Scientific usage of the Pencil Code
A search using ADS (https://ui.adsabs.harvard.edu/) lists the papers in which the PENCIL CODE is being quoted. In the following we present the papers that are making use of the code either for their own scientific work of those authors, or for code comparison purposes. We include conference proceedings, which make up 15–20% of all papers. We classify the references by year and by topic, although the topics are often overlapping. The primary application of the PENCIL CODE lies in astrophysics, in which case we classify the papers mostly by the field of research. Additional applications can also be found in meteorology and combustion.
Fig. 3 Number of papers since 2003 that make use of the PENCIL CODE. In blue are shown the papers that are not co-authored by Brandenburg, in green the number of papers that reference it for code comparison or other purposes, and in red the number of papers that are not yet classified by topic. The enhanced number of papers during 2011–2013 results from publications related to his ERC Advanced Grant.
Papers by year
As of June 2026, the Pencil Code has been used for a total of 792 research papers; see Fig. 3; 437 of those are papers (55%) are not co-authored by Brandenburg (blue line), while 55 of them (6%) are unclassified (red line). In addition, 136 papers reference it for code comparison or other purposes (green line).
24 times in 2026: Anandavijayan & Bhat (2026), Baronett et al. (2026), Brandenburg et al. (2026), Caprini (2026), Eriksson et al. (2026), Gent et al. (2026), Ghosh et al. (2026), Godines et al. (2026), Haugen et al. (2026), Klahr et al. (2026), Käpylä (2026), Leidi et al. (2026), Luo et al. (2026), Maity et al. (2026), Mondal et al. (2026), Mondal & Singh (2026), Mtchedlidze et al. (2026), Muhammed Irshad et al. (2026), Rabus & Mkanda (2026), Schober et al. (2026), Sharma et al. (2026), Vemareddy et al. (2026), Zhang & Brandenburg (2026), von Eckardstein et al. (2026)
53 times in 2025: Baehr et al. (2025), Brandenburg et al. (2025a), Brandenburg et al. (2025b), Brandenburg et al. (2025c), Brandenburg et al. (2025d), Brandenburg et al. (2025e), Brandenburg & Banerjee (2025), Brandenburg & Ntormousi (2025), Brandenburg & Scannapieco (2025), Brandenburg & Vishniac (2025), Buchner (2025a), Dehman & Brandenburg (2025), Elias-López (2025), Eriksson et al. (2025), Gent et al. (2025), Ghosh et al. (2025), Godines et al. (2025), Gurgenidze et al. (2025), Hidalgo et al. (2025), Hosking et al. (2025), Iarygina et al. (2025), Kishore & Singh (2025a), Kishore & Singh (2025b), Koshikumo et al. (2025a), Koshikumo et al. (2025b), Käpylä (2025), Lipatnikov & Sabelnikov (2025), Meftah (2025), Mondal et al. (2025), Mtchedlidze et al. (2025), Pandey & Bourdin (2025), Park (2025a), Park (2025b), Qazi et al. (2025a), Qazi et al. (2025b), Rice et al. (2025), Rogachevskii et al. (2025), Roper Pol & Salvino Midiri (2025), Sabelnikov et al. (2025), Sharma et al. (2025b), Shchutskyi et al. (2025), Shi et al. (2025), Singh et al. (2025a), Singh et al. (2025b), Skalidis et al. (2025), Srivastava et al. (2025a), Srivastava et al. (2025b), Tschernitz & Bourdin (2025a), Tschernitz & Bourdin (2025b), Vachaspati & Brandenburg (2025), Warnecke et al. (2025), Yuvraj et al. (2025), Zhang & Brandenburg (2025)
38 times in 2024: Brandenburg et al. (2024a), Brandenburg et al. (2024b), Brandenburg et al. (2024c), Candelaresi & Del Sordo (2024), Cañas et al. (2024), Dey et al. (2024), Dwivedi et al. (2024), Elias-López et al. (2024), Gent et al. (2024), Hackman et al. (2024), Hidalgo et al. (2024), Iarygina et al. (2024), Kesri et al. (2024), Kirchschlager et al. (2024), Kishore et al. (2024), Korpi-Lagg et al. (2024), Käpylä (2024), Lipatnikov (2024a), Lipatnikov (2024b), Lyra et al. (2024), Maity et al. (2024a), Maity et al. (2024b), Mtchedlidze et al. (2024), Qazi et al. (2024), Saieed & Hickey (2024), Sankar Maity et al. (2024), Schober et al. (2024a), Schober et al. (2024b), Schäfer et al. (2024), Sengupta et al. (2024), Vashishth (2024), Vemareddy (2024), Vemareddy et al. (2024), Wang et al. (2024), Zhou (2024), Zhou & Blackman (2024), Zhou & Jingade (2024), Zhou & Lai (2024)
39 times in 2023: Brandenburg (2023a), Brandenburg (2023b), Brandenburg et al. (2023a), Brandenburg et al. (2023b), Brandenburg et al. (2023c), Brandenburg et al. (2023d), Brandenburg et al. (2023e), Brandenburg & Larsson (2023), Brandenburg & Protiti (2023), Candelaresi & Beck (2023), Carenza et al. (2023), Elias-López et al. (2023), Ganti et al. (2023), Gent et al. (2023), He et al. (2023), Hidalgo et al. (2023), Karak (2023), Käpylä (2023a), Käpylä (2023b), Käpylä et al. (2023), Lipatnikov & Sabelnikov (2023), Lyra (2023), Meftah (2023), Mizerski et al. (2023), Mondal & Bhat (2023), Mtchedlidze et al. (2023), Navarrete et al. (2023), Ortiz-Rodríguez et al. (2023), Park et al. (2023), Pavaskar et al. (2023), Sankar Maity et al. (2023), Sengupta & Umurhan (2023), Sharma et al. (2023), Tharakkal et al. (2023a), Tharakkal et al. (2023b), Warnecke et al. (2023), Yuvraj et al. (2023), Zhang et al. (2023), Zhu & Shi (2023)
42 times in 2022: Baehr et al. (2022), Becerra et al. (2022a), Becerra et al. (2022b), Bhat (2022), Bhatnagar et al. (2022), Brandenburg & Ntormousi (2022), Caldwell et al. (2022b), Chatterjee & Dey (2022), Currie et al. (2022), Dey et al. (2022), Gent et al. (2022), Haugen et al. (2022), Hyder et al. (2022), Kahniashvili et al. (2022), Karchniwy et al. (2022), Kirchschlager et al. (2022), Käpylä (2022), Käpylä et al. (2022), Käpylä & Singh (2022), Li et al. (2022), Lipatnikov & Sabelnikov (2022), Maiti et al. (2022), Masada & Sano (2022), Mattsson & Hedvall (2022), Mtchedlidze et al. (2022), Navarrete et al. (2022a), Navarrete et al. (2022b), Ortiz-Rodríguez et al. (2022), Pekkilä et al. (2022), Rendon Restrepo et al. (2022), Roper Pol (2022a), Roper Pol (2022b), Roper Pol et al. (2022a), Roper Pol et al. (2022b), Schober et al. (2022a), Schober et al. (2022b), Sharma & Brandenburg (2022), Stejko et al. (2022a), Stejko et al. (2022b), Tschernitz & Bourdin (2022), Yang & Zhu (2022), Zhou et al. (2022)
40 times in 2021: Baehr & Zhu (2021a), Baehr & Zhu (2021b), Barekat et al. (2021), Becerra et al. (2021), Bhat et al. (2021), Bhatia & De (2021), Brandenburg et al. (2021a), Brandenburg et al. (2021b), Brandenburg et al. (2021c), Brandenburg et al. (2021d), Brandenburg et al. (2021e), Brandenburg & Das (2021), Brandenburg & Sharma (2021), Gent et al. (2021), Haugen et al. (2021), He et al. (2021a), He et al. (2021b), Hyder et al. (2021), Jakab & Brandenburg (2021), Kahniashvili et al. (2021), Klahr & Schreiber (2021), Käpylä (2021a), Käpylä (2021b), Li & Mattsson (2021), Navarrete et al. (2021), Oliveira et al. (2021), Park & Cheoun (2021), Pencil Code Collaboration et al. (2021), Prabhu et al. (2021), Raettig et al. (2021), Roper Pol (2021), Santos-Lima et al. (2021), Schaffer et al. (2021), Viviani et al. (2021), Viviani & Käpylä (2021), Warnecke et al. (2021), Yang & Zhu (2021), Zhou & Blackman (2021), Zhu & Yang (2021), Zhuleku et al. (2021)
41 times in 2020: Aarnes et al. (2020), Adrover-González & Terradas (2020), Bhatnagar (2020), Bourdin (2020), Brandenburg (2020a), Brandenburg (2020b), Brandenburg et al. (2020b), Brandenburg & Boldyrev (2020), Brandenburg & Brüggen (2020), Brandenburg & Chen (2020), Brandenburg & Das (2020), Brandenburg & Furuya (2020), Brandenburg & Scannapieco (2020), Candelaresi & Del Sordo (2020), Chatterjee (2020), Eriksson et al. (2020), Gent et al. (2020), Gerbig et al. (2020), Hyder et al. (2020), Jakab & Brandenburg (2020), Kahniashvili et al. (2020), Klahr & Schreiber (2020), Käpylä et al. (2020a), Käpylä et al. (2020b), Li et al. (2020), Li & Mattsson (2020), Navarrete et al. (2020), Park (2020), Pusztai et al. (2020), Qian et al. (2020), Roper Pol et al. (2020a), Roper Pol et al. (2020b), Rüdiger et al. (2020), Schober et al. (2020a), Schober et al. (2020b), Seta et al. (2020), Singh et al. (2020), Warnecke & Bingert (2020), Willamo et al. (2020), Yang & Zhu (2020), Zhang et al. (2020)
38 times in 2019: Aarnes et al. (2019a), Aarnes et al. (2019b), Baehr & Klahr (2019), Bhat et al. (2019), Brandenburg (2019a), Brandenburg (2019b), Brandenburg et al. (2019a), Brandenburg et al. (2019b), Brandenburg & Rempel (2019), Candelaresi et al. (2019), Castrejon et al. (2019), Evirgen et al. (2019), Evirgen & Gent (2019), Gerbig et al. (2019), Hedvall & Mattsson (2019), Hernandez et al. (2019), Karchniwy et al. (2019), Käpylä (2019), Käpylä et al. (2019), Li et al. (2019), Losada et al. (2019), Manser et al. (2019), Mao et al. (2019), Mattsson et al. (2019a), Mattsson et al. (2019b), Nauman & Nättilä (2019), Park (2019), Peng et al. (2019a), Peng et al. (2019b), Rempel et al. (2019), Rodrigues et al. (2019), Rüdiger et al. (2019), Schober et al. (2019), Seta & Beck (2019), Smiet et al. (2019), Viviani et al. (2019), Warnecke & Peter (2019a), Warnecke & Peter (2019b)
