Point Mass Source Research Articles

Accretion onto oscillating cosmic string loops

Cosmic string loops are non-linear density fluctuations which form in the early universe and could play an important role in explaining many phenomena which are in tension with the standard ΛCDM model. Hence, the accretion process onto cosmic string loops should be studied in detail. Most previous works view loops as point masses and ignore the impact of a finite loop size. In this work, we utilize the Zel'dovich approximation to calculate the non-linear mass sourced by a static extended loop with a time-averaged density profile derived from the trajectory of the loop oscillation, and compare the result with what is obtained for a point-mass source. We find that the finite size of a loop mainly affects the evolution of turnaround shells during the early stages of accretion, converging to the point mass result after a critical redshift, zc ( II)/( III). For zc ( II)/( III), the total accreted mass surrounding a loop is suppressed relative to the point mass case and has a growth rate proportional to (1+z)-3/2.As an immediate extension, we also qualitatively analyse the accretion onto moving point masses and onto moving extended loops. In addition to the reduction in the nonlinear mass, the loop finite size also changes the shape of the turnaround surface at early stages of accretion.

Mathematical modeling of impurity diffusion process under given statistics of a point mass sources system. I

The model of the impurity diffusion process in the layer where a system of random point mass sources acts, is proposed. Mass sources of various power are uniformly distributed in a certain internal interval of the body. Statistics of random sources are given. The solution of the initial-boundary value problem is constructed as a sum of the homogeneous problem solution and the convolution of the Green's function and the system of the random point mass sources. The solution is averaged over both certain internal subinterval and the entire body region. Simulation units are designed for modeling of the behavior of the averaged concentration function with acting system of point mass sources of various power. On this basis, the averaged concentration field is investigated depending on the internal interval length, power and number of sources in the system as well as the concentration values at the layer boundaries.

A Novel Derivation of Black Hole Entropy in all Dimensions from Truly Point Mass Sources

A Novel Derivation of Black Hole Entropy in all Dimensions from Truly Point Mass Sources

Point source modelling approach for sessile droplet evaporation

Evaporation of sessile droplets from unheated solid surfaces is a ubiquitous process in many practical applications. A reduced order, analytical point source model (PSM) for the axisymmetric diffusion-dominated evaporation of an isolated sessile droplet surrounded by non-saturated, quiescent air was developed. The droplet is modeled as a dynamic point mass source in the limit of an isothermal system. The model also incorporates the spatial variation in the evaporative flux across the droplet free surface. The model is capable of considering the mode of evaporation, i.e., constant contact angle or contract radius. The PSM was simulated using the finite difference method in MATLAB R2020a. The model determines the vapor concentration distribution in the surrounding environment, the instantaneous evaporative flux averaged across the droplet surface and the overall evaporation rate. Calculating the evaporation rate assuming a spatially uniform evaporative flux under-predicts the evaporation rate by up to an order of magnitude. The model results agreed with experimental data in literature and sufficiently captures the evaporation process phenomena. The versatility and accurate predictive power of the PSM allows it to be a robust and computationally inexpensive modeling tool for studying sessile droplet evaporation in a wide range of technical applications.

Mathematical modeling of impurity diffusion process under given statistics of a point mass sources system. II

Modeling of the impurity diffusion process in a layer under the action of a system of random point sources is carried out. Mass sources of different power are uniformly distributed in a certain internal interval, that may also coincide with the entire region of the layer. The statistics of random sources is given. The solution of the initial-boundary value problem is found as the sum of the homogeneous problem solution and the convolution of the Green's function with the system of the random point sources. Averaging of the solution is performed on the internal subinterval and in the entire body region. The formulas for the variance, correlation function of the concentration field and coefficient of correlation are expressed in terms of the second moment of random mass sources. Software modules are developed for simulating the behavior of the averaged concentration, variance and correlation function. Their numerical analysis also is performed. General properties of the considered function are determined depending on the problem parameters.

