Modifcations to gravitational waves due to matter shells
- Authors: Naidoo, Monogaran
- Date: 2021-10-29
- Subjects: Gravitational waves , General relativity (Physics) , Einstein field equations , Cosmology , Matter shells
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/191118 , vital:45062 , 10.21504/10962/191119
- Description: As detections of gravitational waves (GWs) mount, the need to investigate various effects on the propagation of these waves from the time of emission until detection also grows. We investigate how a thin low density dust shell surrounding a gravitational wave source affects the propagation of GWs. The Bondi-Sachs (BS) formalism for the Einstein equations is used for the problem of a gravitational wave (GW) source surrounded by a spherical dust shell. Using linearised perturbation theory, we and the geometry of the regions exterior to, interior to and within the shell. We and that the dust shell causes the gravitational wave to be modified both in magnitude and phase, but without any energy being transferred to or from the dust. This finding is novel. In the context of cosmology, apart from the gravitational redshift, the effects are too small to be measurable; but the effect would be measurable if a GW event were to occur with a source surrounded by a massive shell and with the radius of the shell and the wavelength of the GWs of the same order. We extended our investigation to astrophysical scenarios such as binary black hole (BBH) mergers, binary neutron star (BNS) mergers, and core collapse supernovae (CCSNe). In these scenarios, instead of a monochromatic GW source, as we used in our initial investigation, we consider burst-like GW sources. The thin density shell approach is modified to include thick shells by considering concentric thin shells and integrating. Solutions are then found for these burst-like GW sources using Fourier transforms. We show that GW echoes that are claimed to be present in the Laser Interferometer Gravitational-Wave Observatory (LIGO) data of certain events, could not have been caused by a matter shell. We do and, however, that matter shells surrounding BBH mergers, BNS mergers, and CCSNe could make modifications of order a few percent to a GW signal. These modifications are expected to be measurable in GW data with current detectors if the event is close enough and at a detectable frequency; or in future detectors with increased frequency range and amplitude sensitivity. Substantial use is made of computer algebra in these investigations. In setting the scene for our investigations, we trace the evolution of general relativity (GR) from Einstein's postulation in 1915 to vindication of his theory with the confirmation of the existence of GWs a century later. We discuss the implications of our results to current and future considerations. Calculations of GWs, both analytical and numerical, have normally assumed their propagation from source to a detector on Earth in a vacuum spacetime, and so discounted the effect of intervening matter. As we enter an era of precision GW measurements, it becomes important to quantify any effects due to propagation of GWs through a non-vacuum spacetime Observational confirmation of the modification effect that we and in astrophysical scenarios involving black holes (BHs), neutron stars (NSs) and CCSNe, would also enhance our understanding of the details of the physics of these bodies. , Thesis (PhD) -- Faculty of Science, Mathematics (Pure and Applied), 2021
- Full Text:
- Authors: Naidoo, Monogaran
- Date: 2021-10-29
- Subjects: Gravitational waves , General relativity (Physics) , Einstein field equations , Cosmology , Matter shells
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/191118 , vital:45062 , 10.21504/10962/191119
- Description: As detections of gravitational waves (GWs) mount, the need to investigate various effects on the propagation of these waves from the time of emission until detection also grows. We investigate how a thin low density dust shell surrounding a gravitational wave source affects the propagation of GWs. The Bondi-Sachs (BS) formalism for the Einstein equations is used for the problem of a gravitational wave (GW) source surrounded by a spherical dust shell. Using linearised perturbation theory, we and the geometry of the regions exterior to, interior to and within the shell. We and that the dust shell causes the gravitational wave to be modified both in magnitude and phase, but without any energy being transferred to or from the dust. This finding is novel. In the context of cosmology, apart from the