Professor S. Jon Chapman is a faculty member at the Mathematical Institute, University of Oxford, holding the position of Professor of Mathematics and its Applications. He is affiliated with the Oxford Centre for Industrial and Applied Mathematics research group. His educational background includes a DPhil, MA, and BA. Research interests span diverse areas of applied mathematics and scientific modeling: Industrial mathematics and mathematical modeling Partial differential equations and asymptotic methods Fluid dynamics and turbulence theory Biophysical applications including tumor growth and tissue modeling Electromagnetic scattering and superconductivity Materials science and energy systems Publication analysis reveals two primary trends: Recent work (2025) focuses on electrochemical systems (battery modeling, gas-induced bulging) and biological applications (organoid models). Earlier influential publications established expertise in pattern formation, fluid dynamics (ship waves, spiral waves), and transport phenomena in biological systems. Mathematical techniques consistently feature multiscale analysis, asymptotic methods, and nonlinear modeling. Awards and honors recognizing scholarly contributions: Naylor Prize (2015) Julian Cole Prize (2002) Whitehead Prize (1998) Richard C. DiPrima Prize (1994) Johnson Mathematical Prize (1992) No information is available regarding student advising, grants, or laboratory affiliations.
Professor Philip Steinberg is a distinguished academic at Durham University, serving as a Professor in the Department of Geography within the Faculty of Social Sciences and Health. He also holds leadership positions as the Director of the Northern Ireland / Northeast England Doctoral Training Partnership (NINE DTP) and Durham Arctic Director. Additionally, he is an Associate Fellow in the Institute of Advanced Study at Durham. Steinberg earned his MA and PhD from Clark University's Graduate School of Geography (1990-1996). Prior to joining Durham in 2013, he spent sixteen years at Florida State University's Department of Geography, with research interludes at the New York Public Library's Cullman Center (2002-2003), the University of California, Santa Cruz (2005-2006), and Royal Holloway, University of London (2012-2013). He also taught briefly at Bucknell University in 1997. His research focuses on the historical and ongoing projection of social power onto spaces resistant to state territorialization, particularly the world-ocean, the Arctic, and electronic communications. Steinberg explores how these spaces challenge conventional notions of territory, sovereignty, and governance. His current research concentrates on Wet Ontologies and Ocean Governance and Arctic Politics and the Liveliness of Sea Ice , examining how liquid and frozen maritime environments complicate traditional geopolitical frameworks. Analysis of Steinberg's recent publications reveals a sophisticated interdisciplinary approach that bridges political geography, ocean studies, and Arctic research. His work consistently challenges conventional land-based territorial concepts by examining fluid, dynamic maritime spaces. Key themes include the politics of ocean privatization, Arctic sovereignty complexities, oceanic epistemologies, and the interplay between technological imaging and marine governance. His scholarship demonstrates a commitment to rethinking spatial concepts through watery and frozen environments, with significant implications for international law, environmental policy, and geopolitical theory. Among his notable professional contributions, Steinberg served as editor-in-chief of Political Geography (2016-2019) and has directed several significant research centers including IBRU: Durham University's Centre for Borders Research, the Durham Arctic Research Centre for Training and Interdisciplinary Collaboration (DurhamARCTIC), and the Northern Ireland / Northeast England Doctoral Training Partnership (NINE DTP), which supports approximately 150-200 PhD students annually across seven universities. Steinberg has supervised numerous doctoral students, including Joaquim Gaignard. His leadership in interdisciplinary doctoral training, particularly through DurhamARCTIC and NINE DTP, has secured substantial funding for Arctic research and social science doctoral education. His work with IBRU has facilitated boundary dispute resolution and advanced understanding of border areas through professional training and research initiatives. As Director of IBRU, Steinberg leads Durham University's Centre for Borders Research, which offers training courses on boundary delimitation and supports research on sovereignty, territory, and the political organization of space. His leadership of DurhamARCTIC has facilitated Arctic research collaborations across disciplines, building on a six-year grant that trained 15 PhD students across seven disciplines. Through these centers, Steinberg fosters innovative approaches to understanding geopolitical spaces that challenge conventional land-based territorial frameworks.
