A duel complicated by false targets and uncertainty as to opponent type

An attacker, being one of two types, initiates an attack at some time in the interval [-T, 0]. The a priori probabilities of each type are known. As time elapses the defender encounters false targets which occur according to a known Poisson process and which can be properly classified with known probability. The detection and classification probabilities for each type attacker are given. If the defender responds with a weapon at the time of attack, he survives with a probability which depends on the number of weapons in his possession and on attacker type. If he does not respond, his survival probability is smaller. These probabilities are known, as well as the current number of weapons in the defender's possession. They decrease as the number of weapons decreases. The payoff is the defender's survival probability. An iterative system of first-order differential equations is derived whose unique solution V₁(t),V₂(t),…,V_k(t) is shown to be the value of the game at time t, when the defender has 1, 2,…, k,… weapons, respectively. The optimal strategies are determined. Limiting results are obtained as t→-∞, while the ratio of the number of weapons to the expected number of false targets remaining is held constant.     

Royal Armouries Acquisitions 2012

Abstract

The Royal Armouries collection contains many Indian combination weapons, many of which have neither been published nor displayed. This article sets out to describe three unusual firearm related items. These are what appears to be an elaborate gunner's staff of a unique type, a pair of guns that can be combined and shot as a combination and finally a percussion gun shield.     

Exploiting the Challenges to Bioweapons Development

ABSTRACT

Widespread and often exaggerated generalizations about the global spread weapons of mass destruction (WMDs) have proven to be not only misleading and technologically naïve, but also unhelpful in formulating effective policies to counter their threat. The new book by George Mason University's Sonia Ben Ouagrham-Gormley dispels the popular narrative that governments and terror groups can easily—and inevitably will—develop WMDs, particularly biological weapons, by exploring the complex external and internal conditions that such programs require, as demonstrated by the Cold War-era biological weapon programs of the superpowers. This empirically grounded and realistic assessment of how states try—and often fail—to develop such programs offers a more reliable basis to craft realistic counterproliferation policies that can elicit international support.     

Strategic Ambiguity: Nuclear Sharing and the Secret Strategy for Drafting Articles I and II of the Nonproliferation Treaty

ABSTRACT

Since the 1950s, the United States has engaged in nuclear sharing with its NATO allies. Today, 150-200 tactical nuclear weapons remain on European soil. However, the Treaty on the Non-proliferation of Nuclear Weapons (NPT) prohibits the transfer of nuclear weapons to non-nuclear weapon states. The potential discrepancy between text and practice raises the question of how the NPT's negotiators dealt with NATO's nuclear-sharing arrangements while drafting the treaty that would eventually become the bedrock of the international nonproliferation regime. Using a multitiered analysis of secret negotiations within the White House National Security Council, NATO, and US-Soviet bilateral meetings, this article finds that NATO's nuclear-sharing arrangements strengthened the NPT in the short term by lowering West German incentives to build the bomb. However, this article also finds that decision makers and negotiators in the Lyndon B. Johnson administration had a coordinated strategy of deliberately inserting ambiguous language into drafts of Articles I and II of the Treaty to protect and preserve NATO's pre-existing nuclear-sharing arrangements in Europe. This diplomatic approach by the Johnson administration offers lessons for challenges concerning NATO and relations with Russia today.     

Russia and Strategic Conventional Weapons:

ABSTRACT

Russian political leaders and military strategists are growing increasingly concerned about “strategic conventional weapons”—a broad category that appears to include all non-nuclear, high-precision, standoff weapons—and about long-range, hypersonic weapons, in particular. These concerns are complex and multifaceted (and, in some cases, contradictory), but chief among them are the beliefs that strategic conventional weapons could prove decisive in a major conflict and that Russia is lagging behind in their development. US programs to develop and acquire such weapons—namely, the Conventional Prompt Global Strike program—are of great concern to Russian strategists, who argue both that the United States seeks such weapons for potential use against Russia—its nuclear forces, in particular—and because strategic conventional weapons are more “usable” than nuclear weapons. Asymmetric responses by Russia include increased reliance on tactical nuclear weapons, efforts to enhance the survivability of its nuclear forces, and investments in air and missile defenses. There is also strong—but not completely conclusive evidence—that Russia is responding symmetrically by attempting to develop a long-range, conventionally armed boost-glide weapon.     

