Crystallographic, optical and magnetic properties of Eu2SiO4

The crystallographic properties of Eu2SiO4 are studied in terms of its isomorph Ca2SiO4. The recently discovered monoclinic room-temperature phase is ferroelastic and simultaneously ferromagnetic at low temperatures (T e=5.40°K). The optical absorption and the dispersion properties have been measured in spectral intervals ranging from 0.5 to 3.6 eV and partly for temperatures between 300 and 500°K. This temperature range includes the ferroelastic-paraelastic phase-transition temperature (T e=438°K). An anomaly of the dielectric constant atT e suggests the presence of an unstable phase which would be ferroelectric. The Faraday rotation has been measured on either side of the absorption edge at 300 and 77°K. The recent results on crystal structure allow an explanation of the magnetic behaviour of the two ferromagnetic phases known up to now. Nous présentons une étude des propriétés cristallographiques de Eu2SiO4 en regard de son isomorphe Ca2SiO4. La phase monoclinique découverte récemment comme étant stable à la température ambiante est ferro-élastique et de plus ferromagnétique aux basses températures (T e=5,40°K). Nous avons mesuré l'absorption optique et les propriétés de dispersion dans des intervalles spectraux s'étendant de 0,5 à 3,6 eV et en partie à des températures s'échelonnant entre 300 et 500°K. Ce domaine thermique comprend la température de transition entre les phases ferro-élastique et para-élastique (T e=438°K). Une anomalie de la constante diélectrique àT e suggère la présence d'une phase instable ferro-électrique. Nous avons mesuré la rotation de Faraday de part et d'autre de l'arête d'absorption à 300 et 77°K. Les résultats obtenus récemment sur la structure cristalline fournissent une explication du comportement magnétique des deux phases ferromagnétiques présentement connues

Hadronic mechanics aspects of irreversible physical pendula

All macroscopic physical pendula undergo various types of damping processes which make them irreversible devices. Their repeated use for detecting cosmological micro-anomalies requires the determination of certain observables with very high precision despite an increased variance due to the strictly nonperiodical pendulum behaviour. Using genofields from Hadronic Mechanics, data processing algorithms involving backward and forward convolutions have been developed. They greatly improve precision in the determination of swinging azimuth, swinging amplitude, swinging period and precession period. To the author’s knowledge, the very weak anisotropy of a long Foucault pendulum has been characterized for the first time experimentally in terms of zero-amplitude swinging period and conservative (Hamiltonian) amplitude oscillations

The anisosphere as a new tool for interpreting Foucault pendulum experiments. Part I : harmonic oscillators

In an attempt to explain the tendency of Foucault pendula to develop elliptical orbits, Kamerlingh Onnes derived equations of motion that suggest the use of great circles on a spherical surface as a graphical illustration for an anisotropic bi-dimensional harmonic oscillator, although he did not himself exploit the idea any further. The concept of anisosphere is introduced in this work as a new means of interpreting pendulum motion. It can be generalized to the case of any two-dimensional (2-D) oscillating system, linear or nonlinear, including the case where coupling between the 2 degrees of freedom is present. Earlier pendulum experiments in the literature are revisited and reanalyzed as a test for the anisosphere approach. While that graphical method can be applied to strongly nonlinear cases with great simplicity, this part I is illustrated through a revisit of Kamerlingh Onnes’ dissertation, where a high performance pendulum skillfully emulates a 2-D harmonic oscillator. Anisotropy due to damping is also described. A novel experiment strategy based on the anisosphere approach is proposed. Finally, recent original results with a long pendulum using an electronic recording alidade are presented. A gain in precision over traditional methods by 2–3 orders of magnitude is achieved

The anisosphere model : a novel differential phase space representation for Foucault pendulums and 2D oscillators

: It is customary to describe the behaviour and stability of oscillators with the help of phase space representation. However, two-dimensional (2D) oscillators like the Foucault pendulum call for a 4D phase space that is not simple to visualize. Applying celestial body perturbation theory to the Foucault pendulum in his doctor dissertation, Nobel laureate Kamerlingh Onnes showed that the essential features of a Foucault pendulum are its inherent circular and linear anisotropies. A spherical differential 2D sub-space can be defined, where the group of the points of a spherical surface with respect to the operation rotation about a diametral axis is isomorphic with the group of sequential states of oscillation of a 2D pendulum with respect to the operation translation in time . Any Foucault pendulum is then characterized by two elliptical eigenstates which are represented by the poles of that rotation axis on the so-called anisosphere. Such poles play the role of attractor/repellor when “dichroic” damping is present. Moreover, they move drastically within a meridian plane when nonlinear restoring torque giving rise to Airy precession occurs. The concept of anisosphere constitutes a very powerful tool for analysing and optimizing actual Foucault pendulum implementations. That feature is illustrated by a numerical model

Can gravitation anisotropy be detected by pendulum experiments?

