• Effect of Si-doped InGaN underlayers on photoluminescence efficiency and recombination dynamics in InGaN/GaN quantum wells

      Church, S A; Christian, G M; Barrett, R M; orcid: 0000-0001-8512-0930; Hammersley, S; Kappers, M J; Frentrup, M; Oliver, R A; Binks, D J; email: david.binks@manchester.ac.uk (IOP Publishing, 2021-09-10)
      Abstract: A series of single InGaN/GaN quantum wells (QWs) with a Si-doped InGaN underlayer were studied to investigate the impact of the underlayer on photoluminescence efficiency and recombination dynamics. The thickness of the GaN capping layer was varied between samples, which changed the electric field across the QW due to band bending near the surface. When directly exciting the wells, thermionic emission of carriers results in a rapid drop in the photoluminesence efficiency with increasing temperature such that no emission is observed above 100 K. However, exciting above the energy of the barriers caused the intensity of the QW emission to drop more slowly, with up to 12% of the 10 K emission intensity remaining at 300 K. This difference is attributed to hole transfer from the underlayer into the QW, which increases in efficiency at higher temperatures, and is enhanced by stronger electric fields present in the GaN barriers of samples with thinner GaN capping layers. Further, the sample with the narrowest cap layer of 2 nm has a different shape and characteristic time for its photoluminescence decay transient and a different emission energy temperature dependence than the other samples. This behaviour was ascribed to a change in carrier localisation for this sample due to a reversal of the net field across the well compared to the other samples.
    • Effect of Si-doped InGaN underlayers on photoluminescence efficiency and recombination dynamics in InGaN/GaN quantum wells

      Church, S A; Christian, G M; Barrett, R M; orcid: 0000-0001-8512-0930; Hammersley, S; Kappers, M J; Frentrup, M; Oliver, R A; Binks, D J; email: david.binks@manchester.ac.uk (IOP Publishing, 2021-09-10)
      Abstract: A series of single InGaN/GaN quantum wells (QWs) with a Si-doped InGaN underlayer were studied to investigate the impact of the underlayer on photoluminescence efficiency and recombination dynamics. The thickness of the GaN capping layer was varied between samples, which changed the electric field across the QW due to band bending near the surface. When directly exciting the wells, thermionic emission of carriers results in a rapid drop in the photoluminesence efficiency with increasing temperature such that no emission is observed above 100 K. However, exciting above the energy of the barriers caused the intensity of the QW emission to drop more slowly, with up to 12% of the 10 K emission intensity remaining at 300 K. This difference is attributed to hole transfer from the underlayer into the QW, which increases in efficiency at higher temperatures, and is enhanced by stronger electric fields present in the GaN barriers of samples with thinner GaN capping layers. Further, the sample with the narrowest cap layer of 2 nm has a different shape and characteristic time for its photoluminescence decay transient and a different emission energy temperature dependence than the other samples. This behaviour was ascribed to a change in carrier localisation for this sample due to a reversal of the net field across the well compared to the other samples.
    • Hidden dynamics for piecewise smooth maps

      Glendinning, Paul; orcid: 0000-0003-1544-9161; email: p.a.glendinning@manchester.ac.uk; Jeffrey, Mike R; orcid: 0000-0002-3325-7211; email: mike.jeffrey@bristol.ac.uk (IOP Publishing, 2021-05-07)
      Abstract: We develop a hidden dynamics formulation of regularisation for piecewise smooth maps. This involves blowing up the discontinuity into an interval, but in contrast to piecewise smooth flows every preimage of the discontinuity needs to be blown up as well. This results in a construction similar to classic approaches to the Denjoy counterexample.
    • Hidden dynamics for piecewise smooth maps

      Glendinning, Paul; orcid: 0000-0003-1544-9161; email: p.a.glendinning@manchester.ac.uk; Jeffrey, Mike R; orcid: 0000-0002-3325-7211; email: mike.jeffrey@bristol.ac.uk (IOP Publishing, 2021-05-07)
      Abstract: We develop a hidden dynamics formulation of regularisation for piecewise smooth maps. This involves blowing up the discontinuity into an interval, but in contrast to piecewise smooth flows every preimage of the discontinuity needs to be blown up as well. This results in a construction similar to classic approaches to the Denjoy counterexample.
    • High temperature magnetic characterisation of structural steels using Epstein frame

