In this paper, chaotic dynamics of a mixed Rayleigh–Liénard oscillator driven by parametric periodic damping and external excitations is investigated analytically and numerically. The equilibrium points and their stability evolutions are analytically analyzed, and the transitions of dynamical behaviors are explored in detail. Furthermore, from the Melnikov method, the analytical criterion for the appearance of the homoclinic chaos is derived. Analytical prediction is tested against numerical simulations based on the basin of attraction of initial conditions. As a result, it (...) is found that for ω = ν, the chaotic region decreases and disappears when the amplitude of the parametric periodic damping excitation increases. Moreover, increasing of F 1 and F 0 provokes an erosion of the basin of attraction and a modification of the geometrical shape of the chaotic attractors. For ω ≠ ν and η = 0.8, the fractality of the basin of attraction increases as the amplitude of the external periodic excitation and constant term increase. Bifurcation structures of our system are performed through the fourth-order Runge–Kutta ode 45 algorithm. It is found that the system displays a remarkable route to chaos. It is also found that the system exhibits monostable and bistable oscillations as well as the phenomenon of coexistence of attractors. (shrink)

Summary The resonator and the tuning fork were major instruments in acoustics in the latter half of the nineteenth-century. In particular, the third Baron Rayleigh made extensive use of these instruments throughout his long career as an experimentalist. These instruments underwent a number of alterations during their use as central experimental tools in acoustics. Functional and structural alterations were introduced in the adaptation of these instruments to several major acousticians’ experimental settings. Rayleigh not only adopted the two instruments (...) as objects of mathematical and experimental investigation but also employed them ingeniously for various purposes. His continuing creation of a variety of uses and forms of these instruments contributed to focusing acoustics on pure tones and musical sounds until the early twentieth century. (shrink)

The role of the novel longitudinal vacuum fieldB (3)is discussed in relation to fundamental radiation laws: the Rayleigh-Jeans law, the Planck law, and the Einstein coefficients. The circular index (3) ofB (3)causes electromagnetic energy density to be redistributed from the other indices (1) and (2) of the circular basis, but the presence ofB (3)in the vacuum does not change the value of the Planck constant h. TheB (3)field does not affect, furthermore, the understanding of quantized radiation absorption first proposed (...) by Einstein. Therefore, the experimental observableB (3) does not imply modification of these fundamental, radiation laws, and experimental isolation ofB (3) must take place through its characteristic square root power density dependence when used to magnetize an électron plasma. (shrink)

It is suggested that an understanding of blackbody radiation within classical physics requires the presence of classical electromagnetic zero-point radiation, the restriction to relativistic (Coulomb) scattering systems, and the use of discrete charge. The contrasting scaling properties of nonrelativistic classical mechanics and classical electrodynamics are noted, and it is emphasized that the solutions of classical electrodynamics found in nature involve constants which connect together the scales of length, time, and energy. Indeed, there are analogies between the electrostatic forces for groups (...) of particles of discrete charge and the van der Waals forces in equilibrium thermal radiation. The differing Lorentz- or Galilean-transformation properties of the zero-point radiation spectrum and the Rayleigh-Jeans spectrum are noted in connection with their scaling properties. Also, the thermal effects of acceleration within classical electromagnetism are related to the existence of thermal equilibrium within a gravitational field. The unique scaling and phase-space properties of a discrete charge in the Coulomb potential suggest the possibility of an equilibrium between the zero-point radiation spectrum and matter which is universal (independent of the particle mass), and an equilibrium between a universal thermal radiation spectrum and matter where the matter phase space depends only upon the ratio mc 2/k B T. The observations and qualitative suggestions made here run counter to the ideas of currently accepted quantum physics. (shrink)

Rayleigh and Ramsay discovered the inert gas argon in the atmospheric air in 1895 using a carefully designed sequence of experiments guided by an informal statistical analysis of the resulting data. The primary objective of this article is to revisit this remarkable historical episode in order to make a case that the error‐statistical perspective can be used to bring out and systematize (not to reconstruct) these scientists' resourceful ways and strategies for detecting and eliminating error, as well as dealing (...) with Duhemian ambiguities and underdetermination problems as they arose in the context of their local research settings. *Received December 2009; revised January 2010. †To contact the author, please write to: Department of Economics, 3016 Pamplin Hall, Virginia Tech, Blacksburg, VA 24061; e‐mail: [email protected]. (shrink)