35 times in 2018: Bhatnagar et al. (2018a), Bhatnagar et al. (2018b), Bourdin et al. (2018), Bourdin & Brandenburg (2018), Brandenburg (2018), Brandenburg et al. (2018a), Brandenburg et al. (2018b), Brandenburg & Chatterjee (2018), Brandenburg & Oughton (2018), Bushby et al. (2018), Gent et al. (2018), Korsós et al. (2018), Kuchner et al. (2018), Käpylä (2018), Käpylä et al. (2018), Li et al. (2018b), Li et al. (2018c), Lyra et al. (2018), Mattsson (2018), McNally et al. (2018), Mitra et al. (2018), Perri & Brandenburg (2018), Rice & Nayakshin (2018), Richert et al. (2018), Schaffer et al. (2018), Schober et al. (2018), Schreiber & Klahr (2018), Trivedi et al. (2018), Viviani et al. (2018), Väisälä et al. (2018), Warnecke (2018), Warnecke et al. (2018), Yang et al. (2018), Zhang et al. (2018a), Zhang & Yan (2018)
32 times in 2017: Aarnes et al. (2017), Aiyer et al. (2017), Baehr et al. (2017), Bhat et al. (2017), Bourdin (2017), Brandenburg et al. (2017a), Brandenburg et al. (2017b), Brandenburg et al. (2017c), Brandenburg et al. (2017d), Brandenburg et al. (2017e), Brandenburg & Kahniashvili (2017), Cameron et al. (2017), Gent et al. (2017), Haugen et al. (2017), Hollins et al. (2017), Hord et al. (2017), Jabbari et al. (2017), Kahniashvili et al. (2017), Koch & Code (2017), Käpylä et al. (2017a), Käpylä et al. (2017b), Li et al. (2017), Lyra et al. (2017), Osano & Adams (2017), Park (2017), Pekkilä et al. (2017), Rempel et al. (2017), Reppin & Banerjee (2017), Sharma et al. (2017), Singh et al. (2017), Smiet et al. (2017), Yang et al. (2017)
24 times in 2016: Adams & Osano (2016), Bhat et al. (2016a), Bhat et al. (2016b), Bhat & Brandenburg (2016), Bourdin et al. (2016), Candelaresi et al. (2016), Chamandy (2016), Chamandy et al. (2016), Chatterjee et al. (2016), Cole et al. (2016), Jabbari et al. (2016), Kahniashvili et al. (2016), Karak & Brandenburg (2016), Krüger et al. (2016), Lambrechts et al. (2016), Lyra et al. (2016), Osano & Adams (2016a), Osano & Adams (2016b), Rodrigues et al. (2016), Threlfall et al. (2016), Tian & Chen (2016), Warnecke et al. (2016), Yang & Johansen (2016), Yokoi & Brandenburg (2016)
24 times in 2015: Andrievsky et al. (2015), Babkovskaia et al. (2015), Baehr & Klahr (2015), Bourdin et al. (2015), Brandenburg et al. (2015), Brandenburg & Hubbard (2015), Carrera et al. (2015), Chaudhuri (2015), Chen et al. (2015), Gibbons et al. (2015), Jabbari (2015), Jabbari et al. (2015), Johansen et al. (2015), Karak et al. (2015a), Karak et al. (2015b), Lyra et al. (2015), Park (2015), Park & Park (2015), Raettig et al. (2015), Richert et al. (2015), Singh et al. (2015), Singh & Jingade (2015), Smiet et al. (2015), Snellman et al. (2015)
37 times in 2014: Adams & Osano (2014), Barekat & Brandenburg (2014), Bhat et al. (2014), Bourdin (2014), Bourdin et al. (2014), Brandenburg (2014), Brandenburg et al. (2014), Brandenburg & Stepanov (2014), Carrera et al. (2014), Chian et al. (2014), Cole et al. (2014), Dittrich et al. (2014), Gibbons et al. (2014), Jabbari et al. (2014), Jabbari & Brandenburg (2014), Karak et al. (2014), Käpylä et al. (2014), Losada et al. (2014), Lyra (2014), McNally et al. (2014), Mitra et al. (2014), Modestov et al. (2014), Pan et al. (2014a), Pan et al. (2014b), Pan & Padoan (2014), Park (2014a), Park (2014b), Rheinhardt et al. (2014), Rüdiger & Brandenburg (2014), Singh et al. (2014), Subramanian & Brandenburg (2014), Turner et al. (2014), Väisälä et al. (2014), Warnecke et al. (2014), Warnecke & Brandenburg (2014), Yang & Johansen (2014a), Yang & Johansen (2014b)
45 times in 2013: Bhat & Subramanian (2013), Bingert & Peter (2013), Bourdin et al. (2013a), Bourdin et al. (2013b), Brandenburg (2013), Brandenburg et al. (2013a), Brandenburg et al. (2013b), Brandenburg & Lazarian (2013), Brandenburg & Rädler (2013), Bykov et al. (2013), Candelaresi & Brandenburg (2013a), Candelaresi & Brandenburg (2013b), Chamandy et al. (2013), Del Sordo et al. (2013), Devlen et al. (2013), Di Bernardo & Torkelsson (2013), Dittrich et al. (2013), Félix et al. (2013), Gent et al. (2013a), Gent et al. (2013b), Getling (2013), Hubbard (2013), Jabbari et al. (2013), Kahniashvili et al. (2013), Kemel et al. (2013a), Kemel et al. (2013b), Käpylä et al. (2013a), Käpylä et al. (2013b), Käpylä et al. (2013c), Losada et al. (2013), Lyra (2013), Lyra & Kuchner (2013), Mantere et al. (2013), Mitra et al. (2013), Pan & Padoan (2013), Park (2013a), Park (2013b), Park et al. (2013), Raettig et al. (2013), Rempel et al. (2013), Svedin et al. (2013), Warnecke et al. (2013a), Warnecke et al. (2013b), Warnecke et al. (2013c), van Wettum et al. (2013)
47 times in 2012: Brandenburg et al. (2012a), Brandenburg et al. (2012b), Brandenburg et al. (2012c), Brandenburg et al. (2012d), Brandenburg & Guerrero (2012), Brandenburg & Petrosyan (2012), Candelaresi & Brandenburg (2012), Del Sordo et al. (2012), Félix et al. (2012), Gaburov et al. (2012), Gent (2012), Gibbons et al. (2012), Guerrero et al. (2012), Haugen et al. (2012), Horn et al. (2012), Hubbard (2012), Hubbard & Brandenburg (2012), Johansen et al. (2012), Kahniashvili et al. (2012), Kemel et al. (2012a), Kemel et al. (2012b), Kitchatinov & Brandenburg (2012), Käpylä et al. (2012a), Käpylä et al. (2012b), Lambrechts & Johansen (2012), Latter & Papaloizou (2012), Losada et al. (2012), Lyra & Kuchner (2012), Lyra & Mac Low (2012), Mantere & Cole (2012), McNally (2012), Park & Blackman (2012a), Park & Blackman (2012b), Peter et al. (2012), Peter & Bingert (2012), Rempel et al. (2012), Rheinhardt & Brandenburg (2012), Rice et al. (2012), Rogachevskii et al. (2012), Snellman et al. (2012a), Snellman et al. (2012b), Tevzadze et al. (2012), Warnecke et al. (2012a), Warnecke et al. (2012b), Warnecke et al. (2012c), Yang et al. (2012), Yang & Krumholz (2012)
63 times in 2011: Babkovskaia et al. (2011), Bejarano et al. (2011), Bingert & Peter (2011), Brandenburg (2011a), Brandenburg (2011b), Brandenburg (2011c), Brandenburg (2011d), Brandenburg et al. (2011a), Brandenburg et al. (2011b), Brandenburg et al. (2011c), Brandenburg & Nordlund (2011), Candelaresi et al. (2011a), Candelaresi et al. (2011b), Candelaresi et al. (2011c), Candelaresi & Brandenburg (2011a), Candelaresi & Brandenburg (2011b), Cantiello et al. (2011a), Cantiello et al. (2011b), Chatterjee (2011), Chatterjee et al. (2011a), Chatterjee et al. (2011b), Chatterjee et al. (2011c), Del Sordo & Brandenburg (2011a), Del Sordo & Brandenburg (2011b), Flock et al. (2011), Fromang et al. (2011), Gastine & Dintrans (2011a), Gastine & Dintrans (2011b), Gastine & Dintrans (2011c), Guerrero et al. (2011), Guerrero & Käpylä (2011), Hubbard et al. (2011), Hubbard & Brandenburg (2011), Hydle Rivedal et al. (2011), Johansen et al. (2011a), Johansen et al. (2011b), Johansen et al. (2011c), Kemel et al. (2011a), Kemel et al. (2011b), Kemel et al. (2011c), Käpylä et al. (2011a), Käpylä et al. (2011b), Käpylä et al. (2011c), Käpylä & Korpi (2011), Lambrechts (2011), Lyra & Klahr (2011), Mantere et al. (2011), Mitra et al. (2011), Oishi & Mac Low (2011), Rempel et al. (2011), Rice et al. (2011), Rogachevskii et al. (2011), Ruoskanen et al. (2011), Rädler et al. (2011), Rüdiger et al. (2011), Sordo & Brandenburg (2011), Tarjei Jensen et al. (2011), Warnecke et al. (2011a), Warnecke et al. (2011b), Warnecke & Brandenburg (2011a), Warnecke & Brandenburg (2011b), Zacharias et al. (2011a), Zacharias et al. (2011b)
30 times in 2010: Baggaley et al. (2010), Bai & Stone (2010b), Bingert et al. (2010), Brandenburg (2010a), Brandenburg (2010b), Brandenburg et al. (2010a), Brandenburg et al. (2010b), Brandenburg & Del Sordo (2010), Chatterjee et al. (2010), Del Sordo et al. (2010), Fromang et al. (2010), Gastine & Dintrans (2010), Guerrero et al. (2010), Haugen et al. (2010), Hubbard & Brandenburg (2010), Johansen & Lacerda (2010), Kahniashvili et al. (2010), Korpi et al. (2010), Käpylä et al. (2010a), Käpylä et al. (2010b), Käpylä et al. (2010c), Käpylä et al. (2010d), Lyra et al. (2010), Madarassy & Brandenburg (2010), Mitra et al. (2010a), Mitra et al. (2010b), Mitra et al. (2010c), Rheinhardt & Brandenburg (2010), Rädler & Brandenburg (2010), Warnecke & Brandenburg (2010)
