A new approach to the creation and propagation of exponential moments in the Boltzmann equation

We study the creation and propagation of exponential moments of solutions to the spatially homogeneous $d$-dimensional Boltzmann equation. In particular, when the collision kernel is of the form $|v-v_*|^\beta b(\cos(\theta))$ for $\beta \in (0,2]$ with $\cos(\theta)= |v-v_*|^{-1}(v-v_*)\cdot \sigma$ and $\sigma \in \mathbb{S}^{d-1}$, and assuming the classical cut-off condition $b(\cos(\theta))$ integrable in $\mathbb{S}^{d-1}$, we prove that there exists $a > 0$ such that moments with weight $\exp(a \min{t,1} |v|^\beta)$ are finite for $t>0$, where $a$ only depends on the collision kernel and the initial mass and energy. We propose a novel method of proof based on a single differential inequality for the exponential moment with time-dependent coefficients.Comment: 14 pages. Many typos corrected in this revised versio

Catchment-scale Phosphorus Export through Surface and Drainage Pathways

The site-specific nature of P fate and transport in drained areas exemplifies the need for additional data to guide implementation of conservation practices at the catchment scale. Total P (TP), dissolved reactive P (DRP), and total suspended solids (TSS) were monitored at five sites—two streams, two tile outlets, and a grassed waterway—in three agricultural subwatersheds (221.2–822.5 ha) draining to Black Hawk Lake in western Iowa. Median TP concentrations ranged from 0.034 to 1.490 and 0.008 to 0.055 mg P L−1 for event and baseflow samples, respectively. The majority of P and TSS export occurred during precipitation events and high-flow conditions with greater than 75% of DRP, 66% of TP, and 59% of TSS export occurring during the top 25% of flows from all sites. In one subwatershed, a single event (annual recurrence interval \u3c 1 yr) was responsible for 46.6, 84.0, and 81.0% of the annual export of TP, DRP, and TSS, respectively, indicating that frequent, small storms have the potential to result in extreme losses. Isolated monitoring of surface and drainage transport pathways indicated significant P and TSS losses occurring through drainage; over the 2-yr study period, the drainage pathway was responsible for 69.8, 59.2, and 82.6% of the cumulative TP, DRP, and TSS export, respectively. Finally, the results provided evidence that particulate P losses in drainage were greater than dissolved P losses. Understanding relationships between flow, precipitation, transport pathway, and P fraction at the catchment scale is needed for effective conservation practice implementation

Re-imagining the Borders of US Security after 9/11: Securitisation, Risk, and the Creation of the Department of Homeland Security

The articulation of international and transnational terrorism as a key issue in US security policy, as a result of the 9/11 attacks, has not only led to a policy rethink, it has also included a bureaucratic shift within the US, showing a re-thinking of the role of borders within US security policy. Drawing substantively on the 'securitisation' approach to security studies, the article analyses the discourse of US security in order to examine the founding of the Department of Homeland Security, noting that its mission provides a new way of conceptualising 'borders' for US national security. The securitisation of terrorism is, therefore, not only represented by marking terrorism as a security issue, it is also solidified in the organisation of security policy-making within the US state. As such, the impact of a 'war on terror' provides an important moment for analysing the re-articulation of what security is in the US, and, in theoretical terms, for reaffirming the importance of a relationship between the production of threat and the institutionalisation of threat response. © 2007 Taylor & Francis

First normal stress difference and crystallization in a dense sheared granular fluid

The first normal stress difference (${\mathcal N}_1$) and the microstructure in a dense sheared granular fluid of smooth inelastic hard-disks are probed using event-driven simulations. While the anisotropy in the second moment of fluctuation velocity, which is a Burnett-order effect, is known to be the progenitor of normal stress differences in {\it dilute} granular fluids, we show here that the collisional anisotropies are responsible for the normal stress behaviour in the {\it dense} limit. As in the elastic hard-sphere fluids, ${\mathcal N}_1$ remains {\it positive} (if the stress is defined in the {\it compressive} sense) for dilute and moderately dense flows, but becomes {\it negative} above a critical density, depending on the restitution coefficient. This sign-reversal of ${\mathcal N}_1$ occurs due to the {\it microstructural} reorganization of the particles, which can be correlated with a preferred value of the {\it average} collision angle $\theta_{av}=\pi/4 \pm \pi/2$ in the direction opposing the shear. We also report on the shear-induced {\it crystal}-formation, signalling the onset of fluid-solid coexistence in dense granular fluids. Different approaches to take into account the normal stress differences are discussed in the framework of the relaxation-type rheological models.Comment: 21 pages, 13 figure

Kinetic Theory of a Dilute Gas System under Steady Heat Conduction

The velocity distribution function of the steady-state Boltzmann equation for hard-core molecules in the presence of a temperature gradient has been obtained explicitly to second order in density and the temperature gradient. Some thermodynamical quantities are calculated from the velocity distribution function for hard-core molecules and compared with those for Maxwell molecules and the steady-state Bhatnagar-Gross-Krook(BGK) equation. We have found qualitative differences between hard-core molecules and Maxwell molecules in the thermodynamical quantities, and also confirmed that the steady-state BGK equation belongs to the same universality class as Maxwell molecules.Comment: 36 pages, 4 figures, 5 table

The Cold Peace: Russo-Western Relations as a Mimetic Cold War

In 1989–1991 the geo-ideological contestation between two blocs was swept away, together with the ideology of civil war and its concomitant Cold War played out on the larger stage. Paradoxically, while the domestic sources of Cold War confrontation have been transcended, its external manifestations remain in the form of a ‘legacy’ geopolitical contest between the dominant hegemonic power (the United States) and a number of potential rising great powers, of which Russia is one. The post-revolutionary era is thus one of a ‘cold peace’. A cold peace is a mimetic cold war. In other words, while a cold war accepts the logic of conflict in the international system and between certain protagonists in particular, a cold peace reproduces the behavioural patterns of a cold war but suppresses acceptance of the logic of behaviour. A cold peace is accompanied by a singular stress on notions of victimhood for some and undigested and bitter victory for others. The perceived victim status of one set of actors provides the seedbed for renewed conflict, while the ‘victory’ of the others cannot be consolidated in some sort of relatively unchallenged post-conflict order. The ‘universalism’ of the victors is now challenged by Russia's neo-revisionist policy, including not so much the defence of Westphalian notions of sovereignty but the espousal of an international system with room for multiple systems (the Schmittean pluriverse)

Racial and Imperial Thinking in International Theory and Politics: Truman, Attlee and the Korean War

- Connects the background ideas of race and empire to world politics - Uses case of Truman and Attlee in the Korean War - Argues that liberal-realist internationalists’ assumptions about the US-led post-war order obscure those background ideas and fail to understand the character of the post-war order - Argues liberal-realist internationalism is akin to a legitimating ideology rather than an explanatory theory - Argues that such failings render liberal internationalism inadequate to explain or prescribe ways for the United States/West to manage the ‘rise of the rest’ today This article connects the background ideas of race and empire to world politics by looking at the world views and actions of Truman and Attlee in the Korean War. The article argues that liberal-realist internationalists’ assumptions about the US-led post-war order obscure those background ideas and fail to understand the character of the post-war order. I consider two kinds of ‘background ideas’—policy-makers’ and those embedded in liberal internationalism. Put together, these ideas render liberal-realist internationalism akin to a legitimating ideology rather than an explanatory theory. More broadly, and in the longer run, such failure to comprehend the character of the post-war order, and the roles of race, empire and periphery war in it, renders the theory inadequate to explain or prescribe ways for the United States/West to manage the ‘rise of the rest’ today