      Wilson, John W; orcid: 0000-0003-2139-1250; email: john.wilson@manchester.ac.uk; Zhou, Lei; Davis, Claire L; Peyton, Anthony J (IOP Publishing, 2021-08-23)
      Abstract: Electromagnetic non-destructive testing techniques provide an attractive solution to the problem of monitoring microstructural changes in steels undergoing heat treatment as they are non-contact, have a short response time and are relatively inexpensive. However, to take full advantage of these techniques it is necessary to be able accurately measure the magnetisation characteristics of the materials of interest at temperatures up to the Curie point. This paper details the development of a novel high temperature Epstein frame for installation in a furnace with the design informed and results validated by finite element modelling. Hysteresis loop characteristics are successfully measured for a dual phase steel up to the Curie point for heating and cooling. Results show the developed system has the potential to provide valuable data to inform online electromagnetic monitoring systems.
    • High temperature magnetic characterisation of structural steels using Epstein frame

      Wilson, John W; orcid: 0000-0003-2139-1250; email: john.wilson@manchester.ac.uk; Zhou, Lei; Davis, Claire L; Peyton, Anthony J (IOP Publishing, 2021-08-23)
      Abstract: Electromagnetic non-destructive testing techniques provide an attractive solution to the problem of monitoring microstructural changes in steels undergoing heat treatment as they are non-contact, have a short response time and are relatively inexpensive. However, to take full advantage of these techniques it is necessary to be able accurately measure the magnetisation characteristics of the materials of interest at temperatures up to the Curie point. This paper details the development of a novel high temperature Epstein frame for installation in a furnace with the design informed and results validated by finite element modelling. Hysteresis loop characteristics are successfully measured for a dual phase steel up to the Curie point for heating and cooling. Results show the developed system has the potential to provide valuable data to inform online electromagnetic monitoring systems.
    • Ice-templated hybrid graphene oxide—graphene nanoplatelet lamellar architectures: tuning mechanical and electrical properties

      Yang, Pei; orcid: 0000-0002-4639-2076; Tontini, Gustavo; orcid: 0000-0002-2453-6358; email: gustavotontini@gmail.com; Wang, Jiacheng; orcid: 0000-0001-7301-3310; Kinloch, Ian A; orcid: 0000-0003-3314-6869; Barg, Suelen; orcid: 0000-0002-0723-7081; email: Suelen.Barg@manchester.ac.uk (IOP Publishing, 2021-02-23)
      Abstract: The traditional freeze-casting route for processing graphene-based aerogels is generally restricted to aqueously dispersed flakes of graphene oxide (GO) and post-processing reduction treatments, which brings restrictions to the aerogels electrical properties. In this work, we report a versatile aqueous processing route that uses the ability of GO todisperse graphene nanoplatelets (GNP) to produce rGO-GNP lamellar aerogels via unidirectional freeze-casting. In order to optimise the properties of the aerogel, GO-GNP dispersions were partially reduced by L-ascorbic acid prior to freeze-casting to tune the carbon and oxygen (C/O) ratio. The aerogels were then heat treated after casting to fully reduce the GO. The chemical reduction time was found to control the microstructure of the resulting aeorgels and thus to tune their electrical and mechanical properties. An rGO-GNP lamellar aerogel with density of 20.8 ± 0.8 mg cm−3 reducing using a reduction of 60 min achieved an electrical conductivity of 42.3 S m−1. On the other hand, an optimal reduction time of 35 min led to an aerogel with compressive modulus of 0.51 ±0.06 MPa at a density of 23.2 ± 0.7 mg cm−3, revealing a compromise between the tuning of electrical and mechanical properties. We show the present processing route can also be easily applied to produce lamellar aerogels on other graphene-based materials such as electrochemically exfoliated graphene.
    • Ice-templated hybrid graphene oxide—graphene nanoplatelet lamellar architectures: tuning mechanical and electrical properties