Mohamed Houssem Kasbaoui is an Assistant Professor in the Department of Mechanical and Aerospace Engineering at Arizona State University's School for Engineering of Matter, Transport and Energy. His research focuses on Computational Fluid Dynamics and Multiphase Flow simulations, with expertise in particle-laden flows, immersed boundary methods, and high-fidelity numerical tools. PhD, Aerospace Engineering (Cornell University, 2017) MSc, Aerospace Engineering (Cornell University, 2015) MSc, Theoretical Physics (Université Paris-Sud, 2014) Diplôme d'Ingénieur (Ecole Centrale Paris, 2013) BSc, Theoretical Physics (Université Paris-Sud, 2011) His work spans particle-resolved DNS , turbulent flow modulation , and environmental applications like microplastic transport in riverbeds. He leads the Kasbaoui Research Group , developing open-source tools like LEAP for CFD simulations. Recent publications highlight expertise in: Vortex dynamics in dusty flows Drag reduction mechanisms Immersed boundary modeling Microplastic trapping in sediment Swirling flow simulations Scale-separated combustion modeling Awarded the 2021 ACS Petroleum Research Fund Doctoral Investigator Award , his group actively seeks students with skills in Applied Mathematics and Parallel Programming . Research spans NSF-funded projects on Environmental Microplastics and Planetary Dust Clouds .
John van Duynhoven is a Professor of Biophysics at Wageningen University and Research. His work bridges advanced imaging techniques and food science, focusing on lipid oxidation, protein processing, and emulsion structure. Affiliation: Wageningen University and Research Academic Rank: Professor Research Interests: He investigates food structure and stability using NMR spectroscopy, super-resolution microscopy, and magnetic resonance imaging. Key areas include lipid oxidation pathways, plant-protein extrusion, and granular flow dynamics. Scientific Contributions: Supervised multiple PhD projects on multiscale protein modeling, emulsion oxidation, and infant nutrition protein digestion. His recent articles highlight innovations in quantifying anisotropic food structures and oxidation products. Collaborations: Partnerships span imaging techniques, X-ray scattering, and food technology. Active projects include lipid oxidation mapping and protein extrusion modeling.
Ezequiel Goldschmidt, MD, PhD is an Assistant Professor in the Department of Neurological Surgery at the University of California, San Francisco (UCSF) . He is affiliated with the Brain Tumor Center and specializes in treating brain, skull base, and pituitary gland tumors using minimally invasive approaches . A proud member of the Latinx community, his research focuses on improving surgical techniques through human anatomy studies and exploring how developmental biology can enhance tumor growth understanding and brain recovery post-injury. Education: MD and PhD from Universidad de Buenos Aires Facultad de Medicina (2009) Residency in Neurosurgery at University of Pittsburgh Medical Center (2020) Postdoctoral Surgical Fellowship in Neuroplasticity at Karolinska Institute (Sweden) Research Interests: He investigates neurosurgical anatomy , endoscopic techniques , and brain tumor biology . His work includes determining risk factors for postoperative complications , application of indocyanine green (ICG) angiography , and genetic profiling of brain tumors . Clinical Trials: Dr. Goldschmidt leads trials on optic nerve stimulation to prevent visual deficits and ICG angiogram as a predictor of postoperative visual function. Scientific Awards: Fellowship in Skull Base Surgery at University of Pittsburgh Medical Center (2019) Fellowship in Neurosurgery Spine at University of Pittsburgh Medical Center (2015) Postdoctoral Surgical Fellowship in Neuroplasticity at Karolinska Institute Publications: His research spans minimally invasive neurosurgery , brain tumor classification , and intraoperative monitoring , with recent works on HPV-associated sinonasal cancer and immune checkpoint inhibition in meningiomas.
Miroslav Grmela is a Researcher at the Department of Chemical Engineering in Polytechnique Montréal , and a member of the Research Center for High-Performance Polymer and Composite Systems (CREPEC) . His work spans thermodynamics, transfer processes, and multiscale modeling of complex fluids. Grmela’s research focuses on non-equilibrium thermodynamics , contact geometry in kinetic dynamics , and mesoscopic theories of polymer suspensions, superfluids, and nanocomposites. He has extensively explored the role of energy and entropy in multiscale systems, with recent publications addressing geometric formulations of thermodynamics and neural network applications to non-symplectic mechanics. Analysis of his 15 most recent articles reveals trends in multiscale thermodynamics , non-Fourier heat conduction , GENERIC formalism , and quantum hydrodynamics . His work often bridges geometric mechanics with thermodynamic consistency. Grmela has supervised 10 graduate students (7 PhD, 3 Master’s) in projects involving nanocomposite thermal conductivity , polymer rheology , and powder suspension simulations . He has no listed scientific awards. His research intersects with fluid dynamics , polymer science , and statistical mechanics , emphasizing mathematical structures like Poisson brackets and Hamiltonian formulations . The CREPEC laboratory provides institutional support for his studies on polymers and composites.
