scholarly journals Radiating composite stars with electromagnetic fields

2021 ◽  
Vol 81 (9) ◽  
Author(s):  
Sunil D. Maharaj ◽  
Byron P. Brassel
Keyword(s):  
Charge Distribution ◽  
Spherically Symmetric ◽  
Junction Conditions ◽  
External Observer ◽  
Composite Field ◽  
Special Cases ◽  
Radiating Star ◽  
Special Case ◽  
Internal Charge ◽  
Null String

AbstractWe derive the junction conditions for a general spherically symmetric radiating star with an electromagnetic field across a comoving surface. The interior consists of a charged composite field containing barotropic matter, a null dust and a null string fluid. The exterior atmosphere is described by the generalised Vaidya spacetime. We generate the boundary condition at the stellar surface showing that the pressure is determined by the interior heat flux, anisotropy, null density, charge distribution and the exterior null string density. A new physical feature that arises in our analysis is that the surface pressure depends on the internal charge distribution for generalised Vaidya spacetimes. It is only in the special case of charged Vaidya spacetimes that the matching interior charge distribution is equal to the exterior charge at the surface as measured by an external observer. Previous treatments, for neutral matter and charged matter, arise as special cases in our treatment of composite matter.

scholarly journals Radiating stars with composite matter distributions

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
Sunil D. Maharaj ◽  
Byron P. Brassel
Keyword(s):  
Boundary Condition ◽  
Radiation Field ◽  
Spherical Geometry ◽  
Higher Dimensions ◽  
Junction Conditions ◽  
Matter Distribution ◽  
Radiating Stars ◽  
Radiating Star ◽  
Composite Distribution ◽  
Null String

AbstractIn this paper we study the junction conditions for a generalised matter distribution in a radiating star. The internal matter distribution is a composite distribution consisting of barotropic matter, null dust and a null string fluid in a shear-free spherical spacetime. The external matter distribution is a combination of a radiation field and a null string fluid. We find the boundary condition for the composite matter distribution at the stellar surface which reduces to the familiar Santos result with barotropic matter. Our result is extended to higher dimensions. We also find the boundary condition for the general spherical geometry in the presence of shear and anisotropy for a generalised matter distribution.

Analytical Techniques for the Optimisation of Rocket Trajectories

1963 ◽  
Vol 14 (2) ◽  
pp. 105-124 ◽  
Author(s):  
Derek F. Lawden
Keyword(s):  
Gravitational Field ◽  
Artificial Satellite ◽  
Analytical Techniques ◽  
Present Position ◽  
Mayer Problem ◽  
Special Cases ◽  
Minimum Expenditure ◽  
Law Of Attraction ◽  
Special Case

SummaryThe development during the last two decades of analytical techniques for the solution of problems relating to the optimisation of rocket trajectories is outlined and the present position in this field of research is summarised. It is shown that the determination of optimal trajectories in a general gravitational field can be expressed as a Mayer problem from the calculus of variations. The known solution to such a problem is stated and applied, first to the special case of the launching of an artificial satellite into a circular orbit with minimum expenditure of propellant and, secondly, to the general astronautical problem of the economical transfer of a rocket between two terminals in a gravitational field. The special cases when the field is uniform and when it obeys an inverse square law of attraction to a point are then considered, and the paper concludes with some remarks concerning areas in which further investigations are necessary.

scholarly journals Water entry of an expanding wedge/plate with flow detachment

2016 ◽  
Vol 797 ◽  
pp. 322-344 ◽  
Author(s):  
Yuriy A. Semenov ◽  
Guo Xiong Wu
Keyword(s):  
Free Surface ◽  
General Solution ◽  
Water Entry ◽  
Hodograph Method ◽  
Fixed Length ◽  
Pressure Distributions ◽  
Initial Stage ◽  
Special Cases ◽  
Wedge Plate ◽  
Special Case