Gravity degree–depth relationship using point mass spherical harmonics

SUMMARYRelationships between the degree of a spherical harmonic model of the gravitational field of a body and the depth of a source expressed as a density contrast can be used to study the structure of features. Here, we show that the gravitational acceleration per spherical harmonic degree of a constant density source has an extremum that depends on the depth of the source. Using the spherical harmonics expansion for a point mass source, we use this to derive a degree–depth relationship. Our relationship resembles an earlier one derived by Bowin, with substantial differences at the lower degrees. We also find that a recent relationship derived by Deng et al. overestimates the source depth. The relationship that we derive relates spherical harmonic degree n to depth d for a planet of radius R according to $d = (1-e^{\frac{-1}{n+1}})R$, which simplifies to d = R/(n + 1) for high degrees. We support our new relationship with synthetic models of a density contrast in a planet. We also show how the differences between our relationship and that of Bowin affect band-filtered gravity, for example when inspecting the upper 100 km of the Moon. Using point masses in our modelling results in an approximate relationship where in reality sources can be deeper than estimated, since any source contributes to all spherical harmonic degrees. The use of the contribution per individual degree however provides an intuitive relationship between spherical harmonic degree and depth that can be used to place relative bounds on source depths or to determine the bounds on spherical harmonic expansions when band-filtering gravity field models.

On the Problem of Determining the Position of the Source of Internal Waves

When bodies move in a continuously stratified fluid, the steady wave field moves along with the body and form a field of so-called associated internal waves. The flow incident on the body is usually assumed to be constant; non-stationary waves generated at the initial stage of motion are neglected. In this case, the body is modeled by point mass sources, and the wave field is found using the Green’s function method, followed by the use of asymptotic expansions based on the stationary phase method [1]. The inverse problem of determining the position of the source is solved from the wave field.

The Era of Gravitational Astronomy and Gravitational Field of Non-Rotating Single Point Particle in General Relativity

Utilizing various gauges of the radial coordinate, we give a General Relativistic (GR) description of static spherically symmetric spacetimes with a massive point source and vacuum outside this singularity. We show that in GR there exists a two-parameter family of such solutions to the Einstein equations which are physically distinguishable and describe the gravitational field of a single massive point particle with positive proper mass M0 and positive Keplerian mass M < M0. In particular, we show that the widespread Hilbert form of the Schwarzschild solution, which depends only on the Keplerian mass M and describes Black Holes (BH), does not solve the Einstein equations with a massive point particle stress-energy tensor. Novel normal coordinates for the gravitational field and a new physical class of gauges are proposed, thus achieving a correct description of a point mass source in GR. We also introduce a gravitational mass defect of a point particle and determine the dependence of the solutions on this mass defect. The result can be described as a change of the Newton potential φN = –GNM/r to a modified one φG = –GNM/$$\left( {r + {{G}_{{\text{N}}}}{M \mathord{\left/ {\vphantom {M {{{c}^{2}}}}} \right. \kern-0em} {{{c}^{2}}}}\ln \frac{{{{M}_{0}}}}{M}} \right)$$ and the corresponding modification of the four-interval. We show that the proper 3D flat space, where these two potentials can be compared, is the tangent space above the position of the massive point source. In addition, we present invariant characteristics of the physically and geometrically different classes of spherically symmetric static spacetimes created by a point mass. Our findings are important for description of Extremely Compact Objects (ECOs) studied in relation with possible echoes in Gravitational Waves (GW) recently discovered by the LIGO/VIRGO collaboration.

Numerical investigation of selective withdrawal in a pancreatic cell islet encapsulation apparatus

The development of an efficient microencapsulation apparatus is a major challenge for islet transplantation. To that end, the flow generated by selective withdrawal in an apparatus for micro-encapsulation of pancreatic islets is studied through CFD simulations. Each islet enters individually a chamber containing a twolayer system in which is encapsulated by selective withdrawal. Optimal encapsulation occurs, when the perturbed interface is kept stable and transition to viscous entrainment is prevented. Simulations were validated with experimental data. Contrary to previous studies that simplify the problem by approximating the tubes as a doublet of a point mass source and sink, the model presented here employs a detailed geometry. Numerical results shed light on the dependence of the shape of the interface on flow, geometry and physical parameters. These observations can contribute to the design of encapsulation apparatuses considering polydispersity in size and the different shape of the islets.

