162,086 research outputs found
Mass action models of Falklands War battles
No full textWe develop a dataset describing variables associated with six Falklands War battles: combatant numbers; deaths; temporal aspects; and offensive support. Linear relationships between battle duration and deaths necessitate using force and loss ratios to remove temporal variation. Mass action models of battle attrition fit this dataset poorly (at best coefficient of determination ). The low level rules in simulations used by military force designers frequently share assumptions with, or are, mass action models. Errors in force balance or constitution are dangerous so exposing problems with and exploring improvements on existing combat models is important. While six data points are too few for a thorough analysis, our results are consistent with: a linear relationship between time in danger and number killed; different times in danger for the two sides, dependent on detection and lethality ranges; and data substructure, even when temporal aspects are removed through ratio models. This data substructure indicates at least one extra variable needs to be considered. We contend that this variable is related to suppression, and this contention is not falsified by the high use of offensive support in the most successful attacks. Mathematical modellers should consider cancelling out temporal variation in combat datasets through ratio models and/or exploring the effects of mutable detection and lethality ranges. Suppression is an attempt to manage exposure to death, to introduce non-stationarity and irregularity into the dataset to benefit the suppressor, to change the bounds of the system using a soft controller; we should investigate how to model it. Force designers should ask simulation modellers whether the mathematical models underlying their simulations represent suppression accurately (or at all) and rethink reductions of simultaneously delivered offensive support available on demand based on models ignoring suppression.
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Tractable approximations to multistage decisions in air defence scenarios
No full textSimulations are commonly used to investigate the control and resource allocation problems associated with pitting aircraft against ground based air defences. Such simulations rapidly become computationally intractable as units are added. Previous work described an envelope method that retains computational tractability if the lowest and highest cost target sequences can be defined a priori and used to establish solution bounds. This approach must be modified to be applied to the more common case where there are no obvious best or worst sequences of targets. We show that these bounding sequences can be approximated by using binary comparisons and by basing decisions on a heuristic. This approach compares well with exact results in some computationally tractable situations.
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Dispersed combat as mass action with finite search
No full textImprovements to models of battle attrition are necessary because current models cannot explain battle attrition. Agent based simulations indicate that calculated attrition is substantially different when agents are not assumed to have unlimited detection capabilities. However, agent based models are limited to small force sizes and there is no evidence that the changes in calculated attrition occur for large force sizes. We develop a probabilistic model, based on Bernoulli trials, to check if limited detection capabilities result in significant changes to calculated attrition when force sizes are large, as in battle datasets. Our model is a search model and we convert it to an attrition model via the same processes used in current models, and include the same assumptions for factors other than detection range. We find two series solutions to the model, one for small force sizes, the other for large force sizes, and find numerically that the two solutions strongly overlap. The new model makes a difference to calculated attrition when force sizes are small, but not when they are large. However, the model makes a difference to calculated attrition for all force sizes if the battlefield area is increased to maintain a sparse force density. Our approach is mathematical, not requiring application knowledge, and several of the assumptions underlying mass action models are raised in our discussion.