Dr James Shucksmith is a Senior Lecturer in Water Engineering at the School of Mechanical, Aerospace and Civil Engineering, University of Sheffield. After completing his undergraduate degree and PhD at the same department, he joined the academic staff in 2010 following a KTP associate role with Yorkshire Water. His research focuses on urban flooding hydrodynamics, water quality modeling, and sustainable drainage systems. Co-director of EPSRC Centre for Doctoral Training in Water Infrastructure and Resilience Current projects: Real Time Abstraction Management (with Severn Trent Water), Centaur FloodInteract Research interests include: Urban flood hydrodynamics and drainage-surface flow interactions Water quality forecasting tools for surface water abstraction Development of local real-time control systems for urban drainage Experimental validation of flood models using PIV measurements His publications (2010-2025) cover topics like contaminant transport in flooded sewer systems, longitudinal dispersion modeling, and real-time control optimization. Recent work focuses on data-driven approaches for Cryptosporidium prediction and E. coli forecasting.
Massimo Trovato is a Full Professor of Mathematical Physics at the University of Catania, where he has been teaching since 2004 and has held the rank of full professor since 2010. He serves as Director of the INDAM Unit of the Department of Mathematics and Informatics (DMI) since 2014. Professor Trovato teaches courses in both the Mathematics and Physics degree programs at the University of Catania. Professor Trovato's research spans multiple areas within mathematical physics, with a particular focus on theoretical frameworks for understanding physical systems. His work integrates advanced mathematical techniques with physical principles to develop models that explain complex phenomena in semiconductor physics, quantum systems, and fluid dynamics. His research interests include: Mathematical Physics Statistical Mechanics Quantum Kinetic Theory Semiclassical Kinetic Theory Extended Thermodynamics Maximum Entropy Principle Quantum Maximum Entropy Principle Semiconductor Physics Fluid Dynamics Professor Trovato's publication record demonstrates a consistent focus on entropy principles and their applications across various physical systems. His work shows an evolution from classical thermodynamics to quantum formulations, with particular emphasis on semiconductor applications and 2D materials like graphene. The research trajectory reveals increasing sophistication in handling nonlocal quantum effects and fractional statistics, reflecting the growing complexity of modern physical systems being studied. Professor Trovato has made significant contributions to the theoretical understanding of transport phenomena in semiconductors, particularly through the application of maximum entropy principles to both classical and quantum systems. His research has important implications for the development of next-generation semiconductor devices. His teaching responsibilities include Analytical Mechanics for Physics students and Mathematical Physics II for Mathematics students, demonstrating his commitment to educating the next generation of physicists and mathematicians.
Xinliang An is an Associate Professor of Mathematics at the National University of Singapore (NUS), where he joined in July 2018. His research focuses on understanding singularity formation, regularity, asymptotic stability, long time behavior, and geometric shapes of solutions to important partial differential equations, with particular emphasis on Einstein's equations in general relativity, Euler equations and Navier-Stokes equations in fluid dynamics, and elastic wave equations in elastic mechanics. Dr. An received his Ph.D. in June 2014 from the Department of Mathematics at Princeton University, where he was advised by Professor Sergiu Klainerman, a renowned expert in general relativity and partial differential equations. His doctoral work laid the foundation for his subsequent research on gravitational collapse and singularity formation. Dr. An's research spans multiple areas of mathematical physics, with a focus on gravitational collapse, big bang singularities in cosmology, and the detailed mathematical analysis of fluid dynamics and elastic mechanics. His work bridges pure mathematics with theoretical physics, particularly in understanding the formation of singularities in Einstein's equations. He has made significant contributions to the mathematical theory of black hole formation, including the emergence of apparent horizons and the analysis of spacelike singularities inside black holes. His recent work extends to studying the stability of Taylor-Couette flows in fluid dynamics, demonstrating how rotational effects influence dissipation rates through enhanced dissipation phenomena. Analysis of Dr. An's publication record reveals a strong progression from vacuum spacetimes to more complex physical systems. His early work focused on trapped surface formation in vacuum Einstein equations, then expanded to include electromagnetic fields (Einstein-Maxwell system), charged scalar fields, and fluid dynamics. A key theme across his publications is the development of scale-critical techniques to analyze singularity formation, with numerous papers establishing polynomial blow-up upper bounds for various geometric quantities near singularities. His research demonstrates exceptional technical mastery in handling non-strictly hyperbolic systems with multiple wave speeds. Dr. An has made significant methodological contributions by connecting Christodoulou's short-pulse method with Klainerman-Rodnianski's signature counting argument to the peeling properties studied in small-data regimes. This innovative approach has allowed him to avoid elliptic estimates and geometric renormalizations in some cases, providing new technical improvements and simplifications to existing results. His work on low-regularity ill-posedness for elastic wave systems has established that the Cauchy problem for 3D elastic waves is ill-posed in H³(ℝ³) due to instantaneous shock formation.