      Yang, Pei; orcid: 0000-0002-4639-2076; Tontini, Gustavo; orcid: 0000-0002-2453-6358; email: gustavotontini@gmail.com; Wang, Jiacheng; orcid: 0000-0001-7301-3310; Kinloch, Ian A; orcid: 0000-0003-3314-6869; Barg, Suelen; orcid: 0000-0002-0723-7081; email: Suelen.Barg@manchester.ac.uk (IOP Publishing, 2021-02-23)
      Abstract: The traditional freeze-casting route for processing graphene-based aerogels is generally restricted to aqueously dispersed flakes of graphene oxide (GO) and post-processing reduction treatments, which brings restrictions to the aerogels electrical properties. In this work, we report a versatile aqueous processing route that uses the ability of GO todisperse graphene nanoplatelets (GNP) to produce rGO-GNP lamellar aerogels via unidirectional freeze-casting. In order to optimise the properties of the aerogel, GO-GNP dispersions were partially reduced by L-ascorbic acid prior to freeze-casting to tune the carbon and oxygen (C/O) ratio. The aerogels were then heat treated after casting to fully reduce the GO. The chemical reduction time was found to control the microstructure of the resulting aeorgels and thus to tune their electrical and mechanical properties. An rGO-GNP lamellar aerogel with density of 20.8 ± 0.8 mg cm−3 reducing using a reduction of 60 min achieved an electrical conductivity of 42.3 S m−1. On the other hand, an optimal reduction time of 35 min led to an aerogel with compressive modulus of 0.51 ±0.06 MPa at a density of 23.2 ± 0.7 mg cm−3, revealing a compromise between the tuning of electrical and mechanical properties. We show the present processing route can also be easily applied to produce lamellar aerogels on other graphene-based materials such as electrochemically exfoliated graphene.
    • Interlayer and interfacial stress transfer in hBN nanosheets

      Wang, Weimiao; Li, Zheling; orcid: 0000-0001-8412-0234; Marsden, Alex J; orcid: 0000-0002-3017-1754; Bissett, Mark A; orcid: 0000-0002-8908-7960; Young, Robert J; orcid: 0000-0001-6073-9489; email: robert.young@manchester.ac.uk (IOP Publishing, 2021-06-30)
      Abstract: Stress transfer has been investigated for exfoliated hexagonal boron nitride (hBN) nanosheets (BNNSs) through the use of Raman spectroscopy. Single BNNSs of different thicknesses of up to 100 nm (300 layers) were deposited upon a poly(methyl methacrylate) (PMMA) substrate and deformed in unixial tension. The Raman spectra from the BNNSs were relatively weak compared to graphene, but the in-plane E2g Raman mode (the G band) could be distinguished from the spectrum of the PMMA substrate. It was found that G band down-shifted during tensile deformation and that the rate of band shift per unit strain decreased as the thickness of the BNNSs increased, as is found for multi-layer graphene. The efficiency of internal stress transfer between the different hBN layers was found to be of the order of 99% compared to 60%–80% for graphene, as a result of the stronger bonding between the hBN layers in the BNNSs. The reduction in bandshift rate can be related to the effective Young’s modulus of the 2D material in a nanocomposites and the findings show that it would be expected that even 100 layer BNNSs should have a Young’s modulus of more than half that of hBN monolayer. Interfacial stress transfer between a single hBN nanosheet and the PMMA substrate has been evaluated using shear lag theory. It is found that the interfacial shear stress between the BNNS and the substrate is of the order of 10 MPa, a factor of around 4 higher than that for a graphene monolayer. These findings imply that BNNSs should give better mechanical reinforcement than graphene in polymer-based nanocomposites as a result of good internal interlayer stress transfer within the nanosheets and better interfacial stress transfer to the polymer matrix.
    • Interlayer and interfacial stress transfer in hBN nanosheets