References J. V. Chase. Sea fights: A mathematical investigation of the effect of superiority of force in combats upon the sea. Naval War College Archives, RG 8, Box 109, XTAV (1902), 1902. N. R. Franks and L. W. Partridge. Lanchester battles and the evolution of combat in ants. Anim. Behav., 45:197–199, 1993. doi:10.1006/anbe.1993.1021 G. S. Gradschtein and I. M. Ryzhik. Tables of Series, Products and Integrals. Deutcher Verlag der Wissenschaften, 1996. N. C. Grassly and C. Fraser. Mathematical models of infectious disease transmission. Nat. Rev. Microbiol., 6:477–487, 2008. doi:10.1038/nrmicro1845 D. Kahneman. Thinking Fast and Slow. Penguin, London, 2013. L. R. Kosowski, A. Pincombe and B. Pincombe. Irrelevance of the fractal dimension term in the modified fractal attrition equation. ANZIAM J., 52:C988–C1011, 2011. doi:10.21914/anziamj.v52i0.3963 F. W. Lanchester. Aircraft in warfare: The dawn of the fourth arm. Constable, London, 1916. http://edc448uri.wikispaces.com/file/view/Lanchester+-+Aircraft+in+Warfare.pdf T. W. Lucas and T. Turkes. Fitting Lanchester equations to the Battles of Kursk and Ardennes. Nav. Res. Log., 51:95–116, 2004. doi:10.1002/nav.10101 T. W. Lucas and J. A. Dinges. The effect of battle circumstances on fitting Lanchester equations to the Battle of Kursk. Mil. Oper. Res., 9:17–30, 2004. http://www.mors.org/Publications/MOR-Journal/Online-Issues P. M. Morse and G. E. Kimball. Methods of Operations Research. Wiley, 1951. M. Osipov. The influence of the numerical strength of engaged forces in their casualties. Translated by R. L. Helmbold and A. S. Rehm. Nav. Res. Log., 42:435–490, 1995. doi:10.1002/1520-6750(199504)42:3<435::AID-NAV3220420308>3.0.CO;2-2 R. Peterson. On the logarithmic law of combat and its application to tank combat. Oper. Res., 15:557–558, 1967. doi:10.1287/opre.15.3.557 A. H. Pincombe, B. M. Pincombe and C. E. M. Pearce, Putting the art before the force. ANZIAM J., 51:C482–C496, 2010. doi:10.0000/anziamj.v51i0.2584. A. H. Pincombe, B. M. Pincombe and C. E. M. Pearce. A simple battle model with explanatory power. ANZIAM J., 51:C497–C511, 2010. doi:10.21914/anziamj.v51i0.2585. B. M. Pincombe and A. H. Pincombe. Mass action models of Falklands War battles. ANZIAM J., 57:C235–C252, 2016. doi:10.21914/anziamj.v57i0.10450 J. G. Taylor. Lanchester models of warfare. Operations Research Society of America, Arlington, 1983
An assessment of email and spontaneous dialog visualizations
No full textAbstract not availableMarcus A. Butavicius, Michael D. Lee, Brandon M. Pincombe, Louise G. Mullen, Daniel J. Navarro, Kathryn M. Parsons and Agata McCorma
[Report to Chief J. E. Curry, by an unknown author #1]
No full textReport to Chief J. E. Curry, by an unknown author. The report contains a list of officers who gave depositions to the United States Attorney
[Report to Chief J. E. Curry, by an unknown author #2]
No full textReport to Chief J. E. Curry, by an unknown author. The report contains a list of officers who gave depositions to the United States Attorney
Murder on the mountain: author talk with Peter J. Wosh
No full textAuthor talk by Peter J. Wosh on May 5th, 2022, on his book, "Murder on the Mountain: crime, passion, and punishment in gilded age New Jersey.
Mr. Melvin J. Collier, RWWL AUC, June 2011
No full textThis video is a conversation with Mr. Melvin J. Collier. Mr. Collier talks about his book, "From Mississippi to Africa: A Journey of Discovery". Daniel Le, AUC Woodruff Library, is the interviewer
Effects of multiple stenoses and post-stenotic dilatation on non-Newtonian blood flow in a small arteries
No full textFully-developed one-dimensional Casson flow through a single vessel of varying radius is proposed as a model of low Reynolds number blood flow in small stenosed coronary arteries. A formula for the resistance-to-flow ratio is derived, and results for yield stresses of τ0=0, 0.005 and 0.01 Nm-2, viscosities of μ=3.45×10−3, 4.00×10−3 and 4.55×10−3 Pa·s and fluxes of 2.73×10−6, ×10−5 and ×10−4 m3s−1 are determined for a segment of 0.45 mm radius and 45 mm length, with 15 mm abnormalities at each end where the radius varies by up to ±0.225 mm. When τ0=0.005 Nm-2, μ=4×10−3 Pa·s and Q=1, the numerical values of the resistance-to-flow ratio vary from[`(l)] = 0.525=0525, when the maximum radii of the two abnormal segments are both 0.675 mm, to[`(l)] = 3.06=306, when the minimum radii are both 0.225 mm. The resistance-to-flow ratio moves closer to unity as yield stress increases or as blood viscosity or flux decreases, and the magnitude of these alterations is greatest for yield stress and least for flux.B. Pincombe, J. Mazumdar and I. Hamilton-Crai
A Tripartite Post-Recession Rebalancing
No full textIn this latest Advance & Rutgers Report, entitled “A Tripartite Post-Recession Rebalancing,” Dean James W. Hughes and Professor Joseph J. Seneca deliver an incisive assessment of the current market conditions and obstacles in the path of our economic recovery. They offer a statistical cautionary tale that the private and public sector need to hear and acknowledge in order for the economy to make continued progress.This report was published as Issue Paper Number 7, November 2011, in Advance & Rutgers Report
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