Discrete Deterministic Modelling of Autonomous Missiles Salvos

The paper deals with mathematical models of sequent salvos battle, of autonomous flight missiles (AFM) organized in the groups of combatants. Tactical integration of AFM system distance-controlled weapon is considered by performances of simultaneous approaches on targets, and continual battle models of guerilla and direct fire, are redesigned to the discrete-continual mixed model, for checking missiles sudden, and further salvos, attack effects. Superiority parameters, as well as losses and strengths of full, or the part of salvo battle, for the missiles groups as technology sub-systems combatants’, is expressed by mathematical and simulation examples. Targets engagements capacities of the missiles battle unit, is conducted through designed scenarios and mathematically derived in the research. Model orientated on answers about employment of rapid reaction defending tactics, by distance missiles attacks.Defence Science Journal, Vol. 64, No. 5, September 2014, pp.471-476, DOI:http://dx.doi.org/10.14429/dsj.64.579

Lanchester-Type Models of Warfare, Volume I

The Twentieth Century has been characterized by innumerable attempts to use the Scientific Method as a basis for policy planning in national and international affairs. The emergence of the field of operations research (OR) out of attempts of scientists in the Western Democracies to apply the Scientific Method to military problems during World War II is well known. Since World War II there has been a dramatic growth in both the interest in and use of OR and systems-analysis techniques for such purposes within the U.S. defense establish- ment, especially since the beginning of the so-called McNamara Era of defense planning. A concomitant trend has been an equally dramatic increase in both the number and variety of mathematical models used to support these analytical activities

Combat modeling for Command, Control, and Communications: a primer

This thesis is a primer for a combat modeling course for Joint Command, Control, and Communications (C3) students at the Naval Postgraduate School. It provides the students with a single document which ties together the concepts of several modeling experts pertinent to C3. The thesis examines various aspects of combat models and introduces some of their functions, applications, and results. Areas included in the primer are: combat theory and definitions for command and control reflected in that theory; modeling techniques; measures of effectiveness; attrition models, particularly Lanchester type equations; history of naval modeling; and a survey of current modeling efforts, such as simulation, Chaos Theory, and Decision Support Aids. The thesis introduces basic concepts and identifies readings from which those concepts were extracted. It does not teach students to develop combat models, though it gives insight into how the application affects proper model selection.http://archive.org/details/combatmodelingfo1094530724Lieutenant, United States NavyCaptain, United States Air ForceApproved for public release; distribution is unlimited

Nation-Building Modeling and Resource Allocation Via Dynamic Programming

Dynamic programming is used in many military and industrial applications to solve sequential decision making problems. This research proposes the development of a model and approach to address the application of dynamic programming in nation-building modeling. Through the creation of component indices to capture the state of operational variables: Political, Military, Economic, Social, Infrastructure, and Information (PMESII), a functional form of a system of differential equations is developed to account for the interactions between the state indices and instruments of national power: Diplomatic, Informational, Military, and Economic (DIME). Solving this problem with dynamic programming provides an improved sequence which describes the application of DIME in a manner that minimizes an objective (i.e. cost, time) and allows the model to account for external factors such as an insurgent reaction to US policy. An application of the model is derived for Iraq to demonstrate the utility of the model and explore various aspects of the solution space. This modeling approach offers a potential significant capability when analyzing and planning for nation-building operations

Differential Game for a Class of Warfare Dynamic Systems with Reinforcement Based on Lanchester Equation

This paper concerns the optimal reinforcement game problem between two opposing forces in military conflicts. With some moderate assumptions, we employ Lanchester equation and differential game theory to develop a corresponding optimization game model. After that, we establish the optimum condition for the differential game problem and give an algorithm to obtain the optimal reinforcement strategies. Furthermore, we also discuss the convergence of the algorithm. Finally, a numerical example illustrates the effectiveness of the presented optimal schemes. Our proposed results provide a theoretical guide for both making warfare command decision and assessing military actions

Lewis Fry Richardson: His Intellectual Legacy and Influence in the Social Sciences

