scholarly journals Temporal evolution of a radiating star via Lie symmetries

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Megandhren Govender ◽  
Genly Leon
Keyword(s):  
Exact Solution ◽  
General Solution ◽  
Temporal Evolution ◽  
Singularity Analysis ◽  
Conformally Flat ◽  
Linear Solution ◽  
Vaidya Solution ◽  
Radiating Star ◽  
Particular Solution ◽  
First Time

AbstractIn this work we present for the first time the general solution of the temporal evolution equation arising from the matching of a conformally flat interior to the Vaidya solution. This problem was first articulated by Banerjee et al. (Phys Rev D 40:670, 1989) in which they provided a particular solution of the temporal equation. This simple exact solution has been widely utilised in modeling dissipative collapse with the most notable result being prediction of the avoidance of the horizon as the collapse proceeds. We study the dynamics of dissipative collapse arising from the general solution obtained via the method of symmetries and of the singularity analysis. We show that the end-state of collapse for our model is significantly different from the widely used linear solution.

scholarly journals Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Seyyedeh Roodabeh Moosavi Noori ◽  
Nasir Taghizadeh
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Differential Transform Method ◽  
Hybrid Technique ◽  
Transform Method ◽  
Proportional Delays ◽  
Differential Transform ◽  
Computational Work ◽  
Linear And Nonlinear ◽  
First Time

AbstractIn this study, a hybrid technique for improving the differential transform method (DTM), namely the modified differential transform method (MDTM) expressed as a combination of the differential transform method, Laplace transforms, and the Padé approximant (LPDTM) is employed for the first time to ascertain exact solutions of linear and nonlinear pantograph type of differential and Volterra integro-differential equations (DEs and VIDEs) with proportional delays. The advantage of this method is its simple and trusty procedure, it solves the equations straightforward and directly without requiring large computational work, perturbations or linearization, and enlarges the domain of convergence, and leads to the exact solution. Also, to validate the reliability and efficiency of the method, some examples and numerical results are provided.

scholarly journals Lie Symmetries for a Conformally Flat Radiating Star

2013 ◽  
Vol 52 (9) ◽  
pp. 3244-3254 ◽  
Author(s):  
G. Z. Abebe ◽  
K. S. Govinder ◽  
S. D. Maharaj
Keyword(s):  
Lie Symmetries ◽  
Conformally Flat ◽  
Radiating Star

scholarly journals An application of Ritt’s low power theorem

1977 ◽  
Vol 68 ◽  
pp. 17-19 ◽  
Author(s):  
Michihiko Matsuda
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Low Power ◽  
Singular Solution ◽  
Algebraic Differential Equation ◽  
Classical Concept ◽  
First Order ◽  
Particular Solutions ◽  
Rigorous Definition ◽  
Particular Solution

AbstractConsider an algebraic differential equation F = 0 of the first order. A rigorous definition will be given to the classical concept of “particular solutions” of F = 0. By Ritt’s low power theorem we shall prove that a singular solution of F = 0 belongs to the general solution of F if and only if it is a particular solution of F = 0.

scholarly journals A Relativistic Algorithm with Isotropic Coordinates

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
S. A. Ngubelanga ◽  
S. D. Maharaj
Keyword(s):  
Spherically Symmetric ◽  
Conformally Flat ◽  
Einstein Field Equations ◽  
Elementary Functions ◽  
Field Equations ◽  
Isotropic Coordinates ◽  
New Exact Solutions ◽  
Symmetric Spacetimes ◽  
Particular Solution ◽  
Conformally Flat Metric

We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contain isotropic pressures. We develop an algorithm that produces a new solution if a particular solution is known. The algorithm leads to a nonlinear Bernoulli equation which can be integrated in terms of arbitrary functions. We use a conformally flat metric to show that the integrals may be expressed in terms of elementary functions. It is important to note that we utilise isotropic coordinates unlike other treatments.