gravitational redshift, the effects are too small to be measurable; but the effect would be measurable if a GW event were to occur with a source surrounded by a massive shell and with the radius of the shell and the wavelength of the GWs of the same order. We extended our investigation to astrophysical scenarios such as binary black hole (BBH) mergers, binary neutron star (BNS) mergers, and core collapse supernovae (CCSNe). In these scenarios, instead of a monochromatic GW source, as we used in our initial investigation, we consider burst-like GW sources. The thin density shell approach is modified to include thick shells by considering concentric thin shells and integrating. Solutions are then found for these burst-like GW sources using Fourier transforms. We show that GW echoes that are claimed to be present in the Laser Interferometer Gravitational-Wave Observatory (LIGO) data of certain events, could not have been caused by a matter shell. We do and, however, that matter shells surrounding BBH mergers, BNS mergers, and CCSNe could make modifications of order a few percent to a GW signal. These modifications are expected to be measurable in GW data with current detectors if the event is close enough and at a detectable frequency; or in future detectors with increased frequency range and amplitude sensitivity. Substantial use is made of computer algebra in these investigations. In setting the scene for our investigations, we trace the evolution of general relativity (GR) from Einstein's postulation in 1915 to vindication of his theory with the confirmation of the existence of GWs a century later. We discuss the implications of our results to current and future considerations. Calculations of GWs, both analytical and numerical, have normally assumed their propagation from source to a detector on Earth in a vacuum spacetime, and so discounted the effect of intervening matter. As we enter an era of precision GW measurements, it becomes important to quantify any effects due to propagation of GWs through a non-vacuum spacetime Observational confirmation of the modification effect that we and in astrophysical scenarios involving black holes (BHs), neutron stars (NSs) and CCSNe, would also enhance our understanding of the details of the physics of these bodies. , Thesis (PhD) -- Faculty of Science, Mathematics (Pure and Applied), 2021
- Full Text:
Application of machine learning, molecular modelling and structural data mining against antiretroviral drug resistance in HIV-1
- Sheik Amamuddy, Olivier Serge André
- Authors: Sheik Amamuddy, Olivier Serge André
- Date: 2020
- Subjects: Machine learning , Molecules -- Models , Data mining , Neural networks (Computer science) , Antiretroviral agents , Protease inhibitors , Drug resistance , Multidrug resistance , Molecular dynamics , Renin-angiotensin system , HIV (Viruses) -- South Africa , HIV (Viruses) -- Social aspects -- South Africa , South African Natural Compounds Database
- Language: English
- Type: text , Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/115964 , vital:34282
- Description: Millions are affected with the Human Immunodeficiency Virus (HIV) world wide, even though the death toll is on the decline. Antiretrovirals (ARVs), more specifically protease inhibitors have shown tremendous success since their introduction into therapy since the mid 1990’s by slowing down progression to the Acquired Immune Deficiency Syndrome (AIDS). However, Drug Resistance Mutations (DRMs) are constantly selected for due to viral adaptation, making drugs less effective over time. The current challenge is to manage the infection optimally with a limited set of drugs, with differing associated levels of toxicities in the face of a virus that (1) exists as a quasispecies, (2) may transmit acquired DRMs to drug-naive individuals and (3) that can manifest class-wide resistance due to similarities in design. The presence of latent reservoirs, unawareness of infection status, education and various socio-economic factors make the problem even more complex. Adequate timing and choice of drug prescription together with treatment adherence are very important as drug toxicities, drug failure and sub-optimal treatment regimens leave room for further development of drug resistance. While CD4 cell count and the determination of viral load from patients in resource-limited settings are very helpful to track how well a patient’s immune system is able to keep the virus in check, they can be lengthy in determining whether an ARV is effective. Phenosense assay kits answer this problem using viruses