hallmark of chaotic behavior.
Abstract: The butterfly effect has become a popular metaphor for sensitive dependence on initial conditions—the hallmark of chaotic behavior. I describe how, where, and when this term was conceived in the 1970s. Surprisingly, the butterfly metaphor was predated by more than 70 years by the grasshopper effect.
145 citations
TL;DR: This paper found that a large majority of students thought that net work done or net heat absorbed by a system undergoing a cyclic process must be zero, and only 20% or fewer were able to make effective use of the first law of thermodynamics even after instruction.
Abstract: Students in an introductory university physics course were found to share many substantial difficulties related to learning fundamental topics in thermal physics. Responses to written questions by 653 students in three separate courses were consistent with the results of detailed individual interviews with 32 students in a fourth course. Although most students seemed to acquire a reasonable grasp of the state-function concept, it was found that there was a widespread and persistent tendency to improperly over-generalize this concept to apply to both work and heat. A large majority of interviewed students thought that net work done or net heat absorbed by a system undergoing a cyclic process must be zero, and only 20% or fewer were able to make effective use of the first law of thermodynamics even after instruction. Students’ difficulties seemed to stem in part from the fact that heat, work, and internal energy share the same units. The results were consistent with those of previously published studies of students in the U.S. and Europe, but portray a pervasiveness of confusion regarding process-dependent quantities that has been previously unreported. Significant enhancements of current standard instruction may be required for students to master basic thermodynamic concepts.
TL;DR: In this article, an elementary introduction to perturbative renormalization and group is presented, and the general arguments and results are linked to real phenomena encountered in particle physics and statistical mechanics.
Abstract: An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical theory. We are thus able to disentangle what is specific to field theory and what is intrinsic to renormalization. We link the general arguments and results to real phenomena encountered in particle physics and statistical mechanics.
TL;DR: A simple spring model with pre-load to achieve negative stiffness is considered and when suitably tuned to balance positive and negative stiffness, the system shows a critical equilibrium point giving rise to extreme overall stiffness.
Abstract: When an elastic object is pressed, we expect it to resist by exerting a restoring force. A reversal of this force corresponds to negative stiffness. If we combine elements with positive and negative stiffness in a composite, it is possible to achieve stiffness greater than (or less than) that of any of the constituents. This behavior violates established bounds that tacitly assume that each phase has positive stiffness. Extreme composite behavior has been experimentally demonstrated in a lumped system using a buckled tube to achieve negative stiffness and in a composite material in the vicinity of a phase transformation of one of the constituents. In the context of a composite system, extreme refers to a physical property greater than either constituent. We consider a simple spring model with pre-load to achieve negative stiffness. When suitably tuned to balance positive and negative stiffness, the system shows a critical equilibrium point giving rise to extreme overall stiffness. A stability analysis of a viscous damped system containing negative stiffness springs reveals that the system is stable when tuned for high compliance, but metastable when tuned for high stiffness. The metastability of the extreme system is analogous to that of diamond. The frequency response of the viscous damped system shows that the overall stiffness increases with frequency and goes to infinity when one constituent has a suitable negative stiffness.
TL;DR: In this article, a single-photon counting detector was used to measure the degree of second-order coherence between the output of a beam-plitter and a single photon.
Abstract: While the classical, wavelike behavior of light (interference and diffraction) has been easily observed in undergraduate laboratories for many years, explicit observation of the quantum nature of light (i.e., photons) is much more difficult. For example, while well-known phenomena such as the photoelectric effect and Compton scattering strongly suggest the existence of photons, they are not definitive proof of their existence. Here we present an experiment, suitable for an undergraduate laboratory, that unequivocally demonstrates the quantum nature of light. Spontaneously downconverted light is incident on a beamsplitter and the outputs are monitored with single-photon counting detectors. We observe a near absence of coincidence counts between the two detectors—a result inconsistent with a classical wave model of light, but consistent with a quantum description in which individual photons are incident on the beamsplitter. More explicitly, we measured the degree of second-order coherence between the output...
