Flows of a rarefied gas between coaxial circular cylinders with nonuniform surface properties are studied on the basis of kinetic theory. It is assumed that the outer cylinder is a diffuse reflection boundary and the ...Flows of a rarefied gas between coaxial circular cylinders with nonuniform surface properties are studied on the basis of kinetic theory. It is assumed that the outer cylinder is a diffuse reflection boundary and the inner cylinder is a Maxwell-type boundary whose accommodation coefficient varies in the circumferential direction. Three fundamental flows are studied: 1) a flow caused by the rotation of the outer cylinder (Couette flow), 2) a flow induced between the cylinders at rest kept at different temperatures (heat transfer problem), and 3) a flow induced by the circumferential temperature distribution along the cylindrical surfaces (thermal creep flow). The linearized ES-BGK model of the Boltzmann equation is numerically analyzed using a finite difference method. The time-independent behavior of the gas is studied over a wide range of the gas rarefaction degree, the radii ratio, and a parameter characterizing the distribution of the accommodation coefficient. Due to an effect of nonuniform surface properties, a local heat transfer occurs between the gas and the cylindrical surfaces in Couette flow;a local tangential stress arises in the heat transfer problem. However, the total heat transfer between the two cylinders in Couette flow and the total torque acting on the inner cylinder in the heat transfer problem vanish irrespective of the flow parameters. Two nondegenerate reciprocity relations arise due to the effect of nonuniform surface properties. The reciprocity relations among the above-mentioned three flows are numerically confirmed over a wide range of the flow parameters. The force on the inner cylinder, which also arises due to the effect of nonuniform surface properties in Couette flow and the heat transfer problems, is studied.展开更多
Sommerfeld’s fundamental fine-structure constant α once more gives reason to be amazed. This comment is a Chapter of a publication in preparation dealing mainly with golden ratio signature behind Preston Guynn’s fa...Sommerfeld’s fundamental fine-structure constant α once more gives reason to be amazed. This comment is a Chapter of a publication in preparation dealing mainly with golden ratio signature behind Preston Guynn’s famous matter/space approach. As a result we present a relation of α to the galactic velocity , mediated by the circle constant π, which points to an omnipresent importance of this constant and its intrinsic reciprocity pecularity: α ≈ π<sup>2</sup>|β<sub>g</sub>| respectively . The designation fine-structure constant should be replaced simply by Sommerfeld’s constant. We present golden mean-based approximations for α as well as for electron’s charge and mass and connect the word average value of interaction coupling constant α<sub>s</sub>(m<sub>z</sub>) with |β<sub>g</sub>|.展开更多
In this short contribution, a reciprocity relation between mass constituents of the universe was explained governed by Hardy’s maximum entanglement probability of φ5 = 0.09017. While well explainable through a set-t...In this short contribution, a reciprocity relation between mass constituents of the universe was explained governed by Hardy’s maximum entanglement probability of φ5 = 0.09017. While well explainable through a set-theoretical argumentation, the relation may also be a consequence of a coupling factor attributed to the normed dimensions of the universe. Also, very simple expressions for the mass amounts were obtained, when replacing the Golden Mean φ by the Archimedes’ constant π. A brief statement was devoted to the similarity between the E-Infinity Theory of El Naschie and the Information Relativity Theory of Suleiman. In addition, superconductivity was also linked with Hardy’s entanglement probability.展开更多
Some fundamental physical quantities need an alternative description. We derive the word average value of interaction coupling constant α<sub>s</sub>(m<sub>z</sub>) from the observed maximum g...Some fundamental physical quantities need an alternative description. We derive the word average value of interaction coupling constant α<sub>s</sub>(m<sub>z</sub>) from the observed maximum galactic rotation velocity by the simple relation , where is the velocity, at which the difference between galactic rotation velocity and Thomas precession is equal, and α is Sommerfeld’s constant. The result is in excellent agreement with the value of α<sub>s</sub> = 0.1170 ± 0.0019, recently measured and verified via QCE analysis by CERN researchers. One can formulate a reciprocity relation, connecting α<sub>s</sub> with the circle constant: . It is the merit of Preston Guynn to derive the Milky Way maximum value of the galactic rotation velocity β<sub>g</sub>, pointing to its “extremely important role in all physics”. The mass (energy) constituents of the Universe follow a golden mean hierarchy and can simply be related to the maximum of Guynn’s difference velocity respectively to α<sub>s</sub>(m<sub>z</sub>), therewith excellently confirming Bouchet’s WMAP data analysis. We conclude once more that the golden mean concept is the leading one of nature.展开更多
We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting core inside a penetrable chiral body. We prove the well-posedness of the corresponding direct scattering pr...We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting core inside a penetrable chiral body. We prove the well-posedness of the corresponding direct scattering problem by the variational method. We focus on a uniqueness result for the inverse scattering problem that is under what conditions an obstacle can be identified by the knowledge of the electric far-field pattern corresponding to all time-harmonic incident planes waves with a fixed wave number. To this end, we establish a chiral mixed reciprocity relation that connects the electric far-field pattern of a spherical wave with the scattered field of a plane wave.展开更多
In this paper, we consider the numerical treatment of an inverse acoustic scattering problem that involves an impenetrable obstacle embedded in a layered medium. We begin by employing a modified version of the well kn...In this paper, we consider the numerical treatment of an inverse acoustic scattering problem that involves an impenetrable obstacle embedded in a layered medium. We begin by employing a modified version of the well known <em>factorization method</em>, in which a computationally effective numerical scheme for the reconstruction of the shape of the scatterer is presented. This is possible, due to a <em>mixed reciprocity principle</em>, which renders the computation of the Green function at the background medium unnecessary. Moreover, to further refine our inversion algorithm, an efficient Tikhonov parameter choice technique, called <em>Improved Maximum Product Criterion</em> (IMPC) is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no <em>a priori</em> knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples.展开更多