According to the Rayleigh criterion of classical optics, the finite resolving power of a microscope is due to the width of the central peak of the Fraunhofer diffraction pattern produced by the microscope's finite lens aperture. During the last few decades, theories and techniques for superresolution beyond the Rayleigh criterion have been developed in classical optics. Thus, Heisenberg's microscope could also in principle be made to give superresolution and thereby appear to violate the uncertainty relation. We believe that (...) this paradox is due to the inappropriate use of a definition, based purely on experimental convenience, to support a quantum mechanical theorem. (shrink)

I criticize the widely-defended view that the quantum measurement problem is an example of underdetermination of theory by evidence: more specifically, the view that the unmodified, unitary quantum formalism (interpreted following Everett) is empirically indistinguishable from Bohmian Mechanics and from dynamical-collapse theories like the GRW or CSL theories. I argue that there as yet no empirically successful generalization of either theory to interacting quantum field theory and so the apparent underdetermination is broken by a very large class of quantum experiments (...) that require field theory somewhere in their description. The class of quantum experiments reproducible by either is much smaller than is commonly recognized and excludes many of the most iconic successes of quantum mechanics, including the quantitative account of Rayleigh scattering that explains the color of the sky. I respond to various arguments to the contrary in the recent literature. (shrink)

The exploration of chemical periodicity over the past 250 years led to the development of the Periodic System of Elements and demonstrates the value of vague ideas that ignored early scientific anomalies and instead allowed for extended periods of normal science where new methodologies and concepts are developed. The basic chemical element provides this exploration with direction and explanation and has shown to be a central and historically adaptable concept for a theory of matter far from the reductionist frontier. This (...) is explored in the histories of Prout’s hypothesis, Döbereiner Triads, element inversions necessary when ordering chemical elements by atomic weights, and van den Broeck’s ad-hoc proposal to switch to nuclear charges instead. The development of more accurate methods to determine atomic weights, Rayleigh and Ramsey’s gas separation and analytical techniques, Moseley’s X-ray spectroscopy to identify chemical elements, and more recent accelerator-based cold fusion methods to create new elements at the end of the Periodic Table point to the importance of methodological development complementing conceptual advances. I propose to frame the crossover from physics to chemistry not as a loss of accuracy and precision but as an increased application of vague concepts such as similarity which permit classification. This approach provides epistemic flexibility to adapt to scientific anomalies and the continued growth of chemical compound space and rejects the Procrustean philosophy of reductionist physics. Furthermore, it establishes chemistry with its explanatory and operational autonomy epitomized by the periodic system of elements as a gateway to other experimental sciences. (shrink)

Why do aircraft fly? How do their wings support them? In the early years of aviation, there was an intense dispute between British and German experts over the question of why and how an aircraft wing provides lift. The British, under the leadership of the great Cambridge mathematical physicist Lord Rayleigh, produced highly elaborate investigations of the nature of discontinuous flow, while the Germans, following Ludwig Prandtl in Göttingen, relied on the tradition called “technical mechanics” to explain the flow (...) of air around a wing. Much of the basis of modern aerodynamics emerged from this remarkable episode, yet it has never been subject to a detailed historical and sociological analysis. In The Enigma of the Aerofoil, David Bloor probes a neglected aspect of this important period in the history of aviation. Bloor draws upon papers by the participants—their restricted technical reports, meeting minutes, and personal correspondence, much of which has never before been published—and reveals the impact that the divergent mathematical traditions of Cambridge and Göttingen had on this great debate. Bloor also addresses why the British, even after discovering the failings of their own theory, remained resistant to the German circulation theory for more than a decade. The result is essential reading for anyone studying the history, philosophy, or sociology of science or technology—and for all those intrigued by flight. (shrink)

Recent developments in nonlinear dynamics have found wide application in many areas of science from physics to neuroscience. Nonlinear phenomena such as feedback loops, inter-level relations, wholes constraining and modifying the behavior of their parts, and memory effects are interesting candidates for emergence and downward causation. Rayleigh–Bénard convection is an example of a nonlinear system that, I suggest, yields important insights for metaphysics and philosophy of science. In this paper I propose convection as a model for downward causation in (...) classical mechanics, far more robust and less speculative than the examples typically provided in the philosophy of mind literature. Although the physics of Rayleigh–Bénard convection is quite complicated, this model provides a much more realistic and concrete example for examining various assumptions and arguments found in emergence and philosophy of mind debates. After reviewing some key concepts of nonlinear dynamics, complex systems and the basic physics of Rayleigh–Bénard convection, I begin that examination here by (1) assessing a recently proposed definition for emergence and downward causation, (2) discussing some typical objections to downward causation and (3) comparing this model with Sperry’s examples. (shrink)