engineered to contain the patient sequences and evaluating their growth in the presence of different ARVs, but this can be expensive and too involved for routine checks. As a cheaper and faster alternative, genotypic assays provide similar information from HIV pol sequences obtained from blood samples, inferring ARV efficacy on the basis of drug resistance mutation patterns. However, these are inherently complex and the various methods of in silico prediction, such as Geno2pheno, REGA and Stanford HIVdb do not always agree in every case, even though this gap decreases as the list of resistance mutations is updated. A major gap in HIV treatment is that the information used for predicting drug resistance is mainly computed from data containing an overwhelming majority of B subtype HIV, when these only comprise about 12% of the worldwide HIV infections. In addition to growing evidence that drug resistance is subtype-related, it is intuitive to hypothesize that as subtyping is a phylogenetic classification, the more divergent a subtype is from the strains used in training prediction models, the less their resistance profiles would correlate. For the aforementioned reasons, we used a multi-faceted approach to attack the virus in multiple ways. This research aimed to (1) improve resistance prediction methods by focusing solely on the available subtype, (2) mine structural information pertaining to resistance in order to find any exploitable weak points and increase knowledge of the mechanistic processes of drug resistance in HIV protease. Finally, (3) we screen for protease inhibitors amongst a database of natural compounds [the South African natural compound database (SANCDB)] to find molecules or molecular properties usable to come up with improved inhibition against the drug target. In this work, structural information was mined using the Anisotropic Network Model, Dynamics Cross-Correlation, Perturbation Response Scanning, residue contact network analysis and the radius of gyration. These methods failed to give any resistance-associated patterns in terms of natural movement, internal correlated motions, residue perturbation response, relational behaviour and global compaction respectively. Applications of drug docking, homology-modelling and energy minimization for generating features suitable for machine-learning were not very promising, and rather suggest that the value of binding energies by themselves from Vina may not be very reliable quantitatively. All these failures lead to a refinement that resulted in a highly sensitive statistically-guided network construction and analysis, which leads to key findings in the early dynamics associated with resistance across all PI drugs. The latter experiment unravelled a conserved lateral expansion motion occurring at the flap elbows, and an associated contraction that drives the base of the dimerization domain towards the catalytic site’s floor in the case of drug resistance. Interestingly, we found that despite the conserved movement, bond angles were degenerate. Alongside, 16 Artificial Neural Network models were optimised for HIV proteases and reverse transcriptase inhibitors, with performances on par with Stanford HIVdb. Finally, we prioritised 9 compounds with potential protease inhibitory activity using virtual screening and molecular dynamics (MD) to additionally suggest a promising modification to one of the compounds. This yielded another molecule inhibiting equally well both opened and closed receptor target conformations, whereby each of the compounds had been selected against an array of multi-drug-resistant receptor variants. While a main hurdle was a lack of non-B subtype data, our findings, especially from the statistically-guided network analysis, may extrapolate to a certain extent to them as the level of conservation was very high within subtype B, despite all the present variations. This network construction method lays down a sensitive approach for analysing a pair of alternate phenotypes for which complex patterns prevail, given a sufficient number of experimental units. During the course of research a weighted contact mapping tool was developed to compare renin-angiotensinogen variants and packaged as part of the MD-TASK tool suite. Finally the functionality, compatibility and performance of the MODE-TASK tool were evaluated and confirmed for both Python2.7.x and Python3.x, for the analysis of normals modes from single protein structures and essential modes from MD trajectories. These techniques and tools collectively add onto the conventional means of MD analysis.