A general similarity solution for water-entry problems of a wedge with its inner angle fixed and its sides in expansion is obtained with flow detachment, in which the speed of expansion is a free parameter. The known solutions for a wedge of a fixed length at the initial stage of water entry without flow detachment and at the final stage corresponding to Helmholtz flow are obtained as two special cases, at some finite and zero expansion speeds, respectively. An expanding horizontal plate impacting a flat free surface is considered as the special case of the general solution for a wedge inner angle equal to ${\rm\pi}$. An initial impulse solution for a plate of a fixed length is obtained as the special case of the present formulation. The general solution is obtained in the form of integral equations using the integral hodograph method. The results are presented in terms of free-surface shapes, streamlines and pressure distributions.

scholarly journals On Reay's Relaxed Tverberg Conjecture and Generalizations of Conway's Thrackle Conjecture

10.37236/6516 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Megumi Asada ◽  
Ryan Chen ◽  
Florian Frick ◽  
Frederick Huang ◽  
Maxwell Polevy ◽  
...  
Keyword(s):  
Geometric Property ◽  
Convex Sets ◽  
Convex Hulls ◽  
Open Problems ◽  
Higher Dimensional ◽  
Special Cases ◽  
Minimum Number ◽  
Point Set ◽  
Colored Version ◽  
Special Case

Reay's relaxed Tverberg conjecture and Conway's thrackle conjecture are open problems about the geometry of pairwise intersections. Reay asked for the minimum number of points in Euclidean $d$-space that guarantees any such point set admits a partition into $r$ parts, any $k$ of whose convex hulls intersect. Here we give new and improved lower bounds for this number, which Reay conjectured to be independent of $k$. We prove a colored version of Reay's conjecture for $k$ sufficiently large, but nevertheless $k$ independent of dimension $d$. Pairwise intersecting convex hulls have severely restricted combinatorics. This is a higher-dimensional analogue of Conway's thrackle conjecture or its linear special case. We thus study convex-geometric and higher-dimensional analogues of the thrackle conjecture alongside Reay's problem and conjecture (and prove in two special cases) that the number of convex sets in the plane is bounded by the total number of vertices they involve whenever there exists a transversal set for their pairwise intersections. We thus isolate a geometric property that leads to bounds as in the thrackle conjecture. We also establish tight bounds for the number of facets of higher-dimensional analogues of linear thrackles and conjecture their continuous generalizations.

Five-dimensional spherical gravitational collapse of anisotropic fluid with cosmological constant

2017 ◽  
Vol 14 (02) ◽  
pp. 1750025 ◽  
Author(s):  
Suhail Khan ◽  
Hassan Shah ◽  
Ghulam Abbas
Keyword(s):  
Cosmological Constant ◽  
Apparent Horizon ◽  
Physical Significance ◽  
Anisotropic Fluid ◽  
Spherically Symmetric ◽  
Hole Size ◽  
Junction Conditions ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Exterior Regions

Our aim is to study five-dimensional spherically symmetric anisotropic collapse with a positive cosmological constant (PCC). For this purpose, five-dimensional spherically symmetric and Schwarzschild–de Sitter metrics are chosen in the interior and exterior regions respectively. A set of junction conditions is derived for the smooth matching of interior and exterior spacetimes. The apparent horizon is calculated and its physical significance is studied. It comes out that the whole collapsing process is influenced by the cosmological constant. The collapsing process under the influence of cosmological constant slows down and black hole size also reduced.

scholarly journals Minimizing Total Completion Time For Preemptive Scheduling With Release Dates And Deadline Constraints

2014 ◽  
Vol 39 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Cheng He ◽  
Hao Lin ◽  
Yixun Lin ◽  
Junmei Dou
Keyword(s):  
Completion Time ◽  
Total Completion Time ◽  
Release Dates ◽  
Preemptive Scheduling ◽  
Release Date ◽  
Enumeration Algorithm ◽  
Processing Times ◽  
Special Cases ◽  
Deadline Constraints ◽  
Special Case