TL;DR: In this article, the authors present five lessons for teachers towards an active learning environment in introductory physics classes, including the importance of knowledge structures and problem-solving in an active-learning environment.
Abstract: Preface iiiI TEACHING INTRODUCTORY PHYSICS1. IntroductionDesired Student Outcomes Five Lessons for Teachers Toward an Active-Learning Environment Does it Work?2. Teaching Introductory Physics Things to Consider Laboratories and Recitations 3. Physics Education ResearchWhat is Physics Education Research?Summary of Findings from Physics Education Research Examples of Students' Alternative Conceptions Knowledge Structures and Problem Solving Implications for Instruction - The Five Lessons4. An Active-Learning ClassroomSo What's Wrong with Lectures?Active Learning A Dozen Things you can do to Change Physics Education Just the FAQsII TOPICS IN INTRODUCTORY PHYSICS 5. Introduction 6. Vectors and Mathematics 7. Motion and Kinematics8. Forces and Newton's Laws 9. Impulse and Momentum 10. Energy 11. Oscillations12. Waves 13. Thermal Physics 14. Thermodynamics 15. Electrostatics 16. Electric Fields 17. The Electric Potential 18. Current and Conductivity 19. DC Circuits 20. Magnetic Fields 21. Electromagnetic Induction 22. Geometrical Optics 23. Physical Optics 24. Quantum Physics References and Resources
TL;DR: In this paper, the outflow speed and mass loss rate of the solar wind of plasma particles ejected by the Sun are derived analytically for certain illustrative approximations.
Abstract: This paper presents closed-form analytic solutions to two illustrative problems in solar physics that have been considered not solvable in this way previously. Both the outflow speed and the mass loss rate of the solar wind of plasma particles ejected by the Sun are derived analytically for certain illustrative approximations. The calculated radial dependence of the flow speed applies to both Parker’s isothermal solar wind equation and Bondi’s equation of spherical accretion. These problems involve the solution of transcendental equations containing products of variables and their logarithms. Such equations appear in many fields of physics and are solvable by use of the Lambert W function, which is briefly described. This paper is an example of how new functions can be applied to existing problems.
TL;DR: In this paper, a comparison of student understanding of physics concepts with and without online homework, as measured by the force concept inventory, was reported. But the results of this comparison were limited to the C grade subgroup.
Abstract: We report the results of a comparison of student understanding of physics concepts with and without online homework, as measured by the force concept inventory. We compared students in large introductory courses taught by interactive engagement and noninteractive engagement methods and with ungraded homework and with online homework. We also compared the understanding of students in different grade subgroups. The increase in the average force concept inventory normalized gain was statistically significant for all students taught with online homework, indicating that graded homework increases student understanding of physics concepts. The gain was significantly higher for those students taught with interactive engagement methods together with online homework. The C grade subgroup taught by interactive engagement methods benefited more from the implementation of online homework than the other subgroups.
TL;DR: In this paper, the authors analyzed the bifurcation shift with the help of a simple model and described an inexpensive experiment using a semiconductor laser, where this phenomenon occurs near the threshold of a single-input single-output (SISO) laser.
Abstract: Critical slowing down near a bifurcation or limit point leads to a dynamical hysteresis that cannot be avoided by sweeping a control parameter slowly through the critical point. This paper analytically illustrates, with the help of a simple model, the bifurcation shift. We describe an inexpensive experiment using a semiconductor laser where this phenomenon occurs near the threshold of a semiconductor laser.
TL;DR: In this paper, a relativistic velocity space called rapidity space is developed from the single assumption of Lorentz invariance, and use it to visualize and calculate effects resulting from the successive application of non-collinear Lorenz boosts.
Abstract: We develop a relativistic velocity space called rapidity space from the single assumption of Lorentz invariance, and use it to visualize and calculate effects resulting from the successive application of non-collinear Lorentz boosts. In particular, we show how rapidity space provides a geometric approach to Wigner rotation and Thomas precession in the same way that space–time provides a geometrical approach to kinematic effects in special relativity.