Comprehensive Prohibition of Nuclear Weapons: An Emerging International Norm?

ABSTRACT

There have been calls for the abolition of nuclear weapons from the day they were invented. Over the last fifteen years, some indications can be found that such calls have been getting louder, among them Barack Obama's famous 2009 speech in Prague. In this article, we investigate if support for a comprehensive norm that would prohibit development, possession, and use of nuclear weapons is really growing. To assess the current status of that norm, we use the model of a “norm life cycle,” developed by Martha Finnemore and Kathryn Sikkink. We then analyze 6,545 diplomatic statements from the review process of the Treaty on the Non-Proliferation of Nuclear Weapons as well as from the UN General Assembly First Committee on Disarmament and International Security, covering the years 2000 to 2013. The evidence shows that a comprehensive prohibition can be considered an emerging international norm that finds growing support among states without nuclear weapons and nuclear weapon states alike. Only a core group of states invoke the norm consistently, however. This leads us to conclude that the “tipping point” of the life cycle, at which adherence to a new norm starts to spread rapidly, has yet to be reached.     

Reading the Riot Act: Toward a More Comprehensive Ban on Chemical Weapons

ABSTRACT

The recent use of chemicals in warfare in Syria and Iraq illustrates that, despite the important work of the 1997 Chemical Weapons Convention (CWC), the world has not yet been totally successful in stopping the use of indiscriminate toxic agents in conflicts, either by states or non-state actors. Michael Crowley's excellent and timely new book, Chemical Control, analyzes the use of “riot control agents” (RCAs) and “incapacitating chemical agents” (ICAs), including launch and dispersal systems, by police, paramilitary, and military forces over the last decades and raises the challenging question about where the red line might be drawn between banned and permitted uses of chemicals. He discusses this problem not only in the context of the CWC, which allows use of RCAs for civilian riot control, but also in the context of international law, human rights, and criminal justice, including the Biological and Toxin Weapons Convention and other disarmament and abolition regimes. He proposes a “holistic, three-stage approach” to addressing this issue “for effective regulation or prohibition of the weapon or weapon-related technology of concern.” As we approach the global abolition of a whole class of weapons of mass destruction in the next decade or even sooner, Chemical Control is helpful in better understanding and solving the dilemma of what's actually banned or permitted under international law, and precluding states undermining the chemical weapons ban.     

The Power of the NPT: International Norms and Ukraine's Nuclear Disarmament

ABSTRACT

There is a lingering disagreement among scholars on how the Treaty on the Non-Proliferation of Nuclear Weapons (NPT) affects nonproliferation and disarmament outcomes. Drawing on constructivist scholarship on international norms, this article examines the extent of the NPT's effect in the case of Ukraine's nuclear disarmament. In the wake of the Soviet Union's collapse, Ukraine found itself host to the world's third largest nuclear arsenal. Despite Ukraine's initial commitment to become a non-nuclear state, it proceeded along a difficult path toward NPT accession. Most controversial and directly at odds with the NPT was Ukraine's claim to ownership of its nuclear inheritance as a successor state of the Soviet Union. This article argues that, while much domestic discourse about the fate of these nuclear weapons was embedded in the negotiation of Ukraine's new identity as a sovereign state vis-à-vis Russia and the West, the NPT played an important, structural role by outlining a separate normative space for nuclear weapons and providing the grammar of denuclearization with which Ukraine's decision makers had to grapple.     

Optimal force mix in heterogeneous combat

This article presents models for determining the optimum number of Red weapons required to win a heterogeneous combat in which m(m> 1) types of Red weapons face a single type of Blue weapon under a newly defined termination policy. Red aims at either minimizing the total cost or maximizing the aggregated remaining force strength. Kuhn-Tucker and simulated annealing techniques are used for obtaining the optimal solution. The methodology is illustrated by analysing heterogeneous combat to determine (i) the feasibility of introducing new types of weapons and (ii) the number of weapons required to win if a specific type of weapon, say infantry, dominates. © 1995 John Wiley & Sons, Inc.     