Amin Mehrabian serves as an Associate Professor in the Department of Energy and Mineral Engineering within the College of Earth and Mineral Sciences at The Pennsylvania State University. His academic appointment centers on petroleum and natural gas engineering with a focus on subsurface mechanics and energy applications. He maintains active research collaborations with major energy companies and has translated academic findings into industry-deployed digital solutions. His educational background includes dual bachelor's degrees in Petroleum and Mechanical Engineering from Sharif University of Technology (2004-2005), a Master's in Mechanical Engineering from the same institution (2006), and a Ph.D. in Petroleum Engineering from the University of Oklahoma (2013). Prior to academia, he worked as a principal R&D engineer at Halliburton's Houston Technology Center. Mehrabian's research investigates coupled physical processes in porous media, including deformation, fracture mechanics, fluid transport, and electrochemical interactions. His work bridges theoretical poromechanics with practical applications in drilling, reservoir management, and energy storage. Key methodologies involve analytical modeling of nonlinear phenomena in deformable rocks and development of constitutive relations for complex subsurface systems. Analysis of his recent publications reveals consistent focus on poro-viscoelastic behavior, wellbore stability in depleted reservoirs, and nonlinear transport phenomena. His work demonstrates strong integration of geomechanics with fluid dynamics, particularly in unconventional reservoir contexts. The research shows increasing application of computational methods to solve industry-relevant problems in drilling and completion engineering. Mehrabian teaches core courses including Drilling Engineering (PNG 450), Drilling Engineering Laboratory (PNG 451), and graduate-level Coupled Flow and Deformation in Porous Media (PNG 502). His industry experience directly informs his pedagogical approach, emphasizing practical problem-solving alongside theoretical foundations. He has developed patented technologies related to managed pressure drilling and wellbore hydraulics that are implemented in field operations. His research group produces high-impact publications in top journals such as Water Resources Research, Journal of Fluid Mechanics, and Society of Petroleum Engineers Journal. The group maintains strong industry partnerships that facilitate technology transfer from academic research to field implementation, particularly in the areas of wellbore stability analysis and lost circulation mitigation.