Scaling Analysis of a Moving Point Heat Source in Steady-State on a Semi-Infinite Solid

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Patricio F. Mendez ◽  
Yi Lu ◽  
Ying Wang
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Heat Source ◽  
Asymptotic Analysis ◽  
Numerical Models ◽  
Scaling Analysis ◽  
Point Heat Source ◽  
Maximum Width ◽  
Characteristic Values ◽  
First Time

This paper presents a systematic scaling analysis of the point heat source in steady-state on a semi-infinite solid. It is shown that all characteristic values related to an isotherm can be reduced to a dimensionless expression dependent only on the Rykalin number (Ry). The maximum width of an isotherm and its location are determined for the first time in explicit form for the whole range of Ry, with an error below 2% from the exact solution. The methodology employed involves normalization, dimensional analysis, asymptotic analysis, and blending techniques. The expressions developed can be calculated using a handheld calculator or a basic spreadsheet to estimate, for example, the width of a weld or the size of zone affected by the heat source in a number of processes. These expressions are also useful to verify numerical models.

scholarly journals Monitoring of the Eyjafjallajökull volcanic aerosol plume over the Iberian Peninsula by means of four EARLINET lidar stations

2011 ◽  
Vol 11 (11) ◽  
pp. 29681-29721 ◽  
Author(s):  
M. Sicard ◽  
J. L. Guerrero-Rascado ◽  
F. Navas-Guzmán ◽  
J. Preißler ◽  
F. Molero ◽  
...  
Keyword(s):  
Iberian Peninsula ◽  
Mass Concentration ◽  
Temporal Evolution ◽  
Volcanic Plume ◽  
Volcanic Aerosol ◽  
The Mean ◽  
Sun Photometer ◽  
Volcanic Aerosols ◽  
First Time ◽  
Aerosol Plume

Abstract. Lidar and sun-photometer measurements were performed intensively over the Iberian Peninsula (IP) during the eruption of Eyjafjallajökull volcano (Iceland) in April–May 2010. The volcanic plume hit all the IP stations for the first time on 5 May 2010. A thorough study of the event is conducted for the period 5–8 May. Firstly the spatial and temporal evolution of the plume is described by means of lidar and sun-photometer measurements supported with backtrajectories. The volcanic aerosol layers observed over the IP were rather thin (<1000 m) with a top height up to 11–12 km. The mean optical thicknesses associated to those layers were rather low (between 0.013 and 0.020 over the whole period). Punctually on 7 May the optical thickness reached peak values near 0.10. Secondly the volcanic aerosols are characterized in terms of extinction and backscatter coefficients, lidar ratios, Ångström exponents and linear particle depolarization ratio. Lidar ratios at different sites varied between 30 and 50 sr without a marked spectral dependency. Similar extinction-related Ångström exponents varying between 0.6 and 0.8 were observed at different sites. The temporal evolution of the backscatter-related Ångström exponents points out a possible decrease of the volcanic particle size as the plume moves from west to east. Particle depolarization ratios on the order of 0.06–0.08 confirmed the coexistence of both ash and non-ash particles. Additionally profiles of mass concentration were obtained with a method using the opposite depolarizing effects of ash particles (strongly depolarizing) and non-ash particles (very weakly depolarizing), and sun-photometer observations. In Granada the ash mass concentration was found approximately 1.5 higher than that of non-ash particles, and probably did not exceed the value of 200 μg m−3 during the whole event.

scholarly journals Mutation landscape of SARS-CoV-2 reveals five mutually exclusive clusters of leading and trailing single nucleotide substitutions

2020 ◽  
Author(s):  
Akhilesh Mishra ◽  
Ashutosh Kumar Pandey ◽  
Parul Gupta ◽  
Prashant Pradhan ◽  
Sonam Dhamija ◽  
...  
Keyword(s):  
Clustering Analysis ◽  
High Frequency ◽  
Temporal Evolution ◽  
Viral Evolution ◽  
Vaccine Design ◽  
Nucleotide Substitutions ◽  
Single Nucleotide ◽  
Virus Life Cycle ◽  
Mutation Profile ◽  
First Time