34 times in 2009: Baggaley et al. (2009), Brandenburg (2009a), Brandenburg (2009b), Brandenburg (2009c), Brandenburg (2009d), Brandenburg (2009e), Brandenburg (2009f), Brandenburg et al. (2009a), Brandenburg et al. (2009b), Børve et al. (2009), Fromang et al. (2009), Heinemann & Papaloizou (2009), Hubbard et al. (2009), Hubbard & Brandenburg (2009), Johansen et al. (2009a), Johansen et al. (2009b), Käpylä et al. (2009a), Käpylä et al. (2009b), Käpylä et al. (2009c), Käpylä & Brandenburg (2009), Liljeström et al. (2009), Lyra et al. (2009a), Lyra et al. (2009b), Mitra et al. (2009a), Mitra et al. (2009b), Oishi & Mac Low (2009), Rempel et al. (2009), Rädler & Brandenburg (2009), Snellman et al. (2009), Sur & Brandenburg (2009), Vermersch & Brandenburg (2009), Yang et al. (2009), Zacharias et al. (2009a), Zacharias et al. (2009b)
26 times in 2008: Babkovskaia et al. (2008), Brandenburg (2008a), Brandenburg (2008b), Brandenburg et al. (2008a), Brandenburg et al. (2008b), Brandenburg et al. (2008c), Gastine & Dintrans (2008a), Gastine & Dintrans (2008b), Gastine & Dintrans (2008c), Green et al. (2008), Johansen et al. (2008), Johansen & Levin (2008), Kissmann et al. (2008), Käpylä et al. (2008), Käpylä & Brandenburg (2008), Lyra et al. (2008a), Lyra et al. (2008b), Rieutord (2008), Ruszkowski et al. (2008), Rädler & Brandenburg (2008), Scharmer et al. (2008), Sur et al. (2008), Tilgner & Brandenburg (2008), Workman & Armitage (2008), Youdin & Johansen (2008), Yousef et al. (2008)
19 times in 2007: Brandenburg (2007a), Brandenburg (2007b), Brandenburg et al. (2007a), Brandenburg et al. (2007b), Brandenburg & Käpylä (2007), Brandenburg & Subramanian (2007), Fromang et al. (2007), Fromang & Papaloizou (2007), Gustafsson et al. (2007), Heinemann et al. (2007), Johansen et al. (2007a), Johansen et al. (2007b), Johansen & Youdin (2007), Käpylä & Brandenburg (2007), Oishi et al. (2007), Ruszkowski et al. (2007), Schekochihin et al. (2007), Sur et al. (2007), Youdin & Johansen (2007)
16 times in 2006: Brandenburg (2006a), Brandenburg (2006b), Brandenburg (2006c), Brandenburg & Dintrans (2006), Dobler et al. (2006), Gustafsson et al. (2006), Haugen & Brandenburg (2006), Heinemann et al. (2006), Hupfer et al. (2006), Johansen et al. (2006a), Johansen et al. (2006b), Johansen et al. (2006c), Mee & Brandenburg (2006), Ouyed et al. (2006), Shukurov et al. (2006), Snodin et al. (2006)
19 times in 2005: Brandenburg (2005a), Brandenburg (2005b), Brandenburg (2005c), Brandenburg (2005d), Brandenburg et al. (2005a), Brandenburg et al. (2005b), Brandenburg et al. (2005c), Brandenburg & Blackman (2005), Brandenburg & Käpylä (2005), Brandenburg & Rüdiger (2005), Brandenburg & Subramanian (2005a), Brandenburg & Subramanian (2005b), Brandenburg & Subramanian (2005c), Christensson et al. (2005), Dorch (2005), Johansen et al. (2005), Johansen & Klahr (2005), McMillan & Sarson (2005), Schekochihin et al. (2005)
18 times in 2004: Brandenburg et al. (2004a), Brandenburg et al. (2004b), Brandenburg et al. (2004c), Brandenburg & Matthaeus (2004), Brandenburg & Multamäki (2004), Brandenburg & Sandin (2004), Dobler & Getling (2004), Dorch (2004a), Dorch (2004b), Haugen et al. (2004a), Haugen et al. (2004b), Haugen et al. (2004c), Haugen & Brandenburg (2004a), Haugen & Brandenburg (2004b), Johansen et al. (2004), Nordlund (2004), Pearson et al. (2004), Yousef et al. (2004)
8 times in 2003: Blackman & Brandenburg (2003), Brandenburg (2003), Brandenburg et al. (2003), Dobler et al. (2003), Haugen et al. (2003), McMillan & Sarson (2003), Yousef et al. (2003), Yousef & Brandenburg (2003)
Papers by topic
The Pencil Code has been used for the following research topics:
Interstellar and intercluster medium as well as early Universe
Interstellar and intercluster medium: Korpi-Lagg et al. (2024), Elias-López et al. (2024), Candelaresi & Del Sordo (2024), Gent et al. (2023), Pavaskar et al. (2023), Elias-López et al. (2023), Maiti et al. (2022), Brandenburg & Ntormousi (2022), Gent et al. (2021), Li & Mattsson (2021), Brandenburg & Brüggen (2020), Gent et al. (2020), Candelaresi & Del Sordo (2020), Brandenburg & Furuya (2020), Li & Mattsson (2020), Brandenburg (2019a), Evirgen & Gent (2019), Seta & Beck (2019), Evirgen et al. (2019), Rodrigues et al. (2019), Zhang & Yan (2018), Zhang et al. (2018a), Väisälä et al. (2018), Hord et al. (2017), Hollins et al. (2017), Rodrigues et al. (2016), Chamandy et al. (2016), Chamandy (2016), Chamandy et al. (2013), Gent et al. (2013a), Gent et al. (2013b), Bykov et al. (2013), Rogachevskii et al. (2012), Mantere & Cole (2012), Yang & Krumholz (2012), Gent (2012), Ruoskanen et al. (2011), Ruszkowski et al. (2008), Ruszkowski et al. (2007), Brandenburg et al. (2007b), Gustafsson et al. (2007), Gustafsson et al. (2006), Brandenburg et al. (2005c), Haugen et al. (2004a), Brandenburg et al. (2003)
Small-scale dynamos and reconnection: Qazi et al. (2025a), Warnecke et al. (2025), Kishore & Singh (2025b), Koshikumo et al. (2025a), Qazi et al. (2025b), Brandenburg & Ntormousi (2025), Gent et al. (2025), Skalidis et al. (2025), Zhou & Jingade (2024), Qazi et al. (2024), Gent et al. (2024), Brandenburg et al. (2023b), Brandenburg & Larsson (2023), Warnecke et al. (2023), Bhat (2022), Gent et al. (2022), Zhou et al. (2022), Park & Cheoun (2021), Santos-Lima et al. (2021), Seta et al. (2020), Pusztai et al. (2020), Rüdiger et al. (2020), Park (2020), Bhat et al. (2019), Käpylä (2019), Brandenburg & Rempel (2019), Käpylä et al. (2018), Brandenburg et al. (2018b), Bhat et al. (2016a), Bhat & Subramanian (2013), Brandenburg (2011b), Baggaley et al. (2010), Baggaley et al. (2009), Schekochihin et al. (2007), Schekochihin et al. (2005), Haugen et al. (2004c), Haugen et al. (2004b), Haugen & Brandenburg (2004b), Haugen et al. (2003), Dobler et al. (2003)
Primordial magnetic fields and decaying turbulence: Vachaspati & Brandenburg (2025), Brandenburg & Banerjee (2025), Dehman & Brandenburg (2025), Zhang & Brandenburg (2025), Ghosh et al. (2025), Mtchedlidze et al. (2025), Brandenburg et al. (2024a), Mtchedlidze et al. (2024), Dwivedi et al. (2024), Mtchedlidze et al. (2023), Brandenburg (2023b), Brandenburg et al. (2023e), Mtchedlidze et al. (2022), Bhat et al. (2021), Kahniashvili et al. (2020), Brandenburg et al. (2020b), Brandenburg (2020a), Brandenburg et al. (2019b), Trivedi et al. (2018), Brandenburg et al. (2018a), Brandenburg & Kahniashvili (2017), Osano & Adams (2017), Park (2017), Reppin & Banerjee (2017), Brandenburg et al. (2017e), Kahniashvili et al. (2017), Osano & Adams (2016a), Osano & Adams (2016b), Adams & Osano (2016), Kahniashvili et al. (2016), Brandenburg et al. (2015), Adams & Osano (2014), Kahniashvili et al. (2013), Kahniashvili et al. (2012), Tevzadze et al. (2012), Candelaresi & Brandenburg (2011b), Kahniashvili et al. (2010), Del Sordo et al. (2010), Christensson et al. (2005), Yousef et al. (2004)
Relic gravitational waves & axions: Sharma et al. (2025b), Iarygina et al. (2025), Brandenburg et al. (2024c), Iarygina et al. (2024), Brandenburg et al. (2024b), He et al. (2023), Sharma et al. (2023), Roper Pol (2022b), Roper Pol et al. (2022a), Roper Pol (2022a), Kahniashvili et al. (2022), Sharma & Brandenburg (2022), Kahniashvili et al. (2021), He et al. (2021a), Brandenburg et al. (2021a), Brandenburg et al. (2021c), Roper Pol (2021), He et al. (2021b), Brandenburg & Sharma (2021), Brandenburg et al. (2021d), Brandenburg et al. (2021b), Roper Pol et al. (2020a), Roper Pol et al. (2020b)
Planet formation and inertial particles