Nuclear Disarmament and Stability in the Logic of Habit

ABSTRACT

In 2008, the announcement of the Global Zero campaign—an international effort to eliminate nuclear weapons—coincided with the election of Barack Obama. The new president, avowedly pro-disarmament, made getting to zero nuclear weapons a centerpiece of his foreign policy. This article takes on the question of what impact global disarmament might have on international strategic stability. In a break with much of the literature and analysis on nuclear policy, it explicitly focuses on how publics understand the significance of nuclear weapons. In so doing, the article draws on recent international relations scholarship on the role of habit to argue that eliminating nuclear weapons can generate instability by creating widespread perceptions of insecurity and anxiety. If disarmament campaigners wish to achieve their goal without generating instability, they will need to work over the long-term to break habituated beliefs about nuclear weapons.     

The Canary in the Nuclear Submarine: Assessing the Nonproliferation Risk of the Naval Nuclear Propulsion Loophole

ABSTRACT

The Treaty on the Non-Proliferation of Nuclear Weapons (NPT) allows states to exempt nuclear material from international safeguards for use in nuclear submarine programs. This material, however, could be diverted for nuclear weapons purposes without the knowledge of inspectors, creating a potentially dangerous loophole in the treaty. This article argues that exercising that loophole today would amount to admitting a nuclear weapon program, making it a particularly poor pathway to a weapon for a potential proliferant. Still, if states like Brazil ultimately exempt nuclear material from safeguards for a nuclear submarine effort, they could set a dangerous precedent that makes it easier for others to use the loophole as a route to a nuclear weapon capability. There are several policy options available to mitigate the damage of such a precedent; most promising is the prospect of a voluntary safeguards arrangement that would allow international inspectors to keep an eye on nuclear material even after it has been dedicated to a naval nuclear propulsion program.     

The macuahuitl: an innovative weapon of the Late Post-Classic in Mesoamerica

Abstract

This study is intended to shed some light on a number of issues relating to the famous Aztec weapon called the macuahuitl. This well-known artefact still presents many problems of interpretation, resulting in a polemic that still rages regarding its origin, spatial-temporal distribution and its real role in Mesoamerican cultural development. The subject of warfare in Mesoamerica is still one of the main areas of investigation for many researchers. However, it is common for researchers to analyze the military phenomenon from a completely symbolic standpoint and overlook the practical aspects such as military tactics, weapons systems and battlefield successes. It is against this background that I have developed a programme of investigation that I have called the Research Programme into Military Equipment in Mesoamerica, which considers the phenomenon of war throughout Mesoamerica from various perspectives. I have initially focused this programme on weapons systems among the Mexicas as they relate to the battlefield.     

All Together Now? Questioning WMDs as a Useful Analytical Unit for Understanding Chemical and Biological Weapons Proliferation

ABSTRACT

The popular use of the term “weapons of mass destruction” (WMD) can be understood to imply a relationship between nuclear, chemical, and biological weapons proliferation insofar as it assumes that the separate weapons technologies can be usefully grouped into a single analytic category. This article explores whether WMD is actually a useful construct. It begins by reviewing the literature on nuclear, chemical, and biological weapons proliferation, including a recent study that sought to estimate the relationship between the pursuit and acquisition of these different weapons. It then explores some policy inferences that academics and policy makers may be tempted to draw from these studies, particularly regarding the Barack Obama administration's pursuit of deep nuclear reductions. It argues that many of these policy inferences are premature at best and misleading at worst. It concludes with a call for additional research into the causes and consequences of chemical and biological weapons proliferation, and a call for scholars to remain cautious in their desire to draw premature policy implications from their studies in order to be “policy relevant.”     

A Doctrine without Dogma

ABSTRACT

In No Use: Nuclear Weapons and U.S. National Security Policy, Thomas M. Nichols calls for a constructive rethinking about the history of nuclear weapons and the attitudes that have grown up around them. Despite dramatic reductions since the end of the Cold War, the United States still maintains a robust nuclear triad that far exceeds the needs of realistic deterrence in the twenty-first century. Nichols advocates a new strategy of minimum deterrence that includes deep unilateral reductions to the US nuclear arsenal, a no-first-use pledge, withdrawing US tactical nuclear weapons from Europe, and ending extended nuclear deterrence for allies. The weakest part of his argument eschews nuclear retaliation against small nuclear states that attack the United States, opting instead to use only conventional weapons to guarantee regime change. He admits this will entail enormous cost and sacrifice, but cites the “immorality” of retaliating against a smaller power with few targets worthy of nuclear weaponry, which totally ignores the massive underground facilities constructed to shield military facilities in many of these states. Despite this, Nichols's thoughtful approach to post-Cold War deterrence deserves thoughtful consideration.     