Unsteady Computational Fluid Dynamics Investigation of Effusion Cooling Process in a Lean Burn Aero-Engine Combustor

This work describes the main findings of a computational fluid dynamics (CFD) analysis intended to accurately investigate the flow field and wall heat transfer as a result of the mutual interaction between a swirling flow generated by a lean burn injection system and a slot–effusion liner cooling system. In order to overcome some limitations of Reynolds-averaged Navier–Stokes (RANS) approach, the simulations were performed with shear stress transport (SST)–scale-adaptive simulation (SAS), a hybrid RANS–large eddy simulation (LES) model. Moreover, the significant computational effort due to the presence of more than 600 effusion holes was limited exploiting two different modeling strategies: a homogeneous model based on the application of uniform boundary conditions on both aspiration and injection sides, and another solution that provides a coolant injection through point mass sources within a single cell. CFD findings were compared to experimental results coming from an investigation carried out on a three-sector linear rig. The comparison pointed out that advanced modeling strategies, i.e., based on discrete mass sources, are able to reproduce the effects of mainstream–coolant interactions on convective heat loads. By validating the approach through a benchmark against time-averaged quantities, the transient data acquired were examined in order to better understand the unsteady behavior of the thermal load through a statistical analysis, providing useful information with a design perspective.

Novel Remarks on Point Mass Sources, Firewalls, Null Singularities and Gravitational Entropy

A continuous family of static spherically symmetric solutions of Einstein’s vacuum field equations with a spatial singularity at the origin \( r = 0 \) is found. These solutions are parametrized by a real valued parameter \( \lambda \) (ranging from 0 to 1) and such that the radial horizon’s location is displaced continuously towards the singularity (\( r = 0 \)) as \( \lambda \) increases. In the extreme limit \( \lambda = 1\), the location of the singularity and horizon merges leading to a null singularity. In this extreme case, any infalling observer hits the null singularity at the very moment he/she crosses the horizon. This fact may have important consequences for the resolution of the fire wall problem and the complementarity controversy in black holes. An heuristic argument is provided how one might avoid the Hawking particle emission process in this extreme case when the singularity and horizon merges. The field equations due to a delta-function point-mass source at \( r = 0 \) are solved and the Euclidean gravitational action corresponding to those solutions is evaluated explicitly. It is found that the Euclidean action is precisely equal to the black hole entropy (in Planck area units). This result holds in any dimensions \( D \ge 3 \).

Einstein’s Pseudo-Tensor in &amp;lt;i&amp;gt;n&amp;lt;/i&amp;gt; Spatial Dimensions for Static Systems with Spherical Symmetry

It was noted earlier that the general relativity field equations for static systems with spherical symmetry can be put into a linear form when the source energy density equals radial stress. These linear equations lead to a delta function energymomentum tensor for a point mass source for the Schwarzschild field that has vanishing self-stress, and whose integral therefore transforms properly under a Lorentz transformation, as though the particle is in the flat space-time of special relativity (SR). These findings were later extended to n spatial dimensions. Consistent with this SR-like result for the source tensor, Nordstrom and independently, Schrodinger, found for three spatial dimensions that the Einstein gravitational energy-momentum pseudo-tensor vanished in proper quasi-rectangular coordinates. The present work shows that this vanishing holds for the pseudo-tensor when extended to n spatial dimensions. Two additional consequences of this work are: 1) the dependency of the Einstein gravitational coupling constant κ on spatial dimensionality employed earlier is further justified; 2) the Tolman expression for the mass of a static, isolated system is generalized to take into account the dimensionality of space for n ≥ 3.