Planet formation: Eriksson et al. (2025), Shi et al. (2025), Rice et al. (2025), Elias-López (2025), Baehr et al. (2025), Baehr et al. (2022), Zhu & Yang (2021), Klahr & Schreiber (2021), Baehr & Zhu (2021a), Baehr & Zhu (2021b), Raettig et al. (2021), Yang & Zhu (2021), Gerbig et al. (2020), Eriksson et al. (2020), Yang & Zhu (2020), Klahr & Schreiber (2020), Baehr & Klahr (2019), Manser et al. (2019), Hernandez et al. (2019), Castrejon et al. (2019), Kuchner et al. (2018), Richert et al. (2018), Rice & Nayakshin (2018), Yang et al. (2018), Schreiber & Klahr (2018), McNally et al. (2018), Baehr et al. (2017), Lyra et al. (2016), Yang & Johansen (2016), Lambrechts et al. (2016), Baehr & Klahr (2015), Gibbons et al. (2015), Carrera et al. (2015), Richert et al. (2015), Johansen et al. (2015), Turner et al. (2014), Yang & Johansen (2014b), Carrera et al. (2014), Dittrich et al. (2014), Gibbons et al. (2014), McNally et al. (2014), Yang & Johansen (2014a), Hubbard (2013), Lyra & Kuchner (2013), Dittrich et al. (2013), Lambrechts & Johansen (2012), Johansen et al. (2012), Yang et al. (2012), Horn et al. (2012), Gibbons et al. (2012), Hubbard (2012), Lyra & Kuchner (2012), Johansen et al. (2011c), Johansen et al. (2011b), Lambrechts (2011), Lyra & Klahr (2011), Johansen et al. (2011a), Fromang et al. (2011), Lyra et al. (2010), Johansen & Lacerda (2010), Johansen et al. (2009b), Lyra et al. (2009b), Oishi & Mac Low (2009), Lyra et al. (2009a), Yang et al. (2009), Børve et al. (2009), Lyra et al. (2008a), Lyra et al. (2008b), Johansen et al. (2008), Youdin & Johansen (2008), Johansen et al. (2007a), Johansen & Youdin (2007), Youdin & Johansen (2007), Oishi et al. (2007), Johansen et al. (2007b), Johansen et al. (2006a), Johansen et al. (2006b), Johansen et al. (2006c), Johansen & Klahr (2005), Johansen et al. (2005), Johansen et al. (2004)
Inertial, tracer particles, & passive scalars: Kirchschlager et al. (2024), Saieed & Hickey (2024), Sengupta & Umurhan (2023), Bhatnagar et al. (2022), Haugen et al. (2022), Kirchschlager et al. (2022), Mattsson & Hedvall (2022), Li et al. (2022), Haugen et al. (2021), Schaffer et al. (2021), Bhatnagar (2020), Li et al. (2020), Gerbig et al. (2019), Hedvall & Mattsson (2019), Mattsson et al. (2019a), Aarnes et al. (2019a), Li et al. (2019), Mattsson et al. (2019b), Bhatnagar et al. (2018a), Mitra et al. (2018), Bhatnagar et al. (2018b), Lyra et al. (2018), Schaffer et al. (2018), Sharma et al. (2017), Haugen et al. (2017), Yang et al. (2017), Li et al. (2017), Aarnes et al. (2017), Krüger et al. (2016), Raettig et al. (2015), Pan et al. (2014a), Pan et al. (2014b), Pan & Padoan (2014), Pan & Padoan (2013), Mitra et al. (2013), Haugen et al. (2012), Hydle Rivedal et al. (2011), Haugen et al. (2010)
Accretion discs and shear flows
Accretion discs and shear flows: Meftah (2025), Godines et al. (2025), Cañas et al. (2024), Zhou (2024), Lyra et al. (2024), Sengupta et al. (2024), Meftah (2023), Tharakkal et al. (2023b), Tharakkal et al. (2023a), Mondal & Bhat (2023), Hyder et al. (2022), Hyder et al. (2021), Hyder et al. (2020), Lyra et al. (2017), Singh et al. (2017), Bhat et al. (2017), Tian & Chen (2016), Bhat et al. (2016b), Lyra et al. (2015), Lyra (2014), Väisälä et al. (2014), Raettig et al. (2013), Lyra (2013), Di Bernardo & Torkelsson (2013), Lyra & Mac Low (2012), Rice et al. (2012), Gaburov et al. (2012), Latter & Papaloizou (2012), Flock et al. (2011), Oishi & Mac Low (2011), Rice et al. (2011), Käpylä & Korpi (2011), Korpi et al. (2010), Käpylä et al. (2010c), Fromang et al. (2010), Johansen et al. (2009a), Heinemann & Papaloizou (2009), Fromang et al. (2009), Johansen & Levin (2008), Workman & Armitage (2008), Fromang et al. (2007), Fromang & Papaloizou (2007), Ouyed et al. (2006), Brandenburg (2005a)
Shear flows: Barekat et al. (2021), Singh & Jingade (2015), Modestov et al. (2014), Käpylä et al. (2009c), Vermersch & Brandenburg (2009), Green et al. (2008), Yousef et al. (2008), Babkovskaia et al. (2008), Brandenburg et al. (2004a)
Solar physics
Coronal heating and coronal mass ejections: Singh et al. (2025a), Kishore & Singh (2025b), Kishore & Singh (2025a), Srivastava et al. (2025a), Singh et al. (2025b), Vemareddy et al. (2024), Maity et al. (2024b), Dey et al. (2024), Vemareddy (2024), Kesri et al. (2024), Zhang et al. (2023), Dey et al. (2022), Chatterjee & Dey (2022), Jakab & Brandenburg (2021), Zhuleku et al. (2021), Chatterjee (2020), Warnecke & Bingert (2020), Bourdin (2020), Adrover-González & Terradas (2020), Candelaresi et al. (2019), Warnecke & Peter (2019a), Smiet et al. (2019), Warnecke & Peter (2019b), Korsós et al. (2018), Cameron et al. (2017), Bourdin (2017), Bourdin et al. (2016), Threlfall et al. (2016), Candelaresi et al. (2016), Chatterjee et al. (2016), Smiet et al. (2015), Chen et al. (2015), Bourdin et al. (2015), Warnecke & Brandenburg (2014), Bourdin (2014), Bourdin et al. (2014), Bourdin et al. (2013b), Bingert & Peter (2013), Bourdin et al. (2013a), van Wettum et al. (2013), Peter & Bingert (2012), Warnecke et al. (2012b), Peter et al. (2012), Warnecke et al. (2012a), Bingert & Peter (2011), Warnecke et al. (2011a), Zacharias et al. (2011a), Zacharias et al. (2011b), Warnecke et al. (2011b), Warnecke & Brandenburg (2011b), Warnecke & Brandenburg (2011a), Warnecke & Brandenburg (2010), Bingert et al. (2010), Zacharias et al. (2009b), Zacharias et al. (2009a)
Large-scale dynamos, helical turbulence, and catastrophic quenching: Mondal et al. (2025), Rogachevskii et al. (2025), Brandenburg et al. (2025a), Brandenburg & Vishniac (2025), Hidalgo et al. (2025), Shchutskyi et al. (2025), Brandenburg et al. (2025b), Brandenburg et al. (2025e), Zhou & Blackman (2024), Vashishth (2024), Zhou & Lai (2024), Park et al. (2023), Zhu & Shi (2023), Yang & Zhu (2022), Prabhu et al. (2021), Brandenburg & Scannapieco (2020), Park (2020), Nauman & Nättilä (2019), Rempel et al. (2019), Park (2019), Peng et al. (2019a), Brandenburg (2018), Brandenburg & Chatterjee (2018), Bourdin et al. (2018), Bourdin & Brandenburg (2018), Brandenburg & Oughton (2018), Brandenburg et al. (2017b), Smiet et al. (2017), Rempel et al. (2017), Brandenburg et al. (2017a), Brandenburg et al. (2017c), Karak & Brandenburg (2016), Cole et al. (2016), Brandenburg & Hubbard (2015), Karak et al. (2015b), Brandenburg & Stepanov (2014), Chian et al. (2014), Bhat et al. (2014), Park (2014a), Brandenburg (2014), Subramanian & Brandenburg (2014), Park (2014b), Park et al. (2013), Del Sordo et al. (2013), Candelaresi & Brandenburg (2013b), Rempel et al. (2013), Park (2013a), Brandenburg (2013), Candelaresi & Brandenburg (2013a), Park (2013b), Brandenburg & Lazarian (2013), Brandenburg et al. (2012d), Hubbard & Brandenburg (2012), Park & Blackman (2012b), Park & Blackman (2012a), Rempel et al. (2012), Candelaresi & Brandenburg (2012), Brandenburg & Guerrero (2012), Hubbard & Brandenburg (2011), Candelaresi et al. (2011c), Brandenburg (2011a), Chatterjee et al. (2011a), Mitra et al. (2011), Rempel et al. (2011), Hubbard et al. (2011), Brandenburg (2011d), Candelaresi et al. (2011a), Guerrero et al. (2011), Candelaresi & Brandenburg (2011a), Candelaresi et al. (2011b), Brandenburg (2011c), Mitra et al. (2010a), Hubbard & Brandenburg (2010), Brandenburg (2010a), Guerrero et al. (2010), Rädler & Brandenburg (2010), Brandenburg et al. (2010b), Chatterjee et al. (2010), Mitra et al. (2010c), Brandenburg (2010b), Brandenburg (2009b), Brandenburg et al. (2009b), Käpylä & Brandenburg (2009), Brandenburg (2009e), Brandenburg (2009d), Sur & Brandenburg (2009), Rempel et al. (2009), Brandenburg (2009c), Brandenburg (2009a), Brandenburg (2009f), Brandenburg et al. (2008a), Tilgner & Brandenburg (2008), Brandenburg (2008a), Brandenburg (2008b), Rädler & Brandenburg (2008), Brandenburg & Käpylä (2007), Brandenburg & Subramanian (2007), Brandenburg (2007a), Brandenburg (2007b), Shukurov et al. (2006), Snodin et al. (2006), Mee & Brandenburg (2006), Brandenburg & Dintrans (2006), Brandenburg (2006b), Brandenburg (2006a), Brandenburg (2006c), Brandenburg & Subramanian (2005c), Brandenburg (2005b), Brandenburg & Subramanian (2005b), Brandenburg & Subramanian (2005a), Brandenburg et al. (2005b), Brandenburg (2005c), Brandenburg & Käpylä (2005), Brandenburg (2005d), Brandenburg & Blackman (2005), Brandenburg & Sandin (2004), Brandenburg & Matthaeus (2004), Brandenburg et al. (2004b), Yousef & Brandenburg (2003)
Helioseismology: Kishore et al. (2024), Singh et al. (2020), Singh et al. (2015), Singh et al. (2014)
Strongly stratified MHD turbulence and NEMPI: Losada et al. (2019), Perri & Brandenburg (2018), Jabbari et al. (2017), Warnecke et al. (2016), Jabbari et al. (2016), Jabbari (2015), Jabbari et al. (2015), Losada et al. (2014), Mitra et al. (2014), Jabbari et al. (2014), Brandenburg et al. (2014), Jabbari & Brandenburg (2014), Kemel et al. (2013b), Warnecke et al. (2013a), Brandenburg et al. (2013b), Losada et al. (2013), Jabbari et al. (2013), Kemel et al. (2013a), Käpylä et al. (2013c), Brandenburg et al. (2012c), Kemel et al. (2012b), Käpylä et al. (2012b), Kemel et al. (2012a), Losada et al. (2012), Brandenburg et al. (2011a), Rüdiger et al. (2011), Kemel et al. (2011c), Kemel et al. (2011a), Kemel et al. (2011b), Brandenburg et al. (2010a)