Complexity–nonlinear dynamics for my purposes in this essay–is rich with metaphysical and epistemological implications but is only recently receiving sustained philosophical analysis. I will explore some of the subtleties of causation and constraint in Rayleigh-Bénard convection as an example of a complex phenomenon, and extract some lessons for further philosophical reflection on top-down constraint and causation particularly with respect to causal foundationalism.

Summary Between the 1860s and the 1910s, British acoustics was transformed from an area of empirical research into a mathematically organized field. Musical motives—improving musical scales and temperaments, making better musical instruments, and understanding the nature of musical tones—were among the major driving forces of acoustical researchers in nineteenth-century Britain. The German acoustician, Helmholtz, had a major impact on British acousticians who also had extensive interactions with American and French acousticians. Rayleigh's acoustics, reflecting all these features, bore remarkable fruit (...) in his treatise The Theory of Sound, which successfully subjected empirical acoustics to analytical mathematics. His accomplishments made British acoustics a subfield of physics, thus distinguishing it from the ‘new acoustics’ in early twentieth-century America. (shrink)

Quantum phenomena are notoriously difficult to grasp. The present paper first reviews the most important quantum concepts in a non-technical manner: superposition, uncertainty, collapse of the wave function, entanglement and non-locality. It then tries to clarify these concepts by examining their analogues in complex, self-organizing systems. These include bifurcations, attractors, emergent constraints, order parameters and non-local correlations. They are illustrated with concrete examples that include Rayleigh–Bénard convection, social self-organization and Gestalt perception of ambiguous figures. In both cases, quantum and (...) self-organizing, the core process appears to be a symmetry breaking that irreversibly and unpredictably “collapses” an ambiguous state into one of a number of initially equivalent “eigenstates” or “attractors”. Some speculations are proposed about the non-linear amplification of quantum fluctuations of the vacuum being ultimately responsible for such symmetry breaking. (shrink)

Summary The concept of unified theory is defined in logical and abstract semantic terms, and employed in the analysis of relations between empirical scientific theories. The conceptual framework of the approach applies to binary relations such as the reduction or replacement of one theory by another, and to multiple intertheory relations. Historically, unified theories tend to arise within the contexts of scientific conflicts which they may show susceptible of solution even in the most controversial cases of the logical incompatibility or (...) conceptual incommensurability of competing theories. These conclusions are exemplified by the Planck-Einstein quantum theory of thermal radiation. The analysis shows in which sense it can, and in which it cannot, be said that this theory unifies Wien's law and the Rayleigh-Jeans law of black-body radiation. (shrink)

A companion paper provides a proposal for cosmic singularity resolution based upon general features of a bouncing unitary cosmological model in the mini-superspace approximation. This paper analyses novel phenomenology that can be identified within particular solutions of that model. First, we justify our choice of particular solutions based upon a clearly articulated and observationally-motivated principle. Second, we demonstrate that the chosen solutions follow a classical mini-superspace cosmology before smoothly bouncing off the classically singular region. Third, and most significantly, we identify (...) a 'Rayleigh-scattering' limit for physically reasonable choices of parameters within which the solutions display effective behaviour that is insensitive to the details of rapidly oscillating Planck-scale physics. This effective physics is found to be compatible with an effective period of cosmic inflation well below the Planck scale. The detailed effective physics of this Rayleigh-scattering limit is provided via: i) an exact analytical treatment of the model in the de Sitter limit; and ii) numerical solutions of the full model. (shrink)