      Wang, Weimiao; Li, Zheling; orcid: 0000-0001-8412-0234; Marsden, Alex J; orcid: 0000-0002-3017-1754; Bissett, Mark A; orcid: 0000-0002-8908-7960; Young, Robert J; orcid: 0000-0001-6073-9489; email: robert.young@manchester.ac.uk (IOP Publishing, 2021-06-30)
      Abstract: Stress transfer has been investigated for exfoliated hexagonal boron nitride (hBN) nanosheets (BNNSs) through the use of Raman spectroscopy. Single BNNSs of different thicknesses of up to 100 nm (300 layers) were deposited upon a poly(methyl methacrylate) (PMMA) substrate and deformed in unixial tension. The Raman spectra from the BNNSs were relatively weak compared to graphene, but the in-plane E2g Raman mode (the G band) could be distinguished from the spectrum of the PMMA substrate. It was found that G band down-shifted during tensile deformation and that the rate of band shift per unit strain decreased as the thickness of the BNNSs increased, as is found for multi-layer graphene. The efficiency of internal stress transfer between the different hBN layers was found to be of the order of 99% compared to 60%–80% for graphene, as a result of the stronger bonding between the hBN layers in the BNNSs. The reduction in bandshift rate can be related to the effective Young’s modulus of the 2D material in a nanocomposites and the findings show that it would be expected that even 100 layer BNNSs should have a Young’s modulus of more than half that of hBN monolayer. Interfacial stress transfer between a single hBN nanosheet and the PMMA substrate has been evaluated using shear lag theory. It is found that the interfacial shear stress between the BNNS and the substrate is of the order of 10 MPa, a factor of around 4 higher than that for a graphene monolayer. These findings imply that BNNSs should give better mechanical reinforcement than graphene in polymer-based nanocomposites as a result of good internal interlayer stress transfer within the nanosheets and better interfacial stress transfer to the polymer matrix.
    • Nanometre imaging of Fe 3 GeTe 2 ferromagnetic domain walls

      Hopkinson, David G; orcid: 0000-0003-4259-7450; Seki, Takehito; Clark, Nicholas; Chen, Runze; Zou, Yichao; Kimura, Ayumi; Gorbachev, Roman V; Thomson, Thomas; Shibata, Naoya; Haigh, Sarah J; orcid: 0000-0001-5509-6706; email: sarah.haigh@manchester.ac.uk (IOP Publishing, 2021-02-23)
      Abstract: Fe3GeTe2 is a layered crystal which has recently been shown to maintain its itinerant ferromagnetic properties even when atomically thin. Here, differential phase contrast scanning transmission electron microscopy is used to investigate the domain structure in a Fe3GeTe2 cross-sectional lamella at temperatures ranging from 95 to 250 K and at nanometre spatial resolution. Below the experimentally determined Curie temperature (T C) of 191 K, stripe domains magnetised along 〈0001〉, bounded with 180◦ Bloch type domain walls, are observed, transitioning to mixed Bloch−Néel type where the cross-sectional thickness is reduced below 50 nm. When warming towards T C, these domains undergo slight restructuring towards uniform size, before abruptly fading at T C. Localised loss of ferromagnetic order is seen over time, hypothesised to be a frustration of ferromagnetic order from ambient oxidation and basal cracking, which could enable selective modification of the magnetic properties for device applications.
    • Nanometre imaging of Fe 3 GeTe 2 ferromagnetic domain walls

      Hopkinson, David G; orcid: 0000-0003-4259-7450; Seki, Takehito; Clark, Nicholas; Chen, Runze; Zou, Yichao; Kimura, Ayumi; Gorbachev, Roman V; Thomson, Thomas; Shibata, Naoya; Haigh, Sarah J; orcid: 0000-0001-5509-6706; email: sarah.haigh@manchester.ac.uk (IOP Publishing, 2021-02-23)
      Abstract: Fe3GeTe2 is a layered crystal which has recently been shown to maintain its itinerant ferromagnetic properties even when atomically thin. Here, differential phase contrast scanning transmission electron microscopy is used to investigate the domain structure in a Fe3GeTe2 cross-sectional lamella at temperatures ranging from 95 to 250 K and at nanometre spatial resolution. Below the experimentally determined Curie temperature (T C) of 191 K, stripe domains magnetised along 〈0001〉, bounded with 180◦ Bloch type domain walls, are observed, transitioning to mixed Bloch−Néel type where the cross-sectional thickness is reduced below 50 nm. When warming towards T C, these domains undergo slight restructuring towards uniform size, before abruptly fading at T C. Localised loss of ferromagnetic order is seen over time, hypothesised to be a frustration of ferromagnetic order from ambient oxidation and basal cracking, which could enable selective modification of the magnetic properties for device applications.
    • Optimising use of 4D-CT phase information for radiomics analysis in lung cancer patients treated with stereotactic body radiotherapy