- Full Text:
- Authors: Sheik Amamuddy, Olivier Serge André
- Date: 2020
- Subjects: Machine learning , Molecules -- Models , Data mining , Neural networks (Computer science) , Antiretroviral agents , Protease inhibitors , Drug resistance , Multidrug resistance , Molecular dynamics , Renin-angiotensin system , HIV (Viruses) -- South Africa , HIV (Viruses) -- Social aspects -- South Africa , South African Natural Compounds Database
- Language: English
- Type: text , Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/115964 , vital:34282
- Description: Millions are affected with the Human Immunodeficiency Virus (HIV) world wide, even though the death toll is on the decline. Antiretrovirals (ARVs), more specifically protease inhibitors have shown tremendous success since their introduction into therapy since the mid 1990’s by slowing down progression to the Acquired Immune Deficiency Syndrome (AIDS). However, Drug Resistance Mutations (DRMs) are constantly selected for due to viral adaptation, making drugs less effective over time. The current challenge is to manage the infection optimally with a limited set of drugs, with differing associated levels of toxicities in the face of a virus that (1) exists as a quasispecies, (2) may transmit acquired DRMs to drug-naive individuals and (3) that can manifest class-wide resistance due to similarities in design. The presence of latent reservoirs, unawareness of infection status, education and various socio-economic factors make the problem even more complex. Adequate timing and choice of drug prescription together with treatment adherence are very important as drug toxicities, drug failure and sub-optimal treatment regimens leave room for further development of drug resistance. While CD4 cell count and the determination of viral load from patients in resource-limited settings are very helpful to track how well a patient’s immune system is able to keep the virus in check, they can be lengthy in determining whether an ARV is effective. Phenosense assay kits answer this problem using viruses engineered to contain the patient sequences and evaluating their growth in the presence of different ARVs, but this can be expensive and too involved for routine checks. As a cheaper and faster alternative, genotypic assays provide similar information from HIV pol sequences obtained from blood samples, inferring ARV efficacy on the basis of drug resistance mutation patterns. However, these are inherently complex and the various methods of in silico prediction, such as Geno2pheno, REGA and Stanford HIVdb do not always agree in every case, even though this gap decreases as the list of resistance mutations is updated. A major gap in HIV treatment is that the information used for predicting drug resistance is mainly computed from data containing an overwhelming majority of B subtype HIV, when these only comprise about 12% of the worldwide HIV infections. In addition to growing evidence that drug resistance is subtype-related, it is intuitive to hypothesize that as subtyping is a phylogenetic classification, the more divergent a subtype is from the strains used in training prediction models, the less their resistance profiles would correlate. For the aforementioned reasons, we used a multi-faceted approach to attack the virus in multiple ways. This research aimed to (1) improve resistance prediction methods by focusing solely on the available subtype, (2) mine structural information pertaining to resistance in order to find any exploitable weak points and increase knowledge of the mechanistic processes of drug resistance in HIV protease. Finally, (3) we screen for protease inhibitors amongst a database of natural compounds [the South African natural compound database (SANCDB)] to find molecules or molecular properties usable to come up with improved inhibition against the drug target. In this work, structural information was mined using the Anisotropic Network Model, Dynamics Cross-Correlation, Perturbation Response Scanning, residue contact network analysis and the radius of gyration. These methods failed to give any resistance-associated patterns in terms of natural movement, internal correlated motions, residue perturbation response, relational behaviour and global compaction respectively. Applications of drug docking, homology-modelling and energy minimization for generating features suitable for machine-learning were not very promising, and rather suggest that the value of binding energies by themselves from Vina may not be very reliable quantitatively. All these failures lead to a refinement that resulted in a highly sensitive statistically-guided network construction and analysis, which leads to key findings in the early dynamics associated with resistance across all PI drugs. The latter experiment unravelled a conserved lateral expansion motion occurring at the flap elbows, and an associated contraction that drives the base of the dimerization domain towards the catalytic site’s floor in the case of drug resistance. Interestingly, we found that despite the conserved movement, bond angles were degenerate. Alongside, 16 Artificial Neural Network models were optimised for HIV proteases and reverse transcriptase inhibitors, with performances on par with Stanford HIVdb. Finally, we prioritised 9 compounds with potential protease inhibitory activity using virtual screening and molecular dynamics (MD) to additionally suggest a promising modification to one of the compounds. This yielded another molecule inhibiting equally well both opened and closed receptor target conformations, whereby each of the compounds had been selected against an array of multi-drug-resistant receptor variants. While a main hurdle was a lack of non-B subtype data, our findings, especially from the statistically-guided network analysis, may extrapolate to a certain extent to them as the level of conservation was very high within subtype B, despite all the present variations. This network construction method lays down a sensitive approach for analysing a pair of alternate phenotypes for which complex patterns prevail, given a sufficient number of experimental units. During the course of research a weighted contact mapping tool was developed to compare renin-angiotensinogen variants and packaged as part of the MD-TASK tool suite. Finally the functionality, compatibility and performance of the MODE-TASK tool were evaluated and confirmed for both Python2.7.x and Python3.x, for the analysis of normals modes from single protein structures and essential modes from MD trajectories. These techniques and tools collectively add onto the conventional means of MD analysis.