Convection in Cartesian domains: Pandey & Bourdin (2025), Hosking et al. (2025), Tschernitz & Bourdin (2025b), Käpylä (2025), Tschernitz & Bourdin (2025a), Käpylä (2024), Käpylä (2023b), Ortiz-Rodríguez et al. (2023), Käpylä (2022), Ortiz-Rodríguez et al. (2022), Masada & Sano (2022), Tschernitz & Bourdin (2022), Käpylä (2021b), Brandenburg et al. (2019a), Bushby et al. (2018), Käpylä (2018), Käpylä et al. (2017b), Käpylä et al. (2013b), Félix et al. (2013), Svedin et al. (2013), Getling (2013), Guerrero et al. (2012), Félix et al. (2012), Guerrero & Käpylä (2011), Cantiello et al. (2011a), Käpylä et al. (2011c), Gastine & Dintrans (2011a), Mantere et al. (2011), Gastine & Dintrans (2011b), Cantiello et al. (2011b), Gastine & Dintrans (2011c), Brandenburg et al. (2011b), Käpylä et al. (2010a), Gastine & Dintrans (2010), Käpylä et al. (2009b), Rieutord (2008), Käpylä et al. (2008), Scharmer et al. (2008), Gastine & Dintrans (2008a), Gastine & Dintrans (2008b), Heinemann et al. (2007), Heinemann et al. (2006), Dobler & Getling (2004), Nordlund (2004)
Global convection and dynamo simulations: Hackman et al. (2024), Hidalgo et al. (2024), Käpylä (2023a), Karak (2023), Käpylä et al. (2023), Hidalgo et al. (2023), Navarrete et al. (2023), Becerra et al. (2022a), Stejko et al. (2022b), Navarrete et al. (2022a), Becerra et al. (2022b), Stejko et al. (2022a), Viviani et al. (2021), Viviani & Käpylä (2021), Navarrete et al. (2021), Käpylä (2021a), Becerra et al. (2021), Warnecke et al. (2021), Käpylä et al. (2020b), Jakab & Brandenburg (2020), Navarrete et al. (2020), Willamo et al. (2020), Käpylä et al. (2019), Rüdiger et al. (2019), Viviani et al. (2019), Viviani et al. (2018), Warnecke (2018), Käpylä et al. (2017a), Gent et al. (2017), Karak et al. (2015a), Cole et al. (2014), Käpylä et al. (2014), Warnecke et al. (2014), Käpylä et al. (2013a), Warnecke et al. (2013b), Mantere et al. (2013), Warnecke et al. (2013c), Käpylä et al. (2012a), Warnecke et al. (2012c), Käpylä et al. (2011a), Käpylä et al. (2011b), Käpylä et al. (2010b), Mitra et al. (2010b), Mitra et al. (2009b), Brandenburg et al. (2007a), Dobler et al. (2006), McMillan & Sarson (2005), Dorch (2005), Dorch (2004a), Dorch (2004b), McMillan & Sarson (2003)
Miscellanea
Turbulent transport and test-field method: Candelaresi & Beck (2023), Mizerski et al. (2023), Carenza et al. (2023), Brandenburg & Protiti (2023), Haugen et al. (2022), Käpylä et al. (2022), Käpylä & Singh (2022), Zhou & Blackman (2021), Brandenburg & Chen (2020), Käpylä et al. (2020a), Peng et al. (2019b), Warnecke et al. (2018), Snellman et al. (2015), Andrievsky et al. (2015), Rheinhardt et al. (2014), Rüdiger & Brandenburg (2014), Karak et al. (2014), Brandenburg et al. (2013a), Devlen et al. (2013), Brandenburg & Rädler (2013), Rheinhardt & Brandenburg (2012), Brandenburg et al. (2012a), Kitchatinov & Brandenburg (2012), Snellman et al. (2012a), Snellman et al. (2012b), Brandenburg et al. (2012b), Rogachevskii et al. (2011), Rädler et al. (2011), Chatterjee (2011), Rheinhardt & Brandenburg (2010), Käpylä et al. (2010d), Madarassy & Brandenburg (2010), Brandenburg & Del Sordo (2010), Käpylä et al. (2009a), Hubbard & Brandenburg (2009), Mitra et al. (2009a), Brandenburg et al. (2009a), Snellman et al. (2009), Hubbard et al. (2009), Rädler & Brandenburg (2009), Liljeström et al. (2009), Brandenburg et al. (2008b), Sur et al. (2008), Brandenburg et al. (2008c), Käpylä & Brandenburg (2008), Sur et al. (2007), Käpylä & Brandenburg (2007), Hupfer et al. (2006), Brandenburg et al. (2004c), Yousef et al. (2003)
Hydrodynamic and MHD instabilities: Oliveira et al. (2021), Del Sordo et al. (2012), Chatterjee et al. (2011b), Chatterjee et al. (2011c), Bejarano et al. (2011), Brandenburg & Rüdiger (2005), Brandenburg et al. (2004b), Brandenburg (2003)
Chiral MHD: Gurgenidze et al. (2025), Schober et al. (2024b), Schober et al. (2024a), Brandenburg et al. (2023d), Brandenburg et al. (2023c), Schober et al. (2022a), Schober et al. (2022b), Schober et al. (2020a), Schober et al. (2020b), Schober et al. (2019), Schober et al. (2018), Brandenburg et al. (2017d)
Hydrodynamic and MHD turbulence: Roper Pol & Salvino Midiri (2025), Park (2025b), Brandenburg & Scannapieco (2025), Brandenburg et al. (2025c), Brandenburg et al. (2023a), Brandenburg & Boldyrev (2020), Aiyer et al. (2017), Yokoi & Brandenburg (2016), Brandenburg & Petrosyan (2012), Brandenburg & Nordlund (2011), Del Sordo & Brandenburg (2011a), Del Sordo & Brandenburg (2011b), Haugen & Brandenburg (2006), Brandenburg et al. (2005a), Haugen & Brandenburg (2004a), Pearson et al. (2004)
Turbulent combustion, front propagation, radiation & ionization: Yuvraj et al. (2025), Sabelnikov et al. (2025), Lipatnikov & Sabelnikov (2025), Lipatnikov (2024b), Wang et al. (2024), Yuvraj et al. (2023), Brandenburg (2023a), Lipatnikov & Sabelnikov (2023), Ganti et al. (2023), Karchniwy et al. (2022), Lipatnikov & Sabelnikov (2022), Bhatia & De (2021), Brandenburg & Das (2021), Aarnes et al. (2020), Brandenburg & Das (2020), Qian et al. (2020), Brandenburg (2020b), Zhang et al. (2020), Brandenburg (2019b), Mao et al. (2019), Bhat & Brandenburg (2016), Chaudhuri (2015), Babkovskaia et al. (2015), Barekat & Brandenburg (2014), Brandenburg et al. (2011c), Babkovskaia et al. (2011), Tarjei Jensen et al. (2011), Brandenburg & Multamäki (2004)
Code development, GPU etc: Lyra (2023), Pekkilä et al. (2022), Pencil Code Collaboration et al. (2021), Pekkilä et al. (2017)
Code comparison & reference
The Pencil Code has been quoted in 136 other papers either for detailed code comparison, in connection with related work, or in comparison with other codes: Yeung et al. (2025), Zhou et al. (2025), Sharma et al. (2025a), Son et al. (2025), Irshad P et al. (2025), Lim et al. (2025), Lebreuilly et al. (2025b), Hunana (2025), Abramson et al. (2025), Federrath & Offner (2025), Luo & Fan (2025), Pons et al. (2025), Lebreuilly et al. (2025a), Umurhan et al. (2025), Buchner (2025b), Navarro et al. (2025), Modestov et al. (2024), Owens & Wadsley (2024), Figueroa et al. (2024), Rea et al. (2024), Shariff (2024), Sandnes et al. (2024), Dahl et al. (2024), Hunana (2024), Shi et al. (2024), Raboonik et al. (2024), Achikanath Chirakkara et al. (2024), Schad et al. (2024), Commerçon et al. (2023), Ruszkowski & Pfrommer (2023), Klahr et al. (2023), Lesur et al. (2023), Lecoanet & Edelmann (2023), Modestov et al. (2023), Rasheed et al. (2023), Väisälä et al. (2023), Chouliaras & Gourgouliatos (2022), Caldwell et al. (2022a), Paardekooper et al. (2022), Porter et al. (2022), Väisälä et al. (2021), Hanawa & Matsumoto (2021), Bartman et al. (2021), Sabelnikov et al. (2021), Zhu (2021), Li & Youdin (2021), Matilsky & Toomre (2020), Gressel & Elstner (2020), Guerrero (2020), Brandenburg et al. (2020a), Rosswog (2020a), Rosswog (2020b), Pencil Code Collaboration (2020), Brandenburg (2020c), Tricco (2019), Jóhannesson et al. (2019), Porter et al. (2019), Sapetina et al. (2019), Mignone et al. (2019), Beresnyak (2019), Oishi et al. (2018), Hernandez et al. (2018), Rüdiger et al. (2018), Nixon et al. (2018), Zhang et al. (2018b), Li et al. (2018a), Yamamoto & Makino (2017), Goffrey et al. (2017), Augustson (2017b), Brun & Browning (2017), Emeriau-Viard & Brun (2017), Cabezón et al. (2017), Ryu & Huynh (2017), Augustson (2017a), Kupka & Muthsam (2017), Kulikov et al. (2016), Simon et al. (2016), Surville et al. (2016), Augustson et al. (2015), Brun et al. (2015), Schad et al. (2015), Mocz et al. (2015), Skála et al. (2015), Cheung et al. (2015), Krumholz & Forbes (2015), Hopkins (2015), Duffell & MacFadyen (2015), Charbonneau (2014), Rieutord (2014), Jenkins et al. (2014), Berera & Linkmann (2014), Recchi (2014), Lovelace & Romanova (2014), Skála et al. (2014), Olshevsky et al. (2014), Norton et al. (2014), Charbonneau (2013), Augustson et al. (2013), Martínez Pillet (2013), Cavecchi et al. (2013), Kulikov (2013), Fromang (2013), Gabbasov et al. (2013), Freytag et al. (2012), McNally et al. (2012b), Rein (2012), Bonanno et al. (2012), Maron et al. (2012), McNally et al. (2012a), Ziegler (2011), McNally (2011), Vshivkov et al. (2011), Viallet et al. (2011), Andic (2011), Turck-Chièze (2010), Stone & Gardiner (2010), Rovithis-Livaniou (2010), Bai & Stone (2010a), Hanasz et al. (2010), Brandenburg & Dobler (2010), Lemaster & Stone (2009), Hawley (2009), Garcia de Andrade (2009), Kley (2009), Piontek et al. (2009), Maron & Mac Low (2009), Klahr (2008), Matsumoto & Seki (2008), Gellert et al. (2008), Maron et al. (2008), Turner et al. (2006), Thévenin et al. (2006), Fromang et al. (2006), de Val-Borro et al. (2006), Rüdiger (2005), Maron et al. (2004).
