References
- Aris, R. (1962). Vectors, tensors, and the basic equations of fluid mechanics. Prentice-Hall. (Reprinted by Dover, 1989)
- Artelli, M. A., & Deckro, R. F. (2008). Modeling the Lanchester laws with system dynamics. The Journal of Defense Modeling and Simulation: Applications, Methodology, Technology, 5(1), 1–20. https://doi.org/https://doi.org/10.1177/154851290800500101
- Batchelor, G. K. (1967). An introduction to fluid dynamics. Cambridge University Press.
- Bracken, J. (1995). Lanchester models of the Ardennes campaign. Naval Research Logistics, 42(4), 559–577. https://doi.org/https://doi.org/10.1002/1520-6750(199506)42:4<559::AID-NAV3220420405>3.0.CO;2-R
- Clements, R. R., & Hughes, R. L. (2004). Mathematical modelling of a mediaeval battle: The battle of Agincourt, 1415. Mathematics and Computers in Simulation, 64(2), 259–269. https://doi.org/https://doi.org/10.1016/j.matcom.2003.09.019
- Davis, P. K. (1995). Aggregation, disaggregation, and the 3:1 rule in ground combat (Report MR-638-AF/A/OSD). RAND.
- Fields, M. A. (1993). Modeling large scale troop movement using reaction diffusion equations (Technical Report ARL-TR-200). Army Research Laboratory.
- Greenshields, B. D., Bibbins, J. R., Channing, W. S., & Miller, H. H. (1935). A study of traffic capacity. Highway Research Board Proceedings, 14(1), 448–477.
- Helbing, D. (2001). Traffic and related self-driven many-particle systems. Reviews of Modern Physics, 73(4), 1067–1141. https://doi.org/https://doi.org/10.1103/RevModPhys.73.1067
- Helmbold, R. L. (1971). Decision in battle: Breakpoint hypotheses and engagement termination data (Report R-772-PR). RAND.
- Hughes, R. L. (2002). A continuum theory for the flow of pedestrians. Transportation Research Part B: Methodological, 36(6), 507–535. https://doi.org/https://doi.org/10.1016/S0191-2615(01)00015-7
- Hughes, R. L. (2003). The flow of human crowds. Annual Review of Fluid Mechanics, 35(1), 169–182. https://doi.org/https://doi.org/10.1146/annurev.fluid.35.101101.161136
- Jaiswal, N. K., & Nagabhushana, B. S. (1994). Combat modeling with spatial effects, reserved deployment and termination decision rules. Computers & Operations Research, 21(6), 615–628. https://doi.org/https://doi.org/10.1016/0305-0548(94)90077-9
- Keane, T. (2011a). Combat modeling with partial differential equations. Applied Mathematical Modelling, 35(6), 2723–2735. https://doi.org/https://doi.org/10.1016/j.apm.2010.11.057
- Keane, T. (2011b). Partial differential equations versus cellular automatic for modeling combat. The Journal of Defense Modeling and Simulation: Applications, Methodology, Technology, 8(4), 191–204. https://doi.org/https://doi.org/10.1177/1548512910387627
- Lanchester, F. W. (1914). Aircraft in warfare: The dawn of the fourth arm – No. V: The principle of concentration. Engineering, 98, 422–423.
- Lighthill, M. J., & Whitham, G. B. (1955). On kinematic waves. II. A theory of traffic flow on long crowded roads. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 229(1178), 317–345.
- Lucas, T. W., & Turkes, T. (2004). Fitting Lanchester equations to the battles of Kursk and Ardennes. Naval Research Logistics (NRL), 51(1), 95–116. https://doi.org/https://doi.org/10.1002/nav.10101
- MacKay, N. J. (2009). Lanchester models for mixed forces with semi-dynamical target allocation. Journal of the Operational Research Society, 60(10), 1421–1427. https://doi.org/https://doi.org/10.1057/jors.2008.97
- Matei, S. A., Jones, T. C., Kirchubel, R. (2018). The battle of Smolensk: German troops advances July–August 1941. https://www.youtube.com/watch?v=xx4kNeBJTU4
- McKay, S. C., Chaturvedi, A., & Adams, D. E. (2011). A process for anticipating and shaping adversarial behavior. Naval Research Logistics (NRL), 58(3), 255–280. https://doi.org/https://doi.org/10.1002/nav.20440
- Perry, N. (2012). Applications of historical analyses in combat modeling (Report DSTO-TR-2643). Defence Science and Technology Organization.
- Piskin, T., Podolsky, V. A., Macheret, S. O., & Poggie, J. (2019). Challenges in numerical simulation of nanosecond-pulse discharges. Journal of Physics D: Applied Physics, 52(30), 304002. https://doi.org/https://doi.org/10.1088/1361-6463/ab1fbe
- Pletcher, R. H., Tannehill, J. C., & Anderson, D. A. (2013). Computational fluid mechanics and heat transfer (3rd ed.). CRC Press.
- Protopopescu, V., Santoro, R. T., Cox, R. L., & Rusu, P. (1990). Combat modeling with partial differential equations: The bidimensional case (Report ORNL/TM-11343). Oak Ridge National Laboratory.
- Protopopescu, V., Santoro, R. T., & Dockery, J. (1989). Combat modeling with partial differential equations. European Journal of Operational Research, 38(2), 178–183. https://doi.org/https://doi.org/10.1016/0377-2217(89)90102-1
- Protopopescu, V., Santoro, R. T., Dockery, J., Cox, R. L., & Barnes, J. M. (1987). Combat modeling with partial differential equations (Report ORNL/TM-10636). Oak Ridge National Laboratory.
- Rusu, P. (1988). Two-dimensional combat modeling with partial differential equations (Report ORNL/TM-10973). Oak Ridge National Laboratory.
- Santoro, R. T., Rusu, P., & Barnes, J. M. (1989). Mathematical descriptions of offensive combat maneuvers (Report ORNL/TM-11000). Oak Ridge National Laboratory.
- Scharre, P. (2018). Army of none: Autonomous weapons and the future of war. W. W. Norton.
- Spradlin, C., & Spradlin, G. (2007). Lanchester’s equations in three dimensions. Computers & Mathematics with Applications, 53(7), 999–1011. https://doi.org/https://doi.org/10.1016/j.camwa.2007.01.013
- Taylor, J. G. (1979). Attrition modeling. In R. K. Huber, K. Niemeyer, & H. W. Hofmann (Eds.), Operationsanalytische Spiele für die Verteidigung (pp. 139–189). Oldenbourg.