- Full Text:
Development and evaluation of a web application employing artificial neural networks to facilitate the prediction of antiretroviral drug resistance in patients infected with HIV-1 subtype B
- Authors: Nabatanzi, Margaret
- Date: 2018
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/63396 , vital:28406
- Description: Expected release date-April 2019
- Full Text:
- Authors: Nabatanzi, Margaret
- Date: 2018
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/63396 , vital:28406
- Description: Expected release date-April 2019
- Full Text:
Observational cosmology with imperfect data
- Authors: Bester, Hertzog Landman
- Date: 2016
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/463 , vital:19961
- Description: We develop a formalism suitable to infer the background geometry of a general spherically symmetric dust universe directly from data on the past lightcone. This direct observational approach makes minimal assumptions about inaccessible parts of the Universe. The non-parametric and Bayesian framework we propose provides a very direct way to test one of the most fundamental underlying assumptions of concordance cosmology viz. the Copernican principle. We present the Copernicus algorithm for this purpose. By applying the algorithm to currently available data, we demonstrate that it is not yet possible to confirm or refute the validity of the Copernican principle within the proposed framework. This is followed by an investigation which aims to determine which future data will best be able to test the Copernican principle. Our results on simulated data suggest that, besides the need to improve the current data, it will be important to identify additional model independent observables for this purpose. The main difficulty with current data is their inability to constrain the value of the cosmological constant. We show how redshift drift data could be used to infer its value with minimal assumptions about the nature of the early Universe. We also discuss some alternative applications of the algorithm.
- Full Text:
- Authors: Bester, Hertzog Landman
- Date: 2016
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/463 , vital:19961
- Description: We develop a formalism suitable to infer the background geometry of a general spherically symmetric dust universe directly from data on the past lightcone. This direct observational approach makes minimal assumptions about inaccessible parts of the Universe. The non-parametric and Bayesian framework we propose provides a very direct way to test one of the most fundamental underlying assumptions of concordance cosmology viz. the Copernican principle. We present the Copernicus algorithm for this purpose. By applying the algorithm to currently available data, we demonstrate that it is not yet possible to confirm or refute the validity of the Copernican principle within the proposed framework. This is followed by an investigation which aims to determine which future data will best be able to test the Copernican principle. Our results on simulated data suggest that, besides the need to improve the current data, it will be important to identify additional model independent observables for this purpose. The main difficulty with current data is their inability to constrain the value of the cosmological constant. We show how redshift drift data could be used to infer its value with minimal assumptions about the nature of the early Universe. We also discuss some alternative applications of the algorithm.
- Full Text:
Numerical relativity on cosmological past null cones
- Van der Walt, Petrus Johannes
- Authors: Van der Walt, Petrus Johannes
- Date: 2013
- Subjects: Cosmology Numerical calculations General relativity (Physics) -- Mathematics Einstein field equations Gravity Gravitational waves Horizon
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:5396 , http://hdl.handle.net/10962/d1002959
- Description: The observational approach to cosmology is the endeavour to reconstruct the geometry of the Universe using only data that is theoretically verifiable within the causal boundaries of a cosmological observer. Using this approach, it was shown in [36] that given ideal cosmological observations, the only essential assumption necessary to determine the geometry of the Universe is a theory of gravity. Assuming General Relativity, the full set of Einstein field equations (EFEs) can be used to reconstruct the geometry of the Universe using direct observations on the past null cone (PNC) as initial conditions. Observationally and theoretically this is a very ambitious task and therefore, current developments have been restricted to spherically symmetric dust models while only relaxing the usual assumption of homogeneity in the radial direction. These restricted models are important for the development of theoretical foundations and also useful as verification models since they avoid the circularity of verifying what has already been assumed. The work presented in this thesis is the development of such a model where numerical relativity (NR) is used to simulate the observable universe. Similar to the work of Ellis and co-workers [36], a reference frame based on the PNC is used. The reference frame used here, however, is based on that of the characteristic formalism of NR, which has developed for calculating