TL;DR: In this article, an annotated guide to some of the literature pertaining to the understanding of thermoacoustic engines and refrigerators is provided. But the authors do not provide a detailed discussion of the differences between stack-based and regenerator-based systems.
Abstract: This Resource Letter provides an annotated guide to some of the literature pertaining to the understanding of thermoacoustic engines and refrigerators. These devices incorporate acoustical components and networks to produce mechanical power or to pump heat, or both, without the use of traditional mechanical contrivances such as pistons, linkages, and valves. To bring some order to this research and the variety of thermoacoustic engines and refrigerators produced over the past two decades, these devices also are classified as stack-based and regenerator-based. The background and motivation for this organizational structure is provided in the introduction.
TL;DR: The calculation of the structure of white dwarf and neutron stars is a suitable topic for an undergraduate thesis or an advanced special topics or independent study course as discussed by the authors, which is rich in many different areas of physics, ranging from thermodynamics to quantum statistics to nuclear physics to special and general relativity.
Abstract: The calculation of the structure of white dwarf and neutron stars is a suitable topic for an undergraduate thesis or an advanced special topics or independent study course. The subject is rich in many different areas of physics, ranging from thermodynamics to quantum statistics to nuclear physics to special and general relativity. The computations for solving the coupled structure differential equations (both Newtonian and general relativistic) can be done using a symbolic computational package. In doing so, students will develop computational skills and learn how to deal with units. Along the way they also will learn some of the physics of equations of state and of degenerate stars.
TL;DR: In this paper, the authors give a pedagogical review of a mechanism through which long wavelength photons can become massive during inflation and show that the quantum fluctuations of low mass, scalar fields are enormously amplified during inflation.
Abstract: We give a pedagogical review of a mechanism through which long wavelength photons can become massive during inflation. Our account begins with a discussion of the period of exponentially rapid expansion known as inflation. We next describe how, when the universe is not expanding, quantum fluctuations in charged particle fields cause even empty space to behave as a polarizable medium. This is the routinely observed phenomenon of vacuum polarization. We show that the quantum fluctuations of low mass, scalar fields are enormously amplified during inflation. If one of these fields is charged, the vacuum polarization effect of flat space is strengthened to the point that long wavelength photons acquire mass. Our result for this mass is shown to agree with a simple model in which the massive photon electrodynamics of Proca emerges from applying the Hartree approximation to scalar quantum electrodynamics during inflation. A huge photon mass is not measured today because the original phase of inflation ended when...
TL;DR: In this paper, the authors show that the standard Fierz transformation is one element of a class of transformations that exist between fermion amplitudes that are written with different, arbitrary reorderings, of the spinors.
Abstract: Low energy weak interaction calculations with fermions frequently involve a superposition of quartic products of Dirac spinors, in which the order of the spinors is not the same in all the contributing terms. A common trick that is used to bring them to a uniform ordering is the Fierz transformation. We show that the standard Fierz transformation quoted in textbooks is one element of a class of transformations that exist between fermion amplitudes that are written with different, arbitrary reorderings, of the spinors. The explicit form of all such transformation matrices is given, and in addition to the usual Lorentz scalar quartic products, we consider the pseudoscalar ones. Moreover, we include the cases in which some, or all, of the spinors in the original amplitude appear in the transformed amplitudes in their Lorentz-invariant complex conjugate form. Such manipulations and formulas are useful in practical calculations, as we show with some examples.
TL;DR: In this paper, the authors illustrate situations for which different boundary conditions lead to different self-adjoint operators and hence to different physics, and show that different boundary condition leads to different operators.
Abstract: To construct a self-adjoint operator the domain of the operator has to be specified by imposing an appropriate boundary condition or conditions on the wave functions on which the operator acts. We illustrate situations for which different boundary conditions lead to different operators and hence to different physics.