This is an open access book. Lewis F Richardson (1981-1953), a physicist by training, was a pioneer in meteorology and peace research and remains a towering presence in both fields. This edited volume reviews his work and assesses its influence in the social sciences, notably his work on arms races and their consequences, mathematical models, the size distribution of wars, and geographical features of conflict. It contains brief bibliographies of his main publications and of articles and books written about Richardson and his work and discusses his continuing influence in peace research and international relations as well as his attitude to the ethical responsibilities of a scientist. It will be of interest to a wide range of scholars. This book includes 11 chapters written by Nils Petter Gleditsch, Dina A Zinnes, Ron Smith, Paul F Diehl, Kelly Kadera, Mark Crescenzi, Michael D Ward, Kristian Skrede Gleditsch, Nils B Weidmann, Jürgen Scheffran, Niall MacKay, Aaron Clauset, Michael Spagat and Stijn van Weezel. Lewis F Richardson occupied an important position in two academic fields as different as meteorology and peace research, with academic prizes awarded in both disciplines. In peace research, he pioneered the use of mathematical models and the meticulous compilation of databases for empirical research. As a quaker and pacifist, he refused to work in preparations for war, paid a heavy prize in terms of his career, and (at least in the social sciences) was fully recognized as a pioneering scholar only posthumously with the publication of two major books. Lewis Fry Richardson is one of the 20th century’s greatest but least appreciated thinkers—a creative physicist, psychologist, meteorologist, applied mathematician, historian, pacifist, statistician, and witty stylist. If you’ve heard of weather prediction, chaos, fractals, cliometrics, peace science, big data, thick tails, or black swans, then you have benefited from Richardson’s prescience in bringing unruly phenomena into the ambit of scientific understanding. Richardson’s ideas continue to be relevant today, and this collection is a superb retrospective on this brilliant and lovable man. Steven Pinker, Johnstone Professor, Harvard University, and the author of The Better Angels of Our Nature and Enlightenment No

Lewis Fry Richardson: His Intellectual Legacy and Influence in the Social Sciences

This is an open access book. Lewis F Richardson (1981-1953), a physicist by training, was a pioneer in meteorology and peace research and remains a towering presence in both fields. This edited volume reviews his work and assesses its influence in the social sciences, notably his work on arms races and their consequences, mathematical models, the size distribution of wars, and geographical features of conflict. It contains brief bibliographies of his main publications and of articles and books written about Richardson and his work and discusses his continuing influence in peace research and international relations as well as his attitude to the ethical responsibilities of a scientist. It will be of interest to a wide range of scholars. This book includes 11 chapters written by Nils Petter Gleditsch, Dina A Zinnes, Ron Smith, Paul F Diehl, Kelly Kadera, Mark Crescenzi, Michael D Ward, Kristian Skrede Gleditsch, Nils B Weidmann, Jürgen Scheffran, Niall MacKay, Aaron Clauset, Michael Spagat and Stijn van Weezel. Lewis F Richardson occupied an important position in two academic fields as different as meteorology and peace research, with academic prizes awarded in both disciplines. In peace research, he pioneered the use of mathematical models and the meticulous compilation of databases for empirical research. As a quaker and pacifist, he refused to work in preparations for war, paid a heavy prize in terms of his career, and (at least in the social sciences) was fully recognized as a pioneering scholar only posthumously with the publication of two major books. Lewis Fry Richardson is one of the 20th century’s greatest but least appreciated thinkers—a creative physicist, psychologist, meteorologist, applied mathematician, historian, pacifist, statistician, and witty stylist. If you’ve heard of weather prediction, chaos, fractals, cliometrics, peace science, big data, thick tails, or black swans, then you have benefited from Richardson’s prescience in bringing unruly phenomena into the ambit of scientific understanding. Richardson’s ideas continue to be relevant today, and this collection is a superb retrospective on this brilliant and lovable man. Steven Pinker, Johnstone Professor, Harvard University, and the author of The Better Angels of Our Nature and Enlightenment No

Modeling and Economy’s Dynamics and External Influences Through a System of Differential Equations

This research proposes a methodology to develop models for the greater understanding of the application of the economic instrument of national power through a selection of factors that define the economic condition of a country. The major components of an economy are identified as GDP per capita, a treasury bond yield, and a major stock market index. The components have interconnected dynamics along with external influences from the United Stated Federal Funds Rate and foreign direct investment. These connections are considered through a metamodel in the form of a system of differential equations which is solved as an inverse problem. The validity of the model is verified and the model is then used in making short term forecasts. What-if analysis of various policies is explored resulting in insight to policy changes. Through an increased understanding and awareness of the dynamics of the economic environment, a foundation for analysis is built to begin addressing the impacts of pecuniary warfare tactics