AbstractThe COVID-19 pandemic has spread across the globe at an alarming rate. However, unlike any of the previous global outbreaks the availability of a large number of SARS-CoV-2 sequences provides us with a unique opportunity to understand viral evolution in real time. We analysed 1448 full-length (>29000 nt) sequences available and identified 40 single-nucleotide substitutions occurring in >1% of the genomes. Majority of the substitutions were C to T or G to A. We identify C/Gs with an upstream TTT trinucleotide motif as hotspots for mutations in the SARS-CoV-2 genome. Interestingly, three of the 40 substitutions occur within highly conserved secondary structures in the 5’ and 3’ regions of the genomic RNA that are critical for the virus life cycle. Furthermore, clustering analysis revealed unique geographical distribution of SARS-CoV-2 variants defined by their mutation profile. Of note, we observed several co-occurring mutations that almost never occur individually. We define five mutually exclusive lineages (A1, B1, C1, D1 and E1) of SARS-CoV-2 which account for about three quarters of the genomes analysed. We identify lineage-defining leading mutations in the SARS-CoV-2 genome which precede the occurrence of sub-lineage defining trailing mutations. The identification of mutually exclusive lineage-defining mutations with geographically restricted patterns of distribution has potential implications for diagnosis, pathogenesis and vaccine design. Our work provides novel insights on the temporal evolution of SARS-CoV-2.ImportanceThe SARS-CoV-2 / COVID-19 pandemic has spread far and wide with high infectivity. However, the severeness of the infection as well as the mortality rates differ greatly across different geographic areas. Here we report high frequency mutations in the SARS-CoV-2 genomes which show the presence of linage-defining, leading and trailing mutations. Moreover, we propose for the first time, five mutually exclusive clusters of SARS-CoV-2 which account for 75% of the genomes analysed. This will have implications in diagnosis, pathogenesis and vaccine design

Exact Solution of the Problem of Elastic Bending of a Multilayer Beam under the Action of a Normal Uniform Load

2019 ◽  
Vol 968 ◽  
pp. 475-485 ◽  
Author(s):  
Stanislav Koval’chuk ◽  
Alexey Goryk
Keyword(s):  
Exact Solution ◽  
General Solution ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Theory Of Elasticity ◽  
Transverse Shear Deformation ◽  
Uniform Load ◽  
Principle Of Superposition ◽  
Elastic Bending ◽  
Transverse Bending

An exact solution of the theory of elasticity is presented for the problem of a narrow multilayer bar section transverse bending under the action of a normal uniform load on longitudinal faces. The solution is built using the principle of superposition, by imposing common solutions to the problems of bending a multilayer cantilever with uniform loads on the longitudinal faces and an arbitrary load on the free end, and allows to take into account the orthotropy of the materials of the layers, as well as transverse shear deformation and compression. On the basis of a built-in general solution, a number of particular solutions are obtained for multi-layer beams with various ways of the ends fixing.

Lower Bounds to Eigenvalues by Planelike Surfaces

1974 ◽  
Vol 41 (1) ◽  
pp. 267-268 ◽  
Author(s):  
D. Pnueli
Keyword(s):  
Lower Bound ◽  
General Solution ◽  
Variational Problem ◽  
Lower Bounds ◽  
Particular Solutions ◽  
Particular Solution ◽  
The One

A particular solution of a variational problem is defined as corresponding to a particular set of parameters. A general solution is the one over a continuous region of the parameters. This work presents a method to obtain lower bound to the general solution, when some particular solutions are known.

Solving the fractional heat-like and wave-like equations with variable coefficients utilizing the Laplace homotopy method

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Muhammad Nadeem ◽  
Shao-Wen Yao
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Homotopy Perturbation Method ◽  
Variable Coefficients ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Content Type ◽  
The Laplace Transform ◽  
First Time

Purpose This paper aims to suggest the approximate solution of time fractional heat-like and wave-like (TFH-L and W-L) equations with variable coefficients. The proposed scheme shows that the results are very close to the exact solution. Design/methodology/approach First with the help of some basic properties of fractional derivatives, a scheme that has the capability to solve fractional partial differential equations is constructed. Then, TFH-L and W-L equations with variable coefficients are solved by this scheme, which yields results very close to the exact solution. The derived results demonstrate that this scheme is very effective. Finally, the convergence of this method is discussed. Findings A traditional method is combined with the Laplace transform to construct this scheme. To decompose the nonlinear terms, this paper introduces the homotopy perturbation method with He’s polynomials and thus the solution is provided in the form of a series that converges to the exact solution very quickly. Originality/value The proposed approach is original and very effective because this approach is, to the authors’ knowledge, used for the first time very successfully to tackle the fractional partial differential equations, which are of great interest.

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