US Advanced Conventional Systems and Conventional Prompt Global Strike Ambitions:

ABSTRACT

The dangers and risks of employing a Conventional Prompt Global Strike (CPGS) capability greatly exceed the benefits. More suitable, if less prompt, alternatives exist to deal with fleeting targets. Even a niche CPGS capability—consisting of approximately twenty systems—carries risks, to say nothing of proposals to develop hundreds or more. Most dangerously, CPGS could stir the pre-emption pot, particularly vis-à-vis states that correctly perceive to be within the gunsights of US CPGS weapons; other states, too, may feel emboldened to emulate this US precedent and undertake their own form of prompt, long-range strike capability. Compressed circumstances surrounding such a scenario could foster unwanted erratic behavior, including the misperception that the threatening missile carries a nuclear weapon. But the true Achilles's heel of the CPGS concept is the unprecedented demands it places on the intelligence community to provide decision makers with “exquisite” intelligence within an hour timeframe. Such compressed conditions leave decision makers with virtually no time to appraise the direct—and potentially unintended—consequences of their actions.     

A Proliferation of Royal Air Forces

Australia's interest in nuclear weapons in the 1950s and 60s is usually explained in terms of high politics and grand strategy. This proliferation case study explores, in greater detail than hitherto, the important part played by the Royal Australian Air Force (RAAF) in pressing for a nuclear capability. It seeks to understand the reasons behind the RAAF's lobbying, in particular its previous experience with air power, its visceral desire for advanced manned bomber aircraft, and its strong institutional link to the British Royal Air Force. The decision in 1963 to acquire the supersonic US F-111 strike aircraft, instead of rivals including the British TSR.2, is also considered. Once the RAAF's bomber ambitions were satisfied, interest in nuclear weapons was greatly reduced. Finally, some comments are included on the nuclear interests of other air forces in the British Commonwealth.     

The variance of the coverage of a randomly located area target by a salvo of weapons

We derive formulas for the variance of that proportion of the value of a randomly located, circularly symmetric area target that is destroyed by N independently fired weapons of identical type whose damage functions are circularly symmetric about the respective impact points. The probability density functions of the target center location and of the weapon impact points are also circularly symmetric. The general results are specialized to uniform and Gaussian functions. In the latter case a closed-form solution (triple integral) for the variance of the coverage is derived. Similar to some well-known results on expected coverage, this expression for the variance of the coverage can be easily evaluated by numerical quadrature. Numerical results are given which indicate the target coverage variability caused by the combined effects of random target-locating errors and weapon impact point fluctuations.     

PART I: A CRITICAL EXAMINATION OF “THE MYTH OF NUCLEAR DETERRENCE”

Several years ago, Ward Wilson presented in this journal a wide-ranging challenge to what every generation of national security scholars and practitioners since the end of World War II has been taught about nuclear weapons. He asserted that nuclear deterrence amounts to far less than its proponents have claimed and provocatively suggested that nuclear deterrence is a myth. Relying upon both empirical and theoretical objections to nuclear deterrence, he concluded that its failures were clear-cut and indisputable, whereas its successes were speculative. Yet in spite of a flourishing trade in scholarly articles, think tank reports, blog posts, and opinion pieces concerning nuclear deterrence, nobody—including nuclear weapons scholars—has ventured more than a limited critique of Wilson's essay. There are, however, serious shortcomings in Wilson's arguments—deficiencies that make his essay an unpersuasive brief against nuclear deterrence. Wilson's thesis could be correct. His arguments, however, are unlikely to persuade any skeptical members of Congress, upon whom future progress in arms control depends, to reconsider the value they attach to nuclear weapons and nuclear deterrence.

     

A theory of ideal linear weights for heterogeneous combat forces

Detailed combat simulations can produce effectiveness tables which measure the effectiveness of each weapon class on one side of an engagement, battle, or campaign to each weapon class on the other. Effectiveness tables may also be constructed in other ways This paper assumes that effectiveness tables are given and shows how to construct from them a system of weapon weights each of which is a weighted average of the effects of a given weapon against each of the enemy's weapons. These weights utilize the Perron- Frobenius theory of eigenvectors of nonnegative matrices. Methods of calculation are discussed and some interpretations are given for both the irreducible and reducible cases.