Analytical models describing the motion of colloidal particles in given force fields are presented. In addition to local approaches, leading to well known master equations such as the Langevin and the Fokker–Planck equations, a global description based on path integration is reviewed. A new result is presented, showing that under very broad conditions, during its evolution a dissipative system tends to minimize its energy dissipation in such a way to keep constant the Hamiltonian time rate, equal to the difference between (...) the flux-based and the force-based Rayleigh dissipation functions. In fact, the Fokker–Planck equation can be interpreted as the Hamilton–Jacobi equation resulting from such minumum principle. At steady state, the Hamiltonian time rate is maximized, leading to a minimum resistance principle. In the unsteady case, we consider the relaxation to equilibrium of harmonic oscillators and the motion of a Brownian particle in shear flow, obtaining results that coincide with the solution of the Fokker–Planck and the Langevin equations. (shrink)

Mandelstam’s criticism of the Rayleigh theory of the blue color of the sky (1907) and his polemic with M. Planck (1907–1908) did not become notable events in the history of physics. However, the method of their coverage in the Soviet and in the post-Soviet physics literature is remarkable. Most of Soviet physicists and historians of physics supported Mandelstam's point of view in his criticism of both Raleigh and Planck. The situation changed only at the beginning of the 21st century: (...) in the Russian literature the publications appeared emphasizing that in the Raleigh–Mandelstam and Planck–Mandelstam controversies Mandelstam was not right, Raleigh and Planck were closer to the truth. Which presumptions of this trend can be noted? This was patriotism of the scientific school peculiar to Mandelstam’s graduate students and the former graduate students, the patriotism connected with solidarity which helped Mandelstam’s community to survive in the Soviet totalitarian regime and in the totalitarian organization of science. This was also progressionism which was popular among academics and among men in the street. The phenomenon of common knowledge, mutual knowledge among the members of a scientific community should be taken under consideration. Common knowledge is connected with the non-thematized anonymous inclusion of the ideological terminology into scientific discourse. (shrink)

At present classical physics contains two contradictory groups of derivations of the equilibrium spectrum of random classical electromagnetic radiation. One group of derivations finds Planck's spectrum based upon the use of classical electromagnetic zero-point radiation and fundamental ideas of thermodynamics. The other group of derivations finds the Rayleigh-Jeans spectrum from scattering equilibrium for non-linear mechanical systems in the limit of small charge coupling to radiation. Here we examine the scaling symmetries of classical thermal radiation. We find that, in general, (...) classical mechanical systems do not share the scaling symmetries of thermal radiation. In particular, this is true for the mechanical scattering systems used in the derivations of the Rayleigh-Jeans law. Indeed, relativistic hydrogenlike systems with Coulomb potentials of fixed charge are the only mechanical potential systems which do share the scaling symmetries of thermal radiation. We propose that only these last mechanical systems are allowed in a classical electromagnetic description of nature. (shrink)

Anomaloscope An instrument used for detecting anomalies of color vision. The test subject adjusts the ratio of two monochromatic lights to form a match with a third monochromatic light. The most common form of this procedure involves a Rayleigh match: a match between a mixture of monochromatic green and red lights, and a monochromatic yellow light. Normal subjects will choose a matching ratio of red to green light that falls within a fairly narrow range of values. Subjects with anomalous (...) color vision will choose a ratio of red to green that falls outside this range, and red-green dichromats will accept any ratio of red to green as forming a match. (shrink)

It is pointed out that relativistic classical electron theory with classical electromagnetic zero-point radiation has a scaling symmetry which is suitable for understanding the equilibrium behavior of classical thermal radiation at a spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical electron theory, the masses of the particles are the only scale-giving parameters associated with mechanics while the action-angle variables are scale invariant. The theory thus separates the interaction of the action variables of matter and radiation from the scale-giving (...) parameters. Due to this separation, classical zero-point radiation is invariant under scattering by the charged particles of relativistic classical electron theory. The basic ideas of the matter-radiation interaction are illustrated in a simple relativistic classical electromagnetic example. (shrink)

Kirchhoff’s 1882 theory of optical diffraction forms the centerpiece in the long-term development of wave optics, one that commenced in the 1820s when Fresnel produced an empirically successful theory based on a reinterpretation of Huygens’ principle, but without working from a wave equation. Then, in 1856, Stokes demonstrated that the principle was derivable from such an equation albeit without consideration of boundary conditions. Kirchhoff’s work a quarter century later marked a crucial, and widely influential, point for he produced Fresnel’s results (...) by means of Green’s theorem and function under specific boundary conditions. In the late 1880s, Poincaré uncovered an inconsistency between Kirchhoff’s conditions and his solution, one that seemed to imply that waves should not exist at all. Researchers nevertheless continued to use Kirchhoff’s theory—even though Rayleigh, and much later Sommerfeld, developed a different and mathematically consistent formulation that, however, did not match experimental data better than Kirchhoff’s theory. After all, Kirchhoff’s formula worked quite well in a specific approximation regime. Finally, in 1964, Marchand and Wolf employed the transformation of Kirchhoff’s surface integral that had been developed by Maggi and Rubinowicz for other purposes. The result yielded a consistent boundary condition that, while introducing a species of discontinuity, nevertheless rescued the essential structure of Kirchhoff’s original formulation from Poincaré’s paradox. (shrink)