We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists betw...We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.展开更多
文摘Flows of a rarefied gas between coaxial circular cylinders with nonuniform surface properties are studied on the basis of kinetic theory. It is assumed that the outer cylinder is a diffuse reflection boundary and the inner cylinder is a Maxwell-type boundary whose accommodation coefficient varies in the circumferential direction. Three fundamental flows are studied: 1) a flow caused by the rotation of the outer cylinder (Couette flow), 2) a flow induced between the cylinders at rest kept at different temperatures (heat transfer problem), and 3) a flow induced by the circumferential temperature distribution along the cylindrical surfaces (thermal creep flow). The linearized ES-BGK model of the Boltzmann equation is numerically analyzed using a finite difference method. The time-independent behavior of the gas is studied over a wide range of the gas rarefaction degree, the radii ratio, and a parameter characterizing the distribution of the accommodation coefficient. Due to an effect of nonuniform surface properties, a local heat transfer occurs between the gas and the cylindrical surfaces in Couette flow;a local tangential stress arises in the heat transfer problem. However, the total heat transfer between the two cylinders in Couette flow and the total torque acting on the inner cylinder in the heat transfer problem vanish irrespective of the flow parameters. Two nondegenerate reciprocity relations arise due to the effect of nonuniform surface properties. The reciprocity relations among the above-mentioned three flows are numerically confirmed over a wide range of the flow parameters. The force on the inner cylinder, which also arises due to the effect of nonuniform surface properties in Couette flow and the heat transfer problems, is studied.
文摘Sommerfeld’s fundamental fine-structure constant α once more gives reason to be amazed. This comment is a Chapter of a publication in preparation dealing mainly with golden ratio signature behind Preston Guynn’s famous matter/space approach. As a result we present a relation of α to the galactic velocity , mediated by the circle constant π, which points to an omnipresent importance of this constant and its intrinsic reciprocity pecularity: α ≈ π<sup>2</sup>|β<sub>g</sub>| respectively . The designation fine-structure constant should be replaced simply by Sommerfeld’s constant. We present golden mean-based approximations for α as well as for electron’s charge and mass and connect the word average value of interaction coupling constant α<sub>s</sub>(m<sub>z</sub>) with |β<sub>g</sub>|.
文摘In this short contribution, a reciprocity relation between mass constituents of the universe was explained governed by Hardy’s maximum entanglement probability of φ5 = 0.09017. While well explainable through a set-theoretical argumentation, the relation may also be a consequence of a coupling factor attributed to the normed dimensions of the universe. Also, very simple expressions for the mass amounts were obtained, when replacing the Golden Mean φ by the Archimedes’ constant π. A brief statement was devoted to the similarity between the E-Infinity Theory of El Naschie and the Information Relativity Theory of Suleiman. In addition, superconductivity was also linked with Hardy’s entanglement probability.
文摘Some fundamental physical quantities need an alternative description. We derive the word average value of interaction coupling constant α<sub>s</sub>(m<sub>z</sub>) from the observed maximum galactic rotation velocity by the simple relation , where is the velocity, at which the difference between galactic rotation velocity and Thomas precession is equal, and α is Sommerfeld’s constant. The result is in excellent agreement with the value of α<sub>s</sub> = 0.1170 ± 0.0019, recently measured and verified via QCE analysis by CERN researchers. One can formulate a reciprocity relation, connecting α<sub>s</sub> with the circle constant: . It is the merit of Preston Guynn to derive the Milky Way maximum value of the galactic rotation velocity β<sub>g</sub>, pointing to its “extremely important role in all physics”. The mass (energy) constituents of the Universe follow a golden mean hierarchy and can simply be related to the maximum of Guynn’s difference velocity respectively to α<sub>s</sub>(m<sub>z</sub>), therewith excellently confirming Bouchet’s WMAP data analysis. We conclude once more that the golden mean concept is the leading one of nature.
文摘We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting core inside a penetrable chiral body. We prove the well-posedness of the corresponding direct scattering problem by the variational method. We focus on a uniqueness result for the inverse scattering problem that is under what conditions an obstacle can be identified by the knowledge of the electric far-field pattern corresponding to all time-harmonic incident planes waves with a fixed wave number. To this end, we establish a chiral mixed reciprocity relation that connects the electric far-field pattern of a spherical wave with the scattered field of a plane wave.
文摘In this paper, we consider the numerical treatment of an inverse acoustic scattering problem that involves an impenetrable obstacle embedded in a layered medium. We begin by employing a modified version of the well known <em>factorization method</em>, in which a computationally effective numerical scheme for the reconstruction of the shape of the scatterer is presented. This is possible, due to a <em>mixed reciprocity principle</em>, which renders the computation of the Green function at the background medium unnecessary. Moreover, to further refine our inversion algorithm, an efficient Tikhonov parameter choice technique, called <em>Improved Maximum Product Criterion</em> (IMPC) is exploited. Our regularization parameter is computed via a fast iterative algorithm which requires no <em>a priori</em> knowledge of the noise level in the far-field data. Finally, the effectiveness of IMPC is illustrated with various numerical examples.
文摘We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.