After some 170 years of Foucault pendulum experiments, the linear theory fails to quantitatively explain the results of any honest meticulous experiment. The pendulum motion usually degenerates into elliptical orbits after a few minutes. Moreover, unexplained discrepancies up to ± 20% in precession velocity are not uncommon. They are mostly regarded as a consequence of the elliptic motion of the bob associated with suspension anisotropy or as a lack of care in starting the pendulum motion. Over some 130 years, an impressive amount of talented physicists, engineers and mathematicians have contributed to a better partial understanding of the pendulum behaviour. In this work, the concept of biresonance is introduced to represent the motion of the spherical pendulum. It is shown that biresonance can be represented graphically by the isomorphism of the Poincaré sphere. This new representation of the pendulum motion greatly clarifies its natural response to various anisotropic situations, including Airy precession. Anomalous observations in pendulum experiments by Allais are analyzed. These findings suggest that a pendulum placed within a mass distribution such as the earth, the moon and the sun should be treated as an interior problem, which can better be addressed by Santilli's new theory of gravitation than by those of Newton and Einstein

Anisosphere analysis of the equivalence between a precessing Foucault pendulum and a torsional balance

The residual anisotropy of a real Foucault pendulum is responsible for an oscillatory behaviour of the precession angle according to the original description given by Kamerlingh Onnes in his dissertation. A simulation of the experimental procedure of enchained runs, consisting of starting a short experiment at the azimuth at which a precedent similar experiment has been stopped, has been performed using the anisosphere model. It leads to the conclusion that the precessing pendulum undergoes oscillations in precession associated with an extremely shallow potential well analogous to the potential well of a very slow torsional balance. Such systems are therefore rendered sensitive to extremely-low-energy perturbations. To the author’s knowledge, the hypersensitivity of the oscillatory precession of the anisotropic Foucault pendulum has been unravelled for the first time thanks to the analysis and visualization power of the anisosphere model. In particular, the periodic apparent motion of celestial bodies appears to modify the anisotropy characteristic of the precession potential well. This may provide likelihood for the similar responses of the paraconical pendulum of Allais during the 1950’s and of the torsion pendulum of Saxl and Allen in 1970 to certain Sun-Moon-Earth syzygies

A new method to measure general birefringence in crystals

The scattering properties of an anisotropic solid for polarized light allow the observation and the measurement of linear, circular and elliptic birefringence. A general analysis of the phenomenon for any kind of birefringence and any state of polarization of the incident light vibration is given. Scattering by particles with size a [formula omitted] λ (Rayleigh limit) or a ≈ λ is considered. It follows from the theory that the scattering-center distribution is equivalent to a quasi-continuous array of analyzers providing a simultaneous analyzation of the transmitted beam along its whole path in the (in general elliptically) biréfringent medium. A new technique based on surface scattering is described. It allows visual observations to be made on very perfect (hence weakly scattering) crystals with low-power light sources and without being forced to achieve complete darkness in the surroundings of the sample. The method of surface scattering is especially adequate for precision measurements; it is thoroughly tested with the elliptic birefringence of quartz. Both methods of surface and bulk scattering are applied to various kinds of birefringence in single crystals of Eu2SiO4 and EuTe

Tidal accelerations and dynamical properties of three degrees-of-freedom pendula

Maurice Allais was one of the most original of France's scientific thinkers of the 20th century. In the early 1950’s he was the author of Allais paradox in decision making under uncertainty, and in 1988 he became the only French citizen to receive the Nobel Prize in Economics for his contributions to the theory of non-equilibrium markets. Allais’s research in physics was also important, but very little known. In the mid 1950’s Allais designed and built a highly sensitive ball-borne pendulum – which he named paraconical pendulum. This apparatus reacts to the gravitational force of the Sun and the Moon, and exhibited unexpected behaviour during the solar eclipse of 30 June 1954, which was partial in Paris. This local gravity anomaly is now called the Allais eclipse effect. As a tribute to Allais on the 100th anniversary of his birth, this book concentrates on his contributions to physics, in particular to the exciting and controversial field of gravity anomalies, which may open unexpected and completely new avenues in gravity theory. In addition to a short sampling of Allais papers, the book describes experimental efforts to reproduce the Allais eclipse effect, an endeavour that has turned out to be harder than expected because all eclipses are different. Several papers describe optical and geological anomalies that also interested Allais. A final section contains theoretical essays sketching novel gravity models. The book will be of interest not only to students and practitioners of physics, but also to the informed lay public, and even to philosophers of science, and researchers studying the epistemology and politics behind scientific investigation

Characterizing the suspension anisotropy of a computerized Foucault pendulum

All unsustained physical pendula undergo various types of damping processes which make them irreversible quasi-periodical devices. Their recent use as instruments for detecting cosmological micro-anomalies requires the determination of system anisotropy with the utmost precision, notwithstanding an inherent variance due to the strictly aperiodical behavior. An image processing algorithm has been developed for analyzing a camera monitored Foucault pendulum. This greatly improves precision in the determination of swinging azimuth, precession angle, swinging amplitude and swinging period. To the authors’ knowledge, the very weak anisotropy of a long Foucault pendulum has been, for the first time, experimentally characterized in terms of the zero-amplitude swinging period plus a conservative wave in period and amplitude

A new method to demonstrate and measure birefringence

The polarization properties of the light scattered in the bulk of an anisotropic solid are used to measure circular and linear birefringence. Recently, the extension of the method to scattering at an air-solid interface has increased the precision significantly and the range of measurement by three orders of magnitude. Moreover, the brightness handicap of Rayleigh scattering is surmounted by designing the roughness of the scattering surface adequately and by using an analyser in the scattered beam