Abstract It is known that the single machine preemptive scheduling problem of minimizing total completion time with release date and deadline constraints is NP- hard. Du and Leung solved some special cases by the generalized Baker's algorithm and the generalized Smith's algorithm in O(n2) time. In this paper we give an O(n2) algorithm for the special case where the processing times and deadlines are agreeable. Moreover, for the case where the processing times and deadlines are disagreeable, we present two properties which could enable us to reduce the range of the enumeration algorithm

On the Cherenkov radiation from extended charge distributions

2000 ◽  
Vol 77 (10) ◽  
pp. 775-784 ◽  
Author(s):  
M Villavicencio ◽  
J L Jiménez ◽  
JAE Roa-Neri
Keyword(s):  
Explicit Expression ◽  
Charge Distribution ◽  
Constant Velocity ◽  
Cherenkov Radiation ◽  
Poynting Vector ◽  
Time Dependent ◽  
Spherically Symmetric ◽  
Charge Distributions ◽  
Extended Charge ◽  
A Charge

In this work the Cherenkov effect for extended charge distributions is analyzed using two different methods. In the first method, the Poynting vector is employed to determine the energy radiated, whereas in the second one, we apply the idea of generating time-dependent elemental dipoles, induced by a charge distribution moving with constant velocity, inside a material medium. An explicit expression for the Cherenkov radiation generated by some different kinds of spherically symmetric charge, travelling inside a medium, is obtained.PACS Nos.: 03.50.De, 41.20.Bt, 41.60.-m, 41.60.Bq

scholarly journals Every Local Minimum Value Is the Global Minimum Value of Induced Model in Nonconvex Machine Learning

2019 ◽  
Vol 31 (12) ◽  
pp. 2293-2323 ◽  
Author(s):  
Kenji Kawaguchi ◽  
Jiaoyang Huang ◽  
Leslie Pack Kaelbling
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Local Minimum ◽  
Deep Neural Networks ◽  
Representation Learning ◽  
Minimum Value ◽  
Special Cases ◽  
Optimal Value ◽  
Special Case ◽  
Theoretical Results

For nonconvex optimization in machine learning, this article proves that every local minimum achieves the globally optimal value of the perturbable gradient basis model at any differentiable point. As a result, nonconvex machine learning is theoretically as supported as convex machine learning with a handcrafted basis in terms of the loss at differentiable local minima, except in the case when a preference is given to the handcrafted basis over the perturbable gradient basis. The proofs of these results are derived under mild assumptions. Accordingly, the proven results are directly applicable to many machine learning models, including practical deep neural networks, without any modification of practical methods. Furthermore, as special cases of our general results, this article improves or complements several state-of-the-art theoretical results on deep neural networks, deep residual networks, and overparameterized deep neural networks with a unified proof technique and novel geometric insights. A special case of our results also contributes to the theoretical foundation of representation learning.

scholarly journals The Generalized Gielis Geometric Equation and Its Application

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 645 ◽  
Author(s):  
Peijian Shi ◽  
David A. Ratkowsky ◽  
Johan Gielis
Keyword(s):  
Power Law ◽  
Morphological Features ◽  
Original Version ◽  
Link Function ◽  
Plant Leaves ◽  
Special Cases ◽  
Geometric Equation ◽  
Special Case

Many natural shapes exhibit surprising symmetry and can be described by the Gielis equation, which has several classical geometric equations (for example, the circle, ellipse and superellipse) as special cases. However, the original Gielis equation cannot reflect some diverse shapes due to limitations of its power-law hypothesis. In the present study, we propose a generalized version by introducing a link function. Thus, the original Gielis equation can be deemed to be a special case of the generalized Gielis equation (GGE) with a power-law link function. The link function can be based on the morphological features of different objects so that the GGE is more flexible in fitting the data of the shape than its original version. The GGE is shown to be valid in depicting the shapes of some starfish and plant leaves.

Sign in / Sign up

Export Citation Format

Share Document