Unclassified papers
The following 55 papers could not be classified into any of the predefined categories: Brandenburg et al. (2026), Sharma et al. (2026), Leidi et al. (2026), Vemareddy et al. (2026), Gent et al. (2026), Maity et al. (2026), Mtchedlidze et al. (2026), Eriksson et al. (2026), Käpylä (2026), Baronett et al. (2026), Rabus & Mkanda (2026), Muhammed Irshad et al. (2026), von Eckardstein et al. (2026), Schober et al. (2026), Luo et al. (2026), Haugen et al. (2026), Mondal & Singh (2026), Caprini (2026), Mondal et al. (2026), Klahr et al. (2026), Zhang & Brandenburg (2026), Godines et al. (2026), Anandavijayan & Bhat (2026), Ghosh et al. (2026), Brandenburg et al. (2025d), Srivastava et al. (2025b), Koshikumo et al. (2025b), Park (2025a), Buchner (2025a), Sankar Maity et al. (2024), Lipatnikov (2024a), Schäfer et al. (2024), Maity et al. (2024a), Sankar Maity et al. (2023), Caldwell et al. (2022b), Roper Pol et al. (2022b), Currie et al. (2022), Navarrete et al. (2022b), Rendon Restrepo et al. (2022), Brandenburg et al. (2021e), Aarnes et al. (2019b), Karchniwy et al. (2019), Gent et al. (2018), Mattsson (2018), Li et al. (2018b), Li et al. (2018c), Koch & Code (2017), Park (2015), Park & Park (2015), McNally (2012), Sordo & Brandenburg (2011), Bai & Stone (2010b), Gastine & Dintrans (2008c), Kissmann et al. (2008), Blackman & Brandenburg (2003).
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Brandenburg (2008a). The dual role of shear in large-scale dynamos. Astron. Nachr., 329, 725, September 2008a. doi:10.1002/asna.200811027, arXiv:0808.0959, ads:2008AN....329..725B.
Brandenburg (2008b). Turbulent protostellar discs. Phys. Scripta Vol. T, 130, 014016, August 2008b. doi:10.1088/0031-8949/2008/T130/014016, arXiv:0808.0960, ads:2008PhST..130a4016B.
Brandenburg (2009a). From Fibril to Diffuse Fields During Dynamo Saturation. In M. Dikpati, T. Arentoft, I. González Hernández, C. Lindsey, and F. Hill, editors, Solar-Stellar Dynamos as Revealed by Helio- and Asteroseismology: GONG 2008/SOHO 21, volume 416 of Astron. Soc. Pac. Conf. Ser., 433. arXiv:0904.2842, ads:2009ASPC..416..433B.
Brandenburg (2009b). Large-scale Dynamos at Low Magnetic Prandtl Numbers. Astrophys. J., 697, 1206–1213, June 2009b. doi:10.1088/0004-637X/697/2/1206, arXiv:0808.0961, ads:2009ApJ...697.1206B.
Brandenburg (2009c). Paradigm shifts in solar dynamo modeling. In K. G. Strassmeier, A. G. Kosovichev, and J. E. Beckman, editors, IAU Symp., volume 259 of IAU Symp., 159–166. doi:10.1017/S1743921309030403, arXiv:0901.3789, ads:2009IAUS..259..159B.
Brandenburg (2009d). The critical role of magnetic helicity in astrophysical large-scale dynamos. Plasma Phys. Contr. Fusion, 51, 124043, December 2009d. doi:10.1088/0741-3335/51/12/124043, arXiv:0909.4377, ads:2009PPCF...51l4043B.
Brandenburg (2009e). Advances in Theory and Simulations of Large-Scale Dynamos. Space Sci. Ref., 144, 87–104, April 2009e. doi:10.1007/s11214-009-9490-0, arXiv:0901.0329, ads:2009SSRv..144...87B.
Brandenburg (2009f). Advances in Theory and Simulations of Large-Scale Dynamos. In M. J. Thompson, A. Balogh, J. L. Culhane, Å. Nordlund, S. K. Solanki, and J.-P. Zahn, editors, The Origin and Dynamics of Solar Magnetism, Space Sciences Series of ISSI, Volume 32. ISBN 978-1-4419-0238-2. Springer New York, 2009, p. 87, Springer New York, 87. doi:10.1007/978-1-4419-0239-9_7, ads:2009odsm.book...87B.
Brandenburg (2010a). Magnetic field evolution in simulations with Euler potentials. Month. Not. Roy. Astron. Soc., 401, 347–354, January 2010a. doi:10.1111/j.1365-2966.2009.15640.x, arXiv:0907.1906, ads:2010MNRAS.401..347B.
Brandenburg (2010b). Surface appearance of dynamo-generated large-scale fields. In 38th COSPAR Scientific Assembly, volume 38 of COSPAR Meeting, 2826. ads:2010cosp...38.2826B.
Brandenburg (2011a). Dissipation in dynamos at low and high magnetic Prandtl numbers. Astron. Nachr., 332, 51, January 2011a. doi:10.1002/asna.201011478, arXiv:1010.4805, ads:2011AN....332...51B.
Brandenburg (2011b). Nonlinear Small-scale Dynamos at Low Magnetic Prandtl Numbers. Astrophys. J., 741, 92, November 2011b. doi:10.1088/0004-637X/741/2/92, arXiv:1106.5777, ads:2011ApJ...741...92B.
Brandenburg (2011c). Simulations of astrophysical dynamos. In A. Bonanno, E. de Gouveia Dal Pino, and A. G. Kosovichev, editors, IAU Symp., volume 274 of IAU Symp., 402–409. doi:10.1017/S174392131100737X, arXiv:1012.5079, ads:2011IAUS..274..402B.
Brandenburg (2011d). Chandrasekhar-Kendall functions in astrophysical dynamos. Pramana, 77, 67–76, July 2011d. doi:10.1007/s12043-011-0112-5, arXiv:1103.4976, ads:2011Prama..77...67B.
Brandenburg (2013). Non-linear and chaotic dynamo regimes. In A. G. Kosovichev, E. de Gouveia Dal Pino, and Y. Yan, editors, IAU Symp., volume 294 of IAU Symp., 387–398. doi:10.1017/S1743921313002822, arXiv:1305.1952, ads:2013IAUS..294..387B.
Brandenburg (2014). Magnetic Prandtl Number Dependence of the Kinetic-to-magnetic Dissipation Ratio. Astrophys. J., 791, 12, August 2014. doi:10.1088/0004-637X/791/1/12, arXiv:1404.6964, ads:2014ApJ...791...12B.
Brandenburg (2018). Advances in mean-field dynamo theory and applications to astrophysical turbulence. J. Plasma Phys., 84, 735840404, Aug 2018. doi:10.1017/S0022377818000806, arXiv:1801.05384, ads:2018JPlPh..84d7304B.
Brandenburg (2019a). Ambipolar diffusion in large Prandtl number turbulence. Month. Not. Roy. Astron. Soc., 487, 2673–2684, Aug 2019a. doi:10.1093/mnras/stz1509, arXiv:1903.08976, ads:2019MNRAS.487.2673B.
Brandenburg (2019b). The Limited Roles of Autocatalysis and Enantiomeric Cross-Inhibition in Achieving Homochirality in Dilute Systems. Origins of Life and Evolution of the Biosphere, 49, 49–60, Jun 2019b. doi:10.1007/s11084-019-09579-4, arXiv:1903.07855, ads:2019OLEB...49...49B.
Brandenburg (2020a). Hall cascade with fractional magnetic helicity in neutron star crusts. Astrophys. J., 901(1), 18, September 2020a. doi:10.3847/1538-4357/abad92, arXiv:2006.12984, ads:2020ApJ...901...18B.
Brandenburg (2020b). Piecewise quadratic growth during the 2019 novel coronavirus epidemic. Infectious Disease Modelling, 5, 681–690, February 2020b. doi:10.1016/j.idm.2020.08.014, arXiv:2002.03638, ads:2020arXiv200203638B.
Brandenburg (2020c). Scientific usage of the Pencil Code. $\!\!\!$, DOI:10.5281/zenodo.3466444, July 2020c. doi:10.5281/zenodo.3466444, ads:2020zndo...3466444B.
Brandenburg (2023a). Quadratic growth during the COVID-19 pandemic: merging hotspots and reinfections. J. Phys. A Math., 56(4), 044002, January 2023a. doi:10.1088/1751-8121/acb743, arXiv:2206.15459, ads:2023JPhA...56d4002B.
Brandenburg (2023b). Hosking integral in non-helical Hall cascade. J. Plasma Phys., 89(1), 175890101, February 2023b. doi:10.1017/S0022377823000028, arXiv:2211.14197, ads:2023JPlPh..89a1701B.
Brandenburg, Haugen & Dobler (2003). MHD simulations of small and large scale dynamos. In R. Erdélyi, K. Petrovay, B. Roberts, and M. Aschwanden, editors, Turbulence, Waves, and Instabilities in the Solar Plasma, ed. R. Erdélyi, K. Petrovay, B. Roberts, & M. Aschwanden, Turbulence, Waves, and Instabilities in the Solar Plasma, 33–53. Kluwer Acad. Publ., Dordrecht. arXiv:astro-ph/0303371, ads:2003astro.ph..3371B.
