Chapter 3 orients the student to the basics of LOAC as it exists on today’s battlefields. It moves from long-past history to modern, even contemporary, history by relating today’s LOAC, along with its more recent historical foundations and modern law of war incidents. For example, World War I and the ineffective trials of German war criminals by German courts – the Leipzig trials – are shown to be the impetus for World War II’s Nuremberg and Tokyo international military tribunals. The LOAC import of the League of Nations and the Spanish Civil War are detailed, along with the 1929 Geneva Conventions’ (two Conventions) contributions. The bulk of the chapter is an examination of today’s four 1949 Geneva Conventions, including their “common articles,” the varied routes to the charging of war crimes alleged against both combatants and civilians, along with the significance of “grave breach” war crimes. Indicators of war crimes is detailed, as well.

Chapter 17 attempts to pin down a moving target, cyber and its use and utility in armed conflict. The cyber targets chosen by China, Russia, Iran, and North Korea are detailed. The chapter defines cyber “attacks,” differentiating them from cyber “operations” – akin to a felony-misdemeanor distinction. Cyberattacks are found to be a use of armed force, in the sense of UN Charter Article 2(4), raising the right of victim states to respond with armed force in self-defense. Potential cyber conflicts are classified as international or non-international based upon their perpetrators. The difficulties of attribution of cyberattacks are detailed, including sovereignty and military necessity. A counter to cyberattack is belligerent reprisal, which is explored. Cyberattacks on critical national infrastructure (CNI) are a major problem. After defining CNI, the US position on responses is discussed. Recent changes in US cyber policy authorize far greater cyber retaliation and reprisal, as well as providing federal funding to carry them out. Finally, CNI’s weak link, the unwillingness of civilian corporations to fund their own cyber protection, is noted.

Spatial and temporal samples of physical quantities are among the most common data form in the geosciences and many other fields. Such data are called time series (even if they are samples along a profile in space). This chapter presents examples of geophysical time series in order to illustrate the sorts of scientific questions that may be addressed by the methods inthrough . These time series are used in later chapters and exercises, and numerical values can be downloaded from www.cambridge.org/9781108931007. Virtually all the examples are available on the World Wide Web.

Chapter 13 covers LOAC that permits or restricts the targeting of enemy objects: “military objectives.” Lawful military objectives are defined. Economic targets and war-sustaining targets, contentious issues, are described, with the US minority position noted. World War II’s area bombing by all parties to the conflict is shown to be unlawful, unproductive and, today, unlawful. The widely used targeting criteria, lawful by virtue of nature, location, purpose or use, is expanded upon, with examples of each qualifier. That is followed by relating the six-step targeting process employed by US units in combat. Collateral damage and its avoidance efforts are discussed at length, with emphasis on Chapter 7’s core principles of distinction and proportionality. Unique targeting issues such as “dangerous forces” and dual-use targets are covered, with examples. Precautions in the attack do not sound particularly significant but they are essential LOAC constants. Two recent trial records are included in the Cases and Materials section to illustrate real-world legal consequences of disregarding the illegalities of targeting human beings, even ones’ enemies.

Chapter 5 explains the varieties of armed conflicts. Conflict status determines the law that applies to that conflict, including prohibitions and duties applicable to those involved. Conflict status is the first question a student should answer when looking at any armed conflict. This chapter details the factors that determine conflict status. Common Article 2 conflicts (the designation referring to the Article which is common to all four of the 1949 Geneva Conventions) are international armed conflicts. Those conflicts are discussed, as are common Article 3 conflicts, those between a nation and an armed opposition group – rebels or terrorists. Given that states beyond those directly involved may intervene, interfere, assist or impede one side or the other, this is a challenging but important chapter. It gives the student the information necessary to recognize any conflict’s status. Also discussed are recent developments in conflict classification, for example, gray zone conflicts and hybrid warfare, as well as the LOAC of cross-border terrorist attacks and the lawful ability of attacked state forces to pursue and engage those terrorists across a neighboring state’s border.

Very few problems in quantum mechanics can be solved exactly. For example, in the case of the helium atom, including the inter-electron electrostatic repulsion term in the Hamiltonian changes the problem into one which cannot be solved analytically. Perturbation theory provides a method for finding approximate energy eigenvalues and eigenstates for a system whose Hamiltonian is of the form.

In this chapter we describe the motivation and requirements for converting analog signals to digital time series so that they can be analyzed using digital computers. The process of digitizing analog geophysical signals, for example continuous voltages from seismometers, must ensure that all information about signal amplitudes (the dynamic range) and range of frequencies (the frequency bandwidth) is retained. Important elements of analog to digital conversion include the number of samples to be taken (the sampling rate) and how to represent samples as numbers in a computer. The chapter also presents the standard statistics used to describe time series and introduces the logarithmic decibel scale as a convenient way to compare the relative magnitudes of signals.