      Davey, Angela; orcid: 0000-0002-8377-5113; email: angela.davey@postgrad.manchester.ac.uk; van Herk, Marcel; Faivre-Finn, Corinne; Brown, Sean; McWilliam, Alan (IOP Publishing, 2021-05-24)
      Abstract: Purpose. 4D-CT is routine imaging for lung cancer patients treated with stereotactic body radiotherapy. No studies have investigated optimal 4D phase selection for radiomics. We aim to determine how phase data should be used to identify prognostic biomarkers for distant failure, and test whether stability assessment is required. A phase selection approach will be developed to aid studies with different 4D protocols and account for patient differences. Methods. 186 features were extracted from the tumour and peritumour on all phases for 258 patients. Feature values were selected from phase features using four methods: (A) mean across phases, (B) median across phases, (C) 50% phase, and (D) the most stable phase (closest in value to two neighbours), coined personalised selection. Four levels of stability assessment were also analysed, with inclusion of: (1) all features, (2) stable features across all phases, (3) stable features across phase and neighbour phases, and (4) features averaged over neighbour phases. Clinical-radiomics models were built for twelve combinations of feature type and assessment method. Model performance was assessed by concordance index (c-index) and fraction of new information from radiomic features. Results. The most stable phase spanned the whole range but was most often near exhale. All radiomic signatures provided new information for distant failure prediction. The personalised model had the highest c-index (0.77), and 58% of new information was provided by radiomic features when no stability assessment was performed. Conclusion. The most stable phase varies per-patient and selecting this improves model performance compared to standard methods. We advise the single most stable phase should be determined by minimising feature differences to neighbour phases. Stability assessment over all phases decreases performance by excessively removing features. Instead, averaging of neighbour phases should be used when stability is of concern. The models suggest that higher peritumoural intensity predicts distant failure.
    • Optimising use of 4D-CT phase information for radiomics analysis in lung cancer patients treated with stereotactic body radiotherapy

      Davey, Angela; orcid: 0000-0002-8377-5113; email: angela.davey@postgrad.manchester.ac.uk; van Herk, Marcel; Faivre-Finn, Corinne; Brown, Sean; McWilliam, Alan (IOP Publishing, 2021-05-24)
      Abstract: Purpose. 4D-CT is routine imaging for lung cancer patients treated with stereotactic body radiotherapy. No studies have investigated optimal 4D phase selection for radiomics. We aim to determine how phase data should be used to identify prognostic biomarkers for distant failure, and test whether stability assessment is required. A phase selection approach will be developed to aid studies with different 4D protocols and account for patient differences. Methods. 186 features were extracted from the tumour and peritumour on all phases for 258 patients. Feature values were selected from phase features using four methods: (A) mean across phases, (B) median across phases, (C) 50% phase, and (D) the most stable phase (closest in value to two neighbours), coined personalised selection. Four levels of stability assessment were also analysed, with inclusion of: (1) all features, (2) stable features across all phases, (3) stable features across phase and neighbour phases, and (4) features averaged over neighbour phases. Clinical-radiomics models were built for twelve combinations of feature type and assessment method. Model performance was assessed by concordance index (c-index) and fraction of new information from radiomic features. Results. The most stable phase spanned the whole range but was most often near exhale. All radiomic signatures provided new information for distant failure prediction. The personalised model had the highest c-index (0.77), and 58% of new information was provided by radiomic features when no stability assessment was performed. Conclusion. The most stable phase varies per-patient and selecting this improves model performance compared to standard methods. We advise the single most stable phase should be determined by minimising feature differences to neighbour phases. Stability assessment over all phases decreases performance by excessively removing features. Instead, averaging of neighbour phases should be used when stability is of concern. The models suggest that higher peritumoural intensity predicts distant failure.
    • Research on Water Quality Monitoring and Evaluation System under Agricultural Irrigation Automation