Brandenburg, Dintrans & Haugen (2004a). Shearing and embedding box simulations of the magnetorotational instability. In R. Rosner, G. Rüdiger, and A. Bonanno, editors, MHD Couette Flows: Experiments and Models, volume 733 of Am. Inst. Phys. Conf. Ser., 122–136. doi:10.1063/1.1832142, arXiv:astro-ph/0412363, ads:2004AIPC..733..122B.
Brandenburg, Sandin & Käpylä (2004b). Helical coronal ejections and their role in the solar cycle. In A. V. Stepanov, E. E. Benevolenskaya, and A. G. Kosovichev, editors, Multi-Wavelength Investigations of Solar Activity, volume 223 of IAU Symp., 57–64. doi:10.1017/S1743921304005101, arXiv:astro-ph/0407598, ads:2004IAUS..223...57B.
Brandenburg, Käpylä & Mohammed (2004c). Non-Fickian diffusion and tau approximation from numerical turbulence. Phys. Fluids, 16, 1020–1027, April 2004c. doi:10.1063/1.1651480, arXiv:astro-ph/0306521, ads:2004PhFl...16.1020B.
Brandenburg, Käpylä & Mohammed (2005a). Passive scalar diffusion as a damped wave. In J. Peinke, A. Kittel, S. Barth, and M. Oberlack, editors, Progress in Turbulence, Springer-Verlag, 3–6. arXiv:physics/0404118, ads:2004physics...4118B.
Brandenburg, Haugen, Käpylä & Sandin (2005b). The problem of small and large scale fields in the solar dynamo. Astron. Nachr., 326, 174–185, April 2005b. doi:10.1002/asna.200410373, arXiv:astro-ph/0412364, ads:2005AN....326..174B.
Brandenburg, Haugen & Mee (2005c). Nonhelical turbulent dynamos: shocks and shear. In K. T. Chyzy, K. Otmianowska-Mazur, M. Soida, and R.-J. Dettmar, editors, The Magnetized Plasma in Galaxy Evolution, 139–146. arXiv:astro-ph/0501006, ads:2005mpge.conf..139B.
Brandenburg, Käpylä, Mitra, Moss & Tavakol (2007a). The helicity constraint in spherical shell dynamos. Astron. Nachr., 328, 1118, December 2007a. doi:10.1002/asna.200710881, arXiv:0711.3616, ads:2007AN....328.1118B.
Brandenburg, Korpi & Mee (2007b). Thermal Instability in Shearing and Periodic Turbulence. Astrophys. J., 654, 945–954, January 2007b. doi:10.1086/509143, arXiv:astro-ph/0604244, ads:2007ApJ...654..945B.
Brandenburg, Rädler & Schrinner (2008a). Scale dependence of alpha effect and turbulent diffusivity. Astron. Astrophys., 482, 739–746, May 2008a. doi:10.1051/0004-6361:200809365, arXiv:0801.1320, ads:2008A%26A...482..739B.
Brandenburg, Rädler, Rheinhardt & Käpylä (2008b). Magnetic Diffusivity Tensor and Dynamo Effects in Rotating and Shearing Turbulence. Astrophys. J., 676, 740–751, March 2008b. doi:10.1086/527373, arXiv:0710.4059, ads:2008ApJ...676..740B.
Brandenburg, Rädler, Rheinhardt & Subramanian (2008c). Magnetic Quenching of α and Diffusivity Tensors in Helical Turbulence. Astrophys. J. Lett., 687, L49–L52, November 2008c. doi:10.1086/593146, arXiv:0805.1287, ads:2008ApJ...687L..49B.
Brandenburg, Svedin & Vasil (2009a). Turbulent diffusion with rotation or magnetic fields. Month. Not. Roy. Astron. Soc., 395, 1599–1606, May 2009a. doi:10.1111/j.1365-2966.2009.14646.x, arXiv:0901.2112, ads:2009MNRAS.395.1599B.
Brandenburg, Candelaresi & Chatterjee (2009b). Small-scale magnetic helicity losses from a mean-field dynamo. Month. Not. Roy. Astron. Soc., 398, 1414–1422, September 2009b. doi:10.1111/j.1365-2966.2009.15188.x, arXiv:0905.0242, ads:2009MNRAS.398.1414B.
Brandenburg, Kleeorin & Rogachevskii (2010a). Large-scale magnetic flux concentrations from turbulent stresses. Astron. Nachr., 331, 5, January 2010a. doi:10.1002/asna.200911311, arXiv:0910.1835, ads:2010AN....331....5B.
Brandenburg, Chatterjee, Del Sordo, Hubbard, Käpylä & Rheinhardt (2010b). Turbulent transport in hydromagnetic flows. Phys. Scripta Vol. T, 142, 014028, December 2010b. doi:10.1088/0031-8949/2010/T142/014028, arXiv:1004.5380, ads:2010PhST..142a4028B.
Brandenburg, Kemel, Kleeorin, Mitra & Rogachevskii (2011a). Detection of Negative Effective Magnetic Pressure Instability in Turbulence Simulations. Astrophys. J. Lett., 740, L50, October 2011a. doi:10.1088/2041-8205/740/2/L50, arXiv:1109.1270, ads:2011ApJ...740L..50B.
Brandenburg, Käpylä & Korpi (2011b). From convective to stellar dynamos. In N. H. Brummell, A. S. Brun, M. S. Miesch, and Y. Ponty, editors, IAU Symp., volume 271 of IAU Symp., 279–287. doi:10.1017/S1743921311017704, arXiv:1103.5475, ads:2011IAUS..271..279B.
Brandenburg, Haugen & Babkovskaia (2011c). Turbulent front speed in the Fisher equation: Dependence on Damköhler number. Phys. Rev. E, 83, 016304, January 2011c. doi:10.1103/PhysRevE.83.016304, arXiv:1008.5145, ads:2011PhRvE..83a6304B.
Brandenburg, Rädler & Kemel (2012a). Mean-field transport in stratified and/or rotating turbulence. Astron. Astrophys., 539, A35, March 2012a. doi:10.1051/0004-6361/201117871, arXiv:1108.2264, ads:2012A%26A...539A..35B.
Brandenburg, Rädler & Kemel (2012b). Mean-field transport in stratified and/or rotating turbulence (Corrigendum). Astron. Astrophys., 545, C1, September 2012b. doi:10.1051/0004-6361/201117871e, ads:2012A%26A...545C...1B.
Brandenburg, Kemel, Kleeorin & Rogachevskii (2012c). The Negative Effective Magnetic Pressure in Stratified Forced Turbulence. Astrophys. J., 749, 179, April 2012c. doi:10.1088/0004-637X/749/2/179, arXiv:1005.5700, ads:2012ApJ...749..179B.
Brandenburg, Sokoloff & Subramanian (2012d). Current Status of Turbulent Dynamo Theory. From Large-Scale to Small-Scale Dynamos. Space Sci. Ref., 169, 123–157, September 2012d. doi:10.1007/s11214-012-9909-x, arXiv:1203.6195, ads:2012SSRv..169..123B.
Brandenburg, Gressel, Käpylä, Kleeorin, Mantere & Rogachevskii (2013a). New scaling for the alpha effect in slowly rotating turbulence. Astrophys. J., 762, 127, January 2013a. doi:10.1088/0004-637X/762/2/127, arXiv:1208.5004, ads:2013ApJ...762..127B.
Brandenburg, Kleeorin & Rogachevskii (2013b). Self-assembly of Shallow Magnetic Spots through Strongly Stratified Turbulence. Astrophys. J. Lett., 776, L23, October 2013b. doi:10.1088/2041-8205/776/2/L23, arXiv:1306.4915, ads:2013ApJ...776L..23B.
Brandenburg, Gressel, Jabbari, Kleeorin & Rogachevskii (2014). Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field. Astron. Astrophys., 562, A53, February 2014. doi:10.1051/0004-6361/201322681, arXiv:1309.3547, ads:2014A%26A...562A..53B.
Brandenburg, Kahniashvili & Tevzadze (2015). Nonhelical Inverse Transfer of a Decaying Turbulent Magnetic Field. Phys. Rev. Lett., 114, 075001, February 2015. doi:10.1103/PhysRevLett.114.075001, arXiv:1404.2238, ads:2015PhRvL.114g5001B.
Brandenburg, Schober & Rogachevskii (2017a). The contribution of kinetic helicity to turbulent magnetic diffusivity. Astronomische Nachrichten, 338, 790–793, August 2017a. doi:10.1002/asna.201713384, ads:2017AN....338..790B.
Brandenburg, Petrie & Singh (2017b). Two-scale Analysis of Solar Magnetic Helicity. Astrophys. J., 836, 21, February 2017b. doi:10.3847/1538-4357/836/1/21, arXiv:1610.05410, ads:2017ApJ...836...21B.
Brandenburg, Ashurova & Jabbari (2017c). Compensating Faraday Depolarization by Magnetic Helicity in the Solar Corona. Astrophys. J., 845, L15, August 2017c. doi:10.3847/2041-8213/aa844b, ads:2017ApJ...845L..15B.
Brandenburg, Schober, Rogachevskii, Kahniashvili, Boyarsky, Fröhlich, Ruchayskiy & Kleeorin (2017d). The Turbulent Chiral Magnetic Cascade in the Early Universe. Astrophys. J., 845, L21, August 2017d. doi:10.3847/2041-8213/aa855d, ads:2017ApJ...845L..21B.
Brandenburg, Kahniashvili, Mandal, Roper Pol, Tevzadze & Vachaspati (2017e). Evolution of hydromagnetic turbulence from the electroweak phase transition. Phys. Rev. D, 96, 123528, December 2017e. doi:10.1103/PhysRevD.96.123528, ads:2017PhRvD..96l3528B.
Brandenburg, Durrer, Kahniashvili, Mand al & Yin (2018a). Statistical properties of scale-invariant helical magnetic fields and applications to cosmology. J. Cosmol. Astropart. Phys., 2018, 034, Aug 2018a. doi:10.1088/1475-7516/2018/08/034, arXiv:1804.01177, ads:2018JCAP...08..034B.
Brandenburg, Haugen, Li & Subramanian (2018b). Varying the forcing scale in low Prandtl number dynamos. Month. Not. Roy. Astron. Soc., 479, 2827–2833, September 2018b. doi:10.1093/mnras/sty1570, arXiv:1805.01249, ads:2018MNRAS.479.2827B.
