Point-like Bodies Research Articles

Kinetic Model Implementation of Fluidized Bed Devolatilization

Computational modeling is a powerful tool for studying and investigating the behavior of fluidized bed gasifiers and the modeling of the initial devolatilization step is necessary to provide a reliable description of the whole process involving the feedstock decomposition and the subsequent gasification reaction. In this work, a bench-scale fluidized bed reactor was used to examine the devolatilization of different carbonaceous materials within the temperature range from 650 to 850 °C. The experimental test campaign was used to derive the linear correlation factor to describe the devolatilization in terms of product distribution as a function of temperature and highlight the different behavior between lignocellulosic and plastic feedstocks. Furthermore, the experimental data were used to develop concise kinetic expressions able to fit the experimental devolatilization times ranging from 75 in the case of poplar at a lower temperature and 22 s for the Organic Fraction of Municipal Solid Waste (OFMSW) at a higher temperature. The obtained model produces a simple kinetic expression where the size of the particle is enclosed in the kinetic parameters. The kinetic model sided by the application of linear correlations describes the overall thermal decomposition in a fluidized bed, simplifying its modeling in commercial simulation software, even when particles are considered as point-like bodies.

Gravitational Interaction in the Chimney Lattice Universe

We investigate the influence of the chimney topology T×T×R of the Universe on the gravitational potential and force that are generated by point-like massive bodies. We obtain three distinct expressions for the solutions. One follows from Fourier expansion of delta functions into series using periodicity in two toroidal dimensions. The second one is the summation of solutions of the Helmholtz equation, for a source mass and its infinitely many images, which are in the form of Yukawa potentials. The third alternative solution for the potential is formulated via the Ewald sums method applied to Yukawa-type potentials. We show that, for the present Universe, the formulas involving plain summation of Yukawa potentials are preferable for computational purposes, as they require a smaller number of terms in the series to reach adequate precision.

Gravitational polarization of the quantum vacuum caused by two point-like bodies

ABSTRACT In a recent paper, quantum vacuum was considered as a source of gravity, and the simplest, phenomenon, the gravitational polarization of the quantum vacuum by an immersed point-like body, was studied. In this paper, we have derived the effective gravitational charge density of the quantum vacuum, caused by two immersed point-like bodies. Among others, the obtained result proves that quantum vacuum can have regions with a negative effective gravitational charge density. Hence, quantum vacuum, the ‘ocean’ in which all matter of the Universe is immersed, acts as a complex fluid with a very variable gravitational charge density that might include both positive and negative densities; a crucial prediction that can be tested within the Solar system. In the general case of ${N \ge {\rm{3}}}$ point-like bodies, immersed in the quantum vacuum, the analytical solutions are not possible, and the use of numerical methods is inevitable. The key point is that an appropriate numerical method, for the calculation of the effective gravitational charge density of the quantum vacuum induced by N immersed bodies, might be crucial in description of galaxies, without the involvement of dark matter or a modification of gravity. The development of such a valuable numerical method, is not possible, without a previous (and in this study achieved) understanding of the impact of a two-body system.

Spin precession as a new window into disformal scalar fields

We launch a first investigation into how a light scalar field coupled both conformally and disformally to matter influences the evolution of spinning point-like bodies. Working directly at the level of the equations of motion, we derive novel spin-orbit and spin-spin effects accurate to leading order in a nonrelativistic and weak-field expansion. Crucially, unlike the spin-independent effects induced by the disformal coupling, which have been shown to vanish in circular binaries due to rotational symmetry, the spin-dependent effects we study here persist even in the limit of zero eccentricity, and so provide a new and qualitatively distinct way of probing these kinds of interactions. To illustrate their potential, we confront our predictions withspin-precession measurements from the Gravity Probe B experiment andfind that the resulting constraint improves upon existing bounds fromperihelion precession by over 5 orders of magnitude. Our results therefore establish spin effects as a promising window into the disformally coupled dark sector.

Cells and building structures. Part I.