      Shen, Xinrui; email: xinrui.shen@postgrad.manchester.ac.uk (IOP Publishing, 2021-09)
      Abstract: In order to timely grasp the status and change trend of the irrigated agricultural water environment, we refer to the farmland irrigation water quality evaluation standards, and select 11 monitoring items in different basins to monitor the agricultural irrigation water quality for 2 consecutive years. The article uses the pollution index method to evaluate the monitoring results. The results show that the comprehensive pollution index of surface irrigation water and underground irrigation water quality is less than 1, but there is a rising trend; the concentration of some pollutants in the irrigation return water is higher than that of the irrigation water, and some individual indicators exceed the standard, but they do not constitute comprehensive pollution. Finally, through the design of the remote sensing image water quality monitoring and evaluation system (RWQMES), the unified management of the three functions of water quality remote sensing image analysis and processing, water quality prediction and evaluation is realized.
    • Research on Water Quality Monitoring and Evaluation System under Agricultural Irrigation Automation

      Shen, Xinrui; email: xinrui.shen@postgrad.manchester.ac.uk (IOP Publishing, 2021-09)
      Abstract: In order to timely grasp the status and change trend of the irrigated agricultural water environment, we refer to the farmland irrigation water quality evaluation standards, and select 11 monitoring items in different basins to monitor the agricultural irrigation water quality for 2 consecutive years. The article uses the pollution index method to evaluate the monitoring results. The results show that the comprehensive pollution index of surface irrigation water and underground irrigation water quality is less than 1, but there is a rising trend; the concentration of some pollutants in the irrigation return water is higher than that of the irrigation water, and some individual indicators exceed the standard, but they do not constitute comprehensive pollution. Finally, through the design of the remote sensing image water quality monitoring and evaluation system (RWQMES), the unified management of the three functions of water quality remote sensing image analysis and processing, water quality prediction and evaluation is realized.
    • Single step synthesis of WO 3 nanoparticles by wire explosion process and its photocatalytic behaviour

      Ranjan, Prem; orcid: 0000-0001-7840-9904; email: prem.ranjan@manchester.ac.uk; Suematsu, H.; Sarathi, R. (IOP Publishing, 2021-05-11)
      Tungsten (W) wires are exploded in oxygen ambience to get tungsten oxide (WO3) nanoparticles (NPs). Energy stored in the capacitors (EC) is used to overcome the sublimation energy of wire. Energy ratio (K, ratio of EC and sublimation energy) and oxygen pressure (P) are two control parameters for the particle phase and morphology in the wire explosion process. X-ray diffraction (XRD) patterns confirmed the partial oxidation of W for low values of K. For K = 2, oxidation increases with increase in P. For K = 10, complete oxidation was achieved irrespective of P. Particles are spherical in shape as observed from scanning electron microscope (SEM) and transmission electron microscope (TEM) micrographs. Particle size follows a log-normal distribution with a least mean size of 24.1 nm. UV-vis diffuse reflectance spectroscopy (DRS) was used to measure the absorbance of NPs (complete WO3 with least mean size) for band gap measurement. The band gap was found to be 2.92 eV (visible region). NPs are used as photocatalyst to degrade aqueous solution of methylene blue (MB) under visible light irradiation. 500 mg l−1 of WO3 NPs were optimum to degrade 10 mg l−1 MB in 120 min.
    • Single step synthesis of WO 3 nanoparticles by wire explosion process and its photocatalytic behaviour

