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Content available remote Real time determination of the Poincare-Prey`s anomaly horizontal gradient
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The paper contains a report from studies concerning gravity and position data determination for reductions in the Earth`s gravity field of geodetic and astronomical observations using the horizontal gradient of Poincare-Prey`s anomalies directly in terrain in real time. The author`s indications for establishment of the algorithm of the program GRAWPREY for microcomputer Psion Organiser are given.
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The local gravity anomalies were calculated using two different radii. Obtained gravimetric image was correlated with borecores and results of resistivity and high resolution seismic data. Final conclusions inform on morphology of Quaternary bottom and tectonics of the Cainozoic basement.
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Currently two well established physical theories describe the fundamental interactions: quantum field theory - Standard Model and theory of gravity - General Theory of Relativity. Many theoretical works are conducted to combine these two theories to one "Theory of Everything". Concerning the gravity, experimental data are in agreement with Einstein theory of gravity, from the Mercury perturbation motion to time corrections of GPS satellites clocks. However, a number of questions still remains open. Gravity waves and gravitons are, till now, not observed. Another question is how fast the curvature of spacetime can change. Our proposal of the experiment can contribute to the discussion of these problems.
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Gravimeter with two-dimensional digital data processing about acceleration of gravity is considered in a paper. The result of measurements in gyroscopic gravimeter contains errors. An influence on gravimeter inertial absolute acceleration and other disturbing influences cause the errors of measurements. These of acceleration arise by work gravimeter onboard the plane in structure of air gravimetric system. The structural scheme of gyroscopic gravimeter is proposed in a paper for multiple precision. This construction is providing immediate measurements of acceleration of gravity. The possibility of digital data processing is considered in view of a two-dimensional character of an array of measuring information.
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The purpose of the present article is the study of the effect of the gravity field on an initially stressed micropolar thermoelastic medium with microtemperatures. The analytical method used to obtain the formula of the physical quantities is the normal mode analysis. The comparisons are established graphically in the presence and the absence of gravity, initial stress and micropolar thermoelasticity. The main conclusions state that the gravity, initial stress and the micropolar thermoelasticity are effective physical operators on the variation of the physical quantities. The microtemperatures are very useful theory in the field of geophysics and earthquake engineering.
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Content available remote The Hamiltonian formulation of general relativity: myths and reality
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A conventional wisdom often perpetuated in the literature states that: (i) a 3 + 1 decomposition of spacetime into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation of General Relativity (GR); (ii) the canonical treatment unavoidably breaks the symmetry between space and time in GR and the resulting algebra of constraints is not the algebra of four-dimensional diffeomorphism; (iii) according to some authors this algebra allows one to derive only spatial diffeomorphism or, according to others, a specific field-dependent and non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac [21] and of ADM [22] of the canonical structure of GR are equivalent. We provide some general reasons why these statements should be questioned. Points (i–iii) have been shown to be incorrect in [45] and now we thoroughly re-examine all steps of the Dirac Hamiltonian formulation of GR. By direct calculation we show that Dirac’s references to space-like surfaces are inessential and that such surfaces do not enter his calculations. In addition, we show that his assumption g 0k = 0, used to simplify his calculation of different contributions to the secondary constraints, is unwarranted; yet, remarkably his total Hamiltonian is equivalent to the one computed without the assumption g 0k = 0. The secondary constraints resulting from the conservation of the primary constraints of Dirac are in fact different from the original constraints that Dirac called secondary (also known as the “Hamiltonian” and “diffeomorphism” constraints). The Dirac constraints are instead particular combinations of the constraints which follow directly from the primary constraints. Taking this difference into account we found, using two standard methods, that the generator of the gauge transformation gives diffeomorphism invariance in four-dimensional space-time; and this shows that points (i–iii) above cannot be attributed to the Dirac Hamiltonian formulation of GR. We also demonstrate that ADM and Dirac formulations are related by a transformation of phase-space variables from the metric g μν to lapse and shift functions and the three-metric g km, which is not canonical. This proves that point (iv) is incorrect. Points (i–iii) are mere consequences of using a non-canonical change of variables and are not an intrinsic property of either the Hamilton-Dirac approach to constrained systems or Einstein’s theory itself.
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Content available remote Detecting extra dimensions by Hydrogen-like atoms
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We reconsider the idea in spectroscopy of detecting extra dimensions by regarding the nucleus as a homogeneous sphere. In our results, it turns out that the gravitational potential inside the nucleus is much stronger than the potential induced by a particle in the same regime in ref. [16], and thus a more significant correction of the ground state energy of hydrogen-like atoms is obtained, which can be used to determine the existence of ADD’s extra dimensions. In order to get a larger order of magnitude for the correction, it is better to apply our theory to high-Z atoms or muonic atoms, where the volume of the nucleus can’t be ignored and the relativistic effect is important. Our work is based on the Dirac equation in aweak gravity field, and the result is more precise.
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In geological researches several kinds of methods are applied to discovering the natural resources. Planes, helicopters and UAVs (UnmAnned Vehicle) are used in researches in large areas. The gravity, electromagnetic and magnetic methods, which are used in geological researches, are presented in this paper. The special attention was paid to magnetic systems installed on mobile platforms. The magnetic field of the Earth obtained from mathematical model was compared to the real magnetic field in the selected part of the Baltic Sea. The results of the calculations showed that the mathematical model of the Earth’s magnetic field does not consider local magnetic anomalies. The strong local magnetic anomalies cause serious problems with detection of underwater objects. Special problems appear in the magnetic system on a helicopter, which are presented in this paper.