the propagation of gravitational waves. This provides a formalism that is well established in NR, making the use of existing algorithms possible. The Bondi-Sachs coordinates of the characteristic formalism is, however, not suitable for calculations beyond the observer apparent horizon (AH) since the diameter distance used as a radial coordinate becomes multi-valued when the cosmological PNC reconverges in the history of a universe, smaller in the past. With this taken into consideration, the Bondi-Sachs characteristic formalism is implemented for cosmology and the problem approaching the AH is investigated. Further developments address the limitations approaching the AH by introducing a metric based on the Bondi-Sachs metric where the radial coordinate is replaced with an affine parameter. The model is derived with a cosmological constant Λ incorporated into the EFEs where Λ is taken as a parameter of the theory of gravity rather than as a matter source term. Similar to the conventional characteristic formalism, this model consists of a system of differential equations for numerically evolving the EFEs as a characteristic initial value problem (CIVP). A numerical code implemented for the method has been found to be second order convergent. This code enables simulations of different models given identical data on the initial null cone and provides a method to investigate their physical consistency within the causally connected region of our current PNC. These developments closely follow existing 3D schemes developed for gravitational wave simulations, which should make it natural to extend the affine CIVP beyond spherical symmetric simulations. The developments presented in this thesis is an extended version of two papers published earlier.
- Full Text:
- Authors: Van der Walt, Petrus Johannes
- Date: 2013
- Subjects: Cosmology Numerical calculations General relativity (Physics) -- Mathematics Einstein field equations Gravity Gravitational waves Horizon
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:5396 , http://hdl.handle.net/10962/d1002959
- Description: The observational approach to cosmology is the endeavour to reconstruct the geometry of the Universe using only data that is theoretically verifiable within the causal boundaries of a cosmological observer. Using this approach, it was shown in [36] that given ideal cosmological observations, the only essential assumption necessary to determine the geometry of the Universe is a theory of gravity. Assuming General Relativity, the full set of Einstein field equations (EFEs) can be used to reconstruct the geometry of the Universe using direct observations on the past null cone (PNC) as initial conditions. Observationally and theoretically this is a very ambitious task and therefore, current developments have been restricted to spherically symmetric dust models while only relaxing the usual assumption of homogeneity in the radial direction. These restricted models are important for the development of theoretical foundations and also useful as verification models since they avoid the circularity of verifying what has already been assumed. The work presented in this thesis is the development of such a model where numerical relativity (NR) is used to simulate the observable universe. Similar to the work of Ellis and co-workers [36], a reference frame based on the PNC is used. The reference frame used here, however, is based on that of the characteristic formalism of NR, which has developed for calculating the propagation of gravitational waves. This provides a formalism that is well established in NR, making the use of existing algorithms possible. The Bondi-Sachs coordinates of the characteristic formalism is, however, not suitable for calculations beyond the observer apparent horizon (AH) since the diameter distance used as a radial coordinate becomes multi-valued when the cosmological PNC reconverges in the history of a universe, smaller in the past. With this taken into consideration, the Bondi-Sachs characteristic formalism is implemented for cosmology and the problem approaching the AH is investigated. Further developments address the limitations approaching the AH by introducing a metric based on the Bondi-Sachs metric where the radial coordinate is replaced with an affine parameter. The model is derived with a cosmological constant Λ incorporated into the EFEs where Λ is taken as a parameter of the theory of gravity rather than as a matter source term. Similar to the conventional characteristic formalism, this model consists of a system of differential equations for numerically evolving the EFEs as a characteristic initial value problem (CIVP). A numerical code implemented for the method has been found to be second order convergent. This code enables simulations of different models given identical data on the initial null cone and provides a method to investigate their physical consistency within the causally connected region of our current PNC. These developments closely follow existing 3D schemes developed for gravitational wave simulations, which should make it natural to extend the affine CIVP beyond spherical symmetric simulations. The developments presented in this thesis is an extended version of two papers published earlier.
- Full Text:
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