At some distance from a high-rate source in an elastic half-space, the dominant wave motion at the free surface is a Rayleigh surface wave. The calculation of surface waves generated by a concentrated force in a half-space is a basic problem in elastodynamics. By straightforward manipulations, the result can be used to obtain surface waves for other kinds of wave-generating body-force arrangements. For example, appropriate combinations of double-forces (or dipoles) can be used to represent the surface loading due to (...) laser irradiation, or due to acoustic emission from the opening of a sub-surface crack or from sliding over a fault surface. The surface wave motion is usually obtained by the application of integral transform techniques and the subsequent extraction of the surface waves as the contributions from poles in the integral for the inverse transform. In this paper, we use a much simpler approach based on the elastodynamic reciprocity theorem. We consider a transversely isotropic solid whose axis of symmetry is normal to the surface of the half-space. Surface wave pulses generated by a single force, by irradiation from a laser source, and by opening of a crack, have been determined. (shrink)

SummaryDiffraction gratings have contributed enormously to modern science. Although some historians have written about them, there is much more to be brought to light. This paper discusses their development and use in the period up to about 1880 before Rowland began to produce them. Rittenhouse described the action of a diffraction grating in 1786, but no explanation was possible until the wave theory of light was developed. Fraunhofer discovered the dark lines in the solar spectrum in 1814, and then investigated (...) diffraction, producing the first ruled gratings, making detailed measurements and calculating the wavelengths of prominent spectral lines. After Bunsen and Kirchhoff showed the association between spectral lines and chemical elements there was an upsurge of interest in measuring wavelengths. The gratings used in this work almost all came from one source, a relatively unknown instrument maker called Nobert, who made them by an extremely laborious process using a machine he had built himself. The most significant wavelength measurements were made by Ångström, but Mascart, Van der Willigen, Stefan, Ditscheiner and Cornu also did important work. Nobert gratings were investigated by Quincke, copied photographically by Rayleigh, and were known and discussed in the USA. Nobert's work helped to advance spectroscopy much more than has been acknowledged. (shrink)

Arithmetic optimization algorithm (AOA) is one of the recently proposed population-based metaheuristic algorithms. The algorithmic design concept of the AOA is based on the distributive behavior of arithmetic operators, namely, multiplication (M), division (D), subtraction (S), and addition (A). Being a new metaheuristic algorithm, the need for a performance evaluation of AOA is significant to the global optimization research community and specifically to nature-inspired metaheuristic enthusiasts. This article aims to evaluate the influence of the algorithm control parameters, namely, population size (...) and the number of iterations, on the performance of the newly proposed AOA. In addition, we also investigated and validated the influence of different initialization schemes available in the literature on the performance of the AOA. Experiments were conducted using different initialization scenarios and the first is where the population size is large and the number of iterations is low. The second scenario is when the number of iterations is high, and the population size is small. Finally, when the population size and the number of iterations are similar. The numerical results from the conducted experiments showed that AOA is sensitive to the population size and requires a large population size for optimal performance. Afterward, we initialized AOA with six initialization schemes, and their performances were tested on the classical functions and the functions defined in the CEC 2020 suite. The results were presented, and their implications were discussed. Our results showed that the performance of AOA could be influenced when the solution is initialized with schemes other than default random numbers. The Beta distribution outperformed the random number distribution in all cases for both the classical and CEC 2020 functions. The performance of uniform distribution, Rayleigh distribution, Latin hypercube sampling, and Sobol low discrepancy sequence are relatively competitive with the Random number. On the basis of our experiments’ results, we recommend that a solution size of 6,000, the number of iterations of 100, and initializing the solutions with Beta distribution will lead to AOA performing optimally for scenarios considered in our experiments. (shrink)