      Ranjan, Prem; orcid: 0000-0001-7840-9904; email: prem.ranjan@manchester.ac.uk; Suematsu, H.; Sarathi, R. (IOP Publishing, 2021-05-11)
      Tungsten (W) wires are exploded in oxygen ambience to get tungsten oxide (WO3) nanoparticles (NPs). Energy stored in the capacitors (EC) is used to overcome the sublimation energy of wire. Energy ratio (K, ratio of EC and sublimation energy) and oxygen pressure (P) are two control parameters for the particle phase and morphology in the wire explosion process. X-ray diffraction (XRD) patterns confirmed the partial oxidation of W for low values of K. For K = 2, oxidation increases with increase in P. For K = 10, complete oxidation was achieved irrespective of P. Particles are spherical in shape as observed from scanning electron microscope (SEM) and transmission electron microscope (TEM) micrographs. Particle size follows a log-normal distribution with a least mean size of 24.1 nm. UV-vis diffuse reflectance spectroscopy (DRS) was used to measure the absorbance of NPs (complete WO3 with least mean size) for band gap measurement. The band gap was found to be 2.92 eV (visible region). NPs are used as photocatalyst to degrade aqueous solution of methylene blue (MB) under visible light irradiation. 500 mg l−1 of WO3 NPs were optimum to degrade 10 mg l−1 MB in 120 min.
    • The unequal-time matter power spectrum: impact on weak lensing observables

      de la Bella, Lucia F.; email: lucia.fonsecadelabella@manchester.ac.uk; Tessore, Nicolas; email: n.tessore@ucl.ac.uk; Bridle, Sarah; email: sarah.bridle@manchester.ac.uk (IOP Publishing, 2021-08-02)
      Abstract: We investigate the impact of a common approximation of weak lensing power spectra: the use of single-epoch matter power spectra in integrals over redshift. We disentangle this from the closely connected Limber's approximation. We derive the unequal-time matter power spectrum at one-loop in standard perturbation theory and effective field theory to deal with non-linear physics. We compare these formalisms and conclude that the unequal-time power spectrum using effective field theory breaks for larger scales. As an alternative we introduce the midpoint approximation. We also provide, for the first time, a fitting function for the time evolution of the effective field theory counterterms based on the Quijote simulations. Then we compute the angular power spectrum using a range of approaches: the Limber approximation, and the geometric and midpoint approximations. We compare our results with the exact calculation at all angular scales using the unequal-time power spectrum. We use DES Y1 and LSST-like redshift distributions for our analysis. We find that the use of the Limber's approximation in weak lensing diverges from the exact calculation of the angular power spectrum on large-angle separations, ℓ < 10. Even though this deviation is of order 2% maximum for cosmic lensing, we find the biggest effect for galaxy clustering and galaxy-galaxy lensing. We show that not only is this true for upcoming galaxy surveys, but also for current data such as DES Y1. Finally, we make our pipeline and analysis publicly available as a Python package called unequalpy.
    • The unequal-time matter power spectrum: impact on weak lensing observables

      de la Bella, Lucia F.; email: lucia.fonsecadelabella@manchester.ac.uk; Tessore, Nicolas; email: n.tessore@ucl.ac.uk; Bridle, Sarah; email: sarah.bridle@manchester.ac.uk (IOP Publishing, 2021-08-02)
      Abstract: We investigate the impact of a common approximation of weak lensing power spectra: the use of single-epoch matter power spectra in integrals over redshift. We disentangle this from the closely connected Limber's approximation. We derive the unequal-time matter power spectrum at one-loop in standard perturbation theory and effective field theory to deal with non-linear physics. We compare these formalisms and conclude that the unequal-time power spectrum using effective field theory breaks for larger scales. As an alternative we introduce the midpoint approximation. We also provide, for the first time, a fitting function for the time evolution of the effective field theory counterterms based on the Quijote simulations. Then we compute the angular power spectrum using a range of approaches: the Limber approximation, and the geometric and midpoint approximations. We compare our results with the exact calculation at all angular scales using the unequal-time power spectrum. We use DES Y1 and LSST-like redshift distributions for our analysis. We find that the use of the Limber's approximation in weak lensing diverges from the exact calculation of the angular power spectrum on large-angle separations, ℓ < 10. Even though this deviation is of order 2% maximum for cosmic lensing, we find the biggest effect for galaxy clustering and galaxy-galaxy lensing. We show that not only is this true for upcoming galaxy surveys, but also for current data such as DES Y1. Finally, we make our pipeline and analysis publicly available as a Python package called unequalpy.