AbstractThe rooms of each building can be interpreted as three-dimensional cells. Borders (sides, edges) of rooms can be identified as the two-, one-, or zero-dimensional boundary cells of the three dimensional cell. The building structures identified as two-, one-, or zero-dimensional cells can be modeled by distinguished geometrical forms, surface-, line-, and point-like bodies. In accordance with the latter, building materials (finished products) can also be considered as surface-, line-, and point-like bodies.The aim of the study is to create compliance between the cell elements and the building structures. It will be done at different levels:– interpretation of relationship between building construction and cells,– interpretation of relationship between building construction and selected bodies,– interpretation the loadbearing's structure using cells,– structure of the surface-construction and the cells,– interpretation building types using cells.In this paper (as part I) the first two items will be studied. The other three cases will be studied in another paper (as part II).

Teukolsky formalism for nonlinear Kerr perturbations

We develop a formalism to treat higher order (nonlinear) metric perturbations of the Kerr spacetime in a Teukolsky framework. We first show that solutions to the linearized Einstein equation with nonvanishing stress tensor can be decomposed into a pure gauge part plus a zero mode (infinitesimal perturbation of the mass and spin) plus a perturbation arising from a certain scalar (‘Debye–Hertz’) potential, plus a so-called ‘corrector tensor’. The scalar potential is a solution to the spin −2 Teukolsky equation with a source. This source, as well as the tetrad components of the corrector tensor, are obtained by solving certain decoupled ordinary differential equations involving the stress tensor. As we show, solving these ordinary differential equations reduces simply to integrations in the coordinate r in outgoing Kerr–Newman coordinates, so in this sense, the problem is reduced to the Teukolsky equation with source, which can be treated by a separation of variables ansatz. Since higher order perturbations are subject to a linearized Einstein equation with a stress tensor obtained from the lower order perturbations, our method also applies iteratively to the higher order metric perturbations, and could thus be used to analyze the nonlinear coupling of perturbations in the near-extremal Kerr spacetime, where weakly turbulent behavior has been conjectured to occur. Our method could also be applied to the study of perturbations generated by a pointlike body traveling on a timelike geodesic in Kerr, which is relevant to the extreme mass ratio inspiral problem.

On the gravitational field of a point-like body immersed in a quantum vacuum

ABSTRACT Quantum vacuum and the matter immersed in it interact through electromagnetic, strong and weak interactions. However, we have zero knowledge of the gravitational properties of the quantum vacuum. As an illustration of the possible fundamental gravitational impact of the quantum vacuum, we study the gravitational field of an immersed point-like body. This is done under the working hypothesis, that quantum vacuum fluctuations are virtual gravitational dipoles (i.e. two gravitational charges of the same magnitude but opposite sign); coincidentally, this hypothesis makes quantum vacuum free of the cosmological constant problem. The major result is that a point-like body creates a halo of polarized quantum vacuum around itself, which acts as an additional source of gravity. There is a maximal magnitude ${g_{\rm qv\max}}$ of gravitational acceleration that can be caused by a polarized quantum vacuum; the small size of this magnitude (${g_{\rm qv\max}} < 6\ \times {10^{ - 11}}\,\mathrm{ m\,s}{^{-2}}$) is the reason why in some cases (for instance within the Solar system) the quantum vacuum can be neglected. Advanced experiments at CERN and forthcoming astronomical observations will reveal if this is true or not, but we point to already existing empirical evidence that seemingly supports this fascinating possibility.

Introduction to The Spiral Dynamics and The Spiral Coriolis Force

The spiral dynamics of a point-like body of mass m in spiral differential geometry are introduced. New ideal motions have been studied, the uniform spiral motion and the uniform spiral-polar motion. The analysis is proposed by comparing the ideal spiral motions with the ideal circular motions. The theoretical forces acting on a point-like body of mass m moving in spiral frames were analyzed. The spiral and polar components of the Coriolis forces were compared.

Scalar perturbations in cosmological f(R) models: the cosmic screening approach

We investigate cosmological perturbations for nonlinear f(R) models within the cosmic screening approach. Matter is considered both in the form of a set of discrete point-like massive bodies and in the form of a continuous pressureless perfect fluid. We perform full relativistic analysis of the first-order theory of scalar perturbations for arbitrary nonlinear f(R) models and demonstrate that scalar potentials {varPhi }(t,{mathbf {r}}) and {varPsi }(t,{mathbf {r}}) are determined by a system of only two master equations. Our equations are applicable at all spatial scales as long as the approximation delta R/{bar{R}} ll 1 (which is usually assumed in studies devoted to cosmological perturbations in f(R) models) works.