GICUDA: A parallel program for 3D correlation imaging of large scale gravity and gravity gradiometry data on graphics processing units with CUDA

The 3D correlation imaging for gravity and gravity gradiometry data provides a rapid approach to the equivalent estimation of objective bodies with different density contrasts in the subsurface. The subsurface is divided into a 3D regular grid, and then a cross correlation between the observed data and the theoretical gravity anomaly due to a point mass source is calculated at each grid node. The resultant correlation coefficients are adopted to describe the equivalent mass distribution in a quantitate probability sense. However, when the size of the survey data is large, it is still computationally expensive. With the advent of the CUDA, GPUs lead to a new path for parallel computing, which have been widely applied in seismic processing, astronomy, molecular dynamics simulation, fluid mechanics and some other fields. We transfer the main time-consuming program of 3D correlation imaging into GPU device, where the program can be executed in a parallel way. The synthetic and real tests have been performed to validate the correctness of our code on NVIDIA GTX 550. The precision evaluation and performance speedup comparison of the CPU and GPU implementations are illustrated with different sizes of gravity data. When the size of grid nodes and observed data sets is 1024×1024×1 and 1024×1024, the speed up can reach to 81.5 for gravity data and 90.7 for gravity vertical gradient data respectively, thus providing the basis for the rapid interpretation of gravity and gravity gradiometry data.

3D correlation imaging of the vertical gradient of gravity data

We present a new 3D correlation imaging approach for vertical gradient of gravity data for deriving a 3D equivalent mass distribution in the subsurface. In this approach, we divide the subsurface space into a 3D regular grid, and then at each grid node calculate a cross correlation between the vertical gradient of the observed gravity data and the theoretical gravity vertical gradient due to a point mass source. The resultant correlation coefficients are used to describe the equivalent mass distribution in a probability sense. We simulate a geological syncline model intruded by a dike and later broken by two vertical faults. The vertical gradient of gravity anomaly of the model is calculated and used to test the approach. The results demonstrate that the equivalent mass distribution derived by the approach reflects the basic geological structures of the model. We also test the approach on the transformed vertical gradient of real Bouguer gravity data from a geothermal survey area in Northern China. The thermal reservoirs are located in the lower portion of the sedimentary basin. From the resultant equivalent mass distribution, we produce the depth distribution of the bottom interface of the basin and predict possible hidden faults present in the basin.

The Euclidean gravitational action as black hole entropy, singularities, and spacetime voids

We argue why the static spherically symmetric vacuum solutions of Einstein’s equations described by the textbook Hilbert metric gμν(r) is not diffeomorphic to the metric gμν(∣r∣) corresponding to the gravitational field of a point mass delta function source at r=0. By choosing a judicious radial function R(r)=r+2G∣M∣Θ(r) involving the Heaviside step function, one has the correct boundary condition R(r=0)=0, while displacing the horizon from r=2G∣M∣ to a location arbitrarily close to r=0 as one desires, rh→0, where stringy geometry and quantum gravitational effects begin to take place. We solve the field equations due to a delta function point mass source at r=0, and show that the Euclidean gravitational action (in ℏ units) is precisely equal to the black hole entropy (in Planck area units). This result holds in any dimensions D⩾3. In the Reissner–Nordstrom (massive charged) and Kerr–Newman black hole case (massive rotating charged) we show that the Euclidean action in a bulk domain bounded by the inner and outer horizons is the same as the black hole entropy. When one smears out the point-mass and point-charge delta function distributions by a Gaussian distribution, the area-entropy relation is modified. We postulate why these modifications should furnish the logarithmic corrections (and higher inverse powers of the area) to the entropy of these smeared black holes. To finalize, we analyze the Bars–Witten stringy black hole in 1+1 dimension and its relation to the maximal acceleration principle in phase spaces and Finsler geometries.