TL;DR: In this paper, a more general friction relation is motivated and shown to fit data from simple atomic simulations that can be downloaded and modified to illustrate the fundamental relation between static friction and potential energy, and between kinetic friction and energy dissipation.
Abstract: Recent advances in the understanding of the atomic origins of friction are described and illustrated with simple simulations. Examples of macroscopic and nanometer scale systems that violate Amontons’ laws of friction are discussed. A more general friction relation is motivated and shown to fit data from simple atomic simulations that can be downloaded and modified. The simulations illustrate the fundamental relation between static friction and potential energy, and between kinetic friction and energy dissipation. Conceptual difficulties in understanding how almost all pairs of surfaces lock together in a potential energy minimum are described, and possible resolutions are discussed. We conclude with an explanation of why Amontons’ laws work so well in many macroscopic systems.
TL;DR: In this paper, conservation laws from symmetry operations using the principle of least action were derived for the Lorentz transformation of coordinates due to uniform motion and the Galilean transformation of coordinate changes.
Abstract: We derive conservation laws from symmetry operations using the principle of least action. These derivations, which are examples of Noether’s theorem, require only elementary calculus and are suitable for introductory physics. We extend these arguments to the transformation of coordinates due to uniform motion to show that a symmetry argument applies more elegantly to the Lorentz transformation than to the Galilean transformation.
TL;DR: In this paper, the relativistic trajectories of the Kepler and Coulomb potentials were investigated in connection with Cole and Zou's computer simulation of the hydrogen ground state in classical physics.
Abstract: Relativistic particles in the Kepler and Coulomb potentials may have trajectories that are qualitatively different from the trajectories found in nonrelativistic mechanics. Spiral scattering trajectories were pointed out by C. G. Darwin in 1913 in connection with the relativistic Rutherford scattering of classical charged particles. Relativistic trajectories are of current interest in connection with Cole and Zou’s computer simulation of the hydrogen ground state in classical physics.
TL;DR: In this article, it was shown that a detector undergoing uniform acceleration in a vacuum field responds as though it were immersed in thermal radiation of temperature T =ℏa/2πkc.
Abstract: A detector undergoing uniform acceleration a in a vacuum field responds as though it were immersed in thermal radiation of temperature T=ℏa/2πkc. An intuitive derivation of this result is given for a scalar field in one spatial dimension. The approach is extended to the case where the field detected by the accelerated observer is a spin 1/2 Dirac field.
TL;DR: The authors compared students' responses on four multiple-choice force concept inventory (FCI) questions with similar responses to equivalent open-ended questions and found that distracters on the FCI do not adversely affect performance as measured by the number of correct answers.
Abstract: We have compared students’ responses on four multiple-choice force concept inventory (FCI) questions with similar responses to equivalent open-ended questions. Our results indicate a good agreement between the percentages of correct responses in each of the two formats, indicating that distracters on the FCI do not adversely affect performance as measured by the number of correct answers. However, a significant percentage of the open-ended responses fall into categories that are not included in the FCI multiple choices. When these alternative categories were presented to the students as distracters in a revised multiple-choice format, a significant percentage of the students chose these alternative responses.
TL;DR: This paper found that after traditional instruction in mechanics many students lack the ability to reason about vectors that represent forces and kinematic quantities and showed that modifications to instruction can significantly improve student performance on questions about vector addition and subtraction and increase the likelihood that students employ vectors in their attempt to solve mechanics problems.
Abstract: Most students’ initial exposure to physics is in the context of kinematics and dynamics. An understanding of how these topics relate to each other requires the ability to reason about vectors that represent forces and kinematic quantities. We present data that suggest that after traditional instruction in mechanics many students lack this ability. Modifications to instruction can significantly improve student performance on questions about vector addition and subtraction and increase the likelihood that students employ vectors in their attempt to solve mechanics problems. However, an increased emphasis on these topics has so far been only moderately successful in promoting the level of proficiency required to understand the connection between force and acceleration as vector quantities. We describe some of the procedural and reasoning difficulties we have observed in students’ use of vectors.