Weak-field limit of Kaluza\u2013Klein models with spherically symmetric static scalar field: observational constraints

In a multidimensional Kaluza–Klein model with Ricci-flat internal space, we study the gravitational field in the weak-field limit. This field is created by two coupled sources. First, this is a point-like massive body which has a dust-like equation of state in the external space and an arbitrary parameter varOmega of equation of state in the internal space. The second source is a static spherically symmetric massive scalar field centered at the origin where the point-like massive body is. The found perturbed metric coefficients are used to calculate the parameterized post-Newtonian (PPN) parameter gamma . We define under which conditions gamma can be very close to unity in accordance with the relativistic gravitational tests in the solar system. This can take place for both massive or massless scalar fields. For example, to have gamma approx 1 in the solar system, the mass of scalar field should be mu gtrsim 5.05times 10^{-49}g sim 2.83times 10^{-16}eV. In all cases, we arrive at the same conclusion that to be in agreement with the relativistic gravitational tests, the gravitating mass should have tension: varOmega = -,1/2.

Erratum: Light propagation in the gravitational field of one arbitrarily moving pointlike body in the 2PN approximation [Phys. Rev. D 94 , 124007 (2016)

Erratum: Light propagation in the gravitational field of one arbitrarily moving pointlike body in the 2PN approximation [Phys. Rev. D <b>94</b> , 124007 (2016)

Elementary example of energy and momentum of an extended physical system in special relativity

An instructive paradox concerning the classical description of energy and momentum of extended physical systems in special relativity theory is explained using an elementary example of two point-like massive bodies rotating on a circle in their center-of-mass frame of reference, connected by an arbitrarily light and infinitesimally thin string. From the point of view of the inertial observers who move with respect to the rotating system, the sums of the energies and momenta of the two bodies oscillate, instead of being constant in time. This result is understood in terms of the mechanism that binds the bodies: the string contributes to the total system energy and momentum no matter how light it is. Its contribution eliminates the unphysical oscillations from the system total four-momentum. The generality of the relativistic approach, applied here to the rotor example, suggests that in every extended physical system its binding mechanism contributes to its total energy and momentum.

Light propagation in the Solar System for astrometry on sub-micro-arcsecond level

AbstractWe report on recent advancement in the theory of light propagation in the Solar System aiming at sub-micro-arcsecond level of accuracy: (1)A solution for the light ray in 1.5PN approximation has been obtained in the field of N arbitrarily moving bodies of arbitrary shape, inner structure, oscillations, and rotational motion.(2)A solution for the light ray in 2PN approximation has been obtained in the field of one arbitrarily moving pointlike body.

Publisher’s Note: Light propagation in the gravitational field of one arbitrarily moving pointlike body in the 2PN approximation [Phys. Rev. D 94 , 124007 (2016)

Received 6 March 2017DOI:https://doi.org/10.1103/PhysRevD.95.069905© 2017 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFluids & classical fields in curved spacetimeGeneral relativity equations & solutionsGeneral relativity formalismGravitation, Cosmology & Astrophysics

Light propagation in the gravitational field of one arbitrarily moving pointlike body in the 2PN approximation

An analytical solution for the light trajectory in the near-zone of the gravitational field of one pointlike body in arbitrary slow-motion in the post-post-Newtonian approximation is presented in harmonic gauge. Expressions for total light deflection and time delay are given. The presented solution is a further step toward high-precision astrometry aiming at nano-arcsecond level of accuracy.

Relative Motion in Spacetime

In Minkowski spacetime, we consider an isolated system made of two pointlike bodies interacting at a distance, in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic mechanics", founded on the equal-time condition. The issue of an equivalent one-body description is discussed. We distinguish two different concepts: on the one hand an almost purely kinematic relative particle, on the other hand an effective particle which involves an explicit dynamical formulation; several versions of the latter are possible. Relative and effective particles have the same orbit, but may differ by their schedules.