Brandenburg, Bracco, Kahniashvili, Mand al, Roper Pol, Petrie & Singh (2019a). E and B Polarizations from Inhomogeneous and Solar Surface Turbulence. Astrophys. J., 870, 87, January 2019a. doi:10.3847/1538-4357/aaf383, arXiv:1807.11457, ads:2019ApJ...870...87B.
Brandenburg, Kahniashvili, Mandal, Roper Pol, Tevzadze & Vachaspati (2019b). Dynamo effect in decaying helical turbulence. Phys. Rev. Fluids, 4, 024608, Feb 2019b. doi:10.1103/PhysRevFluids.4.024608, ads:2019PhRvF...4b4608B.
Brandenburg, Candelaresi & Gent (2020a). Introduction to \sf The Physics and Algorithms of the Pencil Code. Geophys. Astrophys. Fluid Dynam., 114, 1–7, March 2020a. doi:10.1080/03091929.2019.1677015, ads:2020GApFD.114....1B.
Brandenburg, Durrer, Huang, Kahniashvili, Mandal & Mukohyama (2020b). Primordial magnetic helicity evolution with a homogeneous magnetic field from inflation. Phys. Rev. D, 102(2), 023536, July 2020b. doi:10.1103/PhysRevD.102.023536, arXiv:2005.06449, ads:2020PhRvD.102b3536B.
Brandenburg, He, Kahniashvili, Rheinhardt & Schober (2021a). Relic Gravitational Waves from the Chiral Magnetic Effect. Astrophys. J., 911(2), 110, April 2021a. doi:10.3847/1538-4357/abe4d7, arXiv:2101.08178, ads:2021ApJ...911..110B.
Brandenburg, He & Sharma (2021b). Simulations of Helical Inflationary Magnetogenesis and Gravitational Waves. Astrophys. J., 922(2), 192, December 2021b. doi:10.3847/1538-4357/ac20d9, arXiv:2107.12333, ads:2021ApJ...922..192B.
Brandenburg, Gogoberidze, Kahniashvili, Mandal, Roper Pol & Shenoy (2021c). The scalar, vector, and tensor modes in gravitational wave turbulence simulations. Class. Quantum Grav., 38(14), 145002, July 2021c. doi:10.1088/1361-6382/ac011c, arXiv:2103.01140, ads:2021CQGra..38n5002B.
Brandenburg, Clarke, He & Kahniashvili (2021d). Can we observe the QCD phase transition-generated gravitational waves through pulsar timing arrays? Phys. Rev. D, 104(4), 043513, August 2021d. doi:10.1103/PhysRevD.104.043513, arXiv:2102.12428, ads:2021PhRvD.104d3513B.
Brandenburg, Clarke, He & Kahniashvili (2021e). Can we observe the QCD phase transition-generated gravitational waves through pulsar timing arrays? arXiv e-prints, February 2021e. arXiv:2102.12428, ads:2021arXiv210212428B.
Brandenburg, Zhou & Sharma (2023a). Batchelor, Saffman, and Kazantsev spectra in galactic small-scale dynamos. Month. Not. Roy. Astron. Soc., 518(3), 3312–3325, January 2023a. doi:10.1093/mnras/stac3217, arXiv:2207.09414, ads:2023MNRAS.518.3312B.
Brandenburg, Rogachevskii & Schober (2023b). Dissipative magnetic structures and scales in small-scale dynamos. Month. Not. Roy. Astron. Soc., 518(4), 6367–6375, February 2023b. doi:10.1093/mnras/stac3555, arXiv:2209.08717, ads:2023MNRAS.518.6367B.
Brandenburg, Kamada, Mukaida, Schmitz & Schober (2023c). Chiral magnetohydrodynamics with zero total chirality. Phys. Rev. D, 108(6), 063529, September 2023c. doi:10.1103/PhysRevD.108.063529, arXiv:2304.06612, ads:2023PhRvD.108f3529B.
Brandenburg, Kamada & Schober (2023d). Decay law of magnetic turbulence with helicity balanced by chiral fermions. Phys. Rev. Res., 5(2), L022028, May 2023d. doi:10.1103/PhysRevResearch.5.L022028, arXiv:2302.00512, ads:2023PhRvR...5b2028B.
Brandenburg, Sharma & Vachaspati (2023e). Inverse cascading for initial MHD turbulence spectra between Saffman and Batchelor. J. Plasma Phys., 89, 905890606, July 2023e. doi:10.1017/S0022377823001253, arXiv:2307.04602, ads:2023arXiv230704602B.
Brandenburg, Neronov & Vazza (2024a). Resistively controlled primordial magnetic turbulence decay. Astron. Astrophys., 687, A186, July 2024a. doi:10.1051/0004-6361/202449267, arXiv:2401.08569, ads:2024A&A...687A.186B.
Brandenburg, Iarygina, Sfakianakis & Sharma (2024b). Magnetogenesis from axion-SU(2) inflation. J. Cosmol. Astropart. Phys., 2024(12), 057, December 2024b. doi:10.1088/1475-7516/2024/12/057, arXiv:2408.17413, ads:2024JCAP...12..057B.
Brandenburg, Clarke, Kahniashvili, Long & Sun (2024c). Relic gravitational waves from the chiral plasma instability in the standard cosmological model. Phys. Rev. D, 109(4), 043534, February 2024c. doi:10.1103/PhysRevD.109.043534, arXiv:2307.09385, ads:2024PhRvD.109d3534B.
Brandenburg, Käpylä, Rogachevskii & Yokoi (2025a). Helicity Effect on Turbulent Passive and Active Scalar Diffusivities. Astrophys. J., 984(1), 88, May 2025a. doi:10.3847/1538-4357/adc691, arXiv:2501.08879, ads:2025ApJ...984...88B.
Brandenburg, Larsson, Del Sordo & Käpylä (2025b). Magnetorotational Instability in a Solar Near-surface Mean-field Dynamo. Astrophys. J., 993(1), 22, November 2025b. doi:10.3847/1538-4357/ae03c4, arXiv:2504.16849, ads:2025ApJ...993...22B.
Brandenburg, Yi & Wu (2025c). Inverse cascade from helical and non-helical decaying columnar magnetic fields. J. Plasma Phys., 91(4), E113, August 2025c. doi:10.1017/S0022377825100664, arXiv:2501.12200, ads:2025JPlPh..91E.113B.
Brandenburg, Larsson, Del Sordo & Käpylä (2025d). Magnetorotational instability in a solar mean-field dynamo. arXiv e-prints, April 2025d. doi:10.48550/arXiv.2504.16849, arXiv:2504.16849, ads:2025arXiv250416849B.
Brandenburg, Ghosh, Vazza & Neronov (2025e). Magnetic field spreading from stellar and galactic dynamos into the exterior. arXiv e-prints, December 2025e. doi:10.48550/arXiv.2512.17770, arXiv:2512.17770, ads:2025arXiv251217770B.
Brandenburg, Ghosh, Vazza & Neronov (2026). Magnetic Field Spreading from Stellar and Galactic Dynamos into the Exterior. Astrophys. J., 1002(2), 165, May 2026. doi:10.3847/1538-4357/ae5ba0, arXiv:2512.17770, ads:2026ApJ..1002..165B.
Brandenburg & Banerjee (2025). Turbulent magnetic decay controlled by two conserved quantities. J. Plasma Phys., 91(1), E5, January 2025. doi:10.1017/S0022377824001508, arXiv:2406.11798, ads:2025JPlPh..91E...5B.
Brandenburg & Blackman (2005). Ejection of Bi-Helical Fields from the Sun. Highlights Astron., 13, 101, January 2005. ads:2005HiA....13..101B.
Brandenburg & Boldyrev (2020). The Turbulent Stress Spectrum in the Inertial and Subinertial Ranges. Astrophys. J., 892, 80, April 2020. doi:10.3847/1538-4357/ab77bd, arXiv:1912.07499, ads:2020ApJ...892...80B.
Brandenburg & Brüggen (2020). Hemispheric Handedness in the Galactic Synchrotron Polarization Foreground. Astrophys. J. Lett., 896, L14, June 2020. doi:10.3847/2041-8213/ab974a, arXiv:2003.14178, ads:2020ApJ...896L..14B.
Brandenburg & Chatterjee (2018). Strong nonlocality variations in a spherical mean-field dynamo. Astronomische Nachrichten, 339, 118–126, February 2018. doi:10.1002/asna.201813472, arXiv:1802.04231, ads:2018AN....339..118B.
Brandenburg & Chen (2020). The nature of mean-field generation in three classes of optimal dynamos. J. Plasma Phys., 86, 905860110, February 2020. doi:10.1017/S0022377820000082, arXiv:1911.01712, ads:2020JPlPh..86a9010B.
Brandenburg & Das (2020). The time step constraint in radiation hydrodynamics. Geophys. Astrophys. Fluid Dynam., 114, 162–195, March 2020. doi:10.1080/03091929.2019.1676894, arXiv:1901.06385, ads:2020GApFD.114..162B.
Brandenburg & Das (2021). Turbulent radiative diffusion and turbulent Newtonian cooling. Phys. Fluids, 33(9), 095125, September 2021. doi:10.1063/5.0065485, arXiv:2010.07046, ads:2021PhFl...33i5125B.
Brandenburg & Del Sordo (2010). Turbulent diffusion and galactic magnetism. Highlights Astron., 15, 432–433, November 2010. doi:10.1017/S1743921310010148, arXiv:0910.0072, ads:2010HiA....15..432B.
Brandenburg & Dintrans (2006). Nonaxisymmetric stability in the shearing sheet approximation. Astron. Astrophys., 450, 437–444, May 2006. doi:10.1051/0004-6361:20054639, arXiv:astro-ph/0111313, ads:2006A%26A...450..437B.
Brandenburg & Dobler (2010). Pencil Code: Finite-difference Code for Compressible Hydrodynamic Flows Astrophysics Source Code Library. arXiv:1010.060, ads:2010ascl.soft10060B.
Brandenburg & Furuya (2020). Application of a helicity proxy to edge-on galaxies. Month. Not. Roy. Astron. Soc., 496(4), 4749–4759, June 2020. doi:10.1093/mnras/staa1795, arXiv:2003.07284, ads:2020MNRAS.496.4749B.
Brandenburg & Guerrero (2012). Cycles and cycle modulations. In C. H. Mandrini and D. F. Webb, editors, IAU Symp., volume 286 of IAU Symp., 37–48. doi:10.1017/S1743921312004619, arXiv:1111.3351, ads:2012IAUS..286...37B.
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