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Content available remote Solving the topographic potential bias as an initial value problem
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If the gravitational potential or the disturbing potential of the Earth be downward continued by harmonic continuation inside the Earth’s topography, it will be biased, the bias being the difference between the downward continued fictitious, harmonic potential and the real potential inside the masses. We use initial value problem techniques to solve for the bias. First, the solution is derived for a constant topographic density, in which case the bias can be expressed by a very simple formula related with the topographic height above the computation point. Second, for an arbitrary density distribution the bias becomes an integral along the vertical from the computation point to the Earth’s surface. No topographic masses, except those along the vertical through the computation point, affect the bias. (To be exact, only the direct and indirect effects of an arbitrarily small but finite volume of mass around the surface point along the radius must be considered.) This implies that the frequently computed terrain effect is not needed (except, possibly, for an arbitrarily small innerzone around the computation point) for computing the geoid by the method of analytical continuation.
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Trade is measured on a gross sales basis while GDP is measured on a net sales basis, i.e. value added. The rapid internationalisation of production in the last two decades has meant that gross trade flows are increasingly unrepresentative of the value-added flows. This fact has important implications for the estimation of the gravity equation. We present empirical evidence that the standard gravity equation performs poorly by some measures when it is applied to bilateral flows where the parts and components trade is important. We also provide a simple theoretical foundation for a modified gravity equation that is suited to explaining trade where international supply chains are important.
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Kinematics engine of the ongoing deformation field around Cairo, Egypt, has been investigated from earthquakes, repeated GPS and gravity observations. First results provided from this combined strategy are presented, by focusing on both stress field and surface kinematics. The spatio-temporal distribution of earthquakes reveals that the Cairo region has suffered not only from interplate earthquakes but also from inland seismic dislocations. Earthquake focal mechanisms indicate that the stress field around Cairo is dominated by the transtensional stress regime (normal faulting with strike-slip component). The results of deformation analysis indicate three different deformation zones in the investigated area. The northem part dominates as a compressional area with a magnitude of 0.19 microstrain/year. The compressions in this area are generally in NW-SE direction. Hwever, an extensional area a magnitude of 0.21 microstrain/year in the NE-SW direction has been observed in the southern part. The central part of the investigation area seems to be in a state of no significant deformation. Repeated gravity measurements around Cairo proved an existence of considerable temporal variations of gravity. These non-tidal changes could be explained by dynamics processes within the upper crust related to the development of local stress conditions. The comparison between the observed GPS and gravity shows a remarkable agreement and provides a convincing explanation for the observed fluctuations with seismic activity.
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The paper is devoted to study the effect of gravity, magnetic field and laser pulse on the general model of the equations of generalized thermoelasticity for a homogeneous isotropic elastic half-space. The formulation is applied under four theories of generalized thermoelasticity: the coupled theory, Lord-Schulman theory, Green-Lindsay theory as well as Green-Naghdi theory. By employing normal mode analysis, the analytical expressions for the displacement components, temperature and the (mechanical and Maxwell’s) stresses distribution are obtained in the physical domain. These expressions are also calculated numerically and corresponding graphs are plotted to illustrate and compare the theoretical results. The effect of gravity, magnetic field and laser pulse are also studied and displayed graphically to show the physical meaning of the phenomena. A comparison has been made between the present results and the results obtained by the others. The results indicate that the effects of magnetic field, laser pulse and gravity field are very pronounced.
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Bone loss is one of the serious health issues in bedridden patients or young generation due to lack of physical activities. Mechanical forces are exerted on the bones through ground reaction forces, liquid loadings and by other contraction activities of the muscles. We are assuming an isotropic half-space with mechanical properties equivalent to that of bone exhibiting microstructures. Consistent couple stress theory introduces an additional material parameter called characteristic length which accounts for inner microstructure of the material. Dispersion relations for leaky Rayleigh waves are derived by considering a model consisting of couple stress half space under the effects of gravity and loaded with inviscid liquid layer of finite thickness or a liquid half space. Impact of the gravity, liquid loadings and microstructures of the material are investigated on propagation of leaky Rayleigh type waves. Phase velocity of leaky Rayleigh waves is studied for five different values of characteristic length parameter which are of the order of internal cell size of the considered material. Variations in phase velocity of leaky Rayleigh waves are also studied under the effect of gravity parameter and thickness of liquid loadings.
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A lattice-gas automaton of hydrodynamics was used to calculate the kinematics of non-cohesive granular materials during 3 different complex two-dimensional problems: granular pile, granular flow in a vertical channel and granular flow in a parallel/converging silo. In the model, collisions and dissipation of particles were taken into account. The simulation results were qualitatively compared with experimental results.
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An attempt of the gravity and gravity vertical gradient obsewations inclustion was taken to the investigations ofone terrestrial dam construction. The specialistic programmes TOPOGRAF and TOPOGRAD were worked aut for microcomputer taking into account the analysis of gravity terrain correction formulae to eliminate water level variations from gravity characteristics.
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Content available remote Love waves in the fiber-reinforced layer over a gravitating porous half-space
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This paper aims to study the propagation of Love waves in fiber-reinforced layer lying over a gravitating anisotropic porous half-space. The closed form of dispersion equation has been derived for the Love waves in terms of Whittaker function and its derivative, which are further expanded asymptotically, retaining the terms up to second degree. The frequency equation shows that the transverse and longitudinal rigidity of reinforced material, as well as gravity and porosity of the porous halfspace have significant effect on the propagation of Love waves. The study reveals that the increment in width of reinforced layer decreases the phase velocity. For a particular width of the reinforced layer, it is also observed that the phase velocity increases with increasing porosity of the half-space, but it decreases with increasing gravity.
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