Gravitational field of one uniformly moving extended body and N arbitrarily moving pointlike bodies in post-Minkowskian approximation

High precision astrometry, space missions and certain tests of General Relativity, require the knowledge of the metric tensor of the solar system, or more generally, of a gravitational system of N extended bodies. Presently, the metric of arbitrarily shaped, rotating, oscillating and arbitrarily moving N bodies of finite extension is only known for the case of slowly moving bodies in the post-Newtonian approximation, while the post-Minkowskian metric for arbitrarily moving celestial objects is known only for pointlike bodies with mass-monopoles and spin-dipoles. As one more step towards the aim of a global metric for a system of N arbitrarily shaped and arbitrarily moving massive bodies in post-Minkowskian approximation, two central issues are on the scope of our investigation. (i) We first consider one extended body with full multipole structure in uniform motion in some suitably chosen global reference system. For this problem a co-moving inertial system of coordinates can be introduced where the metric, outside the body, admits an expansion in terms of Damour–Iyer moments. A Poincaré transformation then yields the corresponding metric tensor in the global system in post-Minkowskian approximation. (ii) It will be argued why the global metric, exact to post-Minkowskian order, can be obtained by means of an instantaneous Poincaré transformation for the case of pointlike mass-monopoles and spin-dipoles in arbitrary motion.

Slender-body theory for viscous flow via dimensional reduction and hyperviscous regularization

A new slender-body theory for viscous flow, based on the concepts of dimensional reduction and hyperviscous regularization, is presented. The geometry of flat, elongated, or point-like rigid bodies immersed in a viscous fluid is approximated by lower-dimensional objects, and a hyperviscous term is added to the flow equation. The hyperviscosity is given by the product of the ordinary viscosity with the square of a length that is shown to play the role of effective thickness of any lower-dimensional object. Explicit solutions of simple problems illustrate how the proposed method is able to represent with good approximation both the velocity field and the drag forces generated by rigid motions of the immersed bodies, in analogy with classical slender-body theories. This approach has the potential to open up the way to more effective computational techniques, since geometrical complexities can be significantly reduced. This, however, is achieved at the expense of involving higher-order derivatives of the velocity field. Importantly, both the dimensional reduction and the hyperviscous regularization, combined with suitable numerical schemes, can be used also in situations where inertia is not negligible.

Non-inertial electromagnetic effects in matter. Gyromagnetic effect

Non-inertial electromagnetic effects in matter, i.e. electromagnetic fields created by a non-inertial motion of material bodies, are discussed within the Drude–Lorentz (plasma) model of matter polarization. It is shown that an oscillatory motion of a point-like body, or wavelike motion in an extended body gives rise to electromagnetic fields with the same frequency as the frequency of the original motion, while shock-like movements of a point-like body generate electromagnetic fields with the characteristic (atomic scale) frequency of the bodies. The polarization of a rigid body induced by rotations is discussed in various circumstances. A uniform rotation produces a static electric field in a dielectric and a stationary current (and a static magnetic field) in a conductor. The latter corresponds to the gyromagnetic effect (while the former may be called the gyroelectric effect). Both fields are computed for a sphere and the gyromagnetic coefficient is derived. A non-uniform rotation induces emission of electromagnetic fields. The equations of motion for the polarization are linearized for slight non-uniformities of the angular velocity and solved both for a dielectric and a conducting sphere. The electromagnetic field emitted by a dielectric spherically shaped body in (a slightly) non-uniform rotation has the characteristic (atomic scale) frequency of the body (slightly shifted by the uniform part of the angular frequency). In the same conditions, a conducting sphere emits an electromagnetic field whose frequency is double the uniform part of the angular frequency.

Hamiltonian Two-Body System in Special Relativity

We consider an isolated system made of two pointlike bodies interacting at a distance in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic mechanics", founded on the equal-time condition. The center of mass is rather a center of energy. Individual energies are separately conserved and the meaning of their positivity is discussed in terms of world-lines. Several results derived decades ago under restrictive assumptions are extended to the general case. Relative motion has a structure similar to that of a nonrelativistic one-body motion in a stationnary external potential, but its evolution parameter is generally not a linear function of the center-of-mass time, unless the relative motion is circular (in this latter case the motion is periodic in the center-of-mass time). Finally the case of an extreme mass ratio is investigated. When this ratio tends to zero the heavy body coincides with the center of mass provided that a certain first integral, related to the binding energy is not too large.