Microlensing by natural wormholes: Theory and simulations

We provide an in depth study of the theoretical peculiarities that arise in effective negative mass lensing, both for the case of a point mass lens and source, and for extended source situations. We describe novel observational signatures arising in the case of a source lensed by a negative mass. We show that a negative mass lens produces total or partial eclipse of the source in the umbra region and also show that the usual Shapiro time delay is replaced with an equivalent time gain. We describe these features both theoretically, as well as through numerical simulations. We provide negative mass microlensing simulations for various intensity profiles and discuss the differences between them. The light curves for microlensing events are presented and contrasted with those due to lensing produced by normal matter. Presence or absence of these features in the observed microlensing events can shed light on the existence of natural wormholes in the Universe.

Electrostatic self-force in -dimensional cosmological gravity

Point sources, which are conical singularities in (2 + 1)-dimensional gravity, as well as the BTZ black hole, modify the global curvature of the space giving rise to self-interaction effects on classical fields. In this work we study the electrostatic self-interaction of a point charge either in the presence of a point mass source or a stationary BTZ black hole in (2 + 1)-dimensional gravity with a cosmological constant . Exact expressions are obtained for the self-force in all cases studied.

Unsteady Abyssal Circulation Driven by a Discrete Buoyancy Source in a Continuously Stratified Ocean

Abstract Analytical and numerical models are presented for linear quasigeostrophic buoyancy-driven flow forced bya time periodic pulsating point mass source in a continuously stratified, incompressible β-plane ocean withconstant Brunt–Vaisala frequency. The source represents the seasonal introduction of dense water into the abyssalocean and is located on a linear sloping bottom of arbitrary orientation. The ocean domain is horizontallyunbounded and of infinite depth. Rayleigh friction is incorporated into the horizontal momentum equations andappears at order Rossby number in the quasigeostrophic expansions. In the density equation the influence ofRayleigh friction and Laplacian friction are each considered in turn. Analytical solutions are obtained in the case of 1) a midlatitude β plane with no bottom slope and 2) an fplane with a bottom slope. In both of these problems the fluid is initially at rest and the mass source is switchedon and maintained. A three-dimensional radiating field of baroclinic Rossb...

The reflection of beams of internal gravity waves at a flat rigid surface

The linear problem of the reflection of a beam of monochromatic internal waves at a rigid inclined wall in an exponentially stratified liquid with viscosity and diffusion is considered. In such a medium there is, as well as the reflected wave, a boundary-layer flow at the plane with split spatial length-scales for the velocity and density variation. Viscosity and diffusion restrict the limiting value of the geometrical compression coefficient of the beam. The solution has no singularities at critical angles of reflection. Calculations for the reflected beam and boundary flow are performed for an incident beam radiated by a point mass source.

Internal wave generation in uniformly stratified fluids. Part 2. Moving point sources

The Green's function method is applied to the generation of internal gravity waves by a moving point mass source. Arbitrary motion of a source of arbitrary time dependence is treated using the impulsive Green's function, while ‘classical’ approaches of uniform motion of a steady or oscillatory source are recovered using the monochromatic Green's function. Waves have locally the structure of impulsive waves, emitted at the retarded time tr, and having propagated with the group velocity; at each position and time an implicit equation defines tr, in terms of which the waves are written. A source both oscillating and moving generates two systems of waves, with respectively positive and negative frequencies, and when oscillations vanish these systems merge into one.Three particular cases are considered: the uniform horizontal and vertical motions of a steady source, and the uniform horizontal motion of an oscillatory source. Waves spread downstream of the steady source. For the oscillatory source they can extend both upstream and downstream, depending on the ratio of the source frequency to the buoyancy frequency, and are contained inside conical wavefronts, parts of which are caustics. For horizontal motion, moreover, the steady analysis (based on the monochromatic Green's function) reveals the presence of two insignificant contributions overlooked by the unsteady analysis (based on the impulsive Green's function), but which for an extended source may become of the same order as the main contribution. Among those is an upstream columnar disturbance associated with blocking.