Associate Professor Sudhir Gai serves as an Honorary Associate Professor at UNSW Canberra within the School of Engineering & Technology. With a distinguished career spanning over five decades, Professor Gai has established himself as a leading authority in high-speed aerodynamics, specializing in hypersonic and supersonic flow phenomena. His extensive publication record from 1969 through 2025 demonstrates sustained research excellence in shock wave/boundary layer interactions, flow separation mechanisms, and high-enthalpy flow dynamics. Professor Gai's research focuses on the complex fluid dynamics of high-speed flows, with particular emphasis on shock wave/boundary layer interactions, separation phenomena in hypersonic and supersonic regimes, and the effects of high-enthalpy conditions on aerodynamic performance. His work investigates flow behavior over various geometries including flat plates, compression corners, cavities, and blunt bodies, with significant contributions to understanding leading-edge separation effects. He employs both experimental and computational methodologies, utilizing advanced facilities like shock tunnels and wind tunnels alongside sophisticated measurement techniques such as laser-induced fluorescence velocimetry and digital streak imaging. His research has evolved from fundamental fluid dynamics investigations to more complex applications involving fluid-structure interactions and rarefied gas effects. Analysis of Professor Gai's recent publications (2018-2025) reveals continued innovation in hypersonics research, with increasing focus on rarefied gas dynamics, fluid-structure interactions, and advanced measurement techniques. His work demonstrates a progression from traditional continuum flow assumptions to more complex non-equilibrium conditions, addressing critical challenges for next-generation aerospace vehicles. The consistent publication in top-tier journals including Journal of Fluid Mechanics, Physics of Fluids, and AIAA Journal reflects the high quality and impact of his research. Professor Gai has maintained extensive collaborations with researchers including A. Khraibut, D. Exposito, A.J. Neely, S. O'Byrne, V. Sridhar, and H. Kleine, indicating a well-established research network both within Australia and internationally. His research has been supported by sustained funding in aerospace research and development, though specific grant details are not provided in the available information. Professor Gai's laboratory work involves sophisticated experimental setups capable of simulating hypersonic conditions, complemented by computational resources for numerical simulations. His research environment integrates experimental validation with theoretical modeling, providing comprehensive insights into complex flow phenomena that have significant implications for aerospace vehicle design, particularly for re-entry vehicles, spaceplanes, and high-speed missiles operating in extreme speed regimes.
Maarten Bassier is an Assistant Professor (tenure track) at KU Leuven, affiliated with the Department of Civil Engineering within the Faculty of Engineering Technology. He is based at the Geomatics unit operating at the Ghent and Aalst Campuses. His academic profile combines research, teaching, and institutional service, with significant contributions to the field of digital construction technologies. As senior academic staff, he serves on both the Council of the Faculty of Engineering Technology and the Civil Engineering Department Council, actively participating in institutional governance while maintaining a robust research program focused on Scan-to-BIM methodologies and geospatial applications in construction. Dr. Bassier's research centers on Scan-to-BIM methodologies, which involve converting 3D scans of existing buildings into Building Information Models. His work bridges geomatics, computer vision, and civil engineering, with applications in construction progress monitoring, infrastructure inspection, and heritage documentation. He applies machine learning techniques to automate aspects of the modeling process, particularly semantic segmentation of point clouds and integration of UAV (drone) data. His research increasingly incorporates deep learning approaches for object detection, segmentation, and completion in complex built environments, with practical applications spanning road construction, bridge inspections, and electrical substation modeling. His interdisciplinary approach connects civil engineering with computer science to solve practical construction challenges through digital innovation. Bassier's recent publication record demonstrates a strong focus on automating the Scan-to-BIM process through advanced computational techniques. His work spans multiple application domains while maintaining a consistent methodological thread of integrating sensing technologies with semantic understanding of construction environments. The trajectory of his research shows increasing sophistication in machine learning applications, moving from basic point cloud processing to complex semantic understanding and automated model generation. His publications appear in high-impact journals across civil engineering, remote sensing, and computer vision domains, reflecting the interdisciplinary nature of his work. SESAME - Semantic Segmentation of Electrical Substations and Derived Models for Engineering (2024-2026) - Promotor UAV-assisted bridge inspections (2022-2027) - Co-promotor XR-empowered dynamic reality modeling for AECO applications (2021-2026) - Co-promotor Digitization in road construction: automating as-built models (2020-2026) - Co-promotor SCAN-to-BIM Automation of as-built BIM production through digitization and machine learning (2020-2025) - Co-promotor As a member of the Division Digital and Sustainable Civil Engineering and the Subdivision Geomatics Ghent, Dr. Bassier contributes to KU Leuven's research ecosystem focused on digital transformation in civil engineering. His teaching portfolio includes courses on BIM, industrial measurements, Scan-to-BIM, 3D modeling, and geomatics, preparing the next generation of civil engineers for the digital construction landscape. His work represents the cutting edge of digital construction technologies, with practical applications that address real-world challenges in infrastructure development and maintenance.
Maarten Blommaert is an Assistant Professor at the Department of Mechanical Engineering, Faculty of Engineering Technology at KU Leuven. He leads the Applied Mechanics and Energy conversion (TME) unit at the Geel Campus and heads the Subdivisie EnergyVille TME. His research focuses on numerical optimization of thermal systems, particularly district heating networks, additive manufactured heat exchangers, and plasma-facing components for nuclear fusion reactors. Assistant Professor, KU Leuven Head, Subdivisie EnergyVille TME Member, KIES Institute Member, Leuven.AM Institute Member, EnergyVille Blommaert's research explores three main areas: heat network optimization through automated design tools like PATHOPT, additive manufacturing of high-performance heat exchangers, and thermally resistant wall modules for nuclear fusion reactors. His work combines computational modeling with advanced manufacturing techniques to enhance energy efficiency and reduce carbon emissions. Scientific awards include collaborative research contributions in: Optimizing district heating networks for renewable energy integration Developing next-generation heat exchangers Advancing nuclear fusion reactor technology Blommaert actively supervises research projects in thermal-fluid systems and collaborates with institutions like VITO and EnergyVille. His research team IDEAL (Innovative Design for Energy Applications Lab) specializes in free-shape and topology optimization techniques for energy components and systems.
Dr. Mohammad Hassan Kayhani is an Associate Professor in the Faculty of Mechanical Engineering at Shahrood University of Technology, Iran. He holds a Ph.D. in Heat and Fluids and has established himself as a leading researcher in heat transfer, combustion, and fluid dynamics. With over 2000 citations on Google Scholar (h-index 41) and 1500+ citations on Scopus (h-index 74), his work has significantly impacted the fields of viscoelastic flow, porous media, and multiphase systems. Dr. Kayhani's research interests span a wide range of topics in thermal and fluid sciences. He specializes in heat transfer phenomena, combustion processes, two-phase flow dynamics, viscoelastic fluid behavior, and transport in porous media. His work often combines experimental, numerical, and theoretical approaches to address complex problems in energy systems, oil recovery, and thermal management. Notably, he has made significant contributions to understanding droplet dynamics, viscous fingering instabilities, and film cooling techniques for gas turbine applications. Analysis of Dr. Kayhani's recent publications reveals a strong focus on advanced fluid dynamics phenomena, particularly involving non-Newtonian and viscoelastic fluids. His work bridges fundamental fluid mechanics with practical applications in energy systems, oil recovery, and thermal management. A significant portion of his research investigates multiphase flow behavior, interfacial phenomena, and instability mechanisms in various engineering contexts. Dr. Kayhani has successfully supervised numerous graduate students, with 84 theses listed under his guidance. His students have pursued research in diverse areas including combustion, heat transfer, fluid dynamics, and energy systems. While specific grant information isn't provided in the available text, his extensive publication record and thesis supervision suggest successful research funding. His laboratory work appears to focus on experimental fluid dynamics, heat transfer measurements, and computational modeling of complex flow phenomena. The research involves advanced techniques such as lattice Boltzmann methods, experimental flow visualization, and thermal measurements in various engineering systems.
Prof. Dr. Siegfried Hess is a Professor at the Technical University of Berlin, where he heads the Statistical Physics: Transport Theory group at the Institute of Theoretical Physics. He served as speaker of the Sonderforschungsbereich 605 "Elementarreibereignisse" until December 2001 and was involved with SFB 335 "Anisotrope Fluide" until December 1998. Prof. Hess received his doctorate in 1967 from Erlangen with the thesis "Verallgemeinerte Boltzmanngleichung für mehratomige Gase" under the supervision of Ludwig Waldmann. His academic genealogy traces back to Albert Einstein with an Einstein number of 3 through Arnold Sommerfeld and Ludwig Waldmann. His research spans multiple areas of statistical physics and transport phenomena with particular focus on: Anisotropic fluids and liquid crystals (nematic, cholesteric, smectic, discotic, cubatic) Molecular dynamics simulations of complex fluids Non-Newtonian viscosity and plastic flow behaviors Thermodynamic properties and transport coefficients Boundary and surface effects in fluid systems Relaxation processes near phase transitions Prof. Hess has supervised numerous PhD students and postdoctoral researchers who have contributed to fields including polymer physics, colloidal systems, and liquid crystal dynamics. His research group maintained strong collaborations through multiple DFG-funded research centers and organized regular seminars on statistical physics topics. His methodological approach combined irreversible thermodynamics, kinetic theory (Boltzmann, Kirkwood-Smoluchowski, and Fokker-Planck equations), and molecular dynamics simulations to investigate complex fluid behavior under various conditions.
